On aerodynamic forces for viscous compressible flow
The paper is aimed at reviewing and adding some new results on a force theory for viscous compressible flows around a finite body. It has been proposed to analyse aerodynamic forces directly in terms of fluid elements of nonzero vorticity and density gradient. Let \(\rho\) denote the density, \({\mathbf u}\) the velocity, and \(\vec \omega\) the vorticity. It is demonstrated that for largely separated flows about bluff bodies, there are two major source elements: \(R_e ({\mathbf x}) =-{1\over 2} {\mathbf u}^2 \nabla \rho \cdot \nabla \varphi\) and \(V_e({\mathbf x}) =-\rho {\mathbf u} \times \vec \omega \cdot \nabla \varphi\), where \(\varphi\) is an acyclic potential, generated by the solid body moving with unit velocity in the negative direction of the force considered. In particular, under mild conditions, the (unique) choice of \(\varphi\) enforces that the elements \(R_e ({\mathbf x})\) and \(V_e ({\mathbf x})\) decay rapidly away from the body. Four kinds of finite bodies are considered: a circular cylinder, a sphere, a hemisphere-cylinder, and a delta wing of elliptic section -- all in transonic-to-supersonic regimes. From an extensive numerical study carried out for these bodies, it is found that these two elements contribute to \(95\%\) or more of the total drag or lift for all the cases under consideration.
scientific article; zbMATH DE number 1174725