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LES and DNS of melt flow and heat transfer in Czochralski crystal growth. (English) Zbl 1391.76241
Nagel, Wolfgang E. (ed.) et al., High performance computing in science and engineering ’06. Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2006. Berlin: Springer (ISBN 3-540-36165-0/hbk). 279-291 (2007).
Summary: In the present work, computations of flow and heat transfer in an idealized cylindrical Czochralski configuration are conducted using Large Eddy Simulation (LES) with the flow solver FASTEST-3D developed at LSTM Erlangen. The results match well with DNS data from the literature. However, detailed data for analysis of turbulent quantities are not available. Therefore, DNS computations are conducted using the code LESOCC, employing explicit time marching. Preliminary simulations show the high efficiency of the solver on the NEC SX-8. Furthermore, from a study of the velocity profiles at the wall, the resolution requirements had to be corrected such that the computational grid will now consist of approximately $$8\times 10^6$$ control volumes. The present run of the DNS took more than 540 hours of walltime on 8 processors. With the results, the LES computations will be thoroughly validated so that appropriate models and parameters can be chosen for efficient and accurate simulations of practically relevant cases.
For the entire collection see [Zbl 1104.76029].

##### MSC:
 76F65 Direct numerical and large eddy simulation of turbulence 76T99 Multiphase and multicomponent flows 76M12 Finite volume methods applied to problems in fluid mechanics 80A20 Heat and mass transfer, heat flow (MSC2010)
##### Software:
FASTEST-3D; LESOCC
Full Text:
##### References:
 [1] Leister, H.J. and Perić, M. (1993) Vectorized Strongly Implicit Solving Procedure for a Seven-Diagonal Coefficient Matrix, Int. Journal for Heat and Fluid Flow, vol. 4, pp. 159-172 [2] Perić, M. (1985) A Finite-Volume Method for the Prediction of Three-Dimensional Fluid Flow in Complex Ducts, PhD thesis, Imperial College, London [3] Stone, H.L. (1968) Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations, SIAM Journal of Numerical Analyses, vol. 5, pp. 530-558 · Zbl 0197.13304 [4] Durst, F., Schäfer, M. and Wechsler, K. (1996) Efficient Simulation of Incompressible Viscous Flows on Parallel Computers, In: Flow Simulation with High-Performance Computers, II, ed. E.H. Hirschel, Notes on Numer. Fluid Mech., vol. 52, pp. 87-101, Vieweg Verlag, Braunschweig · Zbl 0877.76052 [5] Durst, F. and Schäfer, M. (1996) A Parallel Block-StructuredMultigrid Method for the Prediction of Incompressible Flows, Int. Journal Num. Methods Fluids, vol. 22, pp. 549-565 · Zbl 0865.76059 [6] Breuer, M., Rodi, W. (1996) Large-Eddy Simulation of Complex Turbulent Flows of Practical Interest, In: Flow Simulation with High-Performance Computers II, ed. E.H. Hirschel, Notes on Numer. Fluid Mech., vol. 52, pp. 258-274, Vieweg Verlag, Braunschweig · Zbl 0875.76457 [7] Breuer, M. (1998) Large-Eddy Simulation of the Sub-Critical Flow Past a Circular Cylinder: Numerical and Modeling Aspects, Int. J. for Numer. Methods in Fluids, vol. 28, pp. 1281-1302 · Zbl 0933.76041 [8] Breuer, M. (2000) A Challenging Test Case for Large-Eddy Simulation: High Reynolds Number Circular Cylinder Flow, Int. J. of Heat and Fluid Flow, vol. 21, no. 5, pp. 648-654 [9] Breuer, M. (2002) Direkte Numerische Simulation und Large-Eddy Simulation turbulenter Strömungen auf Hochleistungsrechnern, Habilitationsschrift, Universität Erlangen-Nürnberg, Berichte aus der Strömungstechnik, ISBN: 3-8265-9958-6, Shaker Verlag, Aachen [10] Rhie, C.M., Chow, W.L. (1983) A Numerical Study of the Turbulent Flow Past an Isolated Airfoil with Trailing Edge Separation, AIAA Journal, vol. 21, pp. 1525-1532 · Zbl 0528.76044 [11] Smagorinsky, J. (1963) General Circulation Experiments with the Primitive Equations, I, The Basic Experiment, Mon. Weather Rev., vol. 91, pp. 99-165 [12] Basu, B., Enger, S., Breuer, M., and Durst, F. (2000) Three-Dimensional Simulation of Flow and Thermal Field in a Czochralski Melt Using a Block-Structured Finite-Volume Method, Journal of Crystal Growth, vol. 219, pp. 123-143 [13] Enger, S., Basu, B., Breuer, M., and Durst, F. (2000) Numerical Study of Three-Dimensional Mixed Convection due to Buoyancy and Centrifugal Force in an Oxide Melt for Czochralski Growth, Journal of Crystal Growth, vol. 219, pp. 123-143 [14] Kumar, V. (2005) Modeling and Numerical Simulations of Complex Transport Phenomena in Crystal Growth Processes, PhD thesis, Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg [15] Wagner, C. (2003) Turbulente Transportvorgänge in idealisierten Czochralski-Kristallzüchtungsanordnungen, Habilitation, Lehrstuhl für Fluidmechanik, Technische Universität München [16] Grötzbach, G. (1983) Spatial Resolution Requirements for Direct Numerical Simulation of the Rayleigh-Benard Convection, J. Comp. Phys. vol. 49, pp. 241-264 · Zbl 0503.76070 [17] Breuer, M., Lammers, P., Zeiser, Th., Hager, G., Wellein, G.: Towards the Simulation of Turbulent Flows Over Dimples — Code Evaluation and Optimization for NEC SX-8, see rejected report which should be published in this book · Zbl 1391.76204 [18] Bartels, C., Breuer, M., Wechsler, K., and Durst, F. (2001) CFD-Applications on Parallel-Vector Computers: Computations of Stirred Vessel Flows, Int. J. Computers and Fluids, vol. 31, pp. 69-97 · Zbl 1057.76037
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