AIAA%202002-5531%20OBSERVATIONS%20ON%20CFD%20SIMULATION%20UNCERTAINTIES

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AIAA 2002-5531OBSERVATIONS ON CFD SIMULATION
UNCERTAINTIES

• Serhat Hosder, Bernard Grossman, William H.
  Mason, and
• Layne T. Watson
• Virginia Polytechnic Institute and State
  University
• Blacksburg, VA
• Raphael T. Haftka
• University of Florida
• Gainesville, FL
• 9th AIAA/ISSMO Symposium on Multidisciplinary
  Analysis and Optimization
• 4-6 September 2002
• Atlanta, GA

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Introduction

• Computational fluid dynamics (CFD) as an
  aero/hydrodynamic analysis and design tool
• CFD being used increasingly in multidisciplinary
  design and optimization (MDO) problems
• Different levels of fidelity
• from linear potential solvers to RANS codes
• CFD results have an associated uncertainty,
  originating from different sources
• Sources and magnitudes of the uncertainty
  important to assess the accuracy of the results

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Drag polar results from 1st AIAA Drag Prediction
Workshop (Hemsch, 2001)
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Objective of the Paper

• Finding the magnitude of CFD simulation
  uncertainties that a well informed user may
  encounter and analyzing their sources
• We study 2-D, turbulent, transonic flow in a
  converging-diverging channel
• complex fluid dynamics problem
• affordable for making multiple runs

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Transonic Diffuser Problem
Weak shock case (Pe/P0i0.82)
Pe/P0i
experiment
CFD
Strong shock case (Pe/P0i0.72)
Pe/P0i
Separation bubble
streamlines
Contour variable velocity magnitude
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Uncertainty Sources (following Oberkampf and
Blottner)

• Physical Modeling Uncertainty
• PDEs describing the flow
• Euler, Thin-Layer N-S, Full N-S, etc.
• boundary conditions and initial conditions
• geometry representation
• auxiliary physical models
• turbulence models, thermodynamic models, etc.
• Discretization Error
• Iterative Convergence Error
• Programming Errors

We show that uncertainties from different
sources interact
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Computational Modeling

• General Aerodynamic Simulation Program (GASP)
• A commercial, Reynolds-averaged, 3-D, finite
  volume Navier-Stokes (N-S) code
• Has different solution and modeling options. An
  informed CFD user still uncertain about which
  one to choose
• For inviscid fluxes (most commonly used options
  in CFD)
• Upwind-biased 3rd order accurate Roe-Flux scheme
• Flux-limiters Min-Mod and Van Albada
• Turbulence models (typical for turbulent flows)
• Spalart-Allmaras (Sp-Al)
• k-? (Wilcox, 1998 version) with Sarkars
  compressibility correction

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Grids Used in the Computations
Grid 2
y/ht
A single solution on grid 5 requires
approximately 1170 hours of total node CPU time
on a SGI Origin2000 with six processors (10000
cycles)
Grid level Mesh Size (number of cells)
1 40 x 25
2 80 x 50
3 160 x 100
4 320 x 200
5 640 x 400
Grid 2 is the typical grid level used in CFD
applications
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Nozzle efficiency
Nozzle efficiency (neff ), a global indicator of
CFD results H0i Total enthalpy at the
inlet He Enthalpy at the exit Hes Exit
enthalpy at the state that would be reached by
isentropic expansion to the actual pressure at
the exit
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Uncertainty in Nozzle Efficiency
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Uncertainty in Nozzle Efficiency
Strong Shock
Weak Shock
Maximum value of
the total variation in nozzle efficiency 10 4
the discretization error 6 (Sp-Al) 3.5 (Sp-Al)
the relative uncertainty due to the selection of turbulence model 9 (grid 4) 2 (grid 2)
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Discretization Error by Richardsons Extrapolation
order of the method
error coefficient
a measure of grid spacing
grid level
Turbulence model Pe/P0i estimate of p (observed order of accuracy) estimate of (neff)exact Grid level Discretization error ()
Sp-Al 0.72 (strong shock) 1.322 0.71950 1 14.298
Sp-Al 0.72 (strong shock) 1.322 0.71950 2 6.790
Sp-Al 0.72 (strong shock) 1.322 0.71950 3 2.716
Sp-Al 0.72 (strong shock) 1.322 0.71950 4 1.086
Sp-Al 0.82 (weak shock) 1.578 0.81086 1 8.005
Sp-Al 0.82 (weak shock) 1.578 0.81086 2 3.539
Sp-Al 0.82 (weak shock) 1.578 0.81086 3 1.185
Sp-Al 0.82 (weak shock) 1.578 0.81086 4 0.397
k- ? 0.82 (weak shock) 1.656 0.82889 1 4.432
k- ? 0.82 (weak shock) 1.656 0.82889 2 1.452
k- ? 0.82 (weak shock) 1.656 0.82889 3 0.461
k- ? 0.82 (weak shock) 1.656 0.82889 4 0.146
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Major Observations on the Discretization Errors

• Grid convergence is not achieved with grid levels
  that have moderate mesh sizes. For the strong
  shock case, even with the finest mesh level we
  can afford, asymptotic convergence is not certain
• As a consequence of above result, it is difficult
  to separate physical modeling uncertainties from
  numerical errors
• Shock-induced flow separation, thus the flow
  structure, has a significant effect on grid
  convergence
• Discretization error magnitudes are different for
  different turbulence models. The magnitudes of
  numerical errors are affected by the physical
  models chosen.

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Error in Geometry Representation
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Error in Geometry Representation

• Upstream of the shock, discrepancy between the
  CFD results of original geometry and the
  experiment is due to the error in geometry
  representation.
• Downstream of the shock, wall pressure
  distributions are the same regardless of the
  geometry used.

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Error in Geometry Representation

• In nozzle efficiency, the uncertainty due to the
  error in geometry representation is not as large
  as the uncertainties originating from the other
  sources
• negligible for the strong shock case
• can be up to 1.4 for the weak shock case

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Downstream Boundary Condition
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Downstream Boundary Condition

• Extending the geometry or changing the exit
  pressure ratio affect
• location and strength of the shock
• size of the separation bubble

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Conclusions

• Based on the results obtained from this study,
• For attached flows without shocks (or with weak
  shocks), informed users may obtain reasonably
  accurate results
• They may get large errors for the cases with
  strong shocks and substantial separation
• Grid convergence is not achieved with grid levels
  that have moderate mesh sizes (especially for
  separated flows)
• The flow structure has a significant effect on
  the grid convergence
• It is difficult to isolate physical modeling
  uncertainties from numerical errors

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Conclusions

• Uncertainties from different sources interact,
  especially in the simulation of flows with
  separation
• The magnitudes of numerical errors are influenced
  by the physical models (turbulence models)
  used
• In nozzle efficiency results,
• range of variation for the strong shock is much
  larger than the one observed in the weak
  shock case (10 vs. 4)
• the error between grid level 2 and grid level 4
  can be up to 6 (strong shock)
• relative uncertainty due to the selection of the
  turbulence model can be as large as 9 (strong
  shock)