Navier-Stokes solutions of 2-D transonic flow over unconventional airfoils

117 Pages·2017·1.84 MB·English

by  R. A. Cox

Iowa State University Capstones, Theses and
Retrospective Theses and Dissertations
Dissertations
1989
Navier-Stokes solutions of 2-D transonic flow over
unconventional airfoils
R. A. Cox
Iowa State University
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Recommended Citation
Cox, R. A., "Navier-Stokes solutions of 2-D transonic flow over unconventional airfoils " (1989).Retrospective Theses and Dissertations.
8922.
https://lib.dr.iastate.edu/rtd/8922
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Navier-Stokes solutions of 2-D transonic flow over unconventional
airfoils
Cox, R. A., Ph.D.
Iowa State University, 1989
U M I
300N.ZeebRd.
Ann Aibor, MI 48106

Navier-Stokes solutions of 2-D transonic flow
over unconventional airfoils
by
R. A. Cox
A Dissertation Submitted to the
Graduate Faculty in Partial Fulfillment of the
Requirements for the Degree of
DOCTOR OF PHILOSOPHY
Major: Aerospace Engineering
Approved:
Signature was redacted for privacy.
Signature was redacted for privacy.
'For the Major Department
Signature was redacted for privacy.
For the Graduate College
Iowa State University
Ames, Iowa
1989
ii
TABLE OF CONTENTS
NOMENCLATURE v
ACKNOWLEDGEMENTS x
1 INTRODUCTION 1
2 GOVERNING EQUATIONS 4
2.1 Navier-Stokes Equations 4
2.2 Turbulence Model 6
2.2.1 Wall bounded shear flows 6
2.2.2 Wake model 14
3 NUMERICAL METHOD 17
3.1 Grid Generation 20
3.2 Finite-Volume Scheme 20
3.2.1 First-order scheme 21
3.2.2 Second-order scheme 23
3.2.3 Extension to nonuniform grids 25
3.2.4 TVD modifications 29
3.2.5 Viscous terms 33
iii
3.2.6 Implicit algorithm 36
3.3 Boundary Conditions 41
3.3.1 Wake cut 43
3.3.2 Airfoil surface 43
3.3.3 Farfield boundary 45
3.3.4 Downstream boundary 53
3.4 Initial Conditions 55
4 NUMERICAL RESULTS 58
4.1 Validation Test Cases 58
4.1.1 Flat plate 58
4.1.2 NACA 0012 61
4.2 Integrated Technology Airfoil A153W 74
5 CONCLUDING REMARKS 89
6 BIBLIOGRAPHY 91
7 APPENDIX: WAKE EDDY VISCOSITY 97
iv
LIST OF TABLES
Table 3.1: Boundary condition vectors 52
V
LIST OF FIGURES
Figure 1.1: Unconventional airfoil characteristics 2
Figure 3.1: Representative grid for a blunt trailing-edge airfoil 18
Figure 3.2: Computational domain for blunt trailing-edge airfoils .... 19
Figure 3.3: Flux generation 26
Figure 3.4: Cell scaling lengths 28
Figure 3.5: Boundary finite-volume cells 42
Figure 3.6: Far-field x-perturbation velocity 49
Figure 3.7: Far-field y-perturbation velocity 50
Figure 4.1: Variation of skin friction with momentum thickness Reynolds
number 60
Figure 4.2: NACA 0012 pressure coefficients (Moo = 0.5, a = 0°) .... 62
Figure 4.3: NACA 0012 pressure contours (Mm = 0.5, a = 0°) 63
Figure 4.4: NACA 0012 skin friction coefficients (Moo = 0.5, a = 0°) . . 64
Figure 4.5: NACA 0012 trailing-edge velocity vectors (Mœ = 0.5, a = 0°) 66
Figure 4.6: NACA 0012 trailing-edge velocity ve^rs (Moo = 0.5, a = 0°,
thin-layer approximation) 67
Figure 4.7: NACA 0012 pressure coefficients (Moo = 0.70, oc = 1.49°) • 69