Global Heat Transfer Model Research Articles

Effect of crucible location on heat transfer in GaN crystal growth using Na flux method

A global model of heat transfer, considering convection, conduction, radiation as well as mass transfer, is established for GaN single crystal growth system employing the Na flux method. Global simulations are carried out to investigate the effects of crucible locations on the heat and mass transfer during growing. It was found that the crucible location has a significant effect on the heat transfer in the melt. When the crucible moves down, the flow in the upper region of melt is enhanced, while that near the crucible bottom is weaken. This flow structure leads to high supersaturation at the crucible bottom, which is favorable to accelerate crystallization. Therefore, it can be concluded that the crucible location should be lowered properly to achieve a better condition for crystallization. The research provides directions to the design of GaN growing systems.

Boundary Conditions for Simulations of Fluid Flow and Temperature Field during Ammonothermal Crystal Growth—A Machine-Learning Assisted Study of Autoclave Wall Temperature Distribution

Thermal boundary conditions for numerical simulations of ammonothermal GaN crystal growth are investigated. A global heat transfer model that includes the furnace and its surroundings is presented, in which fluid flow and thermal field are treated as conjugate in order to fully account for convective heat transfer. The effects of laminar and turbulent flow are analyzed, as well as those of typically simultaneously present solids inside the autoclave (nutrient, baffle, and multiple seeds). This model uses heater powers as a boundary condition. Machine learning is applied to efficiently determine the power boundary conditions needed to obtain set temperatures at specified locations. Typical thermal losses are analyzed regarding their effects on the temperature distribution inside the autoclave and within the autoclave walls. This is of relevance because autoclave wall temperatures are a convenient choice for setting boundary conditions for simulations of reduced domain size. Based on the determined outer wall temperature distribution, a simplified model containing only the autoclave is also presented. The results are compared to those observed using heater-long fixed temperatures as boundary condition. Significant deviations are found especially in the upper zone of the autoclave due to the important role of heat losses through the autoclave head.

Effect of Internal Radiation on Heat Transfer during Ti:sapphire Crystal Growth Process by Heat Exchanger Method

In this study, the effect of internal radiation on the heat transfer during titanium-doped sapphire (Ti:sapphire) crystal growth process by heat exchanger method (HEM) was comprehensively investigated based on a global heat transfer model. Radiation absorption, emission and scattering in the semitransparent melt and crystal were modeled with the rigorous finite volume method. The numerical results show that internal radiation strongly enhances the heat transport in the melt and crystal, strengthens the melt convection and reduces the temperature gradient in the central body of the crystal. However, it renders the isotherms intensively concentrated in the narrow bottom region of the crystal, resulting in a significant increase in the temperature gradient in this region compared to the case without internal radiation. What's more, internal radiation makes the melt-crystal interface deeply convex towards the melt, which could be responsible for the radial non-uniformity of titanium concentration in the large Ti:sapphire crystal by HEM. The sensitivity of internal radiation to the optical properties was also parametrically studied. It was found that the heat transfer is strongly depended on the absorption coefficients of the crystal and melt. Particularly, the interaction between internal radiation and heat conduction in the crystal is strongest at the intermediate value of the absorption coefficient of the crystal, leading to the largest values of conduction heat transfer rate and maximum temperature gradient at the bottom of the crystal. The influence of scattering in the crystal becomes significant only after the scattering coefficient is larger than absorption coefficient. This study suggested that the effect of internal radiation on the heat transfer during HEM Ti:sapphire crystal growth process shows some difference from that during Kyropoulos and Czochralski oxide crystal growth processes.

Investigations on Quench Recovery Characteristics of High-Temperature Superconducting Coated Conductors for Superconducting Fault Current Limiters

Superconducting fault current limiters (SFCLs) are attracting increasing attention due to their potential for use in modern smart grids or micro grids. Thanks to the unique non-linear properties of high-temperature-superconducting (HTS) tapes, an SFCL is invisible to the grid with faster response compared to traditional fault current limiters. The quench recovery characteristic of an HTS tape is fundamental for the design of an SFCL. In this work, the quench recovery time of an HTS tape was measured for fault currents of different magnitudes and durations. A global heat transfer model was developed to describe the quench recovery characteristic and compared with experiments to validate its effectiveness. Based on the model, the influence of tape properties on the quench recovery time was discussed, and a safe margin for the impact energy was proposed.

Global heat transfer model and dynamic ray tracing algorithm for complex multiple turbine blades of Ni-based superalloys in directional solidification process

High-quality solidification microstructure during directional solidification relies on precise temperature gradient control, so accurate calculation of the temperature field is critical. In this study, a 3D transient global heat transfer model of directional solidification by the Bridgman method based on the finite difference method is developed. The radiation heat in this model is calculated by the discrete transfer method, and a modified method of external surface area for irregular geometric models is proposed to reduce the zigzag shape caused by finite difference grids. Considering the radiative heat transfer between any surface elements of all materials in the directional solidification furnace, a dynamic ray tracing algorithm is developed to simulate the entire process of directional solidification. Then, the simulated results are compared with the theoretical results and experimental results, respectively. Finally, based on the present model and method, the simulation program developed is applied to the directional solidification of actual castings. The simulated results are in good agreement with the experimental results, which indicate that the model and method developed in this study is effective and practical.

Numerical investigation of Directional Solidification process for improving multi-crystalline silicon ingot quality for photovoltaic applications

Numerical simulation is used as a comprehensive tool for analysis and optimization of the multi-crystalline silicon (mc-Si) growth by the Directional Solidification (DS) method. We have used a transient global heat transfer model to optimize the temperature profile of the DS process to produce high-quality multi-crystalline silicon ingots for solar cell application. The melt-crystal interface shape, impurities and von Mises stress were studied by the numerical simulation with different temperature profiles. A slightly convex interface shape, lower thermal stress and lower impurities in the mc-Si were obtained due to the lower temperature gradient by the optimized temperature profile. Simulation results show that the optimized temperature profile is particularly suitable for high quality mc-Si ingot.

3D Global Heat Transfer Model on Floating Zone for Silicon Single Crystal Growth

AbstractIn this paper, a three‐dimensional global heat transfer model to describe the floating zone of silicon single‐crystal growth is proposed. The steady‐state calculations considering argon gas flow, feed rod, silicon melt and crystal are carried out using open source software OpenFOAM with no assumptions of symmetry. From the global calculation, a three dimensional solid‐liquid interface has been obtained. Furthermore, the cooling effect of gas flow in three dimensions is considered, and the three‐dimensional current‐density distribution of the inductor is calculated. By considering the asymmetrical electromagnetic field induced by the inductor, the calculations reveal a deflection of the asymmetrical solid‐liquid interface.

Temperature and thermal stress evolutions in sapphire crystal during the cooling process by heat exchanger method

Transient numerical calculations were carried out to predict the evolutions of temperature and thermal stress in sapphire single crystal during the cooling process by heat exchanger method (HEM). Internal radiation in the semitransparent sapphire crystal was taken into account using the finite volume method (FVM) in the global heat transfer model. The numerical results seem to indicate that the narrow bottom region of the sapphire crystal is subjected to high thermal stress during the cooling process, which could be responsible for the seed cracking of the as-grown crystal, while the thermal stress is relatively small in the central main body of the crystal, and is less than 10MPa during the whole cooling process. The fast decrease of the thermal stress in the bottom region of the crystal during the initial stage of cooling process is dominated by the reduction of the cooling helium gas in the heat exchanger shaft, and is not significantly affected by the heating power reduction rate.

Numerical modelling on stress and dislocation generation in multi-crystalline silicon during directional solidification for PV applications

Numerical modelling has emerged as a powerful tool for the development and optimization of directional solidification process for mass production of multicrystalline silicon. A transient global heat transfer model is performed to investigate the effect of bottom grooved furnace upon the directional solidification (DS) process of multi-crystalline silicon (mc-Si). The temperature distribution, von Mises stress, residual stress and dislocation density rate in multi-crystalline silicon ingots grown by modified directional solidification method have been investigated for five growth stages using finite volume method at the critical Prandtl number, Pr = 0.01. This paper discusses bottom groove furnace instead of seed crystal DS method. It achieves an advanced understanding of the thermal and mechanical behaviour in grown multi-crystalline ingot by bottom grooved directional solidification method. The von Mises stress and dislocation density were reduced while using the bottom grooved furnace. This work was carried out in the different grooves of radius 30 mm, 60 mm and 90 mm of the heat exchanger block of the DS furnace. In this paper, the results are presented for 60 mm radius groove only because it has got better results compared to the other grooves. Also, the computational results of bottom grooved DS method show better performance compared the conventional DS method for stress and dislocation density in grown ingot.

Effect of Crucible Location on Heat Transfer in Sapphire Crystal Growth by Heat Exchanger Method

A global model of heat transfer, including melt convection, solid conduction, surface radiation, and crystal internal radiation, as well as phase change, is established for a sapphire crystal growing system by a heat exchanger method. Global simulations are carried out to investigate the effects of crucible location on heat transfer and sapphire crystal growth in the growing system. It is found that the crucible location has a significant effect on the heat transfer in the crystal and melt domains. When the crucible rises up, the melt flow is enhanced and the convexity of the melt–crystal interface increases at the crystallization stage. The thermal stress in the growing crystal decreases at the annealing stage. It therefore can be concluded that the crucible should be lowered at the crystallization stage, and raised up at the annealing stage, to obtain high-quality sapphire crystals.

Controlling solidification front shape and thermal stress in growing quasi-single-crystal silicon ingots: Process design for seeded directional solidification

To control the solidification front shape and thermal stress in the growing silicon ingot and reduce the small-grain region at its periphery, a moving insulation partition block was designed in an industrial seeded directional solidification furnace for quasi-single-crystal silicon ingots. We propose several moving process designs of the partition block. A transient global model of heat transfer in which all types of heat transfer are included was established to investigate the thermal field, solidification front evolution, and thermal stress in the growing ingot. Corresponding experiments were conducted to validate the simulation results through the relationship between solidification front shape and the small-grain region. It was found that the moving process can significantly influence the thermal field, solidification front shape, and thermal stress in the growing ingot during the solidification process. The moving partition block design is feasible to control the solidification front shape and reduce the small-grain region at the periphery of the solidified ingot. A favorable moving process design of the partition block was obtained that can simultaneously achieve a small small-grain region and low thermal stress in the solidified ingot.

Numerical optimization and reaction flow analysis of syngas production via partial oxidation of natural gas in internal combustion engines

The production of hydrogen is studied numerically under uncatalyzed partial oxidation and homogeneous charge compression ignition (HCCI) conditions in an internal combustion engine fueled by natural gas. The HCCI process is modeled by a single-zone variable volume reactor using a global heat transfer model and elementary-step reaction mechanisms. Numerical optimization is applied to maximize the hydrogen yield at the end of the expansion stroke by varying the equivalence ratio, engine speed and initial pressure for a fixed initial temperature. Suitable constraints were defined, including peak pressure and bounds to the optimization variables. From these results, maximum hydrogen yield profiles and the associated operating parameter profiles as functions of initial temperature were obtained. The profiles exhibit strong linear dependency with initial temperature. Reaction flow analysis was performed to gain detailed insight into the chemical processes involved when the engine is run under optimal conditions for a maximum hydrogen yield. The integral reaction flow analysis shows that substantial amounts of hydrogen are produced from precursors, which are also valuable products, such as methanol, formaldehyde and ethylene.

Development of a Global Model of Heat Transfer in the Czochralski Furnace Taking into Account Specular Reflection at the Crystal Surface

In this study, a global model of heat transfer for the Czochralski crystal growth of oxides is developed by integrating the conventional model and the improved radiation element method by the ray emission model (REM2) in which radiative heat transfer in semitransparent crystals with a specular surface, that is, reflection and refraction at the crystal surface, is considered. The validity of the present model is verified by comparing it with the conventional model. Then, the effects of the optical thickness and the refractive index of the crystal on the temperature distribution in the furnace and on the melt/crystal interface shape are numerically investigated.

Improved seeded directional solidification process for producing high-efficiency multi-crystalline silicon ingots for solar cells

We proposed an improved process design for the industrial mc-Si seeded directional solidification process to produce high-quality multi-crystalline silicon ingots for high-efficiency solar cells. A transient global model of heat transfer was employed to investigate the effects of the process design parameters on the melt–crystal interface shape, thermal field, and thermal stress distribution in the solidified silicon ingot during the solidification process. Ingot casting experiments were carried out and the solar cell performance was measured. The results show that the melt–crystal interface shape in the improved process design remains convex during almost the whole solidification process, and the thermal stress level at the bottom of the solidified ingots is significantly lower than in the original process design. Based on the experimental results, the quality of grown silicon ingots and the conversion efficiency of solar cells were analyzed. The shadow region present in the silicon ingot produced with the original process design disappears and the morphology of the ingot is improved with a more homogeneous distribution of grain orientation using the improved process design. The average yield rate of the solidified silicon ingot is 8.18% higher with the improved process design. The average conversion efficiency of solar cells is higher with the improved process design (17.59%) than with the original process design (17.48%).

Computer modeling of crystal growth of silicon for solar cells

A computer simulator with a global model of heat transfer during crystal growth of Si for solar cells is developed. The convective, conductive, and radiative heat transfers in the furnace are solved together in a coupled manner using the finite volumemethod. A three-dimensional (3D) global heat transfer model with 3D features is especially made suitable for any crystal growth, while the requirement for computer resources is kept permissible for engineering applications. A structured/unstructured combined mesh scheme is proposed to improve the efficiency and accuracy of the simulation. A dynamic model for the melt-crystal (mc) interface is developed to predict the phase interface behavior in a crystal growth process. Dynamic models for impurities and precipitates are also incorporated into the simulator.

Effects of argon flow on heat transfer in a directional solidification process for silicon solar cells

A global heat transfer model, including the melt convection, argon flow, thermal conduction, thermal radiation and fully coupled boundary conditions, was developed to investigate the argon flow effect on the temperature distribution and melt convection in a directional solidification furnace for silicon solar cells. Both the effect of argon flow rate and the effect of furnace pressure were examined. It was found that the heat transfer at the melt free surface due to the gas convection cannot be neglected, though the argon flow contributes little to the global heat transfer at most radiative surfaces. The shear stress caused by the argon flow at the melt free surface becomes larger with the increase in argon flow rate and it further changes the velocity and temperature distributions in the silicon melt. We also found that the effect of argon flow on the melt convection at a low furnace pressure will be enhanced if the argon mass flow rate is kept constant. The solidification process can thus be controlled by modifying the argon flow rate and the furnace pressure.

Modeling and simulation of Si crystal growth from melt

AbstractA numerical simulator was developed with a global model of heat transfer for any crystal growth taking place at high temperature. Convective, conductive and radiative heat transfers in the furnace are solved together in a conjugated way by a finite volume method. A three‐dimensional (3D) global model was especially developed for simulation of heat transfer in any crystal growth with 3D features. The model enables 3D global simulation be conducted with moderate requirement of computer resources. The application of this numerical simulator to a CZ growth and a directional solidification process for Si crystals, the two major production methods for crystalline Si for solar cells, was introduced. Some typical results were presented, showing the importance and effectiveness of numerical simulation in analyzing and improving these kinds of Si crystal growth processes from melt. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Carbon concentration and particle precipitation during directional solidification of multicrystalline silicon for solar cells

The content and uniformity of carbon and silicon carbide (SiC) precipitates have an important impact on the efficiency of solar cells made of multicrystalline silicon. We established a dynamic model of SiC particle precipitation in molten silicon based on the Si–C phase diagram. Coupling with a transient global model of heat transfer, computations were carried out to clarify the characteristics of carbon segregation and particle formation in a directional solidification process for producing multicrystalline silicon for solar cells. The effects of impurity level in silicon feedstock and solidification process conditions on the distributions of substitutional carbon and SiC precipitates in solidified silicon ingots were investigated. It was shown that the content of SiC particles precipitated in solidified ingots increases markedly in magnitude as well as in space with increase in carbon concentration in silicon feedstock when it exceeds 1.26×1017 atoms/cm3. The distribution of SiC precipitates can be controlled by optimizing the process conditions. SiC precipitates are clustered at the center-upper region in an ingot solidified in a fast-cooling process but at the periphery-upper region for a slow-cooling process.

Global analysis of heat transfer in CZ crystal growth of oxide taking into account three-dimensional unsteady melt convection: Effect of meniscus shape

A global model of heat transfer analysis for the Czochralski crystal growth of oxides, in which a three-dimensional unsteady melt flow was taken into account, was developed in our recent study. In the model, however, the focal point was the methodology of formulating the model by coupling a conventional global model of heat transfer, which is based on a pseudosteady axisymmetric assumption, with a model of a three-dimensional, unsteady melt flow via two interface models. Therefore, for simplicity, the shape of the melt free surface was assumed to be flat. In this study, the global model was further developed by considering the meniscus of the melt free surface. It was found that the meniscus of the melt free surface caused the melt flow to be more unstable and shifted the critical Reynolds number at which the melt/crystal interface inversion occurs toward a much lower value.

Global analysis of heat transfer considering three-dimensional unsteady melt flow in CZ crystal growth of oxide

The conventional global model of heat transfer for the Czochralski (CZ) crystal growth of oxides is based on a pseudo-steady axisymmetric assumption. However, because oxide melt flow is commonly three-dimensional and unsteady, an approach to formulate a global model in which a three-dimensional unsteady melt flow is taken into account was proposed in this study. This approach couples a conventional global model of heat transfer and a model of a three-dimensional, unsteady melt flow using two interface models. The newly developed global model was validated and used to investigate the effect of a three-dimensional, unsteady melt flow on oxide crystal growth. The results indicate that the effect of a three-dimensional, unsteady melt flow is too large to be neglected when the crystal rotational Reynolds number is relatively large. It was found that a three-dimensional, unsteady melt flow shifts the critical Reynolds number at which interface inversion occurs at a much lower value than that obtained using a conventional model based on a pseudo-steady axisymmetric assumption.