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.     

Experiments on the unsteady nature of vortex breakdown over delta wings

 Vortex breakdown location over delta wings is not steady and exhibits fluctuations along the axis of the vortices. Experiments on the nature and source of these fluctuations were carried out. Spectral analysis and other statistical concepts were used to quantify the unsteady behaviour of vortex breakdown location obtained from flow visualization. The fluctuations consist of quasi-periodic oscillations and high-frequency low amplitude displacements. The quasi-periodic oscillations are due to an interaction between the vortices, which cause the antisymmetric motion of breakdown locations for left and right vortices. The oscillations are larger and more coherent as the time-averaged breakdown locations get closer to each other as angle of attack or sweep angle is varied. The frequency of this organized motion is much smaller than the frequency of any other known instabilities. On the other hand, the most probable frequency for the high-frequency small-amplitude fluctuations of breakdown location is in the same range as the frequency of Kelvin–Helmholtz instability of the separated shear layer. A mechanism for the interaction between the vortices causing the oscillations of breakdown location was proposed. When a splitter plate was placed in the symmetry plane of the wing, the large amplitude quasi-periodic oscillations of breakdown location were suppressed. Received: 10 March 1998 / Accepted: 27 October 1998     

三角翼前缘涡的某些破裂形式及特性研究

基于流动显示和PIV技术测量的实验结果，对三角翼前缘涡破裂的一些形式和破裂特性进行了分析和讨论。通过PIV测量所得到的涡量分布证实了在螺旋破裂的情况下，涡核的螺旋方向与前缘涡的旋转方向相反，及双螺旋破裂形式的存在等。进而对螺旋波的形成机理提出了与有关文献不同的看法。     

Vortex breakdown over a delta wing with oscillating leading edge flaps

 The effects of oscillating leading-edge flaps on leading-edge vortices and vortex breakdown were investigated for a delta wing with upward-deflected flaps. The variation of breakdown location revealed hysteresis loops. The time-averaged breakdown location over one cycle may move upstream or downstream compared to the quasi-steady case, depending on the amplitude of flap oscillations and angle of attack. Measurements of the phase-averaged velocity upstream of breakdown did not reveal any correlation to the response of breakdown location. The effect of oscillating flaps is largest when the breakdown location is near the trailing-edge region in the static case. Received: 2 February 1997/Accepted: 7 April 1997     

Skin friction fields on delta wings

The normalized skin friction fields on a 65° delta wing and a 76°/40° double-delta wing are measured by using a global luminescent oil-film skin friction meter. The detailed topological structures of skin friction fields on the wings are revealed for different angles of attack and the important features are detected such as reattachment lines, secondary separation lines, vortex bursting and vortex interaction. The comparisons with the existing flow visualization results are discussed.     

Computational modeling of vortex breakdown control on a delta wing

We present an effort to model the development and the control of the vortex breakdown phenomenon on a delta wing. The pair of the vortices formed on the suction side of a delta wing is the major contributor to the lift generation. As the angle of attack increases, these vortices become more robust, having high vorticity values. The critical point of a delta wing operation is the moment when these vortices, after a certain angle of attack, are detached from the wing surface and wing stall occurs. In order to delay or control the vortex breakdown mechanism, various techniques have been developed. In the present work, the technique based on the use of jet-flaps is numerically investigated with computational fluid dynamics by adopting two eddy-viscosity turbulence models. The computational results are compared with the experimental data of Shih and Ding (1996). It is shown that between the two turbulence models, the more advanced one, which adopts a non-linear constitutive expression for the Reynolds-stresses, is capable to capture the vortex breakdown location for a variety of jet exit angles. The performance assessment of the models is followed by the investigation of the effect of the jet-flap on the lift and drag coefficients.     

Vortex breakdown: Transition between bubble- and spiral-type breakdown

Depending on volume flux, flow visualizations in a water tunnel showed bubble-, spiral-type breakdown, and periodic transition between both. The initiation and development of bubble-type breakdown can be explained by a nonlinear feedback model. A growing asymmetry of the circumferential vorticity distribution leads to the transition to spiral-type. These conjectures are supported by experiments in which an artificially generated vortex ring induced initiation of bubble- and transition to spiral-type breakdown. To simulate vortex breakdown Navier-Stokes equations for three-dimensional, unsteady, and incompressible flows were solved. A comparison between experimental and numerical flow visualizations showed a good agreement.

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Sommario La visualizzazione del flusso in una galleria idrodinamica mostra, a seconda della portata volumetrica, una rottura delle linee vorticose di tipo a bolle, a spirale oppure una transizione periodica tra queste due. L'inizio ed il successivo sviluppo del fenomeno di rottura a bolla può venire spiegato attraverso un modello non lineare. Successivamente, all'aumentare dell'asimmetria nel profilo della vorticità circonferenziale, si ha la transizione alla rottura a spirale. Queste ipotesi vengono confermate dagli esperimenti in cui l'insorgere di ciascun tipo di rottura viene indotto attraverso un anello vorticoso generato artificalmente. Per analizzare il fenomeno della rottura delle linee vorticose sono state risolte le equazioni di Navier-Stokes per un flusso incomprimibile, tridimensionale, non stazionario. I risultati numerici ottenuti si sono mostrati in buon accordo con le visualizzazioni sperimentali.

     

Supersonic leeside flow topology on delta wings revisited

The leeside vortex structures on delta wings with sharp leading edges were studied for supersonic flow at the Institute of Theoretical and Applied Mechanics of the Russian Academy of Sciences in Novosibirsk. The experiments were carried out with three wings with sweep angles of χ=68°, 73°, and 78° and parabolic profiles in the 0.6 × 0.6 m² test section of the blow-down wind tunnel T-313 of the institute. The test conditions were varied from Mach numbers M=2 to 4, unit Reynolds numbers from Re _l=26 × 10⁶ to 56 × 10⁶ m⁻¹, and angles of attack from α=0° to 22°. The results of the investigations revealed that for certain flow conditions shocks are formed above, below, and between the primary vortices. The experimental data were accurate enough to detect the onset of secondary and tertiary separation as well as other boundaries. The various flow regimes discussed in the literature were extended in several cases. The major findings are reported. Received: 6 September 1999/Accepted: 24 January 2000     

Hypersonic flow past blunt-edged delta wings

A method is proposed for calculating hypersonic ideal-gas flow past blunt-edged delta wings with aspect ratios = 100–200. Systematic wing flow calculations are carried out on the intervals 6 M 20, 0 20, 60 80; the results are analyzed in terms of hypersonic similarity parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–179, September–October, 1990.     

Vortex control by the spanwise suction flow on the upper surface of delta wing

The numerical investigation has been performed to explore the feasibility of vortex control by leading edge sucking excitation on a delta wing. The results reveal that the flow on the upper surface of the delta wing changes significantly in a wide range of the angle of attack. For the vortical flow at moderate angle of attack, the secondary and tertiary vortices are weakened or suppressed, and the total lift is almost unchanged. For the stalled flow at high angle of attack, the leading edge concentrated vortex is recovered, and the lift is enhanced with increasing suction rate. For the bluff-body flow at even high angles of attack, the lift can still be improved. The concentrated vortex disappears on the upper surface, and the load increment is nearly unchanged along the chordwise direction. The project supported by the National Natural Science Foundation of China (19802018).     

Vortex structure of separated flows on model wings at low freestream velocities

Flow past model wings is experimentally investigated in a subsonic wind tunnel at large angles of attack at which the laminar boundary layer separates near the leading edge of the wing (flow stall). The object of the study was the flow structure within the separation zone. The carbon-oil visualization of surface streamlines used in the experiments showed that in the separation zone there exist one or more pairs of large-scale vortices rotating in the wing plane. Certain general properties of the vortex structures in the separation zone are found to exist, whereas the flow patterns may differ depending on the model aspect ratio, the yaw angle, and other factors.     

Entropy effects in hypersonic flow over blunt delta wings

The problem of hypersonic flow over blunt delta wings is considered. It is shown that in the case of large wing lengths x -100, where x is the longitudinal coordinate measured in blunt nose radii, extremal flow regimes characterized by an essentially nonuniform distribution of the gas dynamic parameters (density, entropy, Mach number) may be realized in the shock layer near the windward surface of the wing. The location of the zones of flow convergence or divergence on the surface of a delta wing with sweep angle x=75° is established. For the same wing the ranges of Mach numbers M and angles of attack leading to extremal flow regimes are indicated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, 178–181, March–April, 1991.     

SBLI control for wings and inlets

Flow control can be applied to shock wave/boundary layer interactions to achieve two different goals;the delay of shock-induced separation and/or the reduction ofstagnation pressure losses, which cause wave drag or inletinefficiencies. This paper introduces the principles and maintechniques for both approaches and assesses their relativesuitability for practical applications. While boundary layersuction is already in wide use for separation control, themost promising novel device is the micro-vortex generator,which can deliver similar benefits to traditional vortex generatorsat much reduced device drag. Shock control is notyet used on practical applications for a number of reasons,but recent research has focused on three-dimensional deviceswhich promise to deliver flow control with improved offdesignbehaviour. Furthermore, there are some indicationsthat a new generation of control devices may be able to combinethe benefits of shock and boundary layer control andreduce shock-induced stagnation pressure losses as well asdelay shock-induced separation.     

Vortex breakdown as a fundamental element of vortex dynamics

This paper presents an extension of an earlier analysis on vortex breakdown in tubes of constant cross section by Keller et al. (1985) to axisymmetric vortex flows in tubes with varying cross-sectional area. A broad investigation into the properties of steady axisymmetric vortex flows is given, insofar as they can be represented by perfect-fluid theory and simple extensions of it. It is argued that the basic physics of such flows, including vortex breakdown phenomena, can be explained with the help of the relatively simple theoretical concepts proposed. Numerical results are presented which show complete flow fields of loss-free transitions in diffusers.     

Effects of a vectored trailing edge jet on delta wing vortex breakdown

Flow visualization was used to study the effects of a vectored trailing edge jet on the leading edge vortex breakdown of a 65° delta wing. The experimental results indicated that there is little effect of the jet on the leading edge vortex breakdown when the angle of the vectored jet is less than 10°. With the increase of the vectored angle ß, the effect of the jet on the flow becomes stronger, i.e., the jet delays the leading edge vortex breakdown in the direction of the vectored jet, and accelerates breakdown of the other leading edge vortex. Moreover, the effect of the jet control tends to be weaker with the angle of attack.     

Computation of field structure and aerodynamic characteristics of delta wings at high angles of attack

A numerical investigation of the structure of the vortical flowfield over delta wings at high angles of attack in longitudinal and with small sideslip angle is presented. Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics that are dominated by the effect of the breakdown of the leading-edge vortices. The methods that analyze the flowfield structure quantitatively were given by using flowfield data from the computational results. In the region before the vortex breakdown, the vortex axes are approximated as being straight line. As the angle of attack increases, the vortex axes are closer to the root chord, and farther away from the wing surface. Along the vortex axes, as the adverse pressure gradients occur, the axial velocity decreases, that is, A is negativee, so the vortex is unstable, and it is possible to breakdown. The occurrence of the breakdown results in the instability of lateral motion for a delta wing, and the lateral moment diverges after a small perturbation occurs at high angles of attack. However, after a critical angle of attack is reached the vortices breakdown completely at the wing apex, and the instability resulting from the vortex breakdown disappears.     

Supersonic flow over delta wings and elements of star-shaped bodies at angles of attack and roll

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 81–87, January–February, 1989.