A Kriging-based method for the parametrization of the response surface spanned by uncertain parameters in computational fluid dynamics is proposed. A multiresolution approach in the sampling space is used to improve the accuracy of the method. It is illustrated considering the problem of the computation of the corrections needed to recover equivalent free-flight conditions from wind-tunnel experiments. Using the surface response approach, optimal corrected values of the freestream Mach number and the angle of attack for the compressible turbulent flow around the RAE 2822 wing are computed. The use of the response surface to gain an insight into the sensitivity of the results with respect to other parameter is also assessed.

Issue Section:
Technical Papers
Keywords:
wind tunnels, computational fluid dynamics, Mach number, compressible flow, turbulence, aerodynamics, kriging, spatial interpolators, optimization, ELSA code, error estimation and control, validation of CFD simulations
Topics:
Computational fluid dynamics, Mach number, Turbulence, Wind tunnels, Simulation, Response surface methodology, Flow (Dynamics), Errors
1.
Haase
,
W.
,
Brandsma
,
F.
,
Elsholz
,
F.
,
Leschziner
,
M.
, and
Schwamborn
,
D.
, eds., 1993,
An European Initiative on Validation of CFD-Codes
,
Notes on Numerical Fluid Mechanics
,
Vieweg-Verlag
,
Braunschweig
.
2.
Cook
,
P. H.
,
McDonald
,
M. A.
, and
Firmin
,
M. C. P.
, “
Aerofoil RAE 2822-Pressure Distributions and Boundary Layer and Wake Measurements
,” AGARD AR 138, pp.
A6
-1–A6-
77
.
3.
Barber
,
T. J.
, 1998, “
Role of Code Validation and Certification in the Design Environment
,”
AIAA J.
0001-1452,
36
(
5
), pp.
753
–
758
.
4.
Benek
,
J. A.
,
Lauer
,
R. F.
, and
Kraft
,
E. M.
, 1998, “
Validation Issues for Engine-Airframe Integration
,”
AIAA J.
0001-1452,
36
(
5
), pp.
759
–
764
.
Crossref
Search ADS
 
5.
Rumsey
,
C. L.
,
Gatski
,
T. B.
, and
Bertelrud
,
A.
, 1998, “
Prediction of High-Lift Flows Using Turbulent Closure Models
,”
AIAA J.
0001-1452,
36
(
5
), pp.
765
–
774
.
Crossref
Search ADS
 
6.
Roache
,
P. J.
, 1998, “
Verification of Codes and Calculations
,”
AIAA J.
0001-1452,
36
(
5
), pp.
697
–
702
.
7.
Rizzi
,
A.
, and
Vos
,
J.
, 1998, “
Toward Establishing Credibility in Computational Fluid Dynamics Simulations
,”
AIAA J.
0001-1452,
36
(
5
), pp.
668
–
675
.
Crossref
Search ADS
 
8.
Mehta
,
U. B.
, 1998, “
Credible Computational Fluid Dynamics Simulations
,”
AIAA J.
0001-1452,
36
(
5
), pp.
665
–
667
.
Crossref
Search ADS
 
9.
Hellstrom
,
T.
, and
Davidson
,
L.
, 1994, “
Reynolds Stress Transport Modelling of Transonic Flow Around the RAE2822 Airfoil
,” AIAA Paper No. 94-0309.
10.
Krige
,
D. G.
, 1951, “
A Statistical Approach to Some Basic Mine Valuations Problems on the Witwatersrand
,”
J. Chem. Metal. Mining Soc. S. Africa
,
52
, pp.
119
–
139
.
11.
Cambier
,
L.
, and
Gazaix
,
M.
, 2002, “
ELSA: An Efficient Object-Oriented Solution to CFD Complexity
,”
40th AIAA Aerospace Science Meeting & Exhibit
, Reno, AIAA Paper No. 2002-0108.
12.
Jameson
,
A.
, 1982,
Steady State Solutions of the Euler Equations for Transonic Flow by a Multigrid Method
,
Advances in Scientific Comput.
,
Academic Press
,
New York
, pp.
37
–
70
.
13.
Jameson
,
A.
,
Schmidt
,
W.
, and
Turkel
,
E.
, 1981, “
Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes
,” AIAA Paper No. 81-1259.
14.
Yoon
,
S.
, and
Jameson
,
A.
, 1987, “
An LU-SSOR Scheme for the Euler and Navier-Stokes Equations
,” AIAA Paper No. 87-0600.
15.
Spalart
,
P. R.
, and
Allmaras
,
S. R.
, 1994, “
A One-Equation Turbulence Model for Aerodynamic Flows
,”
Rech. Aerosp.
0034-1223,
1
, pp.
5
–
21
.
16.
Deniau
,
H.
, 1996, “
Calcul d’Écoulements Supersoniques Pour la Résolution des Équations de Navier-Stokes Parabolisées: Modélisation de la Turbulence, Traitement des Poches Supersoniques
,” Ph.D. thesis, Ecole Nationale Supérieure de l’Aéronautique et de l’Espace.
17.
Jones
,
W. P.
, and
Launder
,
B. I.
, 1972, “
The Prediction of Laminarization With a 2-Equations Model of Turbulence
,”
Int. J. Heat Mass Transfer
0017-9310,
15
, pp.
301
–
314
.
Crossref
Search ADS
 
18.
Wilcox
,
D. C.
, 1994, “
Simulation of Transition with a Two-Equation Turbulence Model
,”
AIAA J.
0001-1452,
32
(
2
), pp.
247
–
255
.
Crossref
Search ADS
 
19.
Smith
,
B. R.
, 1990, “
The k-kl Turbulence Model and Wall Layer Model for Compressible Flows
,” AIAA Paper No. 90-1483.
20.
Dubrule
,
O.
, 1984, “
Comparing Splines and Kriging
,”
Comput. Geosci.
0098-3004,
10
(
2–3
), pp.
327
–
333
.
21.
Oliver
,
M. A.
, and
Webster
,
R.
, 1990, “
Kriging: A Method of Interpolation for Geographical Information System
,”
Int. J. Geogr. Inf. Syst.
0269-3798,
4
(
3
), pp.
313
–
332
.
Crossref
Search ADS
 
22.
Christakos
,
G.
, and
Hristopulos
,
D. T.
, 1988, “
Spatiotemporal Environmental Health Modelling
,”
Kluwer
,
Dordrecht
.
23.
Journel
,
A. G.
, and
Huijbregts
,
C. J.
, 1978,
Mining Geostatistics
,
Academic Press
,
New York
, pp.
600
.
24.
Sacks
,
J.
,
Schiller
,
S.
, and
Welch
,
W.
, 1989, “
Designs for Computer Experiments
,”
Technometrics
0040-1706,
31
, pp.
41
–
47
.
Crossref
Search ADS
 
Copyright © 2006
 by American Society of Mechanical Engineers
You do not currently have access to this content.