Difference between revisions of "UFR 335 Test Case"
(43 intermediate revisions by 3 users not shown)  
Line 4:  Line 4:  
number=35  number=35  
}}  }}  
−  +  __TOC__  
= General Remark =  = General Remark =  
−  The experimental and numerical setups applied in this study were described in detail by Schanderl et al. (2017b) (PIV and LES). The experiment is further described by Jenssen (2019), the numerics in Schanderl & Manhart (2016), Schanderl et al. (2017a) and Schanderl & Manhart (2018). Thus, the following  +  The experimental and numerical setups applied in this study were described in detail by Schanderl et al. (2017b) (PIV and LES). The experiment is further described by Jenssen (2019), the numerics in Schanderl & Manhart (2016), Schanderl et al. (2017a) and Schanderl & Manhart (2018). Thus, the following will provide a brief overview only. 
= Test Case Experiments =  = Test Case Experiments =  
−  In order to provide both numerical and experimental data acquired for the same flow configuration under identical (as  +  In order to provide both numerical and experimental data acquired for the same flow configuration under identical (as much as possible) boundary conditions, we performed a large eddy simulation and a particle image velocimetry experiment. We studied the flow around a wallmounted slender circular cylinder having a height larger than the flow depth an a flow depth of <math> z_0 = 1.5D</math>. The width of the rectangular channel was <math> 11.7D</math> (see Fig. 1). The investigated Reynolds number was approximately <math> Re_D = \frac{u_{\mathrm{b}}D}{\nu} = 39{,}000</math>, the Froude number was in the subcritical region. As inflow condition we applied fullydeveloped openchannel flow. The particular flow conditions were chosen to be as close as possible to the conditions of Dargahi (1989). 
[[File:UFR335_configuration.pngcentreframeFig. 1: Sketch of flow configuration]]  [[File:UFR335_configuration.pngcentreframeFig. 1: Sketch of flow configuration]]  
= Experimental setup =  = Experimental setup =  
−  The experimental setup is shown in Fig. 2. A highlevel water tank fed the flume with a constant energy head. After the inlet, a flow straightener, a surface  +  The experimental setup is shown in Fig. 2. A highlevel water tank fed the flume with a constant energy head. After the inlet, a flow straightener, a surfacewave damper and vortex generators as recommended by (Counihan 1969) were installed such that turbulent openchannel flow developed along the entry length of <math>200D</math> corresponding to 42 hydraulic diameters of the open channel flow. A sluice gate at the end of the flume controlled the water depth before the water recirculated driven by a pump. The experimental parameters are listed in Table 1: 
[[File:UFR335_Flume.pngthumbcentre800pxFig. 2: Experimental setup]]  [[File:UFR335_Flume.pngthumbcentre800pxFig. 2: Experimental setup]]  
Line 66:  Line 66:  
We used a CCDcamera with a <math>2048\times2048\mathrm{px} </math> square sensor. The size of a pixel was <math>36.86 \mu\mathrm{m}</math>, therefore the spatial resolution of the images was <math>2712 \mathrm{px}/D </math>. The size of the interrogation windows was <math>5.8976\cdot 10^{3} D</math>. The temporal resolution was <math>7.25\mathrm{Hz}</math>, which is approximately twice the macro time scale <math>u_{\mathrm{b}}/D = 3.9 \mathrm{Hz}</math>.  We used a CCDcamera with a <math>2048\times2048\mathrm{px} </math> square sensor. The size of a pixel was <math>36.86 \mu\mathrm{m}</math>, therefore the spatial resolution of the images was <math>2712 \mathrm{px}/D </math>. The size of the interrogation windows was <math>5.8976\cdot 10^{3} D</math>. The temporal resolution was <math>7.25\mathrm{Hz}</math>, which is approximately twice the macro time scale <math>u_{\mathrm{b}}/D = 3.9 \mathrm{Hz}</math>.  
The light sheet was approximately 2mm thick provided by a <math>532\mathrm{nm}</math> Nd:YAG laser. The fnumber and the focal length of the lens were <math>2.8</math> and <math>105\mathrm{mm}</math>, respectively.  The light sheet was approximately 2mm thick provided by a <math>532\mathrm{nm}</math> Nd:YAG laser. The fnumber and the focal length of the lens were <math>2.8</math> and <math>105\mathrm{mm}</math>, respectively.  
+  
+  
+  The PIV setup is shown in detail in Fig. 3, including the qualitative size of the fieldofviews (FOV) for investigating the approaching ''boundary layer'' as well as the flow in front of the wallmounted ''cylinder''.  
+  
+  [[File:UFR335_PIV_setup.pngthumbcentre600pxFig. 3: PIV setup]]  
At the measurement section, the flume had transparent walls. Therefore, the laser light, which entered the flow from above could pass with a minimum amount of surface reflections through the bottom wall. However, an acrylic glass plate had to be mounted at the waterair interface to suppress the bow waves of the cylinder and let the light sheet enter the water body perpendicularly (see Fig. 3). The influence of this device at the water surface was tested and considered to be insignificant at the cylinderwall junction.  At the measurement section, the flume had transparent walls. Therefore, the laser light, which entered the flow from above could pass with a minimum amount of surface reflections through the bottom wall. However, an acrylic glass plate had to be mounted at the waterair interface to suppress the bow waves of the cylinder and let the light sheet enter the water body perpendicularly (see Fig. 3). The influence of this device at the water surface was tested and considered to be insignificant at the cylinderwall junction.  
−  Hollow glass spheres were used as seeding and had a diameter of <math>10 \mu\mathrm{m}</math>. The corresponding Stokes number was <math>4.7\cdot 10^{3}</math>, and therefore, the particles were considered to follow the flow precisely.  +  Hollow glass spheres were used as seeding particles and had a diameter of <math>10 \mu\mathrm{m}</math>. The corresponding Stokes number was <math>4.7\cdot 10^{3}</math>, and therefore, the particles were considered to follow the flow precisely. 
+  
+  The total number of recorded double frames was <math>27{,}000</math>, the timedelay between two image frames was <math>700 \mu\mathrm{s}</math>. Therefore, the total sampling time was <math>27{,}000/7.25 = 3724\mathrm{s}</math> or <math>1484D</math>. During the experiment, seeding and other particles accumulated along the bottom plate, which undermined the image quality by increasing the surface reflection. Therefore, the data acquisition was stopped after <math>1500</math> images to allow surface cleaning and to empty the limited capacity of the laboratory PC's RAM. The sampling time of such a batch was <math>1500/7.25 = 207 \mathrm{s}</math> or <math>82D/u_b</math>.  
+  
+  The data acquisition time and the number of valid vectors were validated by the convergence of statistical moments. In the centre of the HV the number of valid samples had its minimum. Therefore, the timeseries at the centre of the HV was analysed as a reference for the entire flow field. The standard error of the mean was <math>0.0065</math> times the standard deviation, the corresponding error in the fourth central moment is <math>0.0545</math>.  
−  
−  The  +  The standard error of the mean value of the measured velocities was determined as follows: 
−  +  <math> \varepsilon_{\mathrm{std}}(\langle u \rangle) = \frac{\sigma(u)}{\sqrt{N_{\mathrm{samples}}}} = \frac{\sqrt{M_2(u)}}{\sqrt{N_{\mathrm{samples}}}} </math>,  
−  +  the standard error of the higher central moments <math> M_n = \langle u'^n \rangle </math> was obtained likewise:  
+  <math> \varepsilon_{\mathrm{std}}\left( \langle u'^n \rangle \right) = \frac{\sigma\left(u'^n\right)}{\sqrt{N_{\mathrm{samples}}}} = \frac{\sqrt{M_{\mathrm{2n}}M_{\mathrm{n}}^2}}{\sqrt{N_{\mathrm{samples}}}} </math>.  
+  The standard errors with respect to the standard deviation <math> \sigma </math> were quantified as follows:  
+  { class="wikitable" style="textalign: center;" border="1" style="margin: auto;"  
+  + style="captionside:bottom;"Tab. 2: Standard errors of extimating selected central moments using the experimental data (PIV)  
+   <math> \varepsilon_{\mathrm{std}}(\langle u \rangle) / \sigma </math>  
+   <math> \varepsilon_{\mathrm{std}}\left( M_2 \right) / \sigma^2</math>  
+   <math> \varepsilon_{\mathrm{std}}\left( M_3 \right) / \sigma^3</math>  
+   <math> \varepsilon_{\mathrm{std}}\left( M_4 \right) / \sigma^4</math>  
+    
+   <math> 0.0065 </math>  
+   <math> 0.0089 </math>  
+   <math> 0.0237 </math>  
+   <math> 0.0545 </math>  
+  }  
= CFD Code and Methods =  = CFD Code and Methods =  
<br/>  <br/>  
−  We applied our inhouse finitevolume code MGLET with a staggered Cartesian grid. The grid was equidistant in the horizontal directions and stretched away from the wall in the vertical direction by a factor smaller than <math>1.01</math>. The horizontal grid spacing was four times as large as the vertical one. The time integration was done by applying a third order RungeKutta sheme, the spatial approximation by second order central differences and the maximum of the CFL number was in the range of 0.55 to 0.82. To model the cylindrical body, a second order immersed boundary method was applied (Peller et al.2006; Peller 2010). The subgrid scales were modelled using the WallAdapting Local EddyViscosity (WALE) model (Nicoud & Ducros 1999). Around the cylinder, the grid was refined by three locally embedded grids (Manhart 2004), each reducing the grid spacing by a factor of two (see Fig. 4). A grid study by Schanderl & Manhart 2016  +  We applied our inhouse finitevolume code MGLET with a staggered Cartesian grid. The grid was equidistant in the horizontal directions and stretched away from the wall in the vertical direction by a factor smaller than <math>1.01</math>. The horizontal grid spacing was four times as large as the vertical one. The time integration was done by applying a third order RungeKutta sheme, the spatial approximation by second order central differences and the maximum of the CFL number was in the range of 0.55 to 0.82. To model the cylindrical body, a second order immersed boundary method was applied (Peller et al.2006; Peller 2010). The subgrid scales were modelled using the WallAdapting Local EddyViscosity (WALE) model (Nicoud & Ducros 1999). Around the cylinder, the grid was refined by three locally embedded grids (Manhart 2004), each reducing the grid spacing by a factor of two (see Fig. 4). A grid study by Schanderl & Manhart 2016 demonstrated that the number of grid refinements was sufficient. The resulting grid resolution in the vertical direction at the bottom plate around the cylinder was smaller than approximately 1.9 wall units based on the wallshear stress of the approaching flow in the precursor, averaged over the span <math> 1.25 < y/D < 1.25</math> (Schanderl & Manhart 2016). The distance of the first grid point in the finest grid level was less than 1.6 wall units based on the local wall shear stress. The fraction of the modelled dissipation is about 30% of the total dissipation rate (Schanderl & Manhart 2018). 
The setup simulated was intended to be identical to the experimental one. To model the bottom and side walls, we applied noslip boundary conditions, whereas the free surface was modelled by a slip boundary condition. Therefore, the Froude number in the LES was infinitesimal and no surface waves occurred. By conducting a precursor simulation a fullydeveloped turbulent openchannel flow was achieved as inflow condition. The streamwise boundary conditions were periodic, and the precursor domain had a length of 30D (see Fig. 4). The wallnearest point of the precursor grid had a distance of 7.5 wall units.  The setup simulated was intended to be identical to the experimental one. To model the bottom and side walls, we applied noslip boundary conditions, whereas the free surface was modelled by a slip boundary condition. Therefore, the Froude number in the LES was infinitesimal and no surface waves occurred. By conducting a precursor simulation a fullydeveloped turbulent openchannel flow was achieved as inflow condition. The streamwise boundary conditions were periodic, and the precursor domain had a length of 30D (see Fig. 4). The wallnearest point of the precursor grid had a distance of 7.5 wall units.  
Line 93:  Line 115:  
{ class="wikitable" style="textalign: center;" border="1" style="margin: auto;"  { class="wikitable" style="textalign: center;" border="1" style="margin: auto;"  
−  + style="captionside:bottom;"Tab.  +  + style="captionside:bottom;"Tab. 3: Applied grids in the LES (Schanderl & Manhart 2016) 
! Grid  ! Grid  
! Level of refinement  ! Level of refinement  
Line 131:  Line 153:  
 3   3  
 <math>250/1000</math>   <math>250/1000</math>  
−   <math>7.5/7.5/1.  +   <math>7.5/7.5/1.9</math> 
 <math>177\cdot 10^6 </math>   <math>177\cdot 10^6 </math>  
}  }  
+  = Inflow condition =  
+  There is a strong influence of the oncoming flow on the flow around the cylinder (Schanderl & Manhart 2016). In this section we provide information on the inflow condition as obtained in the symmetry plane of the channel. The simulation data were taken from the precursor simulation and the experimental data were measured by planar PIV in the empty channel at the position where later the cylinder was placed. We provide only inplane quantities which were measured by the PIV. The data are made dimensionless by the friction velocity in the symmetry plane of the undisturbed flow. In case of the LES it was determined by the velocity gradient at the wall and in case of the PIV it was determined by the method of Clauser (1954).  
−  +  Figure 5 shows the vertical timeaveraged profiles along <math> z^+ = \frac{z\cdot u_{\tau}}{\nu}</math> of the  
−  
−  Figure 5 shows the vertical timeaveraged profiles of the  
<ol style="liststyletype:loweralpha">  <ol style="liststyletype:loweralpha">  
<li>streamwise velocity <math>\langle u^+\rangle = \langle u \rangle / u_{\tau}</math></li>  <li>streamwise velocity <math>\langle u^+\rangle = \langle u \rangle / u_{\tau}</math></li>  
−  <li>Reynolds normal  +  <li>Reynolds normal stress <math> \langle u'u' \rangle / u^2_{\tau}</math></li> 
−  <li>Reynolds normal  +  <li>Reynolds normal stress <math> \langle w'w' \rangle / u^2_{\tau}</math></li> 
−  <li>Reynolds shear  +  <li>Reynolds shear stress <math> \langle u'w' \rangle / u^2_{\tau}.</math></li> 
</ol>  </ol>  
+  For comparison, the data of Bruns et al. (1992) are included at a comparable Reynolds number based on the momentum thickness <math> \delta_2 </math>.  
+  
+  
+  <div><ul>  
+  <li style="display: inlineblock;"> [[File:UFR335_log_law_inflow.pngthumbcentre450pxFig. 5 a) streamwise velocity <math>\langle u^+\rangle = \langle u \rangle / u_{\tau}</math>]] </li>  
+  <li style="display: inlineblock;"> [[File:UFR335_uu_inflow.pngthumbcentre450pxFig. 5 b) Reynolds normal stress <math> \langle u'u' \rangle / u^2_{\tau}</math>]] </li>  
+  </ul></div>  
+  
+  <div><ul>  
+  <li style="display: inlineblock;"> [[File:UFR335_ww_inflow.pngthumbcentre450pxFig. 5 c) Reynolds normal stress <math> \langle w'w' \rangle / u^2_{\tau}</math>]] </li>  
+  <li style="display: inlineblock;"> [[File:UFR335_uw_inflow.pngthumbcentre450pxFig. 5 d) Reynolds shear stress <math> \langle u'w' \rangle / u^2_{\tau}</math>]] </li>  
+  </ul></div>  
+  
+  The corresponding datasets can be downloaded from the data files given below. In these, the first 11 lines belong to the header and are indicated by the #symbol. For both PIV and LES, each column refers to the data listed in Table 4 and is comma separated. For MatLab users, we provide a script at the end of the section [[UFR 335 EvaluationEvaluation]] of this document as an example of reading the data, which can be used as a template to modify for reading the inflow data as well.  
+  { class="wikitable" style="textalign: center;" border="1" style="margin: auto;"  
+  + style="captionside:bottom;"Tab. 4: Structure of the inflow datasets  
+   Column number  
+   1  
+   2  
+   3  
+   4  
+   5  
+   6  
+   7  
+    
+   '''PIV'''/'''LES'''  
+   <math> \frac{z}{D} </math>  
+   <math> \frac{\langle u\rangle}{u_{\mathrm{b}}} </math>  
+   <math> z^+ </math>  
+   <math> u^+ </math>  
+   <math> \frac{\langle u'u'\rangle}{u^2_{\tau}} </math>  
+   <math> \frac{\langle w'w'\rangle}{u^2_{\tau}} </math>  
+   <math> \frac{\langle u'w'\rangle}{u^2_{\tau}} </math>  
+  }  
+  
+  {  
+  * PIV data: [[Media:UFR335_X_inflow_data.txt]]  
+  * LES data: [[Media:UFR335_C_inflow_data.txt]]  
+  }  
   
Latest revision as of 15:54, 4 November 2020
Cylinderwall junction flow
Contents
General Remark
The experimental and numerical setups applied in this study were described in detail by Schanderl et al. (2017b) (PIV and LES). The experiment is further described by Jenssen (2019), the numerics in Schanderl & Manhart (2016), Schanderl et al. (2017a) and Schanderl & Manhart (2018). Thus, the following will provide a brief overview only.
Test Case Experiments
In order to provide both numerical and experimental data acquired for the same flow configuration under identical (as much as possible) boundary conditions, we performed a large eddy simulation and a particle image velocimetry experiment. We studied the flow around a wallmounted slender circular cylinder having a height larger than the flow depth an a flow depth of . The width of the rectangular channel was (see Fig. 1). The investigated Reynolds number was approximately , the Froude number was in the subcritical region. As inflow condition we applied fullydeveloped openchannel flow. The particular flow conditions were chosen to be as close as possible to the conditions of Dargahi (1989).
Experimental setup
The experimental setup is shown in Fig. 2. A highlevel water tank fed the flume with a constant energy head. After the inlet, a flow straightener, a surfacewave damper and vortex generators as recommended by (Counihan 1969) were installed such that turbulent openchannel flow developed along the entry length of corresponding to 42 hydraulic diameters of the open channel flow. A sluice gate at the end of the flume controlled the water depth before the water recirculated driven by a pump. The experimental parameters are listed in Table 1:
Description  Value  Unit 

Cylinder diameter  
Flow depth  
Channel width  
Flow rate  
Depthaveraged velocity of approach flow  
Kinematic viscosity  
Reynolds number  
Reynolds number  
Reynolds number 
Measurement technique
The experimental data were acquired by conducting planar monoscopic 2D2C PIV in the vertical symmetry plane upstream of the cylinder. The PIV snapshots were evaluated by the standard interrogation window based crosscorrelation of . Doing so, we achieved instantaneous velocity fields of the streamwise () and the wallnormal () velocity component. From these data the timeaveraged turbulent statistics were calculated in the postprocessing. We used a CCDcamera with a square sensor. The size of a pixel was , therefore the spatial resolution of the images was . The size of the interrogation windows was . The temporal resolution was , which is approximately twice the macro time scale . The light sheet was approximately 2mm thick provided by a Nd:YAG laser. The fnumber and the focal length of the lens were and , respectively.
The PIV setup is shown in detail in Fig. 3, including the qualitative size of the fieldofviews (FOV) for investigating the approaching boundary layer as well as the flow in front of the wallmounted cylinder.
At the measurement section, the flume had transparent walls. Therefore, the laser light, which entered the flow from above could pass with a minimum amount of surface reflections through the bottom wall. However, an acrylic glass plate had to be mounted at the waterair interface to suppress the bow waves of the cylinder and let the light sheet enter the water body perpendicularly (see Fig. 3). The influence of this device at the water surface was tested and considered to be insignificant at the cylinderwall junction.
Hollow glass spheres were used as seeding particles and had a diameter of . The corresponding Stokes number was , and therefore, the particles were considered to follow the flow precisely.
The total number of recorded double frames was , the timedelay between two image frames was . Therefore, the total sampling time was or . During the experiment, seeding and other particles accumulated along the bottom plate, which undermined the image quality by increasing the surface reflection. Therefore, the data acquisition was stopped after images to allow surface cleaning and to empty the limited capacity of the laboratory PC's RAM. The sampling time of such a batch was or .
The data acquisition time and the number of valid vectors were validated by the convergence of statistical moments. In the centre of the HV the number of valid samples had its minimum. Therefore, the timeseries at the centre of the HV was analysed as a reference for the entire flow field. The standard error of the mean was times the standard deviation, the corresponding error in the fourth central moment is .
The standard error of the mean value of the measured velocities was determined as follows:
,
the standard error of the higher central moments was obtained likewise:
.
The standard errors with respect to the standard deviation were quantified as follows:
CFD Code and Methods
We applied our inhouse finitevolume code MGLET with a staggered Cartesian grid. The grid was equidistant in the horizontal directions and stretched away from the wall in the vertical direction by a factor smaller than . The horizontal grid spacing was four times as large as the vertical one. The time integration was done by applying a third order RungeKutta sheme, the spatial approximation by second order central differences and the maximum of the CFL number was in the range of 0.55 to 0.82. To model the cylindrical body, a second order immersed boundary method was applied (Peller et al.2006; Peller 2010). The subgrid scales were modelled using the WallAdapting Local EddyViscosity (WALE) model (Nicoud & Ducros 1999). Around the cylinder, the grid was refined by three locally embedded grids (Manhart 2004), each reducing the grid spacing by a factor of two (see Fig. 4). A grid study by Schanderl & Manhart 2016 demonstrated that the number of grid refinements was sufficient. The resulting grid resolution in the vertical direction at the bottom plate around the cylinder was smaller than approximately 1.9 wall units based on the wallshear stress of the approaching flow in the precursor, averaged over the span (Schanderl & Manhart 2016). The distance of the first grid point in the finest grid level was less than 1.6 wall units based on the local wall shear stress. The fraction of the modelled dissipation is about 30% of the total dissipation rate (Schanderl & Manhart 2018).
The setup simulated was intended to be identical to the experimental one. To model the bottom and side walls, we applied noslip boundary conditions, whereas the free surface was modelled by a slip boundary condition. Therefore, the Froude number in the LES was infinitesimal and no surface waves occurred. By conducting a precursor simulation a fullydeveloped turbulent openchannel flow was achieved as inflow condition. The streamwise boundary conditions were periodic, and the precursor domain had a length of 30D (see Fig. 4). The wallnearest point of the precursor grid had a distance of 7.5 wall units.
Grid  Level of refinement  Cells per diameter
horizontal / vertical 
Grid spacing

Number of grid cells 

Precursor  0  
Base  0  
Grid 1  1  
Grid 2  2  
Grid 3  3 
Inflow condition
There is a strong influence of the oncoming flow on the flow around the cylinder (Schanderl & Manhart 2016). In this section we provide information on the inflow condition as obtained in the symmetry plane of the channel. The simulation data were taken from the precursor simulation and the experimental data were measured by planar PIV in the empty channel at the position where later the cylinder was placed. We provide only inplane quantities which were measured by the PIV. The data are made dimensionless by the friction velocity in the symmetry plane of the undisturbed flow. In case of the LES it was determined by the velocity gradient at the wall and in case of the PIV it was determined by the method of Clauser (1954).
Figure 5 shows the vertical timeaveraged profiles along of the
 streamwise velocity
 Reynolds normal stress
 Reynolds normal stress
 Reynolds shear stress
For comparison, the data of Bruns et al. (1992) are included at a comparable Reynolds number based on the momentum thickness .
The corresponding datasets can be downloaded from the data files given below. In these, the first 11 lines belong to the header and are indicated by the #symbol. For both PIV and LES, each column refers to the data listed in Table 4 and is comma separated. For MatLab users, we provide a script at the end of the section Evaluation of this document as an example of reading the data, which can be used as a template to modify for reading the inflow data as well.
Column number  1  2  3  4  5  6  7 
PIV/LES 
 PIV data: Media:UFR335_X_inflow_data.txt
 LES data: Media:UFR335_C_inflow_data.txt
Contributed by: Ulrich Jenssen, Wolfgang Schanderl, Michael Manhart — Technical University Munich
© copyright ERCOFTAC 2019