Numerical Procedure for the Computation of Irrotational Conical Flows

In the study described, a finite difference approach to solving the rotational Euler equations, explicitly fitting shocks as a boundary, is applied to a variety of geometrical shapes in the lower supersonic Mach number regime. It is shown how special techniques based on the physics of the flow can be used to circumvent a variety of numerical difficulties encountered with the conical flow problem that are primarily associated with the initial value characteristics of the hyperbolic scheme, causing embedded shock-induced entropy and crossflow layers to develop on the body surface.

Section: Wing-body Effectsupporting

confidence: 52%

“…A relaxation method was applied to the conical full potential flow equation in Ref. 3 that relied heavily on numerical transonic techniques. Numerical solutions were computed successfully for circular/elliptic cones and thin winglike cross sections from low to high incidence at freestream Mach numbers between 1.2 and 3.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Crossflow Shocks on Delta Wings in Supersonic Flow

Siclari

1980

“…In Ref. 2, it was found that because of the type-dependent, or mixed elliptic/hyperbolic, nature of the cross flow, transonic techniques such as those developed early by Jameson 3 could be used to determine numerical solutions. The conical flow problem was extended by Grossman and Siclari 4 to include three-dimensional flow using a fully implicit marching technique where each marching step requires an implicit crossflow solution.…”

Section: Introductionmentioning

confidence: 99%

“…found that the off-diagonal terms of the F xz derivative could be included in the subsonic cross-flow region but not in the supersonic region leading to the following for the b x z operator for U>0, or, &XZ -( ) ?J,k ~ ( ) 1-IJ.k ~ ( ) i,j,k-1 + ( ) /-l,j,k-l AY2 (26)…”

mentioning

confidence: 99%

Approximate factorization schemes for three-dimensional nonlinear supersonic potential flow

Siclari¹

1985

The nonconservative finite difference analog of the three-dimensional full-potential equation is solved implicitly by marching in a radial coordinate system with the marching initiated by a conical flow at the apex. The crossflow is a mixed type and transonic type-dependent differencing is used to determine each spherical plane solution. Two types of approximate factorizations are studied, the AFl or ADI and the AF2 factorization. In the AF2 factorization, one of the second derivatives is split between the two factors. The type of AFl factorization that was found to work for the conical problem was also found to be more sensitive to the coordinate transformations and strong shocks than the AFl scheme. Both schemes were found to require some form of temporal damping for stability for the multishock conical flow problem. The AFl factorization was then extended to include three-dimensional flows with the bow shock fit by explicitly including the hyperbolic third-dimension terms. The AFl factorization was shown to improve the convergence rate markedly for most cases.

“…First major success in computing nonlinear irrotational conical flows was reported by Grossman, 3 who devised a quasilinear finite difference method for this problem. An alternative approach is to extend Jameson's 4 finite difference algorithm for transonic full potential equation in the Euclidean three space as a marching scheme to treat supersonic potential flows.…”

Section: Introductionmentioning

confidence: 99%

Finite area method for nonlinear supersonic conical flows

Sritharan

Seebass

1984

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.