Two-Phase Gas and Dust Free Expansion: Three-Dimensional Benchmark Problem for CFD Codes

In the computational mechanics of multiphase dispersed flows, there is an issue of computing the interaction between phases in a mixture of a carrier fluid and dispersed inclusions. The problem is that an accurate dynamics simulation of a mixture of gas and finely dispersed solids with intense interphase interaction requires much more computational power compared to pure gas or a mixture with moderate interaction between phases. To tackle this problem, effective numerical methods are being searched for to ensure adequate computational cost, accuracy, and stability of the results at an arbitrary intensity of momentum and energy exchange between phases. Thus, to assess the approximation, dispersive, dissipative, and asymptotic properties of numerical methods, benchmark solutions of relevant test problems are required. Such solutions are known for one-dimensional problems with linear plane waves. We introduce a novel analytical solution for the nonlinear problem of spherically symmetric expansion of a gas and dust ball into a vacuum. Therein, the dynamics of carrier and dispersed phases are modeled using equations for a compressible inviscid gas. Solid particles do not have intrinsic pressure and are assumed to be monodisperse. The carrier and dispersed phases exchange momentum. In the derived solution, the velocities of gas and dust clouds depend linearly on the radii. The results were reproduced at high, moderate, and low momentum exchange between phases using the SPH-IDIC (Smoothed Particle Hydrodynamics with Implicit Drag in Cell) method implemented based on the open-source OpenFPM library. We reported an example of using the solution as a benchmark for CFD (computational fluid dynamics) models verification and for the evaluation of numerical methods. Our benchmark solution generator developed in the free Scilab environment is publicly available