Numerical simulation of tangentially injected turbulent swirling flow in a divergent tube

This paper studies the properties of turbulent swirling decaying flow induced by tangential inlets in a divergent pipe using the realizable k–ε turbulence model and discusses the effects of the injector pressure and injection position. The results of transient solutions show that both the recirculation zone near the wall in upstream of the injectors and the vortex breakdown in downstream of the injectors increase in size during the whole period. A nearly axisymmetric conical breakdown is formed and its internal structure consists of two asymmetric spiral‐like vortices rotating in opposite directions. The stagnation point shifts slowly toward the pipe outlet over time. The maxima of the three velocity components, which are located near the wall, decrease gradually with streamwise direction. It can also be inferred that Mach number approaches 1.0 near the injector outlets. The velocities increase with the increasing injector pressure. However, its increasing trend is not significant. With the increase of the injection position, vortex breakdown moves in downstream direction and the pitch along the streamwise direction increases. Copyright © 2008 John Wiley & Sons, Ltd.     

3D numerical simulation of compressible swirling flow induced by means of tangential inlets

The objective of the present work is to predict compressible swirl flow in the nozzle of air‐jet spinning using the realizable k–ε turbulence model and discuss the effect of the nozzle pressure. The periodic change of flow patterns can be observed. The recirculation zone near the wall of the injectors upstream increases in size and moves gradually upstream, whereas the vortex breakdown in the injector downstream shifts slowly towards the nozzle outlet during the whole period. A low axial velocity in the core region moves gradually away from the centerline, and the magnitude of the center reverse flow and the area occupied by it increase with axial distance due to the vortex breakdown. From the tangential velocity profile, there is a very small free‐vortex zone. With increasing nozzle pressure, the velocity increases and the location of vortex breakdown is moved slightly downward. However, the increase in the velocity tends to decline at nozzle pressure up to a high level. Copyright © 2008 John Wiley & Sons, Ltd.     

Dynamic Response of Turbulent Low Emission Flames at Different Vortex Breakdown Conditions

The classic Flame Transfer Function (FTF) used in the thermoacoustic stability analysis of lean premixed combustors is linked, in a mathematically strict way, to the flow coherent structures using Large Eddy Simulation. This is based on a methodology which combines the Wiener-Hopf system identification filter—separating any field variables into a dynamic contribution driven by external forcing plus a noise contribution given by turbulent fluctuations—with the extended formulation of the Proper Orthogonal Decomposition (POD). The method is applied to partially premixed flames stabilized at two different types of Central Recirculation Zone (CRZ) due to the mechanism of vortex breakdown of the flow through a swirl burner: type A, where the CRZ appears rather narrow in the radial direction with apex located close to the burner exit and type B, where the CRZ is entirely located in the combustor and appears more flat at its apex than what observed in case of the type A vortex flow. Rather different properties are observed for the FTF. Flames stabilized at the narrow CRZ (type A), respond to inflow forcing with a time delay which depends much more on the bulk equivalence ratio than flames stabilized at the thick CRZ (type B). On the other hand the amplitude of the FTF in the case of the narrow CRZ is in general lower than in case of the thick and flat CRZ where amplification factors of the order of 4–5 are reached. By allowing a reasonable explanation of the observed trends, the methodology developed here can give an important contribution to the development of gas turbine burners.     

Some Observations of Vortex Breakdown in a Confined Flow with Solid Body Rotation

The occurrence of breakdown in slender vortex flows as a ``bubble'' or ``spiral'' pattern depends on the degree of radial deflection of the vortex core from its original axis as shown in [1]. A smooth transition from a bubble to a spiral-type ``mode'' can be forced by inducing a small asymmetric disturbance which led to the conclusion, that the patterns do not represent different fundamental modes of breakdown. The subject presented herein addresses the following question: how does breakdown evolve in a swirling flow in which the vortex core is forced on a straight axis? In addition, what is the effect of turbulent inflow conditions? This type of vortex conditions is achieved in a spinning tube flow. The swirl is introduced at the entrance of the rotating tube with a honeycomb package and maintained by the viscous action in the boundary layer of the spinning tube. A diffuser at the end induces an adverse pressure gradient to force the breakdown. Flow visualization experiments are carried out to characterize the nature of breakdown over a range of different flow conditions. For some selected characteristic stages, detailed velocity fields were obtained using the method of Digital Particle-Image-Velocimetry (DPIV). The results show, that for the range of parameters investigated, breakdown is initiated at Rossby-numbers below a critical value of Ro ≈ 0.6 similar to those observed in other experiments. The bursted part of the vortex has a near axi-symmetric slender conical shape containing approximately stagnant flow. Its downstream end is characterized by a jump-like contraction where the flow evolves into a jet with enhanced swirl on the axis. It is only in this region downstream of the jump-like contraction that asymmetric instabilities and wavy flow patterns could be observed. Perturbations caused by them travel upstream but do not change the near-axisymmetric shape of the bursted part of the vortex.     

偏转矢量喷流对双三角翼前缘涡破裂影响的实验研究

本文应用染色液流动显示技术对后缘偏转喷流情况下76°/40°双三角翼前缘涡破裂位置的变化进行了观测,实验结果表明偏转喷流主要推迟与喷流方向相同一侧前缘涡的破裂,而使另一侧前缘涡破裂略有提前.随着喷流偏转角度的增大,喷流使两前缘涡破裂位置差逐渐增大.另外,随着模型攻角的增大,前缘涡涡核与双三角翼翼面的夹角逐渐增大,导致偏转喷流的作用逐渐减弱.     

三角翼前缘涡的某些破裂形式及特性研究

基于流动显示和PIV技术测量的实验结果，对三角翼前缘涡破裂的一些形式和破裂特性进行了分析和讨论。通过PIV测量所得到的涡量分布证实了在螺旋破裂的情况下，涡核的螺旋方向与前缘涡的旋转方向相反，及双螺旋破裂形式的存在等。进而对螺旋波的形成机理提出了与有关文献不同的看法。     

Compressible and confined vortex flow

The internal compressible flow of a thin vortex chamber was investigated experimentally by measuring the radial distribution of temperature and pressure, from which the velocity field was calculated. The bulk of the internal vortex was found to be described by u_θr^0.69 = constant. The total resistance of the vortex chamber to the flow was also investigated in the context of fluidic vortex diode behavior under conditions of compressible and choked flow. It was found that the vortex chamber choked at an upstream-to-downstream pressure ratio of about 6 and in doing so passed a mass flow rate of 28% of the equivalent one-dimensional ideal nozzle. The resistance of vortex chambers is known to be strongly influenced by the presence of reversed flow in the exit due to vortex breakdown. Schlieren photography of the swirling exhaust flow was used to show that, while vortex breakdown does occur, it can only do so after the flow has become subsonic downstream of the exit and cannot therefore influence the vortex chamber resistance.     

Thin‐tube vortex simulations for sinusoidal instability in a counter‐rotating vortex pair

A thin‐tube vortex method is developed to investigate the intrinsic instability within a counter‐rotating vortex pair system and the effects from the core size and the wavenumbers (or wavelengths). The numerical accuracy and the advantages of the scheme are theoretically estimated. A nearest‐neighbour‐image method is employed in this three‐dimensional vortex simulation. Agreement with Crow's instability analysis has been achieved numerically for the long‐wave cases. A short‐wave instability for the zeroth radial mode of bending instability has also been found using the thin‐tube vortex simulations. Then, the combinations of long‐ and short‐wave instability are investigated to elucidate the non‐linear effects due to the interactions of two different modes. It is shown that instability is enhanced if both long‐ and short‐wave instabilities occur simultaneously. Although the method used in the paper is not capable of including effects such as axial flow, vortex core deformation and other complicated viscous effects, it effectively predicts and clarifies the first‐order factor that dominates the sinusoidal instability behaviour in a vortex pair. Copyright © 2002 John Wiley & Sons, Ltd.     

A three‐dimensional vortex particle‐in‐cell method for vortex motions in the vicinity of a wall

A new vortex particle‐in‐cell method for the simulation of three‐dimensional unsteady incompressible viscous flow is presented. The projection of the vortex strengths onto the mesh is based on volume interpolation. The convection of vorticity is treated as a Lagrangian move operation but one where the velocity of each particle is interpolated from an Eulerian mesh solution of velocity–Poisson equations. The change in vorticity due to diffusion is also computed on the Eulerian mesh and projected back to the particles. Where diffusive fluxes cause vorticity to enter a cell not already containing any particles new particles are created. The surface vorticity and the cancellation of tangential velocity at the plate are related by the Neumann conditions. The basic framework for implementation of the procedure is also introduced where the solution update comprises a sequence of two fractional steps. The method is applied to a problem where an unsteady boundary layer develops under the impact of a vortex ring and comparison is made with the experimental and numerical literature. Copyright © 2001 John Wiley & Sons, Ltd.     

Flow past a transversely oscillating square cylinder in free stream at low Reynolds numbers

This paper reports simulation results for free‐stream flow past an oscillating square cylinder at Re=100 and 150, for oscillating‐to‐natural‐shedding frequency ratios of 0.5?f_r?3.0 at a fixed oscillation amplitude of 0.2 of the cylinder width. The transformed governing equations are solved in a non‐inertial frame of reference using the finite volume technique. The ‘lock‐in’ phenomena, where the vortex shedding becomes one with the oscillation frequency, is observed near the natural shedding frequency (f_r≈1). Beyond the synchronization band, downstream recovery of the wake to its stationary (natural) state (frequency) is observed in cross‐stream velocity spectra. At higher forcing frequencies, a phase lag between the immediate and the far wake results in a shear layer having multi‐polar vortices. A ‘Vortex‐switch’ accompanied by a change in the direction of energy transfer is identified at the ‘lock‐in’ boundaries. The variation of aerodynamic forces is noticed to be different in the lock‐in regime. The velocity phase portrait in the far wake revealed a chaotic state of flow at higher excitation though a single (natural) frequency appears in the spectra. Copyright © 2008 John Wiley & Sons, Ltd.     

Reduced‐order controllers for control of flow past an airfoil

Reduced‐order controller design by means of reduced‐order model for control of a wake flow is presented. Reduced‐order model is derived by combining the Galerkin projection with proper orthogonal decomposition (POD) or with other related reduced‐order approaches such as singular value decomposition or reduced‐basis method. In the present investigation, we discuss the applicability of the reduced‐order approaches for fast computation of the optimal control for control of vortex shedding behind a thin airfoil through unsteady blowing on the airfoil surface. Accuracy of the reduced‐order model is quantified by comparing flow fields obtained from the reduced‐order models with those from the full‐order simulations under the same free‐stream conditions. A control of vortex shedding is demonstrated for Reynolds number 100. It is found that downstream directed blowing on the upper surface of the airfoil near the leading edge is more efficient in mitigating flow separation and suppressing the vortex shedding. Copyright © 2005 John Wiley & Sons, Ltd.     

Obstacle-induced spiral vortex breakdown

An experimental investigation on vortex breakdown dynamics is performed. An adverse pressure gradient is created along the axis of a wing-tip vortex by introducing a sphere downstream of an elliptical hydrofoil. The instrumentation involves high-speed visualizations with air bubbles used as tracers and 2D Laser Doppler Velocimeter (LDV). Two key parameters are identified and varied to control the onset of vortex breakdown: the swirl number, defined as the maximum azimuthal velocity divided by the free-stream velocity, and the adverse pressure gradient. They were controlled through the incidence angle of the elliptical hydrofoil, the free-stream velocity and the sphere diameter. A single helical breakdown of the vortex was systematically observed over a wide range of experimental parameters. The helical breakdown coiled around the sphere in the direction opposite to the vortex but rotated along the vortex direction. We have observed that the location of vortex breakdown moved upstream as the swirl number or the sphere diameter was increased. LDV measurements were corrected using a reconstruction procedure taking into account the so-called vortex wandering and the size of the LDV measurement volume. This allows us to investigate the spatio-temporal linear stability properties of the flow and demonstrate that the flow transition from columnar to single helical shape is due to a transition from convective to absolute instability.     

Interference effect of two equal‐sized square cylinders in tandem arrangement: With planar shear flow

Numerical simulations have been performed for flow past two equal‐sized square cylinders in tandem arrangement subjected to incoming planar shear flow. Effect of L/d ratio and the shear parameter has been studied. The range of L/d ratio (ratio of center‐to‐center distance (L) to cylinder width (d)) is varied from 2 to 7 and the non‐dimensional shear parameter (K) is varied from 0.0 to 0.4 in steps of 0.1. For all the cases the Reynolds number (Re) based on centerline velocity and cylinder width is fixed at 100. The results are compared with that of isolated square cylinder with uniform flow. Strouhal number decreases with increasing shear parameter. There are more than one shedding frequency at high shear parameters and L/d ratios. The mean drag coefficient is decreased with shear parameter and lesser than that of the single cylinder. The root mean square (RMS) value of both lift and drag coefficients is higher for the downstream cylinder for all values of shear parameter. With increasing L/d ratio, for both lift and drag, the RMS value increases and then decreases for upstream cylinder, whereas it continuously increases for the downstream cylinder. The stagnation point is moved towards the top leading edge with increasing shear. The critical L/d ratio, which is defined as the distance between two cylinders, beyond which the vortex shedding from the upstream cylinder occurs, decreases with increasing shear parameter. Copyright © 2007 John Wiley & Sons, Ltd.     

On the formation of vortex rings and pairs

The axisymmetric vortex sheet model developed by Nitsche & Krasny (1994) has been extended to study the formation of vortex rings (pairs) at the edge of circular (2D) tube and opening. Computations based on this model are in good agreement with the experiments (Didden (1979) for circular tube and Auerbach (1987) for 2D tube and opening). Using this new model, evidences are provided to show that the main failure of the similarity theory (the false prediction of axial trajectory of vortex ring) is due to its ignorance of the self-induced ring velocity (mutual induction for vortex pair). We further reason why the similarity theory succeeds in its prediction of radial movement of vortex ring. The effects of various parameters such as turning angle α and piston speedU _p (t) on the formation of vortex ring are investigated. Numerical result shows that turning angle α has no effect on circulation shed τ. We also discuss Glezer (1988)'s summary on the influence ofU _p upon the shedding circulation, and finally give the variation of core distribution of vortex ring with α andU _p (t). The project is supported by National Natural Science Foundation of China and Doctoral Program of Institution of Higher Education     

Finite element study of vortex‐induced cross‐flow and in‐line oscillations of a circular cylinder at low Reynolds numbers

Vortex‐induced vibrations of a circular cylinder placed in a uniform flow at Reynolds number 325 are investigated using a stabilized space–time finite element formulation. The Navier–Stokes equations for incompressible fluid flow are solved for a two‐dimensional case along with the equations of motion of the cylinder that is mounted on lightly damped spring supports. The cylinder is allowed to vibrate, both in the in‐line and in the cross‐flow directions. Results of the computations are presented for various values of the structural frequency of the oscillator, including those that are sub and superharmonics of the vortex‐shedding frequency for a stationary cylinder. In most of the cases, the trajectory of the cylinder corresponds to a Lissajou figure of 8. Lock‐in is observed for a range of values of the structural frequency. Over a certain range of structural frequency (F_s), the vortex‐shedding frequency of the oscillating cylinder does not match F_s exactly; there is a slight detuning. This phenomenon is referred to as soft‐lock‐in. Computations show that this detuning disappears when the mass of the cylinder is significantly larger than the mass of the surrounding fluid it displaces. A self‐limiting nature of the oscillator with respect to cross‐flow vibration amplitude is observed. It is believed that the detuning of the vortex‐shedding frequency from the structural frequency is a mechanism of the oscillator to self‐limit its vibration amplitude. The dependence of the unsteady solution on the spatial resolution of the finite element mesh is also investigated. Copyright © 1999 John Wiley & Sons, Ltd.     

Evolution of single elliptic vortex rings

The evolution of single elliptic vortex rings for initial aspect ratio (AR)=2,4,6 has been studied. The incompressible Navier-Stokes equations are solved by a dealiased pseudo-spectral method with 64³ grid points in a periodic cube. We find that there are three kinds of vortex motion asAR increases and bifurcation occurs at certainAR. The processes of advection, interaction and decay of vortex ring are discussed. Numerical results coincide with experiments and other authors' numerical simulation. The project is supported by National Natural Science Foundation of China and Doctoral Program of Institution of Higher Education     

Numerical simulation of flow in a circular duct fitted with air‐jet vortex generators

Most of the fundamental studies of the use of air‐jet vortex generators (AJVGs) have concentrated on their potential ability to inhibit boundary layer separation on aerofoils. However, AJVGs may be of use in controlling or enhancing certain features of internal duct flows. For example, they may be of use in controlling the boundary layer at the entrance to engine air intakes, or as a means of increasing mixing and heat transfer. The objective of this paper is to analyse the flow field in the proximity of an air‐jet vortex generator array in a duct by using two local numerical models, i.e. a simple flat plate model and a more geometrically faithful sector model. The sector model mirrors the circular nature of the duct's cross‐section and the centre line conditions on the upper boundary. The flow was assumed fully turbulent and was solved using the finite volume, Navier–Stokes Code CFX 4 (CFDS, AEA Technology, Harwell) on a non‐orthogonal, body‐fitted, grid using the k–ε turbulence model and standard wall functions. Streamwise, vertical and cross‐stream velocity profiles, circulation and peak vorticity decay, peak vorticity paths in cross‐stream and streamwise direction, cross‐stream vorticity profiles and cross‐stream wall shear stress distributions were predicted. Negligible difference in results was observed between the flat plate and the sector model, since the produced vortices were small relative to the duct diameter and close to the surface. The flow field was most enhanced, i.e. maximum thinning of the boundary layer, with a configuration of 30° pitch and 75° skew angle. No significant difference in results could be observed between co‐ and counter‐rotating vortex arrays. Copyright © 2002 John Wiley & Sons, Ltd.     

Volumetric velocity measurements of vortex rings from inclined exits

Vortex rings were generated by driving pistons within circular cylinders of inner diameter D = 72.8 mm at a constant velocity U ₀ over a distance L = D. The Reynolds number, U ₀ L/(2ν), was 2500. The flow downstream of circular and inclined exits was examined using volumetric 3-component velocimetry (V3V). The circular exit yields a standard primary vortex ring that propagates downstream at a constant velocity and a lingering trailing ring of opposite sign associated with the stopping of the piston. By contrast, the inclined nozzle yields a much more complicated structure. The data suggest that a tilted primary vortex ring interacts with two trailing rings; one associated with the stopping of the piston, and the other associated with the asymmetry of the cylinder exit. The two trailing ring structures, which initially have circulation of opposite sign, intertwine and are distorted and drawn through the center of the primary ring. This behavior was observed for two inclination angles. Increased inclination was associated with stronger interactions between the primary and trailing vortices as well as earlier breakdown.     

A numerical investigation of the flow over a pair of identical square cylinders in a tandem arrangement

This paper describes a numerical study of the two‐dimensional and three‐dimensional unsteady flow over two square cylinders arranged in an in‐line configuration for Reynolds numbers from 40 to 1000 and a gap spacing of 4D, where D is the cross‐sectional dimension of the cylinders. The effect of the cylinder spacing, in the range G = 0.3D to 12D, was also studied for selected Reynolds numbers, that is, Re = 130, 150 and 500. An incompressible finite volume code with a collocated grid arrangement was employed to carry out the flow simulations. Instantaneous and time‐averaged and spanwise‐averaged vorticity, pressure, and streamlines are computed and compared for different Reynolds numbers and gap spacings. The time averaged global quantities such as the Strouhal number, the mean and the RMS values of the drag force, the base suction pressure, the lift force and the pressure coefficient are also calculated and compared with the results of a single cylinder. Three major regimes are distinguished according to the normalized gap spacing between cylinders, that is, the single slender‐body regime (G < 0.5), the reattach regime (G < 4) and co‐shedding or binary vortex regime (G ≥4). Hysteresis with different vortex patterns is observed in a certain range of the gap spacings and also for the onset of the vortex shedding. Copyright © 2011 John Wiley & Sons, Ltd.     

Downstream boundary effects on the spectral characteristics of a swirling flowfield

The spectral characteristics and the structural response of a swirling flowfield are investigated subject to a non-axisymmetric disturbance and a contraction imposed downstream. Two natural frequencies are noted in different regions of the undisturbed swirling flowfield, one is due to a precessing vortex core and the other to the most amplified downstream azimuthal instability. The downstream contraction usually causes compression of the central recirculation zone into two side-lobes, increases the dominant frequencies and forms a straight central vortex core with a high axial velocity. The dominant downstream instability frequency depends linearly on the inlet Reynolds number and on the mode of the breakdown. For the downstream non-axisymmetric disturbance, such as the passing of the turbine blades, the fundamental frequency is not altered by the disturbance and the oscillation strength of the downstream instability is greatly reduced as the excitation frequency remains unmatched with the dominant downstream natural frequency. Downstream azimuthal instability promotes the breakdown recirculation.A version of this paper was presented at the 26th AIAA Aerospace Sciences Meeting, Reno, Nevada, 11–14, Jan. 1988