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  • 1
    Digitale Medien
    Digitale Medien
    MOVING BOUNDARY COMPUTATION OF THE FLOAT-ZONE PROCESS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1231-1261 
    Details
    ISSN: 0029-5981
    Schlagwort(e): float zone ; crystal growth ; solidification ; moving boundary ; thermocapillary transport ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A computational capability has been developed to predict the free surface shape, heat transfer and melt-crystal interface shapes in float-zone processing. A moving boundary, second order, finite volume, incompressible Navier-Stokes solver has been developed for the fluid flow and heat transfer calculations. The salient features of the approach include solving the dynamic form of the Young-Laplace equation for the free surface shape, dynamic remeshing to fit the free boundary, a flexible, multi-block, grid generation procedure and the enthalpy method to capture the melt-crystal and the melt-feed interfaces without the need for explicit interface tracking. Important convective heat transfer modes; natural convection and thermocapillary convection have been computed. It is shown that, whereas the overall heat transfer is not substantially affected by convection, the melt-crystal interface shape acquires significant distortion due to the redistribution of the temperature field by the thermocapillary and buoyancy-induced convective mechanisms. It is also demonstrated that the interaction of natural and thermocapillary convection can reduce the melt-crystal interface distortion if they act in opposing directions. It is found that the meniscus deformation can cause the height of the zone to increase but the qualitative nature of the melt-solid interface shapes are not significantly affected. Results are compared with literature to validate the predictive capability developed in this work. © 1997 by John Wiley & Sons, Ltd.
    Zusätzliches Material: 23 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Three-dimensional analysis of the flow in a curved hydraulic turbine draft tube (1986)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 6 (1986), S. 861-882 
    Details
    ISSN: 0271-2091
    Schlagwort(e): Three Dimensional Flow ; Turbine Draft Tube ; Curvilinear Co-ordinates ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: The three-dimensional turbulent flow in a curved hydraulic turbine draft tube is studied numerically. The analysis is based on the steady Reynolds-averaged Navier-Stokes equations closed with the κ-ε model. The governing equations are discretized by a conservative finite volume formulation on a non-orthogonal body-fitted co-ordinate system. Two grid systems, one with 34 × 16 × 12 nodes and another with 50 × 30 × 22 nodes, have been used and the results from them are compared. In terms of computing effort, the number of iterations needed to yield the same degree of convergence is found to be proportional to the square root of the total number of nodes employed, which is consistent with an earlier study made for two-dimensional flows using the same algorithm. Calculations have been performed over a wide range of inlet swirl, using both the hybrid and second-order upwind schemes on coarse and fine grids. The addition of inlet swirl is found to eliminate the stalling characteristics in the downstream region and modify the behaviour of the flow markedly in the elbow region, thereby affecting the overall pressure recovery noticeably. The recovery factor increases up to a swirl ratio of about 0·75, and then drops off. Although the general trends obtained with both finite difference operators are in agreement, the quantitative values as well as some of the fine flow structures can differ. Many of the detailed features observed on the fine grid system are smeared out on the coarse grid system, pointing out the necessity of both a good finite difference operator and a good grid distribution for an accurate result.
    Zusätzliches Material: 21 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650061202
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  • 3
    Digitale Medien
    Digitale Medien
    Assessment of TVD schemes for inviscid and turbulent flow computation (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 161-177 
    Details
    ISSN: 0271-2091
    Schlagwort(e): Convection approximation ; Total variation diminishing schemes ; Shock ; Turbulent and inviscid flows ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: A systematic study has been conducted to assess the performance of the TVD schemes for practical flow computation. The viewpoint adopted here is to treat the TVD schemes as a combination of the standard central difference scheme with numerical dissipation terms. The controlled amount of numerical dissipation modifies the computed fluxes to ensure that the solution is oscillation-free. Four variants of TVD schemes, two with upwind dissipation terms and two with symmetric dissipation terms, have been studied and compared with the conventional Beam-Warming scheme for inviscid and turbulent axisymmetric flow computations. The results obtained show that all four variants can accurately resolve the shock and flow profiles with fewer grid points than the Beam-Warming scheme. The convergence rates of the TVD schemes are also substantially superior to that of the Beam-Warming scheme. The combination of high accuracy, good robustness and improved computational efficiency offered by the TVD schemes makes them attractive for computing high-speed flow with shocks. In terms of the relative performances it is found that the symmetric schemes converge slightly faster but that the upwind schemes are less sensitive to the number of grid points being employed.
    Zusätzliches Material: 12 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650120205
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  • 4
    Digitale Medien
    Digitale Medien
    Computation of complex fluid flows using an adaptive grid method (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 475-489 
    Details
    ISSN: 0271-2091
    Schlagwort(e): Adaptive grid computation ; High Reynolds number flow ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: Recently the concept of adaptive grid computation has received much attention in the computational fluid dynamics research community. This paper continues the previous efforts of multiple one-dimensional procedures in developing and asessing the ideas of adaptive grid computation. The focus points here are the issue of numerical stability induced by the grid distribution and the accuracy comparison with previously reported work. Two two-dimensional problems with complicated characteristics - namely, flow in a channel with a sudden expansion and natural convection in an enclosed square cavity - are used to demonstrate some salient features of the adaptive grid method. For the channel flow, by appropriate distribution of the grid points the numerical algorithm can more effectively dampen out the instabilities, especially those related to artificial boundary treatments, and hence can converge to a steady-state solution more rapidly. For a more accurate finite difference operator, which contains less undesirable numerical diffusion, the present adaptive grid method can yield a steady-state and convergent solution, while uniform grids produce non-convergent and numerically oscillating solutions. Furthermore, the grid distribution resulting from the adaptive procedure is very responsive to the different characteristics of laminar and turbulent flows. For the problem of natural convection, a combination of a multiple one-dimensional adaptive procedure and a variational formulation is found very useful. Comparisons of the solutions on uniform and adaptive grids with the reported benchmark calculations demonstrate the important role that the adaptive grid computation can play in resolving complicated flow characteristics.
    Zusätzliches Material: 13 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650080408
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