Bubbly Cavitating Research Articles

Numerical simulation of unidimensional bubbly flow in Mooney Rivlin fluid through nozzles and a wavy channel

The goal of this paper is to investigate one-dimensional bubbly cavitating flow in Mooney Rivlin fluid as it flows through three different geometries. Cavitating flows are used in a variety of engineering and medical settings. The current research looks at the effects of Mooney Rivlin fluid’s elastic behavior when it passes through a venturi, a converging-diverging nozzle, and a wavy channel. Initially, Rayleigh Plesset’s equation for a single bubble was considered later on effects of more than one bubble were investigated. The flow was examined under the effects of different emerging parameters, namely the Reynolds number (for laminar flow is taken to be 100), weber number , and elasticity parameter which ranges from to . The system of ordinary differential equations was first non-dimensionalized using suitable transformations, then the Runge–Kutta method was used to solve the flow equations. Effects of different parameters on the radius of the bubble and velocity of the flow are illustrated graphically.

Effect of compressibility on bubbly cavitating flows

Cavitating bubbly flows can form in separated flows and shear layers leading to local regions high vapor void fraction, and these flows often exhibit periodic shedding of vaporous clouds. Historically, the presence of a liquid re-entrant flow, driven by the kinematics of liquid flow stagnation, has been identified as an important mechanism leading to cavity shedding. However, high local vapor void fractions can also result in a reduced mixture speed of sound and a possible supersonic flow. Our recent findings on different geometries indicate that propagating bubbly shocks in these flows are a primary mechanism of flow instability. In this study, we discuss the effect of compressibility on four geometries, mainly in the generation of propagating bubbly shocks that can influence the cavitation shedding dynamics. In order to elucidate the differences and similarities of the observed cavitation dynamics, and the influence of compressibility, we report observations from a backward facing step, backward facing wedge, NACA0015 hydrofoil, and a bluff body with a wedge cross section.

Characterization and pressure drop correlation for sprays under the effect of micro scale cavitation

In this study, spray formation and atomization, droplet evolutions, break-up, and corresponding cavitating flows at the outlet of a short micro-channel with an inner diameter of 152 μm were experimentally studied at different injection pressures with the use of a high speed visualization system. High speed visualization was performed at five different segments to cover a ∼27.5 mm distance beginning from the micro-channel outlet (Five segments, at distances of 0–5.5, 5.5–11, 11–16.5, 16.5–22 and 22–27.5 mm from the micro-channel outlet) to assess the spray formation mechanism. High speed visualization revealed that droplet evolution is initiated from the second segment at low upstream pressures (5–30 bars), whereas droplets are discretized from the liquid jet in the fourth and fifth segments at medium and high upstream pressures (40–100 bars). Bigger size droplets formed at the outlet up to an injection pressure of 30 bars, while cavitation effect of intensified cavitating flows became dominant beyond this injection pressure, leading to smaller droplet sizes and a more conical spray. Pressure drop was correlated together with Martinelli parameter for cavitating flows and a new correlation for two-phase pressure drop was developed. Moreover, in order to segment the discretized droplets at low upstream pressure (5–30 bars) from captured images and to perform an in-depth analysis on them, an active contour approach utilizing curve evolution and level set formulation was implemented. As shown by experimental results, droplets were successfully segmented at different low pressure levels. The droplet/bubble evolution can be exploited in biomedical and engineering applications, where destructive effects of bubbly cavitating flows are needed.

Cavity collapse in a bubbly liquid

The effect of an ambient liquid state on a spherical cavity dynamics under atmospheric hydrostatic pressure p and extremely low initial gas pressure p(0) inside was investigated. The equilibrium bubbly (cavitating) medium with sound velocity C as the function of gas phase concentration k was considered as the ambient liquid model. The cavity dynamics is analyzed within the framework of Herring-equation for the following diapasons of main parameters : k = 0—5%, р(0) = 0.02—10(−6) atm. Numerical analysis has shown that the deceleration C by two order does not have an influence neither on an asymptotic value of collapsed cavity radius nor on the acoustical losses under its collapse. It means than in the whole the integral acoustical losses remain invariable. However the collapse cavity dynamics and the radiation structure are essentially changed: from numerous pulsations with a decreasing amplitudes up to a single collapse and from a wave packet up to a single wave, correspondingly. It has turned out that the acoustic corrections in the Herring-equation don’t influence practically on the cavity dynamics if the term of equation with dH/dt is absent. Naturally, the deceleration C exerts essential influence on an empty cavity dynamics. The graphs of dR/Cdt values as a function of R/Ro for different C values are located higher the data of classical models of Herring, Gilmore and Hunter. So the value M = 1 is reached at R/Ro = 0.023 for k = 0, and at the value 0.23 when k = 5 %. [Support RFBR, grant 12-01-00314.]

A novel nonreflecting boundary condition for unsteady flow

SUMMARYA novel nonreflecting boundary condition, which converges to the specified time‐dependent boundary condition within any degree of accuracy, is introduced for the numerical simulation of hyperbolic systems and validated against the solution of two fundamental boundary value problems in fluids. First, transonic nozzle flow with backward acoustic disturbance is considered. Using high‐order aeroacoustic numerical schemes, the proposed nonreflecting boundary condition yields results that are in excellent agreement with those obtained using conventional nonreflecting boundary conditions based on the method of characteristics as well as with the results of the exact solution. The novel nonreflecting boundary condition, implemented into a semi‐analytical solution algorithm of unsteady bubbly cavitating nozzle flows, is also validated against results obtained using a Lagrangian finite volume scheme. Copyright © 2013 John Wiley & Sons, Ltd.

Semianalytical solution of unsteady quasi-one-dimensional cavitating nozzle flows

Unsteady quasi-one-dimensional bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation. The model equations are uncoupled by scale separation leading to two evolution equations, one for the flow speed and the other for the bubble radius. The initial-boundary value problem of the evolution equations is then formulated and a semianalytical solution is constructed. The solution for the mixture pressure, the mixture density, and the void fraction are then explicitly related to the solution of the evolution equations. In particular, a relation independent of flow dimensionality is established between the mixture pressure, the void fraction, and the flow dilation for unsteady bubbly cavitating flows in the model considered. The steady-state compressible and incompressible limits of the solution are also discussed. The solution algorithm is first validated against the numerical solution of Preston et al. [Phys Fluids 14:300–311, 2002] for an essentially quasi-one-dimensional nozzle. Results obtained for a two-dimensional nozzle seem to be in good agreement with the mean pressure measurements at the nozzle wall for attached cavitation sheets despite the observed two-dimensional cavitation structures.

Kidney Stone Erosion by Micro Scale Hydrodynamic Cavitation and Consequent Kidney Stone Treatment

The objective of this study is to reveal the potential of micro scale hydrodynamic bubbly cavitation for the use of kidney stone treatment. Hydrodynamically generated cavitating bubbles were targeted to the surfaces of 18 kidney stone samples made of calcium oxalate, and their destructive effects were exploited in order to remove kidney stones in in vitro experiments. Phosphate buffered saline (PBS) solution was used as the working fluid under bubbly cavitating conditions in a 0.75 cm long micro probe of 147 μm inner diameter at 9790 kPa pressure. The surface of calcium oxalate type kidney stones were exposed to bubbly cavitation at room temperature for 5 to 30 min. The eroded kidney stones were visually analyzed with a high speed CCD camera and using SEM (scanning electron microscopy) techniques. The experiments showed that at a cavitation number of 0.017, hydrodynamic bubbly cavitation device could successfully erode stones with an erosion rate of 0.31 mg/min. It was also observed that the targeted application of the erosion with micro scale hydrodynamic cavitation may even cause the fracture of the kidney stones within a short time of 30 min. The proposed treatment method has proven to be an efficient instrument for destroying kidney stones.

Modelling bubble clusters in compressible liquids

AbstractWe present a new model for bubbly cavitating flows. Based on volume-averaged equations, a subgrid model is added to account for a bubble, or multiple bubbles, within each computational cell. The model converges to the solution of ensemble-averaged bubbly flow equations for weak oscillations and monodisperse systems. In the other extreme, it also converges to the theoretical solution for a single oscillating bubble, and captures the bubble radius evolution and the pressure disturbance induced in the liquid. A substantial saving of computational time is achieved compared to ensemble-averaged models for polydisperse mixtures.

Bubbly Cavitating Flow Generation and Investigation of Its Erosional Nature for Biomedical Applications

This paper presents a study that investigates the destructive energy output resulting from hydrodynamic bubbly cavitation in microchannels and its potential use in biomedical applications. The research performed in this study includes results from bubbly cavitation experiments and findings showing the destructive effects of bubbly cavitating flow on selected solid specimens and live cells. The bubbles generated by hydrodynamic cavitation are highly destructive at the surfaces of the target medium on which they are carefully focused. The resulting destructive energy output could be effectively used for biomedical treatments, such as destroying kidney stones (renal calculi) or killing cancer cells. Motivated by this potential, the cavitation damage to cancerous cells and material removal from chalk pieces (which possess similar material properties as some kidney stones) was investigated. Our results showed that cavitation could induce damage both on chalk pieces and leukemia/lymphoma cells. We discovered that hydrodynamic cavitation exposure had early and delayed effects on cancer cell survival. Hence, the potential of hydrodynamic bubbly cavitation generated at the microscale for biomedical treatments was revealed using the microchannel configuration as a microorifice (with an inner diameter of 147 μm and a length of 1.52 cm), which acts as the source of bubbly cavitating flows.

On the temporal stability of steady-state quasi-1D bubbly cavitating nozzle flow solutions

Quasi-1D unsteady bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the non-linear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation. The various damping mechanisms are considered by a single damping coefficient lumping them together in the form of viscous dissipation and by assuming a polytropic law for the expansion and compression of the gas. The complete system of equations, by appropriate uncoupling, are then reduced to two evolution equations, one for the flow speed and the other for the bubble radius when all damping mechanisms are considered by a single damping coefficient. The evolution equations for the bubble radius and flow speed are then perturbed with respect to flow unsteadiness resulting in a coupled system of linear partial differential equations (PDEs) for the radius and flow speed perturbations. This system of coupled linear PDEs is then cast into an eigenvalue problem and the exact solution of the eigenvalue problem is found by normal mode analysis in the inlet region of the nozzle. Results show that the steady-state cavitating nozzle flow solutions are stable only for perturbations with very small wave numbers. The stable regions of the stability diagram for the inlet region of the nozzle are seen to be broadened by the effect of turbulent wall shear stress.

Thermal Damping in Cavitating Nozzle Flows

Recent investigations of bubbly cavitating nozzle flows using the polytropic law for the partial gas pressure have shown flow instabilities that lead to flashing flow solutions. Here, we investigate the stabilizing effect of thermal damping on these instabilities. For this reason we consider the energy equation within the bubble, assumed to be composed of vapor and gas, in the uniform pressure approximation with low vapor concentration. The partial vapor pressure is fixed by the vapor saturation pressure corresponding to the interface temperature, which is evaluated by assuming the thin boundary layer approximation within the liquid. Consequently, the partial gas pressure is evaluated by its relation to the heat flux through the interface in the uniform pressure approximation. The model is then coupled to the steady-state cavitating nozzle flow equations replacing the polytropic law for the partial gas pressure. The instabilities found in steady cavitating nozzle flows are seen to be stabilized by thermal damping with or without the occurrence of bubbly shock waves.

1207 Chemical reaction in bubbly cavitating flow

1207 Chemical reaction in bubbly cavitating flow

A numerical investigation of unsteady bubbly cavitating nozzle flows

The effects of unsteady bubble dynamics on cavitating flow through a converging-diverging nozzle are investigated numerically. A continuum model that couples the Rayleigh–Plesset equation with the continuity and momentum equations is used to formulate unsteady, quasi-one-dimensional partial differential equations. Flow regimes studied include those where steady-state solutions exist, and those where steady-state solutions diverge at the so-called flashing instability. These latter flows consist of unsteady bubbly shock waves traveling downstream in the diverging section of the nozzle. An approximate analytical expression is developed to predict the critical backpressure for choked flow. The results agree with previous barotropic models for those flows where bubble dynamics are not important, but show that in many instances the neglect of bubble dynamics cannot be justified. Finally the computations show reasonable agreement with an experiment that measures the spatial variation of pressure, velocity and void fraction for steady shockfree flows, and good agreement with an experiment that measures the throat pressure and shock position for flows with bubbly shocks. In the model, damping of the bubble radial motion is restricted to a simple “effective” viscosity, but many features of the flow are shown to be independent of the specific damping mechanism.

Acoustic saturation in bubbly cavitating flow adjacent to an oscillating wall

Bubbly cavitating flow generated by the normal oscillation of a wall bounding a semi-infinite domain of fluid is computed using a continuum two-phase flow model. Bubble dynamics are computed, on the microscale, using the Rayleigh–Plesset equation. A Lagrangian finite volume scheme and implicit adaptive time marching are employed to accurately resolve bubbly shock waves and other steep gradients in the flow. The one-dimensional, unsteady computations show that when the wall oscillation frequency is much smaller than the bubble natural frequency, the power radiated away from the wall is limited by an acoustic saturation effect (the radiated power becomes independent of the amplitude of vibration), which is similar to that found in a pure gas. That is, for large enough vibration amplitude, nonlinear steepening of the generated waves leads to shocking of the wave train, and the dissipation associated with the jump conditions across each shock limits the radiated power. In the model, damping of the bubble volume oscillations is restricted to a simple “effective” viscosity. For wall oscillation frequency less than the bubble natural frequency, the saturation amplitude of the radiated field is nearly independent of any specific damping mechanism. Finally, implications for noise radiation from cavitating flows are discussed.

On the Stability of Parallel Bubbly Cavitating Flows

This paper illustrates the effects of the dynamics of bubbles with arbitrary vapor-gas contents on the inviscid and viscous stability of two-dimensional parallel bubbly flows of low void fraction. The linear perturbation equations derived for the stability analysis include the effects of bubble compressibility, inertia, and energy dissipation due to the viscosity of the liquid and the transfer of heat and mass as a consequence of compression/expansion of the noncondensable gas and evaporation/condensation of the vapor contained in the bubbles. Numerical solution of the spatial stability problem for two-dimensional inviscid shear layers and Blasius boundary layers confirms that the presence of the dispersed phase is generally in favor of stability. Significant deviations from the classical results for compressible and incompressible single phase fluids are observed, especially when the occurrence of large compliant and/or resonant oscillations of the bubbles greatly enhances their dynamic coupling with the perturbation field. More importantly, the present analysis points out some major differences in the stability of parallel flows with noncondensable gas bubbles with respect to cavitating flows containing bubbles with a dominant content of vapor. Unconditional stability is predicted in the travelling bubble cavitation limit for low pressures and high vapor mass fraction of the bubble contents. Results are shown to illustrate these effects for some representative flow configurations and conditions. [S0098-2202(00)00603-9]

Stability Analysis of One-Dimensional Steady Cavitating Nozzle Flows With Bubble Size Distribution

A continuum bubbly mixture model coupled to the Rayleigh-Plesset equation for the bubble dynamics is employed to study one-dimensional steady bubbly cavitating flows through a converging-diverging nozzle. A distribution of nuclei sizes is specified upstream of the nozzle, and the upstream cavitation number and nozzle contraction are chosen so that cavitation occurs in the flow. The computational results show very strong interactions between cavitating bubbles and the flow. The bubble size distribution may have significant effects on the flow; it is shown that it reduces the level of fluctuations and therefore reduces the “cavitation loss” compared to a monodisperse distribution. Another interesting interaction effect is that flashing instability occurs as the flow reaches a critical state downstream of the nozzle. A stability analysis is proposed to predict the critical flow variables. Excellent agreement is obtained between the analytical and numerical results for flows of both equal bubble size and multiple bubble sizes. [S0098-2202(00)00702-1]

A Three-Dimensional Analysis of Rotordynamic Forces on Whirling and Cavitating Helical Inducers

This paper investigates the linearized dynamics of three-dimensional bubbly cavitating flows in helical inducers. The purpose is to understand the impact of the bubble response on the radial and tangential rotordynamic forces exerted by the fluid on the rotor and stator stages of whirling turbomachines under cavitating conditions. The flow in the inducer annulus is modeled as a homogeneous inviscid mixture, containing vapor bubbles with a small amount of noncondensable gas. The effects of several contributions to the damping of the bubble dynamics are included in the model. The governing equations of the inducer flow are written in “body-fitted” orthonormal helical Lagrangian coordinates, linearized for small-amplitude perturbations about the mean flow, and solved by modal decomposition. The whirl excitation generates finite-speed propagation and resonance phenomena in the two-phase flow within the inducer. These, in turn, lead to a complex dependence of the lateral rotordynamic fluid forces on the excitation frequency, the void fraction, the average size of the cavitation bubbles, and the turbopump operating conditions (including, rotational speed, geometry, flow coefficient and cavitation number). Under cavitating conditions the dynamic response of the bubbles induces major deviations from the noncavitating flow solutions, especially when the noncondensable gas content of the bubbles is small and thermal effects on the bubble dynamics are negligible. Then, the quadratic dependence of rotordynamic fluid forces on the whirl speed, typical of cavitation-free operation, is replaced by a more complex behavior characterized by the presence of different regimes where, depending on the whirl frequency, the fluid forces have either a stabilizing or a destabilizing effect on the inducer motion. Results are presented to illustrate the influence of the relevant flow parameters.

Bubbly flow model for the dynamic characteristics of cavitating pumps

This paper is concerned with understanding the dynamic behaviour of cavitating hydraulic machines during unsteady or transient operation. The linear transfer matrices which relate the small fluctuating pressures and mass flow rates at inlet and discharge are functions not only of the frequency but also of the mean operating state of the machine, especially the degree of cavitation. The recent experimental transfer matrices obtained by Ng & Brennen (1978) for some axial flow pumps revealed some dynamic characteristics which were unaccounted for by any existing theoretical analysis; their visual observations suggested that the bubbly cavitating flow in the blade passages could be responsible for these effects.A theoretical model of the dynamic response of this bubbly blade-passage flow is described in the present paper. Void-fraction fluctuations in this flow result not only from pressure fluctuations but also because the fluctuating angle of attack causes fluctuations in the rate of production of bubbles near the leading edge. The latter causes kinematic waves which interact through the boundary conditions with the dynamic waves caused by pressure fluctuation. The resulting theoretical transfer functions which result are in good qualitative agreement with the experiments; with appropriate choices of two parameters (the practical values of which are difficult to assess) good quantitative agreement is also obtained. The theoretical model also provides one possible explanation of the observation that the pump changes from an essentially passive dynamic element in the absence of cavitation to a progressively more active element as the extent of cavitation increases.