Sharp-edged Delta Wing Research Articles

Experiments on a 60-Degree Delta Wing with Rounded Leading-Edge Vortex Flaps

Low-speed wind-tunnel measurements were done on a 1.15-m span 60-deg delta wing with rounded leading-edge vortex flaps. The purpose of the measurements is to assess the benefits of the rounded leading-edge vortex flaps in regard to improving the lift/drag ratio of delta wings. Force and surface pressure measurements were made at a Reynolds number based on a centerline chord of 2 x 10 6 . The increase in the radius of the rounded leading edge reduces the drag significantly both with and without flap deflection except in the minimum drag region. Deflecting the rounded leading-edge vortex flap improves the lift/drag ratio at relatively higher lift coefficients, when compared with the sharp-edged vortex flap. The largest improvement in the lift/drag ratio as compared with the sharp-edged delta wing with vortex flaps is more than 25% in the lift coefficient range between about 0.6 and 0.8 for the rounded-edge delta wing with flaps that were deflected 30 deg downward

Role of flow-consistent grid in CFD

Computational grids can play a crucial role in accurate CFD (computational fluid dynamics) simulations. This is shown here through the example of leading-edge vortex flow. Conventional grids for flow over sharp-edged delta wings do not resolve the near-apex flow due to dissimilar length scales of the flow and the grid. This in turn can affect the simulation of many vortex related phenomena. A grid that is consistent with the special nature of the flow is required to overcome the difficulty. The Euler simulation of a transonic vortex is considered where employment of a flow-consistent grid is shown to give a well-resolved vortex with cross-flow shock and also the shock-induced secondary vortex, right from the apex. On the other hand, when a conventional grid is employed these features are absent in the near-apex flow, and the subsequent flow development is seriously affected. Euler simulation of subsonic vortex breakdown has also been considered. In this case the employment of a flow-consistent grid has led to an unravelling of the fine details of the breakdown process.

The creation of lift by sharp-edged delta wings. An analysis of a self-adaptive numerical simulation using the concept of vorticity content

This article describes the self-adaptive method AMRFLEX3D which is used to compute steady, compressible inviscid and viscous flows. The adaptive capabilities are realized on the basis of structured blocks. This feature can be introduced into any structured multi-block CFD-code. A delta wing geometry at transonic flow conditions serves as test case for both Euler and Navier-Stokes simulations. After a description of the resulting grid-structure, investigations of the generation of circulation along the leading edge are presented. Using the self-adaptive grid system, a correlation between the strength of vortex layers and the circulation is found. A closer look at the circulation in the flow field reveals remarkable differences between Euler and Navier-Stokes simulations.

On the structure of vortex breakdown on a delta wing

This paper presents a detailed description of the vortex breakdown phenomenon on a delta wing. While there have been a number of earlier studies which have given us a broad, overall picture of these interesting and important flow fields, none has so far yielded the kind of fine structure considered here, in spite of using very fine grids. The present work has been made possible by the use of a new type of grid, called the embedded conical grid, which exploits the special nature of the flow field. Based on the Euler equations, the flow field past a 70 degrees sharp–edged delta wing in a subsonic free–stream is resolved here using this grid. The breakdown is found to begin as a rapid deceleration of the inner core due to a sudden increase in the adverse axial pressure gradient. This leads to a sudden broadening of the core and the formation of a deficit velocity region which becomes intensified causing axial flow reversal. The near–axis vorticity lines get tilted away from the vortex axis and their spiralling direction is reversed. The effect of artificial dissipation and grid coarseness on the computed vortex breakdown has been examined. The results presented here, though obtained for the delta wing geometry, are expected to add to our understanding of vortex breakdown in other flow situations as well.

Accurate development of leading-edge vortex using an embedded conical grid

The vortex formation and its development near the apex of a sharp-edged delta wing are poorly represented on conventional grids because of dissimilar length scales of the flow and the grid. The problem is overcome by having an embedded conical grid surrounding the wing. Computed Euler solutions on such an embedded conical grid and on a conventional H-O grid are presented for a range of incidence for a subsonic freestream. The solutions on the embedded conical grid show that the vortex is well resolved right from the apex, even at a very low incidence. The vortex breakdown is well predicted on the embedded conical grid, including the case where the breakdown has just moved upstream of the trailing edge.

Difficulties in predicting vortex breakdown effects on a rolling delta wing

An analysis has been performed of the challenges encountered when trying to predict the unsteady aerodynamics associated with the breakdown of the leading-edge vortices on a 65-deg sharp-edged delta wing, describing roll oscillations around an axis inclined 30 deg to the freestream. It is shown that to produce a realistic prediction the mathematical model has to represent in a satisfactory manner the highly nonlinear, almost discontinuous steady and unsteady aerodynamic characteristics associated with the downstream travel of the vortex breakdown past the trailing edge on the leeside wing half at 5 < | <£ | < 8 deg.

Effect of leeward flow dividers on the wing rock of a delta wing

The effect of a leeward flow divider on the wing rock of a 80-degree sharp-edged delta wing was studied in a wind tunnel experiment. Force and moment measurements and flow visualizations were performed to investigate the effect of divider geometry, size, and placement on wing rock. It was found that the divider can suppress wing rock over a wide range of angle of attack, but can also be destabilizing under certain conditions. A fluid mechanism explaining the effects of the divider on wing rock was proposed.

Further analysis of high-rate rolling experiments of a 65-deg delta wing

Further analyses have been performed of the experimental results obtained in the roll oscillation tests of a 65-deg sharp-edged delta wing at 30-deg inclination of the roll axis in order to uncover the fluid mechanical phenomena causing the unusual, highly nonlinear vehicle dynamics. It was found in an earlier analysis that in addition to the expected effect of convective flow time lag, the test results show highly nonlinear effects on vortex breakdown of the oscillatory rate. The present analysis reveals that these effects are themselves influenced by convective flow time lag. As a result, the past time history of the oscillatory response can in some cases have a strong influence on the final trim condition.

Adaptive computations of flow around a delta wing with vortex breakdown

An adaptive unstructured mesh solution method for the three-dimensional Euler equations was used to simulate the flow around a sharp edged delta wing. Emphasis was on the breakdown of the leading edge vortex at high angle of attack. Large values of entropy, which indicate vortical regions of the flow, specified the region in which adaptation was performed. The aerodynamic normal force coefficients show excellent agreement with wind tunnel data measured by Jarrah, and demonstrate the importance of adaptation in obtaining an accurate solution. The pitching moment coefficient and the location of vortex breakdown are compared with experimental data measured by Hummel and Srinivasan, showing good agreement in cases in which vortex breakdown is located over the wing.

Comment on 'Effect of fuselage on delta wing vortex breakdown'

I T is shown in Ref. 1 that the presence of a fuselage significantly promotes the breakdown of delta wing leadingedge vortices. Applying the equivalent angle-of-attack concept only accounted for a fraction of the measured effect of the fuselage, predicting a 17% increase of the effective angle of attack compared to the measured 45% increase. The present comment describes a flow mechanism that can explain this discrepancy, i.e., the wing-camber effect generated by the fuselage-induced upwash along the leading edge of the delta wing. The effect of longitudinal camber on the breakdown of the leading-edge vortex on a slender delta wing is large (Fig. 1). For the same maximum local angle of attack on the delta wing max a positive camber of Aa/amax = 1 delays breakdown to occur downstream of the trailing edge, whereas a negative camber of the same magnitude, Aa/amax = — 1, causes burst to occur very close to the apex. Obviously, for a pitching delta wing the pitch-rate-induced camber will have similarly large effects on the breakdown of leading-edge vortices. It is described in Refs. 4 and 5 how the roll-rate-induced camber effect would be very similar to the pitch-rate-induced camber effect. In both cases, it is the motion-induced change of the local angle of attack at the leading edge that matters (Fig. 2). For the maximum reduced frequency and amplitude used in the roll oscillation test of a 65-deg, sharp-edged delta wing, the roll-rate-induced camber at the trailing edge was AaLE/a = 0.31. Following the suggestion in Ref. 7, static tests were performed with models deformed to produce the roll-rateinduced camber (Fig. 3). The results were as expected; i.e., the twisted-up side of the delta wing experienced later vortex breakdown than the opposite, twisted-down side, approximately at 70% chord compared to 45% chord (for zero roll angle <£ = 0). It should be noted that the variation of the induced angle of attack along the leading edge is linear, proportional to the local semispan, in the examples given in Figs. 1-3, whereas the variation is nonlinear, roughly inversely proportional to the local semispan, in the case of the body-induced wing camber. However, the results in Ref. 7 serve to illustrate how large the effect of camber is on vortex breakdown. Based upon these results one can expect that the bodyinduced negative wing camber along the delta wing leading edge is a very important parameter. Thus, a better approach than using any mean-alpha value for the delta wing, such as the equivalent angle of attack, is to use the body angle of attack a together with the body-induced wing camber at the trailing edge AaLE/a, to correlate measurements of the breakdown of delta wing leading-edge vortices in the presence of a fuselage.

Unique high-alpha roll dynamics of a sharp-edged 65-deg delta wing

An analysis has been performed of experimental results obtained in roll oscillation tests at 30-deg angle of attack of a 65-deg sharp-edged delta wing in order to uncover the fluid mechanical phenomena causing the unusual, highly nonlinear vehicle dynamics. In addition to the expected effect of convective flow time lag, the test results show highly nonlinear effects of the angular rate, which themselves are influenced by the effect of convective time lag. A flow hypothesis is presented that can explain the unusual experimental results.

Numerical prediction of vortical flow over slender delta wings

Three-dimensional Navier-Stokes numerical simulations are necessary to correctly predict the complex lee- ward-side flow characteristics over delta wings, including leading-edge separation, secondary separation, and vortex breakdown. This article presents Navier-Stokes solutions of subsonic vortical flow over a 75-deg sweep delta wing with a sharp leading edge. The sensitivity of the solution to the numerical scheme is examined using both a partially upwind scheme and a central-differencing scheme. The effect of numerical grid density is also investigated. An embedded grid approach is implemented to enable higher resolution in selected isolated flow regions, such as the leeward-side surface flow region, and the leading-edge vortical flow region. HE main feature of the flow over delta wings at an angle of attack is the separated flow along the leading edges, which form free shear layers rolling up around cores to form leading-edge vortices. The leading-edge vortices induce ad- ditional nonlinear lift, usually called vortex-induced lift. In- crease in the angle of attack strengthens the vortices until eventually a sudden change occurs in the nature of the cores. This sudden change is known as vortex breakdown. In this article vortical flowfields, with and without vortex break- down, over highly-swept sharp-edged delta wings are inves- tigated. Due to its importance to aerodynamics, the vortex break- down over delta wings was explored in early experimental studies.1'2 Vortex breakdown was studied in controlled ex- periments on axisymmetric cylindrical vortices generated in confined tubes.3~6 Three types of vortex breakdown were ob- served for a cylindrical vortex,3 namely bubble breakdown, spiral breakdown, and double helix breakdown. Changes in the pressure gradient were found to have significant effects, thus a pressure increase downstream drives the breakdown upstream. For flows over delta wings, bubble and spiral breakdown are encountered, depending on the angle of incidence and the sweep angle. Experimental studies of flows over a unity aspect ratio delta wing7 show that as the angle of attack increases, bubble-type breakdown precedes spiral-type vortex break- down. The large suction pressure of the leading-edge vortex is diminished when vortex breakdown occurs with a subse- quent loss of lift and nose-up pitching moment. After vortex breakdown, the vortex core is not re-established and the downstream end of the bubble usually is followed by a tur- bulent wake. Experimental studies8-9 for flows over delta wings included surface and flowfield velocity and pressure measurements.

Investigation of vortex breakdown on delta wings using Navier-Stokes equations

An efficient finite-difference scheme solving for the three-dimensional incompressible Navier-Stokes equations is described. Numerical simulations of vortex breakdown are then carried out for a sharp-edged delta wing and a round-edged double-delta wing at high Reynolds numbers. Computed results show that several major features of vortex breakdown are qualitatively in agreement with observations made in experiments.

Experimental investigations of the vortex flow on delta wings at high incidence

It is reported in the literature that strongly asymmetric vortex flow occurs on the lee side of slender delta wings at high incidence, similar to that observed on slender cones, and a boundary is given for the onset of asymmetry vs wing aspect ratio. To study this phenomenon, dye flow-visualization tests were carried out on two slender, sharp-edged delta wings of aspect ratio A = 0.56 and 0.28 up to high incidences in a water tunnel. Another wing with A = 0.56 was studied in a wind tunnel, using a smoke flow-visualization technique. Reynolds numbers based on the root chord in the water tunnel and wind tunnel were Rec — 3.4 x 10 4 and 1.32 x 10 s, respectively. No strongly asymmetric vortex flow was observed in our tests before vortex breakdown occurred on the wing. Subsequent evaluation of flow observations reported elsewhere did not reveal strongly asymmetric vortex flow on slender wings of various planforms. One delta wing reported to exhibit strongly asymmetric vortex configurations; on closer study, it probably had near its apex the shape of something like a thick, elliptic cone, rather than that of a flat, thin delta wing. Theoretical results for inviscid flow past slender cones at incidence strongly suggest that on a thin delta wing no strongly asymmetric vortex flow occurs of the type found on slender, circular, or thick elliptic cones.

Numerical simulation of steady and unsteady asymmetric vortical flow

The unsteady, compressible, thin-layer, Navier-Stokes (NS) equations are solved to simulate steady and unsteady, asymmetric, vortical laminar flow around cones at high incidences and supersonic Mach numbers. The equations are solved by using an implicit, upwind, flux-difference splitting (FDS), finite-volume scheme. The locally conical flow assumption is used and the solutions are obtained by forcing the conserved components of the flowfield vector to be equal at two axial stations located at 0·95 and 1·0. Computational examples cover steady and unsteady asymmetric flows around a circular cone and its control using side strakes. The unsteady asymmetric flow solution around the circular cone has also been validated using the upwind, flux-vector splitting (FVS) scheme with the thin-layer NS equations and the upwind FDS with the full NS equations. The results are in excellent agreement with each other. Unsteady asymmetric flows are also presented for elliptic- and diamond-section cones, which model asymmetric vortex shedding around round- and sharp-edged delta wings.

Computation of vortex-dominated flow for a delta wing undergoing pitching oscillation

The conservative, unsteady Euler equations for the flow relative to a moving frame of reference are used to solve for the three-dimensional steady and unsteady flows around a sharp-edged delta wing. The resulting equations are solved by using an implicit, approximately factored, finite-volume scheme. Implicit second-order and explicit second- and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The grid is generated by locally using a modified Joukowski transformation in crossflow planes at the grid-chord stations. The computational applications cover a steady flow around a delta wing, whose results serve as the initial conditions for the unsteady flow around a pitching delta wing at a large mean angle of attack. The steady results are compared with the experimental data, and the unsteady results are compared with results of a flux-difference splitting scheme.

Unsteady inviscid and viscous computations for vortex-dominated flows

The unsteady supersonic flow around a rigid sharp-edged delta wing is solved using the unsteady Euler and thin-layer Navier-Stokes equations. The problem is formulated relative to a moving frame of reference so that computation of the grid motion is not required. A three-dimensional, implicit, aproximately factored, central-differencing, finite-volume scheme is used to obtain the time-accurate, unsteady, locally conical flow. The inviscid and viscous results are compared during the periodic response of a wing undergoing forced rolling-oscillation motion. The results show substantial differences in the surface pressure results and other distributed flow characteristics. These differences are attributed to the inviscid and viscous flow predictions in the vortex-dominated regions. The results of the total loads do not show any significant differences.

High-resolution upwind schemes for the three-dimensional incompressible Navier-Stokes equations

Based on flux-difference splitting, implicit high resolution schemes are constructed for efficient computations of steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. These schemes use first-order accurate Euler backward-time differencing and second-order central differencing for the viscous shear fluxes. Up to third-order accurate upwind differencing is achieved through a reconstruction of the solution from its cell averages. The reconstruction is accomplished by linear interpolation, where the node stencils are selected such that in regions of smooth solution the flow is highly resolved while spurious oscillations in regions of rapid changes in gradient are still suppressed. Fairly rapid convergence to steady-state solutions is attained with a completely vectorizable hybrid time-marching method. Flows around a sharp-edged delta wing are computed with the maximum accuracy of the upwind-differencing restricted to first-, second-, and third-order, to illustrate the effect of accuracy on the global and on the local vortical flow fields. The results are validated with experimental data.

Computation of steady and unsteady vortex-dominated flows with shockwaves

The unsteady Euler equations have been derived in the conservation form for the flow relative motion with respect to a rotating frame of reference. The resulting equations are solved by using a central-difference finite-volume scheme with four-state Runge-Kutta time stepping. For steady flow applications local time stepping is used, and for unsteady applications the minimum global time stepping is used. A three-dimensional fully vectorized computer program has been developed and applied to steady and unsteady maneuvering delta wings. The capability of the three-dimensional program has been demonstrated for a rigid sharp-edged delta wing undergoing uniform rolling in a conical flow and rolling oscillations in a locally conical flow.

Normal-force characteristics of sharp-edged delta wings at supersonic speeds

An engineering method for estimating the normal-force characteristics of sharp-edged delta wings at supersonic speeds is under development, and the first result is presented. The method utilizes experimental results from several sources and basic flow characteristics such as the vacuum limit, the pressure loss factor, and the face drag of disks. Experimental lift-curve slope data show that the wing thickness-to-chord ratio cannot be ignored, and therefore the present result is prepared for wings with a fixed profile apex half-angle in the flow direction. The analytic expressions for various partial contributions to the normal force of the delta wing are relatively simple and represent experimental data quite satisfactorily. To improve the engineering method, an accurate knowledge of the partitioning of the attached-flow lift-curve slope between the upper and lower surfaces of the delta wing is needed from experiments and/or higher-order flow theories.