Asymptotic theory of Mack-mode receptivity in hypersonic boundary layers due to interaction of a heating/cooling source and a freestream sound wave
Asymptotic theory of Mack-mode receptivity in hypersonic boundary layers due to interaction of a heating/cooling source and a freestream sound wave
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DOI：
10.1017/jfm.2023.272
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发表时间：
2023-05
影响因子：
3.7
通讯作者：
Lei Zhao;Jianhong He;M. Dong
中科院分区：
文献类型：
--
作者：
Lei Zhao;Jianhong He;M. Dong
本文研究了高超声速边界层中表面加热或冷却源（HCS）与自由声波相互作用引起的无粘Mack模的局部感受性。渐近分析表明，在主、壁和Stokes三个不同的层中，前阶感受性是由HCS引起的平均流畸变和壁层声学特征的相互作用引起的;二阶感受性出现在Stokes层;三阶感受性出现在主、壁两层。有趣的是，在一个中等的雷诺数，三阶的感受性效率的贡献可能是定量大于二阶的，但这并不导致故障的渐近理论。假设HCS强度足够弱，渐近预测的四个代表性的情况下，涉及不同的马赫数和壁面温度，这是由有限雷诺数理论的基础上得到的结果进行比较，无论是扩展的可压缩Orr-Sommerfeld方程或谐波线性化Navier-Stokes（HLNS）计算。考虑到前三个订单的感受效率，渐近预测被证实是足够准确的，即使当雷诺数是几千，和协议与有限雷诺数计算更好地当壁面温度的底部流接近绝热壁面温度。HLNS计算也进行了中等HCS强度。结果表明，当HCS的温度畸变达到壁面温度的80%时，非线性对感受系数的影响不大。
Abstract In this paper, we study the local receptivity of the inviscid Mack modes in hypersonic boundary layers induced by the interaction between a surface heating or cooling source (HCS) and a freestream acoustic wave. The asymptotic analysis reveals that among the three distinguished layers, i.e. the main, wall and Stokes layers, the leading-order receptivity is attributed to the interaction of the HCS-induced mean-flow distortion and the acoustic signature in the wall layer; the second-order contribution appears in the Stokes layer; the third-order contribution appears in both the main and wall layers. Interestingly, at a moderate Reynolds number, the third-order contribution to the receptivity efficiency may be quantitatively greater than the second-order one, but this does not lead to breakdown of this asymptotic theory. Assuming the HCS intensity to be sufficiently weak, the asymptotic predictions are made for four representative cases involving different Mach numbers and wall temperatures, which are compared with the results obtained by the finite-Reynolds-number theory based on either the extended compressible Orr–Sommerfeld equations or the harmonic linearised Navier–Stokes (HLNS) calculations. Taking into account the first three orders of the receptivity efficiency, the asymptotic predictions are confirmed to be sufficiently accurate even when the Reynolds number is a few thousands, and the agreement with the finite-Reynolds-number calculations is better when the wall temperature of the base flow approaches the adiabatic wall temperature. The HLNS calculations are also conducted for moderate HCS intensities. It is found that the nonlinearity does not affect the receptivity coefficient much even when the temperature distortion of the HCS reaches $80\,\%$ of the temperature at the wall.