The external drag of a simple axisymmetric body of revolution in subsonic and supersonic flow with variable mass flowthrough ratios

1986 ◽  
Author(s):  
T. OSAWA ◽  
H. HEWITT
Keyword(s):  
Supersonic Flow ◽  
Variable Mass ◽  
Axisymmetric Body ◽  
Body Of Revolution

The Supersonic Flow Past a Slender Ducted Body of Revolution with an Annular Intake

1950 ◽  
Vol 1 (4) ◽  
pp. 305-318
Author(s):  
G. N. Ward
Keyword(s):  
Supersonic Flow ◽  
Velocity Potential ◽  
Operational Calculus ◽  
The Body ◽  
Body Of Revolution ◽  
Internal Flows ◽  
Flow Past ◽  
External Forces ◽  
Internal Pressures ◽  
Slender Body Of Revolution

SummaryThe approximate supersonic flow past a slender ducted body of revolution having an annular intake is determined by using the Heaviside operational calculus applied to the linearised equation for the velocity potential. It is assumed that the external and internal flows are independent. The pressures on the body are integrated to find the drag, lift and moment coefficients of the external forces. The lift and moment coefficients have the same values as for a slender body of revolution without an intake, but the formula for the drag has extra terms given in equations (32) and (56). Under extra assumptions, the lift force due to the internal pressures is estimated. The results are applicable to propulsive ducts working under the specified condition of no “ spill-over “ at the intake.

Measurement of Recovery Factors and Friction Coefficients for Supersonic Flow of Air in a Tube: 2—Results Based on a Two-Dimensional Flow Model for Entrance Region

1952 ◽  
Vol 19 (2) ◽  
pp. 185-194
Author(s):  
J. Kaye ◽  
T. Y. Toong ◽  
R. H. Shoulberg
Keyword(s):  
Boundary Layer ◽  
Supersonic Flow ◽  
Laminar Boundary Layer ◽  
Flow Model ◽  
Variable Mass ◽  
Entrance Region ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Change Of State ◽  
Two Dimensional Flow

Abstract The first part of a program to obtain reliable data on the rate of heat transfer to air moving at supersonic speeds in a tube has been devoted to measurements made on adiabatic supersonic flow of air in a tube. The details of these measurements have been described in a previous paper. The calculated quantities such as the local apparent friction coefficient, recovery factor, Mach number, and so forth, were obtained from the simple one-dimensional flow model for which the properties of the stream are uniform at any section, and boundary-layer effects are ignored. The analysis of some of the same data given in the previous paper is undertaken here with the aid of a simplified two-dimensional flow model. The supersonic flow in the tube is divided into a supersonic core of variable mass with the fluid remaining in the core undergoing a reversible adiabatic change of state, and a laminar boundary layer of variable mass. The compressible laminar boundary layer increases in thickness in the direction of flow, and then undergoes a transition to a turbulent boundary layer. The two-dimensional flow model is limited here to the region where a laminar boundary layer appears to be present in the entrance region of the tube. The results of the analysis based on the two-dimensional flow model indicate that where the flow in the tube boundary layer appears to be laminar, the measured pressures and temperatures in the tube for adiabatic supersonic flow of air could have been predicted, with sufficient accuracy for engineering problems, from measured data for supersonic flow of air over a flat plate with a laminar boundary layer, and with zero pressure gradient.

The behaviour of supersonic flow past a body of revolution, far from the axis

1950 ◽  
Vol 201 (1064) ◽  
pp. 89-109 ◽  
Keyword(s):  
Supersonic Flow ◽  
General Theory ◽  
Body Of Revolution ◽  
Flow Past ◽  
Physical Importance ◽  
Special Case ◽  
Pointed Body ◽  
Asymptotic Forms

A theory is developed of the supersonic flow past a body of revolution at large distances from the axis, where a linearized approximation is valueless owing to the divergence of the characteristics at infinity. It is used to find the asymptotic forms of the equations of the shocks which are formed from the neighbourhoods of the nose and tail. In the special case of a slender pointed body, the general theory at large distances is used to modify the linearized approximation to give a theory which is uniformly valid at all distances from the axis. The results which are of physical importance are summarized in the conclusion (§ 9) and compared with the results of experimental observations.

The Slender Wing with a Half Body of Revolution Mounted Beneath

1968 ◽  
Vol 72 (693) ◽  
pp. 803-807 ◽  
Author(s):  
H. Portnoy
Keyword(s):  
Supersonic Flow ◽  
Slender Body ◽  
Meridian Plane ◽  
Pitching Moment ◽  
Body Of Revolution ◽  
Slender Body Theory ◽  
Lift And Drag ◽  
Body Theory ◽  
Slender Wing

Summary The slender-body theory of Ward is applied to a configuration consisting of a slender, pointed wing, carrying directly beneath it a pointed half-body of revolution divided along a meridian plane. Expressions for lift and drag due to incidence are found which are valid in both subsonic and supersonic flow if the flow is attached. The lift result can be used to find pitching moment. For the supersonic case the drag at zero incidence is also found and the expressions for a conical configuration are developed so that a limiting form of these can be compared with the results of ref. 3.

The Effect of Sting Diameter and Length on Base Pressure at M = 3·88

1968 ◽  
Vol 19 (4) ◽  
pp. 368-374 ◽  
Author(s):  
Walter R. Sieling
Keyword(s):  
Supersonic Flow ◽  
Axisymmetric Body ◽  
Base Pressure ◽  
Base Diameter ◽  
Apparent Change

SummaryThe effects of sting diameter and cylindrical protuberance length on the base pressure of an axisymmetric body in a turbulent supersonic flow are experimentally determined. It is found that the change in base pressure due to the presence of the sting is greater than 4 per cent when the ratio of sting diameter to base diameter is 0·150 or greater. When the ratio of cylindrical protuberance length to base diameter is greater than 1·3 there is no apparent change in base pressure with a change in length. However, when this ratio is less than 1·3, the base pressure varies greatly with length.

Force and moment characteristics of supersonic flow past a cylindrical body of revolution with a fluid wing

1988 ◽  
Vol 22 (5) ◽  
pp. 743-746 ◽  
Author(s):  
V. F. Zakharchenko ◽  
Yu. Kh. Kardanov ◽  
P. V. Sidorov
Keyword(s):  
Supersonic Flow ◽  
Cylindrical Body ◽  
Body Of Revolution ◽  
Flow Past

Supersonic Flow Past Wing-Body Combinations

1953 ◽  
Vol 4 (3) ◽  
pp. 287-314 ◽  
Author(s):  
W. Chester
Keyword(s):  
Supersonic Flow ◽  
Aspect Ratio ◽  
Leading Edge ◽  
The Body ◽  
Infinite Cylinder ◽  
Main Stream ◽  
Exact Equation ◽  
Body Of Revolution ◽  
Flow Past ◽  
General Conditions

SummaryThe supersonic flow past a combination of a thin wing and a slender body of revolution is discussed by means of the linearised equation of motion. The exact equation is first established so that the linearised solution can be fed back and the order of the error terms calculated. The theory holds under quite general conditions which should be realised in practice.The wing-body combination considered consists of a wing symmetrically situated on a pointed body of revolution and satisfying the following fairly general conditions. The wing leading edge is supersonic at the root, and the body is approximately cylindrical downstream of the leading edge. The body radius is of an order larger than the wing thickness, but is small compared with the chord or span of the wing.It is found that if the wing and body are at the same incidence, and the aspect ratio of the wing is greater than 2 (M2-1)-½, where M is the main stream Mach number, the lift is equivalent to that of the complete wing when isolated. If the wing only is at incidence then the lift is equivalent to that of the part of the wing lying outside the body.The presence of the body has a more significant effect on the drag. If, for example, the body is an infinite cylinder of radius a, and the wing is rectangular with aspect ratio greater than 2(M2-1)-½, then the drag of the wing is decreased by a factor (1-2a/b), where 2b is the span of the wing.When these conditions do not hold the results are not quite so simple but are by no means complicated.

On the propagation of weak shock waves

1956 ◽  
Vol 1 (3) ◽  
pp. 290-318 ◽  
Author(s):  
G. B. Whitham
Keyword(s):  
Supersonic Flow ◽  
Delta Wing ◽  
Thickness Distribution ◽  
Leading Edge ◽  
Weak Shock ◽  
Wave Drag ◽  
Main Step ◽  
Body Of Revolution ◽  
Flow Past ◽  
Cone Field

A method is presented for treating problems of the propagation and ultimate decay of the shocks produced by explosions and by bodies in supersonic flight. The theory is restricted to weak shocks, but is of quite general application within that limitation. In the author's earlier work on this subject (Whitham 1952), only problems having directional symmetry were considered; thus, steady supersonic flow past an axisymmetrical body was a typical example. The present paper extends the method to problems lacking such symmetry. The main step required in the extension is described in the introduction and the general theory is completed in §2; the remainder of the paper is devoted to applications of the theory in specific cases.First, in §3, the problem of the outward propagation of spherical shocks is reconsidered since it provides the simplest illustration of the ideas developed in §2. Then, in §4, the theory is applied to a model of an unsymmetrical explosion. In §5, a brief outline is given of the theory developed by Rao (1956) for the application to a supersonic projectile moving with varying speed and direction. Examples of steady supersonic flow past unsymmetrical bodies are discussed in §6 and 7. The first is the flow past a flat plate delta wing at small incidence to the stream, with leading edges swept inside the Mach cone; the results agree with those previously found by Lighthill (1949) in his work on shocks in cone field problems, and this provides a valuable check on the theory. The second application in steady supersonic flow is to the problem of a thin wing having a finite curved leading edge. It is found that in any given direction the shock from the leading edge ultimately decays exactly as for the bow shock on a body of revolution; the equivalent body of revolution for any direction is determined in terms of the thickness distribution of the wing and varies with the direction chosen. Finally in §8, the wave drag on the wing is calculated from the rate of dissipation of energy by the shocks. The drag is found to be the mean of the drags on the equivalent bodies of revolution for the different directions.

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

1951 ◽  
Vol 3 (1) ◽  
pp. 61-79 ◽  
Author(s):  
P. M. Stocker
Keyword(s):  
Supersonic Flow ◽  
Aspect Ratio ◽  
The Body ◽  
Supersonic Stream ◽  
List Type ◽  
Body Of Revolution ◽  
Small Aspect Ratio ◽  
Flow Past ◽  
Special Cases ◽  
Ratio Set

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.

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