A new numerical method to efficiently simulate particulate interactions with high-speed transitional boundary-layer flows is presented. A particulate solver, employing Crowe’s correlation, is used to calculate the particulate trajectory. The solver is fully coupled via a particulate–flow interaction source term to a nonlinear disturbance flow solver based on the compressible Navier–Stokes equations. To efficiently simulate the particulate–flow interactions, an adaptive mesh refinement approach is used to capture the wide range of temporal and spatial scales present in the laminar–turbulent transition process. The particulate impingement simulations for a $M=4$ flow over a 14 deg wedge and two different particulate impingement locations employing the newly developed numerical approach are compared against simulations using a conventional static-mesh approach. For the flow conditions considered, oblique first-mode instability waves dominate the early stage of the transition process. In the second part of this paper, the differences between pulse and particulate impingement simulations are investigated in two and three dimensions for a $M=5.35$ flat-plate boundary-layer flow where two-dimensional second-mode instability waves are most amplified in the primary instability regime.

提出了一种新的数值方法，可以有效地模拟颗粒与高速过渡边界层流的相互作用。利用克劳相关性的颗粒求解器可用于计算颗粒轨迹。求解器通过颗粒-流相互作用源项与基于可压缩Navier-Stokes方程的非线性干扰流求解器完全耦合。为了有效地模拟颗粒流相互作用，自适应网格细化方法用于捕获层流湍流过渡过程中存在的各种时空尺度。颗粒撞击模拟$\mathrm{中号}=4$比较了使用新开发的数值方法在14度楔形上的两个流和两个不同的粒子撞击位置与使用常规静态网格方法进行的模拟。对于所考虑的流动条件，倾斜的第一模式不稳定性波在过渡过程的早期占主导地位。在本文的第二部分中，从二维和三维角度研究了脉冲和颗粒撞击模拟之间的差异，$\mathrm{中号}=5.35$ 平面边界层流，其中二维第二模式不稳定性波在主要不稳定性状态中得到最大放大。