Pressure Distribution Obtained Using Two-Dimensional Vortex Method.

Abstract

The vortex method is powerful for analyzing high Reynolds number flows, and so it is applied to many fluid flow problems. Using this method, the velocity field is obtained from the calculated vorticity field using the Biot-Savart formula. However, the pressure field is not obtained directly. The pressure field has been calculated by (1) using the unsteady Bernoulli equation, (2) solving Poisson's equation using the finite difference method and (3) solving Poisson's equation using the boundary element method. In the present work we show that (1) the pressure field can be analytically obtained on the fluid flow around a two-dimensional circular cylinder, (2) this approach is easily applied to the flow past an arbitrary body, provided that the conformal mapping function is given, and (3) the mapping function is easily obtained when the vortex method is combined with the panel method. To confirm the validity of the present approach, numerical calculations are carried out for the flows around circular and elliptical cylinders using a classical vortex method and a high accurate vortex method. The numerical results show that the pressure distribution around a circular cylinder is in good agreement with that obtained using the unsteady Bernoulli equation.