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This note, prepared for the NACA, contains a discussion of the meaning of vortices, so often mentioned in connection with the creation of lift by wings. The action of wings can be more easily understood without the use of vortices.
In this paper, we make an investigation of the receptivity of boundary layer flows to Gortler vortex modes. A study by Denier, Hall, and Seddougui (1991) of the generation of vortices by wall roughness elements concluded that such elements are extremely poor as mechanisms to stimulate short wavelength modes, but that analysis was in error. We re-examine this problem and demonstrate how the form of the wall roughness is crucial in determining the vortex stability characteristics downstream of the roughness. In particular, we investigate the cases of both isolated and distributed forcing functions and show that, in general, a distributed function is much more important in generating vortices than are either isolated roughness or freestream disturbances.
Wingtip vortices are generated by lifting airfoils; their salient features are compactness and relatively slow rate of decay. The principal motivation for studying the far field evolution of wingtip vortices is the need to understand and predict the extent of the vortex influence during aircraft take-off or landing. On submarines a wingtip vortex ingested into a propeller can be a source of undesirable noise. The main objectives of this research are (1) to establish theoretical understanding of the principal mechanisms that govern the later (diffusive) stages of a turbulent vortex, (2) to develop a turbulence closure model representing the basic physical mechanisms that control the vortex diffusive stage, and further (3) to investigate coupling between the near and far field evolutions; in other words, to study the effect of initial conditions on the vortex lifetime and the ultimate state.
The unsteady flow structure of leading-edge vortices on a delta wing has been investigated using new types of experimental techniques, in order to provide insight into the consequences of various forms of active control. These investigations involve global control of the entire wing and local control applied at crucial locations on or adjacent to the wing. Transient control having long and short time-scales, relative to the convective time-scale C/U(sub infinity), allows substantial modification of the unsteady and time-mean flow structure. Global control at long time-scale involves pitching the wing at rates an order of magnitude lower than the convective time-scale C/U(sub infinity), but at large amplitudes. The functional form of the pitching maneuver exerts a predominant influence on the trajectory of the feeding sheet, the instantaneous vorticity distribution, and the instantaneous location of vortex breakdown. Global control at short time-scales of the order of the inherent frequency of the shear layer separating from the leading-edge and the natural frequency of vortex breakdown shows that 'resonant' response of the excited shear layer-vortex breakdown system is attainable. The spectral content of the induced disturbance is preserved not only across the entire core of the vortex, but also along the axis of the vortex into the region of vortex breakdown. This unsteady modification results in time-mean alteration of the axial and swirl velocity fields and the location of vortex breakdown. Localized control at long and short time-scales involves application of various transient forms of suction and blowing using small probes upstream and downstream of the location of vortex breakdown, as well as distributed suction and blowing along the leading-edge of the wing applied in a direction tangential to the feeding sheet. These local control techniques can result in substantial alteration of the location of vortex breakdown; in some cases, it is possible to accomplish this without net mass addition to the flow field.
A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.
The MSU compact four-wire transverse vorticity probe permits omega(sub z)(t) measurements in a nominally 1 sq mm domain. Note that a conventional coordinate system is used with x and y in the streamwise and normal directions respectively. The purpose of this investigation was to acquire time series data in the same access port at the ceiling of the 80 ft x 120 ft wind tunnel (NASA Ames Research Center) as earlier used by the Wallace group from the University of Maryland and to compare the present results with those of the three-component vorticity probe used in that earlier study.
The nonlinear evolution of long wavelength non-stationary cross-flow vortices in a compressible boundary layer is investigated and the work extends that of Gajjar (1994) to flows involving multiple critical layers. The basic flow profile considered in this paper is that appropriate for a fully three-dimensional boundary layer with O(1) Mach number and with wall heating or cooling. The governing equations for the evolution of the cross-flow vortex are obtained and some special cases are discussed. One special case includes linear theory where exact analytic expressions for the growth rate of the vortices are obtained. Another special case is a generalization of the Bassom & Gajjar (1988) results for neutral waves to compressible flows. The viscous correction to the growth rate is derived and it is shown how the unsteady nonlinear critical layer structure merges with that for a Haberman type of viscous critical layer.
The diagnostic analysis of numerical simulations of the Venus/Titan wind regime reveals an overlooked constraint upon the latitudinal structure of their zonal-mean angular momentum. The numerical experiments, as well as the limited planetary observations, are approximately consistent with the hypothesis that within the latitudes bounded by the wind maxima the total Ertel potential vorticity associated with the zonal-mean motion is approximately well mixed with respect to the neutral equatorial value for a stable circulation. The implied latitudinal profile of angular momentum is of the form M equal to or less than M(sub e)(cos lambda)(exp 2/Ri), where lambda is the latitude and Ri the local Richardson number, generally intermediate between the two extremes of uniform angular momentum (Ri approaches infinity) and uniform angular velocity (Ri = 1). The full range of angular momentum profile variation appears to be realized within the observed meridional - vertical structure of the Venus atmosphere, at least crudely approaching the implied relationship between stratification and zonal velocity there. While not itself indicative of a particular eddy mechanism or specific to atmospheric superrotation, the zero potential vorticity (ZPV) constraint represents a limiting bound for the eddy - mean flow adjustment of a neutrally stable baroclinic circulation and may be usefully applied to the diagnostic analysis of future remote sounding and in situ measurements from planetary spacecraft.
Microwave Limb Sounder (MLS) H2O Cryogenic Limb Array Etalon Spectrometer (CLAES) N2O and potential vorticity calculated from UK Meteorological Office data are used to study mid-stratospheric vortex processes in the northern hemisphere winter of 1991-1992. Areas of moist air (at approx. 20 hPa) and N2O-poor air (at approx. 10hPa) are well-correlated with high values of potential vorticity and there is little or no large scale mixing across the vortex edge. We find evidence for the descent of relatively dry mesospheric air to the 840 K (approx. 10 hPa) level, as well as descent of moist air from the upper stratosphere to the 655 K (approx. 20 hPa) level. A reduction in the areas of the vortex and both the moist and H2O-poor regions is observed and there is evidence of moist and N2O-poor air parcels being extruded from the vortex.
Global total ozone measurements from the Nimbus 7 Total Ozone Mapping Spectrometer (TOMS) are analyzed using potential vorticity (PV) as an approximate vortex-following coordinate. We analyze the time period November 1978-May 1991, prior to the volcanic eruption of Mt. Pinatubo. The TOMS data are remapped into PV coordinates and trends are calculated, thereby characterizing ozone losses inside and outside the winter polar vortices. These analyses show large regions of ozone loss outside of the vortex in both hemispheres. Furthermore, these data suggest that midlatitude losses in the NH during winter-spring do not result solely from the transport of ozone depleted air from inside to outside the vortex.
Subgrid-scale models for Large Eddy Simulation (LES) in both the velocity-pressure and the vorticity-velocity formulations were evaluated and compared in a priori tests using spectral Direct Numerical Simulation (DNS) databases of isotropic turbulence: 128(exp 3) DNS of forced turbulence (Re(sub(lambda))=95.8) filtered, using the sharp cutoff filter, to both 32(exp 3) and 16(exp 3) synthetic LES fields; 512(exp 3) DNS of decaying turbulence (Re(sub(Lambda))=63.5) filtered to both 64(exp 3) and 32(exp 3) LES fields. Gaussian and top-hat filters were also used with the 128(exp 3) database. Different LES models were evaluated for each formulation: eddy-viscosity models, hyper eddy-viscosity models, mixed models, and scale-similarity models. Correlations between exact versus modeled subgrid-scale quantities were measured at three levels: tensor (traceless), vector (solenoidal 'force'), and scalar (dissipation) levels, and for both cases of uniform and variable coefficient(s). Different choices for the 1/T scaling appearing in the eddy-viscosity were also evaluated. It was found that the models for the vorticity-velocity formulation produce higher correlations with the filtered DNS data than their counterpart in the velocity-pressure formulation. It was also found that the hyper eddy-viscosity model performs better than the eddy viscosity model, in both formulations.
Wake vortices from a C-130 airplane were observed at the NASA Wallops Flight Facility with a ground-based, monostatic C-band radar and an antenna-mounted boresight video camera. The airplane wake was viewed from a distance of approximately 1 km, and radar scanning was adjusted to cross a pair of marker smoke trails generated by the C-130. For each airplane pass, changes in radar reflectivity were calculated by subtracting the signal magnitudes during an initial clutter scan from the signal magnitudes during vortex-plus-clutter scans. The results showed both increases and decreases in reflectivity on and near the smoke trails in a characteristic sinusoidal pattern of heightened reflectivity in the center and lessened reflectivity at the sides. Reflectivity changes in either direction varied from -131 to -102 dBm(exp -1); the vortex-plus-clutter to noise ratio varied from 20 to 41 dB. The radar recordings lasted 2.5 min each; evidence of wake vortices was found for up to 2 min after the passage of the airplane. Ground and aircraft clutter were eliminated as possible sources of the disturbance by noting the occurrence of vortex signatures at different positions relative to the ground and the airplane. This work supports the feasibility of vortex detection by radar, and it is recommended that future radar vortex detection be done with Doppler systems.
The results from a concentrated computational effort are presented with the primary objective being directed at evaluating the vortical-flow-prediction capability of an unstructured-grid Euler solver. Both viscous and inviscid solutions, obtained from an established structured-grid method, along with experimental wind-tunnel data are used as benchmark measures to assess the validity of the unstructured-grid Euler results. Viscous effects on vortical flows are first identified by comparing the viscous and inviscid solutions obtained from the structured-grid method. Computational data analysis is then presented which reveals excellent correlations between the inviscid structured and unstructured-grid results in terms of off-surface flow structures, surface pressure distribution, and the predicted longitudinal aerodynamic characteristics. The sensitivity of the unstructured-grid inviscid solutions to grid refinement is also discussed along with an analysis of the convergence and performance characteristics for each method.
Equations, which can be integrated on high-speed computing machines, are developed for all three components of induced velocity at an arbitrary point near the rotor and for an arbitrary harmonic variation of vorticity. Sample calculations for vorticity which varies as the sine of the azimuth angle indicate that the normal component of induced velocity is, in this case, uniform along either side of the lateral axis.
This report presents stereo image theory and the corresponding image processing software developed to analyze stereo imaging data acquired for the wake-vortex hazard flight experiment conducted at NASA Langley Research Center. In this experiment, a leading Lockheed C-130 was equipped with wing-tip smokers to visualize its wing vortices, while a trailing Boeing 737 flew into the wake vortices of the leading airplane. A Rockwell OV-10A airplane, fitted with video cameras under its wings, flew at 400 to 1000 feet above and parallel to the wakes, and photographed the wake interception process for the purpose of determining the three-dimensional location of the trailing aircraft relative to the wake. The report establishes the image-processing tools developed to analyze the video flight-test data, identifies sources of potential inaccuracies, and assesses the quality of the resultant set of stereo data reduction.
The first major area of this study was to develop a vorticity-velocity formulation and numerical solution algorithms suitable for the analyses of incompressible as well as low-to- moderate-speed compressible flows. Research performed towards contributing to the determination of the appropriate vorticity and dilation creation boundary conditions suggested to temporarily set aside this approach and use a primitive-variable approach other than the pseudo-compressibility approach used. The second major area of study was initiated to comprehensively examine the INS-2D and INS-3D programs from the point of view of boundary conditions. The research carried out was documented in the form of two technical papers which are included in Appendices A and B; the boundary-condition related issues for INS-3D are briefly mentioned.
The persistence of the Arctic and Antarctic lower stratospheric vortices is examined over the period 1958 to 1998. Three different vortex-following diagnostics (two using potential vorticity and one based solely on the zonal winds) are compared, and shown to give very similar results for the break up date. The variability in the timing of the breakup of each vortex is qualitatively the same: there are large interannual variations together with smaller decadal-scale variations and there is a significant increase in the persistence since the mid-1980s (all variations are larger for the Arctic vortex). Also, in both hemispheres there is a high correlation between the persistence and the strength and coldness of the spring vortex, with all quantities having the same interannual and decadal variability. However, there is no such correlation between the persistence and the characteristics of the mid-winter vortex. In the northern hemisphere there is also a high correlation between the vortex persistence and the upper tropospheric/lower stratospheric eddy heat flux averaged over the two months prior to the breakup. This indicates that the variability in the wave activity entering the stratosphere over late-winter to early-spring plays a key role in the variability of the vortex persistence (and spring polar temperatures) on both interannual and decadal time scales. However, the decadal variation in the Arctic vortex coldness and persistence for the 1990's falls outside the range of natural variability, while this is not the case for the eddy heat flux. This suggests that the recent increase in vortex persistence is not due solely to changes in the wave activity entering the stratosphere.
Crosswind shear can influence the trailing vortex trajectories significantly, according to both field measurement and numerical simulations. Point vortex models are used in this paper to study the fluid dynamic mechanism in the interactions between trailing vortex pair and shear layers. It has been shown that the shear-layer deformation causes the vortex descent history difference in the two vortices of the vortex pair. When a shear layer is below the vortex pair with the same sign as the left vortex, the right vortex descends less than the left vortex. When the same shear layer is above the vortex pair, the right vortex descends more. The descent altitudes of the two vortices are the same when they go through a constant, non-deformed shear layer. Those trends are in agreement with Navier-Stokes simulations.