Multiphase computational method for thermal interactions between compressible fluid and arbitrarily shaped solids

Summary A numerical method was investigated for multiphase fields consisting of compressible gas and arbitrarily shaped solids. Since the proposed model is based on a one‐fluid model in which variables are averaged according to the phase fractions in the computational cells; it enables us to estimate gas‐solid momentum and thermal interactions without setting up adapting grids even if the solids have extremely complicated shapes. The governing equations are derived with the characteristics of an ideal gas assuming the specific heat to be uniform in the multiphase field. The derived equations in conservative form are discretized with a finite volume method. In addition, the pressure is calculated implicitly in a similar way to incompressible flow solvers. Because of these improvements, the proposed method allows us to calculate low Mach number compressible flows free from the Courant‐Friedrichs‐Lewy condition based on the speed of sound and to conserve the mass more accurately. To confirm the validity of the proposed method, it was applied to natural convection around an isothermal cylinder and a heat‐conducting pipe. In comparison with previous studies, it was confirmed that the gas flows and temperature distributions are predicted reasonably. In addition, a numerical experiment was conducted under more complicated conditions, namely, gas leaking from a container including heat sources. As a result, it was demonstrated that the proposed method enables us to predict unsteady variations of pressure and temperature distributions in the container due to the leakage while still conserving mass accurately. A new computational method was investigated for the multiphase field consisting of compressible gas and arbitrarily shaped solids based on a one‐fluid model to estimate gas‐solid momentum and thermal interactions without setting up adapting grids even if the solids have extremely complicated shapes. In comparisons with previous studies for natural convections around an isothermal cylinder and heat‐conducting pipe, the validity of our proposed method was confirmed. In addition, a numerical experiment was conducted in more complicated conditions, ie, gas leakage from a container including heat sources and its applicability was discussed.