Joe D. Hoffman

Design of compressed truncated perfect nozzles

An analysis is presented for designing and predicting the performance of compressed truncated perfect nozzles. A study was performed to determine the relative merits of such nozzles compared to Rao nozzles. It was found that Rao nozzles always yield higher performance than compressed truncated perfect nozzles. However, the performance differences are quite small (0.04-0.34%), which shows that compressed truncated perfect nozzles are good propulsive nozzles. For nozzle envelopes for which the Rao nozzle design concept fails, compressed truncated perfect nozzles may yield very efficient nozzle designs.

A Second-Order Bicharacteristics Method for Three-Dimensional, Steady, Supersonic Flow

A numerical method based on a bicharacteristics scheme for the solution of three-dimensi onal, steady, supersonic flows has been developed which has second-order accuracy. The method has been tested for order of accuracy using the exact solutions for source flow and Prandtl-Meyer flow. Comparisons with existing methods for the solution of axisymmetric flows have shown that the scheme produces accuracies comparable to that of the twodimensional method of characteristi cs. Flowfields for several three-dimensional nozzle contours were obtained. These results revealed the complex nature of the three-dimensional flows and verified the general inadequacy of quasi three-dimensional analyses which neglect cross flow. Experimental comparisons were made for a threedimensional, super-elliptic contour, and a reasonable correlation between predicted and measured pressures was obtained.

A general method for determining optimum thrust nozzle contours for chemically reacting gas flows.

Optimum thrust nozzle contours for chemically reacting gas flows, obtaining set of partial differential equations for gas dynamic properties

Numerical Boundary Condition Procedures for Euler Solvers

A numerical boundary condition procedure for Euler solvers is presented. The procedure is based on a variation of the method of characteristi cs due to Kentzer. A second-order-a ccurate numerical algorithm using this procedure and the MacCormack explicit finite-difference method is presented. Results are presented for several two-dimensional and three-dimensional inviscid nozzle flowfields. Solutions obtained by the present method agree well with solutions obtained by method of characteristi cs algorithms and experimental data.

Design of Maximum Thrust Nozzle Contours by Direct Optimization Methods

A PROCEDURE for the design of maximum thrust nozzle contours by direct optimization methods is presented. The nozzle contour is a second-degree polynomial having a fixed initial expansion contour. The coefficients of the polynomial are varied by direct optimization methods to determine the maximum thrust contour. Three direct optimization methods are considered: multidimensional line search, the method of steepest descent, and Newtons method. Results are presented to illustrate the behavior of the direct optimization methods, and to demonstrate that second-degree polynomial contours yield thrusts comparable to the thrusts developed by nozzle contours determined by calculus of variations methods.

Flow Computations in Inlets at Incidence Using a Shock Fitting Bicharacteristic Method

An analysis is presented for calculating the flowfield in supersonic mixed-compression aircraft inlets operating at angle of attack. The flowfield is computed by a steady three-dimensional bicharacterist ic method. The bow shock wave and the reflected internal shock wave system are computed by a three-dimensional, discrete shock wave fitting procedure. Viscous and thermal diffusion may be included as source terms in the bicharacteristic method. A production type of computer program capable of determining the flowfield in a variety of axisymmetric mixed-compression supersonic inlets is available. The results of the present analysis agree well with those produced by the two-dimensional method of characteristi cs when axisymmetric flowfields are computed. For three-dimensional flowfields, the results of the present analysis agree well with experimental data except in regions of high viscous interaction and boundary-layer removal. The present analysis does not compute the boundary layer, nor does it account for boundary-layer bleed.

Design of Shrouded-Plug Nozzles for Maximum Thrust

A method for designing the wall contours of shrouded-plug nozzles for maximum thrust is presented. The flow is assumed to be isentropic. The optimization problem is formulated employing the calculus of variations, and the design equations are determined. A numerical technique for implementing the method is presented. A comparison is presented between truncated perfect shrouded-plug nozzles and maximum thrust shrouded-plug nozzles. Some numerical results are presented to demonstrate the application of the method.

Accuracy studies of the numerical method of characteristics for axisymmetric, steady supersonic flows

Abstract A detailed numerical study of the accuracy of the method of characteristics is presented for axisymmetric, supersonic flows. Ten numerical schemes and three grid networks were investigated for both irrotational and rotational flows. In all cases, the Euler predictor-corrector difference scheme was employed, and studies were conducted with predict only, predict-correct, and repetitive application of the corrector. The results illustrate the general character of the various schemes, and some general observations are drawn.

Maximum Thrust Nozzles for Nonequilibrium Simple Dissociating Gas Flows

A formulation, numerical solution technique, and computer program implementing the technique are presented for the design of maximum thrust nozzles for rotational or nonequilibrium simple dissociating gas flows including boundary-layer effects. The formulation is based on the usual assumptions applicable to rotational and nonequilibrium simple dissociating gas flows and on the assumption that the boundary layer is thin. The thrust is maximized by application of the calculus of variations. The resulting design equations are hyperbolic partial differential equations, which are solved by the method of characteristics. The results of a study to determine the magnitude of the performance increases that can be expected by considering more accurate flow chemistry models are presented. The results indicate that significant performance improvements may be possible.

Analytical study of swirler effects in annular propulsive nozzles

THIS paper presents an analytical performance prediction methodology for annular propulsive nozzles with swirl introduced ahead of the combustor that feeds the nozzle. The methodology is applied to investigate the effects of swirier design on nozzle performance. Four types of swirlers are investigated: free vortex, constant angle, forced vortex, and Rankine vortex swirlers. Discharge coefficients and specific impulses are presented. Contents