Body In Hypersonic Flow Research Articles

Calculating heat transfer on the front surface of a blunt body in hypersonic flow

Calculating heat transfer on the front surface of a blunt body in hypersonic flow

Thermal degradation kinetics and surface pyrolysis of vinyl polymers

Atmosphere, Izvestiya Akademii Nauk SSSR, Otdelenie Tekhnicheskikh Nauk, Mekhanika i Mashinostroenie, No. 4, 1965, pp. 36-40. 7 Benjamin, A. S., The Effect of Albative Geometry Change on the Heating and Recession Characteristics of Sphere-Cones, AIAA Paper 66-992, Boston, Mass., 1966. 8 Cresci, R. J., MacKenzie, D. A., and Libby, P. A., An Investigation of Laminar, Transitional, and Turbulent Transfer on Blunt-Nosed Bodies in Hypersonic Flow, Journal of the Aerospace Sciences, Vol. 27, No. 6, June 1960, pp. 401-414. 9 Schlichting, H., Boundary Layer Theory, McGraw-Hill, New York, 1955, pp. 447-449. 10 Dippree, D. F. and Sabersky, R. H., Heat and Momentum Transfer in Smooth and Rough Tubes at Various Prandtl Numbers, International Journal of and Mass Transfer, Vol. 6, No. 5, May 1963, pp. 329-353. 11 Ames Research Staff, Equations, Tables, and Charts for Compressible Flow, Rept. 1135, 1953, NACA. 12 Dunlap, R. and Kuethe, A. M., Effects of Cooling on Boundary Layer Transition on a Hemisphere in Simulated Hypersonic Flow, Journal of the Aerospace Sciences, Vol. 29, No. 12, Dec. 1962, pp. 145^1461. 13 Fay, J. A. and Riddell, F. R., Theory of Stagnation Point Transfer in Dissociated Air, Journal of the Aerospace Sciences, Vol. 25, No. 2, Feb. 1958, pp. 73-85. 14 Sutton, G. W., On the Stable Shape of a Slender Ablating Graphite Body, Journal of the Aerospace Sciences, Vol. 26, No. 10, Oct. 1959, pp. 681-682.

Heat transfer and pressure on a hypersonic blunt cone with mass addition

Surface pressure and heat transfer over blunt conical body in hypersonic flow with uniform mass addition of various gases

Shock-wave shapes on hypersonic axisymmetric power-law bodies

Shock wave shapes over axisymmetric power law bodies in hypersonic flow, noting asymptotic flow theory implications

Axisymmetric bodies of minimum drag in hypersonic flow

The problem of determining the longitudinal contour of a slender, axisymmetric body in hypersonic flow which has minimum drag is considered. The pressure distribution is assumed to be Newtonian, while the skin-friction distribution is for laminar flow and depends on body geometry. This investigation is conducted with the method of steepest descent, whose feasiblity is demonstrated by solving minimum drag problems having known analytical solutions.

Viscous Interaction Theory for Slender Axisymmetric Bodies in Hypersonic Flow

Effects of viscous interaction are investigated for hypersonic flow over slender axisymmetric bodies. The entire range of interaction, from weak to strong, is considered. Extensive numerical results are given for the self-similar flow over a fpower-law body. These results are correlated and used in a local similarity procedure for finding viscous interaction over arbitrary slender body shapes. Analytical expressions are derived for weak interaction on a cone and strong interaction on all slender bodies. Numerical solutions needed for the intermediate interaction regime are obtained for hypersonic flow over a cone. Results are presented for cone surface pressure, shear, heat transfer, drag, and displacement thickness in all interaction regimes. The drag data are in agreement with available experimental cone drag data. This analytical development is a unified treatment of viscous interaction effects on two-dimensional as well as axisymmetric bodies.

Effects of shock impingement on the heat transfer around blunt bodies.

An extraneous shock impinging on a blunt body in hypersonic flow is observed to alter the flow around the body and increase the local heat-transfer rate near the impingement point. A novel, quasi-static technique is developed to study this phenomenon. A hemispherical, glass model, equipped with platinum thin-film thermometers, is injected into a hypersonic tunnel through a slot in a variable-incidence flat plate. Analog networks provide graphs of the heat-transfer rates at various points on the model as a function of the model's position relative to the extraneous shock. Peaks in local heat-transfer rates up to 10 times the local, unperturbed, freestream values are recorded as the model traverses the shock. The peak heating is severest on the side of the model nearest the plate and increases with increasing shock strength, occurring over a narrow region where a shear layer or jet, originating at the intersection of the bow shock and the impinging shock, meets the model surface. A physical model is set up which predicts variations in shock interference patterns, in surface pressure distributions, and in the intensity and extent of the peak heating in accordance with experiment. Nomenclature M = Mach number P = pressure normalized with respect to freestream pressure q = heat-transfer rate, cal-cm~2-sec~1 r = radius of hemisphere, mm t = time, sec T = temperature, °C U = velocity normalized with respect to freestream velocity V = injection speed, m-sec1 x = distance along surface measured from stagnation point, mm

Magnetic coupling in flight magnetoaerodynamics.

Flight control magnetic source interaction with ionized gas induced by bow shock ahead of blunt body in hypersonic flow

On the viscous flow in the nose region of a symmetric blunt body in hypersonic flow

The flow field in the nose region of a blunt body in hypersonic flow is studied by considering the transport of vorticity and enthalpy. The entire region between body and shock is considered to be viscous, not necessarily thin in comparison with the nose radius of the body and to be of slowly varying density. The (given) post-shock vorticity need not be small and the density ratio ρ∞/ρs may either be small or near unity, the analysis being valid asymptotically at both limits.It is found that the vorticity equation may be uncoupled from the total enthalpy equation if μ√ρ is constant. While the equations are not expected to be necessarily restricted to the immediate vicinity of the stagnation line, only there can the solution be written down explicitly; elsewhere, numerical integration is required.

Theory of laminar near wake of blunt bodies in hypersonic flow.

21 Feldman, S., Hypersonic gasdynamic charts for equilibrium air, Avco Rept. (1957). 22 Nagamatsu, H. T., Workman, J. B., and Sheer, R. E., Jr., Hypersonic nozzle expansion of air with atom recombination present, J. Aerospace Sci. 28, 833-837 (1961). 23 von Karman, T. and Tsien, H. S., Boundary layer in compressible fluids, J. Aeronaut. Sci. 6, 227-232 (1938). 24 Kendall, J. M., Jr., An experimental investigation of leading edge shock wave-boundary layer interaction at Mach 5.8, J. Aeronaut. Sci. 24,47-56 (1957). 25 Howarth, L., Modern Developments in Fluid Dynamics High Speed Flow (Oxford University Press, London, 1953), Vol. 1, p. 402. 26 von Karman, T., Turbulence and skin friction, J. Aeronaut. Sci. 1,1-20 (1934). 27 Van Driest, E. R., boundary layer in compressible fluids, J. Aeronaut. Sci. 18,145-160 (1951). 28 Li, T. Y. and Nagamatsu, H. T., Effects of density fluctuations on the turbulent skin friction of an insulated flat plate at high supersonic speeds, J. Aeronaut. Sci. 18, 696-697 (1951). 29 Persh, J., An analytical investigation of turbulent boundary layer heat transfer coefficients for supersonic and hypersonic flow, Naval Ordnance Lab. Rept. 4099 (1955). 30 Lin, C. C., Turbulent Flows and Heat Transfer: High Speed Aerodynamics and Jet Propulsion (Princeton University Press, Princeton, N. J., 1959), Vol. V.

Near wake of a blunt body at hypersonic speeds

An experimental investigation was conducted to determine the characteristics of the near wake of a blunt body in hypersonic flow. Base-pressure and body-surface pressure measurements are combined with hot-wire and pitot-pressure data to describe the free shear layer, the base-flow region, the recompression zone, and the initial development of a laminar wake. It is found that the postulate of thin shear layers is valid for Reynolds numbers greater than about 104, if the Mach number Me external to the shear layer is not large. Detailed measurements with a steady-state hot-wire behind a two-dimensiona l circular cylinder indicate that the maximum pressure rise occurs downstream of the stagnation point formed by the merging shear layers. The hot-wire measurements are corroborated by base-pressure data obtained with cylinders and wedges. Comparison between the experimental and theoretical results points out the importance of the base-flow temperature and the initial shear-layer profile in determining the observable characteristics of the near wake.

Dissociated laminar boundary layer flows over surfaces with arbitrary continuous distributions of catalycity

This paper studies several new types of exact series solutions to the diffusion equation for chemically-frozen, dissociated, laminar boundary-layer flows around bodies with arbitrary continuous distributions of a first-order atom recombination rate along the surface. Plate, wedge, and cone flows are considered. The analysis extends the theory of Chambré and Acrivos for constant surface catalytic efficiency and temperature to the case wherein the surface Damkohler number varies as any power of the distance or is distributed as any polynomial involving integer or fractional positive powers of the distance. Furthermore, by imposing the approximation of local similarity in the velocity profile, the resulting solutions are also applied with good accuracy to highly-cooled bluntnosed bodies in hypersonic flow. An approximate method of solution is also developed which provides an extremely simple closedform representation of the exact series solutions throughout the entire flow field by means of a local nonlinear extrapolation of the leading term in the series. It is shown by several examples that this technique yields very accurate results for surface atom concentration, diffusion flux, and heat-transfer distributions for a variety of streamwise variations in the wall catalycity.

A STUDY OF SLENDER SHAPES OF MINIMUM DRAG USING THE NEWTON-BUSEMANN PRESSURE COEFFICIENT LAW

The problem of minimizing the drag of a slender, two-dimensional or axisymmetric body in hypersonic flow at zero angle of attack is considered under the assumption that the pressure coefficient law is Newton's impact law as modified by Busemann in order to include centripetal acceleration effects. After the condition that the pressure coefficient be nonnegative is accounted for and after arbitrary conditions are imposed on, in addition to the thickness and the length, the enclosed area and the moment of inertia of the contour in the two-dimensional case and the wetted area and the volume in the axisymmetric case, the minimal problem is formulated as a problem of the Mayer type and solved by the combined use of the Euler-Lagrange equations, the transversality condition, the Erdmann-Weierstrass corner condition, and the properties of the switching function. Particular attention is devoted to the class of problems such that, among the four quantities being considered, two are prescribed while the remaining are free. For these problems, the extremal arc is composed of two subarcs: one is characterized by a positive pressure coefficient and is called the regular shape; the other is characterized by a zero pressure coefficient and is called the free layer. In this connection, the analysis shows the existence of two different types of solutions depending on whether the thickness is given or free. If the thickness is given, the expression for the regular shape is a power law, and the transition from the regular shape to the free layer occurs in the second half of the body. In the two-dimensional case, the exponent of the power law is 1 if the length is given 3/2 if the enclosed area is given, and 3 if the moment of inertia of the contour is given; the transition point from the power body to the free layer is located at 50 percent of the length if the length is given, at 66 percent if the enclosed area is given, and at 83 percent if the moment of inertia of the contour is given. In the axisymmetric case, tne exponent of the power law is 3/4 if the length is given, 1 if the wetted area is given, and 3/2 if the volume is given; the transition point from the power body to the free layer is located at 60 percent of the length if the length is given, at 70 percent if the wetted area is given, and at 80 percent if the volume is given. On the otner hand, for problems where the thickness is free, the equation governing the regular shape is not that of a power body, and the point of transition to the free layer is located in the first half of the body. In the two-dimensional case, the transition point is at 28 percent of the length if the length and the en-

Approximate Determination of Position of the Sonic Line for a Blunt Body in Hypersonic Flow

Approximate Determination of Position of the Sonic Line for a Blunt Body in Hypersonic Flow

Shock-Wave Profiles Over Ellipsoidal-Nosed Bodies in Hypersonic Flow

Shock-Wave Profiles Over Ellipsoidal-Nosed Bodies in Hypersonic Flow

On Similar Solutions for Strong Blast Waves and Their Application to Steady Hypseronic Flow

Summary The general solution of the strong blast wave is found in the Newtonian approximation—i.e., neglecting terms of order e (density ratio across the shock) compared with terms of order 1. The expressions obtained for the pressure, temperature, density, and velocity profiles are simple. The results are applied to power-law bodies in hypersonic flow using the equivalence principle. Higher-order approximations for strong blast waves are in­ vestigated for the cases in which the shock layer is thin. A simple pressure formula is found, which constitutes an improve­ ment upon the Newton-Busemann formula, and some of its ap­ plications are shown.

On Thin-Film Heat-Transfer Measurements in Shock Tubes and Shock Tunnels

In the measurement of aerodynamic heat transfer in shock tubes and tunnels utilizing thin-film resistance thermometers, it is assumed that the thermal properties of the gauge (film and substrate) are constant. Since surface temperatures of bodies in hypersonic flow often reach temperatures of several hundred degrees, the validity of this assumption should be tested. A technique is described for measuring the temperature dependence of the product of the density, thermal conductivity, and heat capacity of various substrates for thin-film resistance thermometers. The results for Pyrex, quartz, and plate glass, which have been used as backing materials for thin-film resistance thermometers, indicate that sizable errors may be encountered in inferring heat-transfer rates from measured surface-temperature histories if the thermal properties are assumed constant. The corrections which must be applied to account for the temperature dependence of the thermal conductivity and the specific heat have been established through an approximate theoretical solution of the nonlinear one-dimensional heat-conduction equation. The magnitude of the correction depends on the material of the substrate and the surface temperature. For Pyrex at 150°C it is about 45% and for fused quartz and glass about 15%.

An Investigation of Laminar, Transitional, and Turbulent Heat Transfer on Blunt-Nosed Bodies in Hypersonic Flow

An Investigation of Laminar, Transitional, and Turbulent Heat Transfer on Blunt-Nosed Bodies in Hypersonic Flow

In Investigation of the Pressure Distribution on Conical Bodies in Hypersonic Flows

In Investigation of the Pressure Distribution on Conical Bodies in Hypersonic Flows

Laminar Heat Transfer on Three-Dimensional Blunt Nosed Bodies in Hypersonic Flow

I t is shown t h a t in t h e presence of h igh ly cooled surfaces a n d of m o d e r a t e M a c h n u m b e r s a t t h e o u t e r edge of t h e b o u n d a r y layer, t h e crossflow in t h e b o u n d a r y layer is negl igible even for large t r ansversa l p ressure g r a d i e n t s . F r o m t h i s cons ide ra t ion a r ap id m e t h o d for e s t i m a t i n g t h e h e a t t r ans fe r over t h e nose po r t i on of a r b i t r a r y t h r e e d i m e n s i o n a l b l u n t bodies in hype r son ic flight is derived. T h e a p p r o x i m a t e r e su l t s t h u s o b t a i n e d c o m p a r e very favorably w i t h k n o w n exact so lu t i ons . T h e m e t h o d in q u e s t i o n reduces t h e b o u n d a r y layer p r o b l e m to t h e d e t e r m i n a t i o n of t h e inviscid s t r e a m l i n e p a t t e r n on t h e surface of t h e body ; a p rocedure for o b t a i n i n g t h e s e s t r e a m l i n e s f rom a p ressure d i s t r i b u t i o n m e a s u r e m e n t is o u t l i n e d .