DNS and LES of Separated Flows at Moderate Reynolds Numbers

Francois Cadieux, Julian A. DomaradzkiTaraneh Sayadi, Sanjeeb Bose

AcknowledgementsNASA/Stanford Center for Turbulence Research summer program 2012

Dr. Spalart for providing DNS dataCPU time on Certainty Linux cluster

NSF grant CBET-1233160

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GOALSAssess the capability of LES to reduce computational requirements for simulating separated flows at moderate Reynolds numbers: test the accuracy of LES predictions at resolutions on the order of 1% of DNS resolution.

CONTEXTEnabling accurate 3D wing and blade shape optimization for wind turbines, UAVs, and turbomachinery.

LAMINAR SEPARATION BUBBLE PROBLEM

Rex = 105

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WHY LES?RANS results for these types of flows are not reliable

CODE: numericsSolves full compressible LES equations on staggered grid in curvilinear coordinates

Sixth-order compact finite differences (Prof. Lele)

Implicit (2nd order A-stable) & explicit (RK3) time integration scheme

Compact filtering used at each time step in streamwise and wall-normal directions for stability and matching between explicit and implicit grid

Numerical sponges extend domain to stop reflections and apply suction

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RUN PARAMETERS

RESOLUTION y+(x=7)

DNS 59 x 106 pts 0.5

LES 3.9% of DNS 1.0w/ Dynamic Smag.model

UDNS 1% of DNS 1.6

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RESULTS: vorticity in DNS

Iso-surfaces of vorticity: Kelvin-Helmholtz rolls are visible over the separated shear layer leading to transition to turbulence andsubsequent turbulent flow reattachment, closing of the separation bubble.

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RESULTS: mean flow

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U/U0

Blasius *

RESULTS: pressure & friction

DNS LES with dynamic Smagorinsky model- - UDNS

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Cp Cf

RESULTS: numerical dissipation

1. From restart file after steady state is reached, run regular code for 10 time steps.

2. From same restart file, run code with explicit filtering turned off completely for 10 time steps.

3. Compare total energy curves for x=5 to x=7 and y=0 to y=0.5.

4. Repeat step 2 with higher molecular viscosity until total energy curve matches that of regular run.

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RESULTS: numerical dissipation

Total energy decay curves in turbulent boundary layer following the LSB as a function of time.

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UDNS

UDNS w/o filtering

- - UDNS w/o filtering + 18% larger

- - UDNS w/o filtering + 33% larger

CONCLUSIONS

Time avg Cf, Cp, separation and reattachment point predicted accurately with 1% of DNS resolution. Takes ~5 hrs vs 1 week for DNS.

No-model UDNS performed better than LES due to explicit filtering dissipating enough energy.

SGS models could not be assessed because filtering req for stability acts as implicit SGS model.

Future work: use non-dissipative code to assess SGS models for these LSB flows.

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END

ACKNOWLEDGEMENTS

NASA/Stanford Center for Turbulence Research summer program 2012

Dr. P. Spalart for providing DNS data

CPU time on Certainty Linux cluster (http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0960306)

NSF grant CBET-1233160

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DNS DATABASES

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SETUP: boundary conditions

Normalized wall-normal velocity top boundary condition. S & S 2000 (circles), UDNS (dashed line).

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RESULTS: numerical dissipation

Total energy increase in turbulent boundary layer following the LSB as a function of time. UDNS (squares), UDNS without filtering (line), UDNS without filtering and 18% larger molecular viscosity (dashed line), UDNS without filtering and 33% larger molecular viscosity (dash-dotted line).

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LIMITATIONS

Favorable pressure gradient exists after x=5 caused by the inflow top boundary condition.

Favorable pressure gradients are seldom encountered on the suction side of airfoils in MAVs and blades in turbo-machinery.

Favorable pressure gradient artificially improves agreement of LES and UDNS results with the DNS benchmark because of its effect on the reattachment location.

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CODE: numerical sponges

Sponges are located as follows:

X=[0.03,0.5], X=[8,9.2], y/Y=[1,1.8]

Suction is imposed gradually from: y/Y=[1,1.4]

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