膨胀波透过大孔隙率结构化球阵时气流场的数值模拟

Numerical simulation of airflow field of expansion waves penetrating structured sphere arrays with large porosities

针对膨胀波透过大孔隙率结构化球阵时的气体流动问题,采用三维雷诺时均Navier-Stokes方程和可实现k-epsilon湍流模型,对不同球阵(或固相)体积分数、破膜压比和球阵排列条件下的气流场进行了数值模拟,分析了上述因素对膨胀波的传播特性和球体阻力系数的影响规律。结果表明:入射膨胀波在传播透过球阵时,会被球面不断地反射,这导致大量反射膨胀波的出现。当破膜压比较小时,反射膨胀波具有较强的聚集叠加效应,容易长时间稳定存在,并汇集形成规则的阵面,此时球体阻力系数增大。在确定工况条件下,对于一个给定的球阵排列,存在一个临界体积分数,当实际体积分数大于它时,能够形成反射膨胀波阵面,反之则不能形成。在大孔隙率限制条件下,体积分数的增大,有利于增强反射膨胀波的干涉,从而增大球体阻力系数。对比晶体立方(Crystal cubic,CC)、双面心立方(Bis-face-centered cubic,BFCC)和交错立方(Staggered cubic,SC)三种排列方式,阻力系数的排序为SC排列、BFCC排列、CC排列,这主要由邻近球间距的差异导致。

Aiming at the airflow problem induced by an expansion wave epentrating structured sphere arrays with large porosities, three-dimensional RANS(Reynolds-average Navier-Stokes) equation and realizable k-epsilon turbulence model were used to carry out the numerical simulation for the airflow fields under different(or solid phase) volume fractions of sphere array, rupture pressure ratios and sphere array arrangements. Besides, the influencing rules of the above factors on propagation characteristics of expansion waves and sphere resistance coefficient. The results show that incident expansion waves will be continuously reflected by the surfaces of the spheres when penetrating the sphere array, thus leading to the appearance of lots of incident expansion waves. For smaller rupture pressure ratios, these reflection waves have strong aggregation and superimposition effect, exist stably for a long time and therefore form a regular wavefront easily. At this moment, the resistance coefficient of the sphere increases. Under a certain operating condition, there exists a critical volume fraction for a given sphere array arrangement. When the actual volume fraction is greater than the critical value, a reflected expansion wavefront can form;otherwise, it cannot form. Under a restriction of large porosities, the increase of volume fraction contributes to enhancing the interference of reflected expansion waves, and thus the resistance coefficient of spheres increases. For three different arrangements of spheres, namely, crystal cubic(CC), bis-face-centered cubic(BFCC), and staggered cubic(SC), the resistance coefficients are sorted in descending order as below: SC, BFCC and CC, which is mainly due to the difference of distance between neighboring spheres.