Separated Flow Past a Slender Delta Wing at Incidence

1973 ◽  
Vol 24 (2) ◽  
pp. 120-128 ◽  
Author(s):  
J E Barsby
Keyword(s):  
Delta Wing ◽  
Separated Flow ◽  
Leading Edge ◽  
Vortex Sheet ◽  
Simultaneous Equations ◽  
Delta Wings ◽  
Nested Iteration ◽  
Finite Difference Technique ◽  
Flow Past ◽  
Vortex Systems

SummarySolutions to the problem of separated flow past slender delta wings for moderate values of a suitably defined incidence parameter have been calculated by Smith, using a vortex sheet model. By increasing the accuracy of the finite-difference technique, and by replacing Smith’s original nested iteration procedure, to solve the non-linear simultaneous equations that arise, by a Newton’s method, it is possible to extend the range of the incidence parameter over which solutions can be obtained. Furthermore for sufficiently small values of the incidence parameter, new and unexpected results in the form of vortex systems that originate inboard from the leading edge have been discovered. These new solutions are the only solutions, to the author’s knowledge, of a vortex sheet leaving a smooth surface.Interest has centred upon the shape of the finite vortex sheet, the position of the isolated vortex, and the lift, and variations of these quantities are shown as functions of the incidence parameter. Although no experimental evidence is available, comparisons are made with the simpler Brown and Michael model in which all the vorticity is assumed to be concentrated onto an isolated line vortex. Agreement between these two models becomes very close as the value of the incidence parameter is reduced.

Possible types of flow on lee-surface of delta wings at supersonic speeds

1988 ◽  
Vol 92 (915) ◽  
pp. 185-199 ◽  
Author(s):  
S. N. Seshadri ◽  
K. Y. Narayan
Keyword(s):  
Shock Wave ◽  
Static Pressure ◽  
Delta Wing ◽  
Separation Bubble ◽  
Separated Flow ◽  
Leading Edge ◽  
Delta Wings ◽  
Oil Flow ◽  
Normal Angle ◽  
Secondary Separation

SummaryExperiments were conducted to study the types of flow that occur on the lee surface of delta wings at supersonic speeds. Two sets of flat topped delta wings of different thickness (wedges with 10° and 25° normal angle respectively), each with leading edge sweep angles of 45°, 50°, 60° and 70°, were tested. The measurements, carried out at Mach numbers of 1·4, 1·6, 1·8, 2·0, 2·5 and 3·0, included oil flow visualisations (on both sets of wings) and static pressure distributions (on the thicker wing only). In addition, a 60° sweptback delta wing with a normal angle of 40° was also tested. The tests on this wing included both oil flow visualisations and static pressure measurements. From these and other existing measurements, the leeside flows have been classified into nine distinct types, namely (i) leading edge separated flow with secondary separation, (ii) leading edge separated flow with secondary and tertiary separation, (iii) leading edge separated flow with a shock wave beneath the primary vortex, (iv) leading edge separated flow with shock-induced secondary separation, (v) fully attached flow, (vi) flow attached at the leading edge with inboard shock-induced separation, (vii) mixed type of flow, (viii) flow with a leading edge separation bubble and (ix) leading edge separated flow with a shock wave lying on the lee surface in between the leading edge vortices. These types of flow have been displayed in a plane of Mach number and angle of attack normal to the leading edge. The experimental results indicate that increasing wing thickness has no qualitative effect on the types of flow observed but does shift the boundaries between some of the types of flow.

A Note on the Vorticity Distribution on the Surface of Slender Delta Wings with Leading Edge Separation

1961 ◽  
Vol 65 (603) ◽  
pp. 195-198 ◽  
Author(s):  
B. J. Elle ◽  
J. P. Jones
Keyword(s):  
Experimental Evidence ◽  
Delta Wing ◽  
Leading Edge ◽  
Water Tunnel ◽  
Delta Wings ◽  
Vorticity Distribution ◽  
Edge Separation

A description is given of the distribution of vorticity in the surface of thin wings with large leading edge sweep. Although the delta wing is chosen as the basic plan form the deductions are general and applicable to other types of wing. The conclusions are illustrated with experimental evidence from a water tunnel.

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.

Improved calculations of leading-edge separation from slender, thin, delta wings

1968 ◽  
Vol 306 (1484) ◽  
pp. 67-90 ◽  
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Vortex Sheet ◽  
Lower Surface ◽  
Lateral Position ◽  
Quantitative Agreement ◽  
Delta Wings ◽  
Real Flow ◽  
Edge Separation ◽  
Secondary Separation

In previous calculations (Mangler & Smith 1959) of the vortex-sheet model of leading-edge separation, only qualitative agreement was found with experimental observations. Because the numerical treatment of the model was then necessarily incomplete, it was uncertain how far the lack of quantitative agreement was to be attributed to the limitations of the model. The use of an automatic digital computer has now made it possible to reduce the uncertainties in the calculation to a negligible level. The features of interest in the real flow are more accurately predicted and the remaining discrepancies can be ascribed to the deficiencies in the model. The paper describes the method used to locate the vortex sheet and determine its strength in terms of the two boundary conditions on it; assesses the credibility of the results; and relates them to the observations. It is concluded that the model successfully predicts the observed height of the vortex above the wing, though the predicted lateral position is in error by up to 6% of the semi-span of the wing. This error falls as the incidence increases and is less when transition occurs in the boundary-layer upstream of secondary separation. Normal force is predicted accurately as is the distribution of pressure on the lower surface and the inboard part of the upper surface. The observed suction peak below the vortex changes its character when transition occurs in the boundary-layer upstream of secondary separation. The model predicts the suction peak in the turbulent case fairly well, but it is clear that detailed prediction of the suction peak is not possible by a model which is wholly inviscid.

scholarly journals Aerodynamic Sound Radiated from Longitudinal and Transverse Vortex Systems Generated around the Leading Edge of Delta Wings

2016 ◽  
Vol 06 (02) ◽  
pp. 101-118
Author(s):  
Shigeru Ogawa ◽  
Jumpei Takeda ◽  
Taiki Kawate ◽  
Keita Yano
Keyword(s):  
Leading Edge ◽  
Delta Wings ◽  
Aerodynamic Sound ◽  
Vortex Systems

Control of Highly Loaded Airfoil Boundary Layer Separation

2007 ◽  
Author(s):  
Augusto Lori ◽  
Mahmoud Ardebili ◽  
Yiannis Andreopoulos
Keyword(s):  
Boundary Layer ◽  
Delta Wing ◽  
Separated Flow ◽  
Boundary Layer Separation ◽  
Wall Region ◽  
High Momentum ◽  
Impulsive Motion ◽  
Delta Wings ◽  
Layer Separation ◽  
Highly Loaded

Control of boundary layer separation has been investigated employing micro-actuated delta winglets. The flow with the array is simulated computationally on two-dimensional airfoil boundary layer. The simulations capture vortices formed by the impulsive motion of the delta wings. The vortices are part of recirculating zone in the wake of the actuator, which as they advect downstream, bring high momentum fluid into the near wall region of a separated flow. Preliminary results indicate micro-actuated delta wing array affect boundary layer separation favorably.

scholarly journals Prandtl–Batchelor flow past a flat plate with a forward-facing flap

1984 ◽  
Vol 143 ◽  
pp. 351-365 ◽  
Author(s):  
P. G. Saffman ◽  
S. Tanveer
Keyword(s):  
Flat Plate ◽  
Leading Edge ◽  
Vortex Sheet ◽  
Inviscid Flow ◽  
The Body ◽  
Two Dimensional ◽  
Rear Edge ◽  
Flow Past ◽  
Range Of Values ◽  
Streamline Method

Two-dimensional steady inviscid flow past an inclined flat plate with a forward-facing flap attached to the rear edge is considered for the case when a vortex sheet separates from the leading edge of the flat plate and reattaches at the leading edge of the flap, with uniform vorticity distributed between the vortex sheet and the body. Solutions are found for a particular geometry and a range of values of the vorticity. The method used to calculate the flow is an extension of a free-streamline method widely used in cases where the velocity is a constant on the separating streamline.

Flow Regimes over Delta Wings at Supersonic and Hypersonic Speeds

1976 ◽  
Vol 27 (1) ◽  
pp. 1-14 ◽  
Author(s):  
L C Squire
Keyword(s):  
Shock Layer ◽  
Delta Wing ◽  
Leading Edge ◽  
Flow Regimes ◽  
Lower Surface ◽  
Delta Wings ◽  
Thin Shock Layer ◽  
Wide Range ◽  
Wing Sweep ◽  
Edge Separation

SummaryThis paper concerns the boundaries between flow regimes for sharp-edged delta wings in supersonic flow and the relation of some predictions of thin-shock-layer theory to these boundaries. In particular, it is shown that the theory predicts that the attachment lines on the lower surface of a thin delta wing at supersonic speeds suddenly jump from just inboard of the leading edges to the centre line in certain flight conditions. In general there is close agreement between the conditions for this jump and the flight conditions corresponding to the change-over from attached flow to the leading-edge separation on the upper surface. Since the movement of the attachment lines on the lower surface must change the position of the sonic line and the nature of the expansion around the edge, it is suggested that the two phenomena are directly related. Thus thin-shock-layer theory can be used to establish the boundaries of the various flow regimes for a wide range of Mach number, incidence and wing sweep. The theory can also be used to predict the effects of wing thickness on leading-edge separation, but here the experimental data is very sparse and somewhat contradictory, so the value of the prediction in the case of thickness requires further investigation.

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