Optimum shape of lifting bodies for hypersonic velocities

An attempt is made at solving the variational problem as to the shape of the body possessing a maximum aerodynamic quality, without using some of the simplifying assumptions proposed earlier [1–4]; an attempt is also made to discover the effect of blunted leading edges on the parameters of the optimum bodies.Kazan'. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 82–86, January–February, 1972.     

Heat transfer to surfaces of some lifting bodies at high supersonic speeds

Results are presented of an experimental study of the heat transfer and gas flow on the surface of a semicone and of planar wings with a break in the leading edges at Mach number M=5. It is shown that with the interaction of the gas streams flowing about various portions of the surface of such bodies there may occur local, relatively narrow zones of high or low values of the specific heat flux.Temperature indicating paints were used to measure the heat fluxes, and smearable paints applied to the surface in the form of individual dots were used for flow visualization.     

Optimum lifting body shapes in hypersonic flow at high angles of attack

A variational procedure for the determination of lifting body configurations having a maximum lift-to-drag ratio K _max in hypersonic flight at high angles of attack , is proposed. It is based on an analytical solution to the problem for three-dimensional hypersonic flow over small aspect ratio wings using thin shock-layer theory. This reduces the variational problem of finding K _max, and the corresponding optimized wing shape, to the minimization of a linear functional subject to various constraints. The contributions of nonequilibrium thermochemical effects and laminar or turbulent viscous drag effects are also included in the problem formulation. The solution shows that optimized wings have an unbent forward part and a concave lower surface. Due to bifurcation in the optimization process, the planform may have either a sharp apex or a straight nose cut. Corresponding values of K _max() significantly exceed the limiting value K _N=cot for a flat wing. Real thermochemical effects and air viscosity are shown to cause a decrease in K _max and sometimes to influence the optimized wing geometry; however, the relative increment of K _max to K _N is still retained.     

Shock wave interference on a fenced wing at hypersonic speeds

High-pressure zones on the wing, created by the reflected shocks, are experimentally demonstrated and their influence on the aerodynamic characteristics of the wing is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 135–140, May–June, 1992.The authors are grateful to V. E. Mosharov, V. N. Tarasov, and V. I. Plyashechnik for assisting with the experiments.     

Convective heat-transfer rate distributions over a missile shaped body flying at hypersonic speeds

Experiments are carried out with air as the test gas to obtain the surface convective heating rate on a missile shaped body flying at hypersonic speeds. The effect of fins on the surface heating rates of missile frustum is also investigated. The tests are performed in a hypersonic shock tunnel at stagnation enthalpy of 2 MJ/kg and zero degree angle of attack. The experiments are conducted at flow Mach number of 5.75 and 8 with an effective test time of 1 ms. The measured stagnation-point heat-transfer data compares well with the theoretical value estimated using Fay and Riddell expression. The measured heat-transfer rate with fin configuration is slightly higher than that of model without fin. The normalized values of experimentally measured heat transfer rate and Stanton number compare well with the numerically estimated results.     

Contactless induction acceleration of conductors up to hypersonic speeds

The results of an experimental investigation of the induction acceleration of ring conductors having a mass of 0.5–3 g in the pulsed magnetic field of a single-turn inductor are presented. It is shown that low-inductive capacitive energy stores in conjunction with single-turn single-shot inductors are very efficient. A speed of 3.7 km/sec was obtained experimentally with an aluminum conductor of mass 0.77 g. Methods of measuring the very high speeds of projected objects are described. The interaction of the accelerated conductor with thick and thin barriers was investigated, and the possibility of controlling the area of the damaged surface is pointed out. The results of the experiment agree well with calculations carried out on a computer which indicate the possibility of a further increase in the speed of projection.     

Physical criterion study on forward stagnation point heat flux CFD computations at hypersonic speeds

In order to evaluate uncertainties in computational fluid dynamics （CFD） computations of the stagnation point heat flux, a physical criterion is developed. Based on a quasi-one-dimensional hypothesis along the stagnation line, a new stagnation flow model is applied to obtain the governing equations of the flow near the stagnation point at hypersonic speeds. From the above equations, the compatibility relations are given at the stagnation point and along the stagnation line, which consist of the physical criterion for checking the accuracy in the stagnation point heat flux computations. The verification of the criterion is made with various numerical results.     

Rarefied gas flow near the forward stagnation point of a blunt body at hypersonic speeds

With reduction of the density in a hypersonic stream the transition of the flow from continuum to free molecule takes place gradually. The transition region may be divided into several regimes, in each of which a definite physical phenomenon is most significant. For the case of the flow in the vicinity of the forward stagnation point of a blunt body these phenomena include increase of the thickness of the detached shock wave and of the boundary layer, the presence of viscous flow in the entire disturbed layer ahead of the blunt body, reduction of the number of collisions between molecules and the associated relaxation effects, the increasing role of the interaction of the stream molecules with the surface, and the phenomena of slip and temperature jump.     

Simulation of the aerodynamic drag of three-dimensional star-shaped bodies at hypersonic velocities

The domain of the parameters in which the aerodynamic drag of hypersonic pyramidal bodies, whose wave component is calculated within the framework of conical flows with the boundary layer displacement thickness taken into account, agrees satisfactorily with the experimental data is found. The calculation model is also applicable in the region of minimum aerodynamic drag of star-shaped bodies in the class of conical bodies equivalent in length and mid-sectional area.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 69–79, September–October, 1996.     

Aerodynamic characteristics of V-shaped wings with shock waves detached from leading edges at hypersonic speeds

The direct problem of hypersonic flow past a V-shaped wing with a shock wave detached from the leading edges is solved. The reduced normal force coefficient and the lift-drag (L/D) ratio are calculated for a configuration with a lower part in the shape of a V-wing and a streamwise upper part.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 145–154, May–June, 1993.     

Shock tunnel study of spiked aerodynamic bodies flying at hypersonic Mach numbers

A three-component accelerometer balance system is used to study the drag reduction effect of an aerodisc on large angle blunt cones flying at hypersonic Mach numbers. Measurements in a hypersonic shock tunnel at a freestream Mach number of 5.75 indicate more than 50% reduction in the drag coefficient for a 120° apex angle blunt cone with a forward facing aerospike having a flat faced aerodisc at moderate angles of attack. Enhancement of drag has been observed for higher angles of attack due to the impingement of the flow separation shock on the windward side of the cone. The flowfields around the large angle blunt cone with aerospike assembly flying at hypersonic Mach numbers are also simulated numerically using a commercial CFD code. The pressure and density levels on the model surface, which is under the aerodynamic shadow of the flat disc tipped spike, are found very low and a drag reduction of 64.34% has been deduced numerically.     

Method of curved bodies in problems of unsteady hypersonic flow past slender bodies

The method of curved bodies involves replacing the unsteady flow past a body by steady flow past a different body obtained from the original body by suitable curvature of its form. The idea of the method was proposed by Vetchinkin in 1918 and was first carried out in [1]. Here the authors started from the assumption that the pressure on the body surface is determined only by its local angle of attack.We know that this method is justified only for circular motion of a slender body with constant velocity within the framework of subsonic or supersonic linearized theory.It will be shown below that the method of curved bodies is rigorously justified for hypersonic unsteady flow past slender pointed bodies within the framework of the law of plane sections, which is often used to study unsteady flows, for example [2, 3]. Here the idea of the method involves the selection of a body of form such that for uniform translational motion its wake in a stationary, normally intersected plane coincides in time with the wake of the original body.The general theory is presented for arbitrary bodies, in particular for bodies of the type of slender oscillating wings, but attention is devoted primarily to the motion of a rigid body of rotation. In this case, in the hypersonic approximation (of the type of [4, 5]) the method also extends to slender blunted bodies.In the general case this method reduces the four-dimensional unsteady problem to a three-dimensional steady problem, which presents no particular difficulty in view of the existence of suitable methods and programs (for example [6]). Here, in contrast with the classical version of the method [1], in the general case the original body is replaced at very moment of time by a one-parameter (with parameter t₀) family of curved bodies.In the case which is most often encountered in practice of slow oscillation of the body surface, when the unsteady component of the solution is small in comparison with the steady compoent, the small-parameter method is used, which allows us to represent the solution in a simple form with an explicit linear dependence on the parameter t₀.The basic notation L body length - ₀ body characteristic relative thickness or angle of attack - ₀ characteristic Strouhal number - r₀ maximal radius of the blunt nose - ,a undisturbed medium density and speed of sound - V and M velocity and Mach number of the center of rotation or of the point x₀ - T₀ characteristic time of the unsteady motion (for example, the period of the oscillation) - T=L/V time for the body to pass a fixed plane - V²p pressure The author wishes to thank A. V. Antonets and Yu. M. Lipnitskii for carrying out the calculations and analyzing their results.     

Effect of nose shape on hypersonic flow past slender blunt bodies at an angle of attack

We examine some characteristics of hypersonic flow past slender blunt bodies of revolution at a small angle of attack 1, where is the relative body thickness. It is shown that, within the framework of hypersonic theory, for a correct-consideration of the effect of the conditions in the transitional section between the nose and the lateral surface it is necessary, in the general case, to specify the circumferential distribution of the force effect for the nose and the mass of the gas. For small , the effect of the nose, just as in two-dimensional flows [1–4], shows up only through its drag coefficient c_x, for =0. On this basis, the similarity law [1–4] for flow past such bodies, with arbitrary form of the lateral surface and differing in the shape of the nose blunting, which is valid over the entire disturbed region, with the exception of a small vicinity of the nose, is extended to the case in question.The notation r₀ and L maximum nose radius and characteristic body length - V, M, and density, velocity, Mach number, and adiabatic exponent of the gas in the approaching stream - , V²i, and V²p density, enthalpy, and pressure - x, r, and coordinate system of the cylindrical body with its center at the transitional section between the nose and the side surface - Vu, Vv, and Vw corresponding velocity components