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

Abstract

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.

Computation of non-isothermal and compressible low Mach number gas flows by fully explicit scheme using control method for speed of sound

“…This result shows that 10 −5 and 5.0 × 10 −5 are allowable minimum values of α for Ra = 10 3 and 10 6 to obtain reasonable temperature distributions in this application. Table 3 gives the comparison of Nu h in the steady state between the proposed fully explicit compressible fluid model, our conventional semi-implicit compressible fluid model [1], and a conventional implicit incompressible fluid model [10]. Here, the incompressible fluid model cannot be applied to the case for Ra = 10 6 since β∆ is 0.33 and the density Table 3, obtained Nusselt numbers are in good agreement with the reference results regardless of α values.…”

“…The numerical procedure of the proposed fully explicit method is divided into three stages [1], advection, diffusion, and acoustic stages. The governing equations in each computational stage are discretized on the collocated grid system [7] and variables are updated…”

“…In our conventional semi-implicit method [1], the pressure terms of the momentum and energy equations are treated implicitly in the acoustic stage to improve the CFL condition based on the speed of sound. By contrast, p ′ is adopted in this study, and the next time step velocity u n+1 i and pressure p ′n+1 are calculated explicitly as follows:…”

“…In our previous study [1], a semi-implicit fractional step method for non-isothermal and compressible low Mach number gas flows was proposed to calculate thermal interactions between fluids and solid objects under high temperature difference conditions. In this method, advection and diffusion terms in governing equations written in the conservative form are treated explicitly.…”

“…Especially, the reduced speed of sound technique [5,6] enables to control the speed of sound simply by using an artificial coefficient in the advection term on the mass conservation equation. However, the conventional reduced speed of sound technique [5,6] cannot be applied directly to our original fractional step method [1] since the conventional technique is proposed for the compressive magnetohydrodynamics equations and numerical procedures are different from those of our method.…”