采用直接数值模拟方法对来流马赫数2.9，30°激波角的入射激波与膨胀角湍流边界层干扰问题进行了数值研究。入射激波在壁面上的名义入射点固定在膨胀角角点，膨胀角角度分别取为0°、2°、5°和10°。通过改变膨胀角角度，考察了膨胀效应对干扰区内复杂流动现象的影响规律和作用机制，如分离泡、物面压力脉动特性、膨胀区湍流边界层和物面剪切应力脉动场等。研究发现，膨胀角角度的增大使得分离区流向长度和法向高度急剧降低，尤其是在强膨胀效应下分离泡形态呈现整体往下游偏移的双峰结构。物面压力脉动功率谱结果表明，膨胀角为2°和5°时，分离激波的非定常运动仍表征为大尺度低频振荡，而膨胀角为10°，强膨胀效应极大地抑制了分离激波的低频振荡，加速了下游再附边界层物面压力脉动的恢复过程。膨胀区湍流边界层雷诺剪切应力各象限事件贡献和出现概率呈现逐步恢复到上游湍流边界层的趋势，Görtler-like流向涡结构展向和法向尺度变化剧烈，同时在近壁区将诱导生成大量小尺度流向涡。此外，物面剪切应力脉动场的本征正交分解分析指出，膨胀效应的影响体现在低阶模态能量的急剧降低从而使得高阶模态的总体贡献相对升高。
Direct numerical simulations of impinging shock waves and turbulent boundary layer interactions in an expansion corner for the incident shock of 30° at Mach number 2.9 are performed. The nominal impingement point of incident shock waves at the wall is fixed at the apex of the expansion corner. Four cases for expansion angles of 0°, 2°, 5° and 10° are considered. By changing the expansion angle, this research studies the impact of the expansion effect on the complicated flow phenomena in the interaction region, including the separation bubble, wall pressure fluctuations, the turbulent boundary layer in the expansion region and the fluctuating wall shear stress. Results indicate that the streamwise length and height of the separation region are dramatically decreased when the expansion angle is increased, particularly in the condition of strong expansion effect where the shape of the separation bubble is characterized by double peaks with downstream migration. The power spectrum density of wall pressure fluctuations suggests that the unsteady motion of the separation shock is still dominated by the large-scale low frequency oscillation for the expansion angles of 2° and 5°. When the angle is increased to be 10°, the low-frequency unsteady motion of the separated shock is strongly suppressed and the recovery process of fluctuating wall pressure in the expansion region is obviously accelerated. The quadrant analysis of Reynolds shear stress shows that the contribution and occurrence probability of each quadrant experience a faster recovery as the expansion angle is increased. The Görtler-like vortex structures are dramatically destroyed and more small-scale streamwise vortices are generated in the near-wall region. In addition, the proper orthogonal decomposition analysis of the fluctuating wall shear stress indicates that the influence of the expansion effect is mainly reflected in the sharp decrease of the low-order modes energy and the relative increase of overall contribution of high-order modes.
[1] ARDONCEAU P L. The structure of turbulence in a supersonic shock wave/boundary layer interaction[J]. AIAA Journal, 1984, 22(9):1254-1262.
[2] SETTLES G S, BOGDONOFF S M, VAS I E. Incipient separation of a supersonic turbulent boundary layer at high Reynolds number[J]. AIAA Journal, 1976, 14(1):50-56.
[3] CLEMENS N T, NARAYANASWAMY V. Low frequency unsteadiness of shock wave turbulent boundary layer interactions[J]. Annual Review of Fluid Mechanics, 2014, 46:469-492.
[4] SETTLES G S, FITZPATRICK T J. Detailed study of attached and separated compression corner flowfields in high Reynolds number supersonic flow[J]. AIAA Journal, 1979, 17(6):579-585.
[5] HUMBLE R A, SCARANO F. Unsteady aspects of an incident shock wave turbulent boundary layer interaction[J]. Journal of Fluid Mechanics, 2009, 635:47-74.
[6] ERENGIL M E, DOLLING D S. Correlation of separation shock motion with pressure fluctuations in the incoming boundary layer[J]. AIAA Journal, 1991, 29(11):1868-1877.
[7] ADAMS N A. Direct simulation of the turbulent boundary layer along a compression ramp at M=3 and Reθ=1685[J]. Journal of Fluid Mechanics, 2000, 420:47-83.
[8] DUPONT P, HADDAD C,DEBIEVE J F. Space and time organization in a shock-induced separated boundary layer[J]. Journal of Fluid Mechanics, 2006, 599:255-277.
[9] PIPONNIAU S, DUSSAUGE J P,DEBIEVE J F. A simple model for low frequency unsteadiness in shock induced separation[J]. Journal of Fluid Mechanics, 2009, 629:87-108.
[10] PRIEBE S, WU M,MARTIN M P. Low-frequency unsteadiness in shock wave turbulent boundary layer interaction[J]. Journal of Fluid Mechanics, 2012, 699:1-49.
[11] CHEW Y T. Shock wave and boundary layer interaction in the presence of an expansion corner[J]. Aeronautical Quarterly, 1979, 30:506-527.
[12] CHUNG K M, LU F K. Hypersonic turbulent expansion-corner flow with shock impingement[J]. Journal of Propulsion and Power, 1995, 11(3):441-447.
[13] WHITE M E, AULT D A. Expansion corner effects on hypersonic shock wave/turbulent boundary-layer interactions[J]. Journal of Propulsion and Power, 1996, 12(6):1169-1173.
[14] SATHIANARAYANAN A, VERMA S B. Experimental investigation of an incident shock-induced interaction near an expansion corner[J]. AIAA Journal, 2017, 54(3):769-773.
[15] KONOPKA M, MEINKE M, SCHRODER W. Large-eddy simulation of relaminarization in supersonic flow:AIAA-2012-2978[R]. Reston:AIAA, 2012.
[16] 童福林, 孙东, 袁先旭, 等. 超声速膨胀角入射激波/湍流边界层干扰直接数值模拟[J]. 航空学报, 2020, 41(3):123328. TONG F L, SUN D, YUAN X X, et al. Direct numerical simulation of impinging shock wave/turbulent boundary layer interactions in a supersonic expansion corner[J]. Acta Aeronautica et Astronautica Sinica, 2020,41(3):123328(in Chinese).
[17] BOOKEY P B, WYCKHAM C, SMITS A J. Experimental investigations of Mach 3 shock wave turbulent boundary layer interaction:AIAA-2005-4899[R]. Reston:AIAA, 2005.
[18] PRIEBE S, WU M, MARTIN M P. Direct numerical simulation of a reflected shock wave turbulent boundary layer interaction[J]. AIAA Journal, 2009, 47(5):1173-1185.
[19] NARASIMHA R, VISWANATH P R. Reverse transition at an expansion corner in supersonic flow[J]. AIAA Journal, 1975, 13(5):693-695.
[20] 童福林, 唐志共, 李新亮, 等. 压缩拐角激波与旁路转捩边界层干扰数值研究[J]. 航空学报, 2016, 37(12):3588-3604. TONG F L, TANG Z G, LI X L, et al. Numerical study of shock wave and bypass transitional boundary layer interaction in a supersonic compression ramp[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(12):3588-3604(in Chinese).
[21] 童福林, 周桂宇, 周浩, 等. 激波/湍流边界层干扰物面剪切应力统计特性[J]. 航空学报, 2019, 40(5):122504. TONG F L, ZHOU G Y, ZHOU H, et al. Statistical characteristics of wall shear stress in shock wave and turbulent boundary layer interactions[J]. Acta Aeronautica et Astronautica Sinica, 2019,40(5):122504(in Chinese).
[22] DOLLING D S, OR C T. Unsteadiness of the shock wave structure in attached and separated compression ramp flows[J]. Experiment in Fluids, 1985, 3(1):24-32.
[23] PIROZZOLI S, GRASSO F. Direct numerical simulation of impinging shock wave turbulent boundary layer interaction at M=2.25[J]. Physics of Fluids, 2006, 18:065113.
[24] WALLACE J M. Quadrant analysis in turbulence research:History and evolution[J]. Annual Review of Fluid Mechanics, 2016, 48:131-158.
[25] KROGSTAD P A, SKARE P E. Influence of a strong adverse pressure gradient on the turbulent structure in a boundary layer[J]. Physics of Fluids, 1995, 7:2014-2024.
[26] KIM J, MOIN P, MOSER R. Turbulence statistics in fully developed channel flow at low Reynolds number[J]. Journal of Fluid Mechanics, 1987, 177:133-166.
[27] PASQUARIELLO V, HICKEL S, ADAMS N A. Unsteady effects of strong shock wave/boundary layer interaction at high Reynolds number[J]. Journal of Fluid Mechanics, 2017, 823:617-657.
[28] ZHUANG Y, TAN H J, LI X, et al. Görtler-like vortices in an impinging shock wave/turbulent boundary layer interaction flow[J]. Physics of Fluids, 2018, 30:061702.
[29] BERKOOZ G, HOLMES P, LUMLEY J L. The proper orthogonal decomposition in the analysis of turbulent flows[J]. Annual Review of Fluid Mechanics, 1993, 25:539-575.
CJA