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NASA NTRS1988

Two-dimensional interaction of vortices with a blade

The problem of blade-vortex interaction is studied experimentally and numerically. Vortices are generated in the laboratory by pitching an airfoil upstream of the model. LDV measurements are obtained in the neighborhood of the leading edge of the airfoil. Ensemble-averaged velocity vector fields and vorticity contours are thus constructed. A vortex is modeled numerically by a cloud of discrete ideal point vortices. The problem is solved via a Joukowski transformation. The interaction of distributed vorticity with the leading edge of the airfoil is examined.

Poling, David R.↗

NASA NTRS1988

The fully nonlinear development of Goertler vortices in growing boundary layers

A combination of asymptotic and numerical methods is used to study the fully nonlinear development of small-wavelength Goertler vortices in a growing boundary layer. It is shown that the vortices spread out across the boundary layer, effectively driving the boundary layer, and that the mean flow adjusts so as to make the large-amplitude vortices locally neutral. In the region where the vortices exist, the mean flow is found to have a square-root profile, and the vortex velocity field can be written in closed form. The region of vortex activity is shown to ultimately include almost all of the original boundary layer and much of the free stream.

Hall, P.↗

NASA NTRS1987

Streamline-upwind/Petrov-Galerkin procedures for the vorticity-stream function form of the Navier-Stokes equations

The paper presents procedures for the solution of the Navier-Stokes equations in the vorticity-stream function form. The difficulties involved are related to the convection term in the vorticity transport equation and to the lack of boundary conditions for voritcity at no-slip surfaces. The use of a streamline-upwind/Petrov-Galerkin finite element formulation for the solution of the vorticity transport equation. In the present scheme, the weighting functions are dependent on both spatial and temporal discretizations. A proper numerical treatment of the boundary conditions leading to an implicit treatment of the vorticity at no-slip surfaces is presented. These procedures have successfully been employed to simulate various flows of engineering interest.

Tezduyar, T. E.↗

NASA NTRS1990

Pinning, flow and plastic deformation of flux vortices in high T(sub c) superconductors

In high temperature superconductor (HTSC) materials the vortices are highly mobile and flexible. This is reflected in different models of melt of a vortex lattice. Another aspect of the problem is stressed: an easy nucleation and high mobility of dislocations in the vortex lattice. Some models of plastic deformation of vortex lattice are considered as a result of its interaction with a real crystal structure. Depinning is interpreted as yield of plastic flow is vortex medium. Effect of macroscopic defects in crystal structures (pores, inclusions, grain and domain boundaries) is being considered in detail. Available experimental facts on magnetization and a critical current in HTSC and conventional superconductors are discussed from the points of view of depinning to vortices vs. plastic flow of vortices vs. plastic flow of vortices medium.

Roytburd, A.↗

NASA NTRS1989

The effects of streamwise vortices on transition in the plane channel

The effect of streamwise vorticity on the three-dimensional breakdown of two-dimensional Tollmien-Schlichting waves in a plane-channel flow is studied via direct numerical simulation. Streamwise vortices of the strength inherent to most transition experiments are shown to alter the relative importance of the subharmonic and fundamental modes and to explain discrepancies observed between theory, previous computations, and experiments in both the plane channel and in the flat-plate boundary layer. It is shown that without the inclusion of the vortices, the computations support the theory; with inclusion of the vortices, the computations support the experiments. This work demonstrates the importance of combining theory, experiments, and computations in the study of transition in both internal and external applications.

Singer, Bart A.↗

NASA NTRS1990

Reciprocal interactions of hairpin-shaped vortices and a boundary layer

The present effort simulates the flow dynamics resulting from hairpin-shaped vortices in a boundary layer through the solution of the time-dependent, three-dimensional, compressible Navier-Stokes equations. Two simulations have been carried out. In the first case, the initial condition contains only one imposed hairpin-shaped vortex. In the second case, there are two incipient vortices separated by a short distance in the streamwise direction. The results add to the detailed understanding of the dynamic role of hairpin vortices in the entrainment, production and continual replenishment of turbulent structure, as well as the process of the interaction, intertwining and eventual conglomeration of vortices in boundary layers.

Liu, N.-S.↗

NASA NTRS1990

Blade-vortex interaction experiments - Velocity and vorticity fields

The blade-vortex interaction problem is studied experimentally with laser-Doppler velocimetry. Vortices are generated by pitching a NACA 0012 airfoil about its quarter chord and a target airfoil is mounted two chord lengths downstream of the vortex generator. LDV measurements are obtained in the neighborhood of the target airfoil's leading edge and ensemble-averaged velocity vector fields and vorticity contours are constructed. Vorticity fields are also constructed from velocity time records by assuming that, over short distances, the vorticity propagates with the local velocity. This assumption allows the blade-vortex interaction to be simulated from very few measurements.

Wilder, Michael C.↗

NASA NTRS1989

The breakup of trailing-line vortices

It is now known that Batchelor's trailing-line vortex is extremely unstable to small amplitude disturbances for swirl numbers in the neighborhood of 0.83. The results of numerical calculations are presented that show the response of the vortex in this range of swirl numbers to finite amplitude, temporal, helical disturbances. Phenomena observed include: (1) ejection of axial vorticity and momentum from the core resulting in the creation of secondary, separate vortices; (2) a great intensification of core axial vorticity and a weakening of core momentum; and (3) the production of azimuthal vorticity in the form of a tightly wrapped spiral wave. The second phenomenon eventually stablizes the vortex, which then smooths and gradually returns to an axisymmetric state. The calculations are mixed spectral-finite-difference, fourth-order accurate, and have been carried out at Reynolds numbers of 1000 to 2000. Some linearized results are also discussed in an attempt to explain the process of vortex intensification.

Jacqmin, David↗

NASA NTRS1990

In defense of Ertel's potential vorticity and its general applicability as a meteorological tracer

A potential vorticity theorem and its two summary statements published by Haynes and McIntyre are challenged conceptually by equations, discussions and examples. The apparent simplification proposed by the authors to convert from a mass to volume integral, i.e., by cancelling density against the specific volume in the potential vorticity, changes the physical significance of the integrand. It no longer is the potential vorticity. The resulting mean for either a bulk Eulerian or Lagrangian system is then not analogous to a mixing ratio and therefore not independent of the broad spectrum of internal waves, the independence that makes Ertel's potential vorticity so valuable either as a stratospheric tracer or as a predictive or diagnostic, large scale, meteorological variable.

Danielsen, Edwin F.↗

NASA NTRS1991

Vorticity and divergence in the high-latitude upper thermosphere

Measurements made from the Dynamics Explorer-2 satellite in November 1981 through January 1982 and November 1982 through January 1983 have been analyzed to determine the divergence and the vertical component of vorticity of the high-latitude neutral wind field in the upper thermosphere for quiet (Kp not greater than 3) and active (Kp between 3+ and 6) geomagnetic conditions and for both Northern (winter) and Southern (summer) Hemispheres. This analysis provides the first experimental determination of the large-scale vorticity and divergence patterns in the polar thermosphere and provides insight into the relative strengths of the different sources of momentum and energy responsible for driving the winds. The principal findings from this work include the following: the mean neutral wind pattern is dominated by rotational flow rather than by divergent flow, with a typical vorticity:divergence ratio of about 2:1 for active conditions and about 4:1 for quiet conditions. Comparison of the divergence and vorticity patterns for quiet and active conditions indicates that the divergent component of the neutral flow intensifies more significantly with increasing geomagnetic activity than does the rotational component.

Thayer, J. P.↗

NASA NTRS1992

Polar stratospheric cloud processed air and potential vorticity in the Northern Hemisphere lower stratosphere at mid-latitudes during winter

The present study compares small-scale (less than 100 km) features in ER-2 measurements of ClO, O3, H2O, N2O, and NO(y) outside the lower stratospheric Arctic vortex of 1988-1989 with features on potential vorticity maps from ECMWF. The potential vorticity maps are obtained from T106 analyses and forecasts. Some of the plots were truncated to lower resolution (T63 or T42) which smooths out the finer-scale structure. Comparison of these lower resolution plots shows how much detail is lost by excessive smoothing. It is also evident that the forecast plots lose fine-scale structure due to dissipation in the model resulting mainly from horizontal diffusion. It is concluded that blobs of air on the maps at latitudes between the vortex edge and 25 deg N having potential vorticities characteristic of the vortex did indeed originate from the vortex, but that the real atmosphere is more sharply differentiated than the meteorological analyses, implying that the potential vorticity maps underestimate the amount of peeled-off material.

Tuck, A. F.↗

NASA NTRS1992

Investigation of forced unsteady separated flows using velocity-vorticity form of Navier-Stokes equations

The phenomenon of forced unsteady separation and eruption of boundary-layer vorticity is a highly-complex, high-Reynolds number flow phenomenon, which abruptly leads to the formation of a dynamic stall vortex as demonstrated earlier by the authors for a NACA 0015 airfoil undergoing constant rate pitch-up motion. This, as well as the results of other researchers, have convincingly demonstrated a complex vortical structure within the state of unsteady separation prior to the evolution of dynamic stall. This phenomenon of vortex eruption, although observed in studying dynamic stall phenomena, is also associated with transition from laminar to turbulence flow and its generic nature has been stressed by many researchers including the present investigators. An unsteady Navier-Stokes (NS) analysis is developed for arbitrarily maneuvering bodies using velocity-vorticity variables; this formulation is nearly form-invariant under a generalized non-inertial coordinate transformation. A fully-implicit uniformly second-order accurate method is used, with the nonlinear convective terms approximated using a biased third-order upwind differencing scheme to be able to simulate higher-Re flows. No explicit artificial dissipation is added. The numerical method is fully vectorized and currently achieves a computational index of 7 micro-seconds per time step per mesh point, using a single processor on a CRAY Y-MP. The simulation results show that the energetic free shear from the leading edge is responsible for the wall viscous layer to abruptly erupt near the center of the counterclockwise rotating eddy in the unsteady boundary layer. Primary, secondary, tertiary and quaternary vortices have been observed before the dynamic stall vortex evolves and gathers its maximum strength. This study will discuss the simulation results of Reynolds number up to Re = 45,000 and will also discuss the efforts of initial acceleration in a specific maneuver, on the evolution of the stall vortex.

Ghia, K. N.↗

NASA NTRS1992

Invariant two-dimensional structures of vorticity field in nonviscous fluid

It is shown that a fluid flow which are invariant under translations along their vorticity field directions can be described in terms of a formally 2D system. Its nonviscous behavior of the scalar vorticity is governed by Hamiltonian dynamics, similar to the 2D line vortex case. Applying a statistical mechanical method, the equilibrium distribution of the vorticity field for such a general 2D system is shown to obey a nonlinear partial differential equation that is a generalization of the sinh-Poisson equation derived by Montgomery and Joyce (1973, 1974). Thus, if the domain containing the fluid is finite, similar negative temperature states may occur and the distribution of the vorticity intensity may become localized in space. The results are believed to have applications in studying large-scale partial and temporal properties of flows having small but nonzero viscosity. The analysis can probably be extended to other fluid systems with curved magnetic field lines.

Chen, Hudong↗

NASA NTRS1993

Numerical vorticity capturing for vortex-solid body interaction problems

A new numerical method based on adding a term to the Euler/Navier-Stokes equations has been demonstrated it can effectively treat vortex-dominated flows using low-order numerical schemes and coarse grids. The numerical diffusion introduced by convection schemes can be eliminated by modifying the velocity field as a result of solving the modified flow governing equations. The modification of the velocity field, which conserves the total vorticity, essentially convects the vorticity toward its local extreme to offset the numerical diffusion. This method preserves the vortex structure even when vortices travel on coarse grid region. The method is implemented with two distinctive codes: a Navier-Stokes flow solver based on vorticity-velocity formulation and an Euler code based on velocity-pressure formulation. Problems presented in this paper include airfoil dynamic stall, vortex airfoil interaction, and vortex-fuselage interactions.

Wang, Clin M.↗

NASA NTRS1993

Streaming vorticity flux from oscillating walls with finite amplitude

How to describe vorticity creation from a moving wall is a long standing problem. This paper discusses relevant issues at the fundamental level. First, it is shown that the concept of 'vorticity flux due to wall acceleration' can be best understood by following fluid particles on the wall rather than observing the flow at fixed spatial points. This is of crucial importance when the time-averaged flux is to be considered. The averaged flux has to be estimated in a wall-fixed frame of reference (in which there is no flux due to wall acceleration at all); or, if an inertial frame of reference is used, the generalized Lagrangian mean (GLM) also gives the same result. Then, for some simple but typical configurations, the time-averaged vorticity flux from a harmonically oscillating wall with finite amplitude is analyzed, without appealing to small perturbation. The main conclusion is that the wall oscillation will produce an additional mean vorticity flux (a fully nonlinear streaming effect), which is partially responsible for the mechanism of vortex flow control by waves. The results provide qualitative explanation for some experimentally and/or computationally observed phenomena.

Wu, J. Z.↗

NASA NTRS1994

3D visualization of unsteady 2D airplane wake vortices

Air flowing around the wing tips of an airplane forms horizontal tornado-like vortices that can be dangerous to following aircraft. The dynamics of such vortices, including ground and atmospheric effects, can be predicted by numerical simulation, allowing the safety and capacity of airports to be improved. In this paper, we introduce three-dimensional techniques for visualizing time-dependent, two-dimensional wake vortex computations, and the hazard strength of such vortices near the ground. We describe a vortex core tracing algorithm and a local tiling method to visualize the vortex evolution. The tiling method converts time-dependent, two-dimensional vortex cores into three-dimensional vortex tubes. Finally, a novel approach calculates the induced rolling moment on the following airplane at each grid point within a region near the vortex tubes and thus allows three-dimensional visualization of the hazard strength of the vortices. We also suggest ways of combining multiple visualization methods to present more information simultaneously.

Ma, Kwan-Liu↗

NASA NTRS1995

The decay of longitudinal vortices shed from airfoil vortex generators

An experimental study is conducted to examine the crossplane structure and streamwise decay of vortices shed from airfoil-type vortex generators. The vortex generators are set in a counter-rotating array spanning the full circumference of a straight pipe. The span of the vortex generators above the duct surface, h, is approximately equal to the local turbulent boundary layer thickness, delta. Measurement of three-component mean flow velocity in downstream crossplanes are used to characterize the structure of the shed vortices. Measurements in adjacent crossplanes (closely spaced along the streamwise coordinate) characterize the interaction and decay of the embedded vortices. A model constructed by the superposition of Oseen vortices is compared to the data for one test case.

Wendt, Bruce J.↗

NASA NTRS1994

Vorticity and Vertical Motions Diagnosed from Satellite Deep-Layer Temperatures

Spatial fields of satellite-measured deep-layer temperatures are examined in the context of quasigeostrophic theory. It is found that midtropospheric geostrophic vorticity and quasigeostrophic vertical motions can be diagnosed from microwave temperature measurements of only two deep layers. The lower- ( 1000-400 hPa) and upper- (400-50 hPa) layer temperatures are estimated from limb-corrected TIROS-N Microwave Sounding Units (MSU) channel 2 and 3 data, spatial fields of which can be used to estimate the midtropospheric thermal wind and geostrophic vorticity fields. Together with Trenberth's simplification of the quasigeostrophic omega equation, these two quantities can be then used to estimate the geostrophic vorticity advection by the thermal wind, which is related to the quasigeostrophic vertical velocity in the midtroposphere. Critical to the technique is the observation that geostrophic vorticity fields calculated from the channel 3 temperature features are very similar to those calculated from traditional, 'bottom-up' integrated height fields from radiosonde data. This suggests a lack of cyclone-scale height features near the top of the channel 3 weighting function, making the channel 3 cyclone-scale 'thickness' features approximately the same as height features near the bottom of the weighting function. Thus, the MSU data provide observational validation of the LID (level of insignificant dynamics) assumption of Hirshberg and Fritsch.

Spencer, Roy W.↗