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Vortical flows in three dimensional configurations that are of typical interest to aerodynamicists and researchers in fluid mechanics are reviewed. A list of 10 issues was compiled to understanding complex vortical flows.
A two dimensional model is developed for a turbulent jet injected normally into a uniform crossflow, in which particular emphasis is placed on the contra-rotating vortex pair associated with the jet. By approximating the forces acting on each of the viscous vortices, equations governing the vortex spacing and downstream jet velocity are evolved. No empirical information is incorporated into this model. A description of the variation in total vortex strength is utilized in which vorticity generated by the jet's impulse dominates the farfield. Numerical solution of the governing equations yields results for the vortex trajectory, half spacing, varying circulation, and viscous core size that correlate quite well with experimental data and asymptotic relations. Based on these findings, we conclude that vortex separation and other important characteristics of the jet cross-section are two dimensional and viscous in nature. Hence it becomes possible to predict, on purely theoretical grounds, the behavior of the vortex pair and of the jet itself.
The stability of two-dimensional infinitesimal disturbances of the steady inviscid incompressible flow produced by infinite rows of finite-cored particles is studied. Numerical results are obtained for the growth rate and oscillation frequencies of disturbances of arbitrary subharmonic wavenumber, and the stability boundaries are calculated. The stabilization of the pairing instability by finite area demonstrated by Saffman and Schatzman (1982) is confirmed, as is Kida's (1982) result that this is not the most unstable disturbance when the area is finite. However, the finite area does not stabilize the inviscid Karman vortex street of finite-area vortices to infinitesimal two-dimensional disturbances of arbitrary wavelength. The finite area is always unstable except for one isolated value of the aspect ratio which depends upon the size of the vortices.
Experiments are conducted which demonstrate the feasibility of creating crossflow vortices in a flat-plate flow. A swept leading edge and contoured wind-tunnel walls produce a strong pressure gradient and a typical swept-wing flow on the plate. Detailed three-dimensional measurements, made within the boundary layer using hot-wire anemometry, are supplemented with different flow-visualization techniques. Data are presented on the mean flow characteristics as well as on the behavior of the crossflow vortices. Comparisons are made with theoretical flow-field and stability calculations.
Experiments were run to characterize the global vorticity distribution in an excited plane mixing layer. A reciprocating piston excited the mixing layer at a 0.0053 intensity, a Strouhal number of 0.97, and a 15 Hz frequency. An X-wire anemometer and a pitot tube furnished data in the 13 m/sec free stream velocity flow. Deep depressions were observed in the velocity contours on the high-speed side of the mixing layer, while primary vortex growth occurred on the low-speed side. The cores of the vortices moved at highly differentiated velocities. Phase plots were also generated to show tearing and fusing of the vortex contours.
According to quasi-geostrophic approximation, regions of strong cross flow gradient of geopotential vortivity support Rossby wave propagation. Using potential vorticity as a dynamical tracer, the polar vortex can be considered as a material entity. In addition to synoptic charts of geopotential heights and temperatures, maps of potential vorticity are used to describe some distinct features of the circulation of the winter stratosphere.
The results of a wind tunnel test to investigate the controlling effects of tangential, leading edge blowing on the vortical flow over a delta wing are given. Blowing is used to directly control the crossflow separation points at the rounded leading edge and hence, the trajectory of the feeding sheet and the location of the vortex. Experiments were conducted for both co-flowing and counter-flowing configurations over a range of angles of attack from 0 to 90 degrees. Results in the form of pressure distributions, overall force coefficients and flow mappings were obtained. The emphasis is on data presentation rather than detailed analysis. The initial results indicate that the co-flowing configuration was capable of extending the regime of stable, controlled vortical flow over the upper surface by approximately 30 degrees angle of attack for modest blowing requirements. Increases in maximum normal force coefficient of approximately 30% were achieved and significant rolling moments produced at angles of attack from 30 to 60 degrees. The counter-flowing configuration indicated only minor lift augmentation with the exception of an isolated occurrence at 20 degrees angle of attack. At that condition, with very weak blowing, a lift augmentation of approximately 20 was measured.
In the design analysis of conventional aircraft configurations, the prediction of the strong interaction between vortical wakes and the viscous flow field about bodies is of considerable importance. Interactions between vortical wakes and aircraft components are even more common on rotorcraft and configurations with lifting surfaces forward of the wing. An accurate analysis of the vortex-wake interaction with aircraft components is needed for the optimization of the payload and the reduction of vibratory loads. However, the three-dimensional flow field beneath the rotor disk and the interaction of the rotor wake with solid bodies in the flow field are highly complex. The present paper has the objective to provide a basis for the considered interactions by studying a simpler problem. This problem involves the two-dimensional interaction of external wakes with the viscous flow about a circular cylinder.
Numerical solutions to the Reynolds-averaged Navier-Stokes equations are given for the flow about an elliptical body missile (3:1 ellipse) at a Mach number of 2.5 and a unit Reynolds number of 6.56 x 10 to the 6th/m. At high angles of attack, the flow is dominated by large-scale free vortices which occur in the lee-side flow field due to crossflow boundary-layer separation. Emphasis is focused on the accurate prediction of the lee-side vortical flow. Solutions are presented for both symmetric and asymmetric (body rolled 45 deg) configurations at 10 deg and 20 deg angle of attack. The computed results are compared with experimental surface pressure coefficients and vapor-screen photographs. Excellent agreement is obtained in all cases.
A review is undertaken of some recent advances in the following areas: the encounter of distributed and concentrated vorticity at a single frequency with a leading-edge, the interaction of multiple concentrations of vorticity with an edge, the distortion due to finite scale and angle of attack of the leading-edge, and the penetration of the leading-edge interaction into the near-wake region. Time-sequence flow visualization and phase-coordinated pressure measurements provide physical insight into the mechanisms of flow distortion and loading. Promising paths for future research are suggested on the basis of recent progress.
A new velocity measurement technique is described that provides the simultaneous visualization of a two-dimensional streamline pattern and the quantification of the velocity field. The main advantage of this technique is that the velocity field can be measured with sufficient accuracy and spatial resolution so that the vorticity field can be readily obtained. This technique is ideally suited for the study of unsteady vortical flows, which occur in rotorcraft and in high-angle-of-attack aerodynamics. The technique, some of the important parameters that affect its use, and some recent examples are described.
Using the decomposition for the infinite-space, the issue of the nonuniqueness of the Helmholtz decomposition for the problem of the three-dimensional unsteady incompressible flow around a body is considered. A representation for the velocity that is valid for both the fluid region and the region inside the boundary surface is employed, and the motion of the boundary is described as the limiting case of a sequence of impulsive accelerations. At each instant of velocity discontinuity, vorticity is shown to be generated by the boundary condition on the normal component of the velocity, for both inviscid and viscous flows. In viscous flows, the vorticity is shown to diffuse into the surroundings, and the no-slip conditions are automatically satisfied. A trailing edge condition must be satisfied for the solution to the Euler equations to be the limit of the solution of the Navier-Stokes equations.
Thin layer Navier-Stokes and Euler equations are numerically solved using a multi-block zonal approach to simulate the formation and roll up of tip vortices of wings in subsonic and transonic flows. Several wing planforms were considered to examine the influence of tip-cap shape, planform geometry and free stream Mach number on the formation process. A good definition of the formation and qualitative roll up of tip vortices was achieved.
An exact expression is derived for the viscous dissipation function of a real homogeneous and isotropic fluid, which has terms associated with the square of vorticity, wave radiation, and dilatation. The implications of the principle of maximal dissipation rate, are explored by means of this equation for a parallel channel flow and a cylindrical vortex flow. The consequences of a condition of maximum dissipation rate on the growth of disturbances in an unsteady, laminar shear layer are apparently consistent with predictions and observations of maximum growth rate of vortical disturbances. Finally, estimates of the magnitudes of several dissipative components of an unsteady vortex flow are obtained from measurements of a periodic wall jet.
The development of Gortler vortices in boundary layers over curved walls in the nonlinear regime is investigated. The growth of the boundary layer makes a parallel flow analysis impossible except in the high wavenumber regime so in general the instability equations must be integrated numerically. Here the spanwise dependence of the basic flow is described using Fourier series expansion whilst the normal and streamwise variations are taken into account using finite differences. The calculations suggest that a given disturbance imposed at some position along the wall will eventually reach a local equilibrium state essentially independent of the initial conditions. In fact, the equilibrium state reached is qualitatively similar to the large amplitude high wave-number solution described asymptotically by Hall (1982). In general, it is found that the nonlinear interactions are dominated by a mean field type of interaction between the mean flow and the fundamental. Thus, even though higher harmonics of the fundamental are necessarily generated, most of the disturbance energy is confined to the mean flow correction and the fundamental. A major result of the calculations is finding that the downstream velocity field develops a strongly inflection character as the flow moves downstream. The latter result suggests that the major effect of Gortler vortices on boundary layers of practical importance might be to make them highly receptive to rapidly growing Rayleigh modes of instability.
The properties of ion phase-space vortices are reviewed with particular attention to their role in the formation of small amplitude double layers in current-carrying plasmas. In a one-dimensional analysis, many such double layers simply add up to produce a large voltage drop. A laboratory experiment is carried out in order to investigate the properties of ion phase-space vortices in three dimensions. Their lifetime is significantly reduced as compared with similar results from one-dimensional numerical simulations of the problem.
Progress in the numerical simulation of vortical flow due to three-dimensional flow separation about flight vehicles at high angles of attack and quasi-steady flight conditions is surveyed. Primary emphasis is placed on Euler and Reynolds-averaged Navier-Stokes methods where the vortices are 'captured' as a solution to the governing equations. A discussion of the relevant flow physics provides a perspective from which to assess numerical solutions. Current numerical prediction capabilities and their evolutionary development are surveyed. Future trends and challenges are identified and discussed.
Laser velocimetry (LV) was used to study the development of Goertler vortices in a laminar boundary layer on a 1.83 m chord airfoil model. The vortex pattern was visualized using a sublimating chemical technique. A fixed, essentially uniform vortex spacing was observed throughout the test region for any given freestream velocity but the vortex wavelength varied significantly with change in freestream velocity. An appreciable, abrupt decrease in streak contrast indicated vortex damping in the convex region and was confirmed by disturbance functions determined from LV measurements. Moderate variation in suction levels did not alter the vortex spacing but appreciably modified the vortex strength. The experimental results on the growth of Goertler vortices along the concave surface and the effect of suction are compared with results from linear stability theory.