Calculation of Sphere-Cone Heat Transfer in High-Speed Flow with Commercial Software
The most common turbulence models and the validation results brief overview is given. Calculation results of the high-speed flow around blunted cone are presented. Heat fluxes on sphere-cone surface are obtained with three commercial soft and compared with exper-imental data. Tasks statements in software systems are as close as possible to each other. The influence of the turbulence presence on the surface heat flux value is shown.
Приведён краткий обзор наиболее распространённых моделей турбулентности и име-ющиеся для них результаты валидации. Произведён расчёт обтекания затупленного по сфере конуса высокоскоростным потоком с помощью различных коммерческих кодов. Постановки задач в программных комплексах максимально приближены друг к другу. Проведено срав-нение значений плотности теплового потока на поверхности конуса, полученных численно, с экспериментальными данными. Показано влияние наличия турбулентности в расчёте на величину поверхностной плотности теплового потока.
[1] Roy C. J., Blottner F. G. Review and assessment of turbulence models for hypersonic flows. Progress in Aerospace Sciences 42, 2006, pp. 469–530. https://doi.org/10.1016/j.paerosci.2006.12.002 [2] Spalart P. R, Allmaras S. R. A one-equation turbulence model for aerodynamic flows. AIAA Paper 92-0439; 1992. https://doi.org/10.2514/6.1992-439 [3] Spalart P. R., Allmaras S. R. A one-equation turbulence model for aerodynamic flows. La Rech Aerosp 1994; 1:5–21. [4] Coleman G. T., Stollery J. L. Heat transfer from hypersonic turbulent flow at a wedge compression corner. Journal of Fluid Mechanics 1972; 56:741–52. doi:10.1017/S0022112072002630 [5] Coleman G. T. Hypersonic turbulent boundary layer studies. PhD thesis. Department of Aeronautics, University of London, London; 1973. [6] Elfstrom G. M. Turbulent hypersonic flow at a wedgecompression corner. Journal of Fluid Mechanics 1972; 53(1):113–27. doi:10.1017/S0022112072000060 [7] Kussoy M. I., Horstman C. C. Documentation of two- and three-dimensional hyper-sonic shock wave/turbulent boundary layer interaction flows. NASA TM 101075; January 1989. [8] Goldberg U. Hypersonic flow heat transfer prediction using single equation turbu-lence models. ASME Journal of Heat Transfer 2001; 123:65–9. doi:10.1115/1.1337653 [9] Goldberg U., Batten P., Palaniswamy S., Chakravarthy S., Peroomian O. Hypersonic flow predictions using linear and nonlinear turbulence closures. Journal of Aircraft 2000; 37(4):671–5. https://doi.org/10.2514/2.2650 [10] Menter F. R. Eddy viscosity transport equations and their relation to the k-ε model. Journal of Fluids Engineering-transactions of the Asme 1997; 119(4): 876–84. doi:10.1115/1.2819511 [11] Jones W. L., Launder B. E. The prediction of laminarization with a two-equation model of turbulence. International Journal of Heat and Mass Transfer 1972; 15:301–14. doi:10.1016/0017-9310(72)90076-2 [12] Launder B. E., Sharma B. I., Holden M. S. Studies of the mean and unsteady struc-ture of turbulent boundary layer separation in hypersonic flow. AIAA paper 1991-1778; 1991. [13] Kussoy M. I., Horstman C. C. An experimental documentation of a hypersonic shock-wave turbulent boundary layer interaction flow—with and without separation. NASA TM X-62412; February 1975. [14] Marvin J. G., Horstman C. C., Rubesin M. W., Coakley T. J., Kussoy M. I. An exper-imental and numerical investigation of shock-wave induced turbulent boundary-layer separational hypersonic speeds. AGARDograph-CPP-168; May 1975. [15] Mikulla V., Horstman C. C. Turbulence measurements in hypersonic shock-wave boundary-layer interaction flows. AIAA J 1976; 14(5):568–75. https://doi.org/10.2514/3.7127 [16] Kussoy M. I., Horstman C. C. Documentation of two- and three dimensional shock wave/turbulent boundary layer interaction flows at Mach 8.2. NASA TM 103838; May 1991. [17] Schulein E., Krogmann P., Stanewsky E. Documentation of two-dimensional imping-ing shock/turbulent boundary layer interaction flow. DLR Report IB 223-96 A 49, Gottingen, Ger-many; October 1996. [18] Schulein E. Personal communications; May 23, 2006 and October 30; 2006. [19] Rodi W. Experience with two-layer models combining the k-ε model with a one-equation model near the wall. AIAA paper 1991-0216; 1991. doi:10.2514/6.1991-216 [20] Launder B. E., Sharma B. I. Application of the energy dissipation model of turbu-lence to the calculation of flow near a spinning disk. Letters in Heat and Mass Transfer 1974; 1(2): 131–8. https://doi.org/10.1016/0094-4548(74)90150-7 [21] So R. M., Zhang H. S., Speziale C. G. Near-wall modeling of the dissipation rate equation. AIAA J 1991; 29(12):2069–76. https://doi.org/10.2514/3.10843 [22] Zhang H. S., So R. M., Speziale C. G., Lai Y. G. Near wall two-equation model for compressible turbulent flows. AIAA J 1993; 31:196–9. https://doi.org/10.2514/3.11338 [23] Coakley T. J., Huang P. G. Turbulence modeling for high-speed flows. AIAA paper 92-0436; 1992. https://doi.org/10.2514/6.1992-436 [24] Wilcox D. C. Turbulence modeling for CFD, 1st ed. La Canada, CA: DCW Indus-tries Inc.; 1988. [25] Wilcox D. C. Turbulence modeling for CFD, 2nd ed. La Canada, CA: DCW Indus-tries, Inc.; 1998. [26] Menter F. R. Two-equation eddy-viscosity turbulence models for engineering applica-tions. AIAA J 1994; 32(8): 1598–605. https://doi.org/10.2514/3.12149 [27] Smith B. R. Prediction of hypersonic shock-wave/turbulent boundary-layer interac-tions. Journal of Spacecraft and Rockets 1996; 33(5): 614–9 (see also AIAA Paper 95-0232; 1995). https://doi.org/10.2514/6.1995-232 [28] Smith B. R. A near wall model for the k-l two equation turbulence model. AIAA pa-per 1994-2386; 1994. https://doi.org/10.2514/6.1994-2386 [29] Robinson D. F., Harris J. E., Hassan H. A. Unified turbulence closure model for ax-isymmetric and planar free shear flows. AIAA Journal 1995; 33(12):2324–31. https://doi.org/10.2514/3.12987 [30] Robinson D. F., Hassan H. A. Further development of the k-ζ (enstrophy) turbulence closure model. AIAA Journal 1998; 36(10):1825–33. https://doi.org/10.2514/2.298 [31] Coakley T. J. Turbulence modeling methods for the compressible Navier–Stokes equations. AIAA paper 1983-1693; 1983. https://doi.org/10.2514/6.1983-1693 [32] Shirazi S. A., Truman C. R. Evaluation of Algebraic Turbulence Models for PNS Predictions of Supersonic Flow Past a Sphere-Cone. AIAA Journal, vol. 27, No 5, May 1989, pp. 560–568. doi:10.2514/3.10146 [33] Ausherman D. W., Yanta W. J. and Rutledge W. H. Measurements of the Three-Dimensional Boundary Layers on Conical Bodies at Mach 3 and Mach 5. AIAA Paper 83-1675, 1983. https://doi.org/10.2514/6.1983-1675 [34] Widhopf, G. F. and Hall R. Transitional and Turbulent Heat-Transfer Measurements on a Yawed Blunt Conical Nosetip. AIAA Journal, vol. 10, Oct. 1972, pp. 1318-1325. https://doi.org/10.2514/6.1972-212 [35] Carver D. B. Heat Transfer, Surface Pressure and Flow Field Surveys on Conic and Biconic Models with Boundary Layer Trips at Mach 8 — Phases IV and V. Calspan/AEDC Div., Rept. AEDCTSR-80-V14, 1980. [36] ANSYS Inc. Ansys CFX-Solver Theory Guide. December 2006. [37] ANSYS Inc. ANSYS Fluent Theory Guide. November 2013. [38] Mentor Graphics Corporation. FloEFD Technical Reference. Software Version 17. [39] Суржиков С. Т. Численная интерпретация экспериментальных данных по аэродинамике модели HB-2 с использованием компьютерных кодов USTFEN и PERAT-3D //Физико-химическая кинетика в газовой динамике. 2020. Т. 21, вып. 1. http://chemphys.edu.ru/issues/2020-21-1/articles/900/ [40] Ермаков М. К., Крюков И. А. Верификация и валидация аэродинамических расчётных комплексов на примере задачи обтекания острых и затупленных конусов // Физи-ко-химическая кинетика в газовой динамике. 2021. Т. 22, вып. 4. http://chemphys.edu.ru/issues/2021-22-4/articles/944/