Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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A Study on Improvement γ-Reθt Model for Hypersonic Boundary Layer Analysis

극 초음속 경계층 해석을 위한 γ-Reθt모델 개선 연구

  • Kang, Sunoh (Department of Aerospace Engineering, Pusan National University) ;
  • Oh, Sejong (Department of Aerospace Engineering, Pusan National University) ;
  • Park, Donghun (Department of Aerospace Engineering, Pusan National University)
  • Received : 2019.12.17
  • Accepted : 2020.04.10
  • Published : 2020.05.01
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Abstract

Since boundary layer transition has a significant impact on the aero-thermodynamic performance of hypersonic flight vehicles, capability of accurate prediction of transition location is essential for design and performance analysis. In this study, γ-Reθt model is improved to predict transition of hypersonic boundary layers and validated. A coefficient in the production term of the intermittency transport equation that affects the transition onset location is constructed and applied as a function of Mach number, wall temperature, and freestream stagnation temperature based on the similarity numerical solution of compressible boundary layer. To take into account a Mach number dependency of transition onset momentum thickness Reynolds number and transition length, additional correlation equations are determined as function of Mach number and applied to Reθc and Flength correlations of the baseline model. The suggested model is implemented to a commercial CFD code in consideration of practical use. Analysis of hypersonic flat plate and circular cone boundary layers is carried out by using the model for validation purpose. An improvement of prediction capability with respect to variation of Mach number and unit Reynolds number is identified from the comparison with experimental data.

경계층 천이는 극초음속 비행체의 열공력 성능에 직접적인 영향을 미치기 때문에, 성능 해석과 설계를 위해 천이지점의 정확한 예측 능력이 필수적으로 요구된다. 본 연구에서는 극초음속 경계층 천이 예측을 위한 γ-Reθt 모델을 개선하고 검증하였다. 천이 시작 위치 결정에 영향을 주는 간헐도 수송방정식 생성항의 계수를 압축성 경계층 상사해를 기반으로 마하수와 벽면온도, 자유류 정체온도 등에 대한 함수 형태로 구성하고 적용하였다. 기본 모델의 Reθc와 Flength 상관관계식에 마하수에 따른 천이 시작 운동량두께 레이놀즈수와 천이구간의 길이 변화를 반영할 수 있도록 마하수에 대한 관계식을 추가로 결정하여 적용하였다. 실용적인 사용을 고려하여 제안 모델을 상용 CFD 코드에 적용하였으며, 검증을 위해 모델을 사용하여 극초음속 평판과 원뿔 경계층 해석을 수행하였다. 실험 결과와의 비교를 통해 마하수와 단위 레이놀즈수 변화에 대한 개선된 예측성능을 확인하였다.

Keywords

References

  1. Sayler, K. M., "Hypersonic Weapons: Background and Issues for Congress," Congressional Research Service (CRS) Report for Congress, 2019.
  2. Semper, M. T., "Examining a Hypersonic Turbulent Boundary Layer at Low Reynolds Number," Ph.D. Dissertation, Texas A&M University, 2013.
  3. Wadhams, T., Mundy, E., MacLean, M., and Holden, M., "Pre-flight Ground Testing of the Full-scale HIFiRE-1 Vehicle at Fully Duplicated Flight Conditions: Part II," 46th AIAA Aerospace Sciences Meeting and Exhibit, 2008, p. 639.
  4. Kimmel, R. L., and Adamczak, D. W., "HIFiRE-1 Preliminary Aerothermodynamic Measurements (postprint)" : Air Force Research Lab Wright-Patterson Afb Oh Air Vehicles Directorate/Aeronautical Sciences Div, 2012.
  5. Kimmel, L. R., Adamczak, D., Berger, K., and Choudhari, M., "HIFiRE-5 Flight Vehicle Design," 40th Fluid Dynamics Conference and Exhibit, 2010, p. 4985.
  6. Juliano, T., and Schneider, S., "Instability and Transition on the HIFiRE-5 in a Mach 6 Quiet Tunnel," 40th Fluid Dynamics Conference and Exhibit, 2010, p. 5004.
  7. Berridge, D. C., McKiernan, G., Wadhams, T. P., Holden, M., Wheaton, B. M., Wolf, T. D., and Schneider, S. P., "Hypersonic Ground Tests in Support of the Boundary Layer Transition (BOLT) Flight Experiment," 2018 Fluid Dynamics Conference, 2018, p. 2893.
  8. Wheaton, B. M., Berridge, D. C., Wolf, T. D., Stevens, R. T., and McGrath, B. E., "Boundary Layer Transition (BOLT) Flight Experiment Overview," 2018 Fluid Dynamics Conference, 2018, p. 2892.
  9. Slotnick, J., Khodadoust, A., Alonso, J., Darmofal, D., Gropp, W., Lurie, E., and Mavriplis, D., "CFD Vision 2030 Study: a Path to Revolutionary Computational Aerosciences," NASA Langley Research Center. NASA/CR 2014-218178, Hampton, VA, 2014.
  10. Cebeci, T., Chen, H., Arnal, D., and Huang, T., "Three-dimensional Linear Stability Approach to Transition on Wings and Bodies of Revolution at Incidence," AIAA journal, Vol. 29, No. 12, 1991, pp. 2077-2085. https://doi.org/10.2514/3.10844
  11. Malik, M. R., "Prediction and Control of Transition in Supersonic and Hypersonic Boundary Layers," AIAA journal, Vol. 27, No. 11, 1989, pp. 1487-1493. https://doi.org/10.2514/3.10292
  12. Reed, H. L., Saric, W. S., and Arnal, D., "Linear Stability Theory Applied to Boundary Layers," Annual review of fluid mechanics, Vol. 28, No. 1, 1996, pp. 389-428. https://doi.org/10.1146/annurev.fl.28.010196.002133
  13. Herbert, T., "Parabolized Stability Equations," Annual Review of Fluid Mechanics, Vol. 29, No. 1, 1997, pp. 245-283. https://doi.org/10.1146/annurev.fluid.29.1.245
  14. Mayer, C. S., Von Terzi, D. A., and Fasel, H. F., "Direct Numerical Simulation of Complete Transition to Turbulence via Oblique Breakdown at Mach 3," Journal of Fluid Mechanics, Vol. 674, 2011, pp. 5-42. https://doi.org/10.1017/S0022112010005094
  15. Fezer, A., Kloker, M., Zeitoun, D. E., Periaux, J., Desideri, J. A., and Marini, M., "DNS of Transition Mechanisms at Mach 6.8-Flat Plate vs. Sharp Cone," West East High Speed Flow Fields, 2002, pp. 1-8.
  16. Kim, M. W,, Lim, J. S., Kim, S. T., Jee, S. K., Park, J. Y., and Park, D. H., "Large-eddy Simulation with Parabolized Stability Equations for Turbulent Transition Using OpenFOAM," Computers & Fluids Vol. 189, 2019, pp. 108-117. https://doi.org/10.1016/j.compfluid.2019.04.010
  17. Menter, F. R., Langtry, R. B., Likki, S. R., Suzen, Y. B., Huang, P. G., and Volker, S., "A Correlation-Based Transition Model Using Local Variables-Part I: Model Formulation," Journal of turbomachinery, Vol. 128, No. 3, 2006, pp. 413-422. https://doi.org/10.1115/1.2184352
  18. Langtry, R. B., Menter, F. R., Likki, S. R., Suzen, Y. B., Huang, P. G., and Volker, S., "A Correlation-Based Transition Model Using Local Variables-Part II: Test Cases and Industrial Applications," Journal of Turbomachinery, Vol. 128, No. 3, 2006, pp. 423-434. https://doi.org/10.1115/1.2184353
  19. Langtry, R. B., and Menter, F. R., "Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes," AIAA journal, Vol. 47, No. 12, 2009, pp. 2894-2906. https://doi.org/10.2514/1.42362
  20. Menter, F. R., "Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications," AIAA journal, Vol. 32, No. 8, 1994, pp. 1598-1605. https://doi.org/10.2514/3.12149
  21. Fedorov, A., "Transition and Stability of High-Speed Boundary Layers," Annual review of fluid mechanics, Vol. 43, 2011, pp. 79-95. https://doi.org/10.1146/annurev-fluid-122109-160750
  22. Saric, W. S., Reed, H. L., and White, E. B., "Stability and Transition of Three-Dimensional Boundary Layers," Annual Review of Fluid Mechanics, Vol. 35, No. 1, 2003, pp. 413-440. https://doi.org/10.1146/annurev.fluid.35.101101.161045
  23. Zhou, L., Zhao, R., and Li, R., "A Combined Criteria-Based Method for Hypersonic Three-Dimensional Boundary Layer Transition Prediction," Aerospace Science and Technology, Vol. 73, 2018, pp. 105-117. https://doi.org/10.1016/j.ast.2017.12.002
  24. Coder, J. G., and Maughmer, M. D., "Computational Fluid Dynamics Compatible Transition Modeling Using an Amplification Factor Transport Equation," AIAA journal, Vol. 52, No. 11, 2014, pp. 2506-2512. https://doi.org/10.2514/1.J052905
  25. Xu, J., Bai, J., Zhang, Y., and Qiao, L., "Transition Study of 3D Aerodynamic Configures Using Improved Transport Equations Modeling," Chinese Journal of Aeronautics, Vol. 29, No. 4, 2016, pp. 874-881. https://doi.org/10.1016/j.cja.2016.06.002
  26. Zhang, X., and Zhenghong, G., "A Numerical Research on a Compressibility-Correlated Langtry's Transition Model for Double Wedge Boundary Layer Flows," Chinese Journal of Aeronautics, Vol. 24, No. 3, 2011, pp. 249-257. https://doi.org/10.1016/S1000-9361(11)60030-7
  27. Zhang, X., Zhenghong, G., and Bowen, Z., "Extensions of Menter's SST Transition Model to Simulate Hypersonic and Cross-Flow Transition," International Congress of the Aeronautical Sciences, 2012.
  28. Krause, M., Behr, M., and Ballmann, J., "Modeling of Transition Effects in Hypersonic Intake Flows Using a Correlation-Based Intermittency Model," 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2008, p. 2598.
  29. Frauholz, S., Reinartz, B. U., Muller, S., and Behr, M., "Transition Prediction for Scramjets Using $\gamma$-$Re{\theta}t$ Model Coupled to Two Turbulence Models," Journal of Propulsion and Power, Vol. 31, No. 5, 2015, pp. 1404-1422. https://doi.org/10.2514/1.B35630
  30. Shin, H. C., "Transition Flow Analysis Using Hypersonic Transition Transport Models for Three-Dimensional Scramjet Intake," M. S. Thesis, Konkuk University, 2017.
  31. Kovalev, R., Kudryavtsev, V., and Churakov, D., "On Modeling of Laminar-Turbulent Transition in Supersonic Flows with Engineering Correlations and Reynolds-Averaged Navier-Stokes Equations," Progress in Flight Physics, Vol. 7, 2015, pp. 525-548.
  32. Hao, Z., Yan, C., Qin, Y., and Zhou, L., "Improved $\gamma$-$Re{\theta}t$ Model for Heat Transfer Prediction of Hypersonic Boundary Layer Transition," International Journal of Heat and Mass Transfer, Vol. 107, 2017, pp. 329-338. https://doi.org/10.1016/j.ijheatmasstransfer.2016.11.052
  33. Wang, Y., Li, Y., Xiao, L., Zhang, B., and Li, Y., "Similarity-Solution-Based Improvement of $\gamma$-$Re{\theta}t$ Model for Hypersonic Transition Prediction," International Journal of Heat and Mass Transfer, Vol. 124, 2018, pp. 491-503. https://doi.org/10.1016/j.ijheatmasstransfer.2018.03.092
  34. Xia, C., and Chen, W., "Boundary-Layer Transition Prediction Using a Simplified Correlation-Based Model," Chinese Journal of Aeronautics, Vol. 29, No. 1, 2016, pp. 66-75. https://doi.org/10.1016/j.cja.2015.12.003
  35. Zhou, L., Li, R., Hao, Z., Zaripov, D. I., and Yan, C., "Improved $k-\omega-\gamma$ Model for Crossflow-Induced Transition Prediction in Hypersonic Flow," International Journal of Heat and Mass Transfer, Vol. 115, 2017, pp. 115-130.
  36. Van Driest, E., and Blumer, C., "Boundary Layer Transition-Freestream Turbulence and Pressure Gradient Effects," AIAA journal, Vol. 1, No. 6, 1963, pp. 1303-1306. https://doi.org/10.2514/3.1784
  37. Iyer, V., "Computation of Three-Dimensional Compressible Boundary Layers to Fourth-order Accuracy on Wings and Fuselages," NASA Langley Research Center, NASA-CR-4269, 1990.
  38. White, F. M., and Corfield, I., "Viscous Fluid Flow," McGraw-Hill New York, 2006.
  39. https://www.jmp.com/
  40. Reshotko, E., "Is Retheta/Me a Meaningful Transition Criterion?," AIAA journal, Vol. 45, No. 7, 2007, pp. 1441-1443. https://doi.org/10.2514/1.29952
  41. Mee, D. J., "Boundary-Layer Transition Measurements in Hypervelocity Flows in a Shock Tunnel," AIAA journal, Vol. 40, No. 8, 2002, pp. 1542-1548. https://doi.org/10.2514/2.1851
  42. Marineau, E. C., Moraru, G. C., Lewis, D. R., Norris, J. D., Lafferty, J. F., Wagnild, R. M., and Smith, J. A., "Mach 10 Boundary Layer Transition Experiments on Sharp and Blunted Cones," 19th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2014, p. 3108.
  43. Balakumar, P., and Chou, A., "Transition Prediction in Hypersonic Boundary Layers Using Receptivity and Freestream Spectra," AIAA Journal, 2017, pp. 193-208.