H. Doyle Thompson

Investigation of turbulent transport in an axisymmetric sudden expansion

Simultaneous two-component laser velocimeter measurements were made in the incompressible turbulent flowfield following an axisymmetric sudden expansion. Mean velocities, Reynolds stresses, and triple products were measured and are presented at axial positions ranging from x/H = 0.2-14. A balance of the turbulent kinetic energy in the flow was performed. The production, convection, and diffusion of turbulent kinetic energy were computed directly from the experimental data using central differencing. A specially designed correction lens was employed to correct for optical aberrations introduced by the circular tube. This lens system allowed the accurate simultaneous measurement of axial and radial velocities in the test section. The experimental measurements were compared to predictions generated by a code that employed the k-epsilon turbulence model. Agreement was good for mean axial velocities, turbulent kinetic energy, and turbulent shear stresses. However, the modeled turbulent normal stresses where in poor agreement with the measured values. The modeled diffusion of turbulent kinetic energy was underpredicted in the region between the shear layer and the centerline of the flow giving lower values of turbulent kinetic energy downstream of the potential core than measured.

Design of Maximum Thrust Plug Nozzles for Fixed Inlet Geometry

Abstract : The techniques of the calculus of variations were used to determine the configuration of an optimum thrust plug nozzle. The problem is formulated for a fixed thrust injection angle and cowl lip radius, and the resulting plug contour is then an optimum for a given upstream geometry. The optimum values of the injection angle and cowl lip radius are determined by a parametric study. The analysis is carried out for rotational and irrotational flows and includes boundary layer effects. A method is presented for each of the problem formulations to determine if a given contour is an optimum and a relaxation technique is used to obtain a solution to the irrotational flow problem. A computer program which makes use of the design equations for the irrotational flow problem is developed and described. This program is used to carry out a parametric study to determine the optimum cowl lip radius and injection angle when the plug length is fixed. The resulting optimum nozzle is compared to one designed by Raos Method. The importance of determining the base pressure accurately is illustrated and an example of scramjet nozzle optimization is presented. (Author)

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.

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

Design of maximum thrust plug nozzles with variable inlet geometry

Abstract : The problem of designing two-dimensional or axisymmetric plug nozzles with variable inlet geometry which produce the maximum axial thrust when an engineering constraint is imposed on the plug contour, for example, fixed length, has been formulated and numerically solved. The formulation was written to consider a gas mixture whose composition is either fixed or in chemical equilibrium. The effects of the boundary layer thickness and the wall shear stress are included in the problem formulation. The optimization analysis and the results from selected parametric studies are presented in Volume I of this report. This volume, Volume II, contains a description of the computer program, a discussion of the input parameters, and the results of six sample cases. (Author)

Three-Dimensional Thrust Nozzle Design for Maximum Axial Thrust

Abstract : A technique has been developed for the design of maximum thrust three-dimensional (nonaxisymmetric) nozzles. The thrust expression, written as an integral over a control surface, is maximized by the application of the calculus of variations. Each optimal three-dimensional nozzle designed by this method produces the maximum axial thrust for a prescribed upstream flow field, mass flow rate, exit lip shape and position, and ambient pressure. Solutions for nine sample cases are presented. The performance of each optimal nozzle is compared with that of a three-dimensional nozzle with identical initial conditions and comparable overall dimensions. (Author)

A parametric study of statistical velocity bias

The problem of individual realization bias (more often known as statistical or velocity bias) has bedeviled the users of laser velocimeter systems for many years. Only very recently has a reasonable consensus on the nature of the problem been reached. However, agreement on which correction methods to use and the experimental conditions needed to obtain suitable data for implementing post facto correction methods are still unresolved. In the present study measurements were made in a highly turbulent flow where the relations between turbulence intensity, seeding density, sampling rate, and turbulent time scales could be varied over wide ranges. A number of significant conclusions can be drawn from the results.The problem of individual realization bias (more often known as statistical or velocity bias) has bedeviled the users of laser velocimeter systems for many years. Only very recently has a reasonable consensus on the nature of the problem been reached. However, agreement on which correction methods to use and the experimental conditions needed to obtain suitable data for implementing post facto correction methods are still unresolved. In the present study measurements were made in a highly turbulent flow where the relations between turbulence intensity, seeding density, sampling rate, and turbulent time scales could be varied over wide ranges. A number of significant conclusions can be drawn from the results.

Swirling Flow in Thrust Nozzles

This paper investigates the effects of adding swirl to a dump combustor-nozzle propulsion system. The results of cold-flow testing are summarized and compared to a numerical analysis of the nozzle flowfield. The cold-flow testing included thrust, mass flow rate, and pressure measurements for two different conical nozzles in combination with four swirlers, one of which was a blank. Five-port probe measurements were made across the nozzle entrance. The measurements were used to determine the stagnation pressure and swirl distributions and to provide initial conditions for a nozzle analysis program. The measured results show that swirl has a strong effect on the stagnation pressure distribution. The largest losses occur near the swirl axis. Swirl also significantly reduces the system discharge coefficient. In contrast, the effect of swirl on the nozzle stream thrust efficiency was small, but measurable. Swirl reduced the nozzle stream thrust efficiency by about 0.5% for the highest swirl tested. Computed nozzle flowfields that do not account for the stagnation pressure distribution in the swirling flow can produce highly distorted and unrealistic results. Comparison of measured and computed results (which use measured stagnation pressure and swirl distributions) shows reasonable agreement.

Stability and accuracy studies on a second-order method of characteristics scheme for three-dimensional, steady, supersonic flow

A new explicit method of characteristics (MOC) numerical scheme for three-dimensional steady flow has been developed which has second-order accuracy. A complete numerical algorithm has been developed for computing internal supersonic flows. A comprehensive stability analysis was conducted in which both the Courant-Friedrichs-Lewy (CFL) stability criterion and the von Neumann stability analysis were applied. Although necessary and sufficient criteria for stability exist only for linear difference equations and analytic initial data, experience has indicated that these same criteria are appropriate for nonlinear systems when applied locally to the linearized form of the equations. This thesis is supported by the results of the present research in which the nonlinear scheme was found to be stable only when the analysis of the linearized system indicated stability. The numerical scheme has been tested for order of accuracy using exact solutions for source flow and Prandtl-Meyer flow. The results of these tests have verified the second-order accuracy of the scheme. Additional tests using axisymmetric flows have shown that the accuracy of the scheme is comparable to that of a proven second-order two-dimensional MOC scheme.

Experimental mapping of the turbulent reacting flow field downstream of an axisymmetric sudden expansion

Simultaneous two-component laser velocimeter measurements were made in the turbulent flow field following an axisymmetric sudden expansion with and without combustion. Mean axial and radial velocities and Reynolds stresses are presented. In addition, simultaneous time resolved temperature measurements where made in the reacting flow using fast response thermocouples. Velocity-temperature correlations were formed from the velocity and temperature measurements.Simultaneous two-component laser velocimeter measurements were made in the turbulent flow field following an axisymmetric sudden expansion with and without combustion. Mean axial and radial velocities and Reynolds stresses are presented. In addition, simultaneous time resolved temperature measurements where made in the reacting flow using fast response thermocouples. Velocity-temperature correlations were formed from the velocity and temperature measurements.