Scaling parameters of shock-wave/turbulent boundary-layer interactions generated by a semi-infinite standing cylinder were explored in a combined numerical and experimental effort, consisting of Reynolds-averaged Navier–Stokes simulations and high-speed schlieren imaging. The primary interaction variable, the cylinder diameter ( d ), and a secondary interaction variable, the boundary-layer thickness ( $$\delta $$ δ ), were varied to study the effects of the parameter $$d/\delta $$ d / δ . This was found to be an appropriate scaling parameter for mean features. The characteristic interaction variables (the maximum separation distance, S , and the triple-point height, $$h_\mathrm{tp}$$ h tp ) followed a linear trend when normalized as $$S/\delta $$ S / δ and $$h_\mathrm{tp}/\delta $$ h tp / δ ; however, when the boundary layer became larger than the cylinder diameter, a power law trend became more representative. The parameter $$d/\delta $$ d / δ also determined the role that viscous effects have on the strength of the interaction, where a lower $$d/\delta $$ d / δ was characterized by a greater interaction scale and lower surface pressure peaks. Moreover, the high surface pressure on the cylinder leading edge due to the Edney interaction was found to be reduced for $$d/\delta \le 0.45$$ d / δ ≤ 0.45 , as the boundary layer encompassed the lambda-shock structure. Trends in the shapes or peaks of the auto-spectral density function were not observed based on $$d/\delta $$ d / δ , but appeared to be dominated by broadband low-frequency ( $$f < 1~\hbox {kHz}$$ f < 1 kHz ) content. While the position and structure of the interaction may change as a result of varying $$d/\delta $$ d / δ , the effects on the unsteady dynamics were minimal.

中文翻译：

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圆柱体产生的冲击波/湍流边界层相互作用的缩放

在组合数值和实验工作中探索了由半无限立柱产生的冲击波/湍流边界层相互作用的缩放参数，包括雷诺平均 Navier-Stokes 模拟和高速纹影成像。主要相互作用变量，圆柱直径 ( d ) 和次要相互作用变量，边界层厚度 ( $$\delta $$ δ ) 被改变以研究参数 $$d/\delta $$ 的影响d / δ 。发现这是平均特征的适当缩放参数。特征交互变量（最大分离距离 S 和三点高度 $$h_\mathrm{tp}$$h tp ）在归一化为 $$S/\delta $$ S / δ 时遵循线性趋势和 $$h_\mathrm{tp}/\delta $$h tp / δ ；然而，当边界层变得大于圆柱直径时，幂律趋势变得更具代表性。参数 $$d/\delta $$ d / δ 也决定了粘性效应对相互作用强度的作用，其中较低的 $$d/\delta $$ d / δ 的特征在于更大的相互作用尺度和较低的表面压力峰值。此外，由于边界层包含 lambda 激波结构，因此发现由于 Edney 相互作用导致的圆柱前缘上的高表面压力降低了 $$d/\delta\le 0.45$$d / δ ≤ 0.45。基于 $$d/\delta $$ d / δ 未观察到自动光谱密度函数的形状或峰值的趋势，但似乎以宽带低频为主（ $$f < 1~\hbox { kHz}$$ f < 1 kHz ) 内容。