A comparison of numerical models for evaporative two-phase flow in a self-heated porous medium

Two different numerical models using the finite difference method (FDM) for one-component time-dependent two-phase flows in a porous medium are investigated: the iterative four-variable model (I4VM) and the direct three-variable model (D3VM). The former includes the pressure gradient and uses the iterative method to solve a system of flow equations, whereas for the latter, the formulation without the pressure gradient is simultaneously solved using the algorithm for tri-tridiagonal equations of three dependent variables. The steady-state solution as well as the unsteady results obtained by two models are compared only for the low heat generation rate below the dryout limit. For the high heat generation rate the effects of two numerical models on the time-dependent flow and dryout behavior up to incipient dryout are discussed in terms of liquid volumetric fraction and liquid superficial velocity distributions. It was found that the I4VM is numerically more stable for the case of strongly nonlinear physical models (e.g. the Ergun constants model of Fand, R. M., Kim, B. Y. K., Lam, A. C. and Phan, R. T., Resistance to the flow of fluids through simple and complex porous media whose matrices are composed of randomly packed spheres. J. Fluids Engng, 1987, 109, 268–274) and enables us to analyze those, whereas the D3VM is advantageous for fast analysis of the weakly nonlinear model (e.g. the Ergun constants model of Macdonald, I. F., El-Sayed, M. S., Mow, K. and Dullien, F. A. L., flow through porous media—the Ergun equation revisited. Ind. Engng Chem. Fundam., 1979, 18, 199–208). Finally, a comparative evaluation of both numerical models is presented.