Calculation of the force on solid body in the unsteady flow of incompressible fluid

Abstract

In the paper, a special method to compute the aerodynamic force is presented. This method is especially addressed to the calculation while both the velocity and vorticity fields are found as a result of the vortex method application. In the case of vortex method, the vorticity field is shown as a sum of contributions given by a large number of the vorticity carriers. These carriers of vorticity move and change, but the vorticity distribution given by each of them is known. It means that both the vorticity and induced velocity field connected with them are easy to determine. The velocity field may also contain any potential component. This component assures the fulfillment of the asymptotic condition, and cancels the normal component of the velocity on the rigid body surface [15]. As it is known, the aerodynamic force may be calculated by using the basic definition, but in this case the boundary values of pressure and vorticity or derivatives of velocity field have to be found beforehand. These values are difficult to determine and their properties can be inconvenient. Quartapelle and Napolitano [12] introduced a special method of aerodynamic force calculation. This method does not require any surface integrals. Instead, the areas integrations are held. The integrands consist of vorticity and velocity fields only. The pressure field is excluded by special harmonic projection. The numerical experiment shows that the method of Quartapelle and Napolitano requires improvement in case of complicated, rapidly changing velocity and vorticity fields and the approximation of these fields in the neighborhood of the body not being perfect. However, if the concept of Quartapelle and Napolitano is applied to the area located outside the big sphere surrounding the body and containing the sources of vorticity, where velocity and vorticity fields have suitable properties (which permits to perform analytical calculations), we will get a simple formula for the aerodynamic force. This formula is not limited by additional properties of the pressure and velocity and vorticity fields. The numerical results are in relatively good agreement with the experimental data.