Amplification and attenuation of shock wave strength caused by homogeneous isotropic turbulence

K. Tanaka, T. Watanabe, K. Nagata, A. Sasoh, Y. Sakai, T. Hayase
Amplification and attenuation of shock wave strength caused by homogeneous isotropic turbulence
Physics of Fluids 30(3) 035105 2018

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This article may be found at https://doi.org/10.1063/1.5019867.

Abstract

We study the pressure increase across a planar shock wave with shock Mach numbers Ms of 1.1, 1.3, and 1.5 propagating through homogeneous isotropic turbulence at a low turbulent Mach number (Mt ∼ 10−4) based on direct numerical simulations (DNSs). Fluctuation in the pressure increase, Δp′, on a given shock ray is induced by turbulence around the ray. A local amplification of the shock wave strength, measured with the pressure increase, is caused by the velocity fluctuation opposed to the shock wave propagating direction with a time delay, while the velocity in the opposite direction attenuates the shock wave strength. The turbulence effects on the shock wave are explained based on shock wave deformation due to turbulent shearing motions. The spatial distribution of Δp′ on the shock wave has a characteristic length of the order of the integral scale of turbulence. The influence of turbulent velocity fluctuation at a given location on Δp′ becomes most significant after the shock wave propagates from the location for a distance close to the integral length scale for all shock Mach numbers, demonstrating that the shock wave properties possess strong memory even during the propagation in turbulence. A lower shock Mach number Ms results in a smaller rms value of Δp′, stronger influences on Δp′ by turbulence far away from the shock ray, and a larger length scale in the spatial profile of Δp′ on the shock wave. Relative intensity of Δp′ increases with [𝑀𝑡/(𝑀𝑠−1)]^𝛼

日本語訳 (DeepL翻訳)

一様等方性乱流による衝撃波強度の増幅・減衰

低乱流マッハ数(Mt ∼ 10^-4)の一様等方性乱流中を伝播する衝撃マッハ数1.1, 1.3, 1.5 の平面衝撃波の圧力上昇を直接数値計算(DNS)に基づいて研究した。衝撃波の圧力上昇Δp′は、衝撃波の周りの乱流によって変動する。衝撃波の伝播と反対方向の速度は衝撃波の強さを時間遅れをもって減衰させる。一方、衝撃波伝播と同方向の速度は衝撃波の強さを局所的に増幅させる。衝撃波に対する乱流の効果は、乱流剪断運動による衝撃波の変形に基づいて説明される。衝撃波上のΔp′の空間分布は，乱流の積分スケールのオーダーの特徴的な長さを持つ。ある位置での乱流速度の揺らぎがΔp′に与える影響は、すべての衝撃マッハ数において、衝撃波がその位置から積分長スケール近くまで伝播した後に最も大きくなり、衝撃波の特性が乱流中を伝播する間にも強い記憶を持っていることが示された。衝撃マッハ数Msが低いほどΔp′のrms値は小さくなり、衝撃波から遠く離れた乱流によるΔp′への影響が強くなり、衝撃波上のΔp′の空間プロファイルの長さスケールは大きくなる。Δp′の相対強度は[𝑀/(𝑀-1)]^αで増加する。

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