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Abstract
In this paper the flow generated by a rotlet in the presence of a circular cylinder is considered. We introduce a transformation which simplifies the equations and boundary conditions. We use the finite-difference method to obtain results in excellent agreement with all the available analytical results. Results are presented for Reynolds numbers, based on the diameter of the cylinder, in the range 0 ≤ Re ≤ 20 and the rotational parameter, α , in the range 0 ≤α ≤ 3 and strength of rotlet, β , in the range 0 ≤ β ≤ 3 . The results are found to be applicable over a wide range of values of α and β . The calculated values of the drag, lift and moment coefficients and the general nature of the streamline patterns are in good agreement with analytical results . The method is then utilized to obtain new results for which no analytical solution is possible.
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References
- ALLEN, E., MARTIN, A. and PARIS, F., 1979. Boundary Elements in Potential and Elasticity Theory, Comp. And Stru., 10: 351-362.
- DENNIS, S.C.R. 1960. Finite Differences Associated with Second-order Differential Equations, Quart. J. Mech Appl. Math., 13: 487-496.
- DENNIS, S.C.R. and HUDSON J.D., 1978. A difference Method for solving the Navier-Stokes Equations, Proc, 1st Int. Conf. Numerical Methods Laminar and Turbulent Flow, Pentech Press, London, 69-78.
- DORREPAAL, J.M., O’NEILL, M.E. and RANGER, K.B., 1984. Two-dimensional Stokes Flows with Cylinders and Line Singularities, Mathematika, 31: 65-75.
- FILON, L.N.G., 1926. The Forces on a cylinder in a Stream of Viscous Fluid, Proc. Roy. Soc., A113: 7-27.
- FORNBERG, B., 1980. A Numerical Study of Steady Viscous Flow Past as Circular Cylinder, J.Fluid Mech., 98: 819-855.
- FORNBERG, B., 1985. Steady Viscous Flow Past as Circular Cylinder, up to Reynolds number 600, J. Comput. Phys., 161: 297-320.
- IMAI, I., 1951. On the Asymptotic Behaviour of Viscous Fluid Flow at a Great Distance from a Cylinder Body, Proc. Roy. Soc., A208: 487-516.
- PROUDMAN, I. And Pearson, J.R.A., 1957: Expansions at Small Reynolds Numbers for the Flow Past a Sphere and a Circular Cylinder, J. Fluid Mech., 2: 237-262.
References
ALLEN, E., MARTIN, A. and PARIS, F., 1979. Boundary Elements in Potential and Elasticity Theory, Comp. And Stru., 10: 351-362.
DENNIS, S.C.R. 1960. Finite Differences Associated with Second-order Differential Equations, Quart. J. Mech Appl. Math., 13: 487-496.
DENNIS, S.C.R. and HUDSON J.D., 1978. A difference Method for solving the Navier-Stokes Equations, Proc, 1st Int. Conf. Numerical Methods Laminar and Turbulent Flow, Pentech Press, London, 69-78.
DORREPAAL, J.M., O’NEILL, M.E. and RANGER, K.B., 1984. Two-dimensional Stokes Flows with Cylinders and Line Singularities, Mathematika, 31: 65-75.
FILON, L.N.G., 1926. The Forces on a cylinder in a Stream of Viscous Fluid, Proc. Roy. Soc., A113: 7-27.
FORNBERG, B., 1980. A Numerical Study of Steady Viscous Flow Past as Circular Cylinder, J.Fluid Mech., 98: 819-855.
FORNBERG, B., 1985. Steady Viscous Flow Past as Circular Cylinder, up to Reynolds number 600, J. Comput. Phys., 161: 297-320.
IMAI, I., 1951. On the Asymptotic Behaviour of Viscous Fluid Flow at a Great Distance from a Cylinder Body, Proc. Roy. Soc., A208: 487-516.
PROUDMAN, I. And Pearson, J.R.A., 1957: Expansions at Small Reynolds Numbers for the Flow Past a Sphere and a Circular Cylinder, J. Fluid Mech., 2: 237-262.