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

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
권호 표지
DOI QR코드

DOI QR Code

Transition Prediction of compressible Axi-symmetric Boundary Layer on Sharp Cone by using Linear Stability Theory

선형 안정성 이론을 이용한 압축성 축 대칭 원뿔 경계층의 천이지점 예측

  • 박동훈 (한국과학기술원 항공우주공학과) ;
  • 박승오 (한국과학기술원 항공우주공학과)
  • Published : 2008.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this study, the transition Reynolds number of compressible axi-symmetric sharp cone boundary layer is predicted by using a linear stability theory and the -method. The compressible linear stability equation for sharp cone boundary layer was derived from the governing equations on the body-intrinsic axi-symmetric coordinate system. The numerical analysis code for the stability equation was developed based on a second-order accurate finite-difference method. Stability characteristics and amplification rate of two-dimensional second mode disturbance for the sharp cone boundary layer were calculated from the analysis code and the numerical code was validated by comparing the results with experimental data. Transition prediction was performed by application of the -method with N=10. From comparison with wind tunnel experiments and flight tests data, capability of the transition prediction of this study is confirmed for the sharp cone boundary layers which have an edge Mach number between 4 and 8. In addition, effect of wall cooling on the stability of disturbance in the boundary layer and transition position is investigated.

본 연구에서는 축 대칭 원뿔 형상 위의 압축성 경계층의 천이 지점을 선형 안정성 이론과 -method를 이용하여 예측하였다. 축 대칭 좌표계에서의 압축성 유동 지배 방정식으로부터 압축성 원뿔 경계층의 선형 안정성 방정식을 얻었으며 안정성 방정식을 2차 정확도의 유한 차분법을 이용하여 계산하는 수치 프로그램을 개발하였다. 개발 된 코드로 원뿔 경계층의 안정성 특성 및 2차원 교란의 증폭률을 계산하고 실험결과와의 비교를 통해 검증을 수행하였다. 얻어진 교란의 증폭률을 활용하여 -method를 통해 천이지점 예측을 수행하였다. 풍동 시험 및 비행 시험 결과와의 비교를 통해 비행 조건에 있는 마하수 4와 8사이의 원뿔 경계층에 대한 본 연구의 천이지점의 예측 능력을 확인하였다. 또한 벽면 냉각이 경계층 내부 교란의 안정성 및 천이 지점에 미치는 영향을 분석하였다.

Keywords

References

  1. Schubauer, G. B. and Skramstad, H. F. , "Laminar boundary layer oscillations and the stability of laminar flow", Journal of Aero. Sci., Vol. 14 , pp. 381-384, 1947
  2. Gasperas, G., "The Stability of the Compressilbe Boundary Layer on a Sharp Cone at Zero Angle of Attack", AIAA-87-0494, presented at the AIAA 25th Aerospace Sciences Meeting, Reno, Nevada, January 1987
  3. Lesile, L. Mack, "Stability of Axisymmetric Boundary Layers on Sharp Cones at Hypersonic Mach Numbers",AIAA-87-1413, presented at the AIAA 19thFluid Dynamics, Plasma Dynamics and Lasers Conference, Honolulu, Hawaii, June 1987
  4. M.R.Malik and R.E.Spall, "On the stability of compressuble flow past axisymmetric bodies", J.Fluid.Mech. Vol.228, pp. 443-463, 1991
  5. M.R.Malik, "Numerical Methods for Hypersonic Boundary Layer Stability", Journal of Computational Physics, Vol.86, pp. 376-413, 1990 https://doi.org/10.1016/0021-9991(90)90106-B
  6. Leslie M. Mack, "BOUNDRY-LAYER LINEAR STABILITY THEORY", AGARD CP-709, NATO, Belgium, 1984
  7. Lesile M. Mack , "Remarks on diputed numerical results in compressible boundary-layer stability theory", Physics of Fluids, Vol. 27, pp. 342-347 https://doi.org/10.1063/1.864631
  8. Helen L. Reed, Ponnampalam Balakumar, "Compressible boundary-layer stability theory", Physics of Fluids A Vol. 2, pp. 1341-1349, August 1990 https://doi.org/10.1063/1.857584
  9. 박동훈, 박승오, "축 대칭 압축성 원뿔 경계층의 선형 안정성 해석", 제 14차 유도무기 학술대회논문집, 국방과학연구소, pp. 130-143
  10. 박동훈, 선형 안정성 이론을 이용한 압축성 축 대칭 원뿔 경계층의 천이지점 예측, 한국과학기술원 석사학위논문
  11. Wilkinson, J.H., The Algebraic Eigenvalue Problem, Oxford, 1965
  12. Mujeeb R. Malik, and S. A. Ozang, "Efficient Computation of the Stability of Three-Dimensional Comprssible Boundary Layers", AIAA-81-1277, AIAA 14th Fluid and Plasma Dynamics Conference, 1981
  13. Gaster M, "A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability", Journal of Fluid Mechanics,Vol.14, pp. 222-224, 1962 https://doi.org/10.1017/S0022112062001184
  14. Mujeeb R. Malik, "Prediction and Control of Transition in Supersonic and Hypersonic Boundary Layers", AIAA Journal, Vol. 27, No. 11, November, pp. 1489-1493, 1989
  15. Mujeeb R. Malik, "COSAL—A BLACK-BOX Compressible Stability Analysis Code for Transition Prediction in Three-Dimnensional Boundary Layers", NASA Contractor Report 165925, 1984
  16. Stetson, K. F., Thompson, E. R., Donaldson, J. C., and Siler, L. G., "Laminar Boundary Layer Stability Experiments on a Cone at Mach 8. Part 1 : Sharp Cone", AIAA-83-1761, presented at the AIAA 16th Fluid and Plasma Dynamics Conference, Danvers, Massachusetts, July 1983
  17. Gasperas, G., "The Stability of the Compressilbe Boundary Layer on a Sharp Cone at Zero Angle of Attack", AIAA-87-0494, presented at the AIAA 25th Aerospace Sciences Meeting, Reno, Nevada, January 1987
  18. Lesile, L. Mack, "Stability of Axisymmetric Boundary Layers on Sharp Cones at Hypersonic Mach Numbers", AIAA-87-1413, presented at the AIAA 19thFluid Dynamics, Plasma Dynamics and Lasers Conference, Honolulu, Hawaii, June 1987
  19. T.J.Horvath, "Boundary Layer Transition of Slender Cones in Conventional and Low Disturbance Mach 6 Wind Tunnel", AIAA-2002-2743, 2002.
  20. R.L.Kimmel, "Effect of Total Temperature on Boundary-Layer Stability at Mach 6", AIAA Vol.38, No.9, pp. 1754-1755, 2000 https://doi.org/10.2514/2.1164
  21. G.G.Mateer, "Unusual Boundary Layer Transition Results on Cone in Hypersonic Flow," AIAA Vol.7, No.4, pp. 660-664,1969 https://doi.org/10.2514/3.5183
  22. P.C.Stainback, "Effect of Unit Reynolds Number, Nose Bluntness, Angle of Attack and Roughness on Transition on a 5 degree Half Angle Cone at Mach 8", NASA TN D-4961,1969
  23. Mujeeb R. Malik, "Prediction and Control of Transition in Supersonic and Hypersonic Boundary Layers", AIAA Journal, Vol. 27, No. 11, November, pp. 1489-1493, 1989
  24. S.P.Schneider, "Flight Data for Boundary-Layer Transition at Hypersonic and Supersonic Speeds", Journal of Spacecraft and Rockets, Vol.36, No.1, pp. 8-20, 1999 https://doi.org/10.2514/2.3428