UFR 3-35 Test Case: Difference between revisions

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= 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 =
= Test Case Experiments =
== 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 wall-mounted 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 fully-developed open-channel flow. The particular flow conditions were chosen to be as close as possible to the conditions of Dargahi (1989).
The experimental data were acquired by conducting planar monoscopic 2D-2C PIV in the vertical symmetry plane upstream of the cylinder. The PIV snapshots were evaluated by the standard interrogation window based cross-correlation of 16x16px. Doing so, we achieved instantaneous velocity fields of the streamwise (U) and the wall-normal (W) velocity component. From these data the time-averaged turbulent statistics were calculated in the post-processing.
We used a CCD-camera with a 2048x2048px square sensor. The size of a pixel was 36.86µm, therefore the spatial resolution of the images was 2712 px/D, of the PIV data however, it was 5.8976e-3 D. The temporal resolution was 7.25Hz, which is approximately twice as the macro time scale ub/D = 3.9 Hz.
The light sheet was approximately 2mm thick provided by a 532nm Nd:YAG laser. The f-number and the focal length of the lens was 2.8 and 105mm, respectively.  


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. However, an acrylic glass plate had to be mounted at the water-air interface to suppress the bow waves of the cylinder and let the light sheet enter the water body perpendicularly. The influence of this device at the water surface was tested and considered to be of minor importance for the cylinder-wall junction.
[[File:UFR3-35_configuration.png|centre|frame|Fig. 1: Sketch of flow configuration]]


Hollow glass spheres were used as seeding and had a diameter of 10µm. The corresponding Stokes number was 4.7e-3, and therefore, the particles were considered to follow the flow precisely.
= Experimental set-up =
The experimental set-up is shown in Fig. 2. A high-level water tank fed the flume with a constant energy head. After the inlet, a flow straightener, a surface-wave damper and vortex generators as recommended by (Counihan 1969) were installed such that turbulent open-channel 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:


The hydraulic boundary condition of a turbulent boundary layer developed naturally due to the 200D long entry length and by the use of vortex generators as recommended by (Counihan 1969). The total number of time-steps was 27,000, the time-delay between two image frames of a time-step was 700µs. Therefore, the total sampling time was 27,000/7.25 = 3724s or 1484D. 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 1500 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 1500/7.25 = 207s or 82D.
[[File:UFR3-35_Flume.png|thumb|centre|800px|Fig. 2: Experimental set-up]]


The data acquisition time and number of valid vectors was validated by the convergence of statistical moments. In the centre of the HV the number valid samples had its minimum. Therefore, the time-series at the centre of the HV was analysed as a reference for the entire flow field. The standard error of the mean was 0.0065 times the standard deviation, the corresponding error in the fourth central moment is 0.0545.


The experimental parameters are listed in Table 1:
{| class="wikitable" style="text-align: center;" border="1" style="margin: auto;"
{| border="1"
|+ style="caption-side:bottom;"|Tab. 1: Experimental parameters
|+Table1: Experimental parameters
! Description
! Description
! Value
! Value
! Unit
! Unit
|-
|-
| Cylinder diameter D
| Cylinder diameter <math>D</math>
| 0.1
| <math>0.1</math>
| [m]
| <math>[\mathrm{m}]</math>
|-
|-
| Flow depth z0
| Flow depth <math>z_0</math>
| 0.15
| <math>0.15</math>
| [m]
| <math>[\mathrm{m}]</math>
|-
|-
| Channel width b
| Channel width <math>b</math>
| 1.17
| <math>1.17</math>
| [m]
| <math>[\mathrm{m}]</math>
|-
|-
| Flow rate Q
| Flow rate <math>Q</math>
| 0.069
| <math>0.069</math>
| [m^3 s^-1]
| <math>[\mathrm{m}^3 \mathrm{s}^{-1}]</math>
|-
|-
| Depth-averaged velocity of approach flow ub
| Depth-averaged velocity of approach flow <math>u_{\mathrm{b}}</math>
| 0.3986
| <math>0.3986</math>
| [m s^-1]
| <math>[\mathrm{m}\, \mathrm{s}^{-1}]</math>
|-
|-
| Kinematic viscosity
| Kinematic viscosity <math>\nu</math>
| 1.0502e-6
| <math>1.0502\cdot 10^{-6}</math>
| [m^2 s^-1]
| <math>[\mathrm{m}^2 \mathrm{s}^{-1}]</math>
|-
|-
| Reynolds number Re_D
| Reynolds number <math>Re_D</math>
| 37954
| <math>37{,}954</math>
| [-]
| <math>[-]</math>
|-
| Reynolds number <math>Re_{z_0} = \frac{u_\mathrm{b} \cdot 4R_{\mathrm{hyd}}}{\nu} = \frac{u_\mathrm{b} \cdot 4(b\cdot z_0)/(2z_0+b) }{\nu} </math>
| <math>181{,}162</math>
| <math>[-]</math>
|-
| Reynolds number <math>Re_{\tau} = \frac{u_{\tau} \cdot z_0}{\nu}</math>
| <math>2571</math>
| <math>[-]</math>
|}
|}


== CFD Codes and Methods ==
= Measurement technique =
The experimental data were acquired by conducting planar monoscopic 2D-2C PIV in the vertical symmetry plane upstream of the cylinder. The PIV snapshots were evaluated by the standard interrogation window based cross-correlation of <math>16\times16\mathrm{px} </math>. Doing so, we achieved instantaneous velocity fields of the streamwise (<math>u</math>) and the wall-normal (<math>w</math>) velocity component. From these data the time-averaged turbulent statistics were calculated in the post-processing.
We used a CCD-camera 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 f-number and the focal length of the lens were <math>2.8</math> and <math>105\mathrm{mm}</math>, respectively.
 
 
The PIV set-up is shown in detail in Fig. 3, including the qualitative size of the field-of-views (FOV) for investigating the approaching ''boundary layer'' as well as the flow in front of the wall-mounted ''cylinder''.
 
[[File:UFR3-35_PIV_setup.png|thumb|centre|600px|Fig. 3: PIV set-up]]
 
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 water-air 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 cylinder-wall junction.
 
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 time-delay 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 time-series 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 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="text-align: center;" border="1" style="margin: auto;"
|+ style="caption-side: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 =
<br/>
<br/>
As the numerical details of our large eddy simulation (LES) can be found in (Schanderl & Manhart2016), we provide a brief summary here. The set-up was intended to be identical to the experimental infrastructure. To model the bottom and side walls, we set the boundary conditions to no-slip, 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.
We applied our in-house finite-volume 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 Runge-Kutta 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 sub-grid scales were modelled using the Wall-Adapting Local Eddy-Viscosity (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 wall-shear 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).


We used our in-house finite volume code MGLET with a staggered non-equidistant Cartesian grid. The Runge-Kutta time-integration was of third order, the spatial approximation of second order 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. The sub-grid scales were modelled using the Wall-Adapting Local Eddy-Viscosity (WALE) model, and the portion of the modelled dissipation is about 30% of the total dissipation rate.
The setup simulated was intended to be identical to the experimental one. To model the bottom and side walls, we applied no-slip 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 fully-developed turbulent open-channel 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 wall-nearest point of the precursor grid had a distance of 7.5 wall units.  


By conducting a precursor simulation a fully developed turbulent boundary layer was generated. The streamwise boundary conditions were periodic, and the precursor domain had a length of 30D to prevent the flow from superstructures. The wall resolution of the precursor grid was 7.5 wall units; thus, no wall model was applied. When the statistics of the precursor simulation converged, the fully developed the turbulent boundary layer was fed into the main simulation domain as inflow condition. Around the cylinder, the grid was refined in three steps, each with a factor of two. Schanderl & Manhart (2016) showed while performing a grid study that three refinement levels were enough to achieve 0.95 wall units at the cylinder and based on the oncoming wall-shear stress. When using the local shear stress, the spatial resolution slightly decreased to 1.6 wall units. Furthermore, the sensitivity of the HV system regarding the inflow conditions was also investigated by Schanderl & Manhart (2016).
[[File:UFR3-35_gridLVL.PNG|centre|frame|Fig. 4: Grid arrangement of the LES (Schanderl 2018)]]


[[File:UFR3-35_gridLVL.png]]
(Schanderl 2018)


{| border="1"
{| class="wikitable" style="text-align: center;"  border="1" style="margin: auto;"
|+Table2: Applied grids
|+ style="caption-side:bottom;"|Tab. 3: Applied grids in the LES (Schanderl & Manhart 2016)
! Grid
! Grid
! Level of refinement
! Level of refinement
Line 107: Line 155:
| <math>7.5/7.5/1.9</math>
| <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 in-plane 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 time-averaged profiles along <math> z^+ = \frac{z\cdot u_{\tau}}{\nu}</math> of the
<ol style="list-style-type:lower-alpha">
  <li>streamwise velocity <math>\langle u^+\rangle = \langle u \rangle / u_{\tau}</math></li>
  <li>Reynolds normal stress <math> \langle u'u' \rangle / u^2_{\tau}</math></li>
  <li>Reynolds normal stress <math> \langle w'w' \rangle / u^2_{\tau}</math></li>
  <li>Reynolds shear stress <math> \langle u'w' \rangle / u^2_{\tau}.</math></li>
</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: inline-block;"> [[File:UFR3-35_log_law_inflow.png|thumb|centre|450px|Fig. 5 a) streamwise velocity <math>\langle u^+\rangle = \langle u \rangle / u_{\tau}</math>]] </li>
<li style="display: inline-block;"> [[File:UFR3-35_uu_inflow.png|thumb|centre|450px|Fig. 5 b) Reynolds normal stress <math> \langle u'u' \rangle / u^2_{\tau}</math>]] </li>
</ul></div>
<div><ul>
<li style="display: inline-block;"> [[File:UFR3-35_ww_inflow.png|thumb|centre|450px|Fig. 5 c) Reynolds normal stress <math> \langle w'w' \rangle / u^2_{\tau}</math>]] </li>
<li style="display: inline-block;"> [[File:UFR3-35_uw_inflow.png|thumb|centre|450px|Fig. 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 3-35 Evaluation|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.
{| class="wikitable" style="text-align: center;" border="1" style="margin: auto;"
|+ style="caption-side: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:UFR3-35_X_inflow_data.txt]]
* LES data: [[Media:UFR3-35_C_inflow_data.txt]]
|}
|}



Latest revision as of 15:54, 4 November 2020

Cylinder-wall junction flow

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References

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 wall-mounted 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 fully-developed open-channel flow. The particular flow conditions were chosen to be as close as possible to the conditions of Dargahi (1989).

Fig. 1: Sketch of flow configuration

Experimental set-up

The experimental set-up is shown in Fig. 2. A high-level water tank fed the flume with a constant energy head. After the inlet, a flow straightener, a surface-wave damper and vortex generators as recommended by (Counihan 1969) were installed such that turbulent open-channel 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:

Fig. 2: Experimental set-up


Tab. 1: Experimental parameters
Description Value Unit
Cylinder diameter
Flow depth
Channel width
Flow rate
Depth-averaged velocity of approach flow
Kinematic viscosity
Reynolds number
Reynolds number
Reynolds number

Measurement technique

The experimental data were acquired by conducting planar monoscopic 2D-2C PIV in the vertical symmetry plane upstream of the cylinder. The PIV snapshots were evaluated by the standard interrogation window based cross-correlation of . Doing so, we achieved instantaneous velocity fields of the streamwise () and the wall-normal () velocity component. From these data the time-averaged turbulent statistics were calculated in the post-processing. We used a CCD-camera 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 f-number and the focal length of the lens were and , respectively.


The PIV set-up is shown in detail in Fig. 3, including the qualitative size of the field-of-views (FOV) for investigating the approaching boundary layer as well as the flow in front of the wall-mounted cylinder.

Fig. 3: PIV set-up

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 water-air 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 cylinder-wall 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 time-delay 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 time-series 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:

Tab. 2: Standard errors of extimating selected central moments using the experimental data (PIV)

CFD Code and Methods


We applied our in-house finite-volume 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 Runge-Kutta 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 sub-grid scales were modelled using the Wall-Adapting Local Eddy-Viscosity (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 wall-shear 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 no-slip 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 fully-developed turbulent open-channel 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 wall-nearest point of the precursor grid had a distance of 7.5 wall units.

Fig. 4: Grid arrangement of the LES (Schanderl 2018)


Tab. 3: Applied grids in the LES (Schanderl & Manhart 2016)
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 in-plane 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 time-averaged profiles along of the

  1. streamwise velocity
  2. Reynolds normal stress
  3. Reynolds normal stress
  4. Reynolds shear stress

For comparison, the data of Bruns et al. (1992) are included at a comparable Reynolds number based on the momentum thickness .


  • Fig. 5 a) streamwise velocity
  • Fig. 5 b) Reynolds normal stress
  • Fig. 5 c) Reynolds normal stress
  • Fig. 5 d) Reynolds shear stress

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.

Tab. 4: Structure of the inflow datasets
Column number 1 2 3 4 5 6 7
PIV/LES


Contributed by: Ulrich Jenssen, Wolfgang Schanderl, Michael Manhart — Technical University Munich

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References


© copyright ERCOFTAC 2019