Performance prediction and design of maximum thrust planar supersonic nozzles using a flux-difference-splitting technique

John Howard Doty, Purdue University

Abstract

An analysis and computer program have been developed for the design of maximum thrust nozzles for hypersonic vehicles and applied to planar, inviscid, supersonic rotational flow of a thermally and calorically perfect gas. The flowfield analysis is accomplished by a flux-difference-splitting (FDS) technique. The nozzle wall thrust is maximized for parabolic nozzle contours using a direct search optimization procedure. Three different Riemann solvers were investigated as the basis for the FDS method. The exact Riemann solver is superior to either the approximate or the linearized-approximate Riemann solver when applied to a local Riemann problem. However, when used in the FDS method to solve an entire flowfield, numerical results with all three are comparable. The major advantage of the linearized-approximate Riemann solver is the savings in computational time. First-order accurate FDS solutions agree extremely well with the exact solutions. Excellent agreement between the first-order accurate FDS method and the second-order accurate explicit MacCormack method, as well as the second-order accurate numerical method of characteristics, is also achieved. For the cases studied, the second-order accurate FDS method was more accurate than the first-order accurate FDS method. However, the increase in accuracy must be weighed against the increased computational time and coding complexity. For second-order accurate solutions at a boundary, a nonphysical extrapolation of the flux differences is required. Also, for points just inside a boundary, another nonphysical correction is required to maintain second-order accuracy. In addition, the second-order accurate method must be limited in regions of strong property gradients. Nonuniform initial-value property distributions require no special treatment for the FDS method. Nonuniform nozzle inlet conditions were developed to simulate the downstream properties of a typical supersonic combustor. The analysis of a straight wall nozzle with nonuniform initial-value properties corroborates the existence of injection compression and expansion interaction waves. Validation of the optimization procedure was performed by comparing results with results obtained using the Rao optimization technique. Wall thrust results from the FDS direct optimization technique agree very well with those from the Rao technique. The direct optimization procedure is demonstrated with the design of maximum thrust nozzle contours for combined internal/external flowfields. (Abstract shortened with permission of author.)

Degree

Ph.D.

Advisors

Thompson, Purdue University.

Subject Area

Mechanical engineering

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