On the sources of aerodynamic forces: steady flow around a cylinder or a sphere

Abstract

In the present study, we analyse various force contributions for viscous compressible flow around a finite body. Aerodynamic forces are found to be directly related to fluid elements of non-zero vorticity and density gradient. Since the aerodynamic range is large, relative importance of various sources should, however, be assessed under different flow conditions. The effect of compressibility is our major concern. Let p denote the density, u velocity, and ω vorticity. It is demonstrated that for largely separated flows about bluff bodies, there are two major source elements: Re(x) = -1/2u2∇p.∇ϕ and Ve(x) = -pu x ω . ∇ϕ, where ϕ is an acyclic potential, generated by the solid body moving with unit velocity in the negative direction of the force considered. All the physical quantities are non-dimensionalized. In particular, we consider steady flows around a circular cylinder or a sphere in a transonic-to-supersonic regime. Numerical results indicate that these two elements contribute to 95% or more of the total drag for all the cases under consideration. For flows around either a cylinder or a sphere, it is found that the source elements are concentrated on four regions; they are the front shock region, the boundary layer in front of the body, the shear layer separating from the shoulder of the body, and a region of expansion/compression upstream of the separated shear layer. The separated shear layer is found to be an important source for both elements Re(x) and Ve(x). The region of expansion and the front shock contribute largely and positively to the drag through Re(x), while the front boundary layer contributes largely and negatively to the drag through Ve(x). Other flow structures such as the trailing shock wave and the regions of eddying motion, including the wake and a region of dead air behind the body are shown to play relatively much less significant roles in contributing to the drag.