Flow Past Bodies Of Revolution Research Articles

First- and Second-Order Theory of Supersonic Flow Past Bodies of Revolution

Methods are studied for improving the existing perturbation theories of supersonic flow past bodies of revolution. Applicability of the theory at high Mach Numbers is emphasized. For axial flow, a second-order solution isfound which represents a considerable improvement over the first-order result. For inclined flow, a second-order solution is not feasible except for a cone. Comparison with the exact solutions for cones shows that the slender-body series expansion causes large inaccuracies in both axial and inclined flow. The conclusion that first-order theory predicts the flow no better than slender-body theory is shown to be erroneous. When first-order theory is properly used,making no unnecessaryapproximations, greatly improved agreement is found with exact solutions and with experiment. The order estimates used to justify the approximations are shown to be invalid in most practical cases. A hybrid theory, combining first-order cross flow and second-order axial flow, gives further improvement. A physical explanation is advanced for the marked superiority of first-order theory over the true linearized theory. Nonlinearity in lift is shown to result primarily from viscous separation of the cross flow along the after portions of a long body. The magnitude of the resulting normal force can be estimated with reasonable accuracy using two-dimensional viscous sweep-back theory.

First- and Second-Order Theory of Supersonic Flow Past Bodies of Revolution

First- and Second-Order Theory of Supersonic Flow Past Bodies of Revolution

Three-dimensional vortical flow past bodies of revolution with conical afterbodies

Three-dimensional separated flows past bodies of revolution with conical afterbodies are studied both experimentally and numerically. The sudden increase in drag force due to the small increase in the semi-apex angle of the conical afterbody which is related to the critical geometry is revealed by force measurement and flow visualization. The details of the associated physical phenomenon, i. e. 3D separation and vortex shedding is elucidated by numerical simulations based on the finite-volume solution method for the Navier-Stokes equation in the curvilinear, boundary-fitted grid system. It is shown by the computer graphic drawings that the large-scale structure of separated vortices is composed of ring vortices and longitudinal vortices originating from the center of the ring vortices.

Base pressure of bodies of revolution when gas is blown through their surface into a supersonic flow

One of the most important problems of high-velocity aerodynamics is the investigation of the base pressure and the wake flow behind bodies of revolution under the conditions of surface mass transfer. The present paper reports careful experimental investigations of the flow past bodies of revolution in the presence on their surface of a transverse mass flux, especially at a low blowing intensity. These investigations have yielded new data on the dependence of the base pressure on the main determining parameters, extending and making more accurate the modern picture of the mechanism by which surface mass transfer influences the base pressure and its connection with the state of the boundary layer.

Linearized theory of axisymmetric hypersonic source flow past bodies of revolution

The linearized theory of axisymmetric hypersonic source flow past a slender pointed body is treated by using linearized potential theory, assuming that the hypersonic parameter is less than unity. The governing equation in the transformed co-ordinates with the ratio of specific heats γ = 1.5 shows a modified form relative to the equation for parallel flow, whereas that with γ = 2 shows essentially the same form. Some numerical calculations for a cone and a cone-cylinder are presented, and the surface pressure distributions obtained for both γ = 1.5 and 2 show that there is a considerable pressure-distribution difference between source flow and parallel flow. The pressure on a cone in hypersonic source flow approaches zero downstream, while, if the cone has a cylindrical afterbody, the pressure recovers to the free-stream value quickly. This suggests that the static pressure probe for supersonic parallel flow is useful also in source flow.

Asymptotic pattern of flow past bodies of revolution in a sonic stream of viscous and heat-conducting gas

Asymptotic pattern of flow past bodies of revolution in a sonic stream of viscous and heat-conducting gas

A Linear Perturbation Method for Stability and Flutter Calculations on Hypersonic Bodies

The equations governing linear perturbations in three space variables and time of steady supersonic potential flow past bodies of revolution are derived. The equations are referred to a characteristic coordinate system, and a general numerical process of solution is described. The assumption of potential flow simplifies the theory considerably and is justified in most flutter calculations and in estimating the contribution to stability derivatives from the rear part of a body. However, there is no obstacle in principle to generalizing the technique to apply to nonisentropic flow fields. As an example, to represent the contribution of a typical hypersonic afterbody, the static stability derivatives associated with the exterior surface of a converging conical duct are calculated. Dynamic stability derivatives can be found by a simple extension of this calculation.

A Combination of the Quasi-Cylinder and Slender Body Theories

The Quasi-Cylinder and slender body theories for the supersonic flow past bodies of revolution have been much used in recent years because, for reasonably simple body profiles, these theories permit a simple and rapid calculation of the first-order pressure distributions and aerodynamic forces. It is assumed in both theories that the body profile slope is small; in the quasi-cylinder theory it is also assumed that the body radius is nearly constant, whereas in the slender body theory it is assumed that the thickness ratio of the body (maximum diameter/length) is small.In the present note these two theories are combined completely. From a strictly mathematical point of view nothing is gained by this combination, and, furthermore,application of the combined theory to a particular case is in general a little more laborious than application of either of the original theories.

IV. Experiments on supersonic flow past bodies of revolution with annular gaps of rectangular section

Summary The supersonic flow past flat-nosed circular cylinders with annular gaps of rectangular section was investigated by schlieren photography and pressure measurements. The length of the gap was varied in small steps, from low values, where the gap formed a single dead-air region, to high values, where the flow in the gap consisted of two dead-air regions with an intermediate region of attached How. In particular, the length of the gap for which the How changed from the type with one to the type with two dead-air regions was determined. The experiments throw some light on the details of the flow in the dead-air regions, and it was found that the velocities inside these regions may be of considerable magnitude. Qualitative information was obtained about the effects of the length of the gap on the drag caused by the gap.

Supersonic Flow Past Bodies of Revolution with Thin Wings of Small Aspect Ratio

SummaryThe method developed by G. N. Ward for the treatment of slender pointed bodies in a uniform supersonic stream is applied to three special cases. (i)Supersonic flow past a body of revolution with thin wings of symmetrical section and of small aspect ratio at zero incidence.(ii)Supersonic flow past a body of revolution with plane wings of small aspect ratio set at incidence to the body, the whole being at incidence to the stream.(iii)Supersonic flow past a body of revolution with a plane fin of small aspect ratio set at incidence, the whole being at incidence to the stream.The pressure distribution on the wing has been calculated for a special case of (i) and is given in the Appendix.

First- and Second-Order Theory of Supersonic Flow Past Bodies of Revolution

First- and Second-Order Theory of Supersonic Flow Past Bodies of Revolution

THE POSITION OF THE SHOCK-WAVE IN CERTAIN AERODYNAMIC PROBLEMS

For the motions caused by the uniform expansion of a cylinder or sphere into still air, and for steady symmetrical supersonic flow past a cone, first approximations are obtained to the strength and position of the shock-wave for small disturbances. It is also shown what are the correct approximations to the pressure on the surfaut-. The work is mathematically rigorous, and provides some justification of approximate methods that have been used, for example, in the general theory of supersonic flow past bodies of revolution.