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.     

Head on collisions of compressible vortex rings on a smooth solid surface

An experimental study has been conducted on the effects of distance variation on the impingement process of compressible vortex rings on a stationary solid wall. An experimental incident Mach number of 1.61 was used. Qualitative and quantitative studies compared the impingement and interaction flow characteristics of a compressible vortex ring with a stationary, solid, smooth surface at three distances: 1.66, 3.33, and 5.00 inner diameters. The three distances corresponded to an under-developed vortex ring (1.66 inner diameters), a vortex ring at its development threshold (3.33 inner diameters), and a fully developed one (5.00 inner diameters). Qualitative schlieren results showed that the surface distance affected the shock/vortex interaction process along with the impingement process of the vortex ring and the flow structure of its trailing jet. Quantitative data were extrapolated to evaluate the propagation velocity of the vortex ring prior to impingement. The boundary layer thickness was also estimated. Particle image velocimetry studies showed the main and secondary vortices to have opposite vorticity, with the magnitude of the vorticity of the secondary vortices being approximately half of that of the main vortex. Surface pressure results reveal the symmetrical properties of the impinging flow, along with a direct correlation between the maximum pressure measured at the instant the vortex ring impingement and an increase in surface distance.     

Drop coalescence and deposition in turbulent wet steam pipe flows

The numerical turbulent coalescence/deposition model of Crane and Williams has been used to indicate likely trends in the development of drop size distribution and entrained water flow rate in the cross-over pipes of a nuclear wet steam turbine. Large increases in mean drop diameter have been shown to be possible, the results being very sensitive to the width of the initial size distribution, the entrained wetness fraction and the turbulence intensity. Deposition rate was also found to be strongly dependent on turbulence intensity, but inertial deposition onto and re-entrainment from the turning vanes of a bend did not significantly influence subsequent coalescence and turbulent deposition rates in the single example computed     

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.     

Characterising shortwave instabilities on a vortex dipole

The paper presents a method for characterising shortwave instability on a vortex dipole. Such instabilities cause the initially straight vortex lines to deform in a sinuous manner. In order to quantify the phenomenon, it is necessary to (a) characterise the vortex dipole and (b) characterise instabilities developed on it. In this study, the vortex dipole characteristics were quantified by using a nonlinear least squares fit to a Lamb–Oseen vortex profile with the velocity field measured by means of particle image velocimetry. The instability was recorded by capturing images of hydrogen bubbles, which were used to mark the vortex centre line, with a CCD camera. It was characterised by applying a fast Fourier transform and seeking dominant wavenumber components and a representative amplitude based on a range of wavenumbers within a bandwidth of interest. The method was tested on simulated and real data. Using the simulated data, the shortwave instability growth rate was calculated with an uncertainty of better than 1% and the mean wavelength deduced with an uncertainty of 5.3%. Using real data, a constant initial growth rate was deduced in agreement with the established theory. Further work might improve the algorithms so that spatial variations in wavelength and growth rate can be determined.     

Spatiotemporal complexity of the aortic sinus vortex

The aortic sinus vortex is a classical flow structure of significant importance to aortic valve dynamics and the initiation and progression of calcific aortic valve disease. We characterize the spatiotemporal characteristics of aortic sinus vortex dynamics in relation to the viscosity of blood analog solution as well as heart rate. High-resolution time-resolved (2 kHz) particle image velocimetry was conducted to capture 2D particle streak videos and 2D instantaneous velocity and streamlines along the sinus midplane using a physiological but rigid aorta model fitted with a porcine bioprosthetic heart valve. Blood analog fluids used include a water–glycerin mixture and saline to elucidate the sensitivity of vortex dynamics to viscosity. Experiments were conducted to record 10 heart beats for each combination of blood analog and heart rate condition. Results show that the topological characteristics of the velocity field vary in timescales as revealed using time bin-averaged vectors and corresponding instantaneous streamlines. There exist small timescale vortices and a large timescale main vortex. A key flow structure observed is the counter vortex at the upstream end of the sinus adjacent to the base (lower half) of the leaflet. The spatiotemporal complexity of vortex dynamics is shown to be profoundly influenced by strong leaflet flutter during systole with a peak frequency of 200 Hz and peak amplitude of 4 mm observed in the saline case. While fluid viscosity influences the length and timescales as well as the introduction of leaflet flutter, heart rate influences the formation of counter vortex at the upstream end of the sinus. Higher heart rates are shown to reduce the strength of the counter vortex that can greatly influence the directionality and strength of shear stresses along the base of the leaflet. This study demonstrates the impact of heart rate and blood analog viscosity on aortic sinus hemodynamics.     

Numerical investigation of the effect of inlet condition on self‐excited oscillation of wet steam flow in a supersonic turbine cascade

Self‐excited oscillation can be induced due to the interaction between condensation process and local transonic condition in condensing flow, which is an important problem in wet steam turbine. With an Eulerian/Eulerian numerical model, the self‐excited oscillation of wet steam flow is investigated in a supersonic turbine cascade. Owing to supercritical heat addition to the subsonic flow in the convergent part of the cascade, the oscillation frequency decreases with increased inlet supercooling. Mass flow rate increases in the oscillating flow due to the greater supersaturation in condensation process, while the increase will be suppressed with the flow oscillation. Higher inlet supercooling leads to the fact that the condensation process moves upstream and the loss increases. Moreover, some predictions of oscillation effects on outflow angle and aerodynamic force are also presented. Finally, heterogeneous condensations with inlet wetness and periodic inlet conditions, as a result of the interference between stator and rotor, are discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Hydrodynamic structure of a vortex ring

Hot-wire anemometry and high-speed motion-picture photography have been used in an experimental study of the structure of a vortex ring in air. The velocity field and streamline pattern have been determined, together with the vorticity distribution. It has been shown that the vorticity is almost entirely localized in the region of the core of the vortex ring and quickly diminishes with distance from the core. Analysis of the experimental results permits a conclusion concerning the nonstationarity of vortex rings.The authors thank V. K. Sheremetov and V. A. Kosinov for their assistance.     

Transport in a turbulent vortex ring

Transport in a turbulent vortex ring is considered; the mass of a passive impurity transported by the vortex is found as a function of distance traveled via a formula that agrees closely with experiment. A method is indicated for filling the part of the vortex that transports the impurity without loss. The effects of the following factors on the transport have been examined: initial Reynolds number, roughness in walls of the exit hole, and density difference between the solution and the medium. The transport of aerosols and suspended particles by vortex rings is considered. Two methods of transport measurement are compared.     

Waves on vortex cores

Here we discuss the types of waves which can be supported on compact regions of vorticity. This is a subject first studied by Lord Kelvin for waves propagating along the vortex lines of the Rankine and hollow-core vorticity distributions. Kelvin's major interest was in the stability of vortex rings and the numerous resurgencies in interest have usually been driven by practically important phenomena, e.g., the observations of vortex breakdown and waves on tornado and aircraft vortices in the early 1960's and more recently in technologically and geophysically significant flows and on the quantised vortices of super fluid HeII.

The major wave-types of interest are of varicose, helicoidal and fluted form and represent a periodic swelling and contraction, a bending and a “krinkling” of the core, respectively. The first two propagate along and the third around the vortex lines. All have been studied theoretically, experimentally and numerically in the limit of small wave amplitude and their major characteristics are now clear. Of particular interest is the extension of these results to the non-linear regime in which case the two first types are known to exhibit solitary wave or soliton characteristics in certain parameter ranges. It is these non-linear waves which often dominate observations of vortex flows both in nature and in technological applications and which have caused much controversy in the interpretation of results found under complex circumstances of flow and apparatus geometry.     

Influence of precession on velocity measurements in a strong laboratory vortex

A strong laboratory vortex is generated in a cylindrical cell using a rotating disk and stretched by pumping the fluid out through a hole in the centre of the top of the cell. The velocity field is measured by means of laser Doppler anemometry and Doppler ultrasonic anemometry which are both non intrusive methods. The vortex exhibits a slight precession which induces temporal fluctuations of the velocity at the measurement point. Due to the centrifugal force, the tracers concentrate in a tubular region around the vortex, leading to spatial variations of the measurement counting rate. Under these two effects, the probability density function (PDF) of the one point velocity exhibits a strong non-Gaussian behaviour. In order to access the details of the velocity profile of the vortex in its own system of reference, the influence of the vortex precession, of the spatial variations of the concentration in tracers and of the intrinsic measurement dispersion is investigated and a model is proposed. It allows to recover statistically the characteristics of the vortex and to deduce the trajectory of its centre from the instantaneous velocity profiles. Received: 5 August 1998/Accepted: 20 February 1999     

Meander of a fin trailing vortex and the origin of its turbulence

The low-frequency meander of a trailing vortex shed from a tapered fin installed on a wind tunnel wall has been studied using stereoscopic particle image velocimetry in the near-wake at Mach 0.8. Distributions of the instantaneous vortex position reveal that the meander amplitude increases with downstream distance and decreases with vortex strength, indicating meander is induced external to the vortex. Trends with downstream distance suggest meander begins on the fin surface, prior to vortex shedding. Mean vortex properties are unaltered when considered in the meandering reference frame, apparently because turbulent fluctuations in the vortex shape and strength dominate positional variations. Conversely, a large peak of artificial turbulent kinetic energy is found centered in the vortex core, which almost entirely disappears when corrected for meander, though some turbulence remains near the core radius. Turbulence originating at the wind tunnel wall was shown to contribute to vortex meander by energizing the incoming boundary layer using low-profile vortex generators and observing a substantial increase in the meander amplitude, while greater turbulent kinetic energy penetrates the vortex core. An explanatory mechanism has been hypothesized, in which the vortex initially forms at the apex of the swept leading edge of the fin where it is exposed to turbulent fluctuations within the wind tunnel wall boundary layer, introducing an instability into the incipient vortex core.     

Numerical simulation of vortex effect in an incompressible fluid

An incompressible-fluid flow in a vortex tube is studied at a temperature close to the boiling point. In the near-axial region of the vortex tube, the existence of a precessing steam vortex and secondary vortex structures is confirmed. The radial distributions of the thermodynamic parameters and velocity components are obtained.     

Application of a vortex method to free surface flows

Vortex methods have found wide applications in various practical problems. The use of vortex methods in free surface flow problems, however, is still very limited. This paper demonstrates a vortex method for practical computation of non-linear free surface flows produced by moving bodies. The method is a potential flow formulation which uses the exact non-linear free surface boundary condition at the exact location of the instantaneous free surface. The position of the free surface, on which vortices are distributed, is updated using a Lagrangian scheme following the fluid particles on the free surface. The vortex densities are updated by the non-linear dynamic boundary condition, derived from the Euler equations, with an iterative Lagrangian numerical scheme. The formulation is tested numerically for a submerged circular cylinder in unsteady translation. The iteration is shown to converge for all cases. The results of the unsteady simulations agree well with classical linearized solutions. The stability of the method is also discussed.     

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。     

Nonlinear wind-up in a strained planar vortex

The response of a Gaussian vortex to a strong external strain field is examined using two complementary numerical schemes. When the strain is weak previous calculations have shown that a rebound phenomenon is operative: after enstrophy is transferred from the mean to the azimuthal component by the straining there is a reversal during which a significant fraction of the enstrophy moves back from the azimuthal component to the mean. Concomitantly the perturbation vorticity undergoes spiral wind-up and develops a short-scale radial structure which becomes ever finer with time. We show that the rebound behaviour is suppressed by strong strain and that the intricate radial structure is simultaneously inhibited. We also give some indication of the modifications that are introduced when a strongly strained vortex is allowed to relax after the forcing field is switched off.     

Approximate two-dimensional equations of vortex flow in a plane layer with solid boundaries

Approximate two-dimensional equations governing turbulent vortex flows in plane fluid layers are considered. The equations were derived by the author in his earlier studies using the shallow water approximation and neglecting circulatory flows in the layer cross-sections. It is shown that, due to the centrifugal effect in the vortex flow, return flows in the layer cross-sections have only a slight influence on the fluid flow in the plane layer and can be neglected.     

An experimental study of diabatic spiral vortex flow

In spiral vortex flow, between concentric cylinders with the inner cylinder rotating and the outer stationary, the addition of a thermal gradient across the gap is a known complicating factor. The present diabatic study for narrow and wide gaps (radius ratios N=0.955 and N=0.8), with a heated outer and adiabatic inner cylinder, was undertaken to investigate this problem. The heat transfer characteristics and the modes of transition have been investigated together with the relationship between them. Using standard on-line digital computer techniques, the onset of vortex flow and its higher transitions have been shown to cause a sharp increase in Nusselt number. At higher Taylor numbers, of the order of 10⁶, a marked change in the Nusselt number occurs with the onset of the transition to periodic turbulent vortex flow. Outer wall heating is seen to affect the modes of transition. Diabatic critical Taylor numbers are much higher than those for adiabatic conditions and are found to depend on the close approach of the vortices to the outer wall     

Free-surface deformation due to spiral flow owing to a source/sink and a vortex in Stokes flow

The free-surface shape and cusp formation are analyzed by considering a viscous flow arising from the superposition of a source/sink and vortex below the free surface where the strength of the source and vortex are arbitrary. In the analysis, Stokes’ approximation is used and surface tension effects are included, but gravity is neglected. The solution is obtained analytically by using conformal mapping and complex function theory. From the solution, shapes of the free surface are obtained, and the formation of a cusp on the free surface is discussed. Above some critical capillary number with a sink, the free-surface shape becomes singular and an apparent cusp should form on the free surface below a real fluid. On the other hand, no cusp would occur for sources of zero or positive strength. Typical streamline patterns are also shown for some capillary numbers. As the capillary number vanishes, the solution is reduced to a linearized potential flow solution.