A finite volume, time-marching for solving time-dependent viscoelastic flow in two space dimensions for Oldroyd-B and Phan Thien-Tanner fluids, is presented. A non-uniform staggered grid system is used. The conservati...
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A finite volume, time-marching for solving time-dependent viscoelastic flow in two space dimensions for Oldroyd-B and Phan Thien-Tanner fluids, is presented. A non-uniform staggered grid system is used. The conservation and constitutive equations are solved using the finite volume method with an upwind scheme for the viscoelastic stresses and an hybrid scheme for the velocities. To calculate the pressure field, the semi-implicit method for the pressure linked equation revised method is used. The discretized equations are solved sequentially, using the tridiagonal matrix algorithm solver with under-relaxation. In both, the full approximation storage multigrid algorithm is used to speed up the convergence rate. Simulations of viscoelastic flows in four-to-one abrupt plane contraction are carried out. We will study the behaviour at the entrance corner of the four-to-one planar abrupt contraction. Using this solver, we show convergence up to a Weissenberg number We of 20 for the Oldroyd-B model. No limiting Weissenberg number is observed even though a Phan Thien-Tanner model is used. Several numerical results are presented. Smooth and stable solutions are obtained for high Weissenberg number. Copyright (C) 2002 John Wiley Sons, Ltd.
A new finite volume method for solving the incompressible Navier Stokes equations is presented. The main features of this method are the location of the velocity components and pressure on different staggered grids an...
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A new finite volume method for solving the incompressible Navier Stokes equations is presented. The main features of this method are the location of the velocity components and pressure on different staggered grids and a semi-Lagrangian method for the treatment of convection. An interpolation procedure based on area-weighting is used for the convection part of the computation. The method is applied to ow through a constricted channel, and results are obtained for Reynolds umbers, based on half the ow rate, up to 1000. The behavior of the vortex in the salient corner is investigated qualitatively and quantitatively, and excellent agreement is found with the numerical results of Dennis and Smith [Proc. Roy. Soc. London A, 372 ( 1980), pp. 393-414] and the asymptotic theory of Smith.
Introduction of pulsing phenomenon in thermal plasmas has been anticipated as an outstanding feature to promote industrial applications of thermal plasma technology. Numerical models are found to be effective in givin...
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Introduction of pulsing phenomenon in thermal plasmas has been anticipated as an outstanding feature to promote industrial applications of thermal plasma technology. Numerical models are found to be effective in giving ideas on fundamental plasma properties. Here, a two-dimensional and time-dependent model was solved to predict plasma properties for a 70-mm inner diameter torch. Calculations were carried out for a wide variety of gas combinations: argon, argon-N-2, argon-O-2, argon-air, argon-He, argon-H-2, argon-CO2, and argon-SF6, for step-current modulation and comparative results are presented. The coil current levels for step modulations corresponded to 45- and 35-kW steady-state plasmas. Applying corresponding current transition for all considered plasmas, the time-dependent profiles for plasma power, temperature, velocity, Lorentz force and Joule heating were determined. Comparing the plasma temperatures at mid-coil (z = 151.5 mm) and r = 18 mm for step-down pulsation, it was found that the temperature difference between the two steady-state magnitudes, corresponding to current levels, was the maximum for Ar-SF6 plasma (114 K) and the minimum for Ar plasma (65 K). The response times, determined from the temporal temperature profiles at mid-coil and r = is mm for step-down current pulsation, were the lowest at 4.9 ms for Ar-SF6, the highest at 42.7 ms for Ar-H-2, and between 31 and 35 ms for other ICPs. (C) 2001 Elsevier Science B.V. All rights reserved.
Numerical study of the per-slat heat transfer coefficient was made for an array of co-planar slat-like surfaces which face upstream into an oncoming airflow. The flow washes over the slats as it passes into slot-like ...
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Numerical study of the per-slat heat transfer coefficient was made for an array of co-planar slat-like surfaces which face upstream into an oncoming airflow. The flow washes over the slats as it passes into slot-like gaps between the slats. The computations were performed for several different slat-slot configurations characterized by the ratio of the slot-slat width to the slat width (P/W), the Reynolds number varied from 500 to 7000, and the range of Prandtl number was 0.7-10. Based on the simpler algorithm and the central difference scheme (CDS), parametric studies on the effects of the Reynolds number, P/ Wand the Prandtl number were performed. Numerical results agree well with the test results for mass transfer(Se = 2.5). From the numerical results, a general heat transfer correlation was obtained which covers the following range of parameters: 500 less than or equal to Re less than or equal to 7000. 1.25 less than or equal to P/W less than or equal to 5, 0.7 less than or equal to Pr less than or equal to 10.
A finite volume technique has been introduced in an attempt to simulate the planar 4:1 contraction flow of the Oldroyd B fluid on a non-uniform staggered grid system, which incorporates the simpler algorithm in discre...
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A finite volume technique has been introduced in an attempt to simulate the planar 4:1 contraction flow of the Oldroyd B fluid on a non-uniform staggered grid system, which incorporates the simpler algorithm in discretizing the momentum equations and the deferred correction method in discretizing the constitutive equations. For some combinations of viscoelastic parameters, the size and shape of the corner vortex growth are shown to be in good qualitative agreement with those observed experimentally by others for constant viscosity viscoelastic fluids. In general, however, they seem to be sensitive to the ratio of retardation time to relaxation time.
AbstractAn investigation has been conducted to study the performance of a coupled solution approach for solving the fluid flow equations in body‐fitted co‐ordinates using a covariant velocity formulation. The set of...
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AbstractAn investigation has been conducted to study the performance of a coupled solution approach for solving the fluid flow equations in body‐fitted co‐ordinates using a covariant velocity formulation. The set of discrete equations is solved using a sparse matrix variant of LU decomposition. A series of test problems have been considered to study the effects of Reynolds number, mesh skewness and grid size on the convergence rate. The coupled solution approach has been compared with a state‐of‐the‐art sequential approach. The results indicate that the coupled technique is faster by a factor of about two for reasonable grids. For severely non‐orthogonal grids the performance of the coupled solution approach deteriorates c
Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using simpler algorithm in a non-uniform staggered grid system. It has been shown that for consta...
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