Solid velocity correction schemes for a temperature transforming model for convection phase change

Abstract

PurposeTo study the effects of velocity correction schemes for a temperature transforming model (TTM) for convection controlled solid‐liquid phase‐change problem.Design/methodology/approachThe effects of three different solid velocity correction schemes, the ramped switch‐off method (RSOM), the ramped source term method (RSTM) and the variable viscosity method (VVM), on a TTM for numerical simulation of convection controlled solid‐liquid phase‐change problems are investigated in this paper. The comparison is accomplished by analyzing numerical simulation and experimental results of a convection/diffusion phase‐change problem in a rectangular cavity. Model consistency of the discretized TTM is also examined in this paper. The simulation results using RSOM, RSTM and VVM in TTM are compared with experimental results.FindingsIn order to efficiently use the discretized TTM model and obtain convergent and reasonable results, a grid size must be chosen with a suitable time step (which should not be too small). Applications of RSOM and RSTM‐TTM yield identical results which are more accurate than VVM.Originality/valueThis paper provides generalized guidelines about the solid velocity correction scheme and criteria for selection of time step/grid size for the convection controlled phase change problem.

A comprehensive numerical model for melting with natural convection

“…Okada [26] investigated this problem both experimentally and by use of a deforming grid numerical modeling. Ma and Zhang [13] solved this problem by applying the SIMPLE algorithm, temperature transforming model, and various solid velocity correction schemes. One important finding of Ma and Zhang [13] is that inconsistency, i.e., either a solution convergent to physically unreasonable results or divergent, exists in all the modeling results, no matter what solid velocity correction scheme is used or whether a coarse grid or fine grid is employed, if the dimensionless time step is small as compared with the dimensionless grid size.…”

“…In order to investigate the consistency problem reported by Ma and Zhang [13], the same problem (Fig. 2b) is investigated here, employing the SIMPLE algorithm, temperature transforming model, and power-law difference scheme for convection terms in the governing equations used by Ma and Zhang [13].…”

“…2b) is investigated here, employing the SIMPLE algorithm, temperature transforming model, and power-law difference scheme for convection terms in the governing equations used by Ma and Zhang [13]. In Fig.…”

“…12.057 is not explicitly tracked, but instead is determined by the temperature/enthalpy distribution, which involves much simpler mathematical operations with reasonable accuracy. Three principal methods have been proposed to formulate the energy conservation of the phase change system in a fixed grid framework: the enthalpy method [2][3][4], the equivalent thermal capacity method [5,6], and the temperature transforming model [1,[7][8][9][10][11][12][13][14]. Although these methods were demonstrated to solve benchmark examples, it was reported that the enthalpy method suffered from temperature oscillation, the equivalent heat capacity method encountered difficulty in selecting grid size and time step and often produced physically unrealistic oscillatory results, and the temperature transforming model was associated with inconsistency [13], which all led to unreasonable results or solution procedure divergence.…”

“…In order to force the velocity in the solid phase to be negligibly small, various solid velocity correction methods have been proposed: variable viscosity, switch-off, Darcy source term, ramped switch-off, and ramped source term [13]. All of the proposed methods employ large numbers (e.g., 10 30 ) to either approximate the solid viscosity or to scale the solid velocity.…”