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NASA NTRS1993

Streamwise vorticity generation and mixing enhancement in free jets by delta-tabs

The effect of triangular tabs, placed at the nozzle exit, on the evolution of free jets is investigated. The effect, a large distortion of the jet cross section and a resultant increase in mixing downstream, has been inferred before to be due to a pair of streamwise vortices originating from each tab. In this paper, the generation mechanism of the stream wise vorticity (omega sub x) is considered first. Two sources are postulated. One is the upstream 'pressure hill', produced by the tab, which appears to be the dominant source. Another is due to vortex filaments shed from the sides of the tab and reoriented downstream by the mean shear of the mixing layer. In the case of a 'delta-tab', a triangular tab with its apex leaning downstream, vorticity from the two sources explain the stronger effect in that configuration. Data on the vorticity evolution for the effect of two delta-tabs are presented, up to twelve jet diameters from the exit, which show that the streamwise vortices persist even at the farthest measurement station. The magnitude of omega sub x-maximum decays continually with distance from the nozzle, its ratio to azimuthal vorticity maximum is found to be about 1/5 everywhere. The relative effect of a delta-tab on jets from an axisymmetric nozzle and a 8:1 rectangular nozzle is also studied. The mixing layer distortion is found to be less pronounced in the rectangular case. The jet mixing, as manifested by the mass flux measured at a downstream station, is increased in the axisymmetric jet but it is decreased in the rectangular jet under consideration by the delta-tab.

Zaman, K. B. M. Q.↗

NASA NTRS1993

Strong vortex/boundary layer interactions. I - Vortices high

Detailed measurements with hot-wires and pressure probes are presented for the interaction between a turbulent longitudinal vortex pair with 'common flow' down, and a turbulent boundary layer. The interaction has a larger value of the vortex circulation parameter, and therefore better represents many aircraft/vortex interactions, than those studied previously. The vortices move down towards the boundary layer, but only the outer parts of the vortices actually enter it. Beneath the vortices the boundary layer is thinned by lateral divergence to the extent that it almost ceases to grow. Outboard of the vortices the boundary layer is thickened by lateral convergence. The changes in turbulence structure parameters in the boundary layer appear to be due to the effects of 'extra-rate-of-strain' produced by lateral divergence (or convergence) and by free-stream turbulence. The effect of the interaction on the vortices (other than the inviscid effect of the image vortices below the surface) is small. The flow constitutes a searching test case for prediction methods for three-dimensional turbulent flows.

Cutler, A. D.↗

NASA NTRS1993

Streamwise vorticity generation and mixing enhancement in free jets by 'delta-tabs'

The effect of triangular tabs, placed at the nozzle exit, on the evolution of free jets is investigated. The effect, a large distortion of the jet cross section and a resultant increase in mixing downstream, has been inferred before to be due to a pair of streamwise vortices originating from each tab. In this paper, the generation mechanism of the streamwise vorticity (omega sub x) is considered first. Two sources are postulated. One is the upstream 'pressure hill', produced by the tab, which appears to be the dominant source. Another is due to vortex filaments shed from the sides of the tab and reoriented downstream by the mean shear of the mixing layer. In the case of a 'delta-tab', a triangular tab with its apex leaning downstream, vorticity from the two sources explain the stronger effect in that configuration. Data on the vorticity evolution for the effect of two delta-tabs are presented, up to twelve jet diameters from the exit, which show that the streamwise vortices persist even at the farthest measurement station. The magnitude of omega sub x-maximum decays continually with distance from the nozzle, its ratio to azimuthal vorticity maximum is found to be about 1/5 everywhere. The relative effect of a delta-tab on jets from an axisymmetric nozzle and a 8:1 rectangular nozzle is also studied. The mixing layer distortion is found to be less pronounced in the rectangular case. The jet mixing, as manifested by the mass flux measured at a downstream station, is increased in the axisymmetric jet but it is decreased in the rectangular jet under consideration by the delta-tab.

Zaman, K. B. M. Q.↗

NASA NTRS1993

Plane mixing layer vortical structure kinematics

The objective of the current project was to experimentally investigate the structure and dynamics of the streamwise vorticity in a plane mixing layer. The first part of this research program was intended to clarify whether the observed decrease in mean streamwise vorticity in the far-field of mixing layers is due primarily to the 'smearing' caused by vortex meander or to diffusion. Two-point velocity correlation measurements have been used to show that there is little spanwise meander of the large-scale streamwise vortical structure. The correlation measurements also indicate a large degree of transverse meander of the streamwise vorticity which is not surprising since the streamwise vorticity exists in the inclined braid region between the spanwise vortex core regions. The streamwise convection of the braid region thereby introduces an apparent transverse meander into measurements using stationary probes. These results corroborated with estimated secondary velocity profiles in which the streamwise vorticity produces a signature which was tracked in time.

Leboeuf, Richard L.↗

NASA NTRS1992

The structure of intense vorticity in homogeneous isotropic turbulence

The structure of the intense vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers in the range Re(sub lambda) = 36-171. In accordance with previous investigators, this vorticity is found to be organized in coherent, cylindrical or ribbon-like, vortices ('worms'). A statistical study suggests that they are just especially intense features of the background, O(omega'), vorticity. Their radii scale with the Kolmogorov microscale and their lengths with the integral scale of the flow. An interesting observation is that the Reynolds number based on the circulation of the intense vortices, gamma/nu, increases monotonically with Re(sub lambda), raising the question of the stability of the structures in the limit of Re(sub lambda) approaching infinity. One and two-dimensional statistics of vorticity and strain are presented; they are non-gaussian, and the behavior of their tails depends strongly on the Reynolds number. There is no evidence of convergence to a limiting distribution in our range of Re(sub lambda), even though the energy spectra and the energy dissipation rate show good asymptotic properties in the higher Reynolds number cases. Evidence is presented to show that worms are natural features of the flow and that they do not depend on the particular forcing scheme.

Jimenez, J.↗

NASA NTRS1995

Calculation of three-dimensional (3-D) internal flow by means of the velocity-vorticity formulation on a staggered grid

A method has been developed to accurately compute the viscous flow in three-dimensional (3-D) enclosures. This method is the 3-D extension of a two-dimensional (2-D) method developed for the calculation of flow over airfoils. The 2-D method has been tested extensively and has been shown to accurately reproduce experimental results. As in the 2-D method, the 3-D method provides for the non-iterative solution of the incompressible Navier-Stokes equations by means of a fully coupled implicit technique. The solution is calculated on a body fitted computational mesh incorporating a staggered grid methodology. In the staggered grid method, the three components of vorticity are defined at the centers of the computational cell sides, while the velocity components are defined as normal vectors at the centers of the computational cell faces. The staggered grid orientation provides for the accurate definition of the vorticity components at the vorticity locations, the divergence of vorticity at the mesh cell nodes and the conservation of mass at the mesh cell centers. The solution is obtained by utilizing a fractional step solution technique in the three coordinate directions. The boundary conditions for the vorticity and velocity are calculated implicitly as part of the solution. The method provides for the non-iterative solution of the flow field and satisfies the conservation of mass and divergence of vorticity to machine zero at each time step. To test the method, the calculation of simple driven cavity flows have been computed. The driven cavity flow is defined as the flow in an enclosure driven by a moving upper plate at the top of the enclosure. To demonstrate the ability of the method to predict the flow in arbitrary cavities, results will he shown for both cubic and curved cavities.

Stremel, Paul M.↗

NASA NTRS1996

Nonlinear axisymmetric and three-dimensional vorticity dynamics in a swirling jet model

The mechanisms of vorticity concentration, reorientation, and stretching are investigated in a simplified swirling jet model, consisting of a line vortex along the jet axis surrounded by a jet shear layer with both azimuthal and streamwise vorticity. Inviscid three-dimensional vortex dynamics simulations demonstrate the nonlinear interaction and competition between a centrifugal instability and Kelvin-Helmholtz instabilities feeding on both components of the base flow vorticity. Under axisymmetric flow conditions, it is found that the swirl leads to the emergence of counterrotating vortex rings, whose circulation, in the absence of viscosity, can grow without bounds. Scaling laws are provided for the growth of these rings, which trigger a pinch-off mechanism resulting in a strong decrease of the local jet diameter. In the presence of an azimuthal disturbance, the nonlinear evolution of the flow depends strongly on the initial ratio of the azimuthal and axisymmetric perturbation amplitudes. The long term dynamics of the jet can be dominated by counterrotating vortex rings connected by braid vortices, by like-signed rings and streamwise braid vortices, or by wavy streamwise vortices alone.

Martin, J. E.↗

NASA NTRS2011

Observations of Electron Vorticity in the Inner Plasmasheet and Its Relationship to Reconnection

Spatial derivatives of the electron moments can be estimated using data from the four Cluster spacecraft. Using spatial derivatives of the velocity we have computed the vorticity in the plasmasheet for several crossings. What we have found is that vorticity appears to be a common feature in the inner plasmasheet. We will show a number of examples. In at least some of the observations the vorticity is well correlated with the passage of Cluster through the ion diffusion region of known reconnection events. That most of the vorticity events observed are reconnection related cannot be dismissed and in fact observations of vorticity may provide a means to locate times when the Cluster spacecraft are magnetically connected to regions where reconnection is taking place. Understanding the role and source of the vorticity should advance our understanding of the dissipation of the turbulence associated with reconnection. In the course of the presentation we will also touch on the methods used to estimate the spatial derivatives as well as the limitations and assumptions involved.

Gurgiolo, Chris A.↗

NASA NTRS2016

Martian Polar Vortices: Comparison of Reanalyses

The structure and evolution of the Martian polar vortices is examined using two recently available reanalysis systems: version 1.0 of the Mars Analysis Correction Data Assimilation (MACDA) and a preliminary version of the Ensemble Mars Atmosphere Reanalysis System (EMARS). There is quantitative agreement between the reanalyses in the lower atmosphere, where Mars Global Surveyor (MGS) Thermal Emission Spectrometer (TES) data are assimilated, but there are differences at higher altitudes reflecting differences in the free-running general circulation model simulations used in the two reanalyses. The reanalyses show similar potential vorticity (PV) structure of the vortices: There is near-uniform small PV equatorward of the core of the westerly jet, steep meridional PV gradients on the polar side of the jet core, and a maximum of PV located off of the pole. In maps of 30 sol mean PV, there is a near-continuous elliptical ring of high PV with roughly constant shape and longitudinal orientation from fall to spring. However, the shape and orientation of the vortex varies on daily time scales, and there is not a continuous ring of PV but rather a series of smaller scale coherent regions of high PV. The PV structure of the Martian polar vortices is, as has been reported before, very different from that of Earth's stratospheric polar vortices, but there are similarities with Earth's tropospheric vortices which also occur at the edge of the Hadley Cell, and have near-uniform small PV equatorward of the jet, and a large increase of PV poleward of the jet due to increased stratification.

Waugh, D. W.↗

NASA NTRS2018

Data Mining for Vortices on the Earth's Magnetosphere - Algorithm Application for Detection and Analysis

Unsteady processes in the solar wind– magnetosphere interaction, such as vortices developed at the magnetopause boundary by the Kelvin–Helmholtz instability, may contribute to the process of mass, momentum and energy transfer into the Earth’s magnetosphere. The research described in this paper validates an algorithm to automatically detect and characterize vortices based on velocity data from simulations. The vortex identification algorithm (VIA) systematically searches the 3-D velocity fields to identify critical points where the magnitude of the velocity vector vanishes. The velocity gradient tensor is computed and its invariants are used to assess vortex structure in the flow field. We use the Community Coordinated Modeling Center (CCMC) Runs on Request capability to create a series of model runs initialized from the conditions observed by the Cluster mission in the Hwang et al. (2011) analysis of Kelvin–Helmholtz vortices observed during southward interplanetary magnetic field (IMF) conditions. We analyze further the properties of the vortices found in the runs, including the velocity changes within their motion across the magnetosheath. We also demonstrate the potential of our tool to identify and characterize other transient features (e.g., flux transfer events, FTEs) with vortical internal structures. We find that the vortices are associated with flows on the magnetosheath side of the magnetopause that reach speeds greater than the solar wind speed at the bow shock.

Collado-Vega, Yaireska M.↗

NASA NTRS1977

Vorticity imbalance and stability in relation to convection

A complete synoptic-scale vorticity budget was related to convection storm development in the eastern two-thirds of the United States. The 3-h sounding interval permitted a study of time changes of the vorticity budget in areas of convective storms. Results of analyses revealed significant changes in values of terms in the vorticity equation at different stages of squall line development. Average budgets for all areas of convection indicate systematic imbalance in the terms in the vorticity equation. This imbalance resulted primarily from sub-grid scale processes. Potential instability in the lower troposphere was analyzed in relation to the development of convective activity. Instability was related to areas of convection; however, instability alone was inadequate for forecast purposes. Combinations of stability and terms in the vorticity equation in the form of indices succeeded in depicting areas of convection better than any one item separately.

Read, W. L.↗

NASA NTRS1983

Vortices, stability, and turbulence

The transition process between laminar flow to turbulent flow is discussed in terms of a third state of fluid motion, vortical motion that is approximately periodic in space and/or time and displays symmetrical properties. The possibility that the transition from laminar to turbulent flow is accompanied by intermediate vortical states, with turbulence being an instability of the vortical states, is examined, with consideration given to the hypothesis that the turbulent state retains a memory of the vortex structures. Solutions are sought for the Navier-Stokes equations for a viscous liquid in a channel. Instances of inviscid vortical states and the presence of a three-dimensional instability are studied, demonstrating that transition phenomena can be explained qualitatively in terms of vortical state characteristics.

Saffman, P. G.↗

NASA NTRS1983

The influence of convective activity on the vorticity budget

The influence of convective activity on the vorticity budget was determined during the AVE VII and AVE-SESAME I periods. This was accomplished by evaluating each term in the expanded vorticity equation with twisting and tilting and friction representing the residual of all other terms. Convective areas were delineated by use of radar summary charts. The influence of convective activity was established by analyzing contoured fields of each term as well as numerical values and profiles of the various terms in convective and nonconvective areas. Vertical motion was computed by the kinematic method, and all computations were performed over the central United States using a grid spacing of 158 km. The results show that, in convective areas in particular, the residual is of comparable magnitude to the horizontal advection and divergence terms, and therefore, cannot be neglected. In convective areas, the residual term represents a sink of vorticity below 500 mb and a strong source near 300 mb. In nonconvective areas, the residual was small in magnitude at all levels, but tended to be negative (vorticity sink) at 300 mb. The local change term, over convective areas, tended to be balanced by the residual term, and appeared to be a good indicator of development (vorticity becoming more cyclonic). Finally, the shape of the vertical profiles of the term in the budget equation agreed with those found by other investigators for easterly waves, but the terms were one order of magnitude larger than those for easterly waves.

Townsend, T. L.↗

NASA NTRS1984

The structure of the vorticity field in turbulent channel flow. Part 1: Analysis of instantaneous fields and statistical correlations

An investigation into the existence of hairpin vortices in turbulent channel flow is conducted using a database generated by the large eddy simulation technique. It is shown that away from the wall the distribution of the inclination angle of vorticity vector attains its maximum at about 45 deg to the wall. Two point correlations of velocity and vorticity fluctuations strongly support a flow model consisting of vortical structures inclined at 45 deg to the wall. The instantaneous vorticity vectors plotted in planes inclined at 45 deg show that the flow contains an appreciable number of hairpins. Vortex lines are used to display the three dimensional structure of hairpins, which are shown to be generated from deformation of transverse vortex filaments.

Moin, P.↗

NASA NTRS1985

The structure of the vorticity field in turbulent channel flow. I - Analysis of instantaneous fields and statistical correlations

Moin, P.↗

NASA NTRS1987

Measurement of velocity and vorticity fields in the wake of an airfoil in periodic pitching motion

The velocity field created by the wake of an airfoil undergoing a prescribed pitching motion was sampled using hot wire anemometry. Data analysis methods concerning resolution of velocity components from cross wire data, computation of vorticity from velocity time history data, and calculation of vortex circulation from vorticity field data are discussed. These data analysis methods are applied to a flow field relevant to a two dimensional blade-vortex interaction study. Velocity time history data were differentiated to yield vorticity field data which are used to characterize the wake of the pitching airfoil. Measurement of vortex strength in sinusoidal and nonsinusoidal wakes show vortices in the sinusoidal wake have stronger circulation and more concentrated vorticity distributions than the tailored nonsinusoidal wake.

Booth, Earl R., Jr.↗

NASA NTRS1987

A statistical investigation of the single-point pdf of velocity and vorticity based on direct numerical simulations

Vorticity plays a fundamental role in turbulent flows. The dynamics of vorticity in turbulent flows and the effect on single-point closure models were investigated. The approach was to use direct numerical simulations of turbulent flows to investigate the pdf of velocity and vorticity. The preliminary study of homogeneous shear flow has shown that the expectation of the fluctuating pressure gradient, conditioned with a velocity component, is linear in the velocity component, and that the coefficient is independent of velocity and vorticity. In addition, the work shows that the expectation of the pressure gradient, conditioned with a vorticity component, is essentially zero.

Mortazavi, M.↗

NASA NTRS1988

Weak solutions of the three-dimensional vorticity equation with vortex singularities

The extension of the concept of vortex singularities, developed by Saffman and Meiron (1986) for the case of two-dimensional point vortices in an incompressible vortical flow, to the three-dimensional case of vortex sticks (vortons) is investigated analytically. The derivation of the governing equations is explained, and it is demonstrated that the formulation obtained conserves total vorticity and is a weak solution of the vorticity equation, making it an appropriate means for representing three-dimensional vortical flows with limited numbers of vortex singularities.

Winckelmans, G.↗