Dan-Ling Zeng

Global simulation of a silicon Czochralski furnace in an axial magnetic field

Abstract Control of melt flow in crystal growth process by application of the magnetic field is a practical technique for silicon single crystals. In order to understand the influence of axial magnetic field on the silicon melt flow and oxygen transport in a silicon Czochralski (Cz) furnace, a set of global numerical simulations was conducted using the finite-element method for the magnetic field strength from 0 to 0.3 T, the crystal rotation rates from 0 to 30 rpm and the crucible counter-rotation rates from 0 to −15 rpm. It was assumed that the flow was axisymmetric laminar in both the melt and the gas, the melt was incompressible and a constant temperature was imposed on the outer wall of the Cz furnace. The results indicate significantly different flow patterns, thermal and oxygen concentration fields in the melt pool when a uniform axial magnetic field is applied.

Instability of the Marangoni convection in a liquid bridge with liquid encapsulation under microgravity condition

Abstract Linear stability theory is used to analyze the stability of the basic state solution of Marangoni convection in a liquid bridge with liquid encapsulation. By processing the linear disturbance equations numerically, stability analysis can be evolved to a complex general eigenvalue problem. Inverse iteration algorithm combined with LZ algorithm is employed to solve the complex generalized eigenvalue problem. The results show that the stability of the system can be enhanced greatly by choosing reasonable matching parameters of the two fluid layers. The preferred mode of instability is axial wave number α =2,3 and 4, which means that the system is more sensitive to the disturbance with larger wave lengths.

Numerical analysis of LEC growth of GaAs with an axial magnetic field

A set of numerical analyses for momentum and heat transfer For a 3 in. (0.075 m) diameter Liquid Encapsulant Czochralski (LEC) growth of single-crystal GaAs with or without all axial magnetic field was carried Out using the finite-element method. The analyses assume a pseudosteady axisymmetric state with laminar floats. Convective and conductive heat transfers. radiative heat transfer between diffuse surfaces and the Navier-Stokes equations for both melt and encapsulant and electric current stream function equations Cor melt and crystal Lire considered together and solved simultaneously. The effect of the thickness of encapsulant. the imposed magnetic field strength as well as the rotation rate of crystal and crucible on the flow and heat transfer were investigated

Suppression of Marangoni Convection of Silicon Melt By A Non-Contaminating Method

A set of numerical simulation of the effect of the gas shearing flow over a silicon melt free surface on Marangoni convection under microgravity condition was conducted by using finite element method. For given gas channel width, Marangoni number and aspect ratio a remarkable reduction of Marangoni convection in silicon liquid bridge can be achieved by choosing the optimal gas velocity in accordance with the correlation proposed in the paper. The effectiveness of the reduction of the gas flow under different conditions shows that, in some cases, Marangoni convection reduction of 99% can be realized by this non-contaminating method

The effect of liquid encapsulation on the Marangoni convection in a liquid column under microgravity condition

Abstract The present paper is devoted to the investigation of the effect of liquid encapsulation on the Marangoni convection in its inner columnar liquid layer under a microgravity condition. The asymptotic solution of the mathematic model established in the paper was obtained for the immiscible axisymmetric coaxial liquid columns contained between planar faces. Numerical simulation based on the asymptotic solution was carried out. The main influence factors on the process were discussed in detail. It is found that proper selection of the related parameters will result in a remarkable reduction of the Marangoni convective flow.

Numerical Simulation of Oscillatory Marangoni Flow in Encapsulated Liquid Bridge

The physical and mathematical models of the Marangoni convection of KF-96 silicone oil and FC-70 fluorinart in an encapsulated liquid bridge were established. To contrast to this configuration, the Marangoni convection of KF-96 silicone oil in a liquid bridge was also studied in present work. We conducted a series of unsteady two-dimensional numerical simulations. Simulation conditions correspond to those in the experiments of Majima and Kawamura (2001). The simulation results with large Marangoni number (Ma) predicted oscillatory flows under microgravity. The critical conditions for the onset oscillatory flow were determined and compared with the experimental results. Details of the flow and temperature fields were discussed. Oscillation frequencies were also exhibited.Copyright

The Research on Exergy Transfer of Forced Convective Heat Transfer Through a Duct With Constant Wall Temperature

Based on the first and second thermodynamic laws, a new systematic approach to study in detail the exergy transfer processes of forced convective heat transfer through a duct with constant wall temperature for fully developed turbulent flow is introduced. Some definition formula of the local and mean convective exergy transfer coefficient, convective exergy resistance, exergy flux and exergy-transfer Nusselt number etc have been provided and their new generalized expressions are derived. By reference to smooth duct, the numerical results of exergy transfer are obtained, the effect of Reynolds number and different cross-sectional position in the duct on exergy transfer process is analyzed. In addition, a comparison of the results of exergy transfer with that of energy transfer is also discussed.Copyright

Entropy Generation in Natural Convection of Water Near Its Density Maximum in a Square Cavity

This paper is focused on the entropy generation due to heat transfer and viscous flow in natural convection of water near its density maximum in a square cavity. The present hydrodynamic and temperature fields are obtained by solving numerically the mass, momentum and energy balance equations, using the finite difference method. Local entropy generation distributions are obtained based on the resulting velocity and temperature fields by solving the entropy generation equation. The effect of the Grashof numbers on the total entropy generation is studied. Local entropy generation distribution was found to be dependent on the Grashof number and the dimensionless initial temperature. The results also show that thermal entropy generation is relatively dominant over viscous entropy generation.Copyright

A Numerical Study of Effect of Liquid Encapsulation on Thermocapillary Convection in Liquid Bridge

The physical and mathematical models of the thermocapillary convection in liquid bridge with liquid encapsulation are established in the present paper. A numerical simulation of the thermocapillary convection in liquid bridge with liquid encapsulation is performed by employed vorticity-stream function method and the Alternative Direction Implicit scheme in finite difference. The distribution of temperature and flow in liquid columns is then obtained. It is verified that liquid encapsulation can reduce the thermocapillary convection in liquid bridge and can improve the quality of crystal growth in float zone. The influence law of the thickness of liquid encapsulation on the thermocapillary convection in liquid bridge is obtained, the more thickness of liquid encapsulation decreases, the more the thermocapillary convection in the inner liquid and the outer liquid diminishes. It is found that the flow profile of two liquid columns is much more complex than that of single liquid column.Copyright