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Renwei Mei - One of the best experts on this subject based on the ideXlab platform.
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History force on a sphere due to a step change in the free-Stream Velocity
1993Co-Authors: Renwei MeiAbstract:Abstract Finite-difference solutions for unsteady flows over a stationary sphere due to a step change in the free-Stream Velocity from U 1 to U 2 (0 U 1 UZ ) are obtained, from which the unsteady drag is evaluated, for Reynolds numbers, Re (based on the diameter of the sphere and the free-Stream Velocity U 2 ), ranging from 0.1 to 100 over a large range of time. The history force on the sphere is determined by subtracting the quasi-steady drag from the computed total drag. The numerical result shows a complicated behavior of the history force at finite Re for both U 1 = 0 and U 1 > 0. It decays as t − 1 2 for small time; it then decays as t − n ( n ⩾ 2 with n = 2 for small Re) for an intermediate range of time; and it decays exponentially at large time. The numerical results are used to assess a recently developed expression for the history force for finite Re. Good overall agreement is observed for the history force between the analytical prediction and the finite-difference solution for small and intermediate time for the Re values tested.
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Flow past a sphere with an oscillation in the free-Stream Velocity and unsteady drag at finite Reynolds number
1992Co-Authors: Renwei Mei, Ronald J. AdrianAbstract:Unsteady flow over a stationary sphere with a small fluctuation in the free-Stream Velocity is considered at small Reynolds number, Re. A matched asymptotic solution is obtained for the frequency-dependent (or the acceleration-dependent) part of the unsteady flow at very small frequency, w, under the restriction St % Re 4 1, where St is the Strouhal number. The acceleration-dependent part of the unsteady drag is found to be proportional to St - w instead of the wi dependence predicted by Stokes’ solution. Consequently, the expression for the Basset history force is incorrect for large time even for very small Reynolds numbers. Present results compare well with the previous numerical results of Mei, Lawrence & Adrian (1991) using a finitedifference method for the same unsteady flow at small Reynolds number. Using the principle of causality, the present analytical results at small Re, the numerical results at finite Re for low frequency, and Stokes’ results for high frequency, a modified expression for the history force is proposed in the time domain. It is confirmed by comparing with the finite-difference results at arbitrary frequency through Fourier transformation. The modified history force has an integration kernel that decays as t-*, instead of t-i, at large time for both small and finite Reynolds numbers.
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UNSTEADY DRAG ON A SPHERE AT FINITE REYNOLDS NUMBER WITH SMALL FLUCTUATIONS IN THE FREE-Stream Velocity
1991Co-Authors: Renwei Mei, Christopher J. Lawrence, Ronald J. AdrianAbstract:Unsteady flow over a stationary sphere with small fluctuations in the free-Stream Velocity is considered at finite Reynolds number using a finite-difference method. The dependence of the unsteady drag on the frequency of the fluctuations is examined at various Reynolds numbers. It is found that the classical Stokes solution of the unsteady stokes equation does not correctly describe the behaviour of the unsteady drag at low frequency. Numerical results indicate that the force increases linearly with frequency when the frequency is very small instead of increasing linearly with the square root of the frequency as the classical Stokes solution predicts. This implies that the forces has a much shorter memory in the time domain. The incorrect behaviour of the Basset force at large times may explain the unphysical results found by Reeks & McKee (1984) wherein for a particle introduced to a turbulent flow the initial Velocity difference between the particle and fluid has a finite contribution to the long-time particle diffusivity. The added mass component of the force at finite Reynolds number is found to be the same as predicted by creeping flow and potential theories. Effect of Reynolds number of the unsteady drag due to the fluctuating free-Stream Velocity are presented. The implications for particle motion in turbulence are discussed.
Ronald J. Adrian - One of the best experts on this subject based on the ideXlab platform.
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Flow past a sphere with an oscillation in the free-Stream Velocity and unsteady drag at finite Reynolds number
1992Co-Authors: Renwei Mei, Ronald J. AdrianAbstract:Unsteady flow over a stationary sphere with a small fluctuation in the free-Stream Velocity is considered at small Reynolds number, Re. A matched asymptotic solution is obtained for the frequency-dependent (or the acceleration-dependent) part of the unsteady flow at very small frequency, w, under the restriction St % Re 4 1, where St is the Strouhal number. The acceleration-dependent part of the unsteady drag is found to be proportional to St - w instead of the wi dependence predicted by Stokes’ solution. Consequently, the expression for the Basset history force is incorrect for large time even for very small Reynolds numbers. Present results compare well with the previous numerical results of Mei, Lawrence & Adrian (1991) using a finitedifference method for the same unsteady flow at small Reynolds number. Using the principle of causality, the present analytical results at small Re, the numerical results at finite Re for low frequency, and Stokes’ results for high frequency, a modified expression for the history force is proposed in the time domain. It is confirmed by comparing with the finite-difference results at arbitrary frequency through Fourier transformation. The modified history force has an integration kernel that decays as t-*, instead of t-i, at large time for both small and finite Reynolds numbers.
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UNSTEADY DRAG ON A SPHERE AT FINITE REYNOLDS NUMBER WITH SMALL FLUCTUATIONS IN THE FREE-Stream Velocity
1991Co-Authors: Renwei Mei, Christopher J. Lawrence, Ronald J. AdrianAbstract:Unsteady flow over a stationary sphere with small fluctuations in the free-Stream Velocity is considered at finite Reynolds number using a finite-difference method. The dependence of the unsteady drag on the frequency of the fluctuations is examined at various Reynolds numbers. It is found that the classical Stokes solution of the unsteady stokes equation does not correctly describe the behaviour of the unsteady drag at low frequency. Numerical results indicate that the force increases linearly with frequency when the frequency is very small instead of increasing linearly with the square root of the frequency as the classical Stokes solution predicts. This implies that the forces has a much shorter memory in the time domain. The incorrect behaviour of the Basset force at large times may explain the unphysical results found by Reeks & McKee (1984) wherein for a particle introduced to a turbulent flow the initial Velocity difference between the particle and fluid has a finite contribution to the long-time particle diffusivity. The added mass component of the force at finite Reynolds number is found to be the same as predicted by creeping flow and potential theories. Effect of Reynolds number of the unsteady drag due to the fluctuating free-Stream Velocity are presented. The implications for particle motion in turbulence are discussed.
G. Nath - One of the best experts on this subject based on the ideXlab platform.
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mhd flow over a moving plate in a rotating fluid with magnetic field hall currents and free Stream Velocity
2002Co-Authors: Harmindar S Takhar, Ali J Chamkha, G. NathAbstract:The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free Stream Velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the Velocity profile of the primary flow and the magnetic field reduces/removes the Velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall Velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall Velocity strongly affects the flow field. When the wall Velocity is equal to the free Stream Velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation.
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unsteady flow and heat transfer on a semi infinite flat plate with an aligned magnetic field
1999Co-Authors: Harmindar S Takhar, G. NathAbstract:The unsteady laminar boundary layer flow of an electrically conducting fluid past a semi-infinite flat plate with an aligned magnetic field has been studied when at time t > 0 the plate is impulsively moved with a constant Velocity which is in the same or opposite direction to that of free Stream Velocity. The effect of the induced magnetic field has been included in the analysis. The non-linear partial differential equations have been solved numerically using an implicit finite-difference method. The effect of the impulsive motion of the surface is found to be more pronounced on the skin friction but its effect on the x-component of the induced magnetic field and heat transfer is small. Velocity defect occurs near the surface when the plate is impulsively moved in the same direction as that of the free Stream Velocity. The surface shear stress, x-component of the induced magnetic field on the surface and the surface heat transfer decrease with an increasing magnetic field, but they increase with the reciprocal of the magnetic Prandtl number. However, the effect of the reciprocal of the magnetic Prandtl number is more pronounced on the x-component of the induced magnetic field. (C) 1999 Elsevier Science Ltd. All rights reserved.
Harmindar S Takhar - One of the best experts on this subject based on the ideXlab platform.
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mhd flow over a moving plate in a rotating fluid with magnetic field hall currents and free Stream Velocity
2002Co-Authors: Harmindar S Takhar, Ali J Chamkha, G. NathAbstract:The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free Stream Velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the Velocity profile of the primary flow and the magnetic field reduces/removes the Velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall Velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall Velocity strongly affects the flow field. When the wall Velocity is equal to the free Stream Velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation.
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unsteady flow and heat transfer on a semi infinite flat plate with an aligned magnetic field
1999Co-Authors: Harmindar S Takhar, G. NathAbstract:The unsteady laminar boundary layer flow of an electrically conducting fluid past a semi-infinite flat plate with an aligned magnetic field has been studied when at time t > 0 the plate is impulsively moved with a constant Velocity which is in the same or opposite direction to that of free Stream Velocity. The effect of the induced magnetic field has been included in the analysis. The non-linear partial differential equations have been solved numerically using an implicit finite-difference method. The effect of the impulsive motion of the surface is found to be more pronounced on the skin friction but its effect on the x-component of the induced magnetic field and heat transfer is small. Velocity defect occurs near the surface when the plate is impulsively moved in the same direction as that of the free Stream Velocity. The surface shear stress, x-component of the induced magnetic field on the surface and the surface heat transfer decrease with an increasing magnetic field, but they increase with the reciprocal of the magnetic Prandtl number. However, the effect of the reciprocal of the magnetic Prandtl number is more pronounced on the x-component of the induced magnetic field. (C) 1999 Elsevier Science Ltd. All rights reserved.
Ioan Pop - One of the best experts on this subject based on the ideXlab platform.
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on the stagnation point flow towards a stretching sheet with homogeneous heterogeneous reactions effects
2011Co-Authors: Norfifah Bachok, Anuar Mohd Ishak, Ioan PopAbstract:The effects of homogeneous-heterogeneous reactions on the steady boundary layer flow near the stagnation point on a stretching surface is studied. The possible steady-states of this system are analyzed in the case when the diffusion coefficients of both reactant and auto catalyst are equal. The strength of this effect is represented by the dimensionless parameter K and Ks. It is shown that for a fluid of small kinematic viscosity, a boundary layer is formed when the stretching Velocity is less than the free Stream Velocity and an inverted boundary layer is formed when the stretching Velocity exceeds the free Stream Velocity. The uniqueness of this problem lies on the fact that the solutions are possible for all values of λ>0 (stretching surface), while for λ<0 (shrinking surface), solutions are possible only for its limited range.
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mhd stagnation point flow towards a stretching sheet
2009Co-Authors: Anuar Mohd Ishak, Roslinda Mohd Nazar, Khamisah Jafar, Ioan PopAbstract:The steady two-dimensional MHD stagnation point flow towards a stretching sheet with variable surface temperature is investigated. The governing system of partial differential equations are transformed into ordinary differential equations, which are then solved numerically using a finite-difference scheme known as the Keller-box method. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases with the magnetic parameter when the free Stream Velocity exceeds the stretching Velocity, i.e. e>1, and the opposite is observed when e<1.
