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Cylindrical Coordinates (cylindrical + coordinate)
Selected AbstractsA numerical scheme for strong blast wave driven by explosionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2006Kaori Kato Abstract After the detonation of a solid high explosive, the material has extremely high pressure keeping the solid density and expands rapidly driving strong shock wave. In order to simulate this blast wave, a stable and accurate numerical scheme is required due to large density and pressure changes in time and space. The compressible fluid equations are solved by a fractional step procedure which consists of the advection phase and non-advection phase. The former employs the Rational function CIP scheme in order to preserve monotone signals, and the latter is solved by interpolated differential operator scheme for achieving the accurate calculation. The procedure is categorized into the fractionally stepped semi-Lagrangian. The accuracy of our scheme is confirmed by checking the one-dimensional plane shock tube problem with 103 times initial density and pressure jump in comparison with the analytic solution. The Sedov,Taylor blast wave problem is also examined in the two-dimensional cylindrical coordinate in order to check the spherical symmetry and the convergence rates. Two- and three-dimensional simulations for the blast waves from the explosion in the underground magazine are carried out. It is found that the numerical results show quantitatively good agreement with the experimental data. Copyright © 2006 John Wiley & Sons, Ltd. [source] Three-dimensional thermoelastic stresses in off-axis oriented single crystals with hexagonal symmetryCRYSTAL RESEARCH AND TECHNOLOGY, Issue 3 2007K. Böttcher Abstract A three-dimensional (3D) thermoelastic stress analysis is carried out on a single crystal with axisymmetric geometry but with a hexagonal crystallographic symmetry. The crystallographic orientation is off-axis with respect to the cylindrical coordinate system. By applying a Fourier series expansion with respect to the rotational angle , of the cylindrical coordinates, the 3D boundary value problem is reduced to a sequence of 2D ones on the meridian plane, which are solved by the finite-element method. In our example, the off-axis orientation is towards a direction of high symmetry, and therefore only four of the six stress tensor components are non-zero. In the end, the stress tensor is projected onto the slip system of the crystal. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Steam absorption process of water/LiBr system inside vertical small bore pipesHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 1 2005Masanori Kiyota Abstract In a previous paper, a numerical model for absorption within vertical pipes was proposed and compared with the experiments. Agreements were good for pipes with an OD 28,15 mm but at 10 mm pipe experiments fell below the predicted values. For smaller diameters, the difference between the surface area of the falling liquid film and that of the outer surface of the pipe is not negligible and the thickness of the liquid film is also not negligible. In this paper a new model is formulated in cylindrical coordinates and experiments using pipes with 9.52 mm and 7 mm OD are done. Smooth pipes and two kinds of internally finned pipes, originally developed and used to enhance the heat transfer characteristics of the evaporator and condenser of a refrigerator using HFC as refrigerant, are tested in the experiments. The absorption performance is enhanced by 30% when compared to the smooth pipes, but the difference between the finned pipes is small. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(1): 18,28, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20040 [source] Application of inverse solution in two-dimensional heat conduction problem using Laplace transformationHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 7 2003Masanori Monde Abstract An inverse solution has been explicitly derived for two-dimensional heat conduction in cylindrical coordinates using the Laplace transformation. The applicability of the inverse solution is checked using the numerical temperatures with a normal random error calculated from the corresponding direct solution. For a gradual temperature change in a solid, the surface heat flux and temperature can be satisfactorily predicted, while for a rapid change in the temperature this method needs the help of a time partition method, in which the entire measurement time is split into several partitions. The solution with the time partitions is found to make an improvement in the prediction of the surface heat flux and temperature. It is found that the solution can be applied to experimental data, leading to good prediction. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 602,617, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10115 [source] Simulating turbulent Dean flow in Cartesian coordinatesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009George K. El Khoury Abstract A simplified approach to simulate turbulent flows in curved channels is proposed. A set of governing equations of motion in Cartesian coordinates is derived from the full Navier,Stokes equations in cylindrical coordinates. Terms to first order in the dimensionless curvature parameter are retained, whereas higher-order terms are neglected. The curvature terms are implemented in a conventional Navier,Stokes code using Cartesian coordinates. Direct numerical simulations (DNS) of turbulent flow in weakly curved channels are performed. The pronounced asymmetries in the mean flow and the turbulence statistics observed in earlier DNS studies are faithfully reproduced by the present simplified Navier,Stokes model. It is particularly rewarding that also distinct pairs of counter-rotating streamwise-oriented vortices are embedded in the simulated flow field. Copyright © 2008 John Wiley & Sons, Ltd. [source] Finite volume method with zonal-embedded grids for cylindrical coordinatesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2006Yong Kweon Suh Abstract A zonal-embedded-grid technique has been developed for computation of the two-dimensional Navier,Stokes equations with cylindrical coordinates. As is well known, the conventional regular grid system gives very small grid spacings in the azimuthal direction so it requires a very small time step for a stable numerical solution when the explicit method is used. The fundamental idea of the zonal-embedded-grid technique is that the number of azimuthal grids can be made small near the origin of the coordinates so that the grid size is more uniformly distributed over the domain than with the conventional regular-grid system. The code developed using this technique combined with the explicit, finite-volume method was then applied to calculation of the asymmetric swirl flows and Lamb's multi-polar vortex flows within a full circle and the spin-up flows within a semi-circle. It was shown that the zonal-embedded grids allow a time step far larger than the conventional regular grids. For the case of the Lamb's multi-polar vortex flows, the code was validated by comparing the calculated results with the exact solutions. For the case of the semi-circle spin-up flows, the experimental results were used for the verification. It was seen that the numerical results were in good agreement with the experimental results both qualitatively and quantitatively. 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