Finite volumes simulations of aerodynamic flows based on velocity-vorticity formulations

摘要

In small disturbance theories of aerodynamics, the flow field is decomposed into two regions consisting of an inviscid outer region and a viscous inner region of a boundary or shear layer. In both outer and inner regions the governing equations can be written in terms of the divergence and the curl of the velocity. In the outer region, the flow is assumed to be irrotational. In addition, to account for compressibility effects, the flow is assumed to be isentropic. In the inner region, the vorticity equation is obtained by taking the curl of the momentum equation. Furthermore, the governing equations are simplified using boundary layer approximations. Viscous-inviscid interaction procedures are implemented to implicitly couple the calculations in the two regions. Several finite volumes calculations based on the above velocity-vorticity formulations of the two- and three-dimensional incompressible and compressible flows are presented and the results are discussed together with some concluding remarks. The present work provides the results of a unified physical approach for main aerodynamics calculations.