Reynolds-Stress Model Dual-Time-Stepping Computation of Unsteady Three-Dimensional Flows

AIAA Journal

Volumn 41, Issue 10, 2003, Pages 1882-1894

  Chassaing, J C ^a,b   Gerolymos, G A ^a,c   Vallet, I ^a,b  

^a SORBONNE UNIVERSITÉ   (France)

^b U Propre Ctr Natl la Rech Sci   (France)

^c Laboratoire d'Energétique   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; STRESS ANALYSIS;

THREE-DIMENSIONAL FLOW;

UNSTEADY FLOW;

EID: 0142055958     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/2.1904     Document Type: Article

References (63)

1. Rai, M. M., "3-D Navier-Stokes Simulations of Turbine Rotor/Stator Interaction; Part I - Methodology," Journal of Propulsion and Power, Vol. 5, No. 3, 1989, pp. 305-311.
2. Hah, C., Puterbaugh, S. L., and Copenhaver, W. W., "Unsteady Aerodynamic Flow Phenomena in a Transonic Compressor Stage," Journal of Propulsion and Power, Vol. 13, No. 3, 1997, pp. 329-333; also AIAA Paper 93-1868, June 1993.
3. Sayma, A. I., Vahdati, M., Sbardella, L., and Imregun, M., "Modeling of Three-Dimensional Viscous Compressible Turbomachinery Flows Using Unstructured Hybrid Grids," AIAA Journal, Vol. 38, No. 6, 2000, pp. 945-954.
4. Volmar, T. W., Brouillet, B., Gallus, H. E., and Benetschik, H., "Time-Accurate Three-Dimensional Navier-Stokes Analysis of 1 1/2 stage Axial-Flow Turbine," Journal of Propulsion and Power, Vol. 16, No. 2, 2000, pp. 327-335.
5. Yao, J., Davis, R. L., Alonso, J. J., and Jameson, A., "Massively Parallel Simulation of the Unsteady Flow in an Axial Turbine Stage," Journal of Propulsion and Power, Vol. 18, No. 2, 2002, pp. 465-471.
6. Obahashi, S., Guruswamy, G. P., and Goorjian, P. M., "Streamwise Upwind Algorithm for Computing Unsteady Transonic Flows past Oscillating Wings," AIAA Journal, Vol. 29, No. 10, 1991, pp. 1668-1677.
7. Lee-Rausch, E. M., and Batina, J. T., "Wing Flutter Computations Using an Aerodynamic Model Based on the Navier-Stokes Equations," Journal of Aircraft, Vol. 33, No. 6, 1996, pp. 1139-1147.
8. Gordnier, R. E., and Melville, R. B., "Transonic Flutter Simulations Using an Implicit Aeroelastic Solver," Journal of Aircraft, Vol. 37, No. 5, 2000, pp. 872-879.
9. Weber, S., and Platzer, M. F., "A Navier-Stokes Analysis of the Stall Flutter Characteristics of the Buffum Cascade," Journal of Turbomachinery, Vol. 122, Oct. 2000, pp. 769-776.
10. Gerolymos, G. A., Vallet, I., Bölcs, A., and Ott, P., "Computation of Unsteady Three-Dimensional Transonic Nozzle Flow Using k-ε Turbulence Closure," AIAA Journal, Vol. 34, No. 7, 1996, pp. 1321-1330.
11. Hah, C., Rabe, D. C., Sullivan, T. J., and Wadia, A. R., "Effects of Inlet Distortion on the Flow Field in a Transonic Compressor Rotor," Journal of Turbomachinery, Vol. 120, April 1998, pp. 233-246.
12. Ekaterinaris, J. A., "Numerical Investigations of Dynamic Stall Active Control for Incompressible and Compressible Flows," Journal of Aircraft, Vol. 39, No. 1, 2002, pp. 71-78.
13. Liou, M. S., and Coakley, T. J., "Numerical Simulations of Unsteady Transonic Flow in Diffusers," AIAA Journal, Vol. 22, No. 8, 1984, pp. 1139-1145.
14. Hsieh, T., Bogar, T. J., and Coakley, T. J., "Numerical Simulation and Comparison with Experiment for Self-Excited Oscillations in a Diffuser Flow," AIAA Journal, Vol. 25, No. 7, 1987, pp. 936-943.
15. Rizzetta, D. P., "Numerical Simulation of Supersonic Flow over a 3-D Cavity," AIAA Journal, Vol. 26, No. 7, 1988, pp. 799-807.
16. Yamamoto, K., and Tanida, Y., "Self-Excited Oscillation of Transonic Flow Around an Airfoil in 2-D Channels," Journal of Turbomachinery, Vol. 112, Oct. 1990, pp. 723-731.
17. He, L., "Computational Study of Rotating Stall Inception in Axial Compressors," Journal of Propulsion and Power, Vol. 13, No. 1, 1997, pp. 31-38.
18. Hartwich, P. M., Dobbs, S. K., Arslan, A. E., and Kim, S. C., "Navier-Stokes Computations of Limit-Cycle Oscillations for a B-1-Like Configuration," Journal of Aircraft, Vol. 38, No. 2, 2001, pp. 239-247.
19. Weber, S., Jones, K. D., Ekaterinaris, J. A., and Platzer, M., "Transonic Flutter Computations for the NLR 7301 Supercritical Airfoil," Aerospace Science and Technology, Vol. 5, 2001, pp. 293-304.
20. Grüber, B., and Carstens, V., "The Impact of Viscous Effects on the Aerodynamic Damping of Vibrating Transonic Compressor Blades - A Numerical Study," Journal of Turbomachinery, Vol. 123, 2001, pp. 409-417.
21. Tardu, S. F., and Binder, G., "Wall Shear Stress Modulation in Unsteady Turbulent Channel Flow with High Imposed Frequencies," Physics of Fluids A, Vol. 5, No. 8, 1993, pp. 2028-2037.
22. Fan, S., Lakshminarayana, B., and Barnett, M., "Low-Reynolds-Number k-ε Model for Unsteady Turbulent Boundary-Layer Flows," AIAA Journal, Vol. 31, No. 10, 1993, pp. 1777-1784.
23. Hankey, W. L., and Calarese, W., "Reynolds Stresses for Unsteady Turbulent Flows," AIAA Journal, Vol. 21, No. 8, 1983, pp. 1210, 1211.
24. Rizzetta, D. P., and Visbal, M. R., "Comparative Numerical Study of Two Turbulence Models for Airfoil Static and Dynamic Stall," AIAA Journal, Vol. 31, No. 4, 1993, pp. 784-786.
25. Ekaterinaris, J. A., and Menter, F. R., "Computation of Oscillating Airfoil Flows with One- and Two-Equation Turbulence Models," AIAA Journal, Vol. 32, No. 12, 1994, pp. 2359-2365.
26. Ji, S., and Liu, F., "Flutter Computation of Turbomachinery Cascades Using a Parallel Unsteady Navier-Stokes Code," AIAA Journal, Vol. 37, No. 3, 1999, pp. 320-327.
27. Choi, S. W., Chang, K. S., and Ok, H., "Parametric Study of Transient Spoiler Aerodynamics with 2-Equation Turbulence Models," Journal of Aircraft, Vol. 38, No. 5, 2001, pp. 888-894.
28. Hanjalić, K., "Advanced Turbulence Closure Models: A View of Current Status and Future Prospects," International Journal of Heat Fluid Flow, Vol. 15, No. 3, 1994, pp. 178-203.
29. Rodi, W., "A New Algebraic Relation for Calculating the Reynolds Stresses," Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 56, 1976, pp. T219-T221.
30. Gatski, T. B., and Speziale, C. G., "On Explicit Algebraic Stress Models for Complex Turbulent Flows," Journal of Fluid Mechanics, Vol. 254, 1993, pp. 59-78.
31. Sotiropoulos, F., and Patel, V. C., "Application of Reynolds-Stress Transport Models to Stern and Wake Flows," Journal of Ship Research, Vol. 39, No. 4, 1995, pp. 263-283.
32. Gerolymos, G. A., and Vallet, I., "Near-Wall Reynolds-Stress Three-Dimensional Transonic Flow Computation," AIAA Journal, Vol. 35, No. 2, 1997, pp. 228-236.
33. Chenault, C. F., Beran, P. S., and Bowersox, R. D. W., "Numerical Investigation of Supersonic Injection Using a Reynolds-Stress Turbulence Model," AIAA Journal, Vol. 37, No. 10, 1999, pp. 1257-1269.
34. Batten, P., Craft, T. J., Leschziner, M. A., and Loyau, H., "Reynolds-Stress-Transport Modeling for Compressible Aerodynamics Applications," AIAA Journal, Vol. 37, No. 7, 1999, pp. 785-797.
35. Gerolymos, G. A., and Vallet, I., "Wall-Normal-Free Reynolds-Stress Closure for Three-Dimensional Compressible Separated Flows," AIAA Journal, Vol. 39, No. 10, 2001, pp. 1833-1842.
36. Gerolymos, G. A., Neubauer, J., Sharma, V. C., and Vallet, I., "Improved Prediction of Turbomachinery Flows Using Near-Wall Reynolds-Stress Model," Journal of Turbomachinery, Vol. 124, Jan. 2002, pp. 86-99.
37. Pettersson, B. A., Andersson, H. I., and Brunvoll, A. S., "Modeling near-Wall Effects in Axially Rotating Pipe Flow by Elliptic Relaxation," AIAA Journal, Vol. 36, No. 7, 1998, pp. 1164-1170.
38. Gerolymos, G. A., and Vallet, I., "Contribution to Single-Point-Closure Reynolds-Stress Modelling in Inhomogeneous Flow," American Society of Mechanical Engineers, Paper FEDSM2003-45346, July 2003.
39. Jakirlić, S., and Hanjalić, K., "A New Approach to Modelling near-Wall Turbulence Energy and Stress Dissipation," Journal of Fluid Mechanics, Vol. 459, 2002, pp. 139-166.
40. Pantano, C., and Sarkar, S., "A Study of Compressibility Effects in the High-Speed Turbulent Shear Layer Using Direct Simulation," Journal of Fluid Mechanics, Vol. 451, 2002, pp. 329-371.
41. Wilcox, D. C., "Multiscale Model for Turbulent Flows," AIAA Journal, Vol. 26, No. 11, 1988, pp. 1311-1320.
42. Chassaing, J. C., Gerolymos, G. A., and Vallet, I., "Efficient and Robust Reynolds-Stress Model Computation of Three-Dimensional Compressible Flows," AIAA Journal, Vol. 41, No. 5, 2003, pp. 763-773.
43. Morrison, J. H., "A Compressible Navier-Stokes Solver with 2-Equation and Reynolds-Stress Turbulence Closure Models," NASA CR 4440, May 1992.
44. Vallet, I., "Aérodynamique Numérique 3-D Instationnaire avec Fermeture Bas-Reynolds au Second Ordre," Ph.D. Dissertation, Université Pierreet-Marie-Curie, Paris, Dec. 1995.
45. Batten, P., Leschziner, M. A., and Goldberg, U. C., "Average-State Jacobians and Implicit Methods for Compressible Viscous and Turbulent Flows," Journal of Computational Physics, Vol. 137, 1997, pp. 38-78.
46. Rogers, S. E., Kwak, D., and Kris, C., "Steady and Unsteady Solutions of the Incompressible Navier-Stokes Equations," AIAA Journal, Vol. 29, No. 4, 1991, pp. 603-610.
47. Jameson, A., "Time-Dependent Calculations Using Multigrid, with Applications to Unsteady Flows past Airfoils and Wings," AIAA Paper 91-1596, June 1991.
48. Rumsey, C. L., Sanetrik, M. D., Bierdon, R. T., Melson, N. D., and Parlette, E. B., "Efficiency and Accuracy of Time-Accurate Turbulent Navier-Stokes Computations," Computers and Fluids, Vol. 25, No. 2, 1996, pp. 217-236.
49. Dubuc, L., Cantariti, F., Woodgate, M., Gribben, B., Badcock, K. J., and Richards, B. E., "Solution of the Unsteady Euler Equations Using an Implicit Dual-Time Method," AIAA Journal, Vol. 36, No. 8, 1998, pp. 1417-1424.
50. Landon, R. H., "NACA_0012 Oscillatory and Transient Pictching, " Compendium of Unsteady Aerodynamic Measurements, R-702, AGARD, 1982, pp. 3.1-3.25.
51. Ott, P., Bölcs, A., and Fransson, T. H., "Experimental and Numerical Study of the Time-Dependent Pressure Response of a Shock-Wave Oscillating in a Nozzle," Journal of Turbomachinery, Vol. 117, Jan. 1995, pp. 106-114.
52. Launder, B. E., and Shima, N., "2-Moment Closure for the near-Wall Sublayer: Development and Application," AIAA Journal, Vol. 27, No. 10, 1989, pp. 1319-1325.
53. Thomas, P. D., and Lombard, C. K., "Geometric Conservation Law and its Application to Flow Computations on Moving Grids," AIAA Journal, Vol. 17, No. 10, 1979, pp. 1030-1037.
54. Slater, J. W., Liou, M. S., and Hindman, R. G., "Approach for Dynamic Grids," AIAA Journal, Vol. 33, No. 1, 1995, pp. 63-68.
55. Hixon, R., "Numerically Consistent Strong Conservation Grid Motion for Finite-Difference Schemes," AIAA Journal, Vol. 38, No. 9, 2000, pp. 1586-1593.
56. Anderson, W. K., Thomas, J. L., and Rumsey, C. L., "Extension and Application of Flux-Vector-Splitting to Calculations on Dynamic Meshes," AIAA Journal, Vol. 27, No. 6, 1989, pp. 673, 674; also AIAA Paper 87-1152, June 1987.
57. Anderson, W. K., Thomas, J. L., and Rumsey, C. L., "Extension and Application of Flux-Vector-Splitting to Calculations on Dynamic Meshes," AIAA Journal, Vol. 27, No. 6, 1989, pp. 673, 674; also AIAA Paper 87-1152, June 1987.
58. Anderson, W. K., Thomas, J. L., and Van Leer, B., "Comparison of Finite-Volume Flux-Vector-Splittings for the Euler Equations," AIAA Journal, Vol. 24, No. 9, 1986, pp. 1453-1460.
59. Thomas, J. L., Taylor-Krist, S., and Anderson, W. K., "Navier-Stokes Computations of Vortical Flows over Low-Aspect-Ratio Wings," AIAA Journal, Vol. 28, No. 2, 1990, pp. 205-212.
60. Chassaing, J. C., "Aérodynamique 3-D et Aéroélasticité Nonlinéaire et Linéarisée en Temps," Ph.D. Dissertation, Université Pierre-et-Marie-Curie, Paris, Jan. 2002.
61. Schumann, U., "Realizability of Reynolds-Stress Turbulence Models," Physics of Fluids, Vol. 20, No. 5, 1977, pp. 721-725.
62. Gerolymos, G. A., and Tsanga, G., "Biharmonic 3-D Grid Generation for Axial Turbomachinery with Tip-Clearance," Journal of Propulsion and Power, Vol. 15, No. 3, 1999, pp. 476-479.
63. Launder, B. E., and Sharma, B. I., "Application of the Energy Dissipation Model of Turbulence to the Calculation of Flows near a Spinning Disk," Letters in Heat and Mass Transfer, Vol. 1, 1974, pp. 131-138.