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Some 100 numerical computations have been carried out for unyawed bodies of revolution with detached bow waves. The gas is assumed perfect with gamma = 5/3, 7/5, or 1. Free-stream Mach numbers are taken as 1.2, 1.5, 2, 3, 4, 6, 10, and infinity. The results are summarized with emphasis on the sphere and paraboloid.
An analysis has been performed t o determine the effect of mass injection on heat transfer to an arbitrary surface of revolution. effective heat of ablation is determined, and the downstream effects of injection are investigated. It is found that the linear relation between heat of ablation and difference between wall and free-stream enthalpy, previously verified at the stagnation point, provides a useful approximation at any point on a surface of revolution. From the investigation of the downstream effects of injection it is found that an appreciable rate of heating may be obtained, even at points considerably downstream from the point at which injection ends. However, the radiation equilibrium temperature is proportional to the fourth root of the heating rate; therefore, except in particular cases, it will be difficult to make use of this effect in the design of thermal protection systems. Effects of radiation from a hot gas layer to the ablating surface are investigated by an approximate procedure. The efficiency of ablation is found to approach a maximum value which depends on the ratio of radiant heating to aerodynamic heating and is independent of the enthalpy difference across the boundary layer.
Flight-testing of a channeled center-body axisymmetric supersonic inlet design concept was conducted at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center in collaboration with the NASA Glenn Research Center (Cleveland, Ohio) and TechLand Research, Inc. (North Olmsted, Ohio). This testing utilized the Propulsion Flight Test Fixture, flown on the NASA F-15B research test bed airplane (NASA tail number 836) at local experiment Mach numbers up to 1.50. The translating channeled center-body inlet was designed by TechLand Research, Inc. (U.S. Patent No. 6,276,632 B1) to allow for a novel method of off-design flow matching, with original test planning conducted under a NASA Small Business Innovative Research study. Data were collected in flight at various off-design Mach numbers for fixed-geometry representations of both the channeled center-body design and an equivalent area smooth center-body design for direct comparison of total pressure recovery and limited distortion measurements.
Direct numerical method for calculation of supersonic inviscid flow about axisymmetric blunt body at large angle of attack
Supersonic inviscid flow of equilibrium real gas over blunt axisymmetric bodies at large angles of attack including Apollo and Gemini shapes
Direct calculation method for supersonic inviscid flow around axisymmetric blunt body with conically reentrant afterbody flying at large angle of attack
Flow fields about axisymmetric blunt bodies at large angles of attack calculated by IBM 7094 computer program
Melting ablation for two dimensional and axisymmetric blunt bodies with body force, predicting gas-liquid interface temperature for free stream conditions
General solution of compressible laminar boundary layer in stagnation region of blunt bodies in axisymmetric flow
Hypersonic and supersonic angle of attack flow about asymmetric and axisymmetric blunt bodies based on time dependent finite difference theory and method of characteristics
An application of a simple numerical technique which allows for the rapid construction of orthogonal coordinate systems about axisymmetric blunt bodies is presented. This technique can generate orthogonal meshes which have unequally spaced points in two directions. Relations are given for the numerical generation of the metric coefficients. Body shapes ranging from simple analytical bodies to complex reverse curvature bodies are presented together with their orthogonal coordinate systems. The relatively good accuracy of the technique is shown in tabular data describing coordinate line slopes and metric coefficients. The predictor-corrector numerical method used to generate these results is both simple in concept and easy to program, so that the application of the technique should be broader than the results presented.
The effect of forebody geometry on the stability of the laminar boundary layer on axisymmetric body shapes at Reynolds numbers typical of small and medium sized aircraft in low-subsonic cruise flight is investigated. It is found that small nose radii are important in obtaining n-factors of 9 on axisymmetric bodies of fineness ratio of about 6 at large nondimensional axial distances downstream. Results for the effect of the steepness of the pressure gradient and the value of the minimum pressure on the extent of laminar flows on an axisymmetric body at a given Reynolds number are also presented.
Boundary layer transition over axisymmetric bodies at non-zero angle of attack in supersonic flow is numerically investigated as part of joint research between the National Aeronautics and Space Administration (NASA) and Japan Aerospace Exploration Agency (JAXA). Transition over four axisymmetric bodies (namely, Sears-Haack body, semi-Sears-Haack body, 5-degree straight cone and flared cone) with different axial pressure gradients has been studied at Mach 2 in order to understand the effect of axial pressure gradient on instability amplification along the leeward symmetry plane and in the region of nonzero crossflow away from it. Comparisons are made with measured transition data in Mach 2 facilities as well as with predicted and measured transition characteristics for a 5-degree straight cone in a Mach 3.5 low disturbance tunnel. Limitations of using linear stability correlations for predicting transition over axisymmetric bodies at angle of attack are pointed out.
An optimization method was developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions, and linear stability analysis of the compressible boundary-layer. Boundary-layer transition is predicted by a 'hybrid' transition criterion based on Granville's transition criterion and a criterion using linear stability theory coupled with the e(sup n)-method. A tiptank of a business jet is used as an example to illustrate that the method can be utilized to design an axisymmetric body shape with extensive natural laminar flow. On the original tiptank boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10 6 on the original tiptank. On the designed body shape a transition Reynolds number of 7.22 x 10 6 is predicted using compressible linear stability theory coupled with e n -method.
An optimization method has been developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The new design method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions and linear stability analysis of the compressible boundary-layer. In order to reduce the computer time, Granville's transition criterion is used to predict boundary-layer transition and to calculate the gradients of the objective function, and linear stability theory coupled with the e(exp n)-method is used to calculate the objective function at the end of each design iteration. Use of a method to design an axisymmetric body with extensive natural laminar flow is illustrated through the design of a tiptank of a business jet. For the original tiptank, boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10(exp 6). For the designed body shape, a transition Reynolds number of 7.22 x 10(exp 6) is predicted using compressible linear stability theory coupled with the e(exp n)-method.
A moment method for computing 3D radiative transport in axisymmetric thermochemical nonequilibrium flows is developed. The method uses the P-1 approximation to reduce the governing system of integro-differential equations to a coupled set of partial differential equations. The numerical solution of these equations for realistic variations of the radiation properties is discussed. Representative results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.
A moment method for computing 3-D radiative transport is applied to axisymmetric flows in thermochemical nonequilibrium. Such flows are representative of proposed aerobrake missions. The method uses the P-1 approximation to reduce the governing system of integro-di erential equations to a coupled set of partial di erential equations. A numerical solution method for these equations given actual variations of the radiation properties in thermochemical nonequilibrium blunt body flows is developed. Initial results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.
A cooperative experimental investigation has been performed to obtain a systematic fin-body and fin-plate database for a series of 12 missile fins. These data are intended to complement and extend the information contained in the Triservice missile project and to provide a systematic set of experimental data from which fin-body interference factors can be derived. Data were obtained with the fins mounted on both an axisymmetric body and on a flat plate that was used to simulate fin-alone measurements. The experiments were conducted at Mach numbers from 0.60 to 3.95; fin deflection angles of 0 deg, 10 deg, and -10 deg; and angles of attack up to 30 deg on the body and up to 95 deg on the flat plate. The data were obtained from three-component balances attached to the fins and a six-component balance located in the axisymmetric body. The data obtained in this project are documented in tabular form in this report. In addition, selected data are presented in graphical form to illustrate the effects of the test variables. These variables are configuration angle of attack; Mach number; and fin parameters of deflection angle, planform size, taper ratio, and aspect ratio. A very limited comparison with the Triservice missile data is made to illustrate the consistency between the data from these two projects.