Implicit Solution for the Shock-Layer Flow around General Bodies

Abstract

The simplified forms of the Navier-Stokes equations are solved by an iterative implicit scheme along the body axis for angles of incidence up to 30 deg. The method of solution yields both the inviscid and viscous flows simultaneously and predicts bow shock at stations normal to the axis. The technique is developed from a comparatively simple linearization procedure and has an option to iterate between body stations for higher accuracy. Reliable procedures have been introduced to account for the effect of the axial pressure gradient and to adjust the step increment for a given convergence requirement. A blunt cone and a Shuttle Orbiter-like configuration were studied and good agreement is obtained with available laminar boundary-layer solutions and experimental data. ISCOUS flowfield solutions around a re-entry vehicle are needed for the prediction of heating distributions as well as for the interpretation of aerodynamic data to support the design and flight test processes. The traditional boundary- layer (BL) approach that decouples the viscous flow from the outer inviscid flow has been valuable in the past; however, for the problems of current interest, such as the Space Shuttle Orbiter and the maneuverable re-entry vehicle, a more ac- curate solution is being obtained from the coupled fluid dynamics equations. This paper presents a method suitable for complex configurations that may be described by a lofting technique used by the aerospace industry. The method is devised to solve the Euler equations for the inviscid region and the parabolic Navier-Stokes (PNS) equations for the viscous region along an identifiable main-flow direction. The PNS equations are obtained from the full NS equation by omitting the second-order and the mixed derivatives and by approximating the exact pressure gradient in the designated direction. The flowfield of interest is bounded between the shock, the body, an initial-data plane normal to the specified direction, and a downstream station parallel to the initial plane. Although the length scales associated with the flow phenomena differ greatly on that plane, highly nonuniform grid spacings near the wall are not desirable in practice, as the shock must be calculated accurately. Hence, a detailed shock- layer solution requires a large number of grid points and consequently long computation time. In return for its cost, this method does not have any of the known shortcomings associated with the BL analyses and offers new capabilities for predicting leeside flow and crossflow separation. For this reason, there has been an intensive research effort in this decade to solve for the viscous flow as an integral part of the flowfield.