Statistics of overpressure fluctuations behind a weak shock wave interacting with turbulence

K. Inokuma, T. Watanabe, K. Nagata, Y. Sakai
Statistics of overpressure fluctuations behind a weak shock wave interacting with turbulence
Physics of Fluids, 31 085119 2019

This article may be found at https://doi.org/10.1063/1.5110185.

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Abstract

The overpressure fluctuations behind a weak shock wave interacting with turbulence are studied by wind tunnel experiments, where a spherical shock wave propagates in grid turbulence. The experiments are conducted for various values of the shock Mach number MS0 of the shock wave and turbulent Mach number MT of the grid turbulence. The experimental results show that the root-mean-squared peak-overpressure fluctuation divided by the averaged peak-overpressure, σΔp/⟨Δp⟩, where the inherent noise caused by the experimental facility is removed, follows a power law of MT^2/(MS0^2−1). The probability density functions of the overpressure fluctuations are close to the Gaussian profile for a wide range of MT^2/(MS0^2−1). A shock deformation model based on the deformation due to nonuniform fluid velocity is proposed for the investigation of the influences of turbulence on the shock wave. The deformation changes the cross-sectional area of the ray tube, which is related to the shock Mach number fluctuation of the area. The model for a weak shock wave yields the relation σΔp/⟨Δp⟩≈(1/√3)[MT^2/(MS0^2−1)]^1/2, which agrees well with the experimental results. The model also predicts the Gaussianity of the peak-overpressure fluctuations behind the shock wave interacting with Gaussian velocity fluctuations. Good agreements between the model and experiments imply that the change in the shock wave characteristics by the interaction with turbulence is closely related to the shock wave deformation caused by the fluctuating turbulent velocity field.

日本語訳 (DeepL翻訳)

乱流と相互作用する弱い衝撃波の背後の過圧変動の統計量

乱流と相互作用する弱い衝撃波の背後の過剰圧変動を、球面衝撃波が格子状乱流中を伝播する風洞実験によって研究した。実験は衝撃波の衝撃マッハ数MS0と格子状乱流の乱流マッハ数MTを様々な値に設定して行われた。実験の結果、実験設備による固有のノイズを除去した平均化ピーク過圧で割った二乗平均ピーク過圧変動σΔp/<Δp>は、MT^2/(MS0^2-1)のべき乗則に従うことが示された。過圧変動の確率密度関数は、MT^2/(MS0^2-1)の広い範囲でガウス分布に近いものとなった。衝撃波に対する乱流の影響を調べるために、流体速度の不均一性による変形に基づいた衝撃波変形モデルを提案した。この変形は光線管の断面積を変化させ、その面積が衝撃マッハ数の変動に関係する。弱い衝撃波のモデルは、σΔp/<Δp>≈(1/√3)[MT^2/(MS0^2-1)]^1/2 という関係をもたらし、これは実験結果とよく一致する。このモデルはまた、ガウス型の速度変動と相互作用する衝撃波の背後のピーク圧力変動のガウス性を予測する。モデルと実験の良い一致は、乱流との相互作用による衝撃波の特性の変化が、揺らぐ乱流速度場による衝撃波の変形と密接に関係していることを示唆している。

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