Shock attenuation by densely packed micro-particle wall

Abstract

A wall densely packed with micro-particles is impacted by a planar shock wave in a horizontal multiphase shock tube to investigate the shock attenuation. The incident shock strength $${P_2}$$ is attenuated to the transmitted shock strength $${P_6}$$ . A dimensionless complex $$\theta$$ composed of the pressure drop coefficient $${f_{\text{m}}}$$ , the void fraction $$\varepsilon$$ , the packed particles length $$L$$ , and the particle diameter $$D$$ was derived from the previous experiments of the milli-particle walls to characterize the shock attenuation property of the particle wall. However, the data points of the micro-particle wall are located outside the region surrounded by the relationship of the shock attenuation $${{{P_6}} \mathord{\left/ {\vphantom {{{P_6}} {{P_2}}}} \right. \kern-0pt} {{P_2}}}$$ and the particle wall characteristic $$\theta$$ . Moreover, the data points of the micro-particle wall present a positive correlation between $${{{P_6}} \mathord{\left/ {\vphantom {{{P_6}} {{P_2}}}} \right. \kern-0pt} {{P_2}}}$$ and $$\theta$$ , which is contradictory to the negative correlation presented by the previous experiments. Comparison and analysis of the experimental results reveal that the key factor of the shock attenuation is not the size of the individual particle but of the skeleton densely packed with all particles. And then the individual particle diameter $$D$$ is replaced by the skeleton cross section size $$W$$ , the particle wall characteristic $$\theta$$ is modified. The experimental data points of Bakken et al., Wagner et al., Theofanous et al., and us are all located inside the region based on the modified particle wall characteristic $${\theta ^*}$$ and all obey the negative correlation between $${{{P_6}} \mathord{\left/ {\vphantom {{{P_6}} {{P_2}}}} \right. \kern-0pt} {{P_2}}}$$ and $${\theta ^*}$$ . The modified particle wall characteristic can describe the shock attenuation capability of both milli-particle and micro-particle walls. Numerous particles are densely packed to form a particle skeleton of void fraction $$\varepsilon$$ . The incident shock strength $${P_2}$$ is attenuated to the transmitted shock strength $${P_6}$$ . The circuitous pores among the skeleton provide the passages for the air shock wave. $$\varepsilon W$$ describes the total size of the void on the skeleton cross section, and $${\phi _{\text{p}}}L$$ describes the length of the circuitous pores among the skeleton. The modified particle skeleton characteristic $${\theta ^*}={{\left( {{f_{\text{m}}}{\phi _{\text{p}}}L} \right)} \mathord{\left/ {\vphantom {{\left( {{f_{\text{m}}}{\phi _{\text{p}}}L} \right)} {\varepsilon W}}} \right. \kern-0pt} {\varepsilon W}}$$ describes the shock wave attenuation capability of the particle skeleton and shows the negative correlation with the shock attenuation $${{{P_6}} \mathord{\left/ {\vphantom {{{P_6}} {{P_2}}}} \right. \kern-0pt} {{P_2}}}$$ .