Vortex breakdown of nominally axisymmetric, swirling incompressible flows with jet- and wake-like axial velocity distributions issuing into a semi-infinite domain is studied by means of direct numerical simulations. By selecting a two-parametric velocity profile for which the steady axisymmetric breakdown is well-studied (Grabowski & Berger 1976), issues are addressed regarding the role of three-dimensionality and unsteadiness with respect to the existence, mode selection, and internal structure of vortex breakdown, in terms of the two governing parameters and the Reynolds number. Low Reynolds numbers are found to yield flow fields lacking breakdown bubbles or helical breakdown modes even for high swirl. In contrast, highly swirling flows at large Reynolds numbers exhibit bubble, helical or double-helical breakdown modes, where the axisymmetric mode is promoted by a jet-like axial velocity profile, while a wake-like profile renders the flow helically unstable and ultimately yields non-axisymmetric breakdown modes. It is shown that a transition from super- to subcritical flow, as defined by Benjamin (1962), accurately predicts the parameter combination yielding breakdown, if applied locally to flows with supercritical inflow profiles. Thus the basic form of breakdown is axisymmetric, and a transition to helical breakdown modes is shown to be caused by a sufficiently large pocket of absolute instability in the wake of the bubble, giving rise to a self-excited global mode. Two distinct eigenfunctions corresponding to azimuthal wavenumbers have been found to yield a helical or double-helical breakdown mode, respectively. Here the minus sign represents the fact that the winding sense of the spiral is opposite to that of the flow.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6AB7F50FBF65A5DED546C613E3B29895/S0022112003004749a.pdf/div-class-title-three-dimensional-vortex-breakdown-in-swirling-jets-and-wakes-direct-numerical-simulation-div.pdf

Three-dimensional vortex breakdown in swirling jets and wakes: direct numerical simulation

An experimental and theoretical investigation of the flow at the outlet of a Francis turbine runner is carried out in order to elucidate the causes of a sudden drop in the draft tube pressure recovery coefficient at a discharge near the best efficiency operating point. Laser Doppler anemometry velocity measurements were performed for both axial and circumferential velocity components at the runner outlet. A suitable analytical representation of the swirling flow has been developed taking the discharge coefficient as independent variable. It is found that the investigated mean swirling flow can be accurately represented as a superposition of three distinct vortices. An eigenvalue analysis of the linearized equation for steady, axisymmetric, and inviscid swirling flow reveals that the swirl reaches a critical state precisely (within 1.3%) at the discharge where the sudden variation in draft tube pressure recovery is observed. This is very useful for turbine design and optimization, where a suitable runner geometry should avoid such critical swirl configuration within the normal operating range.

Analysis of the Swirling Flow Downstream a Francis Turbine Runner

Numerical simulation of three-dimensional dynamic stall has been undertaken using computational fluid dynamics. The full Navier–Stokes equations, coupled with a two-equation turbulence model, where appropriate, have been solved on multiblock strucured grids in a time-accurate fashion. Results have neen obtained for wings of square planform and of NACA 0012 section. Efforts have been devoted to the accurate modeling of the flow near the wing tips, which, for this case, were sharp without tip caps. The obtained results revealed the time evolution of the dynamic stall vortex, which, for this case, takes the shape of a capital omega+spanning the wing. The obtained results compare well against experimental data both for the surface pressure distribution on the wing and the flow topology. Of significant importance is the interaction between the three-dimensional dynamic stall vortex and the tip vortex. The present results indicate that once the two vortices are formed both appear to originate from the same region, which is located near the leading edge of the tip. During the ramping of the wing, the two vortices grow significantly in size. The dynamic stall vortex dettaches from the wing in the inboard region but remains close to the wing’s leading edge near the tip. The overall configuration of the developed vortical system takes a form. To our knowledge, this is the first detailed numerical study of three-dimensional dynamic stall appearing in the literature.

Investigation of Three-Dimensional Dynamic Stall Using Computational Fluid Dynamics

A review of helicopter rotor blade tip shapes

Experimental study of the vortex end in centrifugal separators: The nature of the vortex end

Numerical calculations for three-dimensional, unsteady, laminar, bubble-type vortex breakdown within a tube-and-vane-type apparatus at a Reynolds number of 2000 and circulation number Ω=141 are presented This study is unique in that rather than specifying the inlet swirl velocity through a fit to experimental data (or a Burgers profile), the swirl was induced by directing the fluid through an array of 16 turning vanes, the arrangement being similar to that employed in the original experimental works of Sarpkaya [J Fluid Mech 45, 545 (1971); AIAA J 12, 602 (1974)] The interior of the resulting breakdown bubble consisted of one primary torroidal recirculation cell, which was tilted from, and found to gyrate about, the bubble centerline The dominant frequency of gyration was identified, and the mechanism of fluid exchange examined Subsequent calculations were performed using fixed inlet swirl and axial velocity profiles that were obtained from the results computed using the full geometry (including the turning vanes) Results revealed no significant difference in the downstream breakdown location or structure

Numerical simulation of bubble-type vortex breakdown within a tube-and-vane apparatus

The behavior of symmetric parallel jets was investigated experimentally. Two-component hot-wire surveys of the velocity field were performed over a jet region extending from the nozzle plate to a distance seven times the spacing between the nozzles. The objective of this study was to investigate an observed periodic behavior in the near-field region between parallel jets that increases in frequency as the nozzle widths decrease. This behavior was found to occur in parallel jets where nozzle widths are greater than 0.5 times the jet spacer width. The phenomena are attributed to bluff body shedding in the near field and a confining effect of the outer shear layers

Periodic Flow Between Low Aspect Ratio Parallel Jets

A parallel stabilized finite-element/spectral formulation is presented for incompressible large-eddy simulation with complex 2-D geometries. A unique discretization scheme is developed consisting of a streamline-upwind Petrov–Galerkin/Pressure-Stabilized Petrov–Galerkin (SUPG/PSPG) finite-element discretization in the 2-D plane with a collocated spectral/pseudospectral discretization in the out-of-plane direction. This formulation provides an efficient approach for solving 3-D flows over arbitrary 2-D geometries. Utilizing this discretization and through explicit temporal treatment of the non-linear terms, the system of equations for each Fourier mode is decoupled within each time step. A novel parallelization approach is then taken, where the computational work is partitioned in Fourier space. A validation of the algorithm is presented via comparison of results for flow past a circular cylinder with published values for Re=195, 300, and 3900. Copyright © 2003 John Wiley & Sons, Ltd.

Large‐eddy simulation with complex 2‐D geometries using a parallel finite‐element/spectral algorithm

Numerical Investigation into Multiple Vortex Structures Formed over Flat End-Cap Wings

The development of a wingtip vortex in the region adjacent the wing end-cap to approximately two chordlengths downstream from the trailing edge is strongly influenced by the end-cap treatment. The flat end-cap geometry produces multiple, relatively strong vortices in the near-field as opposed to the single vortex generated using the rounded end-cap, configuration. However, difficulties in gridding the sharp edges of the wingtip have resulted in relatively few numerical studies of the near-field development of the wingtip vortex from a flat end-cap configuration. In the present work the formation and merging process of multiple vortex structures formed over flat end-caps is investigated numerically through solutions of the RANS equations using both one equation and differential Reynolds stress turbulence models, and experimentally through flow visualization and hot wire anemometry. Introduction Tip vortices shed from finite-span wings are of considerable technological importance, with applications to airplane and submarine wings, helicopter rotor blades, and marine and aviation propellers to name but a few. In nearly all instances, these vortices have undesirable effects, such as aerodynamic inefficiency, mechanical fatigue, and noise (c.f. Green [1]). Of primary interest in this investigation is the formation and very-near-field development of a tip vortex generated from a rectangular wing with a flat end-cap. This geometry is representative of that encountered in the deployment of flaps for high-lift configurations, where, for instance, tip vortex formation and near-field evolution is an important issue in noise control. Previous experimental studies have shown that the vortex development process for flat end-caps is very different from that for rounded end-caps in that multiple shear-layer vortices exist in the vicinity of the wingtip [2-5]. Using hot wire anemometry, Francis and Kennedy [2] observed, at a Reynolds number of 247,000 and an angle-of-attack of 4°, a single secondary vortex over the flat end-cap, which eventually merged with the primary suction-side vortex near the trailing edge. However, flow visualization studies by Shekarriz et al. [3,4] and Katz and Galdo [5] at lower Reynolds numbers (37,000<#e<220,000) and higher angles of attack (oc<12°) showed multiple secondary vortices. These shear-layer vortices are not observed over rounded end caps, since there is no tendency for the flow to separate as the fluid passes from the pressure side, across the cap, and to the suction side. In addition to experimental work, Reynolds-Averaged Navier-Stokes (RANS) calculations have also been performed previously to investigate the near field structure of a wing-tip vortex. The vast majority of these studies have investigated wings with rounded or beveled end-cap geometries [6-10], and have shown that CFD can accurately predict the initial roll-up stage. None of these studies, however, specifically investigated the development and merging process of multiple vortices that form over wings with flat endcaps. In a more recent work [11], RANS calculations were performed for a generic high-lift configuration at flap deflections of 29° and 39°. Numerical Method and Turbulence Model In the current study, the steady, incompressible, RANS equations were integrated using an unstructured, segregated, pressure-based finite-volume procedure as implemented within the Fluent version 5.0 code (Fluent, Inc., Lebanon, NH). The RANS equations are well known, and hence for purposes of brevity are not shown (c.f. Hinze [12]). In terms of the solution/discretization procedure, pressure-velocity coupling was achieved using the SIMPLEC [13] algorithm. Differencing of the convective terms was implemented using a third-order, bounded QUICK [14] interpolation scheme for the momentum equations and a second-order, bounded upwind scheme for all turbulence equations. The viscous terms were discretized using second-order central differencing. Pressures were interpolated to the cell faces using a second-order interpolation scheme [15]. Two different turbulence models were used: a one-equation Spalart-Allmaras (S-A) model [16] and a differential Reynolds stress model (RSM) [17,18]. * Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. * Assistant Professor, Department of Mechanical and Aerospace Engineering, Senior Member AIAA f Graduate Student, Department of Mechanical and Aerospace Engineering, Student Member AIAA * Professor, Department of Mechanical and Aerospace Engineering, Senior Member AIAA

Deryl O. Snyder

Papers

Numerical simulation of bubble-type vortex breakdown within a tube-and-vane apparatus

Periodic Flow Between Low Aspect Ratio Parallel Jets

Large‐eddy simulation with complex 2‐D geometries using a parallel finite‐element/spectral algorithm

Numerical Investigation into Multiple Vortex Structures Formed over Flat End-Cap Wings

Numerical/experimental investigation into multiple vortex structures formed over wings with flat end-caps