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NASA NTRS1992

A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

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.

Felici, Helene Marie↗

NASA NTRS1994

Transverse vorticity measurements in the NASA Ames 80 x 120 wind tunnel boundary layer

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.

Foss, John F.↗

NASA NTRS1995

Nonlinear stability of non-stationary cross-flow vortices in compressible boundary layers

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.

Gajjar, J. S. B.↗

NASA NTRS1994

Zero potential vorticity envelopes for the zonal-mean velocity of the Venus/Titan atmospheres

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.

Allison, Michael↗

NASA NTRS1993

Northern hemisphere mid-stratosphere vortex processes diagnosed from H2O, N2O and potential vorticity

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.

Lahoz, W. A.↗

NASA NTRS1995

TOMS total ozone trends in potential vorticity coordinates

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.

Randel, William J.↗

NASA NTRS1996

A priori testing of subgrid-scale models for the velocity-pressure and vorticity-velocity formulations

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.

Winckelmans, G. S.↗

NASA NTRS1997

Measured Changes in C-Band Radar Reflectivity of Clear Air Caused by Aircraft Wake Vortices

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.

Mackenzie, Anne I.↗

NASA NTRS1994

On the vortical-flow-prediction capability of an unstructured-grid Euler solver

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.

Unstructured grid↗

NASA NTRS1960

Equations for the Induced Velocities Near a Lifting Rotor with Nonuniform Azimuthwise Vorticity Distribution

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.

Heyson, Harry H.↗

NASA NTRS1998

Stereo-Video Data Reduction of Wake Vortices and Trailing Aircrafts

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.

Alter-Gartenberg, Rachel↗

NASA NTRS1996

Development of a Vorticity-Velocity Navier-Stokes Formulation for the Study of Compressibility Effects on Dynamic Stall

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.

Ghia, K. N.↗

NASA NTRS1999

Persistence of the Lower Stratospheric Polar Vortices

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.

Waugh, Darryn W.↗

NASA NTRS1998

Shear-Layer Effects on Trailing Vortices

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.

Zheng, Z. C.↗

NASA NTRS1999

Constructing Synoptic Maps of Stratospheric Column Ozone from HALOE, SAGE and Balloonsonde Data Using Potential Vorticity Isentropic Coordinate Transformations

In this study we utilize potential vorticity - isentropic (PVI) coordinate transformations as a means of combining ozone data from different sources to construct daily, synthetic three-dimensional ozone fields. This methodology has been used successfully to reconstruct ozone maps in particular regions from aircraft data over the period of the aircraft campaign. We expand this method to create high-resolution daily global maps of profile ozone data, particularly in the lower stratosphere, where high-resolution ozone data are sparse. Ozone climatologies in PVI-space are constructed from satellite-based SAGE II and UARS/HALOE data, both of which-use solar occultation techniques to make high vertical resolution ozone profile measurements, but with low spatial resolution. A climatology from ground-based balloonsonde data is also created. The climatologies are used to establish the relationship between ozone and dynamical variability, which is defined by the potential vorticity (in the form of equivalent latitude) and potential temperature fields. Once a PVI climatology has been created from data taken by one or more instruments, high-resolution daily profile ozone field estimates are constructed based solely on the PVI fields, which are available on a daily basis from NCEP analysis. These profile ozone maps could be used for a variety of applications, including use in conjunction with total ozone maps to create a daily tropospheric ozone product, as input to forecast models, or as a tool for validating independent ozone measurements when correlative data are not available. This technique is limited to regions where the ozone is a long-term tracer and the flow is adiabatic. We evaluate the internal consistency of the technique by transforming the ozone back to physical space and comparing to the original profiles. Biases in the long-term average of the differences are used to identify regions where the technique is consistently introducing errors. Initial results show the technique is useful in the lower stratosphere at most latitudes throughout the year,and in the winter hemisphere in the middle stratosphere. The results are problematic in the summer hemisphere middle stratosphere due to increased ozone photochemistry and weak PV gradients. Alternate techniques in these regions will be discussed. An additional limitation is the quality and resolution of the meteorological data.

Hollandsworth, Stacey M.↗

NASA NTRS2000

Numerical Simulation of Aircraft Trailing Vortices

The increase in air traffic is currently outpacing the development of new airport runways. This is leading to greater air traffic congestion, resulting in costly delays and cancellations. The National Aeronautics and Space Administration (NASA) under its Terminal Area Productivity (TAP) program is investigating new technologies that will allow increased airport capacity while maintaining the present standards for safety. As an element of this program, the Aircraft Vortex Spacing System (AVOSS) is being demonstrated in July 2000, at Dallas Ft-Worth Airport. This system allows reduced aircraft separations, thus increasing the arrival and departure rates, while insuring that wake vortices from a leading aircraft do not endanger trailing aircraft. The system uses predictions or wake vortex position and strength based on input from the current weather state. This prediction is accomplished by a semi-empirical model developed from theory, field observations, and relationships derived from numerical wake vortex simulations. Numerical experiments with a Large Eddy Simulation (LES) model are being conducted in order to provide guidance for the enhancement of these prediction algorithms. The LES Simulations of wake vortices are carried out with NASA's Terminal Area Simulation System (TASS). Previous wake vortex investigations with TASS are described. The primary objective of these numerical studies has been to quantify vortex transport and decay in relation to atmospheric variables. This paper summarizes many of the previous investigations with the TASS model and presents some new results regarding the onset of wake vortex decay.

Proctor, Fred H.↗

NASA NTRS1998

History of Research on Lift-Generated Vortices

A theoretical and experimental program on the structure and possible modification of lift-generated vortices shed by subsonic aircraft has been underway at NASA Ames Research Center since the late 1960's. The objectives of the program were to first obtain a better understanding of the hazard posed by the vortex wakes of subsonic transports, and then to develop methods on how to modify or design the wake-generating aircraft in order to make the vortices less hazardous. Some effort was also expended on the development of methods to avoid vortex wakes. The seminar will present a brief history of the research program beginning with the nature of vortex wakes and their relationship to the span loading on the wake-generating wing. Examples will then be presented to show how span-loading changes were used to influence the dynamics of the vortex wakes shed by subsonic transport aircraft. Video tape segments will be shown to illustrate the dynamics of vortex wakes and the flight tests carried out by NASA to find out how configurations developed in wind tunnels would perform on flight vehicles. The presentation will then summarize some recent results obtained in the 80- by 120-Foot Wind Tunnel at NASA Ames Research Center on the vortex wakes that trail from 0.03 scale models of a B-747 and of a DC-10 at downstream distances of 81 ft and 162 ft behind the wake-generating model; i.e., at scale distances of 0.5 and 1.0 mile. Lastly, a proposed vortex avoidance scheme based on the Global Positioning System will be described. All of the material to be presented is publically available in technical journals.

Rossow, Vernon J.↗

NASA NTRS1996

Numerical Simulation of Wake Vortices Measured During the Idaho Falls and Memphis Field Programs

A numerical large-eddy simulation model is under modification and testing for application to aircraft wake vortices. The model, having a meteorological framework, permits the interaction of wake vortices with environments characterized by crosswind shear, stratification, and humidity. As part of the validation process, model results are compared with measured field data from the 1990 Idaho Falls and the 1994-1995 Memphis field experiments. Cases are selected that represent different aircraft and a cross section of meteorological environments. Also included is one case with wake vortex generation in ground effect. The model simulations are initialized with the appropriate meteorological conditions and a post roll-up vortex system. No ambient turbulence is assumed in our initial set of experiments, although turbulence can be self generated by the interaction of the model wakes with the ground and environment.

Proctor, Fred H.↗