You-Rong Li

Sensitivity analyses of the thermophysical properties of silicon melt and crystal

A set of global numerical simulations based on a simple, laminar, axisymmetric and pseudo steady model of a small silicon CZ furnace was conducted to reveal the influences of the thermophysical properties of the melt and crystal on the non-dimensional crystal pulling rate, i.e., the Peclet number Pe, and the deflection of the melt/crystal interface Δz, for the sensitivity analyses of the properties. The properties investigated here are the temperature coefficient of surface tension, viscosity, thermal conductivity, the thermal expansion coefficient and emissivity of the melt, and the thermal conductivity and emissivity of the crystal. The results demonstrated that, concerning the thermophysical properties of the melt, emissivity is relatively sensitive to Pe and Δz. Concerning the crystal properties, thermal conductivity is more sensitive to Pe, while emissivity is more sensitive to Δz.

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.

Direct numerical simulation of Rayleigh-Bénard convection in a cylindrical container of aspect ratio 1 for moderate Prandtl number fluid

A series of three-dimensional numerical simulations were conducted for the Rayleigh-Benard convection in a cylindrical container with the aspect ratio Γ = 1. The Prandtl number of the fluid is 7 and the Rayleigh number varies from 103 to 105. Results show that the aspect ratio of the cylinder has an important influence on the multiplicity of the steady flow state. The sidewall of the cylinder at Γ = 1 restricts the increase of the number of rolls in the fluid layer. Therefore, only two-roll and single-roll flow patterns are observed at the whole simulation range of the Rayleigh number. During the transition of the Rayleigh-Benard convection to the unsteady flow, it is found that the unsteady flow pattern and the bifurcation sequence of the oscillation flow are very sensitive to the initial condition.

Rotating and thermocapillary-buoyancy-driven flow in a cylindrical enclosure with a partly free surface

In order to understand the characteristics of the complex flow driven by the combined thermocapillary-buoyancy effect and differential rotation of a cylindrical pool and a disk on the free surface, a series of unsteady three-dimensional numerical simulations were performed. Results indicate that the flow is axisymmetric and steady at a small temperature difference and low rotation rates. The basic meridional flow structures are composed of toroidal circulations. With an increase of the rotation rate and/or temperature difference, the basic flow transits to a three-dimensional oscillatory flow. Without rotation, the unstable thermocapillary-buoyancy flow is characterized by pulsating spoke patterns with the periodic growth and decay of temperature and velocity oscillations. When the disk and/or cylinder rotate, the oscillatory flow behaves as temperature and velocity fluctuation waves traveling in the azimuthal direction. The wave propagation velocity and direction, fluctuation amplitude, and wave number depend on the interaction of the thermocapillary, buoyancy, centrifugal and Coriolis forces. The critical conditions for the flow transition are determined. It is found that the critical thermocapillary Reynolds number initially increases before decreasing with the increase of the disk rotation rate, but the rotation of cylinder always retards the flow instability. In addition, the mechanisms of the flow instabilities are discussed and briefly summarized.

An Investigation on the Exergo-Economic Performance of an Evaporator in Orc Recovering Low-Grade Waste Heat

Based on the perspective of exergy recovery (profit), an exergo-economic performance evaluation model of evaporator in ORC recovering low-grade waste heat is established. Selecting dry fluid R600a as a working fluid, an exergo-economic criterion was defined to estimate the effects of operating parameters and tube length on the performance of evaporator when the boiling temperature of evaporator is fixed. The optimal flow rate of organic working fluid Gt (flow rate of exhaust flue gas Gs), the flow rate ratio of exhaust flue gas to organic working fluid y, and tube length l have been discovered to maximize the annual net profit value NPV. Furthermore, there exists the critical values of Gt (Gs), y, and l which make NPV = 0. The results also show that, with the increase of the flow rate ratio of exhaust flue gas to organic working fluid, the maximum annual net profit value first increases sharply, and then decreases slowly, while the optimal tube length of evaporator reduces monotonously. Furthermore, the evaluation method from purely thermodynamic viewpoint is imperfect, and the economic considerations change the results obtained with only the maximization of recovered exergy.

Natural Convection of Water Near its Density Maximum around a Cylinder Inside an Elliptical Enclosure along Slender Orientation

A numerical investigation of natural convection of water near its density maximum around a cylinder inside the concentric elliptical enclosure along slender orientation was carried out. The effects of the aspect ratio, the elliptical ratio, the density inversion parameter, and the Rayleigh number were investigated. The typical flow and thermal fields were exhibited by means of streamlines and isotherms, respectively. Variations of the local and average Nusselt numbers were obtained and discussed with the details of both flow and thermal fields. The mechanism of oscillation was also analyzed when the stable flow transits to the unstable flow. Based on the simulation results, the heat transfer correlation has been proposed.

Three-dimensional flow driven by iso- and counter-rotation of a shallow pool and a disk on the free surface

In order to understand the fundamental characteristics of the forced flow driven by iso- and counter-rotation of a shallow pool and a disk on the free surface, we conducted a series of unsteady three-dimensional numerical simulations in a shallow pool. The ratio of the disk to pool radius is Rs=0.3 and the aspect ratio of pool is H=0.06. The results indicated that the forced flow driven by disk and pool rotation is axisymmetric and steady at the small rotation Reynolds number. However, when Reynolds number exceeds a critical value, the flow will undergo a transition to three-dimensional oscillatory flow, which is characterized by the velocity fluctuation waves traveling in the azimuthal direction. The propagating direction and the velocity of the waves depend on the rotation rates and directions of the disk and pool. Besides, the critical conditions for the onset of the oscillatory flow were determined. The details of the flow fields were discussed and the mechanism of the flow pattern transition was also...

Rayleigh-Bénard convection of cold water near its density maximum in a cubical cavity

In order to understand the characteristics of Rayleigh-Benard convection of cold water near its density maximum in a cubical cavity with different thermal boundaries on the sidewalls, a series of direct numerical simulations were carried out by using the control volume approach. Flow pattern structures and their bifurcation series were detailedly analyzed through the bifurcation diagram, and the heat transfer ability of each branch was discussed. Results showed that both the flow pattern and heat transfer characteristic of Rayleigh-Benard convection of cold water have many notable differences as compared with those of common fluids satisfying the Boussinesq approximation; the flow behavior depends both qualitatively and quantitatively on the thermal boundary conditions on the sidewalls. Furthermore, there are multiple flow pattern coexistence and hysteresis phenomenon during the flow pattern transition.

Aspect ratio and radius ratio dependence of flow pattern driven by differential rotation of a cylindrical pool and a disk on the free surface

The aspect ratio and radius ratio dependence of the flow pattern driven by the differential rotation of a cylindrical pool and a disk on the free surface is investigated through a series of unsteady three-dimensional numerical simulations. The aspect ratio, which is defined as the height to the radius ratio of the pool, varies from 0.06 to 2.0 and the radius ratio of the disk to the cylindrical pool varies from 0.15 to 0.9. The rotation Reynolds numbers of the pool and disk range from 0 to 4730 and 0 to −5677, respectively, where the minus sign means the rotation direction of the disk is contrary to that of the cylindrical pool. The results show that the basic flow state is axisymmetric and steady but has rich structures at the meridian plane depending on the aspect and radius ratios. With the increase of the rotation Reynolds number, the flow transits to three-dimensional oscillatory flow, characterized by the velocity fluctuation waves traveling in the counter-clockwise or clockwise direction at differe...

Asymptotic solution of thermocapillary convection in a thin annular pool of silicon melt

The free surface of the silicon melt in a thin annular pool is subjected to a radial temperature gradient. Since the surface tension depends on the temperature, it will create a thermocapillary force on the free surface and, in turn, yield to thermocapillary convection in the bulk of the liquid by the viscous traction. This paper presents an investigation on the steady two-dimensional thermocapillary convection in a differentially heated annular pool of the silicon melt using the asymptotical way. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces are adiabatic. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the pool height to the gap width, goes to zero. The numerical experiments are also carried out to compare to the asymptotic solution of the steady two-dimensional thermocapillary convection. The results indicate that the expressions of velocity and temperature fields in the ...