A Theory of Uniform Supersonic Flow Past a Thin Oscillating Aerofoil at Appreciable Incidence to the Main Stream

1954 ◽  
Vol 5 (4) ◽  
pp. 185-194
Author(s):  
Geoffrey L. Sewell
Keyword(s):  
Supersonic Flow ◽  
Main Stream ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Fixed Position ◽  
Small Oscillations ◽  
Flow Past ◽  
Special Case ◽  
Number Of Authors

SummaryA number of authors (e.g., Refs. 1 and 2) have dealt with the problem of uniform two-dimensional supersonic flow past a thin oscillating aerofoil, whose angle of incidence to the main stream is small. In this special case, the effects of vorticity are negligible, while the fields of flow on either side of the aerofoil may be treated on the same footing.The object of this paper is to deal with the more general case in which the aerofoil performs small oscillations about a fixed position, in which its incidence to the main stream is appreciable.

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.

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.

Supersonic Flow Past a Wedge with a Flame at its Apex

1968 ◽  
Vol 19 (1) ◽  
pp. 80-90 ◽  
Author(s):  
R. Foster ◽  
J. F. Clarke
Keyword(s):  
Supersonic Flow ◽  
Flame Front ◽  
Flow Patterns ◽  
Chemical Energy ◽  
Two Dimensional ◽  
Pressure Flow ◽  
Simple Waves ◽  
Flow Past ◽  
Flow Deflection ◽  
Plane Flame

SummaryThe wholly supersonic flow past a two-dimensional wedge is analysed on the assumption that release of chemical energy into the stream can be accomplished across a thin discontinuous plane flame front attached to the apex. Forces experienced by the wedge are calculated and representative flow patterns exhibited. Some typical interactions between the flame and shocks or centred simple waves are discussed, with emphasis on the use of pressure-flow-deflection diagrams to obtain results.

Numerical Investigation of Viscous Laminar Supersonic Flow Past an Asymmetric Biconvex Circular-Arc Aerofoil

2013 ◽  
Vol 390 ◽  
pp. 147-151
Author(s):  
Saif Akram ◽  
Nadeem Hasan ◽  
Aqib Khan
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Supersonic Flow ◽  
Numerical Investigation ◽  
Lower Surface ◽  
Two Dimensional ◽  
Circular Arc ◽  
Flow Past ◽  
Supersonic Regime ◽  
Force Characteristics

A numerical investigation of two-dimensional unsteady, viscous and laminar compressible flow past an asymmetric biconvex circular-arc aerofoil in supersonic regime is carried out. The focus of the present work is to investigate the effects of variation of Mach number, at two different angles of attack, on the flow and force characteristics on NACA 2S-(50)(04)-(50)(20) aerofoil. The value of Reynolds number is taken as 5x105. The computations are carried out at Mach numbers of 1.25, 1.5 and 2.0 at an angle of attack of α=0° and α=10°. It is found that the aerofoil works well in the supersonic flow and, unlike the conventional symmetric biconvex aerofoil, generates finite lift at α=0° due to stronger shock waves at the lower surface. Moreover, the L/D ratio at α=10° is always found to be more than 2.5.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

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