https://kbwiki.ercoftac.org/w/api.php?action=feedcontributions&user=Dave.Ellacott&feedformat=atom KBwiki - User contributions [en] 2024-03-29T08:23:46Z User contributions MediaWiki 1.39.2 https://kbwiki.ercoftac.org/w/index.php?title=UFR_4-16_Test_Case&diff=39866 UFR 4-16 Test Case 2021-11-18T21:45:05Z <p>Dave.Ellacott: /* CFD Methods */</p> <hr /> <div>= Flow in a 3D diffuser =<br /> {{UFRHeader<br /> |area=4<br /> |number=16<br /> }}<br /> __TOC__<br /> == Confined flows ==<br /> === Underlying Flow Regime 4-16 ===<br /> <br /> <br /> = Test Case Study =<br /> &lt;!--{{LoremIpsum}}--&gt;<br /> == Brief description of the test case studied ==<br /> The diffuser shapes, dimensions and the coordinate system are shown in<br /> [[UFR_4-16_Test_Case#figure3|Fig. 3]] and<br /> [[UFR_4-16_Test_Case#figure4|Fig. 4]].<br /> Both diffuser configurations considered have the same fully&amp;#8208;developed <br /> flow at channel inlet but slightly different expansion<br /> geometries: the upper-wall expansion angle is reduced from ''11.3&amp;deg;'' (Diffuser<br /> 1) to ''9&amp;deg;'' (Diffuser 2) and the side-wall expansion angle is increased from<br /> ''2.56&amp;deg;'' (Diffuser 1) to ''4&amp;deg;'' (Diffuser2). The flow in the inlet duct (height<br /> ''h=1 cm'', width ''B=3.33 cm'') corresponds to fully-developed turbulent channel<br /> flow (enabled experimentally by a development channel being 62.9 channel<br /> heights long). The ''L=15h'' long diffuser section is followed by a straight<br /> outlet part (''12.5h'' long). Downstream of this the flow goes through a ''10h''<br /> long contraction into a 1 inch diameter tube. The curvature radius at the<br /> walls transitioning between diffuser and the straight duct parts are ''6 cm''<br /> (Diffuser 1) and ''2.8 cm'' (Diffuser 2). The bulk velocity in the inflow duct<br /> is &lt;math&gt;{U_\textrm{bulk}=U_\textrm{inflow}=1 m/s}&lt;/math&gt;<br /> in the ''x''-direction resulting in the Reynolds number based on the<br /> inlet channel height of ''10000''. The origin of the coordinates (''y=0, z=0'')<br /> coincides with the intersection of the two non-expanding walls at the<br /> beginning of the diffuser's expansion (x=0). The working fluid is water<br /> (''&amp;rho;=1000 kg/m&lt;sup&gt;3&lt;/sup&gt;'' and ''&amp;mu;=0.001 Pas'').<br /> <br /> <br /> &lt;div id=&quot;figure3&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=750<br /> |[[Image:UFR4-16_figure3.png|740px]]<br /> |-<br /> |'''Figure 3:''' Geometry of the 3-D diffuser 1 considered (not to scale), [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]; see also [[UFR_4-16_References#14|Jakirli&amp;#x107; ''et&amp;nbsp;al.'' (2010a)]]<br /> |}<br /> <br /> <br /> <br /> <br /> &lt;div id=&quot;figure4&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=750<br /> |[[Image:UFR4-16_figure4.png|740px]]<br /> |-<br /> |'''Figure 4:''' Geometry of the 3-D diffuser 2 considered (not to scale), [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]].<br /> |}<br /> <br /> == Experimental investigation ==<br /> ===Brief description of the experimental setup===<br /> The measurements were performed in a recirculating water channel using the<br /> method of magnetic resonance velocimetry (MRV),<br /> [[UFR_4-16_Test_Case#figure5|Fig. 5.]] MRV makes use of a<br /> technique very similar to that used in conventional medical magnetic<br /> resonance imaging (MRI),<br /> [[UFR_4-16_Test_Case#figure6|Fig. 6.]] Experiments were performed on a 1.5 Tesla<br /> magnet with resolution of 0.9 x 0.9 x 0.9 mm and a 7 Tesla magnet with<br /> resolution of 0.4 x 0.4 x 0.4 mm. Interested readers are referred to<br /> [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008]],<br /> [[UFR_4-16_References#8|2009)]]<br /> for more details about the measurement technique.<br /> <br /> <br /> &lt;div id=&quot;figure5&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;558&quot;<br /> |[[Image:UFR4-16_figure5a.png|548px]]<br /> |-<br /> |[[Image:UFR4-16_figure5b.png|548px]]<br /> |-<br /> |'''Figure 5:''' Schematic of the experimental flow system (upper) and design of the 3D diffuser. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> <br /> <br /> <br /> &lt;div id=&quot;figure6&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;558&quot;<br /> |[[Image:UFR4-16_figure6.jpg|548px]]<br /> |-<br /> |'''Figure 6:''' 3D diffuser arrangement in a medical magnetic resonance imaging device. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> ===Mean velocity and Reynolds stress measurements===<br /> Cherry ''et&amp;nbsp;al.'' provided a detailed reference database comprising the<br /> three-component mean velocity field and the streamwise Reynolds stress component<br /> field within the entire diffuser section. Both diffuser configurations<br /> considered are characterized by a three-dimensional boundary-layer<br /> separation, but the slightly different expansion geometries caused the size<br /> and shape of the separation bubble exhibiting a high degree of geometric<br /> sensitivity to the dimensions of the diffuser as illustrated in<br /> [[UFR_4-16_Test_Case#figure7|Figs. 7]], [[UFR_4-16_Test_Case#figure8|8]]<br /> and [[UFR_4-16_Test_Case#figure9|9]]<br /> <br /> <br /> &lt;div id=&quot;figure7&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure7.png|740px]]<br /> |-<br /> |'''Figure 7:''' Streamwise velocity contours in a plane parallel to the top wall, from [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure8&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; style=&quot;border: 1px solid black;&quot; border=&quot;1&quot;<br /> |align=&quot;center&quot; colspan=&quot;3&quot;|[[Image:UFR4-16_figure8a.png|493px]]<br /> |-<br /> |colspan=&quot;3&quot;|[[Image:UFR4-16_figure8b.png|750px]]<br /> |-<br /> |[[Image:UFR4-16_figure8c.png|247px]]||[[Image:UFR4-16_figure8d.png|247px]]||[[Image:UFR4-16_figure8e.png|247px]]<br /> |-<br /> |colspan=&quot;3&quot;|'''Figure 8:''' Measured streamwise velocity contours in the central plane (upper) of the '''Diffuser 1''' and in the three selected cross-sectional slices positioned at different distances from the diffuser inlet (lower; their locations are denoted by thick white lines in the upper figure). Note that the black line indicates zero streamwise velocity and the purple and pink regions are reverse flow. The velocity values are normalized by the bulk inlet velocity being ''V&lt;sub&gt;ref&lt;/sub&gt;=1&amp;nbsp;m/s''. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure9&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; style=&quot;border: 1px solid black&quot; border=&quot;1&quot;<br /> |colspan=&quot;3&quot; align=&quot;center&quot;|[[Image:UFR4-16_fig9a.png|493px]]<br /> |-<br /> |colspan=&quot;3&quot;|[[Image:UFR4-16_fig9b.png|750px]]<br /> |-<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig9c.png|246px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig9d.png|246px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig9e.png|246px]]<br /> |-<br /> |colspan=&quot;3&quot;|'''Figure 9:''' Measured streamwise velocity contours in the central plane (upper) of the '''Diffuser 2''' and in the three selected cross-sectional slices positioned at different distances from the diffuser inlet (lower; their locations are denoted by thick white lines in the upper figure). Note that the black line indicates zero streamwise velocity and the purple and pink regions are reverse flow. The velocity values are normalized by the bulk inlet velocity being ''V&lt;sub&gt;ref&lt;/sub&gt;=1&amp;nbsp;m/s''. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure10&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; style=&quot;border: 1px solid black&quot;<br /> !x/h=2!!x/h=5!!x/h=8!!x/h=12!!x/h=15<br /> |-<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10a.png|137px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10b.png|139px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10c.png|148px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10d.png|154px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10e.png|162px]]<br /> |-<br /> |align=&quot;center&quot; colspan=&quot;5&quot;|[[Image:UFR4-16_fig10f.png]]<br /> |-<br /> |colspan=&quot;5&quot;|'''Figure 10:''' Measurements of turbulent streamwise stress components taken in cross-sectional slices of the diffuser 1 perpendicular to the mean flow. The region of highest turbulence (red areas; ignore the red areas at the bottom walls) follows the shear layer between forward and reverse flow. ''h''=1cm represents the height of the inflow duct. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> ===Pressure measurements===<br /> In addition<br /> [[UFR_4-16_References#8|Cherry ''et&amp;nbsp;al.'' (2009)]]<br /> provided the pressure distribution along<br /> the bottom non-deflected wall of diffuser 1 at different Reynolds numbers.<br /> Complementary to the Reynolds number 10000 (for which the entire flow field<br /> was measured), two higher Reynolds numbers &amp;mdash; 20000 and 30000 &amp;mdash; were also<br /> considered, [[UFR_4-16_Test_Case#figure11|Fig. 11]]. The surface pressure distribution was evaluated to<br /> yield the coefficient<br /> &lt;math&gt;C_p=(p-p_\textrm{ref})/(0.5\rho U_\textrm{bulk}^2)&lt;/math&gt;;<br /> the reference pressure was taken at the<br /> position ''x/L&amp;nbsp;=&amp;nbsp;0.05''. The pressure curve exhibits a development typical of<br /> flow in diverging ducts. The pressure decrease in the inflow duct is<br /> followed by a steep pressure increase already at the very end of the inflow<br /> duct and especially at the beginning of the diffuser section. The<br /> transition from the initial strong pressure rise to its moderate increase<br /> occurs at ''x/L&amp;nbsp;&amp;#8776;&amp;nbsp;0.3'', (''x/h=4.5'')<br /> corresponding to the position where about 5% of<br /> the entire cross-section is occupied by the flow reversal (see e.g.,<br /> [[UFR_4-16_Test_Case#figure19|Fig. 19]].<br /> The onset of separation causes a certain contraction of the flow cross&amp;#8208;section,<br /> leading to a weakening of the deceleration intensity and,<br /> accordingly, to a slower pressure increase. The region characterized by a<br /> monotonic pressure rise was reached in the remainder of the diffuser<br /> section.<br /> <br /> <br /> &lt;div id=&quot;figure11&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure11.png|740px]]<br /> |-<br /> |'''Figure 11:''' Pressure recovery coefficients relative to the pressure on the bottom wall of the diffuser 1 inlet in a range of flow Reynolds number. L=15 cm represents the length of Diffuser 1, from [[UFR_4-16_References#8|Cherry ''et&amp;nbsp;al.'' (2009)]]<br /> <br /> |}<br /> <br /> ===Measurements uncertainties===<br /> (adopted from [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'', 2008, IJHFF, Vol. 29(3)]])<br /> <br /> Elkins et al. (2004) estimated the maximum relative uncertainty of<br /> individual mean velocity measurements to be about 10% of the measured value<br /> in a similar highly turbulent flow. However, comparisons to PIV in a<br /> backward facing step flow (Elkins et al., 2007) show that only a small<br /> percentage of MRV velocity samples deviate by that much and most are much<br /> more accurate. To test this, the streamwise velocity component was<br /> integrated over 250 cross-sections of the MRV data and the results were<br /> compared to the known volume flow rate. This indicated an uncertainty in<br /> the integral of less than 2% with a 95% confidence level.<br /> <br /> Measurements of turbulent normal stresses in Diffuser 1 were also taken<br /> using the MR technique described by Elkins et al. (2007). This method is<br /> based on diffusion imaging principles in which the turbulence causes a loss<br /> of net magnetization signal from a voxel in the flow. This causes a decay<br /> in signal strength which can be related to turbulent velocity statistics.<br /> Elkins et al found this method to be accurate within 20% everywhere in the<br /> FOV and within 5% in regions of high turbulence. Three turbulence scans<br /> were completed using three different magnetic field gradient strengths. For<br /> each gradient strength, 30 scans were completed and averaged. The three<br /> averaged data sets were then averaged to obtain a final data set.<br /> <br /> ===Experimental data available===<br /> Velocity, (and streamwise Reynolds stress components for diffuser 1) and<br /> coordinate data for both diffusers are available here. &lt;!--at http://stanford.edu/~echerry/--&gt;<br /> <br /> {|<br /> &lt;!--<br /> |[http://stanford.edu/~echerry/AnnularDiffuserData.zip AnnularDiffuserData.zip] (contains 4 files, 134 MBytes)<br /> --&gt;<br /> |-<br /> |[https://www.kbwiki.ercoftac.org/w/Data/UFR4-16/Diffuser_1_data.zip Diffuser 1 data.zip] (contains 1 file, 8.4 MBytes)<br /> |-<br /> &lt;!--<br /> |-<br /> |[http://stanford.edu/~echerry/Diffuser%201%20data.zip Diffuser 1 data.zip] (contains 1 file, 8.4 MBytes)<br /> --&gt;<br /> |-<br /> |[https://www.kbwiki.ercoftac.org/w/Data/UFR4-16/Diffuser_1_turbulence.zip Diffuser 1 turbulence.zip] (contains 1 file, 5.3 MBytes)<br /> |-<br /> |[https://www.kbwiki.ercoftac.org/w/Data/UFR4-16/Diffuser_2_data.zip Diffuser 2 data.zip] (contains 1 file, 4 MBytes)<br /> |}<br /> <br /> The data are seven 3D matlab matrices. The<br /> x, y, and z matrices give the coordinates of each point in the coordinate<br /> system shown in Fig. 5. The units are meters. The Vx, Vy, and Vz matrices<br /> give the corresponding velocity components for each point in m/sec. The<br /> matrix mg gives the relative signal magnitude detected by the MRI machine.<br /> <br /> Experimental data for the pressure coefficient in Diffuser 1 for the inflow<br /> Reynolds number Re=10000 are available [[Media:UFR4-16_Cp_Re=10000.xlsx|here]]<br /> ([[Media:UFR4-16_Cp_Re=10000.xlsx|Cp_Re=10000.xlsx]]). The<br /> coordinate system is the same as the coordinate system described in the<br /> corresponding manuscript (see below). &lt;math&gt;{\ C_p}&lt;/math&gt; is defined as<br /> &lt;math&gt;\left(p-p_\textrm{ref}\right)/\left(\frac{1}{2} \rho V^2\right)&lt;/math&gt;,<br /> where &lt;math&gt;{\ P_\textrm{ref}}&lt;/math&gt; is the pressure at ''x=0.05'' (see Fig. 11)<br /> at the midpoint<br /> (''z/B=0.5'') of the bottom flat wall (opposite the wall expanding at 11.3<br /> degrees), &lt;math&gt;{\ \rho}&lt;/math&gt; is the density, and &lt;math&gt;{\ V}&lt;/math&gt;<br /> is the bulk inlet velocity. The data were<br /> taken in a line along the bottom wall of Diffuser 1 at constant y and z<br /> coordinates. L (=15 cm) indicates the length of the diffuser.<br /> <br /> ''Please acknowledge the authors of the experiment when using their database!''<br /> <br /> == CFD Methods ==<br /> The flow in the present diffuser configuration was intensively investigated<br /> computationally in the framework of two ERCOFTAC-SIG15 Workshops and in<br /> the European ATAAC project.<br /> The workshops focussing on both 3D diffuser configurations (denoted by SIG15<br /> Case 13.2-1 and SIG15 Case 13.2-2, respectively) were organized at the<br /> Technical University of Graz, Austria in September, 2008 and the &quot;LA<br /> Sapienza&quot; University of Rome, Italy in September, 2009. The corresponding<br /> reports are published in the ERCOFTAC Bulletin Issues,<br /> [[UFR_4-16_References#30|Steiner ''et&amp;nbsp;al.'' (2009)]]<br /> and [[UFR_4-16_References#15|Jakirli&amp;#x107; ''et&amp;nbsp;al.'' (2010b)]],<br /> see [[UFR_4-16_References#0|&quot;List of References&quot;]].<br /> Both in the workshops and in the ATAAC project a wide range of<br /> turbulence models in both LES and RANS frameworks as well as some novel<br /> Hybrid LES/RANS formulations have been employed. The computational database<br /> was furthermore enriched by the results of a Direct Numerical Simulation of<br /> the first diffuser performed by<br /> [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]]. The list of all<br /> computational contributions to the workshops including some basic information about the<br /> methods and models used and corresponding grid resolution is given in<br /> the following [[UFR_4-16_Test_Case#table1|tables 1]] and [[UFR_4-16_Test_Case#table2|table 2]].<br /> For more computational details, interested<br /> readers are referred to the &quot;[[UFR_4-16_Evaluation#Available_CFD_results:_ERCOFTAC_SIG15_Workshop_Proceedings|workshop proceedings]]&quot;<br /> &amp;mdash; see the corresponding<br /> links at the end of the Section &quot;[[UFR_4-16_Evaluation#Evaluation_of_the_results|Evaluation of the results]]&quot;.<br /> The results from the ATAAC project and information on the methods used can be obtained through the links<br /> [http://cfd.mace.manchester.ac.uk/twiki/pub/ATAAC/TestCase004Diffuser3D/ATAAC_D3-2-36_excerpt3DDiffuser.pdf ATAAC_D3-2-36_excerpt3DDiffuser.pdf]<br /> (excerpt from an ATAAC report) and<br /> [http://cfd.mace.manchester.ac.uk/twiki/pub/ATAAC/TestCase004Diffuser3D/ATAAC_finalWorkshop_ST04-Diffuser-ANSYS.pdf ATAAC_finalWorkshop_ST04-Diffuser-ANSYS.pdf]<br /> (PowerPoint presentation at ATAAC final workshop).<br /> <br /> <br /> &lt;div id=&quot;table1&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_table1.png|740px]]<br /> |-<br /> |'''Table 1:''' SIG15 Case 13.2-1 (Diffuser 1) &amp;mdash; contributors and methods (note that the DNS grid comprises 220 million cells in the follow-up work published in [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]])<br /> |-<br /> |'''N.B.''' ITS is &quot;Institut f&amp;uuml;r Thermische Str&amp;ouml;mungsmaschinen&quot;<br /> |}<br /> <br /> <br /> &lt;div id=&quot;table2&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_table2.png|740px]]<br /> |-<br /> |'''Table 2:''' SIG15 Case 13.2-2 (Diffuser 2) &amp;mdash; contributors and methods<br /> |-<br /> |'''N.B.''' ITS is &quot;Institut f&amp;uuml;r Thermische Str&amp;ouml;mungsmaschinen&quot;<br /> |}<br /> <br /> <br /> ===Direct numerical simulation of the flow in a 3D diffuser===<br /> <br /> (adopted from [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'', 2010, JFM, Vol. 650]])<br /> <br /> In this part of the present contribution the DNS study of the flow in 3D<br /> Diffuser 1 performed recently by<br /> [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]] will be described in<br /> more details. Ohlsson ''et&amp;nbsp;al.'' participated with this contribution at the<br /> 14th SIG15 Workshop on Refined Turbulence Modeling <br /> ([[UFR_4-16_References#15|Jakirli&amp;#x107; ''et&amp;nbsp;al.'', 2010b]]).<br /> Accordingly, their results are also part of the CFD methods/models<br /> evaluation &amp;mdash; along with the results obtained by different LES, RANS and<br /> Hybrid LES/RANS models (see the [[UFR_4-16_Evaluation#Evaluation_of_the_results|next chapter]]).<br /> In addition, as the DNS<br /> provided a very comprehensive database comprising all three mean velocity<br /> components (and associated integral characteristics such as surface<br /> pressure and friction factor) and all six Reynolds stress components as<br /> well as a certain insight into the physics (not detected by the<br /> experimental investigation) one can regard it also as a reference<br /> investigation, as we do presently.<br /> <br /> The Direct Numerical Simulation of the Diffuser 1 was performed using a<br /> massively parallel high-order spectral element code. The incompressible<br /> Navier-Stokes equations are solved using a Legendre-polynomial-based<br /> spectral-element method, implemented in the code nek5000, developed by<br /> Fischer et al. (2008). The computational domain shown in<br /> [[UFR_4-16_Test_Case#figure12|Fig. 12]] is set up<br /> in close agreement with the diffuser geometry in the experiment<br /> (see [[UFR_4-16_Test_Case#figure3|Fig.3]])<br /> and consists of the inflow development duct of almost 63 duct heights,<br /> ''h'', (starting at the non-dimensional coordinate ''x''&amp;nbsp;=&amp;nbsp;-62.9),<br /> the diffuser<br /> expansion located at ''x''&amp;nbsp;=&amp;nbsp;0 and the converging section upstream of the<br /> outlet. The corners resulting from the diffuser expansion are smoothly<br /> rounded with a radius of 6.0 in accordance with the experimental set-up.<br /> The maximum dimensions are ''Lx =105.4 h, Ly =[h, 4h], Lz =[3.33 h, 4h]''. In<br /> the inflow duct, laminar flow undergoes natural transition by the use of an<br /> unsteady trip forcing (see e.g. Schlatter et al., 2009), which avoids the<br /> use of artificial turbulence and eliminates artificial temporal frequencies<br /> which may arise from inflow recycling methods (Herbst et al., 2007). A<br /> 'sponge region' is added at the end of the contraction in order to smoothly<br /> damp out turbulent fluctuations, thereby eliminating spurious pressure<br /> waves. It is followed by a homogeneous Dirichlet condition for the pressure<br /> and a homogeneous Neumann condition for the velocities. The resolution of<br /> approximately 220 million grid points is obtained by a total of 127750<br /> local tensor product domains (elements) with a polynomial order of 11,<br /> respectively, resulting in &amp;Delta;z&lt;sup&gt;+&lt;/sup&gt;&lt;sub&gt;max&lt;/sub&gt;&amp;asymp;11.6,<br /> &amp;Delta;y&lt;sup&gt;+&lt;/sup&gt;&lt;sub&gt;max&lt;/sub&gt;&amp;asymp;13.2 and<br /> &amp;Delta;x&lt;sup&gt;+&lt;/sup&gt;&lt;sub&gt;max&lt;/sub&gt;&amp;asymp;19.5 in the<br /> duct center and the first grid point being located at z&lt;sup&gt;+&lt;/sup&gt;&amp;asymp;0.074<br /> and y&lt;sup&gt;+&lt;/sup&gt;&amp;asymp;0.37, respectively (note that at the time of the ERCOFTAC SIG15 workshop<br /> the DNS grid had 172 million grid points,<br /> see Chapter &quot;[[UFR_4-16_Evaluation#172million|Evaluation]]&quot;). It was<br /> verified that this resolution yields accurate results in turbulent channel<br /> flow simulations. In the diffuser, the grid is linearly stretched in both<br /> directions, but since the mean resolution requirements decreases with the<br /> velocity, which decreases linearly with the area expansion, the resolution<br /> in the entire domain is hence satisfactory. The simulation was performed on<br /> the Blue Gene/P at ALCF, Argonne National Laboratory (32768 cores and a<br /> total of 8 million core hours) and on the cluster 'Ekman' at PDC, Stockholm<br /> (2048 cores and a total of 4 million core hours). Thirteen flow-through<br /> times, ''t U&lt;sub&gt;b&lt;/sub&gt;/L''=13, based on bulk velocity, ''U&lt;sub&gt;b&lt;/sub&gt;'', and diffuser length, ''L=15&amp;nbsp;h'',<br /> were simulated in order to let the flow settle to an equilibrium state<br /> before turbulent statistics were collected over approximately ''U&lt;sub&gt;b&lt;/sub&gt;t/L''=21<br /> additional flow-through times.<br /> <br /> In addition to the three-dimensional mean velocity field, all six Reynolds<br /> stress components were evaluated, as well as the surface pressure and skin<br /> friction distribution along the bottom wall.<br /> <br /> <br /> &lt;div id=&quot;figure12&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure12.png|740px]]<br /> |-<br /> |'''Figure 12:''' DNS grid of the diffuser 1 geometry showing the development region, diffuser expansion, converging section and outlet. From [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]]<br /> |}<br /> <br /> <br /> [[UFR_4-16_Test_Case#figure13|Fig. 13]] illustrates the mean axial flow field obtained by DNS along with<br /> the experimental data and [[UFR_4-16_Test_Case#figure14|Fig. 14]] depicts the skin friction evolution along<br /> the bottom diffuser wall at the midpoint<br /> (''z/B=0.5''; ''C&lt;sub&gt;f&lt;/sub&gt;=&amp;tau;&lt;sub&gt;wall&lt;/sub&gt;&amp;nbsp;/&amp;nbsp;(0.5&amp;rho;U&lt;sup&gt;2&lt;/sup&gt;&lt;sub&gt;bulk&lt;/sub&gt;'')&amp;nbsp;). The latter DNS<br /> result was evaluated exclusively for the needs of the 14th ERCOFTAC<br /> Workshop; it is not part of the DNS database which can be downloaded [[UFR_4-16_Test_Case#kth_data|here]].<br /> <br /> <br /> &lt;div id=&quot;figure13&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure13.png|740px]]<br /> |-<br /> |'''Figure 13:''' Cross-flow planes of streamwise velocity component at 2, 5, 8 and 15 ''h'' downstream of the diffuser throat. Left: DNS. Right: Experiment by [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]. Each streamwise position has its own colour bar on the right. Contour lines are spaced ''0.1 V&lt;sub&gt;ref&lt;/sub&gt;'' apart. Thick black lines correspond to the zero velocity contour. From [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]]<br /> <br /> <br /> &lt;div id=&quot;figure14&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure14.jpg|740px]]<br /> |-<br /> |'''Figure 14:''' Friction coefficient at the bottom wall of the diffuser 1 with ''L=15 cm'' representing the length of Diffuser 1. The LES and HLR (Hybrid LES/RANS) results are from [[UFR_4-16_References#14|Jakirli&amp;#x107; ''et&amp;nbsp;al.'' (2010a)]] and [[UFR_4-16_References#17|John-Puthenveetil (2012)]].<br /> <br /> ===Available DNS data (last update: 2010-11-23)===<br /> &lt;div id=&quot;kth_data&quot;&gt;&lt;/div&gt;<br /> The entire digitalized DNS database (as well as some high-resolution<br /> images) as listed below can be downloaded from<br /> http://www.mech.kth.se/~johan/data/index.html. The links given below are to local wiki copies of the files.<br /> <br /> This directory contains velocity profiles and mean fluctuations obtained<br /> from the DNS by<br /> [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'', (JFM 650 307&amp;ndash;318)]]<br /> This simulation was<br /> designed to match the experiment by<br /> [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'', 2008, IJHFF 29(3)]]. The<br /> data is given at the same streamwise and spanwise locations as during the<br /> 14th ERCOFTAC SIG15 Workshop on Turbulence Modelling, held in Rome,<br /> September 2009.<br /> <br /> The full Reynolds stress budgets will be available in the future.<br /> <br /> ''The data is free to use; please include a proper reference to the original publications.''<br /> <br /> In case of any questions, e.g. related to the data, or whether you wish for<br /> additional data not presented here, please contact<br /> Johan Malm, ([mailto:johan@mech.kth.se johan@mech.kth.se]),<br /> Philipp Schlatter ([mailto:pschlatt@mech.kth.se pschlatt@mech.kth.se])<br /> or Dan Henningson ([mailto:henning@mech.kth.se henning@mech.kth.se])<br /> <br /> ====Visualizations and computational mesh====<br /> [[Media:UFR4-16_planes_press0000.jpeg|Crossflow planes with instantaneous streamwise velocity]]<br /> <br /> [[Media:UFR4-16_planes_nogrid_iso_vec.jpeg|Crossflow planes with instantaneous streamwise velocity and isosurfaces of streamwise velocity]]<br /> <br /> [[Media:UFR4-16_press_persp0010.jpeg|Instantaneous streamwise velocity in a spanwise midplane with some isosurfaces of instantaneous pressure]]<br /> <br /> [[Media:UFR4-16_mesh_paper.png|Mesh]]<br /> <br /> ====Digitalized DNS database: full 3D mean velocity and Reynolds stress fields====<br /> Explanation:<br /> *E.g., c13.2_Ucont2_KTH_DNS denotes the files comprising the contours of the axial velocity - Ucont - at the streamwise position ''x/h=2'' for the case 13.2 (ERCOFTAC SIG15 denotation). The same data are given at the streamwise locations ''x/h=2, 5, 8, 12'' and ''15''<br /> *E.g., c13.2_urms2_KTH_DNS.txt denotes the file comprising the contours of the root-mean-square values of the streamwise stress component &amp;mdash; urms &amp;mdash; at the streamwise position ''x/h=2''. The same data are given at the streamwise locations ''x/h=2, 5, 8, 12'' and ''15''<br /> *The file c13.2_cp_KTH_DNS.txt denotes the file comprising the pressure coefficient distribution at the bottom flat wall at the midpoint ''z/B=0.5''<br /> *The file c13.2_z0250_x-2_KTH_DNS.txt denotes the file comprising all three mean velocity components, kinetic energy of turbulence and all six Reynolds stress components at the streamwise position ''x/h=-2'' (inflow duct) and the spanwise position ''z/B=0.25''. The same data are given at the streamwise locations ''x/h=0, 2, 4, 6, 8, 10, 12, 14, 15.5, 17, 18.5, 20'' and ''21.5'' at the following spanwise locations ''z/B=0.25, 0.5, 0.75'' and ''0.875''.<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;1&quot; cellpadding=&quot;5&quot;<br /> |[[Media:c13.2_cp_KTH_DNS.txt|c13.2_cp_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont2_KTH_DNS.txt|c13.2_Ucont2_KTH_DNS.txt]]||[[Media:c13.2_urms2_KTH_DNS.txt|c13.2_urms2_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont5_KTH_DNS.txt|c13.2_Ucont5_KTH_DNS.txt]]||[[Media:c13.2_urms5_KTH_DNS.txt|c13.2_urms5_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont8_KTH_DNS.txt|c13.2_Ucont8_KTH_DNS.txt]]||[[Media:c13.2_urms8_KTH_DNS.txt|c13.2_urms8_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont12_KTH_DNS.txt|c13.2_Ucont12_KTH_DNS.txt]]||[[Media:c13.2_urms12_KTH_DNS.txt|c13.2_urms12_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont15_KTH_DNS.txt|c13.2_Ucont15_KTH_DNS.txt]]||[[Media:c13.2_urms15_KTH_DNS.txt|c13.2_urms15_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x-2_KTH_DNS.txt|c13.2_z0250_x-2_KTH_DNS.txt]]||[[Media:c13.2_z0500_x-2_KTH_DNS.txt|c13.2_z0500_x-2_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x-2_KTH_DNS.txt|c13.2_z0750_x-2_KTH_DNS.txt]]||[[Media:c13.2_z0875_x-2_KTH_DNS.txt|c13.2_z0875_x-2_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x0_KTH_DNS.txt|c13.2_z0250_x0_KTH_DNS.txt]]||[[Media:c13.2_z0500_x0_KTH_DNS.txt|c13.2_z0500_x0_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x0_KTH_DNS.txt|c13.2_z0750_x0_KTH_DNS.txt]]||[[Media:c13.2_z0875_x0_KTH_DNS.txt|c13.2_z0875_x0_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x2_KTH_DNS.txt|c13.2_z0250_x2_KTH_DNS.txt]]||[[Media:c13.2_z0500_x2_KTH_DNS.txt|c13.2_z0500_x2_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x2_KTH_DNS.txt|c13.2_z0750_x2_KTH_DNS.txt]]||[[Media:c13.2_z0875_x2_KTH_DNS.txt|c13.2_z0875_x2_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x4_KTH_DNS.txt|c13.2_z0250_x4_KTH_DNS.txt]]||[[Media:c13.2_z0500_x4_KTH_DNS.txt|c13.2_z0500_x4_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x4_KTH_DNS.txt|c13.2_z0750_x4_KTH_DNS.txt]]||[[Media:c13.2_z0875_x4_KTH_DNS.txt|c13.2_z0875_x4_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x6_KTH_DNS.txt|c13.2_z0250_x6_KTH_DNS.txt]]||[[Media:c13.2_z0500_x6_KTH_DNS.txt|c13.2_z0500_x6_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x6_KTH_DNS.txt|c13.2_z0750_x6_KTH_DNS.txt]]||[[Media:c13.2_z0875_x6_KTH_DNS.txt|c13.2_z0875_x6_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x8_KTH_DNS.txt|c13.2_z0250_x8_KTH_DNS.txt]]||[[Media:c13.2_z0500_x8_KTH_DNS.txt|c13.2_z0500_x8_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x8_KTH_DNS.txt|c13.2_z0750_x8_KTH_DNS.txt]]||[[Media:c13.2_z0875_x8_KTH_DNS.txt|c13.2_z0875_x8_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x10_KTH_DNS.txt|c13.2_z0250_x10_KTH_DNS.txt]]||[[Media:c13.2_z0500_x10_KTH_DNS.txt|c13.2_z0500_x10_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x10_KTH_DNS.txt|c13.2_z0750_x10_KTH_DNS.txt]]||[[Media:c13.2_z0875_x10_KTH_DNS.txt|c13.2_z0875_x10_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x12_KTH_DNS.txt|c13.2_z0250_x12_KTH_DNS.txt]]||[[Media:c13.2_z0500_x12_KTH_DNS.txt|c13.2_z0500_x12_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x12_KTH_DNS.txt|c13.2_z0750_x12_KTH_DNS.txt]]||[[Media:c13.2_z0875_x12_KTH_DNS.txt|c13.2_z0875_x12_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x14_KTH_DNS.txt|c13.2_z0250_x14_KTH_DNS.txt]]||[[Media:c13.2_z0500_x14_KTH_DNS.txt|c13.2_z0500_x14_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x14_KTH_DNS.txt|c13.2_z0750_x14_KTH_DNS.txt]]||[[Media:c13.2_z0875_x14_KTH_DNS.txt|c13.2_z0875_x14_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x155_KTH_DNS.txt|c13.2_z0250_x155_KTH_DNS.txt]]||[[Media:c13.2_z0500_x155_KTH_DNS.txt|c13.2_z0500_x155_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x155_KTH_DNS.txt|c13.2_z0750_x155_KTH_DNS.txt]]||[[Media:c13.2_z0875_x155_KTH_DNS.txt|c13.2_z0875_x155_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x17_KTH_DNS.txt|c13.2_z0250_x17_KTH_DNS.txt]]||[[Media:c13.2_z0500_x17_KTH_DNS.txt|c13.2_z0500_x17_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x17_KTH_DNS.txt|c13.2_z0750_x17_KTH_DNS.txt]]||[[Media:c13.2_z0875_x17_KTH_DNS.txt|c13.2_z0875_x17_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x185_KTH_DNS.txt|c13.2_z0250_x185_KTH_DNS.txt]]||[[Media:c13.2_z0500_x185_KTH_DNS.txt|c13.2_z0500_x185_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x185_KTH_DNS.txt|c13.2_z0750_x185_KTH_DNS.txt]]||[[Media:c13.2_z0875_x185_KTH_DNS.txt|c13.2_z0875_x185_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x20_KTH_DNS.txt|c13.2_z0250_x20_KTH_DNS.txt]]||[[Media:c13.2_z0500_x20_KTH_DNS.txt|c13.2_z0500_x20_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x20_KTH_DNS.txt|c13.2_z0750_x20_KTH_DNS.txt]]||[[Media:c13.2_z0875_x20_KTH_DNS.txt|c13.2_z0875_x20_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x215_KTH_DNS.txt|c13.2_z0250_x215_KTH_DNS.txt]]||[[Media:c13.2_z0500_x215_KTH_DNS.txt|c13.2_z0500_x215_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x215_KTH_DNS.txt|c13.2_z0750_x215_KTH_DNS.txt]]||[[Media:c13.2_z0875_x215_KTH_DNS.txt|c13.2_z0875_x215_KTH_DNS.txt]]<br /> |}<br /> &lt;br/&gt;<br /> &lt;br/&gt;<br /> <br /> ==Reference DNS and experimental data: mean flow and turbulence evolution==<br /> The following figures display and compare the reference experimental and<br /> DNS database results (the present results can be analysed along with the<br /> axial velocity contours shown in<br /> [[UFR_4-16_Test_Case#figure7|Figs. 7]] &amp;ndash;<br /> [[UFR_4-16_Test_Case#figure9|9]] and [[UFR_4-16_Test_Case#figure13|13]]):<br /> <br /> <br /> In order to get an impression about the mean flow structure and about the<br /> available reference DNS and experimental results<br /> [[UFR_4-16_Test_Case#figure15|Figs. 15]] and<br /> [[UFR_4-16_Test_Case#figure16|16]] display<br /> the velocity field development in the vertical central plane of both<br /> diffusers (''z/B=0.5''; ''B=3.33 cm'' is the width of the inflow duct) typical for<br /> the flow in an expanding duct. The bulk flow exhibits deceleration, leading<br /> to an asymmetry of the velocity profile, particularly so for the axial<br /> velocity component. The effect of the adverse pressure gradient is<br /> especially visible in the flow region along the upper expanding wall. The<br /> velocity profile approaches gradually the form characterizing a separating<br /> flow, exhibiting regions of the zero velocity gradient (at separation and<br /> reattachment points) and profile inflection. The through-flow, that is the<br /> flow in the positive streamwise direction, is characterized by a spreading<br /> dictated by the pressure gradient arising from the geometry expansion.<br /> Accordingly, the position of the reduced velocity maximum is gradually<br /> shifted towards the upper wall, eventually reaching the center (''y/h=2'') of<br /> the straight outlet channel (with the height ''4h''). In this post-reattachment<br /> zone the velocity profile exhibits a fairly flattened form, being almost<br /> symmetric. The consequence of the velocity-profile flattening is a<br /> continuous monotonic decrease of the wall shear stress. The velocity<br /> profile evolution is similar in other longitudinal vertical planes. The<br /> specific differences are related to the vicinity of both bottom and upper<br /> walls, especially the latter upper wall, where the flow passes regions of<br /> three-dimensional flow reversal.<br /> <br /> <br /> &lt;div id=&quot;figure15&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure15a.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure15b.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure15c.jpg|740px]]<br /> |-<br /> |'''Figure 15:''' Diffuser 1 - Evolution of the profiles of all three velocity components in the vertical plane ''x-y'' at the central spanwise locations ''z/B=1/2'' obtained experimentally and by means of DNS<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure16&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure16a.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure16b.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure16c.jpg|740px]]<br /> |-<br /> |'''Figure 16:''' Diffuser 2 - Evolution of the profiles of all three velocity components in the vertical plane ''x-y'' at the central spanwise locations ''z/B=1/2'' obtained experimentally<br /> |}<br /> <br /> <br /> In the top part of [[UFR_4-16_Test_Case#figure17|Fig. 17 &amp;ndash; upper]]<br /> the development of the streamwise<br /> turbulence intensity is shown for diffuser 1. The lowest turbulence<br /> intensity is situated in the region coinciding with the mean velocity<br /> maximum &amp;mdash; flow zone with approximately zero velocity gradient &amp;mdash; along the<br /> entire diffuser section. The Reynolds stress profiles exhibit their highest<br /> values in the regions with the most intensive flow deformation. These are<br /> the near-wall layer in the attached-flow regions and the flow zone along<br /> the shear layer bordering the recirculation zone. The peak of the<br /> turbulence intensity originating from the boundary layer at the top inflow<br /> duct wall increases initially, after the strong rise in pressure (see<br /> pressure coefficient development in<br /> [[UFR_4-16_Test_Case#figure11|Fig. 11]]), and weakens slightly after<br /> flow transition to the second part of the diffuser section, that is<br /> characterized by a decreasingly adverse pressure gradient. The streamwise<br /> turbulence intensity in the outlet duct is uniformly distributed over the<br /> cross-section.<br /> <br /> <br /> &lt;div id=&quot;figure17&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17a.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17b.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17c.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17d.jpg|740px]]<br /> |-<br /> |'''Figure 17:''' Diffuser 1 - Evolution of the profiles of the Reynolds stress components in the vertical plane ''x-y'' at the central spanwise locations ''z/B=1/2'' obtained experimentally and by means of DNS<br /> |}<br /> <br /> <br /> [[UFR_4-16_Test_Case#figure18|Fig. 18]]<br /> shows contour plots of the axial velocity component at five<br /> streamwise cross-sectional areas in both diffuser configurations obtained<br /> experimentally indicating the evolution of the flow separation pattern. The<br /> recirculation-zone development displayed here can be analyzed in parallel<br /> with the quantitative information about the fraction of the diffuser cross-<br /> sectional area occupied by the reverse flow depicted in<br /> [[UFR_4-16_Test_Case#figure19|Fig. 19]]. The<br /> adverse pressure gradient is imposed onto the intersecting boundary layers<br /> along flat walls upon entering the diffuser section. According to the<br /> experimental investigation the boundary layers along all walls are of<br /> comparable thickness. The separation starts immediately after the beginning<br /> of the diffuser section at ''x/L = 0 (x/h=0)''. The onset of separation is<br /> located in the upper-right diffuser corner, formed by the deflected side<br /> wall and the top wall, see e.g. the position ''x/h&amp;nbsp;&amp;asymp;&amp;nbsp;2 (x/L=0.13)'' in<br /> [[UFR_4-16_Test_Case#figure19|Fig. 18]].<br /> Initial growth of this corner bubble reveals its spreading rate along the<br /> two sloped walls being approximately of the same intensity, see position<br /> ''x/h=5''. As the adverse pressure gradient along the upper wall outweighs<br /> significantly the one along the side wall due to the substantially higher<br /> angle of expansion in diffuser 1, 11.3&amp;deg; vs. 2.55&amp;deg;, the separation zone<br /> spreads gradually over the entire top wall surface, see position ''x/h=8''. The<br /> behaviour is different in diffuser 2. There one notes a strong three-<br /> dimensional nature of the separation pattern. The maximum occupation of the<br /> diffuser cross-sectional area by the flow reversal, around 22% and 15% for<br /> the diffusers 1 and 2, respectively <br /> ([[UFR_4-16_Test_Case#figure19|Fig. 19]]), is documented at the<br /> position ''x/h=12-17 (x/L=0.8-1.13)''. The thickness of the flow reversal zone<br /> in the diffuser 1 (its dimension in the normal-to-wall direction) is almost<br /> constant over the diffuser width in this region, resembling approximately a<br /> 2-D pattern. After this position the intensity of the back-flow weakens.<br /> The experimental results indicate that the reattachment region is located<br /> within the straight outlet duct,<br /> [[UFR_4-16_Test_Case#figure19|Fig. 19]]. The separation pattern and the<br /> differences between diffuser 1 and 2 can also be seen clearly from the 3D<br /> plots given in<br /> [[UFR_4-16_Evaluation#figure26|Fig. 26]], which were obtained by LES.<br /> <br /> <br /> &lt;div id=&quot;figure18&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |colspan=&quot;2&quot; style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure18.png|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot; align=&quot;center&quot;|'''Diffuser 1'''<br /> |style=&quot;border: 1px solid darkgray;&quot; align=&quot;center&quot;|'''Diffuser 2'''<br /> |-<br /> |colspan=&quot;2&quot;|'''Figure 18:''' Comparison between experimentally obtained iso-contours of the axial velocity field in the cross planes ''y-z'' at five selected streamwise locations within the both diffuser section (the thick line denotes the zero-velocity line). From [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]<br /> |}<br /> <br /> <br /> <br /> &lt;div id=&quot;figure19&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure19.png|740px]]<br /> |-<br /> |'''Figure 19:''' Fraction of the cross-sectional area occupied by the flow reversal in both diffuser configurations. From [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]<br /> |}<br /> <br /> <br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Suad Jakirli&amp;#x107;, Gisa John-Puthenveettil<br /> |organisation=Technische Universit&amp;auml;t Darmstadt<br /> }}<br /> {{UFRHeader<br /> |area=4<br /> |number=16<br /> }}<br /> <br /> <br /> © copyright ERCOFTAC {{CURRENTYEAR}}</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=UFR_4-16_Test_Case&diff=39865 UFR 4-16 Test Case 2021-11-18T21:44:20Z <p>Dave.Ellacott: /* CFD Methods */</p> <hr /> <div>= Flow in a 3D diffuser =<br /> {{UFRHeader<br /> |area=4<br /> |number=16<br /> }}<br /> __TOC__<br /> == Confined flows ==<br /> === Underlying Flow Regime 4-16 ===<br /> <br /> <br /> = Test Case Study =<br /> &lt;!--{{LoremIpsum}}--&gt;<br /> == Brief description of the test case studied ==<br /> The diffuser shapes, dimensions and the coordinate system are shown in<br /> [[UFR_4-16_Test_Case#figure3|Fig. 3]] and<br /> [[UFR_4-16_Test_Case#figure4|Fig. 4]].<br /> Both diffuser configurations considered have the same fully&amp;#8208;developed <br /> flow at channel inlet but slightly different expansion<br /> geometries: the upper-wall expansion angle is reduced from ''11.3&amp;deg;'' (Diffuser<br /> 1) to ''9&amp;deg;'' (Diffuser 2) and the side-wall expansion angle is increased from<br /> ''2.56&amp;deg;'' (Diffuser 1) to ''4&amp;deg;'' (Diffuser2). The flow in the inlet duct (height<br /> ''h=1 cm'', width ''B=3.33 cm'') corresponds to fully-developed turbulent channel<br /> flow (enabled experimentally by a development channel being 62.9 channel<br /> heights long). The ''L=15h'' long diffuser section is followed by a straight<br /> outlet part (''12.5h'' long). Downstream of this the flow goes through a ''10h''<br /> long contraction into a 1 inch diameter tube. The curvature radius at the<br /> walls transitioning between diffuser and the straight duct parts are ''6 cm''<br /> (Diffuser 1) and ''2.8 cm'' (Diffuser 2). The bulk velocity in the inflow duct<br /> is &lt;math&gt;{U_\textrm{bulk}=U_\textrm{inflow}=1 m/s}&lt;/math&gt;<br /> in the ''x''-direction resulting in the Reynolds number based on the<br /> inlet channel height of ''10000''. The origin of the coordinates (''y=0, z=0'')<br /> coincides with the intersection of the two non-expanding walls at the<br /> beginning of the diffuser's expansion (x=0). The working fluid is water<br /> (''&amp;rho;=1000 kg/m&lt;sup&gt;3&lt;/sup&gt;'' and ''&amp;mu;=0.001 Pas'').<br /> <br /> <br /> &lt;div id=&quot;figure3&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=750<br /> |[[Image:UFR4-16_figure3.png|740px]]<br /> |-<br /> |'''Figure 3:''' Geometry of the 3-D diffuser 1 considered (not to scale), [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]; see also [[UFR_4-16_References#14|Jakirli&amp;#x107; ''et&amp;nbsp;al.'' (2010a)]]<br /> |}<br /> <br /> <br /> <br /> <br /> &lt;div id=&quot;figure4&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=750<br /> |[[Image:UFR4-16_figure4.png|740px]]<br /> |-<br /> |'''Figure 4:''' Geometry of the 3-D diffuser 2 considered (not to scale), [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]].<br /> |}<br /> <br /> == Experimental investigation ==<br /> ===Brief description of the experimental setup===<br /> The measurements were performed in a recirculating water channel using the<br /> method of magnetic resonance velocimetry (MRV),<br /> [[UFR_4-16_Test_Case#figure5|Fig. 5.]] MRV makes use of a<br /> technique very similar to that used in conventional medical magnetic<br /> resonance imaging (MRI),<br /> [[UFR_4-16_Test_Case#figure6|Fig. 6.]] Experiments were performed on a 1.5 Tesla<br /> magnet with resolution of 0.9 x 0.9 x 0.9 mm and a 7 Tesla magnet with<br /> resolution of 0.4 x 0.4 x 0.4 mm. Interested readers are referred to<br /> [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008]],<br /> [[UFR_4-16_References#8|2009)]]<br /> for more details about the measurement technique.<br /> <br /> <br /> &lt;div id=&quot;figure5&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;558&quot;<br /> |[[Image:UFR4-16_figure5a.png|548px]]<br /> |-<br /> |[[Image:UFR4-16_figure5b.png|548px]]<br /> |-<br /> |'''Figure 5:''' Schematic of the experimental flow system (upper) and design of the 3D diffuser. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> <br /> <br /> <br /> &lt;div id=&quot;figure6&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;558&quot;<br /> |[[Image:UFR4-16_figure6.jpg|548px]]<br /> |-<br /> |'''Figure 6:''' 3D diffuser arrangement in a medical magnetic resonance imaging device. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> ===Mean velocity and Reynolds stress measurements===<br /> Cherry ''et&amp;nbsp;al.'' provided a detailed reference database comprising the<br /> three-component mean velocity field and the streamwise Reynolds stress component<br /> field within the entire diffuser section. Both diffuser configurations<br /> considered are characterized by a three-dimensional boundary-layer<br /> separation, but the slightly different expansion geometries caused the size<br /> and shape of the separation bubble exhibiting a high degree of geometric<br /> sensitivity to the dimensions of the diffuser as illustrated in<br /> [[UFR_4-16_Test_Case#figure7|Figs. 7]], [[UFR_4-16_Test_Case#figure8|8]]<br /> and [[UFR_4-16_Test_Case#figure9|9]]<br /> <br /> <br /> &lt;div id=&quot;figure7&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure7.png|740px]]<br /> |-<br /> |'''Figure 7:''' Streamwise velocity contours in a plane parallel to the top wall, from [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure8&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; style=&quot;border: 1px solid black;&quot; border=&quot;1&quot;<br /> |align=&quot;center&quot; colspan=&quot;3&quot;|[[Image:UFR4-16_figure8a.png|493px]]<br /> |-<br /> |colspan=&quot;3&quot;|[[Image:UFR4-16_figure8b.png|750px]]<br /> |-<br /> |[[Image:UFR4-16_figure8c.png|247px]]||[[Image:UFR4-16_figure8d.png|247px]]||[[Image:UFR4-16_figure8e.png|247px]]<br /> |-<br /> |colspan=&quot;3&quot;|'''Figure 8:''' Measured streamwise velocity contours in the central plane (upper) of the '''Diffuser 1''' and in the three selected cross-sectional slices positioned at different distances from the diffuser inlet (lower; their locations are denoted by thick white lines in the upper figure). Note that the black line indicates zero streamwise velocity and the purple and pink regions are reverse flow. The velocity values are normalized by the bulk inlet velocity being ''V&lt;sub&gt;ref&lt;/sub&gt;=1&amp;nbsp;m/s''. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure9&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; style=&quot;border: 1px solid black&quot; border=&quot;1&quot;<br /> |colspan=&quot;3&quot; align=&quot;center&quot;|[[Image:UFR4-16_fig9a.png|493px]]<br /> |-<br /> |colspan=&quot;3&quot;|[[Image:UFR4-16_fig9b.png|750px]]<br /> |-<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig9c.png|246px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig9d.png|246px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig9e.png|246px]]<br /> |-<br /> |colspan=&quot;3&quot;|'''Figure 9:''' Measured streamwise velocity contours in the central plane (upper) of the '''Diffuser 2''' and in the three selected cross-sectional slices positioned at different distances from the diffuser inlet (lower; their locations are denoted by thick white lines in the upper figure). Note that the black line indicates zero streamwise velocity and the purple and pink regions are reverse flow. The velocity values are normalized by the bulk inlet velocity being ''V&lt;sub&gt;ref&lt;/sub&gt;=1&amp;nbsp;m/s''. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure10&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; style=&quot;border: 1px solid black&quot;<br /> !x/h=2!!x/h=5!!x/h=8!!x/h=12!!x/h=15<br /> |-<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10a.png|137px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10b.png|139px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10c.png|148px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10d.png|154px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10e.png|162px]]<br /> |-<br /> |align=&quot;center&quot; colspan=&quot;5&quot;|[[Image:UFR4-16_fig10f.png]]<br /> |-<br /> |colspan=&quot;5&quot;|'''Figure 10:''' Measurements of turbulent streamwise stress components taken in cross-sectional slices of the diffuser 1 perpendicular to the mean flow. The region of highest turbulence (red areas; ignore the red areas at the bottom walls) follows the shear layer between forward and reverse flow. ''h''=1cm represents the height of the inflow duct. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> ===Pressure measurements===<br /> In addition<br /> [[UFR_4-16_References#8|Cherry ''et&amp;nbsp;al.'' (2009)]]<br /> provided the pressure distribution along<br /> the bottom non-deflected wall of diffuser 1 at different Reynolds numbers.<br /> Complementary to the Reynolds number 10000 (for which the entire flow field<br /> was measured), two higher Reynolds numbers &amp;mdash; 20000 and 30000 &amp;mdash; were also<br /> considered, [[UFR_4-16_Test_Case#figure11|Fig. 11]]. The surface pressure distribution was evaluated to<br /> yield the coefficient<br /> &lt;math&gt;C_p=(p-p_\textrm{ref})/(0.5\rho U_\textrm{bulk}^2)&lt;/math&gt;;<br /> the reference pressure was taken at the<br /> position ''x/L&amp;nbsp;=&amp;nbsp;0.05''. The pressure curve exhibits a development typical of<br /> flow in diverging ducts. The pressure decrease in the inflow duct is<br /> followed by a steep pressure increase already at the very end of the inflow<br /> duct and especially at the beginning of the diffuser section. The<br /> transition from the initial strong pressure rise to its moderate increase<br /> occurs at ''x/L&amp;nbsp;&amp;#8776;&amp;nbsp;0.3'', (''x/h=4.5'')<br /> corresponding to the position where about 5% of<br /> the entire cross-section is occupied by the flow reversal (see e.g.,<br /> [[UFR_4-16_Test_Case#figure19|Fig. 19]].<br /> The onset of separation causes a certain contraction of the flow cross&amp;#8208;section,<br /> leading to a weakening of the deceleration intensity and,<br /> accordingly, to a slower pressure increase. The region characterized by a<br /> monotonic pressure rise was reached in the remainder of the diffuser<br /> section.<br /> <br /> <br /> &lt;div id=&quot;figure11&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure11.png|740px]]<br /> |-<br /> |'''Figure 11:''' Pressure recovery coefficients relative to the pressure on the bottom wall of the diffuser 1 inlet in a range of flow Reynolds number. L=15 cm represents the length of Diffuser 1, from [[UFR_4-16_References#8|Cherry ''et&amp;nbsp;al.'' (2009)]]<br /> <br /> |}<br /> <br /> ===Measurements uncertainties===<br /> (adopted from [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'', 2008, IJHFF, Vol. 29(3)]])<br /> <br /> Elkins et al. (2004) estimated the maximum relative uncertainty of<br /> individual mean velocity measurements to be about 10% of the measured value<br /> in a similar highly turbulent flow. However, comparisons to PIV in a<br /> backward facing step flow (Elkins et al., 2007) show that only a small<br /> percentage of MRV velocity samples deviate by that much and most are much<br /> more accurate. To test this, the streamwise velocity component was<br /> integrated over 250 cross-sections of the MRV data and the results were<br /> compared to the known volume flow rate. This indicated an uncertainty in<br /> the integral of less than 2% with a 95% confidence level.<br /> <br /> Measurements of turbulent normal stresses in Diffuser 1 were also taken<br /> using the MR technique described by Elkins et al. (2007). This method is<br /> based on diffusion imaging principles in which the turbulence causes a loss<br /> of net magnetization signal from a voxel in the flow. This causes a decay<br /> in signal strength which can be related to turbulent velocity statistics.<br /> Elkins et al found this method to be accurate within 20% everywhere in the<br /> FOV and within 5% in regions of high turbulence. Three turbulence scans<br /> were completed using three different magnetic field gradient strengths. For<br /> each gradient strength, 30 scans were completed and averaged. The three<br /> averaged data sets were then averaged to obtain a final data set.<br /> <br /> ===Experimental data available===<br /> Velocity, (and streamwise Reynolds stress components for diffuser 1) and<br /> coordinate data for both diffusers are available here. &lt;!--at http://stanford.edu/~echerry/--&gt;<br /> <br /> {|<br /> &lt;!--<br /> |[http://stanford.edu/~echerry/AnnularDiffuserData.zip AnnularDiffuserData.zip] (contains 4 files, 134 MBytes)<br /> --&gt;<br /> |-<br /> |[https://www.kbwiki.ercoftac.org/w/Data/UFR4-16/Diffuser_1_data.zip Diffuser 1 data.zip] (contains 1 file, 8.4 MBytes)<br /> |-<br /> &lt;!--<br /> |-<br /> |[http://stanford.edu/~echerry/Diffuser%201%20data.zip Diffuser 1 data.zip] (contains 1 file, 8.4 MBytes)<br /> --&gt;<br /> |-<br /> |[https://www.kbwiki.ercoftac.org/w/Data/UFR4-16/Diffuser_1_turbulence.zip Diffuser 1 turbulence.zip] (contains 1 file, 5.3 MBytes)<br /> |-<br /> |[https://www.kbwiki.ercoftac.org/w/Data/UFR4-16/Diffuser_2_data.zip Diffuser 2 data.zip] (contains 1 file, 4 MBytes)<br /> |}<br /> <br /> The data are seven 3D matlab matrices. The<br /> x, y, and z matrices give the coordinates of each point in the coordinate<br /> system shown in Fig. 5. The units are meters. The Vx, Vy, and Vz matrices<br /> give the corresponding velocity components for each point in m/sec. The<br /> matrix mg gives the relative signal magnitude detected by the MRI machine.<br /> <br /> Experimental data for the pressure coefficient in Diffuser 1 for the inflow<br /> Reynolds number Re=10000 are available [[Media:UFR4-16_Cp_Re=10000.xlsx|here]]<br /> ([[Media:UFR4-16_Cp_Re=10000.xlsx|Cp_Re=10000.xlsx]]). The<br /> coordinate system is the same as the coordinate system described in the<br /> corresponding manuscript (see below). &lt;math&gt;{\ C_p}&lt;/math&gt; is defined as<br /> &lt;math&gt;\left(p-p_\textrm{ref}\right)/\left(\frac{1}{2} \rho V^2\right)&lt;/math&gt;,<br /> where &lt;math&gt;{\ P_\textrm{ref}}&lt;/math&gt; is the pressure at ''x=0.05'' (see Fig. 11)<br /> at the midpoint<br /> (''z/B=0.5'') of the bottom flat wall (opposite the wall expanding at 11.3<br /> degrees), &lt;math&gt;{\ \rho}&lt;/math&gt; is the density, and &lt;math&gt;{\ V}&lt;/math&gt;<br /> is the bulk inlet velocity. The data were<br /> taken in a line along the bottom wall of Diffuser 1 at constant y and z<br /> coordinates. L (=15 cm) indicates the length of the diffuser.<br /> <br /> ''Please acknowledge the authors of the experiment when using their database!''<br /> <br /> == CFD Methods ==<br /> The flow in the present diffuser configuration was intensively investigated<br /> computationally in the framework of two ERCOFTAC-SIG15 Workshops and in<br /> the European ATAAC project.<br /> The workshops focussing on both 3D diffuser configurations (denoted by SIG15<br /> Case 13.2-1 and SIG15 Case 13.2-2, respectively) were organized at the<br /> Technical University of Graz, Austria in September, 2008 and the &quot;LA<br /> Sapienza&quot; University of Rome, Italy in September, 2009. The corresponding<br /> reports are published in the ERCOFTAC Bulletin Issues,<br /> [[UFR_4-16_References#30|Steiner ''et&amp;nbsp;al.'' (2009)]]<br /> and [[UFR_4-16_References#15|Jakirli&amp;#x107; ''et&amp;nbsp;al.'' (2010b)]],<br /> see [[UFR_4-16_References#0|&quot;List of References&quot;]].<br /> Both in the workshops and in the ATAAC project a wide range of<br /> turbulence models in both LES and RANS frameworks as well as some novel<br /> Hybrid LES/RANS formulations have been employed. The computational database<br /> was furthermore enriched by the results of a Direct Numerical Simulation of<br /> the first diffuser performed by<br /> [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]]. The list of all<br /> computational contributions to the workshops including some basic information about the<br /> methods and models used and corresponding grid resolution is given in<br /> the following [[UFR_4-16_Test_Case#table1|tables 1]] and [[UFR_4-16_Test_Case#table2|table 2]].<br /> For more computational details, interested<br /> readers are referred to the &quot;[[UFR_4-16_Evaluation#Available_CFD_results:_ERCOFTAC_SIG15_Workshop_Proceedings|workshop proceedings]]&quot;<br /> &amp;mdash; see the corresponding<br /> links at the end of the Section &quot;[[UFR_4-16_Evaluation#Evaluation_of_the_results|Evaluation of the results]]&quot;.<br /> The results from the ATAAC project and information on the methods used can be obtained through the links<br /> [https://cfd.mace.manchester.ac.uk/twiki/pub/ATAAC/TestCase004Diffuser3D/ATAAC_D3-2-36_excerpt3DDiffuser.pdf ATAAC_D3-2-36_excerpt3DDiffuser.pdf]<br /> (excerpt from an ATAAC report) and<br /> [http://cfd.mace.manchester.ac.uk/twiki/pub/ATAAC/TestCase004Diffuser3D/ATAAC_finalWorkshop_ST04-Diffuser-ANSYS.pdf ATAAC_finalWorkshop_ST04-Diffuser-ANSYS.pdf]<br /> (PowerPoint presentation at ATAAC final workshop).<br /> <br /> <br /> &lt;div id=&quot;table1&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_table1.png|740px]]<br /> |-<br /> |'''Table 1:''' SIG15 Case 13.2-1 (Diffuser 1) &amp;mdash; contributors and methods (note that the DNS grid comprises 220 million cells in the follow-up work published in [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]])<br /> |-<br /> |'''N.B.''' ITS is &quot;Institut f&amp;uuml;r Thermische Str&amp;ouml;mungsmaschinen&quot;<br /> |}<br /> <br /> <br /> &lt;div id=&quot;table2&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_table2.png|740px]]<br /> |-<br /> |'''Table 2:''' SIG15 Case 13.2-2 (Diffuser 2) &amp;mdash; contributors and methods<br /> |-<br /> |'''N.B.''' ITS is &quot;Institut f&amp;uuml;r Thermische Str&amp;ouml;mungsmaschinen&quot;<br /> |}<br /> <br /> <br /> ===Direct numerical simulation of the flow in a 3D diffuser===<br /> <br /> (adopted from [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'', 2010, JFM, Vol. 650]])<br /> <br /> In this part of the present contribution the DNS study of the flow in 3D<br /> Diffuser 1 performed recently by<br /> [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]] will be described in<br /> more details. Ohlsson ''et&amp;nbsp;al.'' participated with this contribution at the<br /> 14th SIG15 Workshop on Refined Turbulence Modeling <br /> ([[UFR_4-16_References#15|Jakirli&amp;#x107; ''et&amp;nbsp;al.'', 2010b]]).<br /> Accordingly, their results are also part of the CFD methods/models<br /> evaluation &amp;mdash; along with the results obtained by different LES, RANS and<br /> Hybrid LES/RANS models (see the [[UFR_4-16_Evaluation#Evaluation_of_the_results|next chapter]]).<br /> In addition, as the DNS<br /> provided a very comprehensive database comprising all three mean velocity<br /> components (and associated integral characteristics such as surface<br /> pressure and friction factor) and all six Reynolds stress components as<br /> well as a certain insight into the physics (not detected by the<br /> experimental investigation) one can regard it also as a reference<br /> investigation, as we do presently.<br /> <br /> The Direct Numerical Simulation of the Diffuser 1 was performed using a<br /> massively parallel high-order spectral element code. The incompressible<br /> Navier-Stokes equations are solved using a Legendre-polynomial-based<br /> spectral-element method, implemented in the code nek5000, developed by<br /> Fischer et al. (2008). The computational domain shown in<br /> [[UFR_4-16_Test_Case#figure12|Fig. 12]] is set up<br /> in close agreement with the diffuser geometry in the experiment<br /> (see [[UFR_4-16_Test_Case#figure3|Fig.3]])<br /> and consists of the inflow development duct of almost 63 duct heights,<br /> ''h'', (starting at the non-dimensional coordinate ''x''&amp;nbsp;=&amp;nbsp;-62.9),<br /> the diffuser<br /> expansion located at ''x''&amp;nbsp;=&amp;nbsp;0 and the converging section upstream of the<br /> outlet. The corners resulting from the diffuser expansion are smoothly<br /> rounded with a radius of 6.0 in accordance with the experimental set-up.<br /> The maximum dimensions are ''Lx =105.4 h, Ly =[h, 4h], Lz =[3.33 h, 4h]''. In<br /> the inflow duct, laminar flow undergoes natural transition by the use of an<br /> unsteady trip forcing (see e.g. Schlatter et al., 2009), which avoids the<br /> use of artificial turbulence and eliminates artificial temporal frequencies<br /> which may arise from inflow recycling methods (Herbst et al., 2007). A<br /> 'sponge region' is added at the end of the contraction in order to smoothly<br /> damp out turbulent fluctuations, thereby eliminating spurious pressure<br /> waves. It is followed by a homogeneous Dirichlet condition for the pressure<br /> and a homogeneous Neumann condition for the velocities. The resolution of<br /> approximately 220 million grid points is obtained by a total of 127750<br /> local tensor product domains (elements) with a polynomial order of 11,<br /> respectively, resulting in &amp;Delta;z&lt;sup&gt;+&lt;/sup&gt;&lt;sub&gt;max&lt;/sub&gt;&amp;asymp;11.6,<br /> &amp;Delta;y&lt;sup&gt;+&lt;/sup&gt;&lt;sub&gt;max&lt;/sub&gt;&amp;asymp;13.2 and<br /> &amp;Delta;x&lt;sup&gt;+&lt;/sup&gt;&lt;sub&gt;max&lt;/sub&gt;&amp;asymp;19.5 in the<br /> duct center and the first grid point being located at z&lt;sup&gt;+&lt;/sup&gt;&amp;asymp;0.074<br /> and y&lt;sup&gt;+&lt;/sup&gt;&amp;asymp;0.37, respectively (note that at the time of the ERCOFTAC SIG15 workshop<br /> the DNS grid had 172 million grid points,<br /> see Chapter &quot;[[UFR_4-16_Evaluation#172million|Evaluation]]&quot;). It was<br /> verified that this resolution yields accurate results in turbulent channel<br /> flow simulations. In the diffuser, the grid is linearly stretched in both<br /> directions, but since the mean resolution requirements decreases with the<br /> velocity, which decreases linearly with the area expansion, the resolution<br /> in the entire domain is hence satisfactory. The simulation was performed on<br /> the Blue Gene/P at ALCF, Argonne National Laboratory (32768 cores and a<br /> total of 8 million core hours) and on the cluster 'Ekman' at PDC, Stockholm<br /> (2048 cores and a total of 4 million core hours). Thirteen flow-through<br /> times, ''t U&lt;sub&gt;b&lt;/sub&gt;/L''=13, based on bulk velocity, ''U&lt;sub&gt;b&lt;/sub&gt;'', and diffuser length, ''L=15&amp;nbsp;h'',<br /> were simulated in order to let the flow settle to an equilibrium state<br /> before turbulent statistics were collected over approximately ''U&lt;sub&gt;b&lt;/sub&gt;t/L''=21<br /> additional flow-through times.<br /> <br /> In addition to the three-dimensional mean velocity field, all six Reynolds<br /> stress components were evaluated, as well as the surface pressure and skin<br /> friction distribution along the bottom wall.<br /> <br /> <br /> &lt;div id=&quot;figure12&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure12.png|740px]]<br /> |-<br /> |'''Figure 12:''' DNS grid of the diffuser 1 geometry showing the development region, diffuser expansion, converging section and outlet. From [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]]<br /> |}<br /> <br /> <br /> [[UFR_4-16_Test_Case#figure13|Fig. 13]] illustrates the mean axial flow field obtained by DNS along with<br /> the experimental data and [[UFR_4-16_Test_Case#figure14|Fig. 14]] depicts the skin friction evolution along<br /> the bottom diffuser wall at the midpoint<br /> (''z/B=0.5''; ''C&lt;sub&gt;f&lt;/sub&gt;=&amp;tau;&lt;sub&gt;wall&lt;/sub&gt;&amp;nbsp;/&amp;nbsp;(0.5&amp;rho;U&lt;sup&gt;2&lt;/sup&gt;&lt;sub&gt;bulk&lt;/sub&gt;'')&amp;nbsp;). The latter DNS<br /> result was evaluated exclusively for the needs of the 14th ERCOFTAC<br /> Workshop; it is not part of the DNS database which can be downloaded [[UFR_4-16_Test_Case#kth_data|here]].<br /> <br /> <br /> &lt;div id=&quot;figure13&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure13.png|740px]]<br /> |-<br /> |'''Figure 13:''' Cross-flow planes of streamwise velocity component at 2, 5, 8 and 15 ''h'' downstream of the diffuser throat. Left: DNS. Right: Experiment by [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]. Each streamwise position has its own colour bar on the right. Contour lines are spaced ''0.1 V&lt;sub&gt;ref&lt;/sub&gt;'' apart. Thick black lines correspond to the zero velocity contour. From [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]]<br /> <br /> <br /> &lt;div id=&quot;figure14&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure14.jpg|740px]]<br /> |-<br /> |'''Figure 14:''' Friction coefficient at the bottom wall of the diffuser 1 with ''L=15 cm'' representing the length of Diffuser 1. The LES and HLR (Hybrid LES/RANS) results are from [[UFR_4-16_References#14|Jakirli&amp;#x107; ''et&amp;nbsp;al.'' (2010a)]] and [[UFR_4-16_References#17|John-Puthenveetil (2012)]].<br /> <br /> ===Available DNS data (last update: 2010-11-23)===<br /> &lt;div id=&quot;kth_data&quot;&gt;&lt;/div&gt;<br /> The entire digitalized DNS database (as well as some high-resolution<br /> images) as listed below can be downloaded from<br /> http://www.mech.kth.se/~johan/data/index.html. The links given below are to local wiki copies of the files.<br /> <br /> This directory contains velocity profiles and mean fluctuations obtained<br /> from the DNS by<br /> [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'', (JFM 650 307&amp;ndash;318)]]<br /> This simulation was<br /> designed to match the experiment by<br /> [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'', 2008, IJHFF 29(3)]]. The<br /> data is given at the same streamwise and spanwise locations as during the<br /> 14th ERCOFTAC SIG15 Workshop on Turbulence Modelling, held in Rome,<br /> September 2009.<br /> <br /> The full Reynolds stress budgets will be available in the future.<br /> <br /> ''The data is free to use; please include a proper reference to the original publications.''<br /> <br /> In case of any questions, e.g. related to the data, or whether you wish for<br /> additional data not presented here, please contact<br /> Johan Malm, ([mailto:johan@mech.kth.se johan@mech.kth.se]),<br /> Philipp Schlatter ([mailto:pschlatt@mech.kth.se pschlatt@mech.kth.se])<br /> or Dan Henningson ([mailto:henning@mech.kth.se henning@mech.kth.se])<br /> <br /> ====Visualizations and computational mesh====<br /> [[Media:UFR4-16_planes_press0000.jpeg|Crossflow planes with instantaneous streamwise velocity]]<br /> <br /> [[Media:UFR4-16_planes_nogrid_iso_vec.jpeg|Crossflow planes with instantaneous streamwise velocity and isosurfaces of streamwise velocity]]<br /> <br /> [[Media:UFR4-16_press_persp0010.jpeg|Instantaneous streamwise velocity in a spanwise midplane with some isosurfaces of instantaneous pressure]]<br /> <br /> [[Media:UFR4-16_mesh_paper.png|Mesh]]<br /> <br /> ====Digitalized DNS database: full 3D mean velocity and Reynolds stress fields====<br /> Explanation:<br /> *E.g., c13.2_Ucont2_KTH_DNS denotes the files comprising the contours of the axial velocity - Ucont - at the streamwise position ''x/h=2'' for the case 13.2 (ERCOFTAC SIG15 denotation). The same data are given at the streamwise locations ''x/h=2, 5, 8, 12'' and ''15''<br /> *E.g., c13.2_urms2_KTH_DNS.txt denotes the file comprising the contours of the root-mean-square values of the streamwise stress component &amp;mdash; urms &amp;mdash; at the streamwise position ''x/h=2''. The same data are given at the streamwise locations ''x/h=2, 5, 8, 12'' and ''15''<br /> *The file c13.2_cp_KTH_DNS.txt denotes the file comprising the pressure coefficient distribution at the bottom flat wall at the midpoint ''z/B=0.5''<br /> *The file c13.2_z0250_x-2_KTH_DNS.txt denotes the file comprising all three mean velocity components, kinetic energy of turbulence and all six Reynolds stress components at the streamwise position ''x/h=-2'' (inflow duct) and the spanwise position ''z/B=0.25''. The same data are given at the streamwise locations ''x/h=0, 2, 4, 6, 8, 10, 12, 14, 15.5, 17, 18.5, 20'' and ''21.5'' at the following spanwise locations ''z/B=0.25, 0.5, 0.75'' and ''0.875''.<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;1&quot; cellpadding=&quot;5&quot;<br /> |[[Media:c13.2_cp_KTH_DNS.txt|c13.2_cp_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont2_KTH_DNS.txt|c13.2_Ucont2_KTH_DNS.txt]]||[[Media:c13.2_urms2_KTH_DNS.txt|c13.2_urms2_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont5_KTH_DNS.txt|c13.2_Ucont5_KTH_DNS.txt]]||[[Media:c13.2_urms5_KTH_DNS.txt|c13.2_urms5_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont8_KTH_DNS.txt|c13.2_Ucont8_KTH_DNS.txt]]||[[Media:c13.2_urms8_KTH_DNS.txt|c13.2_urms8_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont12_KTH_DNS.txt|c13.2_Ucont12_KTH_DNS.txt]]||[[Media:c13.2_urms12_KTH_DNS.txt|c13.2_urms12_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont15_KTH_DNS.txt|c13.2_Ucont15_KTH_DNS.txt]]||[[Media:c13.2_urms15_KTH_DNS.txt|c13.2_urms15_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x-2_KTH_DNS.txt|c13.2_z0250_x-2_KTH_DNS.txt]]||[[Media:c13.2_z0500_x-2_KTH_DNS.txt|c13.2_z0500_x-2_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x-2_KTH_DNS.txt|c13.2_z0750_x-2_KTH_DNS.txt]]||[[Media:c13.2_z0875_x-2_KTH_DNS.txt|c13.2_z0875_x-2_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x0_KTH_DNS.txt|c13.2_z0250_x0_KTH_DNS.txt]]||[[Media:c13.2_z0500_x0_KTH_DNS.txt|c13.2_z0500_x0_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x0_KTH_DNS.txt|c13.2_z0750_x0_KTH_DNS.txt]]||[[Media:c13.2_z0875_x0_KTH_DNS.txt|c13.2_z0875_x0_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x2_KTH_DNS.txt|c13.2_z0250_x2_KTH_DNS.txt]]||[[Media:c13.2_z0500_x2_KTH_DNS.txt|c13.2_z0500_x2_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x2_KTH_DNS.txt|c13.2_z0750_x2_KTH_DNS.txt]]||[[Media:c13.2_z0875_x2_KTH_DNS.txt|c13.2_z0875_x2_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x4_KTH_DNS.txt|c13.2_z0250_x4_KTH_DNS.txt]]||[[Media:c13.2_z0500_x4_KTH_DNS.txt|c13.2_z0500_x4_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x4_KTH_DNS.txt|c13.2_z0750_x4_KTH_DNS.txt]]||[[Media:c13.2_z0875_x4_KTH_DNS.txt|c13.2_z0875_x4_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x6_KTH_DNS.txt|c13.2_z0250_x6_KTH_DNS.txt]]||[[Media:c13.2_z0500_x6_KTH_DNS.txt|c13.2_z0500_x6_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x6_KTH_DNS.txt|c13.2_z0750_x6_KTH_DNS.txt]]||[[Media:c13.2_z0875_x6_KTH_DNS.txt|c13.2_z0875_x6_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x8_KTH_DNS.txt|c13.2_z0250_x8_KTH_DNS.txt]]||[[Media:c13.2_z0500_x8_KTH_DNS.txt|c13.2_z0500_x8_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x8_KTH_DNS.txt|c13.2_z0750_x8_KTH_DNS.txt]]||[[Media:c13.2_z0875_x8_KTH_DNS.txt|c13.2_z0875_x8_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x10_KTH_DNS.txt|c13.2_z0250_x10_KTH_DNS.txt]]||[[Media:c13.2_z0500_x10_KTH_DNS.txt|c13.2_z0500_x10_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x10_KTH_DNS.txt|c13.2_z0750_x10_KTH_DNS.txt]]||[[Media:c13.2_z0875_x10_KTH_DNS.txt|c13.2_z0875_x10_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x12_KTH_DNS.txt|c13.2_z0250_x12_KTH_DNS.txt]]||[[Media:c13.2_z0500_x12_KTH_DNS.txt|c13.2_z0500_x12_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x12_KTH_DNS.txt|c13.2_z0750_x12_KTH_DNS.txt]]||[[Media:c13.2_z0875_x12_KTH_DNS.txt|c13.2_z0875_x12_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x14_KTH_DNS.txt|c13.2_z0250_x14_KTH_DNS.txt]]||[[Media:c13.2_z0500_x14_KTH_DNS.txt|c13.2_z0500_x14_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x14_KTH_DNS.txt|c13.2_z0750_x14_KTH_DNS.txt]]||[[Media:c13.2_z0875_x14_KTH_DNS.txt|c13.2_z0875_x14_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x155_KTH_DNS.txt|c13.2_z0250_x155_KTH_DNS.txt]]||[[Media:c13.2_z0500_x155_KTH_DNS.txt|c13.2_z0500_x155_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x155_KTH_DNS.txt|c13.2_z0750_x155_KTH_DNS.txt]]||[[Media:c13.2_z0875_x155_KTH_DNS.txt|c13.2_z0875_x155_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x17_KTH_DNS.txt|c13.2_z0250_x17_KTH_DNS.txt]]||[[Media:c13.2_z0500_x17_KTH_DNS.txt|c13.2_z0500_x17_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x17_KTH_DNS.txt|c13.2_z0750_x17_KTH_DNS.txt]]||[[Media:c13.2_z0875_x17_KTH_DNS.txt|c13.2_z0875_x17_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x185_KTH_DNS.txt|c13.2_z0250_x185_KTH_DNS.txt]]||[[Media:c13.2_z0500_x185_KTH_DNS.txt|c13.2_z0500_x185_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x185_KTH_DNS.txt|c13.2_z0750_x185_KTH_DNS.txt]]||[[Media:c13.2_z0875_x185_KTH_DNS.txt|c13.2_z0875_x185_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x20_KTH_DNS.txt|c13.2_z0250_x20_KTH_DNS.txt]]||[[Media:c13.2_z0500_x20_KTH_DNS.txt|c13.2_z0500_x20_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x20_KTH_DNS.txt|c13.2_z0750_x20_KTH_DNS.txt]]||[[Media:c13.2_z0875_x20_KTH_DNS.txt|c13.2_z0875_x20_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x215_KTH_DNS.txt|c13.2_z0250_x215_KTH_DNS.txt]]||[[Media:c13.2_z0500_x215_KTH_DNS.txt|c13.2_z0500_x215_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x215_KTH_DNS.txt|c13.2_z0750_x215_KTH_DNS.txt]]||[[Media:c13.2_z0875_x215_KTH_DNS.txt|c13.2_z0875_x215_KTH_DNS.txt]]<br /> |}<br /> &lt;br/&gt;<br /> &lt;br/&gt;<br /> <br /> ==Reference DNS and experimental data: mean flow and turbulence evolution==<br /> The following figures display and compare the reference experimental and<br /> DNS database results (the present results can be analysed along with the<br /> axial velocity contours shown in<br /> [[UFR_4-16_Test_Case#figure7|Figs. 7]] &amp;ndash;<br /> [[UFR_4-16_Test_Case#figure9|9]] and [[UFR_4-16_Test_Case#figure13|13]]):<br /> <br /> <br /> In order to get an impression about the mean flow structure and about the<br /> available reference DNS and experimental results<br /> [[UFR_4-16_Test_Case#figure15|Figs. 15]] and<br /> [[UFR_4-16_Test_Case#figure16|16]] display<br /> the velocity field development in the vertical central plane of both<br /> diffusers (''z/B=0.5''; ''B=3.33 cm'' is the width of the inflow duct) typical for<br /> the flow in an expanding duct. The bulk flow exhibits deceleration, leading<br /> to an asymmetry of the velocity profile, particularly so for the axial<br /> velocity component. The effect of the adverse pressure gradient is<br /> especially visible in the flow region along the upper expanding wall. The<br /> velocity profile approaches gradually the form characterizing a separating<br /> flow, exhibiting regions of the zero velocity gradient (at separation and<br /> reattachment points) and profile inflection. The through-flow, that is the<br /> flow in the positive streamwise direction, is characterized by a spreading<br /> dictated by the pressure gradient arising from the geometry expansion.<br /> Accordingly, the position of the reduced velocity maximum is gradually<br /> shifted towards the upper wall, eventually reaching the center (''y/h=2'') of<br /> the straight outlet channel (with the height ''4h''). In this post-reattachment<br /> zone the velocity profile exhibits a fairly flattened form, being almost<br /> symmetric. The consequence of the velocity-profile flattening is a<br /> continuous monotonic decrease of the wall shear stress. The velocity<br /> profile evolution is similar in other longitudinal vertical planes. The<br /> specific differences are related to the vicinity of both bottom and upper<br /> walls, especially the latter upper wall, where the flow passes regions of<br /> three-dimensional flow reversal.<br /> <br /> <br /> &lt;div id=&quot;figure15&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure15a.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure15b.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure15c.jpg|740px]]<br /> |-<br /> |'''Figure 15:''' Diffuser 1 - Evolution of the profiles of all three velocity components in the vertical plane ''x-y'' at the central spanwise locations ''z/B=1/2'' obtained experimentally and by means of DNS<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure16&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure16a.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure16b.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure16c.jpg|740px]]<br /> |-<br /> |'''Figure 16:''' Diffuser 2 - Evolution of the profiles of all three velocity components in the vertical plane ''x-y'' at the central spanwise locations ''z/B=1/2'' obtained experimentally<br /> |}<br /> <br /> <br /> In the top part of [[UFR_4-16_Test_Case#figure17|Fig. 17 &amp;ndash; upper]]<br /> the development of the streamwise<br /> turbulence intensity is shown for diffuser 1. The lowest turbulence<br /> intensity is situated in the region coinciding with the mean velocity<br /> maximum &amp;mdash; flow zone with approximately zero velocity gradient &amp;mdash; along the<br /> entire diffuser section. The Reynolds stress profiles exhibit their highest<br /> values in the regions with the most intensive flow deformation. These are<br /> the near-wall layer in the attached-flow regions and the flow zone along<br /> the shear layer bordering the recirculation zone. The peak of the<br /> turbulence intensity originating from the boundary layer at the top inflow<br /> duct wall increases initially, after the strong rise in pressure (see<br /> pressure coefficient development in<br /> [[UFR_4-16_Test_Case#figure11|Fig. 11]]), and weakens slightly after<br /> flow transition to the second part of the diffuser section, that is<br /> characterized by a decreasingly adverse pressure gradient. The streamwise<br /> turbulence intensity in the outlet duct is uniformly distributed over the<br /> cross-section.<br /> <br /> <br /> &lt;div id=&quot;figure17&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17a.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17b.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17c.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17d.jpg|740px]]<br /> |-<br /> |'''Figure 17:''' Diffuser 1 - Evolution of the profiles of the Reynolds stress components in the vertical plane ''x-y'' at the central spanwise locations ''z/B=1/2'' obtained experimentally and by means of DNS<br /> |}<br /> <br /> <br /> [[UFR_4-16_Test_Case#figure18|Fig. 18]]<br /> shows contour plots of the axial velocity component at five<br /> streamwise cross-sectional areas in both diffuser configurations obtained<br /> experimentally indicating the evolution of the flow separation pattern. The<br /> recirculation-zone development displayed here can be analyzed in parallel<br /> with the quantitative information about the fraction of the diffuser cross-<br /> sectional area occupied by the reverse flow depicted in<br /> [[UFR_4-16_Test_Case#figure19|Fig. 19]]. The<br /> adverse pressure gradient is imposed onto the intersecting boundary layers<br /> along flat walls upon entering the diffuser section. According to the<br /> experimental investigation the boundary layers along all walls are of<br /> comparable thickness. The separation starts immediately after the beginning<br /> of the diffuser section at ''x/L = 0 (x/h=0)''. The onset of separation is<br /> located in the upper-right diffuser corner, formed by the deflected side<br /> wall and the top wall, see e.g. the position ''x/h&amp;nbsp;&amp;asymp;&amp;nbsp;2 (x/L=0.13)'' in<br /> [[UFR_4-16_Test_Case#figure19|Fig. 18]].<br /> Initial growth of this corner bubble reveals its spreading rate along the<br /> two sloped walls being approximately of the same intensity, see position<br /> ''x/h=5''. As the adverse pressure gradient along the upper wall outweighs<br /> significantly the one along the side wall due to the substantially higher<br /> angle of expansion in diffuser 1, 11.3&amp;deg; vs. 2.55&amp;deg;, the separation zone<br /> spreads gradually over the entire top wall surface, see position ''x/h=8''. The<br /> behaviour is different in diffuser 2. There one notes a strong three-<br /> dimensional nature of the separation pattern. The maximum occupation of the<br /> diffuser cross-sectional area by the flow reversal, around 22% and 15% for<br /> the diffusers 1 and 2, respectively <br /> ([[UFR_4-16_Test_Case#figure19|Fig. 19]]), is documented at the<br /> position ''x/h=12-17 (x/L=0.8-1.13)''. The thickness of the flow reversal zone<br /> in the diffuser 1 (its dimension in the normal-to-wall direction) is almost<br /> constant over the diffuser width in this region, resembling approximately a<br /> 2-D pattern. After this position the intensity of the back-flow weakens.<br /> The experimental results indicate that the reattachment region is located<br /> within the straight outlet duct,<br /> [[UFR_4-16_Test_Case#figure19|Fig. 19]]. The separation pattern and the<br /> differences between diffuser 1 and 2 can also be seen clearly from the 3D<br /> plots given in<br /> [[UFR_4-16_Evaluation#figure26|Fig. 26]], which were obtained by LES.<br /> <br /> <br /> &lt;div id=&quot;figure18&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |colspan=&quot;2&quot; style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure18.png|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot; align=&quot;center&quot;|'''Diffuser 1'''<br /> |style=&quot;border: 1px solid darkgray;&quot; align=&quot;center&quot;|'''Diffuser 2'''<br /> |-<br /> |colspan=&quot;2&quot;|'''Figure 18:''' Comparison between experimentally obtained iso-contours of the axial velocity field in the cross planes ''y-z'' at five selected streamwise locations within the both diffuser section (the thick line denotes the zero-velocity line). From [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]<br /> |}<br /> <br /> <br /> <br /> &lt;div id=&quot;figure19&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure19.png|740px]]<br /> |-<br /> |'''Figure 19:''' Fraction of the cross-sectional area occupied by the flow reversal in both diffuser configurations. From [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]<br /> |}<br /> <br /> <br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Suad Jakirli&amp;#x107;, Gisa John-Puthenveettil<br /> |organisation=Technische Universit&amp;auml;t Darmstadt<br /> }}<br /> {{UFRHeader<br /> |area=4<br /> |number=16<br /> }}<br /> <br /> <br /> © copyright ERCOFTAC {{CURRENTYEAR}}</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=UFR_4-16_Test_Case&diff=39864 UFR 4-16 Test Case 2021-11-18T21:21:16Z <p>Dave.Ellacott: /* Experimental data available */</p> <hr /> <div>= Flow in a 3D diffuser =<br /> {{UFRHeader<br /> |area=4<br /> |number=16<br /> }}<br /> __TOC__<br /> == Confined flows ==<br /> === Underlying Flow Regime 4-16 ===<br /> <br /> <br /> = Test Case Study =<br /> &lt;!--{{LoremIpsum}}--&gt;<br /> == Brief description of the test case studied ==<br /> The diffuser shapes, dimensions and the coordinate system are shown in<br /> [[UFR_4-16_Test_Case#figure3|Fig. 3]] and<br /> [[UFR_4-16_Test_Case#figure4|Fig. 4]].<br /> Both diffuser configurations considered have the same fully&amp;#8208;developed <br /> flow at channel inlet but slightly different expansion<br /> geometries: the upper-wall expansion angle is reduced from ''11.3&amp;deg;'' (Diffuser<br /> 1) to ''9&amp;deg;'' (Diffuser 2) and the side-wall expansion angle is increased from<br /> ''2.56&amp;deg;'' (Diffuser 1) to ''4&amp;deg;'' (Diffuser2). The flow in the inlet duct (height<br /> ''h=1 cm'', width ''B=3.33 cm'') corresponds to fully-developed turbulent channel<br /> flow (enabled experimentally by a development channel being 62.9 channel<br /> heights long). The ''L=15h'' long diffuser section is followed by a straight<br /> outlet part (''12.5h'' long). Downstream of this the flow goes through a ''10h''<br /> long contraction into a 1 inch diameter tube. The curvature radius at the<br /> walls transitioning between diffuser and the straight duct parts are ''6 cm''<br /> (Diffuser 1) and ''2.8 cm'' (Diffuser 2). The bulk velocity in the inflow duct<br /> is &lt;math&gt;{U_\textrm{bulk}=U_\textrm{inflow}=1 m/s}&lt;/math&gt;<br /> in the ''x''-direction resulting in the Reynolds number based on the<br /> inlet channel height of ''10000''. The origin of the coordinates (''y=0, z=0'')<br /> coincides with the intersection of the two non-expanding walls at the<br /> beginning of the diffuser's expansion (x=0). The working fluid is water<br /> (''&amp;rho;=1000 kg/m&lt;sup&gt;3&lt;/sup&gt;'' and ''&amp;mu;=0.001 Pas'').<br /> <br /> <br /> &lt;div id=&quot;figure3&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=750<br /> |[[Image:UFR4-16_figure3.png|740px]]<br /> |-<br /> |'''Figure 3:''' Geometry of the 3-D diffuser 1 considered (not to scale), [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]; see also [[UFR_4-16_References#14|Jakirli&amp;#x107; ''et&amp;nbsp;al.'' (2010a)]]<br /> |}<br /> <br /> <br /> <br /> <br /> &lt;div id=&quot;figure4&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=750<br /> |[[Image:UFR4-16_figure4.png|740px]]<br /> |-<br /> |'''Figure 4:''' Geometry of the 3-D diffuser 2 considered (not to scale), [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]].<br /> |}<br /> <br /> == Experimental investigation ==<br /> ===Brief description of the experimental setup===<br /> The measurements were performed in a recirculating water channel using the<br /> method of magnetic resonance velocimetry (MRV),<br /> [[UFR_4-16_Test_Case#figure5|Fig. 5.]] MRV makes use of a<br /> technique very similar to that used in conventional medical magnetic<br /> resonance imaging (MRI),<br /> [[UFR_4-16_Test_Case#figure6|Fig. 6.]] Experiments were performed on a 1.5 Tesla<br /> magnet with resolution of 0.9 x 0.9 x 0.9 mm and a 7 Tesla magnet with<br /> resolution of 0.4 x 0.4 x 0.4 mm. Interested readers are referred to<br /> [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008]],<br /> [[UFR_4-16_References#8|2009)]]<br /> for more details about the measurement technique.<br /> <br /> <br /> &lt;div id=&quot;figure5&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;558&quot;<br /> |[[Image:UFR4-16_figure5a.png|548px]]<br /> |-<br /> |[[Image:UFR4-16_figure5b.png|548px]]<br /> |-<br /> |'''Figure 5:''' Schematic of the experimental flow system (upper) and design of the 3D diffuser. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> <br /> <br /> <br /> &lt;div id=&quot;figure6&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;558&quot;<br /> |[[Image:UFR4-16_figure6.jpg|548px]]<br /> |-<br /> |'''Figure 6:''' 3D diffuser arrangement in a medical magnetic resonance imaging device. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> ===Mean velocity and Reynolds stress measurements===<br /> Cherry ''et&amp;nbsp;al.'' provided a detailed reference database comprising the<br /> three-component mean velocity field and the streamwise Reynolds stress component<br /> field within the entire diffuser section. Both diffuser configurations<br /> considered are characterized by a three-dimensional boundary-layer<br /> separation, but the slightly different expansion geometries caused the size<br /> and shape of the separation bubble exhibiting a high degree of geometric<br /> sensitivity to the dimensions of the diffuser as illustrated in<br /> [[UFR_4-16_Test_Case#figure7|Figs. 7]], [[UFR_4-16_Test_Case#figure8|8]]<br /> and [[UFR_4-16_Test_Case#figure9|9]]<br /> <br /> <br /> &lt;div id=&quot;figure7&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure7.png|740px]]<br /> |-<br /> |'''Figure 7:''' Streamwise velocity contours in a plane parallel to the top wall, from [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure8&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; style=&quot;border: 1px solid black;&quot; border=&quot;1&quot;<br /> |align=&quot;center&quot; colspan=&quot;3&quot;|[[Image:UFR4-16_figure8a.png|493px]]<br /> |-<br /> |colspan=&quot;3&quot;|[[Image:UFR4-16_figure8b.png|750px]]<br /> |-<br /> |[[Image:UFR4-16_figure8c.png|247px]]||[[Image:UFR4-16_figure8d.png|247px]]||[[Image:UFR4-16_figure8e.png|247px]]<br /> |-<br /> |colspan=&quot;3&quot;|'''Figure 8:''' Measured streamwise velocity contours in the central plane (upper) of the '''Diffuser 1''' and in the three selected cross-sectional slices positioned at different distances from the diffuser inlet (lower; their locations are denoted by thick white lines in the upper figure). Note that the black line indicates zero streamwise velocity and the purple and pink regions are reverse flow. The velocity values are normalized by the bulk inlet velocity being ''V&lt;sub&gt;ref&lt;/sub&gt;=1&amp;nbsp;m/s''. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure9&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; style=&quot;border: 1px solid black&quot; border=&quot;1&quot;<br /> |colspan=&quot;3&quot; align=&quot;center&quot;|[[Image:UFR4-16_fig9a.png|493px]]<br /> |-<br /> |colspan=&quot;3&quot;|[[Image:UFR4-16_fig9b.png|750px]]<br /> |-<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig9c.png|246px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig9d.png|246px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig9e.png|246px]]<br /> |-<br /> |colspan=&quot;3&quot;|'''Figure 9:''' Measured streamwise velocity contours in the central plane (upper) of the '''Diffuser 2''' and in the three selected cross-sectional slices positioned at different distances from the diffuser inlet (lower; their locations are denoted by thick white lines in the upper figure). Note that the black line indicates zero streamwise velocity and the purple and pink regions are reverse flow. The velocity values are normalized by the bulk inlet velocity being ''V&lt;sub&gt;ref&lt;/sub&gt;=1&amp;nbsp;m/s''. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure10&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; style=&quot;border: 1px solid black&quot;<br /> !x/h=2!!x/h=5!!x/h=8!!x/h=12!!x/h=15<br /> |-<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10a.png|137px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10b.png|139px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10c.png|148px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10d.png|154px]]<br /> |valign=&quot;bottom&quot;|[[Image:UFR4-16_fig10e.png|162px]]<br /> |-<br /> |align=&quot;center&quot; colspan=&quot;5&quot;|[[Image:UFR4-16_fig10f.png]]<br /> |-<br /> |colspan=&quot;5&quot;|'''Figure 10:''' Measurements of turbulent streamwise stress components taken in cross-sectional slices of the diffuser 1 perpendicular to the mean flow. The region of highest turbulence (red areas; ignore the red areas at the bottom walls) follows the shear layer between forward and reverse flow. ''h''=1cm represents the height of the inflow duct. Courtesy of J. Eaton (Stanford University)<br /> |}<br /> <br /> ===Pressure measurements===<br /> In addition<br /> [[UFR_4-16_References#8|Cherry ''et&amp;nbsp;al.'' (2009)]]<br /> provided the pressure distribution along<br /> the bottom non-deflected wall of diffuser 1 at different Reynolds numbers.<br /> Complementary to the Reynolds number 10000 (for which the entire flow field<br /> was measured), two higher Reynolds numbers &amp;mdash; 20000 and 30000 &amp;mdash; were also<br /> considered, [[UFR_4-16_Test_Case#figure11|Fig. 11]]. The surface pressure distribution was evaluated to<br /> yield the coefficient<br /> &lt;math&gt;C_p=(p-p_\textrm{ref})/(0.5\rho U_\textrm{bulk}^2)&lt;/math&gt;;<br /> the reference pressure was taken at the<br /> position ''x/L&amp;nbsp;=&amp;nbsp;0.05''. The pressure curve exhibits a development typical of<br /> flow in diverging ducts. The pressure decrease in the inflow duct is<br /> followed by a steep pressure increase already at the very end of the inflow<br /> duct and especially at the beginning of the diffuser section. The<br /> transition from the initial strong pressure rise to its moderate increase<br /> occurs at ''x/L&amp;nbsp;&amp;#8776;&amp;nbsp;0.3'', (''x/h=4.5'')<br /> corresponding to the position where about 5% of<br /> the entire cross-section is occupied by the flow reversal (see e.g.,<br /> [[UFR_4-16_Test_Case#figure19|Fig. 19]].<br /> The onset of separation causes a certain contraction of the flow cross&amp;#8208;section,<br /> leading to a weakening of the deceleration intensity and,<br /> accordingly, to a slower pressure increase. The region characterized by a<br /> monotonic pressure rise was reached in the remainder of the diffuser<br /> section.<br /> <br /> <br /> &lt;div id=&quot;figure11&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure11.png|740px]]<br /> |-<br /> |'''Figure 11:''' Pressure recovery coefficients relative to the pressure on the bottom wall of the diffuser 1 inlet in a range of flow Reynolds number. L=15 cm represents the length of Diffuser 1, from [[UFR_4-16_References#8|Cherry ''et&amp;nbsp;al.'' (2009)]]<br /> <br /> |}<br /> <br /> ===Measurements uncertainties===<br /> (adopted from [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'', 2008, IJHFF, Vol. 29(3)]])<br /> <br /> Elkins et al. (2004) estimated the maximum relative uncertainty of<br /> individual mean velocity measurements to be about 10% of the measured value<br /> in a similar highly turbulent flow. However, comparisons to PIV in a<br /> backward facing step flow (Elkins et al., 2007) show that only a small<br /> percentage of MRV velocity samples deviate by that much and most are much<br /> more accurate. To test this, the streamwise velocity component was<br /> integrated over 250 cross-sections of the MRV data and the results were<br /> compared to the known volume flow rate. This indicated an uncertainty in<br /> the integral of less than 2% with a 95% confidence level.<br /> <br /> Measurements of turbulent normal stresses in Diffuser 1 were also taken<br /> using the MR technique described by Elkins et al. (2007). This method is<br /> based on diffusion imaging principles in which the turbulence causes a loss<br /> of net magnetization signal from a voxel in the flow. This causes a decay<br /> in signal strength which can be related to turbulent velocity statistics.<br /> Elkins et al found this method to be accurate within 20% everywhere in the<br /> FOV and within 5% in regions of high turbulence. Three turbulence scans<br /> were completed using three different magnetic field gradient strengths. For<br /> each gradient strength, 30 scans were completed and averaged. The three<br /> averaged data sets were then averaged to obtain a final data set.<br /> <br /> ===Experimental data available===<br /> Velocity, (and streamwise Reynolds stress components for diffuser 1) and<br /> coordinate data for both diffusers are available here. &lt;!--at http://stanford.edu/~echerry/--&gt;<br /> <br /> {|<br /> &lt;!--<br /> |[http://stanford.edu/~echerry/AnnularDiffuserData.zip AnnularDiffuserData.zip] (contains 4 files, 134 MBytes)<br /> --&gt;<br /> |-<br /> |[https://www.kbwiki.ercoftac.org/w/Data/UFR4-16/Diffuser_1_data.zip Diffuser 1 data.zip] (contains 1 file, 8.4 MBytes)<br /> |-<br /> &lt;!--<br /> |-<br /> |[http://stanford.edu/~echerry/Diffuser%201%20data.zip Diffuser 1 data.zip] (contains 1 file, 8.4 MBytes)<br /> --&gt;<br /> |-<br /> |[https://www.kbwiki.ercoftac.org/w/Data/UFR4-16/Diffuser_1_turbulence.zip Diffuser 1 turbulence.zip] (contains 1 file, 5.3 MBytes)<br /> |-<br /> |[https://www.kbwiki.ercoftac.org/w/Data/UFR4-16/Diffuser_2_data.zip Diffuser 2 data.zip] (contains 1 file, 4 MBytes)<br /> |}<br /> <br /> The data are seven 3D matlab matrices. The<br /> x, y, and z matrices give the coordinates of each point in the coordinate<br /> system shown in Fig. 5. The units are meters. The Vx, Vy, and Vz matrices<br /> give the corresponding velocity components for each point in m/sec. The<br /> matrix mg gives the relative signal magnitude detected by the MRI machine.<br /> <br /> Experimental data for the pressure coefficient in Diffuser 1 for the inflow<br /> Reynolds number Re=10000 are available [[Media:UFR4-16_Cp_Re=10000.xlsx|here]]<br /> ([[Media:UFR4-16_Cp_Re=10000.xlsx|Cp_Re=10000.xlsx]]). The<br /> coordinate system is the same as the coordinate system described in the<br /> corresponding manuscript (see below). &lt;math&gt;{\ C_p}&lt;/math&gt; is defined as<br /> &lt;math&gt;\left(p-p_\textrm{ref}\right)/\left(\frac{1}{2} \rho V^2\right)&lt;/math&gt;,<br /> where &lt;math&gt;{\ P_\textrm{ref}}&lt;/math&gt; is the pressure at ''x=0.05'' (see Fig. 11)<br /> at the midpoint<br /> (''z/B=0.5'') of the bottom flat wall (opposite the wall expanding at 11.3<br /> degrees), &lt;math&gt;{\ \rho}&lt;/math&gt; is the density, and &lt;math&gt;{\ V}&lt;/math&gt;<br /> is the bulk inlet velocity. The data were<br /> taken in a line along the bottom wall of Diffuser 1 at constant y and z<br /> coordinates. L (=15 cm) indicates the length of the diffuser.<br /> <br /> ''Please acknowledge the authors of the experiment when using their database!''<br /> <br /> == CFD Methods ==<br /> The flow in the present diffuser configuration was intensively investigated<br /> computationally in the framework of two ERCOFTAC-SIG15 Workshops and in<br /> the European ATAAC project.<br /> The workshops focussing on both 3D diffuser configurations (denoted by SIG15<br /> Case 13.2-1 and SIG15 Case 13.2-2, respectively) were organized at the<br /> Technical University of Graz, Austria in September, 2008 and the &quot;LA<br /> Sapienza&quot; University of Rome, Italy in September, 2009. The corresponding<br /> reports are published in the ERCOFTAC Bulletin Issues,<br /> [[UFR_4-16_References#30|Steiner ''et&amp;nbsp;al.'' (2009)]]<br /> and [[UFR_4-16_References#15|Jakirli&amp;#x107; ''et&amp;nbsp;al.'' (2010b)]],<br /> see [[UFR_4-16_References#0|&quot;List of References&quot;]].<br /> Both in the workshops and in the ATAAC project a wide range of<br /> turbulence models in both LES and RANS frameworks as well as some novel<br /> Hybrid LES/RANS formulations have been employed. The computational database<br /> was furthermore enriched by the results of a Direct Numerical Simulation of<br /> the first diffuser performed by<br /> [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]]. The list of all<br /> computational contributions to the workshops including some basic information about the<br /> methods and models used and corresponding grid resolution is given in<br /> the following [[UFR_4-16_Test_Case#table1|tables 1]] and [[UFR_4-16_Test_Case#table2|table 2]].<br /> For more computational details, interested<br /> readers are referred to the &quot;[[UFR_4-16_Evaluation#Available_CFD_results:_ERCOFTAC_SIG15_Workshop_Proceedings|workshop proceedings]]&quot;<br /> &amp;mdash; see the corresponding<br /> links at the end of the Section &quot;[[UFR_4-16_Evaluation#Evaluation_of_the_results|Evaluation of the results]]&quot;.<br /> The results from the ATAAC project and information on the methods used can be obtained through the links<br /> [http://cfd.mace.manchester.ac.uk/twiki/pub/ATAAC/TestCase004Diffuser3D/ATAAC_D3-2-36_excerpt3DDiffuser.pdf ATAAC_D3-2-36_excerpt3DDiffuser.pdf]<br /> (excerpt from an ATAAC report) and<br /> [http://cfd.mace.manchester.ac.uk/twiki/pub/ATAAC/TestCase004Diffuser3D/ATAAC_finalWorkshop_ST04-Diffuser-ANSYS.pdf ATAAC_finalWorkshop_ST04-Diffuser-ANSYS.pdf]<br /> (PowerPoint presentation at ATAAC final workshop).<br /> <br /> <br /> &lt;div id=&quot;table1&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_table1.png|740px]]<br /> |-<br /> |'''Table 1:''' SIG15 Case 13.2-1 (Diffuser 1) &amp;mdash; contributors and methods (note that the DNS grid comprises 220 million cells in the follow-up work published in [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]])<br /> |-<br /> |'''N.B.''' ITS is &quot;Institut f&amp;uuml;r Thermische Str&amp;ouml;mungsmaschinen&quot;<br /> |}<br /> <br /> <br /> &lt;div id=&quot;table2&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_table2.png|740px]]<br /> |-<br /> |'''Table 2:''' SIG15 Case 13.2-2 (Diffuser 2) &amp;mdash; contributors and methods<br /> |-<br /> |'''N.B.''' ITS is &quot;Institut f&amp;uuml;r Thermische Str&amp;ouml;mungsmaschinen&quot;<br /> |}<br /> <br /> <br /> ===Direct numerical simulation of the flow in a 3D diffuser===<br /> <br /> (adopted from [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'', 2010, JFM, Vol. 650]])<br /> <br /> In this part of the present contribution the DNS study of the flow in 3D<br /> Diffuser 1 performed recently by<br /> [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]] will be described in<br /> more details. Ohlsson ''et&amp;nbsp;al.'' participated with this contribution at the<br /> 14th SIG15 Workshop on Refined Turbulence Modeling <br /> ([[UFR_4-16_References#15|Jakirli&amp;#x107; ''et&amp;nbsp;al.'', 2010b]]).<br /> Accordingly, their results are also part of the CFD methods/models<br /> evaluation &amp;mdash; along with the results obtained by different LES, RANS and<br /> Hybrid LES/RANS models (see the [[UFR_4-16_Evaluation#Evaluation_of_the_results|next chapter]]).<br /> In addition, as the DNS<br /> provided a very comprehensive database comprising all three mean velocity<br /> components (and associated integral characteristics such as surface<br /> pressure and friction factor) and all six Reynolds stress components as<br /> well as a certain insight into the physics (not detected by the<br /> experimental investigation) one can regard it also as a reference<br /> investigation, as we do presently.<br /> <br /> The Direct Numerical Simulation of the Diffuser 1 was performed using a<br /> massively parallel high-order spectral element code. The incompressible<br /> Navier-Stokes equations are solved using a Legendre-polynomial-based<br /> spectral-element method, implemented in the code nek5000, developed by<br /> Fischer et al. (2008). The computational domain shown in<br /> [[UFR_4-16_Test_Case#figure12|Fig. 12]] is set up<br /> in close agreement with the diffuser geometry in the experiment<br /> (see [[UFR_4-16_Test_Case#figure3|Fig.3]])<br /> and consists of the inflow development duct of almost 63 duct heights,<br /> ''h'', (starting at the non-dimensional coordinate ''x''&amp;nbsp;=&amp;nbsp;-62.9),<br /> the diffuser<br /> expansion located at ''x''&amp;nbsp;=&amp;nbsp;0 and the converging section upstream of the<br /> outlet. The corners resulting from the diffuser expansion are smoothly<br /> rounded with a radius of 6.0 in accordance with the experimental set-up.<br /> The maximum dimensions are ''Lx =105.4 h, Ly =[h, 4h], Lz =[3.33 h, 4h]''. In<br /> the inflow duct, laminar flow undergoes natural transition by the use of an<br /> unsteady trip forcing (see e.g. Schlatter et al., 2009), which avoids the<br /> use of artificial turbulence and eliminates artificial temporal frequencies<br /> which may arise from inflow recycling methods (Herbst et al., 2007). A<br /> 'sponge region' is added at the end of the contraction in order to smoothly<br /> damp out turbulent fluctuations, thereby eliminating spurious pressure<br /> waves. It is followed by a homogeneous Dirichlet condition for the pressure<br /> and a homogeneous Neumann condition for the velocities. The resolution of<br /> approximately 220 million grid points is obtained by a total of 127750<br /> local tensor product domains (elements) with a polynomial order of 11,<br /> respectively, resulting in &amp;Delta;z&lt;sup&gt;+&lt;/sup&gt;&lt;sub&gt;max&lt;/sub&gt;&amp;asymp;11.6,<br /> &amp;Delta;y&lt;sup&gt;+&lt;/sup&gt;&lt;sub&gt;max&lt;/sub&gt;&amp;asymp;13.2 and<br /> &amp;Delta;x&lt;sup&gt;+&lt;/sup&gt;&lt;sub&gt;max&lt;/sub&gt;&amp;asymp;19.5 in the<br /> duct center and the first grid point being located at z&lt;sup&gt;+&lt;/sup&gt;&amp;asymp;0.074<br /> and y&lt;sup&gt;+&lt;/sup&gt;&amp;asymp;0.37, respectively (note that at the time of the ERCOFTAC SIG15 workshop<br /> the DNS grid had 172 million grid points,<br /> see Chapter &quot;[[UFR_4-16_Evaluation#172million|Evaluation]]&quot;). It was<br /> verified that this resolution yields accurate results in turbulent channel<br /> flow simulations. In the diffuser, the grid is linearly stretched in both<br /> directions, but since the mean resolution requirements decreases with the<br /> velocity, which decreases linearly with the area expansion, the resolution<br /> in the entire domain is hence satisfactory. The simulation was performed on<br /> the Blue Gene/P at ALCF, Argonne National Laboratory (32768 cores and a<br /> total of 8 million core hours) and on the cluster 'Ekman' at PDC, Stockholm<br /> (2048 cores and a total of 4 million core hours). Thirteen flow-through<br /> times, ''t U&lt;sub&gt;b&lt;/sub&gt;/L''=13, based on bulk velocity, ''U&lt;sub&gt;b&lt;/sub&gt;'', and diffuser length, ''L=15&amp;nbsp;h'',<br /> were simulated in order to let the flow settle to an equilibrium state<br /> before turbulent statistics were collected over approximately ''U&lt;sub&gt;b&lt;/sub&gt;t/L''=21<br /> additional flow-through times.<br /> <br /> In addition to the three-dimensional mean velocity field, all six Reynolds<br /> stress components were evaluated, as well as the surface pressure and skin<br /> friction distribution along the bottom wall.<br /> <br /> <br /> &lt;div id=&quot;figure12&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure12.png|740px]]<br /> |-<br /> |'''Figure 12:''' DNS grid of the diffuser 1 geometry showing the development region, diffuser expansion, converging section and outlet. From [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]]<br /> |}<br /> <br /> <br /> [[UFR_4-16_Test_Case#figure13|Fig. 13]] illustrates the mean axial flow field obtained by DNS along with<br /> the experimental data and [[UFR_4-16_Test_Case#figure14|Fig. 14]] depicts the skin friction evolution along<br /> the bottom diffuser wall at the midpoint<br /> (''z/B=0.5''; ''C&lt;sub&gt;f&lt;/sub&gt;=&amp;tau;&lt;sub&gt;wall&lt;/sub&gt;&amp;nbsp;/&amp;nbsp;(0.5&amp;rho;U&lt;sup&gt;2&lt;/sup&gt;&lt;sub&gt;bulk&lt;/sub&gt;'')&amp;nbsp;). The latter DNS<br /> result was evaluated exclusively for the needs of the 14th ERCOFTAC<br /> Workshop; it is not part of the DNS database which can be downloaded [[UFR_4-16_Test_Case#kth_data|here]].<br /> <br /> <br /> &lt;div id=&quot;figure13&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure13.png|740px]]<br /> |-<br /> |'''Figure 13:''' Cross-flow planes of streamwise velocity component at 2, 5, 8 and 15 ''h'' downstream of the diffuser throat. Left: DNS. Right: Experiment by [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]. Each streamwise position has its own colour bar on the right. Contour lines are spaced ''0.1 V&lt;sub&gt;ref&lt;/sub&gt;'' apart. Thick black lines correspond to the zero velocity contour. From [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'' (2010)]]<br /> <br /> <br /> &lt;div id=&quot;figure14&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure14.jpg|740px]]<br /> |-<br /> |'''Figure 14:''' Friction coefficient at the bottom wall of the diffuser 1 with ''L=15 cm'' representing the length of Diffuser 1. The LES and HLR (Hybrid LES/RANS) results are from [[UFR_4-16_References#14|Jakirli&amp;#x107; ''et&amp;nbsp;al.'' (2010a)]] and [[UFR_4-16_References#17|John-Puthenveetil (2012)]].<br /> <br /> ===Available DNS data (last update: 2010-11-23)===<br /> &lt;div id=&quot;kth_data&quot;&gt;&lt;/div&gt;<br /> The entire digitalized DNS database (as well as some high-resolution<br /> images) as listed below can be downloaded from<br /> http://www.mech.kth.se/~johan/data/index.html. The links given below are to local wiki copies of the files.<br /> <br /> This directory contains velocity profiles and mean fluctuations obtained<br /> from the DNS by<br /> [[UFR_4-16_References#24|Ohlsson ''et&amp;nbsp;al.'', (JFM 650 307&amp;ndash;318)]]<br /> This simulation was<br /> designed to match the experiment by<br /> [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'', 2008, IJHFF 29(3)]]. The<br /> data is given at the same streamwise and spanwise locations as during the<br /> 14th ERCOFTAC SIG15 Workshop on Turbulence Modelling, held in Rome,<br /> September 2009.<br /> <br /> The full Reynolds stress budgets will be available in the future.<br /> <br /> ''The data is free to use; please include a proper reference to the original publications.''<br /> <br /> In case of any questions, e.g. related to the data, or whether you wish for<br /> additional data not presented here, please contact<br /> Johan Malm, ([mailto:johan@mech.kth.se johan@mech.kth.se]),<br /> Philipp Schlatter ([mailto:pschlatt@mech.kth.se pschlatt@mech.kth.se])<br /> or Dan Henningson ([mailto:henning@mech.kth.se henning@mech.kth.se])<br /> <br /> ====Visualizations and computational mesh====<br /> [[Media:UFR4-16_planes_press0000.jpeg|Crossflow planes with instantaneous streamwise velocity]]<br /> <br /> [[Media:UFR4-16_planes_nogrid_iso_vec.jpeg|Crossflow planes with instantaneous streamwise velocity and isosurfaces of streamwise velocity]]<br /> <br /> [[Media:UFR4-16_press_persp0010.jpeg|Instantaneous streamwise velocity in a spanwise midplane with some isosurfaces of instantaneous pressure]]<br /> <br /> [[Media:UFR4-16_mesh_paper.png|Mesh]]<br /> <br /> ====Digitalized DNS database: full 3D mean velocity and Reynolds stress fields====<br /> Explanation:<br /> *E.g., c13.2_Ucont2_KTH_DNS denotes the files comprising the contours of the axial velocity - Ucont - at the streamwise position ''x/h=2'' for the case 13.2 (ERCOFTAC SIG15 denotation). The same data are given at the streamwise locations ''x/h=2, 5, 8, 12'' and ''15''<br /> *E.g., c13.2_urms2_KTH_DNS.txt denotes the file comprising the contours of the root-mean-square values of the streamwise stress component &amp;mdash; urms &amp;mdash; at the streamwise position ''x/h=2''. The same data are given at the streamwise locations ''x/h=2, 5, 8, 12'' and ''15''<br /> *The file c13.2_cp_KTH_DNS.txt denotes the file comprising the pressure coefficient distribution at the bottom flat wall at the midpoint ''z/B=0.5''<br /> *The file c13.2_z0250_x-2_KTH_DNS.txt denotes the file comprising all three mean velocity components, kinetic energy of turbulence and all six Reynolds stress components at the streamwise position ''x/h=-2'' (inflow duct) and the spanwise position ''z/B=0.25''. The same data are given at the streamwise locations ''x/h=0, 2, 4, 6, 8, 10, 12, 14, 15.5, 17, 18.5, 20'' and ''21.5'' at the following spanwise locations ''z/B=0.25, 0.5, 0.75'' and ''0.875''.<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;1&quot; cellpadding=&quot;5&quot;<br /> |[[Media:c13.2_cp_KTH_DNS.txt|c13.2_cp_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont2_KTH_DNS.txt|c13.2_Ucont2_KTH_DNS.txt]]||[[Media:c13.2_urms2_KTH_DNS.txt|c13.2_urms2_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont5_KTH_DNS.txt|c13.2_Ucont5_KTH_DNS.txt]]||[[Media:c13.2_urms5_KTH_DNS.txt|c13.2_urms5_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont8_KTH_DNS.txt|c13.2_Ucont8_KTH_DNS.txt]]||[[Media:c13.2_urms8_KTH_DNS.txt|c13.2_urms8_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont12_KTH_DNS.txt|c13.2_Ucont12_KTH_DNS.txt]]||[[Media:c13.2_urms12_KTH_DNS.txt|c13.2_urms12_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_Ucont15_KTH_DNS.txt|c13.2_Ucont15_KTH_DNS.txt]]||[[Media:c13.2_urms15_KTH_DNS.txt|c13.2_urms15_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x-2_KTH_DNS.txt|c13.2_z0250_x-2_KTH_DNS.txt]]||[[Media:c13.2_z0500_x-2_KTH_DNS.txt|c13.2_z0500_x-2_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x-2_KTH_DNS.txt|c13.2_z0750_x-2_KTH_DNS.txt]]||[[Media:c13.2_z0875_x-2_KTH_DNS.txt|c13.2_z0875_x-2_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x0_KTH_DNS.txt|c13.2_z0250_x0_KTH_DNS.txt]]||[[Media:c13.2_z0500_x0_KTH_DNS.txt|c13.2_z0500_x0_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x0_KTH_DNS.txt|c13.2_z0750_x0_KTH_DNS.txt]]||[[Media:c13.2_z0875_x0_KTH_DNS.txt|c13.2_z0875_x0_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x2_KTH_DNS.txt|c13.2_z0250_x2_KTH_DNS.txt]]||[[Media:c13.2_z0500_x2_KTH_DNS.txt|c13.2_z0500_x2_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x2_KTH_DNS.txt|c13.2_z0750_x2_KTH_DNS.txt]]||[[Media:c13.2_z0875_x2_KTH_DNS.txt|c13.2_z0875_x2_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x4_KTH_DNS.txt|c13.2_z0250_x4_KTH_DNS.txt]]||[[Media:c13.2_z0500_x4_KTH_DNS.txt|c13.2_z0500_x4_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x4_KTH_DNS.txt|c13.2_z0750_x4_KTH_DNS.txt]]||[[Media:c13.2_z0875_x4_KTH_DNS.txt|c13.2_z0875_x4_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x6_KTH_DNS.txt|c13.2_z0250_x6_KTH_DNS.txt]]||[[Media:c13.2_z0500_x6_KTH_DNS.txt|c13.2_z0500_x6_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x6_KTH_DNS.txt|c13.2_z0750_x6_KTH_DNS.txt]]||[[Media:c13.2_z0875_x6_KTH_DNS.txt|c13.2_z0875_x6_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x8_KTH_DNS.txt|c13.2_z0250_x8_KTH_DNS.txt]]||[[Media:c13.2_z0500_x8_KTH_DNS.txt|c13.2_z0500_x8_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x8_KTH_DNS.txt|c13.2_z0750_x8_KTH_DNS.txt]]||[[Media:c13.2_z0875_x8_KTH_DNS.txt|c13.2_z0875_x8_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x10_KTH_DNS.txt|c13.2_z0250_x10_KTH_DNS.txt]]||[[Media:c13.2_z0500_x10_KTH_DNS.txt|c13.2_z0500_x10_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x10_KTH_DNS.txt|c13.2_z0750_x10_KTH_DNS.txt]]||[[Media:c13.2_z0875_x10_KTH_DNS.txt|c13.2_z0875_x10_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x12_KTH_DNS.txt|c13.2_z0250_x12_KTH_DNS.txt]]||[[Media:c13.2_z0500_x12_KTH_DNS.txt|c13.2_z0500_x12_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x12_KTH_DNS.txt|c13.2_z0750_x12_KTH_DNS.txt]]||[[Media:c13.2_z0875_x12_KTH_DNS.txt|c13.2_z0875_x12_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x14_KTH_DNS.txt|c13.2_z0250_x14_KTH_DNS.txt]]||[[Media:c13.2_z0500_x14_KTH_DNS.txt|c13.2_z0500_x14_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x14_KTH_DNS.txt|c13.2_z0750_x14_KTH_DNS.txt]]||[[Media:c13.2_z0875_x14_KTH_DNS.txt|c13.2_z0875_x14_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x155_KTH_DNS.txt|c13.2_z0250_x155_KTH_DNS.txt]]||[[Media:c13.2_z0500_x155_KTH_DNS.txt|c13.2_z0500_x155_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x155_KTH_DNS.txt|c13.2_z0750_x155_KTH_DNS.txt]]||[[Media:c13.2_z0875_x155_KTH_DNS.txt|c13.2_z0875_x155_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x17_KTH_DNS.txt|c13.2_z0250_x17_KTH_DNS.txt]]||[[Media:c13.2_z0500_x17_KTH_DNS.txt|c13.2_z0500_x17_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x17_KTH_DNS.txt|c13.2_z0750_x17_KTH_DNS.txt]]||[[Media:c13.2_z0875_x17_KTH_DNS.txt|c13.2_z0875_x17_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x185_KTH_DNS.txt|c13.2_z0250_x185_KTH_DNS.txt]]||[[Media:c13.2_z0500_x185_KTH_DNS.txt|c13.2_z0500_x185_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x185_KTH_DNS.txt|c13.2_z0750_x185_KTH_DNS.txt]]||[[Media:c13.2_z0875_x185_KTH_DNS.txt|c13.2_z0875_x185_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x20_KTH_DNS.txt|c13.2_z0250_x20_KTH_DNS.txt]]||[[Media:c13.2_z0500_x20_KTH_DNS.txt|c13.2_z0500_x20_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x20_KTH_DNS.txt|c13.2_z0750_x20_KTH_DNS.txt]]||[[Media:c13.2_z0875_x20_KTH_DNS.txt|c13.2_z0875_x20_KTH_DNS.txt]]<br /> |-<br /> |[[Media:c13.2_z0250_x215_KTH_DNS.txt|c13.2_z0250_x215_KTH_DNS.txt]]||[[Media:c13.2_z0500_x215_KTH_DNS.txt|c13.2_z0500_x215_KTH_DNS.txt]]<br /> |[[Media:c13.2_z0750_x215_KTH_DNS.txt|c13.2_z0750_x215_KTH_DNS.txt]]||[[Media:c13.2_z0875_x215_KTH_DNS.txt|c13.2_z0875_x215_KTH_DNS.txt]]<br /> |}<br /> &lt;br/&gt;<br /> &lt;br/&gt;<br /> <br /> ==Reference DNS and experimental data: mean flow and turbulence evolution==<br /> The following figures display and compare the reference experimental and<br /> DNS database results (the present results can be analysed along with the<br /> axial velocity contours shown in<br /> [[UFR_4-16_Test_Case#figure7|Figs. 7]] &amp;ndash;<br /> [[UFR_4-16_Test_Case#figure9|9]] and [[UFR_4-16_Test_Case#figure13|13]]):<br /> <br /> <br /> In order to get an impression about the mean flow structure and about the<br /> available reference DNS and experimental results<br /> [[UFR_4-16_Test_Case#figure15|Figs. 15]] and<br /> [[UFR_4-16_Test_Case#figure16|16]] display<br /> the velocity field development in the vertical central plane of both<br /> diffusers (''z/B=0.5''; ''B=3.33 cm'' is the width of the inflow duct) typical for<br /> the flow in an expanding duct. The bulk flow exhibits deceleration, leading<br /> to an asymmetry of the velocity profile, particularly so for the axial<br /> velocity component. The effect of the adverse pressure gradient is<br /> especially visible in the flow region along the upper expanding wall. The<br /> velocity profile approaches gradually the form characterizing a separating<br /> flow, exhibiting regions of the zero velocity gradient (at separation and<br /> reattachment points) and profile inflection. The through-flow, that is the<br /> flow in the positive streamwise direction, is characterized by a spreading<br /> dictated by the pressure gradient arising from the geometry expansion.<br /> Accordingly, the position of the reduced velocity maximum is gradually<br /> shifted towards the upper wall, eventually reaching the center (''y/h=2'') of<br /> the straight outlet channel (with the height ''4h''). In this post-reattachment<br /> zone the velocity profile exhibits a fairly flattened form, being almost<br /> symmetric. The consequence of the velocity-profile flattening is a<br /> continuous monotonic decrease of the wall shear stress. The velocity<br /> profile evolution is similar in other longitudinal vertical planes. The<br /> specific differences are related to the vicinity of both bottom and upper<br /> walls, especially the latter upper wall, where the flow passes regions of<br /> three-dimensional flow reversal.<br /> <br /> <br /> &lt;div id=&quot;figure15&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure15a.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure15b.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure15c.jpg|740px]]<br /> |-<br /> |'''Figure 15:''' Diffuser 1 - Evolution of the profiles of all three velocity components in the vertical plane ''x-y'' at the central spanwise locations ''z/B=1/2'' obtained experimentally and by means of DNS<br /> |}<br /> <br /> <br /> &lt;div id=&quot;figure16&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure16a.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure16b.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure16c.jpg|740px]]<br /> |-<br /> |'''Figure 16:''' Diffuser 2 - Evolution of the profiles of all three velocity components in the vertical plane ''x-y'' at the central spanwise locations ''z/B=1/2'' obtained experimentally<br /> |}<br /> <br /> <br /> In the top part of [[UFR_4-16_Test_Case#figure17|Fig. 17 &amp;ndash; upper]]<br /> the development of the streamwise<br /> turbulence intensity is shown for diffuser 1. The lowest turbulence<br /> intensity is situated in the region coinciding with the mean velocity<br /> maximum &amp;mdash; flow zone with approximately zero velocity gradient &amp;mdash; along the<br /> entire diffuser section. The Reynolds stress profiles exhibit their highest<br /> values in the regions with the most intensive flow deformation. These are<br /> the near-wall layer in the attached-flow regions and the flow zone along<br /> the shear layer bordering the recirculation zone. The peak of the<br /> turbulence intensity originating from the boundary layer at the top inflow<br /> duct wall increases initially, after the strong rise in pressure (see<br /> pressure coefficient development in<br /> [[UFR_4-16_Test_Case#figure11|Fig. 11]]), and weakens slightly after<br /> flow transition to the second part of the diffuser section, that is<br /> characterized by a decreasingly adverse pressure gradient. The streamwise<br /> turbulence intensity in the outlet duct is uniformly distributed over the<br /> cross-section.<br /> <br /> <br /> &lt;div id=&quot;figure17&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17a.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17b.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17c.jpg|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure17d.jpg|740px]]<br /> |-<br /> |'''Figure 17:''' Diffuser 1 - Evolution of the profiles of the Reynolds stress components in the vertical plane ''x-y'' at the central spanwise locations ''z/B=1/2'' obtained experimentally and by means of DNS<br /> |}<br /> <br /> <br /> [[UFR_4-16_Test_Case#figure18|Fig. 18]]<br /> shows contour plots of the axial velocity component at five<br /> streamwise cross-sectional areas in both diffuser configurations obtained<br /> experimentally indicating the evolution of the flow separation pattern. The<br /> recirculation-zone development displayed here can be analyzed in parallel<br /> with the quantitative information about the fraction of the diffuser cross-<br /> sectional area occupied by the reverse flow depicted in<br /> [[UFR_4-16_Test_Case#figure19|Fig. 19]]. The<br /> adverse pressure gradient is imposed onto the intersecting boundary layers<br /> along flat walls upon entering the diffuser section. According to the<br /> experimental investigation the boundary layers along all walls are of<br /> comparable thickness. The separation starts immediately after the beginning<br /> of the diffuser section at ''x/L = 0 (x/h=0)''. The onset of separation is<br /> located in the upper-right diffuser corner, formed by the deflected side<br /> wall and the top wall, see e.g. the position ''x/h&amp;nbsp;&amp;asymp;&amp;nbsp;2 (x/L=0.13)'' in<br /> [[UFR_4-16_Test_Case#figure19|Fig. 18]].<br /> Initial growth of this corner bubble reveals its spreading rate along the<br /> two sloped walls being approximately of the same intensity, see position<br /> ''x/h=5''. As the adverse pressure gradient along the upper wall outweighs<br /> significantly the one along the side wall due to the substantially higher<br /> angle of expansion in diffuser 1, 11.3&amp;deg; vs. 2.55&amp;deg;, the separation zone<br /> spreads gradually over the entire top wall surface, see position ''x/h=8''. The<br /> behaviour is different in diffuser 2. There one notes a strong three-<br /> dimensional nature of the separation pattern. The maximum occupation of the<br /> diffuser cross-sectional area by the flow reversal, around 22% and 15% for<br /> the diffusers 1 and 2, respectively <br /> ([[UFR_4-16_Test_Case#figure19|Fig. 19]]), is documented at the<br /> position ''x/h=12-17 (x/L=0.8-1.13)''. The thickness of the flow reversal zone<br /> in the diffuser 1 (its dimension in the normal-to-wall direction) is almost<br /> constant over the diffuser width in this region, resembling approximately a<br /> 2-D pattern. After this position the intensity of the back-flow weakens.<br /> The experimental results indicate that the reattachment region is located<br /> within the straight outlet duct,<br /> [[UFR_4-16_Test_Case#figure19|Fig. 19]]. The separation pattern and the<br /> differences between diffuser 1 and 2 can also be seen clearly from the 3D<br /> plots given in<br /> [[UFR_4-16_Evaluation#figure26|Fig. 26]], which were obtained by LES.<br /> <br /> <br /> &lt;div id=&quot;figure18&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot; cellspacing=&quot;0&quot;<br /> |colspan=&quot;2&quot; style=&quot;border: 1px solid darkgray;&quot;|[[Image:UFR4-16_figure18.png|740px]]<br /> |-<br /> |style=&quot;border: 1px solid darkgray;&quot; align=&quot;center&quot;|'''Diffuser 1'''<br /> |style=&quot;border: 1px solid darkgray;&quot; align=&quot;center&quot;|'''Diffuser 2'''<br /> |-<br /> |colspan=&quot;2&quot;|'''Figure 18:''' Comparison between experimentally obtained iso-contours of the axial velocity field in the cross planes ''y-z'' at five selected streamwise locations within the both diffuser section (the thick line denotes the zero-velocity line). From [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]<br /> |}<br /> <br /> <br /> <br /> &lt;div id=&quot;figure19&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; width=&quot;750&quot;<br /> |[[Image:UFR4-16_figure19.png|740px]]<br /> |-<br /> |'''Figure 19:''' Fraction of the cross-sectional area occupied by the flow reversal in both diffuser configurations. From [[UFR_4-16_References#7|Cherry ''et&amp;nbsp;al.'' (2008)]]<br /> |}<br /> <br /> <br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Suad Jakirli&amp;#x107;, Gisa John-Puthenveettil<br /> |organisation=Technische Universit&amp;auml;t Darmstadt<br /> }}<br /> {{UFRHeader<br /> |area=4<br /> |number=16<br /> }}<br /> <br /> <br /> © copyright ERCOFTAC {{CURRENTYEAR}}</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Test_Data_AC7-01&diff=39602 Test Data AC7-01 2021-09-30T11:11:39Z <p>Dave.Ellacott: /* Deposited activity evaluation method */</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=01<br /> }}<br /> __TOC__<br /> =Aerosol deposition in the human upper airways=<br /> '''Application Challenge AC7-01'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2019<br /> =Test Data=<br /> ==Overview of Tests==<br /> Major portions of this section were adopted from<br /> [[Best_Practice_Advice_AC7-01#lizal2015|Lizal ''et&amp;nbsp;al.'' (2015)]]. The positron emission<br /> tomography (PET) method provides the best spatial resolution<br /> (among radiological methods). In addition to local deposition in the various sections,<br /> the deposition hot spots can also be evaluated. However, in comparison to the PET methodology,<br /> which is routinely applied to clinical examination, using this method in the ''in&amp;nbsp;vitro'' design<br /> requires major modifications both in the aerosol preparation and, in particular, in the experiment<br /> evaluation approach. The method, based on PET and fulfilling the above mentioned criteria,<br /> is presented in the following.<br /> <br /> ==The aerosol exposure procedure==<br /> It is a common practice to coat the inner surface of the model, especially when using solid<br /> particles, to prevent bouncing of the particles hitting the surface. Since we used liquid<br /> di-ethylhexyl sebacate (DEHS) particles, we did not need to coat the inner surface of the<br /> model. Another reason for the coating is to prevent surface wetting. In our case the<br /> exposure time was short (5 to 15 mins) and only small amounts of DEHS deposited on the<br /> walls, therefore the possible flooding of the surface was not an issue. Aerosol particles were<br /> generated by a TSI 3475 Condensation Monodisperse Aerosol Generator (CMAG) from<br /> TSI, Inc., which works on the controlled heterogeneous condensation principle. Vapours of<br /> a suitable material, specifically DEHS, condense by a controlled method on small sodium<br /> chloride particles serving as the condensation nuclei. The advantage of DEHS is that it is<br /> not hydrophilic and does not evaporate, resulting in a constant size of generated particles.<br /> In a standard operating mode, the generator can produce particles with aerodynamic<br /> diameters within the 0.1 to 8&amp;mu;m range. The density of DEHS used for the experiments was<br /> 0.914 g/cm&lt;sup&gt;3&lt;/sup&gt; at 25&amp;deg;C. Radioactive aerosol particles were needed for the PET measurement<br /> of deposition. Therefore, the solution in the atomizer of the generator had to be tagged<br /> by a suitable radioactive substance. Fluorine 18 was the logical Choice of the positron<br /> emitter, being easily available at the cooperating PET center and possessing a suitable<br /> half-life (109 minutes). A solution of fluorine 18 in the form of fluoride ions was prepared<br /> by irradiation of H&lt;sub&gt;2&lt;/sub&gt;&lt;sup&gt;18&lt;/sup&gt;0 enriched water on an IBA Cyclone 18/9 cyclotron (irradiation time<br /> 25 min, integrated irradiation current 11 &amp;mu;Ah) at the UJV Rez's PET Centre in Brno. The<br /> irradiated water was transferred by a capillary transport system to a shielded dispensing<br /> box, where the fluorine 18 ions were captured on an ion—exchange resin (AG1—X8, BioRad)<br /> column and subsequently eluted with 300 ml of 10% sodium Chloride solution, followed by<br /> 1&amp;Acirc; ml of water for injection. The resulting solution was repeatedly diluted with water for<br /> injection until the desired initial radioactivity was achieved. The CMAG was modified for<br /> the deposition measurement by using PET so that the atomizer vessel was accommodated<br /> in a protective lead container to shield of ionizing radiation. The atomizer was filled<br /> with a sodium Chloride solution containing &lt;sup&gt;18&lt;/sup&gt;F at an initial activity of 2.5 GBq. The<br /> concentration of sodium Chloride solution was 20 mg/L. The experimental rig is shown in [[Test_Data_AC7-01#figure5|Figure 5]].<br /> <br /> <br /> &lt;div id=&quot;figure5&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_fig5.png|650px]]<br /> |-<br /> |align=&quot;left&quot; width=650|'''Figure 5:''' A scheme of the experimental setup during the PET measurement of aerosol deposition.<br /> |}<br /> <br /> <br /> The generated aerosol was fed through a &lt;sup&gt;85&lt;/sup&gt;''Kr'' based NEKR-10 charge equilibrator<br /> (Eckert &amp; Ziegler Cesio) to a PAM aerosol monitor (TSI 3375) for continuous particle<br /> size and concentration measurement. The operation and precision of the aerosol monitor<br /> was validated using Aerodynamic particle sizer (APS) TSI 3321. The validation was<br /> performed prior to the experiment using the identical setup, apart from adding of the<br /> radioactive substance into the atomizer. The size of the particles generated by CMAG was<br /> adjusted according to APS and the size displayed by the aerosol monitor was recorded.<br /> Subsequently, during the experiment, only the radioactive substance was added to the<br /> atomizer and particles of the same size were produced. Usually only a small correction of<br /> saturator flow was needed at the beginning of the experiments. Only one size of particles<br /> was measured during one day; therefore no further adjustments of the generator were<br /> needed. The aerosol monitor served as an on-line indication of the process of aerosol<br /> generation being stable. It was easily accomplished, as the exposure of the model to<br /> the aerosol lasted only 5 to 15 mins. Filters consisting of Millipore AP40 glass fibers<br /> were attached to the output branches of the respiratory tract model. The entire system<br /> ([[Test_Data_AC7-01#figure6|Figure 6]])<br /> was enclosed in a plastic bag which was kept in a vacuum to prevent the active<br /> aerosol from leaking into the laboratory. All the 10 terminal branches with flow meters<br /> for flow rate control were combined into one branch with a protective High efficiency<br /> particulate air (HEPA) filter. The vacuum was generated with a Busch R, 5 PA 0008 C<br /> rotary oil vacuum pump. The flow distribution in each section of the model is provided<br /> in [[Test_Data_AC7-01#table3|Table&amp;nbsp;3]].<br /> <br /> <br /> &lt;div id=&quot;figure6&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_fig6.png|342px]]<br /> |-<br /> |align=&quot;left&quot; width=342|'''Figure 6:''' A photograph of the physical model prior to the PET measurement.<br /> |}<br /> <br /> <br /> The whole exposure of the model to the aerosol was performed in a shielded laboratory<br /> with an underpressure ventilating system, which would prevent the aerosol from escaping<br /> the room in case of a primary safety system failure. The laboratory personnel were not<br /> present in the laboratory during the exposure, with the exception of the regular instrument<br /> supervision. Whenever they had to enter the lab, they wore half mask respirators. The<br /> experiments were performed in a steady-state inhalation mode with the flow rates of 15,<br /> 30, and 60 L/min. Liquid monodisperse particles with mass median aerodynamic diameter<br /> of 2.5 and 4.3&lt;math&gt;{\mu m}&lt;/math&gt; were used.<br /> The standard geometric deviation of size was less than 1.24<br /> for all measured regimes. The models were exposed for 10 to 15 minutes depending on<br /> radioactivity decrease by radionuclide decay. The peak activity in the models was 4 to 60<br /> &lt;math&gt;{Bq/cm^2}&lt;/math&gt; (depending on the particle size and concentration, measuring mode, and model<br /> used), as measured with an RP-2000 portable contamination meter (VF Zilina, CZ).<br /> <br /> &lt;div id=&quot;old2.3&quot;&gt;&lt;/div&gt;<br /> <br /> ==Deposited activity evaluation method==<br /> The model was transported to a Siemens Biograph 64 Truepoint PET-CT scanner<br /> immediately after the radioactive exposure. The transportation took approximately 3 minutes.<br /> The PET-CT scanner acquired firstly CT images, which were promptly followed by PET<br /> images.<br /> <br /> &lt;div id=&quot;table3&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_table3.png|500px]]<br /> |-<br /> |align=&quot;left&quot; width=500|'''Table 3:''' Flowrates through the individual sections of the model (section identification numbers are presented in [[Description_AC7-01#figure4|Figure&amp;nbsp;4]]). Sections 13&amp;nbsp;&amp;ndash;&amp;nbsp;22 lead to the 10 outlets. Flowrates in the intermediated sections (4&amp;nbsp;&amp;ndash;&amp;nbsp;12) are calculated using mass continuity.<br /> |} <br /> <br /> Both the CT and PET images could be attributed unambiguously to the given<br /> geometry, owing to the assigned geometrical coordinates. The CT images are important<br /> for a precise localization of the edges of the sections, whereas the PET images contain the<br /> essential information about aerosol deposition. The CT and PET images were imported<br /> into Carimas 2.47 ver. 2.2.44.7002 SW (Turku PET Centre 2012) with the CT images<br /> as the main images and the PET images as background images. The software Carimas<br /> is a medical image processing tool, which was developed primarily for analysis of PET<br /> images at Turku PET Centre in Finland and is available as a freeware for non-commercial<br /> use from: http://www.turkupetcentre.fi/carimas/download/. The Carimas was<br /> developed in an “interactive data language” (IDL) and runs on IDL Virtual Machine&amp;trade;, a<br /> cross-platform utility for running IDL code. It supports multiple input formats (DICOM,<br /> ECAT, Analyse, Interfile, Nifti, Interfile, MicroPET) and general bitmap formats (JPG,<br /> TIFF, PNG and BMP). Researchers can perform visualization, segmentation, statistical<br /> analysis, or modelling of PET data. It is possible to perform the image fusion, i.e. to<br /> coregistrate PET and CT or MR, images. Users can define a volume of interest (VOI) and,<br /> by using the static image analysis, they can calculate the mean activity in the VOI (in<br /> units of the PET image), standard deviation, minimal and maximal values, the number<br /> of voxels analysed, and the volume of the region. The software was tested and compared<br /> to commercial tools with an excellent agreement as documented by<br /> [[Best_Practice_Advice_AC7-01#nesterov2009|Nesterov ''et&amp;nbsp;al.'' (2009)]]<br /> and [[Best_Practice_Advice_AC7-01#nesterov2009|Harms ''et&amp;nbsp;al.'' (2014)]].<br /> To facilitate the identification of the hot spots in the Carimas<br /> software, the BGRY colour system was used to display the PET images and the system<br /> range was reduced so that the hot spots were clearly seen in the model sections<br /> ([[Test_Data_AC7-01#figure7|Figure 7]]).<br /> The sections of the model were marked as volumes of interest (VOI), and the mean<br /> volume activity (in Bq/mL) was evaluated using the Carimas software. Each section was<br /> enveloped in an independent VOI. A cylinder or a sphere was selected as the starting<br /> shape of the VOI, depending on the shape of the sections. Firstly, the starting shape of<br /> the VOI was positioned and shaped as a whole to attain a suitable orientation and an<br /> adequate size. In the next step, each VOI was shaped in the vertex mode for a local mesh<br /> adjustment, so that the VOI surrounded the section with an overreach, while preventing<br /> an overlap of different VOIs. If the latter was not avoided, the observed activity would be<br /> attributed to both VOIs, resulting in biased results. The degree of mesh density can be<br /> modified by reducing the number of nodes or by enlarging or shrinking the mesh.<br /> <br /> <br /> &lt;div id=&quot;figure7&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_fig7.png|474px]]<br /> |-<br /> |align=&quot;center&quot;|'''Figure 7:''' CT and PET image presentation in the Carimas software.<br /> |} <br /> <br /> <br /> With regard to the PET precision, a VOI should optimally overreach the section by<br /> roughly 5mm on all sides to cover all the radiation emitted from the section. However, due<br /> to the complex lung geometry, it was impossible to form all the VOIs with such a large<br /> overreach, and so the uncounted radioactivity was accounted for in a correction VOI. Two<br /> additional VOIs had to be created to determine the magnitude of the correction: a VOI for<br /> the top part of the box, accommodating the model with the hoses, and a correction VOI<br /> for the bottom part of the box, accommodating the filters downstream of the terminal<br /> branches. They encompass the large top space with the model and the bottom space<br /> between the two horizontal partitions respectively in [[Test_Data_AC7-01#figure6|Figure 6]].<br /> Two separate corrections<br /> were needed for the model and filters, because the difference in volume radioactivity is<br /> within few orders of magnitude and therefore it is necessary to assign the uncounted<br /> radioactivity to its real source. It is essential to preserve the true ratio of the radiation<br /> deposited in model sections and on filters. The correction factor for the sections was<br /> calculated as the ratio of the total activity obtained from the VOI encompassing the<br /> whole model to the activity obtained by summing up the section VOIs. Similarly, the<br /> correction factor for the filters was calculated as the ratio of the total activity of the large<br /> VOI encompassing all the filters, to the sum of the activities of the filter VOIs. The<br /> corrections for the model sections<br /> (&lt;math&gt;{Corr_m}&lt;/math&gt;) and for the filters (&lt;math&gt;{Corr_f}&lt;/math&gt;) were calculated as<br /> follows:<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{Corr_m=\frac{A_{cm}}{\sum_1^n A_i}}&lt;/math&gt;||width=20 align=right|&lt;math&gt;{(1)}&lt;/math&gt;<br /> |-<br /> |align=center|&lt;math&gt;{Corr_f=\frac{A_{cf}}{\sum_1^n A_j}}&lt;/math&gt;||align=right|&lt;math&gt;{(2)}&lt;/math&gt;<br /> |}<br /> <br /> <br /> where &lt;math&gt;{A_i}&lt;/math&gt; and &lt;math&gt;{A_j}&lt;/math&gt; are the activities measured in the model<br /> sections and on the filters respectively, and &lt;math&gt;{A_{cm}}&lt;/math&gt; and<br /> &lt;math&gt;{A_{cf}}&lt;/math&gt; are the activities measured in the correction VOI for the<br /> model and filters respectively. We assume that the distribution of uncounted radioactivity<br /> is proportional to the measured activity in the sections of the model. The higher the<br /> activity measured in the filter, the higher the activity spread around the section.<br /> Therefore, the uncounted activity is to be accounted for by the sections proportionally to their<br /> measured activity. The correction formula then is simply:<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{A_i^\mbox{*}=Corr_m \cdot A_i}&lt;/math&gt;||width=20 align=right|&lt;math&gt;{(3)}&lt;/math&gt;<br /> |-<br /> |align=center|&lt;math&gt;{A_j^\mbox{*}=Corr_f \cdot A_j}&lt;/math&gt;||align=right|&lt;math&gt;{(4)}&lt;/math&gt;<br /> |} <br /> <br /> <br /> The asterisk (&lt;math&gt;\mbox{*}&lt;/math&gt;) indicates that the data has been corrected. The magnitude of the<br /> correction factor can also be regarded as a model tightness indicator. If the model was not<br /> tight enough and some aerosol leaked beyond the model, the amount of aerosol in the<br /> correction VOI would be appreciably higher than in the sections; also, the calculated<br /> correction factor would be higher.<br /> The correction factors for the model sections and for the<br /> filters lie largely within the ranges of 1.0 to 1.2 and 1.0 to 1.1 respectively. Aerosol leaks<br /> should be suspected if these ranges were exceeded. The VOIs created can be saved in<br /> VRML format in the Carimas software and imported to another model. Therefore, the<br /> same set of VOIs was used for the analysis of all models. The corrected activities served to<br /> calculate the deposition fractions (DF) for two aerosol particle sizes (DF is defined as the<br /> ratio of inhaled particles deposited in the lungs section &lt;math&gt;{A_i^\mbox{*}}&lt;/math&gt;<br /> to the total number of particles<br /> entering the lungs). The total amount of aerosol was calculated as the sum of activities in<br /> the model, in the output sections, in the connection hoses and on the filters. The observed<br /> activity is assumed to be directly proportional to the number of deposited particles. This<br /> is based on the fact that the radioactive atoms are dispersed uniformly in the constantly<br /> stirred atomizer and that each particle generated contains a nucleus of the same size, on<br /> which DEHS has condensed.<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{DF_i=\frac{A_i^\mbox{*}}{\sum_i^n A_i^\mbox{*}}}&lt;/math&gt;<br /> |width=20 align=right|&lt;math&gt;{(5)}&lt;/math&gt;<br /> |} <br /> <br /> <br /> where &lt;math&gt;{n}&lt;/math&gt; is the total number of all sections including the hoses and filters.<br /> <br /> ==Measurement errors==<br /> ===Sources of error in PET imaging===<br /> <br /> The quality of the images obtained with PET is affected by the following parameters:<br /> the spatial resolution, sensitivity, noise, scattered radiation and contrast. The parameters<br /> are interrelated, thus any efforts to reduce the effect of one parameter often result in an<br /> increased effect of another parameter ([[Best_Practice_Advice_AC7-01#saha2010|Saha,&amp;nbsp;2010]]).<br /> The accuracy of determining of the<br /> deposition point for a specific particle is related to the attainable spatial resolution of the<br /> PET scanner. The resolution is affected by the detector size, positron range,<br /> noncolinearity, reconstruction method and localization of the detectors: The actual spatial resolution<br /> of a particular PET scanner is measured by the standardized method recommended by<br /> the NEMA&amp;nbsp;&amp;ndash;&amp;nbsp;National Electrical Manufacturers Association (2001). The full width at half<br /> maximum (FWHM) is the quantity serving as the measure of resolution. This quantity<br /> can be understood as the magnitude of point source “blurring” in the photograph or as<br /> the shortest distance at which two point sources can be discerned as such. The spatial<br /> resolutions (based on NEMA (2001)) for the PET Siemens Biograph 64 system are listed<br /> in [[Test_Data_AC7-01#table4|Table&amp;nbsp;4]].<br /> <br /> &lt;div id=&quot;table4&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_table4.png|500px]]<br /> |-<br /> |align=&quot;left&quot; width=500|'''Table 4:''' Spatial resolution of the PET scanner used for experiments (Siemens 2014)<br /> |} <br /> <br /> The remaining parameters of our PET scanner were: the sensitivity 4.2 cps/kBq, noise<br /> equivalent count rate 96 kcps at 35 kBq/cc, and scatter fraction&amp;nbsp;&lt;&amp;nbsp;38%<br /> ([[Best_Practice_Advice_AC7-01#lizal2015|Lizal&amp;nbsp;''et&amp;nbsp;al.'',&amp;nbsp;2015]]).<br /> As noted in [[Description_AC7-01#limitations|the model limitations section]]<br /> the possible electrical charge on the walls of the physical<br /> model should be considered. The amount of depositing particles due to the mirror charge<br /> is probably low, however, it should be confirmed by an additional experiment.<br /> <br /> ===Inter-person variability===<br /> To assess the error connected to the analysis of images, in particular to the definition of<br /> VOIs, the whole process, beginning with forming the VOIs, was performed by two<br /> technicians independently and their results were compared. The average of the differences<br /> between corresponding sections was 3% of the average value of the calculated radioactivity.<br /> More experiments should be performed to calculate the actual uncertainty of the<br /> whole method, but the above mentioned test confirmed that even if the VOIs were formed<br /> independently by two different individuals, their results were in close agreement<br /> ([[Best_Practice_Advice_AC7-01#lizal2015|Lizal&amp;nbsp;''et&amp;nbsp;al.'',&amp;nbsp;2015]]).<br /> <br /> ===Validation of the method===<br /> The experimental setup and deposition measuring technique was validated by optical microscopy.<br /> Nickel coated particles (M-18-Ni, Cospheric, Santa Barbara, CA, USA) with<br /> MMAD 14.1&amp;mu;m were dispersed by the Small Scale Powder Disperser TSI 3433 and deposited in the model.<br /> The model was disassembled and particles were rinsed out of each<br /> section using ultrasonic bath. The particles were then filtered out and counted using optical microscopy.<br /> The results were consistent with the results acquired by PET. However,<br /> the presented PET method is capable of achieving a significantly higher spatial resolution.<br /> Therefore, more detailed data on local deposition can be obtained, as the size of VOIs can<br /> be smaller than the size of the sections of the model and is limited only by the spatial<br /> resolution of the PET scanner, in our case 5 mm ([[Best_Practice_Advice_AC7-01#lizal2015|Lizal&amp;nbsp;''et&amp;nbsp;al.'',&amp;nbsp;2015]]).<br /> <br /> ==Measured data==<br /> The proposed method was used to evaluate deposition during steady-state inhalation for<br /> the following cases:<br /> #15 L/min, &lt;math&gt;{d_p = 4.3{\mu}m^2}&lt;/math&gt;<br /> #30 L/min, &lt;math&gt;{d_p = 2.5{\mu}m^2}&lt;/math&gt;<br /> #60 L/min, &lt;math&gt;{d_p = 4.3{\mu}m^2}&lt;/math&gt;<br /> <br /> The measurement for 60 L/min was made in duplicate. The Deposition Fraction difference<br /> between the two measurements was calculated for each section, and the observed difference<br /> within the repeated measurements was drawn in the plot in the form of error lines as the<br /> estimate of measurement variability.<br /> <br /> The plot in [[Test_Data_AC7-01#figure8|fig.&amp;nbsp;8]] demonstrates that the majority of<br /> particles was deposited in the oral<br /> cavity and in the trachea in all the applied variants. A comparison of the regimes shows<br /> that the amount of deposited particles increases with their increasing momentum, which<br /> confirms that inertial impaction was the dominant deposition mechanism in our case. The<br /> results demonstrate that the ''in vitro'' deposition measurement method based on the PET<br /> technique enables the DF to be evaluated with adequate precision for distinguishing the<br /> effects of the particle size and the breathing regime.<br /> <br /> <br /> &lt;div id=&quot;figure8&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_fig8.png|650px]]<br /> |-<br /> |align=&quot;left&quot; width=650|'''Figure 8:''' Results obtained by measurements in the realistic model (section identification numbers are presented in [[Description_AC7-01#figure4|Figure&amp;nbsp;4]]). Error bars indicate the difference between two measurements performed on two separate, but geometrically identical models. Measurements for 15 and 30 L/min were performed just once.<br /> |} <br /> <br /> <br /> In the following step, a comparison with previously published data was performed.<br /> Few studies presenting ''in&amp;nbsp;vitro'' measured local aerosol deposition in tracheobronchial<br /> airways have been published in past years. The most suitable for comparison with our data<br /> were the results acquired by<br /> [[Best_Practice_Advice_AC7-01#zhou2005|Zhou&amp;nbsp;&amp;&amp;nbsp;Cheng&amp;nbsp;(2005)]] and<br /> [[Best_Practice_Advice_AC7-01#chan1980|Chan&amp;nbsp;&amp;&amp;nbsp;Lippmann&amp;nbsp;(1980)]] as they<br /> both used realistic lung casts. However, their models had less generations of branching<br /> (four and six, respectively) compared to our model. The comparison of deposition efficiency (DE)<br /> defined as the ratio of the number of particles deposited in the section to<br /> the number of particles entering the section showed close agreement with both studies<br /> mentioned above (see [[Test_Data_AC7-01#figure9|Figure&amp;nbsp;9]]).<br /> The practical calculation of DE was performed as a ratio<br /> of corrected activity in the examined section to the sum of activities in all downstream<br /> sections including filters and hoses, and the activity in the examined section:<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{DE_i=\frac{A_i^\mbox{*}}{A_f^\mbox{*}+A_i^\mbox{*}}}&lt;/math&gt;<br /> |width=20 align=right|&lt;math&gt;{(6)}&lt;/math&gt;<br /> |}<br /> <br /> <br /> where &lt;math&gt;{A_f^\mbox{*}}&lt;/math&gt; is the corrected activity in the section downstream the i-th section. DE was<br /> plotted as a function of Stokes number defined as:<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{Stk=\frac{\rho d_p^2U}{18\mu D}}&lt;/math&gt;<br /> |width=20 align=right|&lt;math&gt;{(7)}&lt;/math&gt;<br /> |}<br /> <br /> <br /> where &lt;math&gt;{d_p (\mu m)}&lt;/math&gt; is the aerodynamic diameter of a particle,<br /> &lt;math&gt;{U (m/s)}&lt;/math&gt; is the velocity, &lt;math&gt;{\mu (Pa.s)}&lt;/math&gt;<br /> is the Viscosity of air and &lt;math&gt;{D (m)}&lt;/math&gt; is the characteristic diameter (of the airway), which was<br /> measured in the digital geometry in Rhinoceros 4.0 software (McNeel Seattle, WA7 USA).<br /> The diameter of the entrance airway was used as the characteristic diameter, in accordance<br /> with [[Best_Practice_Advice_AC7-01#zhou2005|Zhou&amp;nbsp;&amp;&amp;nbsp;Cheng&amp;nbsp;(2005)]].<br /> [[Best_Practice_Advice_AC7-01#chan1980|Chan&amp;nbsp;&amp;&amp;nbsp;Lippmann&amp;nbsp;(1980)]] introduced the following correlation<br /> fit based on their experimental data for the first six generations:<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{DE=1.606Stk+0.0023}&lt;/math&gt;<br /> |width=20 align=right|&lt;math&gt;{(8)}&lt;/math&gt;<br /> |}<br /> <br /> <br /> Similar correlation fit was calculated based on the current data for 1st to 4th generation.<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{DE=1.038Stk+0.0012}&lt;/math&gt;<br /> |width=20 align=right|&lt;math&gt;{(9)}&lt;/math&gt;<br /> |}<br /> <br /> <br /> Both the empirical equations were plotted in the graph of [[Test_Data_AC7-01#figure9|Figure&amp;nbsp;9]].<br /> The airways in the<br /> 4th to 7th generation, which create separate parts of the model (identification numbers 13<br /> to 22), were evaluated as a whole section and plotted in<br /> [[Test_Data_AC7-01#figure9|Figure&amp;nbsp;9]] as well. The deposition<br /> fraction can be calculated in a higher resolution (creating smaller sections) down to the<br /> resolution of the PET scanner (5&amp;Acirc; mm). This resolution is significantly better than<br /> the resolution of other commonly used methods (e.g. gravimetry or fluorometry), but<br /> the evaluation of deposition in single airways with diameters smaller than PET scanner<br /> resolution is not possible.<br /> <br /> The measured Deposition data reported in [[Test_Data_AC7-01#figure8|figure&amp;nbsp;8]] can be found<br /> in file&amp;nbsp;[[Media:AC7-01_DF_in-vitro.xlsx|DF_in-vitro.xlsx]].<br /> <br /> &lt;div id=&quot;figure9&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_fig9.png|650px]]<br /> |-<br /> |align=&quot;left&quot; width=650|'''Figure 9:''' The comparison of the current results with previously published experimental data (symbols) and correlation fits (lines). The filled triangles represent the current data for single bifurcations in the 1st to 4th generation. The filled circles represent the current data for the model sections no. 13 to 22 ([[Description_AC7-01#figure4|Figure 4]]), which contain multiple bifurcations.<br /> |} <br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=P. Koullapis&lt;sup&gt;a&lt;/sup&gt;, F. Lizal&lt;sup&gt;b&lt;/sup&gt;, J. Jedelsky&lt;sup&gt;b&lt;/sup&gt;, L. Nicolaou&lt;sup&gt;c&lt;/sup&gt;, K. Bauer&lt;sup&gt;d&lt;/sup&gt;, O. Sgrott&lt;sup&gt;e&lt;/sup&gt;, M. Jicha&lt;sup&gt;b&lt;/sup&gt;, M. Sommerfeld&lt;sup&gt;e&lt;/sup&gt;, S. C. Kassinos&lt;sup&gt;a&lt;/sup&gt;<br /> |organisation=&lt;br&gt;&lt;sup&gt;a&lt;/sup&gt;Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus&lt;br&gt;&lt;sup&gt;b&lt;/sup&gt;Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic&lt;br&gt;&lt;sup&gt;c&lt;/sup&gt;Division of Pulmonary and Critical Care, School of Medicine, Johns Hopkins University, Baltimore, USA&lt;br&gt;&lt;sup&gt;d&lt;/sup&gt;Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Freiberg, Germany&lt;br&gt;&lt;sup&gt;e&lt;/sup&gt;Institute Process Engineering, Otto von Guericke University, Halle (Saale), Germany<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=01<br /> }}<br /> <br /> <br /> © copyright ERCOFTAC 2019</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Test_Data_AC7-01&diff=39601 Test Data AC7-01 2021-09-30T11:10:54Z <p>Dave.Ellacott: /* Deposited activity evaluation method */</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=01<br /> }}<br /> __TOC__<br /> =Aerosol deposition in the human upper airways=<br /> '''Application Challenge AC7-01'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2019<br /> =Test Data=<br /> ==Overview of Tests==<br /> Major portions of this section were adopted from<br /> [[Best_Practice_Advice_AC7-01#lizal2015|Lizal ''et&amp;nbsp;al.'' (2015)]]. The positron emission<br /> tomography (PET) method provides the best spatial resolution<br /> (among radiological methods). In addition to local deposition in the various sections,<br /> the deposition hot spots can also be evaluated. However, in comparison to the PET methodology,<br /> which is routinely applied to clinical examination, using this method in the ''in&amp;nbsp;vitro'' design<br /> requires major modifications both in the aerosol preparation and, in particular, in the experiment<br /> evaluation approach. The method, based on PET and fulfilling the above mentioned criteria,<br /> is presented in the following.<br /> <br /> ==The aerosol exposure procedure==<br /> It is a common practice to coat the inner surface of the model, especially when using solid<br /> particles, to prevent bouncing of the particles hitting the surface. Since we used liquid<br /> di-ethylhexyl sebacate (DEHS) particles, we did not need to coat the inner surface of the<br /> model. Another reason for the coating is to prevent surface wetting. In our case the<br /> exposure time was short (5 to 15 mins) and only small amounts of DEHS deposited on the<br /> walls, therefore the possible flooding of the surface was not an issue. Aerosol particles were<br /> generated by a TSI 3475 Condensation Monodisperse Aerosol Generator (CMAG) from<br /> TSI, Inc., which works on the controlled heterogeneous condensation principle. Vapours of<br /> a suitable material, specifically DEHS, condense by a controlled method on small sodium<br /> chloride particles serving as the condensation nuclei. The advantage of DEHS is that it is<br /> not hydrophilic and does not evaporate, resulting in a constant size of generated particles.<br /> In a standard operating mode, the generator can produce particles with aerodynamic<br /> diameters within the 0.1 to 8&amp;mu;m range. The density of DEHS used for the experiments was<br /> 0.914 g/cm&lt;sup&gt;3&lt;/sup&gt; at 25&amp;deg;C. Radioactive aerosol particles were needed for the PET measurement<br /> of deposition. Therefore, the solution in the atomizer of the generator had to be tagged<br /> by a suitable radioactive substance. Fluorine 18 was the logical Choice of the positron<br /> emitter, being easily available at the cooperating PET center and possessing a suitable<br /> half-life (109 minutes). A solution of fluorine 18 in the form of fluoride ions was prepared<br /> by irradiation of H&lt;sub&gt;2&lt;/sub&gt;&lt;sup&gt;18&lt;/sup&gt;0 enriched water on an IBA Cyclone 18/9 cyclotron (irradiation time<br /> 25 min, integrated irradiation current 11 &amp;mu;Ah) at the UJV Rez's PET Centre in Brno. The<br /> irradiated water was transferred by a capillary transport system to a shielded dispensing<br /> box, where the fluorine 18 ions were captured on an ion—exchange resin (AG1—X8, BioRad)<br /> column and subsequently eluted with 300 ml of 10% sodium Chloride solution, followed by<br /> 1&amp;Acirc; ml of water for injection. The resulting solution was repeatedly diluted with water for<br /> injection until the desired initial radioactivity was achieved. The CMAG was modified for<br /> the deposition measurement by using PET so that the atomizer vessel was accommodated<br /> in a protective lead container to shield of ionizing radiation. The atomizer was filled<br /> with a sodium Chloride solution containing &lt;sup&gt;18&lt;/sup&gt;F at an initial activity of 2.5 GBq. The<br /> concentration of sodium Chloride solution was 20 mg/L. The experimental rig is shown in [[Test_Data_AC7-01#figure5|Figure 5]].<br /> <br /> <br /> &lt;div id=&quot;figure5&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_fig5.png|650px]]<br /> |-<br /> |align=&quot;left&quot; width=650|'''Figure 5:''' A scheme of the experimental setup during the PET measurement of aerosol deposition.<br /> |}<br /> <br /> <br /> The generated aerosol was fed through a &lt;sup&gt;85&lt;/sup&gt;''Kr'' based NEKR-10 charge equilibrator<br /> (Eckert &amp; Ziegler Cesio) to a PAM aerosol monitor (TSI 3375) for continuous particle<br /> size and concentration measurement. The operation and precision of the aerosol monitor<br /> was validated using Aerodynamic particle sizer (APS) TSI 3321. The validation was<br /> performed prior to the experiment using the identical setup, apart from adding of the<br /> radioactive substance into the atomizer. The size of the particles generated by CMAG was<br /> adjusted according to APS and the size displayed by the aerosol monitor was recorded.<br /> Subsequently, during the experiment, only the radioactive substance was added to the<br /> atomizer and particles of the same size were produced. Usually only a small correction of<br /> saturator flow was needed at the beginning of the experiments. Only one size of particles<br /> was measured during one day; therefore no further adjustments of the generator were<br /> needed. The aerosol monitor served as an on-line indication of the process of aerosol<br /> generation being stable. It was easily accomplished, as the exposure of the model to<br /> the aerosol lasted only 5 to 15 mins. Filters consisting of Millipore AP40 glass fibers<br /> were attached to the output branches of the respiratory tract model. The entire system<br /> ([[Test_Data_AC7-01#figure6|Figure 6]])<br /> was enclosed in a plastic bag which was kept in a vacuum to prevent the active<br /> aerosol from leaking into the laboratory. All the 10 terminal branches with flow meters<br /> for flow rate control were combined into one branch with a protective High efficiency<br /> particulate air (HEPA) filter. The vacuum was generated with a Busch R, 5 PA 0008 C<br /> rotary oil vacuum pump. The flow distribution in each section of the model is provided<br /> in [[Test_Data_AC7-01#table3|Table&amp;nbsp;3]].<br /> <br /> <br /> &lt;div id=&quot;figure6&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_fig6.png|342px]]<br /> |-<br /> |align=&quot;left&quot; width=342|'''Figure 6:''' A photograph of the physical model prior to the PET measurement.<br /> |}<br /> <br /> <br /> The whole exposure of the model to the aerosol was performed in a shielded laboratory<br /> with an underpressure ventilating system, which would prevent the aerosol from escaping<br /> the room in case of a primary safety system failure. The laboratory personnel were not<br /> present in the laboratory during the exposure, with the exception of the regular instrument<br /> supervision. Whenever they had to enter the lab, they wore half mask respirators. The<br /> experiments were performed in a steady-state inhalation mode with the flow rates of 15,<br /> 30, and 60 L/min. Liquid monodisperse particles with mass median aerodynamic diameter<br /> of 2.5 and 4.3&lt;math&gt;{\mu m}&lt;/math&gt; were used.<br /> The standard geometric deviation of size was less than 1.24<br /> for all measured regimes. The models were exposed for 10 to 15 minutes depending on<br /> radioactivity decrease by radionuclide decay. The peak activity in the models was 4 to 60<br /> &lt;math&gt;{Bq/cm^2}&lt;/math&gt; (depending on the particle size and concentration, measuring mode, and model<br /> used), as measured with an RP-2000 portable contamination meter (VF Zilina, CZ).<br /> <br /> &lt;div id=&quot;old2.3&quot;&gt;&lt;/div&gt;<br /> <br /> ==Deposited activity evaluation method==<br /> The model was transported to a Siemens Biograph 64 Truepoint PET-CT scanner<br /> immediately after the radioactive exposure. The transportation took approximately 3 minutes.<br /> The PET-CT scanner acquired firstly CT images, which were promptly followed by PET<br /> images.<br /> <br /> &lt;div id=&quot;table3&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_table3.png|500px]]<br /> |-<br /> |align=&quot;left&quot; width=500|'''Table 3:''' Flowrates through the individual sections of the model (section identification numbers are presented in [[Description_AC7-01#figure4|Figure&amp;nbsp;4]]). Sections 13&amp;nbsp;&amp;ndash;&amp;nbsp;22 lead to the 10 outlets. Flowrates in the intermediated sections (4&amp;nbsp;&amp;ndash;&amp;nbsp;12) are calculated using mass continuity.<br /> |} <br /> <br /> Both the CT and PET images could be attributed unambiguously to the given<br /> geometry, owing to the assigned geometrical coordinates. The CT images are important<br /> for a precise localization of the edges of the sections, whereas the PET images contain the<br /> essential information about aerosol deposition. The CT and PET images were imported<br /> into Carimas 2.47 ver. 2.2.44.7002 SW (Turku PET Centre 2012) with the CT images<br /> as the main images and the PET images as background images. The software Carimas<br /> is a medical image processing tool, which was developed primarily for analysis of PET<br /> images at Turku PET Centre in Finland and is available as a freeware for non-commercial<br /> use from: http://www.turkupetcentre.fi/carimas/download/. The Carimas was<br /> developed in an “interactive data language” (IDL) and runs on IDL Virtual Machine&amp;trade;, a<br /> cross-platform utility for running IDL code. It supports multiple input formats (DICOM,<br /> ECAT, Analyse, Interfile, Nifti, Interfile, MicroPET) and general bitmap formats (JPG,<br /> TIFF, PNG and BMP). Researchers can perform visualization, segmentation, statistical<br /> analysis, or modelling of PET data. It is possible to perform the image fusion, i.e. to<br /> coregistrate PET and CT or MR, images. Users can define a volume of interest (VOI) and,<br /> by using the static image analysis, they can calculate the mean activity in the VOI (in<br /> units of the PET image), standard deviation, minimal and maximal values, the number<br /> of voxels analysed, and the volume of the region. The software was tested and compared<br /> to commercial tools with an excellent agreement as documented by<br /> [[Best_Practice_Advice_AC7-01#nesterov2009|Nesterov ''et&amp;nbsp;al.'' (2009)]]<br /> and [[Best_Practice_Advice_AC7-01#nesterov2009|Harms ''et&amp;nbsp;al.'' (2014)]].<br /> To facilitate the identification of the hot spots in the Carimas<br /> software, the BGRY colour system was used to display the PET images and the system<br /> range was reduced so that the hot spots were clearly seen in the model sections<br /> ([[Test_Data_AC7-01#figure7|Figure 7]]).<br /> The sections of the model were marked as volumes of interest (VOI), and the mean<br /> volume activity (in Bq/mL) was evaluated using the Carimas software. Each section was<br /> enveloped in an independent VOI. A cylinder or a sphere was selected as the starting<br /> shape of the VOI, depending on the shape of the sections. Firstly, the starting shape of<br /> the VOI was positioned and shaped as a whole to attain a suitable orientation and an<br /> adequate size. In the next step, each VOI was shaped in the vertex mode for a local mesh<br /> adjustment, so that the VOI surrounded the section with an overreach, while preventing<br /> an overlap of different VOIs. If the latter was not avoided, the observed activity would be<br /> attributed to both VOIs, resulting in biased results. The degree of mesh density can be<br /> modified by reducing the number of nodes or by enlarging or shrinking the mesh.<br /> <br /> <br /> &lt;div id=&quot;figure7&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_fig7.png|474px]]<br /> |-<br /> |align=&quot;center&quot;|'''Figure 7:''' CT and PET image presentation in the Carimas software.<br /> |} <br /> <br /> <br /> With regard to the PET precision, a VOI should optimally overreach the section by<br /> roughly 5mm on all sides to cover all the radiation emitted from the section. However, due<br /> to the complex lung geometry, it was impossible to form all the VOIs with such a large<br /> overreach, and so the uncounted radioactivity was accounted for in a correction VOI. Two<br /> additional VOIs had to be created to determine the magnitude of the correction: a VOI for<br /> the top part of the box, accommodating the model with the hoses, and a correction VOI<br /> for the bottom part of the box, accommodating the filters downstream of the terminal<br /> branches. They encompass the large top space with the model and the bottom space<br /> between the two horizontal partitions respectively in [[Test_Data_AC7-01#figure6|Figure 6]].<br /> Two separate corrections<br /> were needed for the model and filters, because the difference in volume radioactivity is<br /> within few orders of magnitude and therefore it is necessary to assign the uncounted<br /> radioactivity to its real source. It is essential to preserve the true ratio of the radiation<br /> deposited in model sections and on filters. The correction factor for the sections was<br /> calculated as the ratio of the total activity obtained from the VOI encompassing the<br /> whole model to the activity obtained by summing up the section VOIs. Similarly, the<br /> correction factor for the filters was calculated as the ratio of the total activity of the large<br /> VOI encompassing all the filters, to the sum of the activities of the filter VOIs. The<br /> corrections for the model sections<br /> (&lt;math&gt;{Corr_m}&lt;/math&gt;) and for the filters (&lt;math&gt;{Corr_f}&lt;/math&gt;) were calculated as<br /> follows:<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{Corr_n=\frac{A_{cm}}{\sum_1^n A_i}}&lt;/math&gt;||width=20 align=right|&lt;math&gt;{(1)}&lt;/math&gt;<br /> |-<br /> |align=center|&lt;math&gt;{Corr_f=\frac{A_{cf}}{\sum_1^n A_j}}&lt;/math&gt;||align=right|&lt;math&gt;{(2)}&lt;/math&gt;<br /> |}<br /> <br /> <br /> where &lt;math&gt;{A_i}&lt;/math&gt; and &lt;math&gt;{A_j}&lt;/math&gt; are the activities measured in the model<br /> sections and on the filters respectively, and &lt;math&gt;{A_{cm}}&lt;/math&gt; and<br /> &lt;math&gt;{A_{cf}}&lt;/math&gt; are the activities measured in the correction VOI for the<br /> model and filters respectively. We assume that the distribution of uncounted radioactivity<br /> is proportional to the measured activity in the sections of the model. The higher the<br /> activity measured in the filter, the higher the activity spread around the section.<br /> Therefore, the uncounted activity is to be accounted for by the sections proportionally to their<br /> measured activity. The correction formula then is simply:<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{A_i^\mbox{*}=Corr_m \cdot A_i}&lt;/math&gt;||width=20 align=right|&lt;math&gt;{(3)}&lt;/math&gt;<br /> |-<br /> |align=center|&lt;math&gt;{A_j^\mbox{*}=Corr_f \cdot A_j}&lt;/math&gt;||align=right|&lt;math&gt;{(4)}&lt;/math&gt;<br /> |} <br /> <br /> <br /> The asterisk (&lt;math&gt;\mbox{*}&lt;/math&gt;) indicates that the data has been corrected. The magnitude of the<br /> correction factor can also be regarded as a model tightness indicator. If the model was not<br /> tight enough and some aerosol leaked beyond the model, the amount of aerosol in the<br /> correction VOI would be appreciably higher than in the sections; also, the calculated<br /> correction factor would be higher.<br /> The correction factors for the model sections and for the<br /> filters lie largely within the ranges of 1.0 to 1.2 and 1.0 to 1.1 respectively. Aerosol leaks<br /> should be suspected if these ranges were exceeded. The VOIs created can be saved in<br /> VRML format in the Carimas software and imported to another model. Therefore, the<br /> same set of VOIs was used for the analysis of all models. The corrected activities served to<br /> calculate the deposition fractions (DF) for two aerosol particle sizes (DF is defined as the<br /> ratio of inhaled particles deposited in the lungs section &lt;math&gt;{A_i^\mbox{*}}&lt;/math&gt;<br /> to the total number of particles<br /> entering the lungs). The total amount of aerosol was calculated as the sum of activities in<br /> the model, in the output sections, in the connection hoses and on the filters. The observed<br /> activity is assumed to be directly proportional to the number of deposited particles. This<br /> is based on the fact that the radioactive atoms are dispersed uniformly in the constantly<br /> stirred atomizer and that each particle generated contains a nucleus of the same size, on<br /> which DEHS has condensed.<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{DF_i=\frac{A_i^\mbox{*}}{\sum_i^n A_i^\mbox{*}}}&lt;/math&gt;<br /> |width=20 align=right|&lt;math&gt;{(5)}&lt;/math&gt;<br /> |} <br /> <br /> <br /> where &lt;math&gt;{n}&lt;/math&gt; is the total number of all sections including the hoses and filters.<br /> <br /> ==Measurement errors==<br /> ===Sources of error in PET imaging===<br /> <br /> The quality of the images obtained with PET is affected by the following parameters:<br /> the spatial resolution, sensitivity, noise, scattered radiation and contrast. The parameters<br /> are interrelated, thus any efforts to reduce the effect of one parameter often result in an<br /> increased effect of another parameter ([[Best_Practice_Advice_AC7-01#saha2010|Saha,&amp;nbsp;2010]]).<br /> The accuracy of determining of the<br /> deposition point for a specific particle is related to the attainable spatial resolution of the<br /> PET scanner. The resolution is affected by the detector size, positron range,<br /> noncolinearity, reconstruction method and localization of the detectors: The actual spatial resolution<br /> of a particular PET scanner is measured by the standardized method recommended by<br /> the NEMA&amp;nbsp;&amp;ndash;&amp;nbsp;National Electrical Manufacturers Association (2001). The full width at half<br /> maximum (FWHM) is the quantity serving as the measure of resolution. This quantity<br /> can be understood as the magnitude of point source “blurring” in the photograph or as<br /> the shortest distance at which two point sources can be discerned as such. The spatial<br /> resolutions (based on NEMA (2001)) for the PET Siemens Biograph 64 system are listed<br /> in [[Test_Data_AC7-01#table4|Table&amp;nbsp;4]].<br /> <br /> &lt;div id=&quot;table4&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_table4.png|500px]]<br /> |-<br /> |align=&quot;left&quot; width=500|'''Table 4:''' Spatial resolution of the PET scanner used for experiments (Siemens 2014)<br /> |} <br /> <br /> The remaining parameters of our PET scanner were: the sensitivity 4.2 cps/kBq, noise<br /> equivalent count rate 96 kcps at 35 kBq/cc, and scatter fraction&amp;nbsp;&lt;&amp;nbsp;38%<br /> ([[Best_Practice_Advice_AC7-01#lizal2015|Lizal&amp;nbsp;''et&amp;nbsp;al.'',&amp;nbsp;2015]]).<br /> As noted in [[Description_AC7-01#limitations|the model limitations section]]<br /> the possible electrical charge on the walls of the physical<br /> model should be considered. The amount of depositing particles due to the mirror charge<br /> is probably low, however, it should be confirmed by an additional experiment.<br /> <br /> ===Inter-person variability===<br /> To assess the error connected to the analysis of images, in particular to the definition of<br /> VOIs, the whole process, beginning with forming the VOIs, was performed by two<br /> technicians independently and their results were compared. The average of the differences<br /> between corresponding sections was 3% of the average value of the calculated radioactivity.<br /> More experiments should be performed to calculate the actual uncertainty of the<br /> whole method, but the above mentioned test confirmed that even if the VOIs were formed<br /> independently by two different individuals, their results were in close agreement<br /> ([[Best_Practice_Advice_AC7-01#lizal2015|Lizal&amp;nbsp;''et&amp;nbsp;al.'',&amp;nbsp;2015]]).<br /> <br /> ===Validation of the method===<br /> The experimental setup and deposition measuring technique was validated by optical microscopy.<br /> Nickel coated particles (M-18-Ni, Cospheric, Santa Barbara, CA, USA) with<br /> MMAD 14.1&amp;mu;m were dispersed by the Small Scale Powder Disperser TSI 3433 and deposited in the model.<br /> The model was disassembled and particles were rinsed out of each<br /> section using ultrasonic bath. The particles were then filtered out and counted using optical microscopy.<br /> The results were consistent with the results acquired by PET. However,<br /> the presented PET method is capable of achieving a significantly higher spatial resolution.<br /> Therefore, more detailed data on local deposition can be obtained, as the size of VOIs can<br /> be smaller than the size of the sections of the model and is limited only by the spatial<br /> resolution of the PET scanner, in our case 5 mm ([[Best_Practice_Advice_AC7-01#lizal2015|Lizal&amp;nbsp;''et&amp;nbsp;al.'',&amp;nbsp;2015]]).<br /> <br /> ==Measured data==<br /> The proposed method was used to evaluate deposition during steady-state inhalation for<br /> the following cases:<br /> #15 L/min, &lt;math&gt;{d_p = 4.3{\mu}m^2}&lt;/math&gt;<br /> #30 L/min, &lt;math&gt;{d_p = 2.5{\mu}m^2}&lt;/math&gt;<br /> #60 L/min, &lt;math&gt;{d_p = 4.3{\mu}m^2}&lt;/math&gt;<br /> <br /> The measurement for 60 L/min was made in duplicate. The Deposition Fraction difference<br /> between the two measurements was calculated for each section, and the observed difference<br /> within the repeated measurements was drawn in the plot in the form of error lines as the<br /> estimate of measurement variability.<br /> <br /> The plot in [[Test_Data_AC7-01#figure8|fig.&amp;nbsp;8]] demonstrates that the majority of<br /> particles was deposited in the oral<br /> cavity and in the trachea in all the applied variants. A comparison of the regimes shows<br /> that the amount of deposited particles increases with their increasing momentum, which<br /> confirms that inertial impaction was the dominant deposition mechanism in our case. The<br /> results demonstrate that the ''in vitro'' deposition measurement method based on the PET<br /> technique enables the DF to be evaluated with adequate precision for distinguishing the<br /> effects of the particle size and the breathing regime.<br /> <br /> <br /> &lt;div id=&quot;figure8&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_fig8.png|650px]]<br /> |-<br /> |align=&quot;left&quot; width=650|'''Figure 8:''' Results obtained by measurements in the realistic model (section identification numbers are presented in [[Description_AC7-01#figure4|Figure&amp;nbsp;4]]). Error bars indicate the difference between two measurements performed on two separate, but geometrically identical models. Measurements for 15 and 30 L/min were performed just once.<br /> |} <br /> <br /> <br /> In the following step, a comparison with previously published data was performed.<br /> Few studies presenting ''in&amp;nbsp;vitro'' measured local aerosol deposition in tracheobronchial<br /> airways have been published in past years. The most suitable for comparison with our data<br /> were the results acquired by<br /> [[Best_Practice_Advice_AC7-01#zhou2005|Zhou&amp;nbsp;&amp;&amp;nbsp;Cheng&amp;nbsp;(2005)]] and<br /> [[Best_Practice_Advice_AC7-01#chan1980|Chan&amp;nbsp;&amp;&amp;nbsp;Lippmann&amp;nbsp;(1980)]] as they<br /> both used realistic lung casts. However, their models had less generations of branching<br /> (four and six, respectively) compared to our model. The comparison of deposition efficiency (DE)<br /> defined as the ratio of the number of particles deposited in the section to<br /> the number of particles entering the section showed close agreement with both studies<br /> mentioned above (see [[Test_Data_AC7-01#figure9|Figure&amp;nbsp;9]]).<br /> The practical calculation of DE was performed as a ratio<br /> of corrected activity in the examined section to the sum of activities in all downstream<br /> sections including filters and hoses, and the activity in the examined section:<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{DE_i=\frac{A_i^\mbox{*}}{A_f^\mbox{*}+A_i^\mbox{*}}}&lt;/math&gt;<br /> |width=20 align=right|&lt;math&gt;{(6)}&lt;/math&gt;<br /> |}<br /> <br /> <br /> where &lt;math&gt;{A_f^\mbox{*}}&lt;/math&gt; is the corrected activity in the section downstream the i-th section. DE was<br /> plotted as a function of Stokes number defined as:<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{Stk=\frac{\rho d_p^2U}{18\mu D}}&lt;/math&gt;<br /> |width=20 align=right|&lt;math&gt;{(7)}&lt;/math&gt;<br /> |}<br /> <br /> <br /> where &lt;math&gt;{d_p (\mu m)}&lt;/math&gt; is the aerodynamic diameter of a particle,<br /> &lt;math&gt;{U (m/s)}&lt;/math&gt; is the velocity, &lt;math&gt;{\mu (Pa.s)}&lt;/math&gt;<br /> is the Viscosity of air and &lt;math&gt;{D (m)}&lt;/math&gt; is the characteristic diameter (of the airway), which was<br /> measured in the digital geometry in Rhinoceros 4.0 software (McNeel Seattle, WA7 USA).<br /> The diameter of the entrance airway was used as the characteristic diameter, in accordance<br /> with [[Best_Practice_Advice_AC7-01#zhou2005|Zhou&amp;nbsp;&amp;&amp;nbsp;Cheng&amp;nbsp;(2005)]].<br /> [[Best_Practice_Advice_AC7-01#chan1980|Chan&amp;nbsp;&amp;&amp;nbsp;Lippmann&amp;nbsp;(1980)]] introduced the following correlation<br /> fit based on their experimental data for the first six generations:<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{DE=1.606Stk+0.0023}&lt;/math&gt;<br /> |width=20 align=right|&lt;math&gt;{(8)}&lt;/math&gt;<br /> |}<br /> <br /> <br /> Similar correlation fit was calculated based on the current data for 1st to 4th generation.<br /> <br /> <br /> {|align=&quot;center&quot; border=&quot;0&quot; cellpadding=&quot;0&quot;<br /> |width=630 align=center|&lt;math&gt;{DE=1.038Stk+0.0012}&lt;/math&gt;<br /> |width=20 align=right|&lt;math&gt;{(9)}&lt;/math&gt;<br /> |}<br /> <br /> <br /> Both the empirical equations were plotted in the graph of [[Test_Data_AC7-01#figure9|Figure&amp;nbsp;9]].<br /> The airways in the<br /> 4th to 7th generation, which create separate parts of the model (identification numbers 13<br /> to 22), were evaluated as a whole section and plotted in<br /> [[Test_Data_AC7-01#figure9|Figure&amp;nbsp;9]] as well. The deposition<br /> fraction can be calculated in a higher resolution (creating smaller sections) down to the<br /> resolution of the PET scanner (5&amp;Acirc; mm). This resolution is significantly better than<br /> the resolution of other commonly used methods (e.g. gravimetry or fluorometry), but<br /> the evaluation of deposition in single airways with diameters smaller than PET scanner<br /> resolution is not possible.<br /> <br /> The measured Deposition data reported in [[Test_Data_AC7-01#figure8|figure&amp;nbsp;8]] can be found<br /> in file&amp;nbsp;[[Media:AC7-01_DF_in-vitro.xlsx|DF_in-vitro.xlsx]].<br /> <br /> &lt;div id=&quot;figure9&quot;&gt;&lt;/div&gt;<br /> {|align=&quot;center&quot; border=0<br /> |-<br /> |align=&quot;center&quot;|[[Image:AC7-01_fig9.png|650px]]<br /> |-<br /> |align=&quot;left&quot; width=650|'''Figure 9:''' The comparison of the current results with previously published experimental data (symbols) and correlation fits (lines). The filled triangles represent the current data for single bifurcations in the 1st to 4th generation. The filled circles represent the current data for the model sections no. 13 to 22 ([[Description_AC7-01#figure4|Figure 4]]), which contain multiple bifurcations.<br /> |} <br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=P. Koullapis&lt;sup&gt;a&lt;/sup&gt;, F. Lizal&lt;sup&gt;b&lt;/sup&gt;, J. Jedelsky&lt;sup&gt;b&lt;/sup&gt;, L. Nicolaou&lt;sup&gt;c&lt;/sup&gt;, K. Bauer&lt;sup&gt;d&lt;/sup&gt;, O. Sgrott&lt;sup&gt;e&lt;/sup&gt;, M. Jicha&lt;sup&gt;b&lt;/sup&gt;, M. Sommerfeld&lt;sup&gt;e&lt;/sup&gt;, S. C. Kassinos&lt;sup&gt;a&lt;/sup&gt;<br /> |organisation=&lt;br&gt;&lt;sup&gt;a&lt;/sup&gt;Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus&lt;br&gt;&lt;sup&gt;b&lt;/sup&gt;Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic&lt;br&gt;&lt;sup&gt;c&lt;/sup&gt;Division of Pulmonary and Critical Care, School of Medicine, Johns Hopkins University, Baltimore, USA&lt;br&gt;&lt;sup&gt;d&lt;/sup&gt;Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Freiberg, Germany&lt;br&gt;&lt;sup&gt;e&lt;/sup&gt;Institute Process Engineering, Otto von Guericke University, Halle (Saale), Germany<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=01<br /> }}<br /> <br /> <br /> © copyright ERCOFTAC 2019</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Best_Practice_Advice_AC7-04&diff=39459 Best Practice Advice AC7-04 2021-06-07T12:15:05Z <p>Dave.Ellacott: Dave.Ellacott moved page Best Practice Advice AC7-04 to Lib:Best Practice Advice AC7-04</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> =Best Practice Advice=<br /> ==Key Fluid Physics==<br /> ==Application Uncertainties==<br /> ==Computational Domain and Boundary Conditions==<br /> ==Discretisation and Grid Resolution==<br /> ==Physical Modelling==<br /> ==Recommendations for Future Work==<br /> ==References==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Best_Practice_Advice_AC7-04&diff=39458 Best Practice Advice AC7-04 2021-06-07T12:14:49Z <p>Dave.Ellacott: </p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> =Best Practice Advice=<br /> ==Key Fluid Physics==<br /> ==Application Uncertainties==<br /> ==Computational Domain and Boundary Conditions==<br /> ==Discretisation and Grid Resolution==<br /> ==Physical Modelling==<br /> ==Recommendations for Future Work==<br /> ==References==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Best_Practice_Advice_AC7-04&diff=39457 Best Practice Advice AC7-04 2021-06-07T12:12:45Z <p>Dave.Ellacott: Created page with &quot;=Best Practice Advice= ==Key Fluid Physics== ==Application Uncertainties== ==Computational Domain and Boundary Conditions== ==Discretisation and Grid Resolution== ==Physical M...&quot;</p> <hr /> <div>=Best Practice Advice=<br /> ==Key Fluid Physics==<br /> ==Application Uncertainties==<br /> ==Computational Domain and Boundary Conditions==<br /> ==Discretisation and Grid Resolution==<br /> ==Physical Modelling==<br /> ==Recommendations for Future Work==</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Evaluation_AC7-04&diff=39455 Evaluation AC7-04 2021-06-07T12:10:46Z <p>Dave.Ellacott: Dave.Ellacott moved page Evaluation AC7-04 to Lib:Evaluation AC7-04</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> =Evaluation=<br /> ==Comparison of Test Data and CFD==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Evaluation_AC7-04&diff=39454 Evaluation AC7-04 2021-06-07T12:10:27Z <p>Dave.Ellacott: Created page with &quot;{{ACHeader |area=7 |number=04 }} __TOC__ =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison= '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;...&quot;</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> =Evaluation=<br /> ==Comparison of Test Data and CFD==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=CFD_Simulations_AC7-04&diff=39453 CFD Simulations AC7-04 2021-06-07T12:06:07Z <p>Dave.Ellacott: </p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> =CFD Simulations=<br /> ==Overview of CFD Simulations==<br /> ==Solution Strategy==<br /> ==Computational Domain==<br /> ==Boundary Conditions==<br /> ==Application of Physical Models==<br /> ==Numerical Accuracy==<br /> ==CFD Results==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=CFD_Simulations_AC7-04&diff=39451 CFD Simulations AC7-04 2021-06-07T12:04:24Z <p>Dave.Ellacott: Dave.Ellacott moved page CFD Simulations AC7-04 to Lib:CFD Simulations AC7-04</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> =CFD Simulations=<br /> ==Overview of Tests==<br /> ==Description of Experiment==<br /> ==Boundary Data==<br /> ==Measurement Errors==<br /> ==Measured Data==<br /> ==References==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=CFD_Simulations_AC7-04&diff=39450 CFD Simulations AC7-04 2021-06-07T12:04:09Z <p>Dave.Ellacott: Created page with &quot;{{ACHeader |area=7 |number=04 }} __TOC__ =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison= '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;...&quot;</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> =CFD Simulations=<br /> ==Overview of Tests==<br /> ==Description of Experiment==<br /> ==Boundary Data==<br /> ==Measurement Errors==<br /> ==Measured Data==<br /> ==References==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Test_Data_AC7-04&diff=39449 Test Data AC7-04 2021-06-07T12:03:03Z <p>Dave.Ellacott: </p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> =Test Data=<br /> ==Overview of Tests==<br /> ==Description of Experiment==<br /> ==Boundary Data==<br /> ==Measurement Errors==<br /> ==Measured Data==<br /> ==References==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Test_Data_AC7-04&diff=39447 Test Data AC7-04 2021-06-07T12:01:27Z <p>Dave.Ellacott: Dave.Ellacott moved page Test Data AC7-04 to Lib:Test Data AC7-04</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> =Test Data=<br /> ==Introduction==<br /> ==Relevance to Industrial Sector==<br /> ==Design or Assessment Parameters==<br /> ==Flow Domain Geometry==<br /> ==Flow Physics and Fluid Dynamics Data==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Test_Data_AC7-04&diff=39446 Test Data AC7-04 2021-06-07T12:01:07Z <p>Dave.Ellacott: Created page with &quot;{{ACHeader |area=7 |number=04 }} __TOC__ =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison= '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;...&quot;</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> =Test Data=<br /> ==Introduction==<br /> ==Relevance to Industrial Sector==<br /> ==Design or Assessment Parameters==<br /> ==Flow Domain Geometry==<br /> ==Flow Physics and Fluid Dynamics Data==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Description_AC7-04&diff=39445 Description AC7-04 2021-06-07T12:00:10Z <p>Dave.Ellacott: </p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> =Description=<br /> ==Introduction==<br /> ==Relevance to Industrial Sector==<br /> ==Design or Assessment Parameters==<br /> ==Flow Domain Geometry==<br /> ==Flow Physics and Fluid Dynamics Data==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Description_AC7-04&diff=39444 Description AC7-04 2021-06-07T11:57:20Z <p>Dave.Ellacott: </p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> ==Application Area 7: Biomedical Flows==<br /> =Description=<br /> ==Introduction==<br /> ==Relevance to Industrial Sector==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Description_AC7-04&diff=39443 Description AC7-04 2021-06-07T11:56:45Z <p>Dave.Ellacott: </p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> '''Application Challenge AC7-04'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021==Application Area 7: Biomedical Flows==<br /> =Description=<br /> ==Introduction==<br /> ==Relevance to Industrial Sector==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Description_AC7-04&diff=39442 Description AC7-04 2021-06-07T11:53:51Z <p>Dave.Ellacott: </p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> ==Application Area 7: Biomedical Flows==<br /> ===Application Challenge AC7-04===<br /> <br /> =Turbulent Blood Flow in a Ventricular Assist Device=<br /> '''Application Challenge AC7-03'''&amp;nbsp;&amp;nbsp;&amp;nbsp;© copyright ERCOFTAC 2021<br /> <br /> =Description=<br /> ==Introduction==<br /> =Description=<br /> ==Introduction==<br /> ==Relevance to Industrial Sector==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Description_AC7-04&diff=39441 Description AC7-04 2021-06-07T11:51:31Z <p>Dave.Ellacott: </p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> ==Application Area 7: Biomedical Flows==<br /> ===Application Challenge AC7-04===<br /> <br /> =Description=<br /> ==Introduction==<br /> ==Relevance to Industrial Sector==<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Description_AC7-04&diff=39440 Description AC7-04 2021-06-07T11:49:03Z <p>Dave.Ellacott: </p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __TOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> ==Application Area 7: Biomedical Flows==<br /> ===Application Challenge AC7-04===<br /> <br /> =Description=<br /> ==Introduction==&lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Description_AC7-04&diff=39438 Description AC7-04 2021-06-07T11:47:06Z <p>Dave.Ellacott: Dave.Ellacott moved page Description AC7-04 to Lib:Description AC7-04</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __NOTOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> ==Application Area 7: Biomedical Flows==<br /> ===Application Challenge AC7-04===<br /> <br /> =Abstract=<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Description_AC7-04&diff=39437 Description AC7-04 2021-06-07T11:46:51Z <p>Dave.Ellacott: Created page with &quot;{{ACHeader |area=7 |number=04 }} __NOTOC__ =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison= ==Application Area 7: Biomedical Flows== ===Applica...&quot;</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __NOTOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> ==Application Area 7: Biomedical Flows==<br /> ===Application Challenge AC7-04===<br /> <br /> =Abstract=<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=AC7-04&diff=39436 AC7-04 2021-06-07T11:45:53Z <p>Dave.Ellacott: Dave.Ellacott moved page AC7-04 to Lib:AC7-04</p> <hr /> <div>#REDIRECT [[Lib:AC7-04]]</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Abstr:AC7-04&diff=39435 Abstr:AC7-04 2021-06-07T11:45:52Z <p>Dave.Ellacott: Dave.Ellacott moved page AC7-04 to Lib:AC7-04</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __NOTOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> ==Application Area 7: Biomedical Flows==<br /> ===Application Challenge AC7-04===<br /> <br /> =Abstract=<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Abstr:AC7-04&diff=39434 Abstr:AC7-04 2021-06-07T11:44:41Z <p>Dave.Ellacott: Created page with &quot;{{ACHeader |area=7 |number=04 }} __NOTOC__ =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison= ==Application Area 7: Biomedical Flows== ===Applica...&quot;</p> <hr /> <div>{{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> __NOTOC__<br /> =A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison=<br /> ==Application Area 7: Biomedical Flows==<br /> ===Application Challenge AC7-04===<br /> <br /> =Abstract=<br /> &lt;br/&gt;<br /> ----<br /> {{ACContribs<br /> |authors=Morgane Garreau<br /> |organisation=University of Montpellier, France<br /> }}<br /> {{ACHeader<br /> |area=7<br /> |number=04<br /> }}<br /> <br /> © copyright ERCOFTAC 2021</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Lib_Bio&diff=39433 Lib Bio 2021-06-07T11:41:42Z <p>Dave.Ellacott: </p> <hr /> <div>{| border=&quot;1&quot;<br /> ! AC !!Application Challenge !! Contributor !! Organisation<br /> &lt;!--<br /> |- style=&quot;background-color:white;&quot;<br /> !7-01<br /> |[[AC7-01|Aerosol deposition in the human upper airways]] || P. Koullapis ''et al.'' || University of Cyprus<br /> --&gt;<br /> &lt;!--<br /> |- style=&quot;background-color:white;&quot;<br /> !7-02<br /> |[[AC7-02|Airflow in the human upper airways]] || S. Kassinos ''et al.'' || University of Cyprus<br /> --&gt;<br /> |- style=&quot;background-color:white;&quot;<br /> !7-03<br /> |[[AC7-03|Turbulent Blood Flow in a Ventricular Assist Device]] || B. Torner || University of Rostock, Germany<br /> |- style=&quot;background-color:white;&quot;<br /> !7-04<br /> |[[AC7-04|A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison]] || M. Garreau || University of Montpellier, France</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=Lib_Bio&diff=39432 Lib Bio 2021-06-07T11:41:14Z <p>Dave.Ellacott: </p> <hr /> <div>{| border=&quot;1&quot;<br /> ! AC !!Application Challenge !! Contributor !! Organisation<br /> &lt;!--<br /> |- style=&quot;background-color:white;&quot;<br /> !7-01<br /> |[[AC7-01|Aerosol deposition in the human upper airways]] || P. Koullapis ''et al.'' || University of Cyprus<br /> --&gt;<br /> &lt;!--<br /> |- style=&quot;background-color:white;&quot;<br /> !7-02<br /> |[[AC7-02|Airflow in the human upper airways]] || S. Kassinos ''et al.'' || University of Cyprus<br /> --&gt;<br /> |- style=&quot;background-color:white;&quot;<br /> !7-03<br /> |[[AC7-03|Turbulent Blood Flow in a Ventricular Assist Device]] || B. Torner || University of Rostock, Germany<br /> |- style=&quot;background-color:white;&quot;<br /> !7-04<br /> |[[AC7-04|A pusatile 3D flow relevant to thoracic hemodynamics: CFD - 4D MRI comparison]] || M. Garreau || University of Montpellier, France</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=UFR_4-21_References&diff=39184 UFR 4-21 References 2021-02-11T15:34:23Z <p>Dave.Ellacott: Dave.Ellacott moved page UFR 4-21 References to Lib:UFR 4-21 References</p> <hr /> <div>#REDIRECT [[Lib:UFR 4-21 References]]</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=UFR_4-21_Best_Practice_Advice&diff=39181 UFR 4-21 Best Practice Advice 2021-02-11T15:33:33Z <p>Dave.Ellacott: Dave.Ellacott moved page UFR 4-21 Best Practice Advice to Lib:UFR 4-21 Best Practice Advice</p> <hr /> <div>#REDIRECT [[Lib:UFR 4-21 Best Practice Advice]]</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=UFR_4-21_Evaluation&diff=39178 UFR 4-21 Evaluation 2021-02-11T15:32:33Z <p>Dave.Ellacott: Dave.Ellacott moved page UFR 4-21 Evaluation to Lib:UFR 4-21 Evaluation</p> <hr /> <div>#REDIRECT [[Lib:UFR 4-21 Evaluation]]</div> Dave.Ellacott https://kbwiki.ercoftac.org/w/index.php?title=UFR_4-21_Test_Case&diff=39175 UFR 4-21 Test Case 2021-02-11T15:29:33Z <p>Dave.Ellacott: Dave.Ellacott moved page UFR 4-21 Test Case to Lib:UFR 4-21 Test Case</p> <hr /> <div>#REDIRECT [[Lib:UFR 4-21 Test Case]]</div> Dave.Ellacott