cadieux aps presentation 2012
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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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DNS & LES of Separated Flows | 2
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.
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LAMINAR SEPARATION BUBBLE PROBLEM
Rex = 105
DNS & LES of Separated Flows | 3
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DNS & LES of Separated Flows | 4
WHY LES?RANS results for these types of flows are not reliable
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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
DNS & LES of Separated Flows | 5
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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
DNS & LES of Separated Flows | 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.
DNS & LES of Separated Flows | 7
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RESULTS: mean flow
DNS & LES of Separated Flows | 8
U/U0
Blasius *
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RESULTS: pressure & friction
DNS LES with dynamic Smagorinsky model- - UDNS
DNS & LES of Separated Flows | 8
Cp Cf
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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.
DNS & LES of Separated Flows | A4
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RESULTS: numerical dissipation
Total energy decay curves in turbulent boundary layer following the LSB as a function of time.
DNS & LES of Separated Flows | 10
UDNS
UDNS w/o filtering
- - UDNS w/o filtering + 18% larger
- - UDNS w/o filtering + 33% larger
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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.
DNS & LES of Separated Flows | 11
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END
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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
DNS & LES of Separated Flows | 12
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DNS DATABASES
DNS & LES of Separated Flows | 5
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SETUP: boundary conditions
Normalized wall-normal velocity top boundary condition. S & S 2000 (circles), UDNS (dashed line).
DNS & LES of Separated Flows | A1
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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).
DNS & LES of Separated Flows | A2
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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.
DNS & LES of Separated Flows | A3
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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]
DNS & LES of Separated Flows | A6
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