Boundary-layer separation and reattachment with and without ablation
Laminar boundary layer separation and reattachment on ablating and nonablating axisymmetric bodies at low Reynolds number and high Mach number
REATTACHED FLOW↗
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Approximate relations for laminar heat-transfer and shear-stress functions in equilibrium dissociated air
Approximate equations for computing enthalpy and velocity derivatives at surface of flat plate, cone, or blunt axisymmetric body
Zoby, E. V.↗
Flow field analysis of aircraft configurations using a numerical solution to the three-dimensional unified supersonic/hypersonic small disturbance equations, part 1
The unified small disturbance equations are numerically solved using the well-known Lax-Wendroff finite difference technique. The method allows complete determination of the inviscid flow field and surface properties as long as the flow remains supersonic. Shock waves and other discontinuities are accounted for implicity in the numerical method. This technique was programed for general application to the three-dimensional case. The validity of the method is demonstrated by calculations on cones, axisymmetric bodies, lifting bodies, delta wings, and a conical wing/body combination. Part 1 contains the discussion of problem development and results of the study. Part 2 contains flow charts, subroutine descriptions, and a listing of the computer program.
Gunness, R. C., Jr.↗
Computer program for calculating laminar and turbulent boundary layer development in compressible flow
A computer program is described which performs a numerical integration of the equations of motion for a compressible two-dimensional boundary layer. Boundary layer calculations may be carried out for both laminar and turbulent flow for arbitrary Reynolds number and free stream Mach number distribution on planar or axisymmetric bodies with wall heating or cooling, longitudinal wall curvature, wall suction or blowing, and a rough or a smooth wall. A variety of options are available as initial conditions. The program can generate laminar initial conditions such as Falkner-Skan similarity solutions (so that initial wedge flows can be simulated including Blasius or stagnation point flow) or approximate equilibrium turbulent profiles. Alternatively, initial profile input data can be utilized.
Herring, H. J.↗
Numerical analysis of the transient response of an axisymmetric ablative char layer considering internal flow effects
The differential equations governing the transient response of the char layer of an ablating axisymmetric body, internal pyrolysis gas flow effects being considered, have been derived. These equations have been expanded into finite difference form and programed for numerical solution on a digital computer. Numerical results compare favorably with simplified exact solutions. The complete numerical analysis was used to obtain solutions for two representative body shapes subjected to a typical entry heating environment. Pronounced effects of the lateral flow of pyrolysis gases on the mass flow field within the char layer and the associated surface and pyrolysis interface recession rates are shown.
Pittman, C. M.↗
Dispersion of SST trails in the stratosphere.
A simple theory for the dispersion of the exhaust of a supersonic transport cruising in the stratosphere is presented. This model shows that far downstream from the aircraft, buoyancy dominates the growth of the wake. This growth is limited by the stable stratification of the atmosphere. Data on the visible width of the wake from scaled experiments in a towing tank and from studies on the growth of contrails of subsonic aircraft verify the growth of the wake in an unstratified atmosphere is predicted by the model. This growth is faster than would be predicted for the wake of an axisymmetric body with no buoyancy.
Overcamp, T. J.↗
Computer programs for calculating potential flow in propulsion system inlets
In the course of designing inlets, particularly for VTOL and STOL propulsion systems, a calculational procedure utilizing three computer programs evolved. The chief program is the Douglas axisymmetric potential flow program called EOD which calculates the incompressible potential flow about arbitrary axisymmetric bodies. The other two programs, original with Lewis, are called SCIRCL AND COMBYN. Program SCIRCL generates input for EOD from various specified analytic shapes for the inlet components. Program COMBYN takes basic solutions output by EOD and combines them into solutions of interest, and applies a compressibility correction.
Stockman, N. O.↗
Gravitational perturbations of equatorial orbits.
Asymptotic solutions are developed for the motion of a geocentric satellite in the equatorial plane due to gravitational perturbations such as nonsphericity (especially oblateness) of the primary body. Axisymmetric potentials are considered. A class of transformations is developed and the equations of motion are solved by the method of generalized multiple scales. Further it is shown that the equations of motion can be transformed into the required form to within any specified degree of accuracy. The transformations form an Abelian group of infinite order which leaves the differential equations of motion invariant. Solutions are developed in terms of elementary functions instead of elliptic or other higher transcendental functions and are shown to agree with known results.
Ramnath, R.↗
Nonlinear analysis of structures
The development of nonlinear analysis techniques within the framework of the finite-element method is reported. Although the emphasis is concerned with those nonlinearities associated with material behavior, a general treatment of geometric nonlinearity, alone or in combination with plasticity is included, and applications presented for a class of problems categorized as axisymmetric shells of revolution. The scope of the nonlinear analysis capabilities includes: (1) a membrane stress analysis, (2) bending and membrane stress analysis, (3) analysis of thick and thin axisymmetric bodies of revolution, (4) a general three dimensional analysis, and (5) analysis of laminated composites. Applications of the methods are made to a number of sample structures. Correlation with available analytic or experimental data range from good to excellent.
Armen, H., Jr.↗
The effect of ablation injection on radiative and convective heating
A viscous shock-layer analysis is for calculating high energy equilibrium flow fields about blunt axisymmetric bodies is applied to the problem of massive ablation injection with radiation transport. A nongray radiation model is used that accounts for both line and continuum radiation. The solution method is direct and provides both stagnation and downstream solutions. Results for shock heated air show that phenolic-nylon injection is substantially more effective in reducing the wall radiant flux than air injection. Also, for large included body angles, the wall radiative flux and the coupled phenolic-nylon injection rate do not continue to decrease with increasing distance downstream.
Moss, J. N.↗
Stagnation and downstream viscous shock-layer solutions with radiation and coupled ablation injection
This paper describes a rigorous viscous shock-layer analysis for investigating high energy equilibrium flow fields about blunt axisymmetric bodies. The analysis includes radiation transfer, mass injection, diffusion, and viscous effects. Radiation transfer is calculated with a nongray radiation model that accounts for line and continuum radiation. The analysis can treat all levels of blowing for both stagnation and downstream flow. Results are presented for selected earth entry conditions that demonstrate the essential features of this analysis. Particular emphasis is given to the effects of mass injection on stagnation and downstream flow. Results for both specified and coupled ablation injection are presented.
Moss, J. N.↗
Turbulent heat transfer prediction method for application to scramjet engines
An integral method for predicting boundary layer development in turbulent flow regions on two-dimensional or axisymmetric bodies was developed. The method has the capability of approximating nonequilibrium velocity profiles as well as the local surface friction in the presence of a pressure gradient. An approach was developed for the problem of predicting the heat transfer in a turbulent boundary layer in the presence of a high pressure gradient. The solution was derived with particular emphasis on its applicability to supersonic combustion; thus, the effects of real gas flows were included. The resulting integrodifferential boundary layer method permits the estimation of cooling reguirements for scramjet engines. Theoretical heat transfer results are compared with experimental combustor and noncombustor heat transfer data. The heat transfer method was used in the development of engine design concepts which will produce an engine with reduced cooling requirements. The Langley scramjet engine module was designed by utilizing these design concepts and this engine design is discussed along with its corresponding cooling requirements. The heat transfer method was also used to develop a combustor cooling correlation for a combustor whose local properties are computed one dimensionally by assuming a linear area variation and a given heat release schedule.
Pinckney, S. Z.↗
Roughness induced transition criteria for space shuttle-type vehicles
Tripping effectiveness of surface roughness on a delta wing shuttle orbiter model at 20 deg angle of attack is compared to that on plane and axisymmetrical bodies with and without longitudinal pressure gradients. The experimental data presented are compared on the basis of effective roughness Reynolds number since this parameter is not sensitive to flow conditions downstream of the roughness. The discussion covers the effective roughness Reynolds number as a function of roughness position Reynolds number, effective size ratio as a function of pressure gradient and distance from vehicle nose, and effect of spanwise roughness position on roughness effectiveness. It is shown that conventional criteria for sizing roughness elements which promote transition in two-dimensional zero-pressure gradient flows are insufficient for high-pressure gradient flows and three-dimensional flows. Roughness much smaller than that given by conventional criteria can cause transition and significantly increase the heating load.
Morrisette, E. L.↗
STAN5: A program for numerical computation of two-dimensional internal and external boundary layer flows
A large variety of two dimensional flows can be accommodated by the program, including boundary layers on a flat plate, flow inside nozzles and diffusers (for a prescribed potential flow distribution), flow over axisymmetric bodies, and developing and fully developed flow inside circular pipes and flat ducts. The flows may be laminar or turbulent, and provision is made to handle transition.
Crawford, M. E.↗
The effect of ablation injection on radiative and convective heating
A viscous shock-layer analysis for calculating high energy equilibrium flow fields about blunt axisymmetric bodies is applied to the problem of massive ablation injection with radiation transport. A nongray radiation model is used that accounts for both line and continuum radiation. The solution method is direct and provides both stagnation and downstream solutions. Results for shock heated air show that phenolic-nylon injection is substantially more effective in reducing the wall radiant flux than air injection. Also, for large included body angles, the wall radiative flux and the coupled phenolic-nylon injection rate do not continue to decrease with increasing distance downstream.
Moss, J. N.↗
Comparative study of the convergence rates of two numerical techniques
The paper examines the applicability of the three-step Stetter (1968) method to the problem of hypersonic viscous flow over a blunt axisymmetric body used for planetary entry probes at zero angle of attack. The flow-field results using the two-step finite-difference MacCormack (1969) method are reported by Kumar and Graves (1977). Only the computational efficiency of Stetter's method is compared with that of MacCormack's in terms of the iterative time steps and computing time required for the steady-state solution. Advantages of Stetter's method over MacCormack's are established.
Kumar, A.↗
A study of nonadiabatic boundary-layer stabilization time in a cryogenic tunnel for typical wing and fuselage models
A theoretical study has been made of the time varying effect of nonadiabatic wall conditions on boundary layer properties for a two-dimensional wing section and an axisymmetric body of revolution typical of a fuselage. The wing section and body of revolution are representative of the root chord and fuselage of what is considered to be a typical size transport model for the National Transonic Facility. The transient analysis was made at a Mach number of 0.85, for stagnation pressures of 2, 6, and 9 atmospheres at several cryogenic values of total temperature for a solid wing and for three different fuselage skin thickness configurations. The analysis considered wing and fuselage sections made from stainless steel, beryllium copper, and aluminum. Examples are presented that may be used to determine the time required to reach an adiabatic condition after a change in total temperature.
Johnson, C. B.↗
Flowfield calculations past an entry probe with ablated nose shape
The effects of ablated nose shapes on the flowfield solutions are studied, using a time-dependent finite-difference method developed by Kumar, et al. (1979). Solutions are obtained for the laminar flow of a radiating mixture of H-He in chemical equilibrium past a blunt axisymmetric body at zero angle of attack. The freestream conditions correspond to a point on a typical Jovian entry trajectory, and the initial probe shape is a 45-deg half-angle spherically blunted cone. It is found that as nose bluntness increases, the following occur: in the nose region, shock standoff distances and radiative heating rates increase substantially; surface pressure level increases, but convective heating rates decrease.
Kumar, A.↗