Vortex Ring Model Research Articles

An experimental study on fuel spray-induced vortex-like structures

The properties of spray-induced vortex-like structures for asymmetric pressure swirl atomizer were studied experimentally with different injection pressures. The high-speed Particle Imaging Velocimetry (PIV) was used to study the spray characteristics such as velocity and vorticity. The vortex centers were identified by velocity weighted vorticity. The translational velocity components of vortex centers were computed from its displacement divided by the time interval. For five different pressure conditions, the motion trajectories of vortex center were the same in an earlier period of spray, but were different in a later period of spray. The normalized translational velocity of vortex center and normalized time were introduced to compare with vortex ring model. The results indicated that the normalized axial translational velocity decreased with increasing normalized time, which converged to the predictions of the model in long time limit where α=−0.75 in the turbulent case. However, the results for the normalized radial translational velocity were different from the predictions of the model. The normalized radial translational velocity decreased with the increase of the normalized time when the injection pressure was lower than a critical value, but it obviously increased with the increase of the normalized time in case of the injection pressure higher than the critical value. Furthermore, the average vorticities at the vortex center were obtained and increased with the increase of the injection pressure. This study provides references for developing spray theory and improving injection technology.

Multi-oscillations of a bubble in a compressible liquid near a rigid boundary

AbstractBubble dynamics near a rigid boundary are associated with wide and important applications in cavitation erosion in many industrial systems and medical ultrasonics. This classical problem is revisited with the following two developments. Firstly, computational studies on the problem have commonly been based on an incompressible fluid model, but the compressible effects are essential in this phenomenon. Consequently, a bubble usually undergoes significantly damped oscillation in practice. In this paper this phenomenon will be modelled using weakly compressible theory and a modified boundary integral method for an axisymmetric configuration, which predicts the damped oscillation. Secondly, the computational studies so far have largely been concerned with the first cycle of oscillation. However, a bubble usually oscillates for a few cycles before it breaks into much smaller ones. Cavitation erosion may be associated with the recollapse phase when the bubble is initiated more than the maximum bubble radius away from the boundary. Both the first and second cycles of oscillation will be modelled. The toroidal bubble formed towards the end of the collapse phase is modelled using a vortex ring model. The repeated topological changes of the bubble are traced from a singly connected to a doubly connected form, and vice versa. This model considers the energy loss due to shock waves emitted at minimum bubble volumes during the beginning of the expansion phase and around the end of the collapse phase. It predicts damped oscillations, where both the maximum bubble radius and the oscillation period reduce significantly from the first to second cycles of oscillation. The damping of the bubble oscillation is alleviated by the existence of the rigid boundary and reduces with the standoff distance between them. Our computations correlate well with the experimental data (Philipp & Lauterborn,J. Fluid Mech., vol. 361, 1998, pp. 75–116) for both the first and second cycles of oscillation. We have successively reproduced the bubble ring in direct contact with the rigid boundary at the end of the second collapse phase, a phenomenon that was suggested to be one of the major causes of cavitation erosion by experimental studies.

The role of large-scale vortical structures in transient convective heat transfer augmentation

AbstractThe physical mechanism by which large-scale vortical structures augment convective heat transfer is a fundamental problem of turbulent flows. To investigate this phenomenon, two separate experiments were performed using simultaneous heat transfer and flow field measurements to study the vortex–wall interaction. Individual vortices were identified and studied both as part of a turbulent stagnation flow and as isolated vortex rings impacting on a surface. By examining the temporal evolution of both the flow field and the resulting heat transfer, it was observed that the surface thermal transport was governed by the transient interaction of the vortical structure with the wall. The magnitude of the heat transfer augmentation was dependent on the instantaneous strength, size and position of the vortex relative to the boundary layer. Based on these observations, an analytical model was developed from first principles that predicts the time-resolved surface convection using the transient properties of the vortical structure during its interaction with the wall. The analytical model was then applied, first to the simplified vortex ring model and then to the more complex stagnation region experiments. In both cases, the model was able to accurately predict the time-resolved convection resulting from the vortex interactions with the wall. These results reveal the central role of large-scale turbulent structures in the augmentation of thermal transport and establish a simple model for quantitative predictions of transient heat transfer.

Jet and Vortex Ring-Like Structures in Internal Combustion Engines: Stability Analysis and Analytical Solutions

Recently developed models, describing the disintegration of liquid jets and the dynamics of vortex ring-like structures at Die- sel and gasoline engine-like conditions, are reviewed. The results of comparative analysis of modal and non-modal hydrody- namic instabilities of round viscous fluid jets are presented. Analytical formulae for vortex ring translational velocities, pre- dicted by vortex ring models, are compared with the results of numerical solutions to the underlying equations and experimen- tal data. A new approach to numerical simulation of two-phase two-dimensional flows, based on a combination of the full La- grangian method for the dispersed phase and the vortex blob method for the carrier phase, is discussed.

Nested DE based parameter estimation for multiple vortex ring microburst model

Modelling of microburst is significant for flight simulations. The most widely used model of microburst is the one based on the principle of multiple vortex ring. The characteristics of the microburst are directly determined by the parameters of the model. The conventional method to fix the parameters of multiple vortex ring microburst model is using experiential formula, which is not flexible enough. In this paper, we treat the parameters estimation of multiple vortex ring model as an optimization problem, and introduce the differential evolution algorithm to solve it. In the process of estimating the parameters by the maximum wind velocity, there are two interrelated optimization processes. Therefore, we improved the standard differential evolution algorithm in this paper. A nested differential evolution algorithm is proposed to accomplish the two optimization process, intermediate optimization and objective optimization. The numerical experiments show that this method can flexibly generate microburst with any maximum wind velocity, and the error meet the requirement set by the user.

Force and power of flapping plates in a fluid

AbstractThe force and power of flapping plates are studied by vortex dynamic analysis. Based on the dynamic analysis of the numerical results of viscous flow past three-dimensional flapping plates, it is found that the force and power are strongly dominated by the vortical structures close to the body. Further, the dynamics of the flapping plate is investigated in terms of viscous vortex-ring model. It is revealed that the model can reasonably reflect the essential properties of the ring-like vortical structure in the wake, and the energy of the plate transferred to the flow for the formation of each vortical structure possesses a certain relation. Moreover, simplified formulae for the thrust and efficiency are proposed and verified to be reliable by the numerical solutions and experimental measurements of animal locomotion. The results obtained in this study provide physical insight into the understanding of the dynamic mechanisms relevant to flapping locomotion.

Lift force reduction due to body image of vortex for a hovering flight model

AbstractThe effect of the body on the lift force in hovering flight is studied here by including the effect of image vortex rings (IVRs) in the inviscid vortex ring model proposed by Rayner (J. Fluid Mech., vol. 91, 1979, pp. 697–730) and used by Wang & Wu (J. Fluid Mech., vol. 654, 2010, pp. 453–472) to study lift force due to wakes. The body is treated simply as an equivalent sphere following the data of Ellington (Phil. Trans. R. Soc. Lond.B, vol. 305, 1984a, pp. 17–40). It is shown that the body image reduces the lift by inducing a further downwash near the wing tip and an additional contraction to the real vortex rings (RVRs). The amount of force reduction due to body image is found to grow cubically with relative body size, defined by the equivalent radius relative to the wing span, and approximately linearly with the feathering parameter. ForApisandBombuswith large relative body size and large feathering parameter, the body images reduce lift by an amount near 8 % according to the present simplified analysis.

Experimental investigation of a twice-shocked spherical gas inhomogeneity with particle image velocimetry

Results are presented from an experimental investigation into the interaction of a planar shock wave with a vortex ring. A free-falling spherical soap bubble is traversed by the incident shock wave and develops into a vortex ring as a result of baroclinically deposited vorticity (\({\nabla\rho\times\nabla p \neq 0}\)). The vortex ring translates with a velocity relative to the particle velocity behind the shock wave due to circulation. After the shock wave reflects from the tube end wall, it traverses the vortex ring (this process is called “reshock”) and deposits additional vorticity. Planar Mie scattering is used to visualize the atomized soap film at high frame rates (up to 10,000 fps). Particle image velocimetry (PIV) was performed for an argon bubble in nitrogen accelerated by a M = 1.35 shock wave. Circulation was determined from the PIV velocity field and found to agree well with Kelvin’s vortex ring model.

Dynamics of vortex rings and spray-induced vortex ring-like structures

Analytical formulae, predicted by recently developed vortex ring models, in the limit of small Reynolds numbers ( R e ), are compared with numerical solutions of the underlying equation for vorticity and experimental data. Particular attention is focused on the recently developed generalised vortex ring model in which the time evolution of the thickness of the vortex ring core L is approximated as a t b , where a and b are constants ( 1 / 4 ≤ b ≤ 1 / 2 ). This model incorporates both the laminar model for b = 1 / 2 and the fully turbulent model for b = 1 / 4 . A new solution for the normalised vorticity distribution is found in the form ω 0 + R e ω 1 , where ω 0 is the value of normalised vorticity predicted by the classical Phillips solution. This solution shows the correct trends in the redistribution of vorticity due to the Reynolds number effect, and it predicts the increase in the volume of fluid carried inside the vortex ring. It is emphasised that although the structures of vortex rings predicted by analytical formulae, based on the linear approximation, and numerical calculations for arbitrary R e are visibly different for realistic Reynolds numbers, the values of integral characteristics, such as vortex ring translational velocity and energy, predicted by both approaches, turn out to be remarkably close. The values of velocities in the region of maximal vorticity, predicted by the generalised vortex ring model, are compared with the results of experimental studies of vortex ring-like structures in gasoline engine-like conditions with a high-pressure (100 bar) injector. The data analysis is focused on the direct measurements of droplet axial velocities in the regions of maximal vorticity. Most of the values of these velocities lie between the theoretically predicted values corresponding to the later stage of vortex ring development between b = 1 / 4 (fully developed turbulence) and 1 / 2 (laminar case).

Vortex ring-like structures in gasoline fuel sprays under cold-start conditions

A phenomenological study of vortex ring-like structures in gasoline fuel sprays is presented for two types of production fuel injectors: a low-pressure, port fuel injector (PFI) and a high-pressure atomizer that injects fuel directly into an engine combustion chamber (G-DI). High-speed photography and phase Doppler anemometry (PDA) were used to study the fuel sprays. In general, each spray was seen to comprise three distinct periods: an initial, unsteady phase; a quasi-steady injection phase; and an exponential trailing phase. For both injectors, vortex ring-like structures could be clearly traced in the tail of the sprays. The location of the region of maximal vorticity of the droplet and gas mixture was used to calculate the temporal evolution of the radial and axial components of the translational velocity of the vortex ring-like structures. The radial components of this velocity remained close to zero in both cases. The experimental results were used to evaluate the robustness of previously developed models of laminar and turbulent vortex rings. The normalized time, , and normalized axial velocity, , were introduced, where tinit is the time of initial observation of vortex ring-like structures. The time dependence of on was approximated as and for the PFI and G-DI sprays respectively. The G-DI spray compared favourably with the analytical vortex ring model, predicting , in the limit of long times, where α = 3/2 in the laminar case and α = 3/4 when the effects of turbulence are taken into account. The results for the PFI spray do not seem to be compatible with the predictions of the available theoretical models.

A generalized vortex ring model

A conventional laminar vortex ring model is generalized by assuming that the time dependence of the vortex ring thickness ℓ is given by the relation ℓ = atb, where a is a positive number and 1/4 ≤ b ≤ 1/2. In the case in which $a=\sqrt{2\nu}$, where ν is the laminar kinematic viscosity, and b = 1/2, the predictions of the generalized model are identical with the predictions of the conventional laminar model. In the case of b = 1/4 some of its predictions are similar to the turbulent vortex ring models, assuming that the time-dependent effective turbulent viscosity ν∗ is equal to ℓℓ′. This generalization is performed both in the case of a fixed vortex ring radius R0 and increasing vortex ring radius. In the latter case, the so-called second Saffman's formula is modified. In the case of fixed R0, the predicted vorticity distribution for short times shows a close agreement with a Gaussian form for all b and compares favourably with available experimental data. The time evolution of the location of the region of maximal vorticity and the region in which the velocity of the fluid in the frame of reference moving with the vortex ring centroid is equal to zero is analysed. It is noted that the locations of both regions depend upon b, the latter region being always further away from the vortex axis than the first one. It is shown that the axial velocities of the fluid in the first region are always greater than the axial velocities in the second region. Both velocities depend strongly upon b. Although the radial component of velocity in both of these regions is equal to zero, the location of both of these regions changes with time. This leads to the introduction of an effective radial velocity component; the latter case depends upon b. The predictions of the model are compared with the results of experimental measurements of vortex ring parameters reported in the literature.

Simplified Rotor Inflow Model for Descent Flight

A simplified inflow model called the ‘ring vortex model’ is developed for a rotor in descent condition. The ring vortexmodelaccountsforthe flowinteractionbetweenrotorwakeandsurroundingairflowindescent flightbyusing a series of vortex rings along the rotor wake. Important features of the ring vortex model are illustrated in detail, including the convection speed, the vortex strength, and the number of vortex rings. An augmentation to total mass flow parameter in the existing inflow equation is proposed to create a steady-state transition between the helicopter and the windmill branches. With the ring vortex model, it is feasible to predict rotor inflow over a wide range of descent conditions. Numerical results show good correlation with experimental data for both axial and inclined descent. In addition, the ring vortex model is used to explain the influence of model parameters (such as blade twist and blade taper) on rotor-induced velocity during descent flight. Nomenclature CQ = rotor torque coefficient CT = rotor thrust coefficient CT = average rotor thrust coefficient kring = nondimensional factor used to compute induced velocity from a vortex ring k� = strength factor of a vortex ring Nb = number of blades Nring = number of vortex rings R = rotor radius T = rotor thrust Vh = rotor-induced velocity at hover Vi = rotor-induced velocity Vver;con = vertical convection speed of a vortex ring Vx = rotor horizontal speed (positive forward) Vz = rotor vertical speed (positive in climb) � = angle of descent � = strength of a vortex ring � T = amplitude of thrust fluctuation with respect to mean value of thrust � Vi = increment of rotor-induced velocity due to the presence of vortex rings � = normalized rotor vertical speed (positive in climb) � peak = normalized rotor vertical speed corresponding to the peak value of induced velocity � = nondimensional total inflow � m = nondimensional average induced velocity � = average total inflow � = advance ratio � z = nondimensional climb rate in the tip path plane � � = rotor advance ratio normalized by induced flow at

Propulsive force calculations in swimming frogs II. Application of a vortex ring model to DPIV data

Frogs propel themselves by kicking water backwards using a synchronised extension of their hind limbs and webbed feet. To understand this propulsion process, we quantified the water movements and displacements resulting from swimming in the green frog Rana esculenta, applying digital particle image velocimetry (DPIV) to the frog's wake. The wake showed two vortex rings left behind by the two feet. The rings appeared to be elliptic in planform, urging for correction of the observed ring radii. The rings' long and short axes (average ratio 1.75:1) were about the same size as the length and width of the propelling frog foot and the ellipsoid mass of water accelerated with it. Average thrust forces were derived from the vortex rings, assuming all propulsive energy to be compiled in the rings. The calculated average forces (F(av)=0.10+/-0.04 N) were in close agreement with our parallel study applying a momentum-impulse approach to water displacements during the leg extension phase. We did not find any support for previously assumed propulsion enhancement mechanisms. The feet do not clap together at the end of the power stroke and no "wedge-action" jetting is observed. Each foot accelerates its own water mantle, ending up in a separate vortex ring without interference by the other leg.

Low-Speed Aerodynamics, Second Edition

Low-Speed Aerodynamics, Second Edition

Dynamics of vortices on a uniformly shelving beach

Laboratory experiments are described which investigate the dynamics of a vortex dipole moving in water towards a planar sloping beach inclined at an angle α to the horizontal. Results are compared with those of a vortex ring model first developed by Peregrine (1996). The vortices separate as they travel up the beach, eventually moving in opposite directions and nearly parallel to the shoreline. The ranges of conditions examined are 3°[les ]α[les ]45°, 1×103[les ]Re[les ]6×103 and 0.05[les ]Fr[les ]0.14, where Re and Fr are the on-slope Reynolds number and the Froude number of the vortices, respectively. The minimum distance from the shoreline reached by the vortices and their along-shore speed are in general agreement with the predictions when, respectively, R*i<3 (where R*i is the non-dimensional initial distance of the vortices from the shore-line) and Re[gsim ]1500. The vortex ring model is likely to have useful applications to the study of the dynamics of the near-shore zone.

Hydrodynamic lift and drag fluctuations of a sphere—empirical model

An empirical model is developed to estimate the unsteady lift and drag induced on a spherical body subjected to a steady, uniform flow. A wind tunnel is used to measure the statistics of the surface pressure fluctuations on a sphere under subcritical Reynolds number conditions. The measurement results are incorporated into the model for predicting the unsteady force induced on the sphere. The model is based on a separable assumption of the cross-power spectral densities of the surface pressure fluctuations. This assumption is shown to be a proper engineering approximation except in low-frequency ranges. The model functions are obtained using least mean-square curve fits of the data. Tow tank experiments are performed, where the flow-induced unsteady side force and drag are measured independently of each other on spheres configured as acoustic velocity hydrophones. The empirical model and the tow tank measurements are in very good agreement with each other and also with a simplified vortex ring model presented in the accompanying paper. The predicted forces are used to determine the flow-induced noise on underwater inertial sensors subjected to a steady, uniform flow. [Work supported by ONR Code 321 SS.]

Assessment of microburst models for downdraft estimation

The effectiveness of three microburst models in estimating the downdraft from horizontal velocity measurements is assessed. The development of the models and their characteristics are discussed. The simplest model, a linear one, works well for altitudes below 200 m and near the microburst core. A ring-vortex model and an empirical model give the best overall results. The former is the most complex, requiring four variables to define it. The empirical model uses three variables.

Magnetics and the New Understanding of Materials Given by the New Frame in Physics

A new framework uniting classical and quantum physics, along with implications for the study of magnetic materials, are discussed. Features of this framework include emphasis on the Schrödinger representation of time-dependent wave functions, which alone enables a continuous transition from classical to quantum mechanical phenomena, and the adoption of an "electron field" model, replacing the vortex ring model of the electron. Consequences for magnetics, such as in statistical thermodynamic treatment of magnetized materials and the manifest nature of the Meisner effect in superconductors, are indicated.

On the coherent structure of the axisymmetric mixing layer: a flow-visualization study

In an effort to resolve some controversies regarding the turbulent mixing-layer structure, the near field of a large (18 cm diameter) air jet has been investigated for the jet exit speed of 30 m s−1. The smoke-laden axisymmetric mixing layer has been illuminated by a thin sheet of laser light in an azimuthal plane passing through the jet axis. High-speed visualization films of the mixing layer in the region of its self-preservation (of which a few picture sequences depicting space-time evolutions of the structure of the layer are presented) reveal that most of the time the mixing layer is in a state of disorganization, consisting of relatively smaller scale, random and diffuse turbulent motions; only occasionally are organized distinct large-scale coherent structures formed. The survival distances of the large-scale structures are found to be comparable to their average sizes. The survival time of these structures is about one ‘turnover’ time, each being roughly about five times the local characteristic time scale of the mixing layer. It is seen that tearing is as dominant a mode of large-scale interaction as pairing is; large-scale structures are continually sheared and typically fragmented due to a segment on the high-speed side being torn and swept away from the slower-moving outer portion. Evolution of the large structures occur not primarily through complete pairing as widely believed but quite frequently through ‘fractional pairing’ between segments which have been torn from different upstream large-scale coherent structures or through ‘partial pairing’ when one structure captures only a part of another. The movies show that along with entrainment of non-vortical ambient fluid, radially outward ejection of vortical fluid into the ambient is an important aspect of jet mixing. From aligned displays of ciné film frame sequences, space-time trajectories of identifiable vortical fluid elements have been traced. The convection velocity variation across the shear layer and even the overall structure convection velocity measured from these trajectories agree with those determined from the wave-number-celerity spectra, obtained from double-Fourier transformation of longitudinal velocity space-time correlation measurements with hot-wires.The visualization films do not bear out the two-street vortex ring model recently propounded by Lau. Based on our observations, we propose that tearing, ‘slippage’ and fractional and partial pairings are responsible for the observed radial variation of structure passage frequency, and the causes of the different coherent structures educed by Bruun on the high- and low-speed sides of the mixing layer and for Yule's failure in educing a coherent structure on the low-speed side of the layer.

On turbulence and noise of an axisymmetric shear flow

The noise produced by mean flow-turbulence interaction of a circular subsonic jet is investigated theoretically, and expanded in azimuthal constituents of the turbulent pressure fluctuations. It is found that the low-order azimuthal constituents are the most efficient sound sources. On the basis of pressure correlation measurements, the azimuthal constituents are determined in a low Mach number jet. It is found that, in a range of Strouhal numbers between 0·2 and 1, the first three to four azimuthal constituents clearly dominate over the rest of the turbulent source quantity. A strictly axisymmetric ring vortex model for the coherent structure of the turbulence is, however, shown to be inappropriate.