Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

Inviscid Rotational Flows Near a Corner and Within a Triangle

  • Suh, Yong-Kweon (School of Mechanical and Industrial System Engineering, Dong-A University)
  • Published : 2001.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

Solutions of inviscid rotational flows near the corners of an arbitrary angle and within a triangle of arbitrary shapes are presented. The corner-flow solutions has a rotational component as a particular solution. The addition of irrotatoinal components yields a general solution, which is indeterminate unless the far-field condition is imposed. When the corner angle is less than 90$^{\circ}$the flow asymptotically becomes rotational. For the corner angle larger than 90$^{\circ}$it tends to become irrotational. The general solution for the corner flow is then applied to rotational flows within a triangle (Method I). The error level depends on the geometry, and a parameter space is presented by which we can estimate the error level of solutions. On the other hand, Method II employing three separate coordinate systems is developed. The error level given by Method II is moderate but less dependent on the geometry.

Keywords

References

  1. van Heijst, G.J.F., 1989, 'Spin-up Phenomena in Non-Axisymmetric Containers,' J. Fluid Mech., Vol. 206, pp. 171-191 https://doi.org/10.1017/S0022112089002272
  2. van Heijst, G.J.F., Davies, P.A. and Davis, R.G., 1990, 'Spin-up in a Rectangular Container,' Phys. Fluids, Vol. A2, pp. 150-159
  3. van Heijst, G.J. F.l, Mass, L.R. M. and Williams, C.W.M., 1994, 'The Spin-up of Fluid in a Rectangular Container with a Sloping Bottom,' J. Fluid Mech., Vol. 265, pp. 125-159 https://doi.org/10.1017/S0022112094000789
  4. Henderson, D.M., Lopez, J.M. and Stewart, D.L., 1996, 'Vortex Evolution in Non-Axisymmetric Impulsive Spin-up from Rest,' J. Fluid Mech., Vol. 324, pp. 109-134 https://doi.org/10.1017/S0022112096007859
  5. van de Konijnenberg, J.A., Wessels, T.L. and van Heijst, G.J.F., 1996, 'Spin-up in a Circular Tank with a Radial Barrier,' Phys. Fluids, Vol. 8, pp. 2943-2952 https://doi.org/10.1063/1.869007
  6. van de Konijnenberg, J.A. and van Heijst, G.J.F., 1997, 'Spin-up in a Rectandular Tank with a Discontinuous Topography,' Phys. Fluids, Vol. 8, pp. 2943-2952 https://doi.org/10.1063/1.869073
  7. van de Konijnenberg, J.A. and van Heijst, G.J.F., 1997, 'Free-Surface Effects on Spin-up in a Rectandular Tank,' J. Fluid Mech., Vol. 334, pp. 189-210 https://doi.org/10.1017/S0022112096004296
  8. Milne-Thomson, L.M., 1968, Theoretical Hydrodynamics, Macmillan, London
  9. Moore, D.W., Saffman and Tanveer, S., 1988, 'The Calculation of Some Batchelor Flows: The Sadovskii Vortex and Rotational Corner Flow,' Phys. Fluids, Vol. 31, pp. 978-990 https://doi.org/10.1063/1.866718
  10. Suh, Y.K., 1994, 'Numerical Study on Two-Dimensional Spin-up in a Rectangle,' Phys. Fluids, Vol. 6, pp. 2333-2344 https://doi.org/10.1063/1.868183
  11. Sun, Y.K. and van Heijst, G.J.F., 2000, 'Spin-up in a Rectangular Container with an Internal Cylindrical Obstacle,' Phys. Fluids, Vol. 12, pp. 1986-1996 https://doi.org/10.1063/1.870446