Pressure loading on curved leading edge wings in supersonic flow

1986 ◽  
Vol 23 (7) ◽  
pp. 574-581 ◽  
Author(s):  
Milton E. Vaughn ◽  
John E. Burkhalter
Keyword(s):  
Supersonic Flow ◽  
Leading Edge ◽  
Pressure Loading

Surface pressures on a wing moving with supersonic speed

1974 ◽  
Vol 341 (1625) ◽  
pp. 177-193 ◽  
Keyword(s):  
Supersonic Flow ◽  
Delta Wing ◽  
Leading Edge ◽  
Ideal Gas ◽  
Numerical Results ◽  
Coordinate Surface ◽  
Supersonic Speed ◽  
Extrapolation Procedure ◽  
Specific Heats ◽  
Limiting Values

Estimates for pressures on the surface of a given delta wing at zero incidence in a steady uniform stream of air are obtained by numerically integrating two semi-characteristic forms of equations which govern the inviscid supersonic flow of an ideal gas with constant specific heats. In one form of the equations coordinate surfaces are fixed in space so that the surface of the wing, which has round sonic leading edges, is a coordinate surface. In the other, two families of coordinates are chosen to be stream-surfaces. For each form of the equations, a finite difference method has been used to compute the supersonic flow around the wing. Convergence of the numerical results, as the mesh is refined, is slow near the leading edge of the wing and an extrapolation procedure is used to predict limiting values for the pressures on the surface of the wing at two stations where theoretical and experimental results have been given earlier by another worker. At one station differences between the results given here and the results given earlier are significant. The two methods used here produce consistent values for the pressures on the surface of the wing and, on the basis of this numerical evidence together with other cited numerical results, it is concluded that the pressures given here are close to the true theoretical values.

Fan Stability With Leading Edge Damage: Blind Prediction and Validation

2021 ◽  
Author(s):  
E. J. Gunn ◽  
T. Brandvik ◽  
M. J. Wilson ◽  
R. Maxwell
Keyword(s):  
Supersonic Flow ◽  
High Speed ◽  
Leading Edge ◽  
Rotating Stall ◽  
Stall Inception ◽  
Blind Prediction ◽  
Edge Damage ◽  
The Impact ◽  
Operating Points ◽  
Relative Flow

Abstract This paper considers the impact of a damaged leading edge on the stall margin and stall inception mechanisms of a transonic, low pressure ratio fan. The damage takes the form of a squared-off leading edge over the upper half of the blade. Full-annulus, unsteady CFD simulations are used to explain the stall inception mechanisms for the fan at low- and high-speed operating points. A combination of steady and unsteady simulations show that the fan is predicted to be sensitive to leading edge damage at low speed, but insensitive at high speed. This blind prediction aligns well with rig test data. The difference in response is shown to be caused by the change between subsonic and supersonic flow regimes at the leading edge. Where the inlet relative flow is subsonic, rotating stall is initiated by growth and propagation of a subsonic leading edge flow separation. This separation is shown to be triggered at higher mass flow rates when the leading edge is damaged, reducing the stable flow range. Where the inlet relative flow is supersonic, the flow undergoes a supersonic expansion around the leading edge, creating a supersonic flow patch terminated by a shock on the suction surface. Rotating stall is triggered by growth of this separation, which is insensitive to leading edge shape. This creates a marked difference in sensitivity to damage at low- and high-speed operating points.

On the flow field of a rapidly oscillating airfoil in a supersonic flow

1974 ◽  
Vol 62 (4) ◽  
pp. 811-827 ◽  
Author(s):  
M. Kurosaka
Keyword(s):  
Supersonic Flow ◽  
Flow Field ◽  
Leading Edge ◽  
Flow Region ◽  
Relative Magnitude ◽  
Frequency Parameter ◽  
Unsteady Supersonic Flow ◽  
Long Time ◽  
Intimate Knowledge ◽  
Repeated Use

This paper examines the features of the flow field off the surface of an oscillating flat-plate airfoil immersed in a two-dimensional supersonic flow Although the exact linearized solution for a supersonic unsteady airfoil has been known for a long time, its expression in the form of an integral is not convenient for a physical interpretation. In the present paper, the quintessential features of the flow field are extracted from the exact solution by obtaining an asymptotic expansion in descending powers of a frequency parameter through the repeated use of the stationary-phase and steepest descent methods. It is found that the flow field consists of two dominant and competing signals: one is the acoustic ray or that component arising from Lighthill's ‘convecting slab’ and the other is the leading-edge disturbance propagating as a convecting wavelet. The flow field is found to be divided into several identifiable regions defined by the relative magnitude of the signals, and the asymptotic expansions appropriate for each flow region are derived along with their parametric restrictions. Such intimate knowledge of the flow field in unsteady, supersonic flow is of interest for interference aerodynamics and related acoustic problems.

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.

Note on the Extension of Evvard’s Method to Wings with Subsonic Leading Edges Moving at Supersonic Speeds

1957 ◽  
Vol 8 (1) ◽  
pp. 87-102 ◽  
Author(s):  
G. J. Hancock
Keyword(s):  
Flat Plate ◽  
Delta Wing ◽  
Leading Edge ◽  
Wing Surface ◽  
List Type ◽  
Pressure Loading ◽  
Supersonic Speed ◽  
Triangular Wing ◽  
Finite Wing ◽  
The Relationship

SummaryEvvard’s technique is applied to the problem of a thin finite wing moving at a supersonic speed when the leading edge is subsonic. It is developed in two methods:—(i) in which the relationship between the pressure loading and the integrals of the downwash over the wing surface is extended as far as possible, and which has to be computed numerically;(ii) in which approximations are made for the upwash velocities in the neighbourhood of the leading edge, resulting in a series of standard integrals for the estimation of the pressure loading.Method (ii) is applied to the pressure loading on a flat plate triangular wing and cropped delta wing, and the application to more general shapes is discussed.

2336 Effect of the Leading Edge Plate of Cavity on Cavity-Induced Acoustic Oscillations in Supersonic Flow

2006 ◽  
Vol 2006.2 (0) ◽  
pp. 85-86
Author(s):  
Shigeru MATSUO ◽  
Md.Mahbubul Alam ◽  
Masanori TANAKA ◽  
Toshiaki SETOGUCHI
Keyword(s):  
Supersonic Flow ◽  
Leading Edge ◽  
Acoustic Oscillations

2335 Effect of the Leading Edge Cutout of Cavity on Cavity-Induced Acoustic Oscillations in Supersonic Flow

2006 ◽  
Vol 2006.2 (0) ◽  
pp. 83-84
Author(s):  
Md.Mahbubul Alam ◽  
Shigeru MATSUO ◽  
Masanori TANAKA ◽  
Toshiaki SETOGUCHI
Keyword(s):  
Supersonic Flow ◽  
Leading Edge ◽  
Acoustic Oscillations

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.

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