The standard hyperbolic methods used to solve the compressible Euler equations are not effective in the limit of incompressible flow. The sound waves dominate the system and it becomes poorly conditioned for numerical solution. For steady flow governed by the incompressible Euler equations, artificial compressibility is a technique that removes the troublesome sound waves. It leads to a hyperbolic system of equations that we solve by finite-volume differences centred in space, and explicit multistage time-stepping. The stability of this novel system is analysed, its allowable discontinuities are described, and appropriate far-field and solid-wall boundary conditions are introduced. Results are presented for both two- and three-dimensional flows, including vorticity shed from a delta wing. Whether vorticity is produced or not depends very strongly on the body geometry, the accuracy of the solution method, and the transient discontinuities that evolve in the flow field. The results are analysed for the total-pressure losses in the flow fields, and for the diffusion of the vortex sheets.

Computation of inviscid incompressible flow with rotation

A comprehensive research program designed to investigate the ability of computational methods to predict stability and control characteristics of realistic flight vehicles has been undertaken. The integrated approach to simulating static and dynamic stability characteristics for a generic UCAV and the X-31 configuration was performed by NATO RTO Task Group AVT-161. The UCAV, named SACCON (Stability and Control Configuration), and the X-31 are the subject of an intensive computational and experimental study. The stability characteristics of the vehicles are being evaluated via a highly integrated approach, where CFD and experimental results are being used in a parallel and collaborative fashion. The results show that computational methods have made great strides in predicting static and dynamic stability charactersitics, but several key issues need to be resolved before efficient, affordable, and reliable predictions are available.

An Integrated Computational/Experimental Approach to UCAV Stability & Control Estimation: Overview of NATO RTO AVT-161

A comprehensive research program designed to investigate the ability of computational methods to predict
stability and control characteristics of a generic unmanned combat air vehicle has been undertaken. The integrated
approach to simulating static and dynamic stability characteristics was performed by the NATO Research and
Technology Organization Task Group AVT-161. The vehicle named Stability and Control CONfiguration
(SACCON) was the subject of an intensive computational and experimental study. The stability characteristics of the
vehicle were evaluated via a highly integrated approach, where computational fluid dynamics and experimental
results were used in a parallel and collaborative fashion. The results show that computational methods have made
great strides in predicting static and dynamic stability characteristics, but several key issues need to be resolved
before efficient, affordable, and reliable predictions are available.

Integrated Computational/Experimental Approach to Unmanned Combat Air Vehicle Stability and Control Estimation

Separation in three-dimensional flows leads to the formation of vortical structures resulting from rolling up of the viscous flow "sheet," initially contained in a thin boundary layer, which springs up from the surface into the outer perfect fluid flow. A clear physical understanding of this phenomenon must be based on a rational analysis of the flowfield structure using the critical-point theory. With the help of this theory, it is possible to interpret correctly the surface flow patterns that constitute the imprints of the outer flow and to give a rational and coherent description of the vortical system generated by separation. This kind of analysis is applied to separated flows forming on typical obstacles, the field of which has been thoroughly studied by means of visualizations and probings using multihole pressure probes and laser velocimetry. Thus, the skin friction line patterns of a transonic channel flow and of a multibody launcher are interpreted. Then, the vortical systems of a delta wing and an afterbody at an incidence are considered. The last two configurations are a missile fuselage-type body and an oblate ellipsoid. I. Introduction F LIGHT at high-incidenc e of combat aircraft or hypersonic vehicles during re-entry, as well as that of tactical missiles, raises practical interest on the study of three-dimensional separated flows. Applications also concern internal flows, in particular air intakes and turbomachines in which the often complex geometry of the channel and the existence of shock waves almost inevitably lead to boundary-laye r separation. In three-dimensional flows, separation entails the formation of vortical structures—frequently, but improperly, called vortices to simplify—form ed by rolling up of the viscous flow "sheet," previously confined in a thin layer attached to the wall, which suddenly springs into the outer nondissipative flow. Although it has been known for a long time, this phenomenon is still incompletely understood from a physical point of view and it is delicate to model due to the flowfield complexity, all the components of which are difficult to capture properly. Many predictive methods are based on perfect fluid models, the first of which use the vortex sheet concept. Such a sheet is defined as a surface of tangential discontinuity for the velocity field. The computational method can use different schemes: doublets, vortex filaments, vortex particles, and so forth. Publications in this domain are too numerous to be cited here. A greater accuracy in flow prediction can be obtained in the solution of the complete Euler equations, which allows, in theory, automatic capture of sheet-like disconti

Physics of Vortical Flows

The near-surface flow structure and topology on a delta wing of low sweep angle, having sinusoidal leading edges of varying amplitude and wavelength, are investigated using a stereoscopic technique of high-image-density particle image velocimetry at a Reynolds number of 15,000. Identification of critical points, in conjunction with surface-normal vorticity and velocity, provides a basis for determining the effectiveness of a given leading edge. At high angle of attack, where large-scale three-dimensional separation occurs from the wing with a straight leading edge, an amplitude of the leading-edge protuberance as small as one-half of one percent of the chord of the wing can substantially alter the near-surface topology. When the amplitude reaches a value of four percent of the chord, it is possible to completely eradicate the negative focus of large-scale, three-dimensional separation, in favor of a positive focus of attachment. Moreover, alteration of the near-surface topology is most effective when the ratio of the wavelength to amplitude of the sinusoidal leading edge is maintained at a small value.

Flow past a delta wing with a sinusoidal leading edge: near-surface topology and flow structure

An experimental and theoretical investigation is described of the flow above and downstream of a 76° delta wing and two double-delta wings (sweep 76°/60° and 76°/40°, respectively, kink at 50 % chord). The flow pattern is visualized employing a laser-light-sheet technique. For the case of the delta wing experimental results are compared with numerical results of a free-vortex sheet method for computing three-dimensional flow about slender wings, a free-vortex sheet method for the limiting case of conical flow and a computational procedure for computing two-dimensional time-dependent vortex wake roll-up. Based on the laser-light-sheet investigation a vortex-sheet model is proposed for the flow about double-delta wings with leading-edge vortex separation on both wing panels. Presented as AIAA Paper 82-0949 at the AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference, June 7-11 1982, St. Louis, Missouri, USA.

On the vortex flow over delta and double-delta wings

Etude theorique et experimentale de l'ecoulement sur une aile delta et une aile en double delta

Vortex flow over delta and double-delta wings

The effects of the Reynolds number on the flow over 76/40-deg double-delta or strake-wing configurations and the capability of numerical solutions to predict these effects are discussed. The flow over the strake appears to be little affected by the Reynolds number. On the wing strong effects are evident on the flow on and off the wing surface. Numerical solutions tend to reasonably well predict the flow over these types of configurations

Effects of Reynolds Number on Flow over 76/40-Degree Double-Delta Wings

The leeward vortices occurring over low-aspect-ratio delta wings typical of many current fighter aircraft cause highly nonlinear forces and moments. Near stall the vortices break down over the wing surface and introduce additional discontinuities and transients in the aerodynamics. Experimental studies of these flows are needed to develop mathematical models to represent the interaction between the vehicle motion and the forces and moments. The models will permit design for increased maneuverability in future fighters. Many static and dynamic tests of a common 65-deg swept delta wing in pitch and roll were conducted. Here, the effects of sideslip on the flow over a flat-plate 65-deg swept delta wing tested at a geometric angle of attack of 30 deg are described. At this angle of attack, the major part of the flow over the wing is affected by vortex core breakdown. Sideslip causes a strong asymmetry in the breakdown location

Wind-tunnel study on a 65-deg delta wing at sideslip

The experimental study focuses on the effects of the leading-edge radius on the flow over 50 deg swept delta wing models. Three models were tested; one model has a sharp leading edge, and two others have a semicircular leading edge of a different radius. Six-component balancemeasurementswere performedand indicated that the leading-edge radius affects the level and slope of the forces acting on the models. The vortical flow on and off the surface of the models was investigated using an oil flow visualization and a stereo particle image velocimetry technique. The leading-edge radius is shown to affect the location, size, and strength of the vortices and also the vortex breakdown location over the models. The flow data are correlated with the balance data.

N. G. Verhaagen

Papers

On the vortex flow over delta and double-delta wings

Vortex flow over delta and double-delta wings

Effects of Reynolds Number on Flow over 76/40-Degree Double-Delta Wings

Wind-tunnel study on a 65-deg delta wing at sideslip

Leading-Edge Radius Effects on Aerodynamic Characteristics of 50-Degree Delta Wings