Finite area method for nonlinear supersonic conical flows

Abstract

A fully conservative numerical method for the computation of steady inviscid supersonic flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell; a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is desymmetrized by adding artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point liftoff correctly. Results are compared with those of other investigators.

Numerical Solution of Compressible Euler and Magnetohydrodynamic flow past an infinite cone

“…The exact value of each of these coordinates in each cell is not important, so it can be freely assumed that ξ 1 , ξ 2 ∈ [0, 1] in each cell. The relationship between the spherical coordinates and the mesh coordinates can be computed as described in [4]. Basis functions are defined inside the cell which are given by:…”

“…The unique character of the systems made them incompatible with basic numerical methods. Numerical methods have been developed for the conical Euler equations subject to the assumption of irrotational flow in [3] and [4] with success. These however did not so easily extend to the more general conical equations.…”

A design method for supersonic transport wings

“…While this flow is supersonic, the cross-flow plane equations are mixed, being hyperbolic outside the conical shock wave and inside the local "supersonic" cross-flow region, but subsonic elsewhere. The fictitious gas method that has proved successful for supercritical airfoils and wings applies here as well, [14], [31]. We first describe the method here, not in this context of supersonic flows such as this conical flow, but in the context of subsonic supercritical flows.…”

“…A brief review of these design tools is provided in [11]. Among these tools only one, the fictitious gas method of Sobieczky [12], provides a method that may also be used for three-dimensional flows [13] and, remarkably for supersonic flows as well [31]. Knowledge derived from this tool provided the necessary insight for optimization routines to be used to generate shock-free airfoils and wings [15].…”

Compressible Euler Equations on a Sphere and Elliptic-Hyperbolic Property

“…In [16], Sritharan used the machinery of tensor calculus to project the mass equation onto the unit sphere for the case of potential flow. In related works, [18,6], the more sophisticated finite volume methods available at the time were used to compute numerical solutions for cones of arbitrary cross section. Now, with even more sophisticated numerical methods for fluid flow equations and a renewed interest in hypersonics, we add to this body of knowledge by extending Sritharan's work and deriving the conical form of the full system of Euler equations.…”