Leading-edge Sweep Angle Research Articles

Compressible inviscid vortex flow of a sharp edge delta wing

An analysis is presented on the compressible inviscid vortex flow over three delta wings with sharp leading edges with leading edge sweep angles φ=60, 70, and 76 deg using numerical solutions of the Euler equations. Presentations of results are given for Mach numbers ranging from M∞=0.1 to 0.8 and for angles of attack up to the onset of vortex breakdown. The paper focuses the attention on the effects of the vortex flow on the flowfield of a delta wing. The occurrence of shock waves of two types, crossflow and terminating (or rear) shocks in the vortical flowfields, are investigated; the possibility of shock-induced vortex breakdown and the effects of compressibility on the rapid performance degradation of delta wings after vortex bursting are studied in detail. It is shown that the onset of the vortex bursting at the wing trailing edge is only weakly influenced by the freestream Mach number. The upstream progression of the vortex bursting, however, is faster for supersonic vortex cores. For transonic flows, terminating shocks are observed downstream of vortex bursting. Crossflow shocks, however, may already develop for low-subsonic freestream Mach numbers. Also, it is found that the core flow is already compressible for freestream Mach numbers M∞≃0.1 and that significant amounts of entropy and circulation are generated within the core

Influence of sideslip on double delta wing aerodynamics

Introduction D OUBLE delta wings are planforms that incorporate two distinct leading-edge sweep angles. The first part of the double delta wing, the strake, has a much higher sweep angle than its aft portion, the main wing. A double delta wing has been shown to have better aerodynamic performance than a simple delta wing of comparable area having the same sweep as the main wing of the double delta. The improved aerodynamic performance is due to the interaction of the vortices created by the strake and main wing. Very few studies have examined the performance of double delta wings in sideslip. In sideslip, each side of the wing experiences an effective change in sweep angle. The side leading into the flow, the windward side, will see an effective decrease in sweep angle, whereas the side trailing, the leeward side, will see an effective increase in sweep angle. On a double delta wing this can result in some very complex vortical interactions. This Note discusses the nonlinear behavior of a double delta wing examined in a low-speed wind tunnel at high angle of attack in sideslip. A significantly larger amount of data on the effects of sideslip for double delta wings is contained in previous references. 5

Aerodynamic effects of delta planform tip sails on wing performance

An experimental investigation was conducted to establish the effects of delta planform tip sails (DPTSs) on a planar rectangular wing. The DPTS is a small wingtip-mounted device analogous to a conventional tip sail, but with a slender planform. It is suggested that using a sharp-edged, slender tip device may alleviate some of the design complexities (e.g., twist and camber) associated with keeping attached flow on winglets and tip sails. The results indicate that performance improvements can be obtained with DPTSs. Increases in the wing lift curve slope, maximum lift coefficient and, for some configurations, the Oswald efficiency factor were obtained compared to the basic wing. Increasing the DPTS leading-edge sweep angle and taper ratio resulted in an increase in the wing's Oswald efficiency factor.

Effect of tunnel walls on vortex breakdown location over delta wings

Vortex breakdown has been the subject of many investigations during the past few decades. Many of the investigations were performed by visualizing the vortical flowfield above delta wings in water or wind tunnels. In spite of the extensive use of this technique, little attention has been paid to the possible influence of the test section walls on the measured location of the vortex breakdown. The present work suggests a possible model by which the walls may affect the vortex breakdown location. The suggested model is associated with the upwash induced on the wing surface due to the presence of the walls. This upwash was found to be relatively small near the wing's apex and larger on the trailing edge, thus creating an effectively cambered wing. The effective camber tends to shift the vortex breakdown location downstream as compared to a flat wing with the same projected geometry. The influence of the walls was tested in a series of experiments in a water tunnel using delta wings with different sizes, relative to the test section dimensions. The anticipated trend was observed in the experimental results. Nomenclature Cr = wing root chord length H = test section height V = undisturbed velocity S =wing span W = test section width Xbd - vortex breakdown location along the wing root chord a = angle of attack ALE = leading-edge sweep angle

Results of an experimental and numerical study of the aerodynamic heating of the undersurface of delta wings with sharp leading edges at mach numbers M?=6.1 and 8

The heat transfer between a supersonic flow and the undersurface of delta wings with leading-edge sweep angles x=65 and 70° is investigated in a shock tunnel at angles of attackα ≤ 15°. The supersonic inviscid flow over these wings in regimes in which the bow shock is attached to the sharp leading edges is calculated numerically. The compressible boundary layer problem is solved for the calculated inviscid flow fields in the laminar, transition and turbulent flow zones. The calculations and experimental values of the heat flux on the surface of the wings are compared. The calculations are in satisfactory agreement with the experimental data in the laminar and transition zones, but diverge significantly (by up to 20%) in the turbulent zone.

Reply by the Authors to J.G. Leishman

Reply by the Authors to J.G. Leishman

Navier-Stokes computations of lee-side flows over delta wings

Solutions to the Navier-Stokes equations for the flow over delta wings are computed with emphasis on the separated vortical flows developing on the lee side at high angles of attack. A recently developed implicit algorithm is used which employs upwind differencing for the pressure and convection terms and central differencing for the shear stress and heat transfer terms. Solutions to both the three-dimensional equations and the approximate conical flow equations are compared parametrically with an extensive experimental data base at supersonic speeds. The computations indicate that the conical flow approximation provides results in close agreement with the three-dimensional equations, even to angles of attack as high as 20 degrees. Good agreement with experimentally measured pressures and vapor screen photographs is obtained for the conditions investigated. The method predicts the classical pattern of vortical flow over a delta wing and transition to other flow patterns as the leading edge sweep angle and leading edge normal Mach number are varied.

Keel Design for Low Viscous Drag

Foil and planform parameters which govern the level of viscous drag produced by the keel of a sailing yacht are discussed. It is shown that the application of laminar boundary-layer flow offers great potential for increased boat speed resulting from the reduction in viscous drag. Three foil shapes have been designed and it is shown that their hydrodynamic characteristics are very much dependent on location and mode of boundary-layer transition. The planform parameter which strongly affects the capabilities of the keel to achieve laminar flow is leading-edge sweep angle. The two significant phenomena related to keel sweep angle which can cause premature transition of the laminar boundary layer are crossflow instability and turbulent contamination of the leading-edge attachment line. These flow phenomena and methods to control them are discussed in detail. The remaining factors that affect the maintainability of laminar flow include surface roughness, surface waviness, and freestream turbulence. Recommended limits for these factors are given to insure achievability of laminar flow on the keel. In addition, the application of a simple trailing-edge flap to improve the hydrodynamic characteristics of a foil at moderate-to-high leeway angles is studied.

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

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.

Shock-induced separated flows on the lee surface of delta wings

Experiments were conducted to study shock-induced separated flows on the lee surface of delta wings with sharp leading edge at supersonic speeds. Two sets of delta wings of different thickness (10° and 25° normal angle), each with leading edge sweep angles varying from 45° to 70°, were tested. The measurements, carried out in a Mach number range from 1.4 to 3.0, included oil flow visualisations (on both sets of wings) and static pressure distributions (on the thicker wings only). Using the test results, some features of shock-induced separated flows, including in particular the boundary between this type of flow and fully attached flow, have been determined. The experimental results indicate that this boundary does not seem to show any significant dependence on wing thickness within the limit of thicknesses tested. It is shown that this boundary can be predicted for thin delta wings using a well known criterion for incipient separation in a glancing shock wave boundary layer interaction, namely that a pressure rise of 1.5 is required across the shock. Comparison of the predicted boundary with experimental results (from oil flow visualisations) shows good agreement.

Unsteady transonic flow calculations for wing/fuselage configurations

Unsteady transonic flow calculations are presented for wing/fuselage configurations. Calculations are performed by extending the XTRAN3S (version 1.5) unsteady transonic small-disturbance code to allow the treatment of a fuselage. The research was conducted as part of a larger effort directed toward developing the capability to treat a complete flight vehicle. Details of the XTRAN3S fuselage modeling are discussed in the context of the small-disturbance equation. Transonic calculations are presented for two wing/fuselage configurations with leading-edge sweep angles of 0 and 36.65 deg, the results of which compare well with available experimental steady-pressure data. Unsteady calculations are performed for simple bending and torsion modal oscillations of the wing. Comparisons of sectional lift and moment coefficients for the wing-alone and wing/fuselage cases reveal effects of fuselage aerodynamic interference on the unsteady wing loading. Tabulated generalized aerodynamic forces, typically used in flutter analyses, indicate small changes in the real (in-phase) component and as much as a 30% change in the imaginary (out-of-phase) component when the fuselage is included in the calculation. These changes result in a 2-5% increase in total magnitude and a several degree increase in phase.

Leeside flows over delta wings at supersonic speeds

An experimental investigation of the lee-side flow on sharp leading-edge delta wings at supersonic speeds has been conducted. Pressure data were obtained at Mach numbers from 1.5 to 2.8, and three types of flow-visualization data (oil-flow, tuft, and vapor-screen) were obtained at Mach numbers from 1.7 to 2.8 for wing leading-edge sweep angles from 52.5 deg to 75 deg. From the flow-visualization data, the lee-side flows were classified into seven distinct types and a chart was developed that defines the flow mechanism as a function of the conditions normal to the wing leading edge, specifically, angle of attack and Mach number. Pressure data obtained experimentally and by a semiempirical prediction method were employed to investigate the effects of angle of attack, leading-edge sweep, and Mach number on vortex strength and vortex position. In general, the predicted and measured values of vortex-induced normal force and vortex position obtained from experimental data have the same trends with angle of attack, Mach number, and leading-edge sweep; however, the vortex-induced normal force is underpredicted by 15 to 30 percent, and the vortex spanwise location is overpredicted by approximately 15 percent.

Trailing edge flap influence on leading edge vortex flap aerodynamics

A study has been conducted to explore the effects of trailing edge flaps (TEF) on leading edge vortex flap (LEVF) aerodynamics. A variety of LEVF and TEF configurations were tested on flat plate delta wings with leading edge sweep angles of 60 and 75 deg. Results indicated that the well-established vortex flowfield of the 75deg wing was not substantially improved with the deflection of trailing edge flaps. Significant changes were seen to occur to the marginal vortices of the 60-deg wing. For the 60-deg wing with inverted constant chord LEVFs, the deflection of TEFs resulted in substantial increases in lift coefficient at low angles of attack without sacrificing other performance parameters. Also shown is the capability for eliminating the adverse longitudinal characteristics of constant chord LEVFs.

Load Distribution on Multielement Deformed Airfoils with Gap Effects

b Bn Bp c c The aerodynamic loading for deformed wings with elevens in subsonic flow is considered. The solution procedure falls into the potential flow category with appropriate restrictions. Lifting surface Kernel function formulation is used in which the local pressure loading for both wing and elevon is determined simultaneously and written as a summation equation. The solution procedure allows closed-form results to be obtained for the elevon hinge moments. Cases under study include gaps between wing and elevon in addition to arbitrary wing- elevon deformations. Fuselage effects and leading-edge suction are also used to apply results to a general con- figuration. Results for all cases compare very well with experimental data. Experimental data taken in a low- speed wind tunnel are presented for a cropped delta wing and rectangular elevon in which the wing-elevon gap was the primary test variable. Nomenclature aspect ratio wing span wing loading coefficients elevon loading coefficients local wing chord mean aerodynamic chord of the configuration (excluding gap length), reference length root chord of elevon tip chord of elevon section lift section hinge moment coefficient lift coefficient pitching moment coefficient about wing root chord leading edge pressure coefficient (p-px) Iq^ integral of the chordwise term of the pressure loading function, see Eq. (12) lift force on the wing freestream Mach number freestream dynamic pressure wing-elevon planform area (excluding gap area), reference area nondimensional perturbation velocity parallel to z axis Cartesian coordinates angle of attack Mach flow parameter, Vl -M2* elevon angle relative to wing (trailing edge down is positive) gap width between wing trailing edge and elevon leading edge wing leading-edge sweep angle nondimensional spanwise variable nondimensional variables, see Eq. (2) Sijibscripts E = elevon H = hinge characteristics HL = hinge line LE = leading edge nm = points or constants associated with the wing pq = points or constants associated with the elevon T = total TE = trailing edge VLE — leading-edge vortex W = wing 0 = denotes wing coordinate variables oo = freestream conditions

Effect of sweep angles on aerodynamic performance of double arrow wing - An analytical study

Hybrid wing planforms are studied for adoption on supersonic transport and fighter aircraft. The free vortex sheet method is used to determine effects of the leading-edge sweep angles on the aerodynamic performance of a double arrow wing with a strake. Results show lift and drag increase with the increase of the inboard and outboard leading-edge sweep angles. However, the lift-to-drag ratio is little influenced by the changes in these sweep angles. Spanwise surface pressure distributions on the aft region are influenced by the inboard sweep angle while the outboard sweep angle has no effect on these pressures. Finally, the experimental data and predicted results are compared to show good agreement.

Analytical Prediction of Vortex Lift

General integral expressions are derived for the nonlinear lift and pitching moment of arbitrary wing planforms in subsonic flow. The analysis uses the suction analogy and an assumed pressure distribution based on classical linear theory results. The potential flow lift constant and certain wing geometric parameters are the only unknowns in the integral expressions. Results of the analysis are compared with experimental data and other numerical methods for several representative wings, including ogee and double-delta planforms. The present method is shown to be as accurate as other numerical schemes for predicting total lift, induced drag, and pitching moment. b c c CL CD Cm CT Cs cc, ccd E2 Nomenclature = aspect ratio = wing span =chord = reference length = lift coefficient = drag coefficient = pitching moment coefficient = thrust coefficient = suction coefficient = section lift coefficient = section induced drag coefficient = section suction coefficient = pressure loading coefficient = drag = proportionality constant, Eq. (32) = proportionality constant, Eq. (53) = chordwise function, Eq. (44) ff(rj) = span wise f unction, Eq. (28) K = potential constant L =lift loading constant, Eq. (5) S = suction force SR = reference area s = suction force per unit length T = leading edge thrust, Eq. (7) T' = leading edge thrust per unit length V = freestream speed Wj = downwash velocity component, Eq. (11) a. = angle of attack F = vorticity p = freestream density £ = nondimensional chordwise coordinate 77 = nondimensional spanwise coordinate A = leading edge sweep angle Subscripts P = potential flow E =edge / = induced VLE = leading edge vortex VSE = side edge vortex

Transition and the Spread of Turbulence on a 60° Swept-Back Wing

Two interesting flow phenomena have been observed during the course of some transition measurements carried out on a swept-back wing with a curved tip. Firstly, the influence of leading-edge sweep angle on the type of instability responsible for transition has resulted in two distinct types of transition occurring simultaneously over different portions of the wing under certain critical conditions. Secondly, unlimited spanwise turbulent contamination of the flow was observed with an excrescence located close to the leading edge. The circumstances in which this occurred are believed to be somewhat exceptional, although much further work is desirable on this point.