H. Ouyang

Computational techniques for complex transport phenomena

1. Introduction 2. Numerical scheme for treating convection and pressure 3. Computational acceleration with parallel computing and multigrid methods 4. Multiblock methods 5. Two-equation turbulence models with non-equilibrium, rotation, and compressibility effects 6. Volume-averaged macroscopic transport equations 7. Practical applications References Index.

Development of pressure-based composite multigrid methods for complex fluid flows

Abstract Progress in the development of a multiblock, multigrid algorithm, and a critical assessment of the κ-e two-equation turbulent model for solving fluid flows in complex geometries is presented. The basic methodology employed is a unified pressure-based method for both incompressible and compressible flows, along with a TVD-based controlled variation scheme (CVS), which uses a second-order flux estimation bounded by flux limiters.Performance of the CVS is assessed in terms of its accuracy and convergence properties for laminar and turbulent recirculating flows as well as compressible flows containing shocks. Several other conventional schemes are also employed, including the first-order upwind, central difference, hybrid, second-order upwind and QUICK schemes. For better control over grid quality and to obtain accurate solutions for complex flow domains, a multiblock procedure is desirable and often a must.Here, a a composite grid algorithm utilizing patched (abutting) grids is discussed and a conservative flux treatment for interfaces between blocks is presented.A full approximation storage-full multigrid (FAS-FMG) algorithm that is incorporated in the flow solver for increasing the efficiency of the computation is also described. For turbulent flows, implementation of the κ-e two-equation model and in particular the wall functions at solid boundaries is also detailed.In addition, different modifications to the basic k-e model, which take the non-equilibrium between the production and dissipation of κ and e and rotational effects into account, have also been assessed.Selected test cases are used to demonstrate the robustness of the solver in terms of the convection schemes, the multiblock interface treatment, the multigrid speedup and the turbulence models.

Numerical simulation of CdTe vertical Bridgman growth

Abstract Numerical simulation has been conducted for steady-state Bridgman growth of the CdTe crystal with two ampoule configurations, namely, flat base and semi-spherical base. The present model accounts for conduction, convection and radiation, as well as phase change dynamics. The enthalpy formulation for phase change has been incorporated into a pressure-based algorithm with multi-zone curvilinear grid systems. The entire system which consists of the furnace enclosure wall, the encapsulated gas and the ampoule, contains irregularly configured domains. To meet the competing needs of producing accurate solutions with reasonable computing resources, a two-level approach is employed. The present study reveals that although the two ampoule configurations are quite different, their influence on the melt-solid interface shape is modest, and the undesirable concave interface appears in both cases. Since the interface shape strongly depends on thermal conductivities between the melt and the crystal, as well as ampoule wall temperature, accurate prescriptions of materials transport properties and operating environment are crucial for successful numerical predictions.

Multi-zone simulation of the bridgman growth process of β-NiAl crystal

Abstract A computational model has been developed for the Bridgman growth process of β-NiAl crystal. The model accounts for heat transfer in the whole furnace system, including the encapsulated fluid between the heater and the ampoule, conjugate heat transfer around and within the ampoule, and phase change dynamics between melt and crystal. To handle the geometrical and physical complexities of the crystal growth processes, a two-level approach has been developed. At the global furnace level, combined convection/conduction/radiation calculations with realistic geometrical and thermal boundary conditions are made inside the whole system. Refined calculations are then made within the ampoule, with the boundary conditions supplied by the global furnace simulations. The present multi-level model can help improve the predictive capabilities for crystal growth techniques by optimizing the use of the computing resources; it allows one to probe the effects of different physical and geometrical variables on the crystal quality.

Simulation and measurement of a vertical Bridgman growth system for β-NiAI crystal

A coordinated theoretical and experimental study of the temperature distribution inside a customized vertical Bridgman system for growing β-NiAl crystal has been conducted. The theoretical model accounts for the combined effects of phase change dynamics, the coupled heat transfer processes of conduction, convection and radiation, variable material properties, and complex geometry pertaining to the system. Comparisons between numerical predictions and experimental measurements show satisfactory agreement. The accuracy of the melting temperature of NiAl with stoichiometric composition, along with important processing parameters such as interface curvatures and temperature gradients across the interface, have been discussed in detail. Also assessed are possibilities of improving the solidification process, including coating the ampoule outer wall with a material of high radiative emissivity or decreasing the ampoule wall thickness.

Transient natural convection and conjugate heat transfer in a crystal growth device

Abstract In crystal growth devices, in order to control the growth defects and compositional homogeneity of the crystal, a thorough understanding of the heat transfer characteristics is required. In this effort, the combined natural convection and conjugate heat transfer in an axisymmetric configuration representative of the container used in float zone devices are numerically simulated. The geometry adopted contains two concentric cylinders, the inner one representing the crystal within which heat conduction takes place, and the outer one being the container wall; between them is the domain of a height-to-width ratio of 40, filled with encapsulated argon gas. The main parameters varied in this study are Rayleigh number (Ra) and heating location. Substantial refinement in grid size, from 61 × 81 to 201 × 301 nodes, has been exercised to assess the numerical accuracy of the solutions. For Ra = 1.25 × 10 4 , steady-state solutions exist regardless of the heating location. For Ra = 1.25 × 10 5 , on the other hand, persistently oscillatory convective patterns appear, exhibiting both co-rotating (buoyancy-induced) cells and contra-rotating (shear-induced) cells. Consequently, the overall heat transfer rates fluctuate in time. The heat transfer fluctuation in the heated region is not as strong as in other regions; however, the magnitudes of the heat flux there are strongly influenced by the heating location, indicating that, in order to maintain a uniform thermal environment, the power level of the heat source needs to be adaptively adjusted according to the heating location. This challenge to the design and operation of the materials processing equipment can be met with the aid of knowledge gained from numerical simulations.