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== Brief Description of the Study Test Case ==
== Brief Description of the Study Test Case ==
{{Demo_UFR_Test_Brief}}
A detailed description of the chosen test  case  (TC  with  ''L''&nbsp;=&nbsp;3.7''D'') is available
[[Media:UFR2-12_NASA_ypg.pdf|here]].
<!--at
[https://info.aiaa.org/tac/ASG/FDTC/DG/BECAN_files_/BANCII_category2/Problem_statement_tandem_cylinder_v1.010.pdf this link]-->
So in the following we present only  its brief overview.
 
 
A schematic of the airflow  past  the  TC  configuration  is  shown  in [[UFR_2-12_Test_Case#figure1|Figure 1]].
The model is comprised of two  cylinders  of  equal  diameter aligned with the streamwise flow direction.
The  polar  angle,&nbsp;<math>{\theta}</math>, is measured from the upstream stagnation point  and  is  positive
in the clockwise direction.
 
 
<div id="figure1"></div>
{|align="center"
|[[Image:UFR2-12_figure1.png]]
|-
|align="center"|'''Figure 1:''' Schematic of TC configuration [[UFR_2-12_References#3|[3]]]
|}
 
 
Geometric and regime parameters defining the test case  are  summarized in
[[UFR_2-12_Test_Case#table1|Table 1]].
 
<div id="table1">
{|align="center" border="1" cellpadding=10
|+ '''Table 1:''' Flow parameters
|-
!Parameter!!Notation!!Value
|-
|Reynolds number||Re=<math>U_0D/\nu</math>||1.66&times;10<sup>5</sup>
|-
|Mach number||M||0.128
|-
|Separation distance||<math>L/D</math>||3.7
|-
|TC aspect ratio||<math>L_z/D</math>||12.4
|-
|Cylinder diameter||<math>D</math>||0.05715 m
|-
|Free stream velocity||<math>U_0</math>||44 m/s
|-
|Free stream turbulence intensity||<math>K</math>||0.1%
|}
 
 
The principal measured quantities by which the success or failure of CFD calculations are to be judged are as follows:
*Mean Flow
**Distributions of time-averaged pressure coefficient, <math>C_p=\langle (p-p_0) \rangle / (1/2 \rho_0 U_0^2)</math>, over the surface of both cylinders;
**Distribution  of  time-averaged  mean  streamwise  velocity <math>{\left.\langle u\rangle/U_0\right.}</math> along a line connecting the centres of the cylinders;
*Unsteady Characteristics
**Distributions of the  root-mean-square  (rms)  of  the  pressure coefficient over the surface of both cylinders;
**Power spectral density of the pressure coefficient (dB/Hz versus Hz) on the upstream cylinder at <math>\theta</math>&nbsp;=&nbsp;135&deg;;
**Power spectral density of the pressure coefficient (dB/Hz versus Hz) on the downstream cylinder at <math>\theta</math>&nbsp;=&nbsp;45&deg;;
*Turbulence kinetic energy
** ''x&nbsp;&ndash;&nbsp;y'' cut of the field of time-averaged two-dimensional  turbulent kinetic energy <math>\text{TKE}=\frac{1}{2}\left(\langle u'u'\rangle + \langle v'v'\rangle\right)/U_0^2</math>;
**2D TKE distribution along ''y''&nbsp;=&nbsp;0;
**2D TKE  distribution  along  ''x''&nbsp;=&nbsp;1.5&nbsp;''D''  (in  the  gap  between  the cylinders);
**2D TKE distribution  along  ''x''&nbsp;=&nbsp;4.45&nbsp;''D''  (0.75&nbsp;''D''  downstream  of  the centre of the rear cylinder).
 
All these and some other data are available here in both Windows and Unix compressed formats:
 
{|align="center" border="1" cellpadding="5"
!Windows!!Unix
|-
|colspan="2" align="center"|[[Media:UFR2-12_readme.txt|readme.txt]]
|-
|colspan="2" align="center"|[[Media:UFR2-12_Tandem_Cylinder_Problem_Statement_v1.08.pdf|problem_statement.pdf]]
|-
|colspan="2" align="center"|[[Media:UFR2-12_problem2_data_and_guidelines.pdf|problem_data_and_guidelines.pdf]]
|-
|[[Media:UFR2-12_data.zip|data.zip]]||[[Media:UFR2-12_data.tgz|data.tgz]]
|-
|[[Media:UFR2-12_figures.zip|figures.zip]]||[[Media:UFR2-12_figures.tgz|figures.tgz]]
|}
 
<!--on the
[https://info.aiaa.org/tac/ASG/FDTC/DG/Forms/AllItems.aspx?RootFolder=https%3A%2F%2Finfo.aiaa.org%2Ftac%2FASG%2FFDTC%2FDG%2FBECAN_files_%2FBANCII_category2&FolderCTID=0x0120007FEBD4B8002BD94694D9BBB199BB01DA web site of the BANC-I Workshop].-->
These data are gratefully made available by the BANC-I Workshop.
 
== Test Case Experiments ==
== Test Case Experiments ==
{{Demo_UFR_Test_Expt}}
A detailed description of the  experimental  facility  and  measurement techniques is given in the original publications
[[UFR_2-12_References#2|[2-4]]]. <!--and available on the
[https://info.aiaa.org/tac/ASG/FDTC/DG/Forms/AllItems.aspx?RootFolder=https%3A%2F%2Finfo.aiaa.org%2Ftac%2FASG%2FFDTC%2FDG%2FBECAN_files_%2FBANCII_category2&FolderCTID=0x0120007FEBD4B8002BD94694D9BBB199BB01DA web site of the BANC-I Workshop].-->
So here we  present  only  concise information about these aspects of the test case.
 
 
<div id="figure2"></div>
{|align="center"
|[[Image:UFR2-12_figure2.png]]
|-
|align="center"|'''Figure 2:''' TC configuration in the BART facility [[UFR_2-12_References#3|[3]]]
|}
 
 
<div id="tce"></div>
Experiments have been  conducted  in  the  Basic  Aerodynamic  Research Tunnel (BART) at NASA Langley Research Center
(see [[UFR_2-12_Test_Case#figure2|Figure 2]]).
This is a subsonic, atmospheric wind-tunnel for investigation of the  fundamental characteristics of complex flow-fields.
The tunnel has  a  closed  test section with a height of 0.711 m, a width of 1.016 m, and a  length  of 3.048 m.
The span size of the cylinders was equal to  the  entire  BART tunnel height, thus resulting in the aspect ratio
''L<sub>z</sub>&nbsp;/&nbsp;D''&nbsp;=&nbsp;12.4.
The free stream velocity was set to 44 m/s giving a  Reynolds  number  based  on cylinder diameter equal to
1.66&nbsp;&times;&nbsp;10<sup>5</sup> and  Mach  number equal  to  0.128 (flow temperature ''T''&nbsp;=&nbsp;292 K).
 
 
The free stream turbulence level was less  than  0.10%.
In  the  first series of the experiments  [[UFR_2-12_References#2|[2, 3]]],
in  order  to  ensure  a  turbulent separation from  the  upstream  cylinder
at  the  considered  Reynolds number, the boundary layers  on  this  cylinder  were  tripped  between azimuthal locations of
50 and 60 degrees from  the  leading  stagnation point using a transition strip.
For the  downstream  cylinder,  it  was assumed that trip-like effect of turbulent wake  impingement  from  the upstream cylinder
would  automatically  ensure  turbulent  separation.
However, later on [[UFR_2-12_References#4|[4]]]
it was found that the effect of tripping  of  the downstream cylinder at ''L/D''&nbsp;=&nbsp;3.7
is also  rather  tangible  (resulted  in reduced  peaks  in  mean  ''C''<sub>p</sub>  distribution  along  the  rear  cylinder,
accompanied by an earlier  separation  from  the  cylinder  surface,  a reduced pressure recovery, lower levels of mean TKE
in  the  wake  and reduced levels of peak surface pressure fluctuations).
For this reason, exactly these (with tripping of both cylinders) experimental  data
[[UFR_2-12_References#4|[4]]] were used for the comparison
with fully turbulent CFD.
 
 
In the course of experiments, steady and unsteady pressure measurements were carried out along with 2-D Particle Image
Velocimetry  (PIV)  and hot-wire anemometry used for documenting the  flow  interaction  around the two cylinders
(mean streamlines and instantaneous vorticity fields, shedding frequencies and spectra).
 
 
Information on the data accuracy available in the original publications
[[UFR_2-12_References#2|[2-4]]] is summarized in [[UFR_2-12_Test_Case#table2|Table 2]].
Most absolute values are given based on nominal tunnel conditions or  on  an  average  data  value.
Percentage values are quoted for parameters where the uncertainty  equations  were posed in terms of the uncertainty relative
to the nominal value of  the parameter.
 
 
<div id="table2"></div>
{| align="center" border="1" cellpadding="5"
|+'''Table 2:''' Estimated Experimental Uncertainties
|-
!Quantity!!Uncertainty
|-
|Steady ''C''<sub>p</sub>||0.02
|-
|Drag Coefficient||0.0005
|-
|PIV: ''U''<sub>mean</sub>, ''V''<sub>mean</sub>||0.03 (normalized)
|-
|PIV: Spanwise velocity||1.8 (normalized)
|-
|PIV: TKE||4%
|-
|Power Spectral Density (PSD)||10&nbsp;&ndash;&nbsp;20%
|-
|''C''<sub>p</sub>' rms||5&nbsp;&ndash;&nbsp;11%
|-
|Diameter, ''D''; Sensor spacing &Delta;z||0.005 inch
|}
 
== CFD Methods ==
== CFD Methods ==
{{Demo_UFR_Test_CFD}}
The key physical features of the UFR  (see [[UFR_2-12_Description#Description|Description]])
present  significant difficulties  for  all  the  existing  approaches
to  turbulence representation, whether from the standpoint of solution  fidelity  (for the conventional (U)RANS models)
or in terms of  computational  expense for full LES (especially if the turbulent boundary  layers  are  to  be resolved).
For this reason, most of the computational studies of multi-body flows, in general, and the TC configuration,  in  particular,
are currently relying upon hybrid RANS-LES approaches.
This  is  true  also with regard to simulations carried out in the course of the BANC-I  and II Workshops and in the framework
of the ATAAC project, where different hybrid RANS-LES models of the DES type were used
(see [[UFR_2-12_Test_Case#table3|Table 3]])
<ref>Some participants of the BANC Workshops have  used  pure  LES  rather than DES-like approaches but these computations had the
most  difficulty simulating the high Reynolds aspects of the flow
[[UFR_2-12_References#5|[5]]].</ref>.
 
 
<div id="table3"></div>
{|align="center" border="1" cellpadding="5" width="700"
|+'''Table 3:''' Summary of simulations
|-
!Partner!!Turbulence Modelling approach!!Compressible/Incompressible!!''L''<sub>z</sub>!!Grid!!Side Walls
|-
|Beijing Tsinghua University '''BTU'''||SST DDES||Compressible||3''D''||Mandatory||Slip
|-
|German Aerospace Center, Göttingen '''DLR'''||SA DDES||Compressible||3''D''||Mandatory||Slip
|-
|New Technologies and Services, St.-Petersburg, Russia '''NTS'''
|SA DDES
SA IDDES
|Incompressible and Compressible||3''D'', 16''D''||Mandatory||Slip
|-
|Technische Universität Berlin '''TUB'''
|SA DDES
SA IDDES
|Incompressible||3''D''||Mandatory||Slip
|-
|colspan="6"|SST - ''k''&ndash;&omega; Shear Stress Transport model [[UFR_2-12_References#9|[9]]]; SA - Spalart-Allmaras model [[UFR_2-12_References#10|[10]]]; SA and SST DDES - Delayed DES based on the SA and SST models [[UFR_2-12_References#11|[11]]]; SA IDDES - Improved DDES based on the SA model [[UFR_2-12_References#12|[12]]].
|}
 
 
As mentioned in the [[UFR_2-12_Test_Case#Test_Case_Experiments|experiments section]] above, in the experiments the  boundary
layers  on both cylinders were tripped ahead of their separation, thus justifying the "fully turbulent" simulations.
 
 
All the partners used their own flow solvers.
 
 
Particularly, '''BTU''' employed  in-house  ''compressible''  Navier-Stokes  code with weighted, central-upwind,
approximation  of  the  inviscid  fluxes based on a modification of the  high-order  symmetric  total  variation diminishing scheme.
The method combines 6<sup>th</sup> order central and 5<sup>th</sup> order WENO schemes. For the time integration, an implicit
LU-SGS algorithm is applied with Newton-like sub-iterations.
 
 
'''DLR'''  used  their  unstructured  TAU  code  with  a  finite  volume ''compressible''  Navier-Stokes  solver.
The  solver  employs  a  standard central scheme with matrix dissipation with dual time stepping strategy of Jameson.
The 3W Multi-Grid cycle was applied for  the  momentum  and energy equations, whilst the SA transport equation was  solved
on  the finest grid only.
Time  integration  was  performed  with  the  use  of explicit 3-level Runge-Kutta scheme.
The method is of the 2<sup>nd</sup> order  in both space and time.
 
 
'''NTS''' used in-house NTS finite-volume  code.
It  is  a  structured  code accepting  multi-block  overset  grids  of  Chimera  type.
The ''incompressible'' branch of the code employs Rogers and Kwak's  scheme
[[UFR_2-12_References#13|[13]]] and  for  ''compressible''  flows  Roe  scheme  is  applied.
The  spatial approximation of the inviscid fluxes within these methods is  performed differently  in  different  grid  blocks
(see  [[UFR_2-12_Test_Case#figure3|Figure  3]]  below).
In particular, in the outer block, the 3<sup>rd</sup>-order upwind-biased  scheme  is used,  whereas  in  the  other  blocks,
a  weighted  5<sup>th</sup>-order upwind-biased&nbsp;/&nbsp;4<sup>th</sup>-order central  scheme  with  automatic  (solution-dependent)
blending function [[UFR_2-12_References#14|[14]]] is employed.
For the time integration,  implicit 2<sup>nd</sup>-order backward Euler scheme with sub-iterations was applied.
 
 
Finally, '''TUB''' applied their in-hose multi-block structured code ELAN  in the framework of  the  ''incompressible''  flow  assumption.
The  pressure velocity coupling is based on the SIMPLE algorithm.
For the  convective terms a hybrid approach [[UFR_2-12_References#14|[14]]]
with blending  of  2<sup>nd</sup>-order  central  and upwind-biased TVD schemes was used.
The time integration was similar to that of NTS.
 
 
The viscous terms of the governing  equations  in  all  the  codes  are approximated with the 2<sup>nd</sup> order centered scheme.
 
<div id="figure3"></div>
{|align="center" border="0" width="750"
|[[Image:UFR2-12_figure3a.png|740px]]
|-
|[[Image:UFR2-12_figure3b.png|740px]]||[[Image:UFR2-12_figure3_gnomon.png]]
|-
|colspan="2" align="center"|'''Figure 3:''' Mandatory grid in ''X-Y'' plane.
|}
 
All the simulations were carried out on  the  same,  "mandatory",  grid which ''X-Y'' cut
is shown in [[UFR_2-12_Test_Case#figure3|Figure 3]]).
This is a  multi-block  structured grid designed according to guidelines for  DES-like
simulations [[UFR_2-12_References#15|[15]]].
The grid has 5 main blocks: 1 block in the outer or Euler Region  (ER), 3 blocks in the Focus Region (FR), which includes the gap
between  the cylinders and the near wake of the downstream cylinder, and 1 block  in the Departure Region (DR).
The  distance  between  the  nodes  on  the forward half of the upstream cylinder is close  to  0.02''D''  and  on  its backward part
it is 0.01''D'' with smooth transition between the two.
As  a result, the total number of  nodes  on  the  surface  of  the  upstream cylinder is 245.
On the downstream cylinder  there  are  380  uniformly distributed nodes (the distance between the nodes is  0.008''D'').
In  the law of the wall units, the ''r''-step closest to cylinders  walls  is  less than 1.0.
In the major part of the FR the cells  are  nearly  isotropic with a size of about 0.02''D''.
In the ER and DR the  grid  steps  increase gradually (linearly with ''r'').
The total size of the grid in the ''XY'' plane is 82,000 cells.
 
 
According to recommendations of the organizers of the BANC-I  Workshop, a mandatory spanwise size of the computational domain,
''L''<sub>z</sub>, in  all  the simulations was set equal to 3''D''.
The grid-step in  span-direction,  &Delta;z, was 0.02''D'', resulting in the nearly cubic cells in the focus region  and a
total number of cells about 11 million.
 
 
The boundary conditions used in the simulations were as follows.
 
 
No-slip conditions were imposed on the  cylinders  walls  and  periodic conditions were used in the z-direction,
whereas the lateral boundaries were treated as frictionless walls (free-slip condition) in order to account for the blockage effect
of the sidewalls
of the experimental test-section at &plusmn;8.89''D''.
 
 
Inflow  and  outflow  boundary  conditions  were  different  in  the incompressible  and  compressible  simulations.
Particularly,  in  the compressible  simulations  of  BTU  and  DLR  characteristic  boundary conditions were imposed on both
inflow and outflow boundaries  with  no sponge  layers,  whereas  NTS  applied  boundary  conditions  of characteristic
type only at the inflow boundary, whereas at the outflow boundary a constant static pressure was specified,  and  the  remaining
flow parameters were extrapolated to the boundary from the interior  of the domain.
In order to avoid reflections of the waves from the outflow boundary, a sponge layer was used allocated to an additional
Cartesian grid block of length 15''D''.
 
 
In the  incompressible  simulations  of  NTS  a  uniform  velocity  and constant pressure were specified at  the  inflow  and  outflow
of  the domain respectively.
<br/>
<br/>
----
----
<references />
{{ACContribs
{{ACContribs
|authors=A. Garbaruk, M. Shur and M. Strelets
|authors=A. Garbaruk, M. Shur and M. Strelets
|organisation=
|organisation=New Technologies and Services LLC (NTS) and St.-Petersburg State Polytechnic University
}}
}}
{{UFRHeader
{{UFRHeader

Latest revision as of 14:30, 7 November 2019

Turbulent Flow Past Two-Body Configurations

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References

Flows Around Bodies

Underlying Flow Regime 2-12

Test Case Study

Brief Description of the Study Test Case

A detailed description of the chosen test case (TC with L = 3.7D) is available here. So in the following we present only its brief overview.


A schematic of the airflow past the TC configuration is shown in Figure 1. The model is comprised of two cylinders of equal diameter aligned with the streamwise flow direction. The polar angle, , is measured from the upstream stagnation point and is positive in the clockwise direction.


UFR2-12 figure1.png
Figure 1: Schematic of TC configuration [3]


Geometric and regime parameters defining the test case are summarized in Table 1.

Table 1: Flow parameters
Parameter Notation Value
Reynolds number Re= 1.66×105
Mach number M 0.128
Separation distance 3.7
TC aspect ratio 12.4
Cylinder diameter 0.05715 m
Free stream velocity 44 m/s
Free stream turbulence intensity 0.1%


The principal measured quantities by which the success or failure of CFD calculations are to be judged are as follows:

  • Mean Flow
    • Distributions of time-averaged pressure coefficient, , over the surface of both cylinders;
    • Distribution of time-averaged mean streamwise velocity along a line connecting the centres of the cylinders;
  • Unsteady Characteristics
    • Distributions of the root-mean-square (rms) of the pressure coefficient over the surface of both cylinders;
    • Power spectral density of the pressure coefficient (dB/Hz versus Hz) on the upstream cylinder at  = 135°;
    • Power spectral density of the pressure coefficient (dB/Hz versus Hz) on the downstream cylinder at  = 45°;
  • Turbulence kinetic energy
    • x – y cut of the field of time-averaged two-dimensional turbulent kinetic energy ;
    • 2D TKE distribution along y = 0;
    • 2D TKE distribution along x = 1.5 D (in the gap between the cylinders);
    • 2D TKE distribution along x = 4.45 D (0.75 D downstream of the centre of the rear cylinder).

All these and some other data are available here in both Windows and Unix compressed formats:

Windows Unix
readme.txt
problem_statement.pdf
problem_data_and_guidelines.pdf
data.zip data.tgz
figures.zip figures.tgz

These data are gratefully made available by the BANC-I Workshop.

Test Case Experiments

A detailed description of the experimental facility and measurement techniques is given in the original publications [2-4]. So here we present only concise information about these aspects of the test case.


UFR2-12 figure2.png
Figure 2: TC configuration in the BART facility [3]


Experiments have been conducted in the Basic Aerodynamic Research Tunnel (BART) at NASA Langley Research Center (see Figure 2). This is a subsonic, atmospheric wind-tunnel for investigation of the fundamental characteristics of complex flow-fields. The tunnel has a closed test section with a height of 0.711 m, a width of 1.016 m, and a length of 3.048 m. The span size of the cylinders was equal to the entire BART tunnel height, thus resulting in the aspect ratio Lz / D = 12.4. The free stream velocity was set to 44 m/s giving a Reynolds number based on cylinder diameter equal to 1.66 × 105 and Mach number equal to 0.128 (flow temperature T = 292 K).


The free stream turbulence level was less than 0.10%. In the first series of the experiments [2, 3], in order to ensure a turbulent separation from the upstream cylinder at the considered Reynolds number, the boundary layers on this cylinder were tripped between azimuthal locations of 50 and 60 degrees from the leading stagnation point using a transition strip. For the downstream cylinder, it was assumed that trip-like effect of turbulent wake impingement from the upstream cylinder would automatically ensure turbulent separation. However, later on [4] it was found that the effect of tripping of the downstream cylinder at L/D = 3.7 is also rather tangible (resulted in reduced peaks in mean Cp distribution along the rear cylinder, accompanied by an earlier separation from the cylinder surface, a reduced pressure recovery, lower levels of mean TKE in the wake and reduced levels of peak surface pressure fluctuations). For this reason, exactly these (with tripping of both cylinders) experimental data [4] were used for the comparison with fully turbulent CFD.


In the course of experiments, steady and unsteady pressure measurements were carried out along with 2-D Particle Image Velocimetry (PIV) and hot-wire anemometry used for documenting the flow interaction around the two cylinders (mean streamlines and instantaneous vorticity fields, shedding frequencies and spectra).


Information on the data accuracy available in the original publications [2-4] is summarized in Table 2. Most absolute values are given based on nominal tunnel conditions or on an average data value. Percentage values are quoted for parameters where the uncertainty equations were posed in terms of the uncertainty relative to the nominal value of the parameter.


Table 2: Estimated Experimental Uncertainties
Quantity Uncertainty
Steady Cp 0.02
Drag Coefficient 0.0005
PIV: Umean, Vmean 0.03 (normalized)
PIV: Spanwise velocity 1.8 (normalized)
PIV: TKE 4%
Power Spectral Density (PSD) 10 – 20%
Cp' rms 5 – 11%
Diameter, D; Sensor spacing Δz 0.005 inch

CFD Methods

The key physical features of the UFR (see Description) present significant difficulties for all the existing approaches to turbulence representation, whether from the standpoint of solution fidelity (for the conventional (U)RANS models) or in terms of computational expense for full LES (especially if the turbulent boundary layers are to be resolved). For this reason, most of the computational studies of multi-body flows, in general, and the TC configuration, in particular, are currently relying upon hybrid RANS-LES approaches. This is true also with regard to simulations carried out in the course of the BANC-I and II Workshops and in the framework of the ATAAC project, where different hybrid RANS-LES models of the DES type were used (see Table 3) [1].


Table 3: Summary of simulations
Partner Turbulence Modelling approach Compressible/Incompressible Lz Grid Side Walls
Beijing Tsinghua University BTU SST DDES Compressible 3D Mandatory Slip
German Aerospace Center, Göttingen DLR SA DDES Compressible 3D Mandatory Slip
New Technologies and Services, St.-Petersburg, Russia NTS SA DDES

SA IDDES

Incompressible and Compressible 3D, 16D Mandatory Slip
Technische Universität Berlin TUB SA DDES

SA IDDES

Incompressible 3D Mandatory Slip
SST - k–ω Shear Stress Transport model [9]; SA - Spalart-Allmaras model [10]; SA and SST DDES - Delayed DES based on the SA and SST models [11]; SA IDDES - Improved DDES based on the SA model [12].


As mentioned in the experiments section above, in the experiments the boundary layers on both cylinders were tripped ahead of their separation, thus justifying the "fully turbulent" simulations.


All the partners used their own flow solvers.


Particularly, BTU employed in-house compressible Navier-Stokes code with weighted, central-upwind, approximation of the inviscid fluxes based on a modification of the high-order symmetric total variation diminishing scheme. The method combines 6th order central and 5th order WENO schemes. For the time integration, an implicit LU-SGS algorithm is applied with Newton-like sub-iterations.


DLR used their unstructured TAU code with a finite volume compressible Navier-Stokes solver. The solver employs a standard central scheme with matrix dissipation with dual time stepping strategy of Jameson. The 3W Multi-Grid cycle was applied for the momentum and energy equations, whilst the SA transport equation was solved on the finest grid only. Time integration was performed with the use of explicit 3-level Runge-Kutta scheme. The method is of the 2nd order in both space and time.


NTS used in-house NTS finite-volume code. It is a structured code accepting multi-block overset grids of Chimera type. The incompressible branch of the code employs Rogers and Kwak's scheme [13] and for compressible flows Roe scheme is applied. The spatial approximation of the inviscid fluxes within these methods is performed differently in different grid blocks (see Figure 3 below). In particular, in the outer block, the 3rd-order upwind-biased scheme is used, whereas in the other blocks, a weighted 5th-order upwind-biased / 4th-order central scheme with automatic (solution-dependent) blending function [14] is employed. For the time integration, implicit 2nd-order backward Euler scheme with sub-iterations was applied.


Finally, TUB applied their in-hose multi-block structured code ELAN in the framework of the incompressible flow assumption. The pressure velocity coupling is based on the SIMPLE algorithm. For the convective terms a hybrid approach [14] with blending of 2nd-order central and upwind-biased TVD schemes was used. The time integration was similar to that of NTS.


The viscous terms of the governing equations in all the codes are approximated with the 2nd order centered scheme.

UFR2-12 figure3a.png
UFR2-12 figure3b.png UFR2-12 figure3 gnomon.png
Figure 3: Mandatory grid in X-Y plane.

All the simulations were carried out on the same, "mandatory", grid which X-Y cut is shown in Figure 3). This is a multi-block structured grid designed according to guidelines for DES-like simulations [15]. The grid has 5 main blocks: 1 block in the outer or Euler Region (ER), 3 blocks in the Focus Region (FR), which includes the gap between the cylinders and the near wake of the downstream cylinder, and 1 block in the Departure Region (DR). The distance between the nodes on the forward half of the upstream cylinder is close to 0.02D and on its backward part it is 0.01D with smooth transition between the two. As a result, the total number of nodes on the surface of the upstream cylinder is 245. On the downstream cylinder there are 380 uniformly distributed nodes (the distance between the nodes is 0.008D). In the law of the wall units, the r-step closest to cylinders walls is less than 1.0. In the major part of the FR the cells are nearly isotropic with a size of about 0.02D. In the ER and DR the grid steps increase gradually (linearly with r). The total size of the grid in the XY plane is 82,000 cells.


According to recommendations of the organizers of the BANC-I Workshop, a mandatory spanwise size of the computational domain, Lz, in all the simulations was set equal to 3D. The grid-step in span-direction, Δz, was 0.02D, resulting in the nearly cubic cells in the focus region and a total number of cells about 11 million.


The boundary conditions used in the simulations were as follows.


No-slip conditions were imposed on the cylinders walls and periodic conditions were used in the z-direction, whereas the lateral boundaries were treated as frictionless walls (free-slip condition) in order to account for the blockage effect of the sidewalls of the experimental test-section at ±8.89D.


Inflow and outflow boundary conditions were different in the incompressible and compressible simulations. Particularly, in the compressible simulations of BTU and DLR characteristic boundary conditions were imposed on both inflow and outflow boundaries with no sponge layers, whereas NTS applied boundary conditions of characteristic type only at the inflow boundary, whereas at the outflow boundary a constant static pressure was specified, and the remaining flow parameters were extrapolated to the boundary from the interior of the domain. In order to avoid reflections of the waves from the outflow boundary, a sponge layer was used allocated to an additional Cartesian grid block of length 15D.


In the incompressible simulations of NTS a uniform velocity and constant pressure were specified at the inflow and outflow of the domain respectively.


  1. Some participants of the BANC Workshops have used pure LES rather than DES-like approaches but these computations had the most difficulty simulating the high Reynolds aspects of the flow [5].


Contributed by: A. Garbaruk, M. Shur and M. Strelets — New Technologies and Services LLC (NTS) and St.-Petersburg State Polytechnic University

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