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At least 19 records

Cut-and-connect of two antiparallel vortex tubes

Motivated by an early conjecture that vortex cut-and-connect plays a key role in mixing and production of turbulence, helicity and aerodynamic noise, the cross-linking of two antiparallel viscous vortex tubes via direct numerical simulation is studied. The Navier-Stokes equations are solved by a dealiased pseudo-spectral method with 64 cubed grid points in a periodic domain for initial Reynolds numbers Re up to 1000. The vortex tubes are given an initial sinusoidal perturbation to induce a collision and keep the two tubes pressed against each other as annihilation continues. Cross-sectional and wire plots of various properties depict three stages of evolution: (1) Inviscid induction causing vortex cores to first approach and form a contact zone with a dipole cross-section, and then to flatten and stretch; (2) Vorticity annihilation in the contact zone accompanied by bridging between the two vortices at both ends of the contact zone due to a collection of cross-linked vortex lines, now orthogonal to the initial vortex tubes. The direction of dipole advection in the contact zone reverses; and (3) Threading of the remnants of the original vortices in between the bridges as they pull apart. The crucial stage 2 is shown to be a simple consequence of vorticity annihilation in the contact zone, link-up of the un-annihilated parts of vortex lines, and stretching and advection by the vortex tube swirl of the cross-linked lines, which accumulate at stagnation points in front of the annihilating vortex dipole. It is claimed that bridging is the essence of any vorticity cross-linking and that annihilation is sustained by stretching of the dipole by the bridges. Vortex reconnection details are found to be insensitive to asymmetry. Modeling of the reconnection process is briefly examined. The 3D spatial details of scalar transport (at unity Schmidt number), enstrophy production, dissipation and helicity are also examined.

Melander, Mogens V.↗

Cross-linking of two antiparallel vortex tubes

The detailed mechanisms in vortex cross-linking are unveiled by adequately resolved, direct numerical simulation of two viscous vortex tubes. There are three characteristic phases: (1) inviscid induction followed by core flattening and stretching; (2) bridging of the two vortices by accumulation of annihilated and then cross-linked vortex lines; and (3) threading of the remnants of the initial vortex pair in between the two bridges as they pull apart. These phases and the role of threading (along with bridging) in the mixing and the enstrophy cascade are explained, and it is shown that the mechanism is insensitive to asymmetries.

Melander, M. V.↗

Vortex tubes in turbulent flows: Identification, representation, reconstruction

In many cases the structure of a fluid flow is well-characterized by its vortices, especially for the purpose of visualization. In this paper we present a new algorithm for identifying vortices in complex flows. The algorithm produces a skeleton line along the center of a vortex by using a two-step predictor-corrector scheme. The vorticity vector field serves as the predictor and the pressure gradient (in the perpendicular plane) serves as the corrector. We describe an economical description of the vortex tube's cross-section: a 5-term truncated Fourier series is generally sufficient, and it compresses the representation of the flow by a factor of 4000 or more. We reconstruct the vortex tubes as generalized cylinders, providing a polygonal mesh suitable for display on a graphics workstation. We show how the reconstructed geometry of vortex tubes can be enhanced to help visualize helical motion in a static image.

Banks, David C.↗

Progress in Air Separation with the Vortex Tube

The current study is characterized by two distinct phases in the development of the vortex tube (VT) technology as a primary means for in-flight air separation. The purpose of the first phase was to systematically identify parameters that influence oxygen concentration and recovery and to quantify the extent of that influence. To that end, the project team used a series of planned factorial experiments to identify statistically significant variables (factors) and their interactions. These experiments identified a best range of the operating envelope that includes nozzle diameter, orifice diameter, inlet air pressure, and liquid phase content in the inlet air. The best results observed in this envelope were an oxygen content of approximately 68% and a recovery factor of approximately 38%. The primary objectives of the second phase of the current study were to investigate the application effects of the two different air separation efficiency enhancement methods. One of these methods resulted in a concentration increase of 12% and second resulted in a concentration increase of 5%. Several aspects of these methods application are subject to optimize.

Balepin, Vladimir↗

Progress in Air Separation with the Vortex Tube

The current study is characterized by two distinct phases in the development of the vortex tube (VT) technology as a primary means for in-flight air separation. The purpose of the first phase was to systematically identify parameters that influence oxygen concentration and recovery and to quantify the extent of that influence. To that end, the project team used a series of planned factorial experiments to identify statistically significant variables (factors) and their interactions. These experiments identified a best range of the operating envelope that includes nozzle diameter, orifice diameter, inlet air pressure, and liquid phase content in the inlet air. The best results observed in this envelope were an oxygen content of approximately 68% and a recovery factor of approximately 38%. The primary objectives of the second phase of the current study were to investigate the application effects of the two different air separation efficiency enhancement methods. One of these methods resulted in a concentration increase of 12% and second resulted in a concentration increase of 5%. Several aspects of these methods application are subject to optimize.

Balepin, V.↗

Close interactions of 3-D vortex tubes

The motivation for studying close vortex interactions is briefly discussed in the light of turbulence and coherent structures. Particular attention is given to the interaction known as reconnection. Two reconnection mechanisms are discussed. One is annihilation of vorticity by cross-diffusion, the other is an inviscid head-tail formation. At intermediate Reynolds numbers both mechanisms are operating.

Melander, Mogens V.↗

On the dynamical buoyancy of vortices

In this paper we consider the effect of dynamical buoyancy (Parker) on the motion of stratified fluid vortex tubes. We find that the dynamical buoyancy force does not necessarily lead to a buoyant rise if there exists a flow field external to a tube. In particular, the vortex tubes presented in our previous work are shown to have a pressure force exactly canceling the buoyancy force so that they do not move vertically (i.e., parallel to gravity) at all. Moreover, we construct a more general class of vortex tubes and find that their vertical motion can be either up or down, depending on the detailed vorticity distribution, regardless of the fact that they are all dynamically buoyant. We find that the vertical motion is intimately related to the horizontal self-motion of stratified fluid vortex tubes. Finally, we note that the presence of dynamical buoyancy implies that steady state compressible flow solutions for isolated fluid regions in a gravitational field do not exist. These results may have relevance to astrophysical convection.

Arendt, Steve↗

Experimental and analytical studies in fluids

The first objective was to analyze and design a true airspeed sensor which will replace the conventional pitot-static pressure transducer for small commercial aircraft. The second objective was to obtain a numerical solution and predict the frequency response which is generated by the vortex whistle at a certain airspeed. It was concluded flow rate measurements indicate that the vortex tube sound frequency is linearly proportional to the frequency response. The vortex tube whistle frequency is dependent upon geometrical parameters to such an extent that: an increase in vortex tube length produces a decrease in frequency response and that an increase in the exhaust nozzle length produces an increase in the frequency precession. An increase in the vortex tube diameter produces a decrease in frequency precession. An increase in swirler diameter produces a decrease in frequency. An increase in the location distance of the microphone pickup signal point from the inside edge of the exit nozzle produces an increase in frequency response. The experimental results indicate that those parameters most significantly effecting frequency are in descending order of importance microphone location, vortex tube diameter, exit nozzle length, vortex tube length, and swirler diameter.

Goglia, Gene L.↗

A visual investigation of turbulence in stagnation flow about a circular cylinder

A visual investigation of turbulence in stagnation flow around a circular cylinder was carried out in order to gain a physical insight into the model advocated by the corticity-amplification theory. Motion pictures were taken from three different viewpoints, and a frame by frame examination of selected movie strips was conducted. Qualitative and quantitative analyses of the flow events focused on tracing the temporal and spatial evolution of a cross-vortex tube outlined by the entrained smoke filaments. The visualization supplied evidence verifying: (1) the selective stretching of cross-vortex tubes which is responsible for the amplification of cross vorticity and, hence, of streamwise turbulence; (2) the streamwise tilting of stretched cross-vortex tubes; (3) the existence of a coherent array of vortices near the stagnation zone; (4) the interaction of the amplified vorticity with the body laminar boundary layer; and, (5) the growth of a turbulent boundary layer.

Sadeh, W. Z.↗

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↗

Study of the velocity gradient tensor in turbulent flow

The behavior of the velocity gradient tensor, A(ij)=delta u(i)/delta x(j), was studied using three turbulent flows obtained from direct numerical simulation The flows studies were: an inviscid calculation of the interaction between two vortex tubes, a homogeneous isotropic flow, and a temporally evolving planar wake. Self-similar behavior for each flow was obtained when A(ij) was normalized with the mean strain rate. The case of the interaction between two vortex tubes revealed a finite sized coherent structure with topological characteristics predictable by a restricted Euler model. This structure was found to evolve with the peak vorticity as the flow approached singularity. Invariants of A(ij) within this structure followed a straight line relationship of the form: gamma(sup 3)+gammaQ+R=0, where Q and R are the second and third invariants of A(ij), and the eigenvalue gamma is nearly constant over the volume of this structure. Data within this structure have local strain topology of unstable-node/saddle/saddle. The characteristics of the velocity gradient tensor and the anisotropic part of a related acceleration gradient tensor H(ij) were also studied for a homogeneous isotropic flow and a temporally evolving planar wake. It was found that the intermediate principal eigenvalue of the rate-of-strain tensor of H(ij) tended to be negative, with local strain topology of the type stable-node/saddle/saddle. There was also a preferential eigenvalue direction. The magnitude of H(ij) in the wake flow was found to be very small when data were conditioned at high local dissipation regions. This result was not observed in the relatively low Reynolds number simulation of homogeneous isotropic flow. A restricted Euler model of the evolution of A(ij) was found to reproduce many of the topological features identified in the simulations.

Cheng, Wei-Ping↗