Solution Of Phase Change Problems Research Articles

Numerical study of the vertical solidification process

A parametric study of chemical segregation during the solidification of concentrated binary alloy under uniform magnetic field effect was performed. The purpose of this work is to present and discuss a numerical solution of phase change problem for a vertical Bridgman system with varying temperature gradient at the boundary. During growth, three regions appear; liquid, mushy and solid zones. The mushy zone is assimilated to porous medium. The transport equations for continuity, momentum, energy and spices transfer are solved. Numerical results for flow in the bath, solute distribution and radial segregation have been obtained for different values of the governing parameters. The effects of various physical parameters like Rayleigh number and Hartmann number on dimensionless heat and mass transfer during phase change under magnetic field effect characteristics are discussed in detail. In particular, it has been found that increase in Rayleigh number increase convection in the melt and complicates the solute distribution in the mushy zone, while increase in the strength of the magnetic field leads to decrease the radial segregation and stratified the solute distribution during growth.

Accuracy of the two-iteration spectral method for phase change problems

The accuracy of the solution of phase change problems using a spectral method is studied. Two iterations in the expansion are used to obtain the interface location of a solidification problem in semi-infinite domain. Asymptotic expansion of the current approach is compared to the existing analytical solution of the problem, and the validity of the expansion is studied. The results indicate the accuracy of a numerical application of the current approach to finite and semi-infinite geometries.

Gas dynamics and radiation heat transfer in the vapor plume produced by pulsed laser irradiation of aluminum

The interaction of pulsed laser irradiation of nanosecond duration with a metal surface is studied by numerical simulation. The heat transfer in the solid substrate and the melted liquid is modeled as one-dimensional transient heat conduction using the enthalpy formulation for the solution of phase change problems. A discontinuity layer is assumed just above the liquid surface. Mass, momentum, and energy conservation are expressed across this layer, while the vapor across the discontinuity is modeled as an ideal gas. The compressible gas dynamics is computed numerically by solving the system of Euler equations for mass, momentum, and energy, supplemented with an isentropic equation of state in a two-dimensional axisymmetric system of coordinates. The excimer laser-beam absorption and radiation transport in the vapor phase are modeled using the discrete ordinates method. The rates for ionization are computed using the Saha–Eggert equation assuming conditions of local thermal equilibrium. The inverse bremsstrahlung mechanism is considered as the main mechanism of plasma absorption. Results show that a thin, submicron vapor layer is formed above the target surface in the duration of laser pulse while thermal radiation plays the key role for plume cooling during the period of strong absorption by the plasma. The release of a very strong shock wave, propagating with a speed of 104 m/s, is observed in the evaporating plume.

A fixed grid method for the numerical solution of phase change problems

AbstractA fixed grid method using an updated iterative implicit scheme is developed to solve one‐dimensional phase change problems. The temperature field is deduced from the resolution of the governing equations whose discretization takes into account the discontinuous variation of the temperature derivative at the phase change front. At each iteration an updated position of the moving front is found from the resolution of the energy conservation at the solid‐liquid interface. The accuracy of the proposed numerical method has been checked on three test problems.

Solution of phase change problems by Ivantsov's approach

With no assumptions regarding the shape and mode of growth of the interface, Ivantsov's method is extended to solve two phase problems involving non-isothermal solid and liquid phases separated by an isothermal interface. The interfacial energy balance is generalized to yield a nonlinear partial differential equation, involving an arbitrary function, for the temperature throughout each phase. The complete integral for each of these equations is obtained and is used to find the singular integral which gives both the shape and mode of growth of the interface. The temperature distribution itself is determined from the conduction equation for each phase. For the illustrative problem considered, the singular integral yields a spherical crystal growing unsteadily in a shape preserving manner. Planar and cylindrical crystals occur as special one and two-dimensional cases.

On the numerical solution of phase change problems in transient non‐linear heat conduction

AbstractA finite difference solution for the transient non‐linear heat conduction with phase change in a finite slab is proposed. A two‐time level implicit method is used while Taylor's forward projection method is employed for taking into account the non‐linearities. The stability due to the boundary conditions at the moving front is verified. The numerical solution is compared with the analytical solutions and found to be in close agreement.