The aerodynamic design of high Mach number nozzles utilizing axisymmetric flow with application to a nozzle of square test section
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Beckwith, Ivan E↗
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Second-order slender-body theory : axisymmetric flow
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Van Dyke, Milton D↗
Viscous Shock-Layer Analysis of Two-Dimensional and Axisymmetric Flows
Results are obtained for cylindrical leading edges of proposed transatmospheric vehicles by employing a two-dimensional viscous shock-layer code for nonequilibrium gas flows. The accuracy and efficiency of the planar code is verified through detailed comparisons with other predictions. This study includes results for 6-deg half-angle bodies with nose radii ranging from 0.01 to 2.0 ft for both cylindrically blunted wedges and spherically blunted cones (included for comparison). Some results are presented as a ratio of the noncatalytic to the corresponding fully catalytic heating value to illustrate the maximum potential for a heating reduction in dissociated nonequilibrium flows. Generally, this ratio and the individual heating rates are smaller for cylindrically blunted wedges with small nose radii as compared to the spherically blunted cones (for the same nose radius). Therefore, a larger potential exists for heating reduction in cylindrically blunted as compared with the spherically blunted surfaces. However, the results presented at higher altitudes (where the slip effects become important) show that the spherically, blunted nose gives lower stagnation-point heating due to stronger merged shock-layer effects as compared with a cylindrically blunted nose.
Gupta, Roop N.↗
Computations of Axisymmetric Flows in Hypersonic Shock Tubes
A time-accurate two-dimensional fluid code is used to compute test times in shock tubes operated at supersonic speeds. Unlike previous studies, this investigation resolves the finer temporal details of the shock-tube flow by making use of modern supercomputers and state-of-the-art computational fluid dynamic solution techniques. The code, besides solving the time-dependent fluid equations, also accounts for the finite rate chemistry in the hypersonic environment. The flowfield solutions are used to estimate relevant shock-tube parameters for laminar flow, such as test times, and to predict density and velocity profiles. Boundary-layer parameters such as bar-delta(sub u), bar-delta(sup *), and bar-tau(sub w), and test time parameters such as bar-tau and particle time of flight t(sub f), are computed and compared with those evaluated by using Mirels' correlations. This article then discusses in detail the effects of flow nonuniformities on particle time-of-flight behind the normal shock and, consequently, on the interpretation of shock-tube data. This article concludes that for accurate interpretation of shock-tube data, a detailed analysis of flowfield parameters, using a computer code such as used in this study, must be performed.
Sharma, Surendra P.↗
Second-Order Slender-Body Theory-Axisymmetric Flow
Slender-body theory for subsonic and supersonic flow past bodies of revolution is extended to a second approximation, Methods are developed for handling the difficulties that arise at round ends, Comparison is made with experiment and with other theories for several simple shapes.
VanDyke, Milton D.↗
Gas Generator Feedline Orifice Sizing Methodology: Effects of Unsteadiness and Non-Axisymmetric Flow
Engine LH2 and LO2 gas generator feed assemblies were modeled with computational fluid dynamics (CFD) methods at 100% rated power level, using on-center square- and round-edge orifices. The purpose of the orifices is to regulate the flow of fuel and oxidizer to the gas generator, enabling optimal power supply to the turbine and pump assemblies. The unsteady Reynolds-Averaged Navier-Stokes equations were solved on unstructured grids at second-order spatial and temporal accuracy. The LO2 model was validated against published experimental data and semi-empirical relationships for thin-plate orifices over a range of Reynolds numbers. Predictions for the LO2 square- and round-edge orifices precisely match experiment and semi-empirical formulas, despite complex feedline geometry whereby a portion of the flow from the engine main feedlines travels at a right-angle through a smaller-diameter pipe containing the orifice. Predictions for LH2 square- and round-edge orifice designs match experiment and semi-empirical formulas to varying degrees depending on the semi-empirical formula being evaluated. LO2 mass flow rate through the square-edge orifice is predicted to be 25 percent less than the flow rate budgeted in the original engine balance, which was subsequently modified. LH2 mass flow rate through the square-edge orifice is predicted to be 5 percent greater than the flow rate budgeted in the engine balance. Since CFD predictions for LO2 and LH2 square-edge orifice pressure loss coefficients, K, both agree with published data, the equation for K has been used to define a procedure for orifice sizing.
Rothermel, Jeffry↗
On the stability of compressible flow past axisymmetric bodies
Compressible linear stability theory for axisymmetric flows is presented. The theory is applied to flow past a cylinder and a sharp cone at a Mach number of 5 with adiabatic wall conditions. The effect of transverse curvature and body divergence is studied. It is found that transverse curvature has a stabilizing influence on axisymmetric (first and second mode) disturbances while it has a destabilizing influence on the asymmetric (oblique first mode) disturbances. The body divergence effects are stabilizing for both symmetric and asymmetric disturbances. Comparisons made with the results of planar stability theory show that, for a cylinder, curvature effects become more pronounced with increasing distance along the cylinder. For a sharp cone, these effects become less significant further away from the cone tip since the body radius increases faster than the growth of the boundary layer. The effect of cone angle on stability is also studied.
Malik, M. R.↗
Space shuttle booster multi-engine base flow analysis
A comprehensive review of currently available techniques pertinent to several prominent aspects of the base thermal problem of the space shuttle booster is given along with a brief review of experimental results. A tractable engineering analysis, capable of predicting the power-on base pressure, base heating, and other base thermal environmental conditions, such as base gas temperature, is presented and used for an analysis of various space shuttle booster configurations. The analysis consists of a rational combination of theoretical treatments of the prominent flow interaction phenomena in the base region. These theories consider jet mixing, plume flow, axisymmetric flow effects, base injection, recirculating flow dynamics, and various modes of heat transfer. Such effects as initial boundary layer expansion at the nozzle lip, reattachment, recompression, choked vent flow, and nonisoenergetic mixing processes are included in the analysis. A unified method was developed and programmed to numerically obtain compatible solutions for the various flow field components in both flight and ground test conditions. Preliminary prediction for a 12-engine space shuttle booster base thermal environment was obtained for a typical trajectory history. Theoretical predictions were also obtained for some clustered-engine experimental conditions. Results indicate good agreement between the data and theoretical predicitons.
Tang, H. H.↗
BLSTA: A boundary layer code for stability analysis
A computer program is developed to solve the compressible, laminar boundary-layer equations for two-dimensional flow, axisymmetric flow, and quasi-three-dimensional flows including the flow along the plane of symmetry, flow along the leading-edge attachment line, and swept-wing flows with a conical flow approximation. The finite-difference numerical procedure used to solve the governing equations is second-order accurate. The flow over a wide range of speed, from subsonic to hypersonic speed with perfect gas assumption, can be calculated. Various wall boundary conditions, such as wall suction or blowing and hot or cold walls, can be applied. The results indicate that this boundary-layer code gives velocity and temperature profiles which are accurate, smooth, and continuous through the first and second normal derivatives. The code presented herein can be coupled with a stability analysis code and used to predict the onset of the boundary-layer transition which enables the assessment of the laminar flow control techniques. A user's manual is also included.
Wie, Yong-Sun↗
Imilar flows about axisymmetric bodies rotating in a fluid at rest. similar flows about axisymmetric bodies rotating in a fluid at rest.
Similar flows about axisymmetric bodies rotating in fluid at rest
AXISYMMETRIC FLOW↗
Inviscid transonic flow over axisymmetric bodies
Axisymmetric transonic flow is of interest not only because of its practical application to missile and launch vehicle aerodynamics but also because of its relation, in terms of area rule, to fully three dimensional flow. RAXBOD computer program analyzes steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses finite-difference relaxation method to solve numerically exact formulation of disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important.
South, J. C., Jr.↗
Theoretical studies of supersonic two- dimensional and axisymmetric nonequilibrium flow, including calculations of flow through a nozzle
Supersonic two-dimensional and axisymmetric nonequilibrium flow theory and calculations for axisymmetric flow through nozzles
NONEQUILIBRIUM FLOW↗
Conservative full-potential calculations for axisymmetric, transonic flow
A conservative, finite-difference, full-potential relaxation code has been developed to solve transonic flow around axisymmetric or nonlifting, planar, two-dimensional bodies. The program utilizes the artificial compressibility method to provide an upwind bias in supersonic regions. Calculated examples include a wide variety of axisymmetric and planar two-dimensional shapes with various blunt, pointed and open ends in subsonic, transonic, and low supersonic free streams. Comparisons between conservative and nonconservative full-potential calculations show perfect agreement at convergence when the flow is entirely subsonic. Noticeable differences exist, however, between the conservative and nonconservative solutions for transonic flows with shocks.
Green, L. L.↗
Numerical solution of axisymmetric boattail flow fields with plume simulators
Turbulent separating flows over axisymmetric afterbody-boattail configurations with solid sting plume simulators are computed with a time-dependent finite-difference method to solve the compressible Navier-Stokes equations. The Reynolds stress terms are replaced with a two-layer eddy viscosity model including a relaxation formula to model the nonequilibrium effects of the separated flow. The mesh is alined with the boattail body through an analytic transformation which accommodates a wide variety of boattail geometries. Numerical results for a series of boattail geometries over a wide range of Reynolds number (140,000 to 140 million) are presented and, when possible, compared with experimental data or independent numerical results.
Holst, T. L.↗
A Computer Code for Swirling Turbulent Axisymmetric Recirculating Flows in Practical Isothermal Combustor Geometries
A primitive pressure-velocity variable finite difference computer code was developed to predict swirling recirculating inert turbulent flows in axisymmetric combustors in general, and for application to a specific idealized combustion chamber with sudden or gradual expansion. The technique involves a staggered grid system for axial and radial velocities, a line relaxation procedure for efficient solution of the equations, a two-equation k-epsilon turbulence model, a stairstep boundary representation of the expansion flow, and realistic accommodation of swirl effects. A user's manual, dealing with the computational problem, showing how the mathematical basis and computational scheme may be translated into a computer program is presented. A flow chart, FORTRAN IV listing, notes about various subroutines and a user's guide are supplied as an aid to prospective users of the code.
Lilley, D. G.↗
Application of a numerically generated orthogonal coordinate system to the solution of inviscid axisymmetric supersonic flow over blunt bodies
A numerically generated orthogonal coordinate system (with the body surface and shock wave as opposite boundaries) was applied with a time asymptotic method to obtain steady flow solutions for axisymmetric inviscid flow over several blunt bodies including spheres, paraboloids, ellipsoids, hyperboloids, hemisphere cylinders, spherically blunted cones, and a body with a concavity in the stagnation region. Comparisons with experimental data and with the results of other computational methods are discussed. The numerically generated orthogonal coordinate system is described and applications of the method to complex body shapes, particularly those with concave regions, are discussed.
Hamilton, H. H., II↗
Axisymmetric supersonic flow in rotating impellers
General equations are developed for isentropic, frictionless, axisymmetric flow in rotating impellers with blade thickness taken into account and with blade forces eliminated in favor of the blade-surface function. It is shown that the total energy of the gas relative to the rotating coordinate system is dependent on the stream function only, and that if the flow upstream of the impeller is vortex-free, a velocity potential exists which is a function of only the radial and axial distances in the impeller. The characteristic equations for supersonic flow are developed and used to investigate flows in several configurations in order to ascertain the effect of variations of the boundary conditions on the internal flow and the work input. Conditions varied are prerotation of the gas, blade turning rate, gas velocity at the blade tips, blade thickness, and sweep of the leading edge.
Goldstein, Arthur W↗
Computational studies of hard-body and 3-D effects in plume flows
Axisymmetric and three-dimensional, multi-nozzle plume flows around generic rocket geometries are investigated with a three-dimensional Navier-Stokes solver to study the interactive effects between hard body and the plume. Time-asymptotic, laminar, ideal-gas solutions obtained with a two-factor, flux-split scheme and a diagonal, upwind scheme are presented. Computed solutions to three-dimensional, multi-nozzle problems and single-nozzle, axisymmetric problems demonstrate flow field features including three-dimensionality and hard-body effects. Geometry and three-dimensional effects are shown to be significant in multi-nozzle flows.
Venkatapathy, Ethiraj↗