Vortex Bubble Research Articles

A direct numerical simulation study of coherent oscillation effects of swirling flows

In this study, we carried out a direct numerical simulation of swirling jets to investigate the temporal characteristics of coherent structures related to the vortex breakdown. The type of coherent motion of oscillation, as a temporal characteristic of vortex breakdown, is observed through the analysis of correlation functions. It indicates that the vortex breakdown is accompanied with the resonance of fluctuations of flow velocity, pressure, vortices and etc. Moreover, it is found that the coherent oscillation occurs only for the swirling flows with a high level of swirl (larger than the critical value) when the bubble vortex breakdown takes place, and only at relatively moderate Reynolds numbers transiting from laminar to turbulence.

Numerical study of particle–particle collision in swirling jets: A DEM–DNS coupling simulation

The particle–particle collisions in swirling jets are studied by a coupling method of discrete element method (DEM, a hard-sphere approach) and direct numerical simulation (DNS). The characteristics of distribution of collision in configuration and velocity spaces are investigated in detail through probability density functions (PDFs) in the generalized coordinates. The dependency of particle–particle collision on turbulence characteristics, such as turbulent kinetic energy (TKE), dissipation rate (TDR), fluctuation, and correlated fluctuations, is studied by exploring the PDFs and the correlations between them. The results show that the spatial distribution of particle–particle collision in swirling jets is highly dependent on the Stokes numbers. For small particles, collision is dominated by the enclosure of bubble vortices whereas for large particles it is mainly determined by the configuration of the flow domain. The distribution of collision in velocity space has corresponding features of dependency on the particle property. Small particles are most probable to collide with each other near zero streamwise velocity within the recirculation zone, whereas large particles are most probable to take collision with their axial velocities close to the inflow velocity of fluid. The dependency of collision on TKE and TDR is fairly complicated. For example, for Stokes number slightly less than unity and far larger than unity, collision is relatively well-correlated to TKE, resulting in an augmented effect of turbulence modulation. It is investigated in detail and the physical mechanisms are well interpreted. Finally, the correlation between the PDF of collision and fluctuations of turbulence indicates that collision probability is positively correlated to the normal components of Reynolds stress tensor, but negatively correlated to the shearing components of Reynolds stress tensor.

MEASUREMENT OF THE FLOW RATE AND VOLUME VOID FRACTION OF GAS-LIQUID BUBBLE FLOW USING A VORTEX FLOW METER

Measurement of flow rate and volume void fraction by means of a conventional meter plays an important role in the development of measurement techniques for multiphase flow parameters. Owing to its advantage in insensitivity to most physical properties of the fluid-like viscosity and density, a vortex flow meter was used to measure the flow rate and volume void fraction of gas-liquid bubble flows in this study. The performance of the vortex flow meter under such flow conditions was investigated. First, regular Karman vortex shedding was found in bubble flows with less than 30% volume void fraction, but its stability was influenced by the introduction of a gas-phase component. Second, the frequency of the bubble vortex shedding was approximately in linear proportion to the two-phase Reynolds number, whereas the volume void fraction had little impact on the frequency. Third, the amplitude of the bubble vortex signal could be expressed as a power function format. Moreover, when the volume void fraction was in the range 0–25.90% and Reynolds number between 9.47 × 104 and 20.44 × 104, the meter coefficient of the vortex flow meter was kept constant. Correlations between the vortex shedding characteristics and two-phase flow parameters were established based on mathematical modeling and experimental calibrations. Finally, the two-phase mixture flow rate and the volume void fraction were obtained from the proposed correlations. These findings provide a possibility of using only a single vortex flow meter to measure double parameters in gas-liquid bubble flows.

Water flow model turbine flow visualization study of the unsteady interaction of secondary flow vortices with the downstream rotor

This article presents detailed flow visualization photographs, root mean square processed photography, and computational fluid dynamics (CFD) results of the interaction of the vane passage vortex and horseshoe vortex with the rotor of an axial flow turbine model. Different modes of vortex breakdown behaviour have been experimentally observed inside the rotating passage of the turbine blade. These are spiral vortex mode and bubble mode breakdown. The breakdown mode changes as the vortices are influenced by the periodic pressure field of the rotor. The measurements were taken in a vertical water channel with ink injection for flow visualization. Unsteady CFD analyses have been made with some success in prediction of the unsteady flow structures. In particular, the pre-instability behaviour of the passage vortex in the experiments matches the results of the numerical investigations.

Development and Field Assessment of DO Control System in an Aeration Tank for Automation of Sewage Treatment Plant

Activated sludge sewage treatment processes are difficult to be controlled because of their complex and nonlinear behaviour, however, the control of the dissolved oxygen level in the reactors plays an important role in the operation of the facility. For this reason, this study is designed to present a system which accurately measures DO, MLSS, pH and ORP in the aeration tank to alleviate situations above and provide the automatization of a sewage treatment plant (STP) using new DO control system. The automatic control systems must be guaranteed the accuracy. Therefore, the proposed automatic DO control system in this study could be commercial applications in the aeration tanks by means of operating cost analysis and user-friendly for operation and maintenance. We could get accurate data from the lab tank which has water quality checker because there was no vortex and air bubble during the measurement process. Improvement of confidence in the lab tank enabled effective and automatic operation of sewage treatment plants so that operation costs and manpower could be saved. If this result is put in place in every sewage treatment plant nationwide for practical purposes, it is estimated to cost 18.5 million dollars in installing the lab tank and to save 9.8 million dollars in management cost a year, except for cost saved by automation.

Growth, oscillation and collapse of vortex cavitation bubbles

The growth, oscillation and collapse of vortex cavitation bubbles are examined using both two- and three-dimensional numerical models. As the bubble changes volume within the core of the vortex, the vorticity distribution of the surrounding flow is modified, which then changes the pressures at the bubble interface. This interaction can be complex. In the case of cylindrical cavitation bubbles, the bubble radius will oscillate as the bubble grows or collapses. The period of this oscillation is of the order of the vortex time scale, τV= 2πrc/uθ,max, wherercis the vortex core radius anduθ,maxis its maximum tangential velocity. However, the period, oscillation amplitude and final bubble radius are sensitive to variations in the vortex properties and the rate and magnitude of the pressure reduction or increase. The growth and collapse of three-dimensional bubbles are reminiscent of the two-dimensional bubble dynamics. But, the axial and radial growth of the vortex bubbles are often strongly coupled, especially near the axial extents of the bubble. As an initially spherical nucleus grows into an elongated bubble, it may take on complex shapes and have volume oscillations that also scale with τV. Axial flow produced at the ends of the bubble can produce local pinching and fission of the elongated bubble. Again, small changes in flow parameters can result in substantial changes to the detailed volume history of the bubbles.

Numerical simulation of the postformation evolution of a laminar vortex ring

Direct numerical simulations are used to study the postformation evolution of a laminar vortex ring. The vortex structure is described by calculating the embedded boundaries of the vortex inner core, vortex core, and vortex bubble. The topology of the vortex ring is found to be self-similar during the entire postformation phase. We also show that extracting the vortex inner core provides an objective method in setting the upper value for the cutoff vorticity level separating the vortex from its tail. The computed power laws describing the decay of the translation velocity and integrals of motion (circulation, impulse, and energy) are shown to be consistent with both studies of Dabiri and Gharib [J. Fluid Mech. 511, 311 (2004)] and Maxworthy [J. Fluid Mech. 51, 15 (1972)]. We prove that the apparently different scaling laws reported in these two studies collapse if a virtual time origin is properly defined. Finally, the computationally generated vortex rings are matched to the classical Norbury–Fraenkel model and the recent model proposed by Kaplanski and Rudi [Phys. Fluids 17, 087101 (2005)]. The former model provides not only a good prediction of normalized energy and circulation but also a good estimation of individual integrals of motion. The latter model offers, in addition to a good prediction of integral quantities, a more accurate description of the vortex ring topology when comparing the contours of the inner cores or vortex signatures. Both models underestimate the volume of fluid carried inside the vortex bubble.

Large‐eddy simulation of the flow in a low‐speed centrifugal compressor

AbstractThe results of a series of numerical simulations for the NASA low‐speed centrifugal compressor are presented. Large‐eddy simulation (LES) is carried out together with the most commonly used Reynolds‐averaged Navier–Stokes (RANS) models, including the mixing length, k–ε and k–ω models. Predictions are compared with the available experimental data. It is seen that quantitative predictions of LES are better than those of RANS models for the tip jet and wake regions. LES, unlike these RANS models and the past computational fluid dynamics predictions, shows separation near the casing starting around the halfway of the impeller and reveals a vortex bubble close the impeller exit/casing corner. The tip leakage flow, which is the main characteristic of an unshrouded compressor, is investigated using the probability density function (PDF) and the power spectral density (PSD) of the instantaneous velocity values. The skewness and flatness calculated from the PDF profiles show that the unsteady flow in the tip wake region is less‐intermittent compared with the flow in the tip jet region. The PSD analysis shows that the turbulent energy transfer rate from the larger scales to the smaller scales and the frequency range where the inertial region is valid increase in the tip wake region. Copyright © 2008 John Wiley & Sons, Ltd.

Vortex breakdown control in confined swirling flows

Confined steady flows, which display on-axis or off-axis vortex breakdown, have been numerically studied, with particular attention focused on means of controlling the vortex breakdown bubbles. Firstly, the model flow driven by one end disk of a cylindrical enclosure, which exhibits two distinct on-axis vortex bubbles, has been considered. The resulting computations revealed that, sloping slightly the stationary sidewall, beyond a threshold angle, provided an effective means of removing the secondary vortex structure, and the flow remains steady. Besides, this technique is shown to significantly modify the flow topology which displays off-axis bubbles, induced by the co-rotation of the end disks. Then, the effectiveness of adding a near-axis swirl, as suggested in recent experimental works, has been analysed numerically and found to substantially alter on-axis reverse flows.

Large-Eddy Simulation of Lean Premixed Turbulent Flames of Three Different Combustion Configurations using a Novel Reaction Closure

This large eddy simulation (LES) study is applied to three different premixed turbulent flames under lean conditions at atmospheric pressure. The hierarchy of complexity of these flames in ascending order are a simple Bunsen-like burner, a sudden-expansion dump combustor, and a typical swirl-stabilized gas turbine burner–combustor. The purpose of this paper is to examine numerically whether the chosen combination of the Smagorinsky turbulence model for sgs fluxes and a novel turbulent premixed reaction closure is applicable over all the three combustion configurations with varied degree of flow and turbulence. A quality assessment method for the LES calculations is applied. The cold flow data obtained with the Smagorinsky closure on the dump combustor are in close proximity with the experiments. It moderately predicts the vortex breakdown and bubble shape, which control the flame position on the double-cone burner. Here, the jet break-up at the root of the burner is premature and differs with the experiments by as much as half the burner exit diameter, attributing the discrepancy to poor grid resolution. With the first two combustion configurations, the applied subgrid reaction model is in good correspondence with the experiments. For the third case, a complex swirl-stabilized burner–combustor configuration, although the flow field inside the burner is only modestly numerically explored, the level of flame stabilization at the junction of the burner–combustor has been rather well captured. Furthermore, the critical flame drift from the combustor into the burner was possible to capture in the LES context (which was not possible with the RANS plus k–ɛ model), however, requiring tuning of a prefactor in the reaction closure.

Dual stream function visualization of flows fields dependent on two variables

The construction of streamlines is one of the most common methods for visualising fluid motion. Streamlines can be computed from the intersection of two nonparallel stream surfaces, which are iso-surfaces of dual stream functions. Stream surfaces are also useful to isolate part of the flow domain for detailed study. This paper introduces a technique for calculating dual stream functions for momentum fields that are defined analytically and depend on only two variables. For axi-symmetric flows, one of the dual stream functions is the well-known Stokes stream function. The analysis reduces the problem from the solution of partial differential equations to the solution of two ordinary differential equations. Example applications include the Moffat [17] vortex bubble, for which new solutions are presented.

Bubble vortex at surfaces of evaporating liquids

Air bubble in volatile liquid on exiting to the surface spins a vortex maintaining integrity of the film over an indefinite period of time. The shear stress associated with the surface tension increase in the adiabatic evaporation cooling drags the warmer liquid inwards into the film counteracting its capillary drainage out under gravity. The chaotic patterns, visualized with the aid of light interferometry, depend on liquid volatility, degree of vapor saturation, and air convection. The circulation intensifies and the frequency of hydrodynamic instabilities in the multiphase flow increases on the transition to strong turbulent regimes with increasing evaporation rate. Self-consistency of the physical mechanisms of solute and evaporation inhibition of bubble coalescence is verified through dimensional parametric analysis.

Vortex scenario and bubble generation in a cylindrical cavity with rotating top and bottom

The creation of recirculation bubbles in a steady, viscous flow in a cylindrical cavity with co-rotating top and bottom is investigated numerically. By varying the Reynolds number and the aspect ratio of the cylinder various axial-symmetric flow regimes are studied. It is observed that the topology of re-circulating vortex structures is associated with a change in helical symmetry of the vortex lines. The computations show that symmetry changes take place at increasing Reynolds numbers and that flow reversal on the center axis is associated with a growth of the twist parameter of the vortex lines. For all studied flow cases, independent of aspect ratio and Reynolds number, it was observed that the twist parameter of the central vortex attains a threshold value of K ≅ 0.6 at the point where flow reversal takes place.

Axial core-variations of axisymmetric shape on a curved slender vortex filament with a similar, Rankine, or bubble core

The dynamics of axial core-variations of axisymmetric shape on a vortex filament is derived from the Navier–Stokes equations in the slenderness limit. The core of the vortex is of similar, Rankine, or bubble type with a centerline of any shape. In this limit, a two-time-scale asymptotic approach is used to study the dynamics of the axial core-variations and of the centerline. The short-time dynamical equations of the axial core-variations are given and are inviscid at leading and first orders. The induced short-time and normal-time dynamics of the centerline is obtained. The full two-time-scale dynamics of the axial variations and of the filament motion is discussed qualitatively. The normal-time dynamics of vortex filaments without axial core-variations is given in a short form. Within the two-time-scale framework, the dynamics of axial core-variations around this one-time base flow is then studied in the small amplitude limit. The normal-time equations of a vortex bubble are given. The bubble has no axial variations, a centerline of any shape and can have a nonpotential core. The equation for the ultra-short-time dynamics of axial variations on this bubble is given.

Effect of entrained bubbles on the structure of vortex rings

The effect of entrained bubbles on the structure of a vortex ring is studied using particle image velocimetry. Quantitative information on the velocity and vorticity distribution within the vortex core is obtained from multiple images recorded with two 65 frames per second, 35 mm cameras. Bubble trajectories and velocities are also determined from these images. It is demonstrated that for certain combinations of vortex strengths and bubble diameters, a few microscopic bubbles, at very low overall void fraction, shift and macroscopically deform the structure of the vortex. For example, five 512 μm diameter bubbles, entrained by a vortex with core diameter of 2 cm and strength of 160 cm2 s−1, displace the core by 3.5 mm and fragment the core into two regions with peak vorticities that are 20% higher than the original maximum vorticity. The same phenomenon is observed with laminar, transitional and turbulent vortices. Dimensional analysis along with the experimental data show that the distortion is maximum when the bubbles settle, following entrainment by the vortex, in a region located between 20% and 40% of core radius. The governing dimensionless parameters and trends are identified and discussed. The vortex distortions are explained in terms of changes to the liquid momentum caused by the entrainment of the bubbles. It is argued and proven in detail in Appendix A that the change to the liquid momentum due to the presence of the bubble is equal to the bubble volume multiplied by the local stresses that exist in the absence of the bubble. These stresses include the gravity-induced (buoyancy) and hydrodynamic pressure gradients as well as viscous stresses. The buoyancy displaces the core of the vortex upward whereas the force due to hydrodynamic pressure gradients reduces the core size and as a result increases the vorticity. Estimated distortions agree with the experimental data.

Propagation of Multiple Short-Length-Scale Stall Cells in an Axial Compressor Rotor

Evolution and structure of multiple stall cells with short-length-scale in an axial compressor rotor have been investigated experimentally. In a low-speed research compressor rotor tested, a short-length-scale stall cell appeared at first, but did not grow rapidly in size, unlike a so-called “spike-type stall inception” observed in many multistage compressors. Alternatively, the number of cells increased to a certain stable state (a mild stall state) under a fixed throttle condition. In the mild stall state the multiple stall cells, the size of which was on the same order of the inception cell (a few blade spacings), were rotating at 72 percent of rotor speed and at intervals of 4.8 blade spacings. With further throttling, a long-length-scale wave appeared overlapping the multiple short-length-scale waves, then developed to a deep stall state with a large cell. In order to capture the short-length-scale cells in the mild stall state, a so-called “double phase-locked averaging technique” has been developed, by which the flow field can be measured phase locked to both the rotor and the stall cell rotation. Then, time-dependent ensemble averages of the three-dimensional velocity components upstream and downstream of the rotor have been obtained with a slanted hot-wire, and the pressure distributions on the casing wall with high-response pressure transducers. By a physically plausible explanation for the experimental results, a model for the flow mechanism of the short-length-scale stall cell has been presented. The distinctive feature of the stall cell structure is on the separation vortex bubble with a leg traveling ahead of the rotor, with changing the blade in turn on which the vortex leg stands. [S0889-504X(00)00701-7]

Flame–vortex interaction in a reacting vortex ring

Direct numerical simulations are used to study the flame–vortex interaction in a laminar reacting vortex ring. The chemical reaction occurs by a one-step, Arrhenius-type reaction that mimics the combustion of typical hydrocarbon and air. The ring is generated by an axisymmetric jet that is impulsed to emit a cold fuel through a nozzle. The fuel enters a quiescent ambient at a much higher temperature. By adjusting the ratio of the ambient and fuel temperatures, the ignition either occurs during the formation or post-formation phase of the ring. When ignition occurs during the formation phase of the ring, the bulk of combustion is by a flame at the front of the vortex bubble. When ignition is delayed until after the formation phase, most of the reaction occurs inside the vortex ring. It is found that premixing the fuel and the oxidizer enhances the amount of product formation. The heat released from the reaction significantly affects production, redistribution, and diffusion of the vorticity throughout the field. The results of the simulations also reveal that the heat of reaction affects the strain rate fields differently depending on when the ignition of the ring occurs.

Steady states and oscillatory instability of swirling flow in a cylinder with rotating top and bottom

In this study we present a numerical investigation of steady states, onset of oscillatory instability, and slightly supercritical oscillatory states of an axisymmetric swirling flow of a Newtonian incompressible fluid in a cylinder, with independently rotating top and bottom. The first part of the study is devoted to the influence of co- and counter-rotation of the bottom on the steady vortex breakdown, which takes place in the well-known problem of flow in a cylinder with a rotating top. It is shown that weak counter-rotation of the bottom may suppress the vortex breakdown. Stronger counter-rotation may induce a stable steady vortex breakdown at relatively large Reynolds numbers for which a vortex breakdown does not appear in the case of the stationary bottom. Weak corotation may promote the vortex breakdown at lower Reynolds numbers than in the cylinder with the stationary bottom. Stronger corotation leads to the detachment of the recirculation zone from the axis and the formation of an additional vortex ring. The second part of the study is devoted to the investigation of the onset of oscillatory instability of steady flows. It is shown that the oscillatory instability sets in due to a Hopf bifurcation. The critical Reynolds number and the critical frequency of oscillations were calculated as a function of the rotation ratio (ξ=Ωbottom/Ωtop) for a fixed value of the aspect ratio γ (height/radius) of the cylinder γ=1.5. The stability analysis showed that there are several most unstable linear modes of the perturbation that become successively dominant with a continuous change of ξ. It is shown that the oscillatory instability may lead to an appearance and coexistence of more than one oscillating separation vortex bubble.

Direct numerical simulation of a laminar vortex ring

Results are presented of direct numerical simulations (DNS) of a viscous, laminar ring. The effects of different generator configurations and velocity programs on the formation and post-formation characteristics of the ring are studied. It is shown that during the formation phase of the ring, total circulation and impulse in the flowfield are approximately the same for the ‘‘nozzle’’ and ‘‘orifice’’ generators. It is also found that throughout this period the slug flow model under-predicts the total circulation in the flow. During the formation phase, the simulation results for the time evolution of total circulation and location of the vortex spiral center are in agreement with the experimental findings of Didden [J. Appl. Mech. Phys. (ZAMP) 30, 101 (1979)]. The results of the flow visualization studies show that during the post-formation phase a vortex bubble is formed. As the bubble propels itself forward a wake is formed in the rear of the bubble. The impulse and vorticity from the bubble are continuously shed into this wake. It is found that the total value of the circulation in the flow varies as (t1*)−0.33 which is consistent with Maxworthy’s [J. Fluid Mech. 81, 465 (1977)] prediction of the decay of circulation for a vortex ring. The transport of a passive Shvab-Zeldovich scalar variable is used to study the mixing and to obtain the maximum product formation in a chemical reaction of the type A+B→Products in a vortex ring. It is found that as the bubble containing the fuel propels itself forward, the outside oxidizer flow is entrained into it and reacts to form a product. Some of this product then is de-entrained into the wake of the bubble.

EVOLUTION AND CLASSIFICATION OF INSECT FLIGHT KINEMATICS.

Classification of the main types of insect in-flight kinematics is proposed here, based on comparative data of wing movement during flapping flight. By comparing the described kinematic patterns with the results of studies of the vortex-wake structures of flying insects, these patterns can be explained as adaptations for overcoming the negative effects of mutual deceleration of fore- and hind wing starting vortex bubbles, which take place in insects with the most primitive type of wing kinematics. The aerodynamic efficiency of the flying system can be decreased if natural selection favors behavioral patterns that involve suboptimal wing kinematics.