Error estimates for two-phase stefan problems in several space variables, I: Linear boundary conditions

CALCOLO ◽  
1985 ◽  
Vol 22 (4) ◽  
pp. 457-499 ◽  
Author(s):  
Ricardo H. Nochetto
Keyword(s):  
Boundary Conditions ◽  
Error Estimates ◽  
Linear Boundary ◽  
Two Phase ◽  
Stefan Problems

scholarly journals Relationship between Neumann solutions for two-phase Lamé-Clapeyron-Stefan problems with convective and temperature boundary conditions

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 187-197 ◽  
Author(s):  
Domingo Tarzia
Keyword(s):  
Boundary Conditions ◽  
Two Phase ◽  
Convective Boundary ◽  
Stefan Problems ◽  
Temperature Boundary ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Neumann Solutions ◽  
Change Material ◽  
Appl Math

We obtain for the two-phase Lam?-Clapeyron-Stefan problem for a semi-infinite material an equivalence between the temperature and convective boundary conditions at the fixed face in the case that an inequality for the convective transfer coefficient is satisfied. Moreover, an inequality for the coefficient which characterizes the solid-liquid interface of the classical Neumann solution is also obtained. This inequality must be satisfied for data of any phase-change material, and as a consequence the result given in Tarzia, Quart. Appl. Math., 39 (1981), 491-497 is also recovered when a heat flux condition was imposed at the fixed face.

A Validated Two-Phase Flow Large Eddy Simulation Methodology

2013 ◽  
Author(s):  
Feng Xiao ◽  
Mehriar Dianat ◽  
James J. McGuirk
Keyword(s):  
Boundary Conditions ◽  
Level Set ◽  
Two Phase Flow ◽  
Local Level ◽  
Density Ratio ◽  
Cross Flow ◽  
Liquid Jet ◽  
Phase Flow ◽  
Two Phase ◽  
Primary Breakup

A robust two-phase flow LES methodology is described, validated and applied to simulate primary breakup of a liquid jet injected into an airstream in either co-flow or cross-flow configuration. A Coupled Level Set and Volume of Fluid method is implemented for accurate capture of interface dynamics. Based on the local Level Set value, fluid density and viscosity fields are treated discontinuously across the interface. In order to cope with high density ratio, an extrapolated liquid velocity field is created and used for discretisation in the vicinity of the interface. Simulations of liquid jets discharged into higher speed airstreams with non-turbulent boundary conditions reveals the presence of regular surface waves. In practical configurations, both air and liquid flows are, however, likely to be turbulent. To account for inflowing turbulent eddies on the liquid jet interface primary breakup requires a methodology for creating physically correlated unsteady LES boundary conditions, which match experimental data as far as possible. The Rescaling/Recycling Method is implemented here to generate realistic turbulent inflows. It is found that liquid rather than gaseous eddies determine the initial interface shape, and the downstream turbulent liquid jet disintegrates much more chaotically than the non-turbulent one. When appropriate turbulent inflows are specified, the liquid jet behaviour in both co-flow and cross-flow configurations is correctly predicted by the current LES methodology, demonstrating its robustness and accuracy in dealing with high liquid/gas density ratio two-phase systems.

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