case c3.6 dns and les of the flow over a 2d periodic hil · case c3.6 dns and les of the flow over...

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1 Corentin Carton de Wiart Research Engineer, PhD Student (UCL)

Contact: [email protected]

Case C3.6 DNS and LES of the flow over a 2D periodic hill

2nd International Workshop on High-Order CFD Methods

Doc. ref.: PPPPPP-NS-000-00

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Motivation

•  Benchmark for wall-bounded turbulent flows, with smooth separation, recirculation and natural reattachment

•  Simple setup: periodic domain, 2D geometry •  Numerical and experimental

results available at wide range of Reynolds number

•  Possibility to assess solvers for

DNS, LES, WMLES, RANS-LES,… •  Detailed description, data, references,… on the

Ercoftac QNET-CFD wiki forum / 2D periodic hill

© 2013 Cenaero – All rights reserved HO Workshop C3.6

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Body force to provide the correct mass flow rate:

© 2013 Cenaero – All rights reserved

Geometry and flow conditions

HO Workshop C3.6

Testcase XXDNS and LES of the flow over a 2D periodic hill

K. Hillewaert†, C. Carton de Wiart

†and L. Bricteux

‡

†Cenaero, Argo group

‡Universite de Mons, Departement fluides et machines.

contact: koen.hillewaert at cenaero.be

1 Overview

This testcase has been taken up as a standard benchmark in ercoftac. See

• testcase 9.2 of the ERCOFTAC SIG 15 http://www.ercoftac.org/fileadmin/user_upload/bigfiles/sig15/database/9.2/index.html

• Underlying flow regime case 3-30 of the ERCOFTACQNET-CFD database.

http://uriah.dedi.melbourne.co.uk/w/index.php/UFR_3-30

for a thorough description.

2 Governing Equations

The incompressible or compressible Navier-Stokes equations should be used,

complemented by a subgrid scale model. The compressible fluid should have

the same behaviour as air, i.e. it should satisfy

γ =Cp

Cv= 1.4

Pr =µCp

κ= 0.71

(1)

with Cp and Cv the specific heats at constant pressure and volume respectively,

µ the dynamic viscosity and κ the heat conductivity.

3 Flow Conditions

The flow conditions are determined by the Reynolds number based upon the

bulk velocity above the crest

Reb =ubh

ν(2)

with

ub =1

2.035h

� 3.035h

hu(y)dy (3)

1



†and L. Bricteux

‡




1 Overview










γ =Cp

Cv= 1.4

Pr =µCp

κ= 0.71

(1)



3 Flow Conditions



Reb =ubh

ν(2)

with

ub =1

2.035h

� 3.035h

hu(y)dy (3)

1



†and L. Bricteux

‡




1 Overview










γ =Cp

Cv= 1.4

Pr =µCp

κ= 0.71

(1)



3 Flow Conditions



Reb =ubh

ν(2)

with

ub =1

2.035h

� 3.035h

hu(y)dy (3)

1



†and L. Bricteux

‡




1 Overview










γ =Cp

Cv= 1.4

Pr =µCp

κ= 0.71

(1)



3 Flow Conditions



Reb =ubh

ν(2)

with

ub =1

2.035h

� 3.035h

hu(y)dy (3)

1

h

9h 4.5h

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Mesh generated with IGG, curved with Gmsh


CGNS Gmsh (2nd order) 128 x 64 x 64 64 x 32 x 32 256 x 128 x 64 128 x 64 x 64 512 x 256 x 256 256 x 128 x 128

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Experimental/numerical results available

•  Experiments: •  Rapp (2009), Munich •  Re = [5.6, 10.6, 19, 37] x 103

•  Incompressible flow •  PIV and LDA agreement •  Periodicity achieved by using 10

successive hills and 18h in span

•  CFD: •  Breuer et al. (2009) •  MGLET and LESOCC:

•  Finite Volume methods (central) •  Incompressible solvers •  Explicit time-stepping

•  DNS and LES up to Re=37k © 2013 Cenaero – All rights reserved HO Workshop C3.6

Breuer et al. (2009)

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Summary of the reference CFD


Re Sim. Ntot/106 Nspan Δt/10-‐3 Tavg Code

1400 DNS 13.1 200 1.1 1249 LESOCC

1400 DNS 20.0 132 1.5 540 MGLET

2800 DNS 13.1 200 2.0 1249 LESOCC

2800 DNS 48.0 304 1.0 562 MGLET

5600 DNS 13.1 200 2.0 1214 LESOCC

5600 DNS 231.0 404 1.0 343 MGLET

10,595 LES 13.1 200 1.8 1277 LESOCC

10,595 LES 4.1 104 1.0 241 MGLET

37,000 LES 4.1 104 1.0 439 MGLET

DNS

LES

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Participants

•  Heinrich Luedeke, DLR •  DNS at Re = 2800, M=0.1 •  Compressible 4th order compact FD with 8th order Pade filter •  128 x 64 x 64 and 256 x 128 x 128 dof

•  David Moxey, Imperial College London •  DNS at Re = 2800 •  Incompressible 6th order SEM/Fourier pseudospectral method •  518 x 108 x 160 dof

•  Corentin Carton de Wiart, Cenaero •  DNS at Re = 2800, M=0.1 •  Compressible 4th order DGM/SIP •  512 x 256 x 256 dof (128 x 64 x 64 elem with p=3)


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Summary of contributors


ParBcipant Method Grid size DOF’s Time step Averaging period (tc)

CPU Bme (WU)/tc

Breuer et al. (2009) MGLET

FVM, Explicit RK3, Incomp.

…x…x304

48M

1.0 x 10-‐3

562

-‐

C. Carton de Wiart (Cenaero)

DG3, Implicit 3BDF, Comp.

512x256x256

33.5M

1.0 x10-‐2

180

193955

H. Luedeke (DLR)

4th order FD, Explicit RK4, Comp.

128x64x64 524.3k 1.0 x 10-‐4 723 4406

256x128x128 4.1M 5.0 x 10-‐5 270 102346

D. Moxey (Imperial College)

6th order SEM/PS, Explicit RK4, Incomp.

518x308x160

25.5M

1.0 x 10-‐3

70

31917

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Mean Velocity U


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Mean Velocity U - Zoom


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Mean Velocity V


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Correlations u’u’


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Correlations v’v’


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Correlations u’v’


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Conclusion

•  Overall agreement between the DNS results on the mean velocity profiles

•  To capture the averaged fluctuations, need very fine resolution (>10M dof), especially in the wake of the shearlayer

•  Still small discrepancies: •  Coarse mesh for DLR •  Average period should contain 200 tc of sampling (80 tc ICL, 180

for Cenaero) •  Influence of the time step on the forcing term and impact on the

statistics need to be investigated (Cenaero)

•  Need true reference for DNS… •  Expensive test case… Decrease Reynolds number? •  We need candidates to compute the LES at Re=10950!


case c3.6 dns and les of the flow over a 2d periodic hil · case c3.6 dns and les of the flow over...

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