The effect of shock waves on the dispersion characteristics of a particle cloud is investigated both numerically and analytically. A one-dimensional analytical model is developed for the estimation of the cloud topology in the wake of a shock wave, as a function of time, space, and characteristic response time τp of the cloud based on the one-way formalism. The model is compared with the results obtained with numerical simulations over a wide range of incident Mach numbers Ms and particle volume fraction τv,0. An extension of the one-way formalism to the two-way is proposed by taking into account the post-shock gas deceleration due to the presence of particles. A significant increase in the cloud density is noticed. The effects of different parameters affecting the shock–spray interaction are elucidated and discussed. The two-way formalism is seen to better describe the effects of the particles on the propagation of the shock wave.The effect of shock waves on the dispersion characteristics of a particle cloud is investigated both numerically and analytically. A one-dimensional analytical model is developed for the estimation of the cloud topology in the wake of a shock wave, as a function of time, space, and characteristic response time τp of the cloud based on the one-way formalism. The model is compared with the results obtained with numerical simulations over a wide range of incident Mach numbers Ms and particle volume fraction τv,0. An extension of the one-way formalism to the two-way is proposed by taking into account the post-shock gas deceleration due to the presence of particles. A significant increase in the cloud density is noticed. The effects of different parameters affecting the shock–spray interaction are elucidated and discussed. The two-way formalism is seen to better describe the effects of the particles on the propagation of the shock wave.

中文翻译：

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用冲击波模拟可压缩气流中的粒子云扩散

冲击波对粒子云分散特性的影响进行了数值和分析研究。一维分析模型被开发用于在冲击波之后估计云拓扑，作为基于单向形式的云的时间、空间和特征响应时间 τp 的函数。将该模型与在大范围的入射马赫数 Ms 和粒子体积分数 τv,0 上通过数值模拟获得的结果进行比较。通过考虑由于粒子的存在引起的冲击后气体减速，提出了将单向形式主义扩展到双向形式。注意到云密度显着增加。阐明和讨论了影响冲击-喷雾相互作用的不同参数的影响。双向形式可以更好地描述粒子对激波传播的影响。从数值和解析两方面研究了激波对粒子云弥散特性的影响。一维分析模型被开发用于在冲击波之后估计云拓扑，作为基于单向形式的云的时间、空间和特征响应时间 τp 的函数。将该模型与在大范围的入射马赫数 Ms 和粒子体积分数 τv,0 上通过数值模拟获得的结果进行比较。通过考虑由于粒子的存在引起的冲击后气体减速，提出了将单向形式主义扩展到双向形式。注意到云密度显着增加。阐明和讨论了影响冲击-喷雾相互作用的不同参数的影响。双向形式可以更好地描述粒子对冲击波传播的影响。