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NASA NTRS1986

The structure of the vorticity field in turbulent channel flow. II - Study of ensemble-averaged fields

Several conditional sampling techniques are applied to a data base generated by large-eddy simulation of turbulent channel flow. It is shown that the bursting process is associated with well-organized horseshoe vortices inclined at about 45 deg to the wall. These vortical structures are identified by examining the vortex lines of three-dimensional, ensemble averaged vorticity fields. Two distinct horseshoe-shaped vortices corresponding to the sweep and ejection events are detected. These vortices are associated with high Reynolds shear stress and hence make a significant contribution to turbulent energy production. The dependency of the ensemble averaged vortical structures on the detection criteria, and the question of whether this ensemble-averaged structure is an artifact of the ensemble averaging process are examined. The ensemble-averaged pattern of these vortical structures that emerge from the analysis could provide the basis for a hypothetical model of the organized structures of wall-bounded shear flows.

Kim, J.↗

NASA NTRS2007

Hairpin Vortices and the Final Stages of Transition

A spatially developing direct numerical simulation has been performed for flow over a flat plate that is subjected to a one-time fluid injection through an elongated slit in the wall. The flow parameters have been chosen to closely approximate the experimental conditions of Haidari, Taylow, and Smith (AIAA-89-0964). A hairpin vortex quickly develops near the upstream end of the slit, and a pair of necklace vortices form around the slow-moving injection fluid. As seen in the experiments and reported in Haidari and Smith (in review, JFM), the hairpin vortex spawns both in-line and sidelobe secondary vortices. However, no subdsidiary vortices (those formed by the inviscid deformation of a vortex-line bundle) are observed. At later times, a set of three different types of vortices are identified: hairpin vortex structures with heads that rise away from the wall horseshoe-shaped vortices that do not rise out of the boundary layer, and quasi-streamwise vortices. These structures interact with each other and with the wall layer to generate new vortices that are similar in structure to those mentioned above, although a particular parent vortex may have an offspring that more nearly resembles another member of the set. Perturbation velocity and vertical vorticity contours reveal an arrowhead shape of the highly disturbed region that is reminiscent of a turbulent spot. Spatially averaged velocity profiles in the highly disturbed area are nonlaminar, but as yet do not show typical low-of-the-wall behavior.

Singer, Bart A.↗

NASA NTRS1987

Heat transfer with very high free-stream turbulence and heat transfer with streamwise vortices

Two experimental programs related to augmentation of heat transfer by complex flow characteristics are reviewed. The first program deals with very high turbulence (up to 63 percent) which was shown to result in Stanton numbers as much as five times the expected values. Results from a number of trials show that fixing the free stream velocity, x-Reynolds number, turbulence intensity and integral length scale does not fix the Stanton number. Two such cases were found in which the Stanton number of one was 40 percent larger than the other. Mean velocity and mean temperature profiles are presented, as well as profiles of turbulence intensity within the boundary layer. The second program deals with vortices originating at bluff bodies and traveling downstream embedded in the wall boundary layer. Velocity vector maps from the boundary layers and distributions of Stanton number on the wall are presented for three types of bodies: square, cylindrical and teardrop. The heat transfer and velocity maps do not show evidence of the expected horseshoe vortices but, instead, show a strong common flow up vortex pair. The fluid mechanic mechanism responsible for this secondary flow field has not yet been identified.

Moffat, Robert J.↗

NASA NTRS1991

Increased heat transfer to a cylindrical leading edge due to spanwise variations in the freestream velocity

The present study numerically demonstrates how small spanwise variations in velocity upstream of a body can cause relatively large increases in the spanwise-averaged heat transfer to the leading edge. Vorticity introduced by spanwise variations, first decays as it drifts downstream, then amplifies in the stagnation region as a result of vortex stretching. This amplification can cause a periodic array of 3D structures, similar to horseshoe vortices, to form. The numerical results indicate that, for the given wavelength, there is an amplitude threshold below which a structure does not form. A one-dimensional analysis, to predict the decay of vorticity in the absence of the body, in conjunction with the full numerical results indicated that the threshold is more accurately stated as minimum level of vorticity required in the leading edge region for a structure to form. It is possible, using the one-dimensional analysis, to compute an optimum wavelength in terms of the maximum vorticity reaching the leading edge region for given amplitude. A discussion is presented which relates experimentally observed trends to the trends of the present phenomena.

Rigby, D. L.↗

NASA NTRS1993

Separated flow generated by a vectored jet in a crossflow

Results of an experimental investigation to determine the characteristics of the separated flow region generated by a subsonic vectored rectangular jet in a subsonic crossflow is presented. Using surface visualization techniques, it was found that the upstream separated flow consist of horseshoe vortices that are formed periodically with a frequency corresponding to that of the vortex shedding behind the jet. The size of the recirculation region around the jet is found to decrease with increasing jet vector angle. The variation of the mean primary separation distance upstream of the jet, with velocity ratio revealed the existence of two different flow regimes. The change from one to the other depends on the velocity ratio and the jet vector angle. It is shown that the Strouhal number, based on the vortex shedding frequency and a combination of jet exit and freestream velocities, varies uniquely with velocity ratio.

Krothapalli, A.↗

NASA NTRS1991

Increased heat transfer to a cylindrical leading edge due to spanwise variations in the freestream velocity

The present study numerically demonstrates how small spanwise variations in velocity upstream of a body can cause relatively large increases in the spanwise-averaged heat transfer to the leading edge. Vorticity introduced by spanwise variations, first decays as it drifts downstream, then amplifies in the stagnation region as a result of vortex stretching. This amplification can cause a periodic array of 3 D structures, similar to horseshoe vortices, to form. The numerical results indicate that, for the given wavelength, there is an amplitude threshold below which a structure does not form. A one-dimensional analysis, to predict the decay of vorticity in the absence of the body, in conjunction with the full numerical results indicated that the threshold is more accurately stated as minimum level of vorticity required in the leading edge region for a structure to form. It is possible, using the one-dimensional analysis, to compute an optimum wavelength in terms of the maximum vorticity reaching the leading edge region for given amplitude. A discussion is presented which relates experimentally observed trends to the trends of the present phenomena.

Rigby, D. L.↗

NASA NTRS1993

Reduction in size and unsteadiness of a VTOL ground vortex by ground fences

A ground vortex, produced when a jet impinges on the ground in the presence of cross flow, is encountered by V/STOL aircraft hovering near the ground and is known to be hazardous to the aircraft. The objective of this research was to identify a ground-based technique by which both the mean size and fluctuation in size of the ground vortex could be reduced. A simple passive method was identified and examined in the laboratory. Specifically, one or two fine wire mesh screens (ground fences) bent in a horseshoe shape and located on the ground in front of the jet impingement point proved to be very effective. The ground fences work by decreasing the momentum of the upstream-traveling wall jet, effectively causing a higher freestream-to-jet velocity ratio (V(sub infinity)/V(sub j)) and thus, a ground vortex smaller in size and unsteadiness. At(V(sub infinity)/V(sub j)) = 0.15, the addition of a single ground fence resulted in a 70 percent reduction in mean size of the ground vortex. With two ground fences, the mean size decreased by about 85 percent. Fluctuations in size decreased nearly in proportion to the mean size, for both the single and double fence configurations. These results were consistent over a wide range of jet Reynolds number (10(exp 4) less than Re(sub jet) less than 10(exp 5)); further development and full-scale Reynolds number testing are required, however, to determine if this technique can be made practical for the case of actual VTOL aircraft.

Cimbala, John M.↗

NASA NTRS1990

A review of vortex structures and associated coherent motions in turbulent boundary layers

The experimental and computational evidence for the existence and role of vortices in turbulent boundary layers is briefly reviewed. Quasi-streamwise and transverse vortices are considered, and various published conceptual models for horseshoe-like vortical structures are compared. The causes for upright and inverted horseshoe-shaped vorticity lines are discussed, and the distinction between vorticity lines and vortices is demonsrated. Finally, results from a numerically-simulated turbulent boundary layer are used to compute distributions of diameter, height, and strength for quasi-streamwise and spanwise vortices. These results confirm that quasi-streamwise vortices are clustered near the wall, while spanwise vortices are distributed throughout the layer. The variation of spanwise vortex core diameter with distance from the wall is found to be consistent with the mixing-length distribution for a boundary layer.

Robinson, Stephen K.↗

NASA NTRS1985

Structure of turbulence in the presence of uniform shear

The structure of the vorticity field in homogeneous turbulent shear flow is analyzed using a database generated by direct numerical solution of the unsteady Navier-Stokes equations with up to 128x128x128 grid points. For two Reynolds numbers, the probability distribution of the inclination angle of the vorticity vectors, two-point correlations of the velocity and vorticity fields, and the instantaneous vorticity vectors and vortex lines in three-dimensional space were examined. It is shown that homogeneous turbulent shear flow contains a large number of horseshoe vortices. These vortices are most often found in planes inclined at 45 deg to the flow direction and are formed from the roll-up of sheets of transverse vorticity. These findings and similar results obtained in turbulent channel flow, lead to the conclusion that hairpin vortices are the characteristic vortical structures in all turbulent shear flows.

Moin, P.↗

NASA NTRS1993

LinAir: A multi-element discrete vortex Weissinger aerodynamic prediction method

LinAir is a vortex lattice aerodynamic prediction method similar to Weissinger's extended lifting-line theory, except that the circulation around a wing is represented by discrete horseshoe vortices, not a continuous distribution of vorticity. The program calculates subsonic longitudinal and lateral/directional aerodynamic forces and moments for arbitrary aircraft geometries. It was originally written by Dr. Ilan Kroo of Stanford University, and subsequently modified by the author to simplify modeling of complex configurations. The Polhamus leading-edge suction analogy was added by the author to extend the range of applicability of LinAir to low aspect ratio (i.e., fighter-type) configurations. A brief discussion of the theory of LinAir is presented, and details on how to run the program are given along with some comparisons with experimental data to validate the code. Example input and output files are given in the appendices to aid in understanding the program and its use. This version of LinAir runs in the VAX/VMS, Cray UNICOS, and Silicon Graphics Iris workstation environments at the time of this writing.

Durston, Donald A.↗

NASA NTRS1977

Vortices induced in a stagnation region by wakes - Their incipient formation and effects on heat transfer from cylinders

Horseshoe-like vortices, induced by wakes in the stagnation region of bluff bodies, are proposed as an efficient mechanism for augmentation of convective heat transfer. The vortex 'flow module' induced by single or multiple wakes, which had not been observed previously, was first documented and the resulting flow field was studied using various visualization techniques and hot-wire anemometry. In an attempt to understand the driving force behind this flow module, the conditions at which incipient formation of the vortices occurs were investigated. Existence of such a threshold is essential and was hitherto an open question in analytical studies of stability of flow in stagnation region. Finally, effects of the flow module on heat transfer from a cylinder were measured.

Nagib, H. M.↗

NASA NTRS2002

Transient Mixing Driven by Buoyancy Flows

Mixing driven by buoyancy-induced flows is of particular interest to microgravity processes, as the body force that governs the intensity of flow fields can be directly controlled. We consider a model experimental system to explore the dynamics of mixing which employs two miscible liquids inside a cavity separated initially by a divider. The two liquids are oriented vertically inside a rectangular cavity with constant width and height, and varying depths to span the range of a Hele-Shaw cell to a 3-[) configuration. The two miscible liquids can be sufficiently diluted and died, for example water and deuterium oxide, such that a distinct interface exists across the divider. The transient mixing characteristic of the two fluids is addressed by following the Lagrangian history of the interface for various aspect ratios in the z-plane (depth variation) as well as a range of pulling velocities of the divider. The mixing characteristics of the two fluids are quantified from measurement of the length stretch of the interface and its flow field using respectively image processing techniques and Particle Imaging Velocimetry. Scaling analysis shows that the length stretch depends on four governing parameters, namely the Grashof number (Gr), Schmidt number (Sc), aspect ratio (Ar), and Reynolds number (Re). Variation of the Schmidt number is taken into account through thermophysical property variation. Thus our problem reduces to a codimension three bifurcation in parametric space for Gr, Ar, and Re. Our experimental results show that for Gr on the order of 106 and a nominal cavity aspect ratio Ar = 0.2, the net effect of removal of the divider and the overwhelming buoyancy force causes an overturning motion which stretches and folds the interface to produce ml internal breakwave. The structure of the breakwave is similar to the ubiquitous Rayleigh-Taylor instability morphology. The breakwave is dissipated either through internal or wall collision depending on the impulsive velocity of the divider as prescribed by the Reynolds number. The decay of the collision event occurs through sloshing oscillations over a short time scale. The two fluids then become stably stratified with a diffusive band at the interface indicating local mass transport. The local bifurcation of the internal breakwave is investigated as a function of aspect ratio. Results show that for narrow cavities on the order of 2mm (Ar = 0.04) folding does not occur, the interface only stretches. As the cavity size increases folding occurs through a supercritical bifurcation. Insight into the mechanism of folding is obtained from measurement of the flow field which shows that in the neighborhood of the folding event, there exists hyperbolic points caused by multiple vortex interactions. The global length stretch of the interface as a function of time is nearly Gaussian; calculations of finite-time Liapunov exponents as well as construction of horseshoe maps indicate the likelihood of a chaotic transient.

W.M.B. Duval↗

NASA NTRS1980

Nonlinear dynamics; Proceedings of the International Conference, New York, NY, December 17-21, 1979

Papers were presented on turbulence, ergodic and integrable behavior, chaotic maps and flows, chemical and fully developed turbulence, and strange attractors. Specific attention was given to measures describing a turbulent flow, stochastization and collapse of vortex systems, a subharmonic route to turbulent convection, and weakly nonlinear turbulence in a rotating convection layer. The Korteweg-de Vries and Hill equations, plasma transport in three dimensions, a horseshoe in the dynamics of a forced beam, and the explosion of strange attractors exhibited by Duffing's equation were also considered.

Helleman, R. H. G.↗

NASA NTRS2007

Development of Hairpin Vortices in Turbulent Spots and End-Wall Transition

The end-stage phase of boundary layer transition is characterized by the development of hairpin-like vortices which evolve rapidly into patches of turbulent behavior. In general, the characteristics of the evolution form this hairpin stage to the turbulent stage is poorly understood, which has prompted the present experimental examination of hairpin vortex development and growth processes. Two topics of particular relevance to the workshop focus will be covered: 1) the growth of turbulent spots through the generatio and amalgamation of hairpin-like vortices, and 2) the development of hairpin vortices during transition in an end-wall junction flow. Brief summaries of these studies are described below. Using controlled generation of hairpin vortices by surface injection in a critical laminar boundary layer, detailed flow visualization studies have been done of the phases of growth of single hairpin vortices, from the initial hairgin generation, through the systematic generation of secondary hairpin-like flow structures, culminating in the evolution to a turbulent spot. The key to the growth process is strong vortex-surface interactions, which give rise to strong eruptive events adjacent to the surface, which results in the generation of subsequent hairpin vortex structures due to inviscid-viscuous interactions between the eruptive events and the free steam fluid. The general process of vortex-surface fluid interaction, coupled with subsequent interactions and amalgamation of the generated multiple hairpin-type vortices, is demonstrated as a physical mechanism for the growth and development of turbulent spots. When a boundary layer flow along a surface encounters a bluff body obstruction extending from the surface (such as cylinder or wing), the strong adverse pressure gradients generated by these types of flows result in the concentration of the impinging vorticity into a system of discrete vortices near the end-wall juncture of the obstruction, with the extensions of the vortices engirdling the obstruction to form "necklace" or "horseshoe" vortices. Recent hydrogen bubble and particle image visualization have shown that as Reynolds number is increased for a laminar approach flow, the flow will become critical, and a destabilization of the necklace vortices results in the development of an azimuthal waviness, or "kinks", in the vortices. These vortex kinks are accentuated by Biot-Savart effects, causing portions of a distorted necklace vortex to make a rapid approach to the surface, precipitating processes of localized, three-dimensional surface interactions. These interactions result in the rapid generation, focussing, and ejection of thin tongues of surface fluid, which rapidly roll-over and appear as hairpin vortices in the junction region. Subsequent amalgamation of these hairpin vortices with the necklace vortices produces a complex transitional-type flow. A presentation of key results from both these studies will be done, emphasizing both the ubiquity of such hairpin-type flow structures in manifold transitional-type flows, and the importance of vortex-surface interactions n the development of hairpin vortices.

Smith, Charles R.↗