Milovan Peric

Second-Moment Calculation Procedure for Turbulent Flows with Collocated Variable Arrangement

The paper presents a finite-volume calculation procedure using second-moment turbulence closure. A special interpolation technique is employed in connection with a collocated variable arrangement to avoid oscillatory solutions that might otherwise result from inappropriate coupling of the mean velocity, pressure, and Reynolds stress fields. The apparent diffusion fluxes arising from the interpolation procedure ensure numerical stability of the iterative solution process. The application of the second-moment closure model to backward-facing step flows yields slightly improved results as compared with k-e model predictions. Shortcomings of the current second-moment model are an overproportionally large damping of normal stresses due to inadequacies in the modeling of the pressure-strain terms and the predicted behavior in the reattachment region.

EFFICIENT SEMI-IMPLICIT SOLVING ALGORITHM FOR NINE-DIAGONAL COEFFICIENT MATRIX

In numerical calculations of fluid flows and heat transfer it is often necessary to solve a system of algebraic equations with a nine-diagonal coefficient matrix. Two examples are the diffusion and pressure-correction equations when discretized on nonorthogonal grids. A method of solving such systems of equations, based on the strongly implicit procedure of Stone [1] for five-diagonal matrices, is presented. It operates on the upper and lower triangular matrices with only seven nonzero diagonals, thus requiring less storage and computing time per iteration than the alternative extensions of the strongly implicit procedure to nine-diagonal coefficient matrices. It is also more efficient than the alternative methods—for the land of equations studied—when the missing diagonals in the upper and lower triangular matrices correspond to points lying in “sharp” corners of a computational molecule. Results of various test calculations and comparisons of performance with alternative solvers are presented to support...

Numerical simulation of a 3D Czochralski-melt flow by a finite volume multigrid-algorithm

Abstract The flow in a model Czochralski-apparatus as investigated by Jones [J. Crystal Growth 94 (1989) 421] is studied numerically. The numerical method is based on a three-dimensional finite volume multigrid-algorithm with boundary fitted non-orthogonal grids. Although the numerical experiment assumed axisymmetric and steady boundary conditions, most of the characteristic features of the three-dimensional unsteady flow were obtained. Especially a precessing wave pattern on the free surface with four bulges has been reproduced. The calculation showed that the numerical grid must be fine enough in order to produce a reasonably accurate prediction of the unsteady flow in a Czochralski arrangement.

Numerical study of transport phenomena in MOCVD reactors using a finite volume multigrid solver

Abstract A mathematical model for epitaxial growth in metalorganic chemical vapor deposition reactors (MOCVD) has been developed which is based on the conservation equations for mass, momentum, heat, and species including thermodiffusion and chemical reactiond. The model was implemented in a finite volume numerical solution procedure for two-dimensional (plane and axisymmetric) laminar flows. Second-order central differencing was used to discretize both convection and diffusion fluxes. To speed up the convergence of the computations, a “Full Approximation Scheme” of a multigrid technique was employed. The growth of GaAs from trimethyl-gallium (TMGa), arsine, and hydrogen was considered where the deposition process is assumed to be in the transport-limited regime. The calculated deposition rates in the reactor were compared with experimental results from literature. The model gives accurate results for growth at subcritical Rayleigh numbers. Computational results show that the two-species model gives more accurate results compared with the one-species model without gas phase reactions. Deposition at the upper wall was found to have a remarkable influence on the growth rate of the film on the substrate.

Study of laminar, unsteady piston-cylinder flows

The present paper concerns numerical investigation of a piston-driven, axisymmetric flow in a pipe assembly containing a sudden expansion. The piston closes the larger of the two pipes. The impulsively starting intake flow is the topic of this investigation. Results of numerical calculations and laser-Doppler measurements are presented to provide an insight into the features of the flow. The calculation procedure employed in this study is based on a finite-volume method with staggered grids and SIMPLE algorithm for pressure-velocity coupling. The convection and diffusion fluxes in the Navier-Stokes equations are discretized with first order upwind and second order central differences, respectively. A fully implicit Euler scheme is used to discretize the temporal derivatives. The Navier-Stokes equations were suitably transformed to allow prediction of the flow within the inlet pipe and cylinder region simultaneously. Laser-Doppler measurements of both axial and radial velocity components were performed. Refractive index matching was used to eliminate the wall curvature effects. For each measuring point 20 cycles were measured, showing high repetition rates. Comparison of measured and predicted velocity profiles shows good agreement.