TY - JOUR

T1 - Two-Phase Gas and Dust Free Expansion: Three-Dimensional Benchmark Problem for CFD Codes

AU - Stoyanovskaya, Olga P.

AU - Grigoryev, Vitaliy V.

AU - Suslenkova, Anastasiya N.

AU - Davydov, Maxim N.

AU - Snytnikov, Nikolay V.

N1 - Funding Information: Funding: This research was funded by the Russian Science Foundation, grant number 19-71-10026. Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/2

Y1 - 2022/2

N2 - 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.

AB - 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.

KW - Aerodynamic drag

KW - Benchmark problem

KW - CFD verification test

KW - Dusty gas

KW - Free expansion

KW - Gas and dust medium

KW - Intense interaction between phases

KW - Monodisperse mixture

KW - Multifluid model

KW - Nemchinov–Dyson problem

KW - Smoothed particle hydrodynamics

UR - http://www.scopus.com/inward/record.url?scp=85123934576&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/ecc0fc90-ce58-332c-aa53-a3e73e4ea15a/

U2 - 10.3390/fluids7020051

DO - 10.3390/fluids7020051

M3 - Article

AN - SCOPUS:85123934576

VL - 7

JO - Fluids

JF - Fluids

SN - 2311-5521

IS - 2

M1 - 51

ER -