Search

Numerical modeling of cavitating bubbly flows is challenging due to the wide range of characteristic lengths of the physics at play: from micrometers (e.g., bubble nuclei radius) to meters (e.g., propeller diameter or sheet cavity length). To address this, we present here a multiscale approach which integrates a Discrete Singularities Model (DSM) for dispersed microbubbles and a two-phase Navier Stokes solver for the bubbly medium, which includes a level set approach to describe large cavities or gaseous pockets. Inter-scale schemes are used to smoothly bridge the two transitioning subgrid DSM bubbles into larger discretized cavities. This approach is demonstrated on several problems including cavitation inception and vapor core formation in a vortex flow, sheet-to-cloud cavitation over a hydrofoil, cavitation behind a blunt body, and cavitation on a propeller. These examples highlight the capabilities of the developed multiscale model in simulating various form of cavitation.

The effects of gravity on a phase separator are studied numerically using an Eulerian/Lagrangian two-phase flow approach. The separator utilizes high intensity swirl to separate bubbles from the liquid. The two-phase flow enters tangentially a cylindrical swirl chamber and rotate around the cylinder axis. On earth, as the bubbles are captured by the vortex formed inside the swirl chamber due to the centripetal force, they also experience the buoyancy force due to gravity. In a reduced or zero gravity environment buoyancy is reduced or inexistent and capture of the bubbles by the vortex is modified. The present numerical simulations enable study of the relative importance of the acceleration of gravity on the bubble capture by the swirl flow in the separator. In absence of gravity, the bubbles get stratified depending on their sizes, with the larger bubbles entering the core region earlier than the smaller ones. However in presence of gravity, stratification is more complex as the two acceleration fields — due to gravity and to rotation — compete or combine during the bubble capture.

Cavitation flow behind a blunt body is modeled using a physics-based numerical model of cavitation initiation and transition to larger cavities. The calculations initiate from the dynamics of nuclei, then tracks the dispersed bubble phase with a two-phase viscous model. This solver includes a level set method to model coalescence of the nuclei into large cavities and to track the dynamics of the resulting free surfaces. A transition scheme enables collection of the bubbles into a large cavity and also enables breakup of a large cavity into a bubble cloud. Using this model, simulations are conducted for different flow velocities and corresponding cavitation regimes. When the velocity is relatively small (i.e., large cavitation number), flow separation behind the body results in the shedding of vortices, which capture nuclei in their cores to form elongated vortical cavities. As the flow velocity increases (or as the ambient pressure decreases) the flow evolves into a separated flow with a large cavity behind the body. A reentrant jet may form and move upstream into the cavity towards the body. This jet periodically shears off portions of the cavity volume, resulting in large amounts of bubble clouds. These results are in good qualitative agreements with experimental observations.

A multi-bubble dynamics code accounting for gas diffusion in the liquid and through the bubble wall was developed and used to study the modification of a bubble nuclei population dynamics by a propeller. The propeller flow field was obtained using a Reynolds-Averaged Navier-Stokes (RANS) solver and bubble nuclei populations were propagated in this field. The numerical procedure enabled establishment of the possibility of production behind the propeller of relatively large visible bubbles starting from typical ocean nuclei size distributions. The resulting larger bubbles are seen to cluster in the blade wakes and tip vortices. Parametric investigations of the initial nuclei size distribution, the dissolved gas concentration, and the cavitation number were conducted to identify their effects on bubble entrainment and the resultant void fractions and bubble distribution modifications downstream from the propeller. Imposed synthetic turbulence-like fluctuations unto the average RANS flow field were also used to study the effect averaging in the RANS procedure has on the results.

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.

Cavitation inception in a ducted propulsor was studied numerically using Navier-Stokes computations and bubble dynamics models. Experimental observations of the propulsor model and previous numerical computations using Reynolds-averaged Navier-Stokes (RANS) codes indicated that cavitation inception occurred in the region of interaction of the leakage and trailing tip vortices. The RANS simulations failed, however, to predict correctly both the cavitation inception index value and the inception location. To improve the numerical predictions, we complemented here the RANS computations with a direct Navier-Stokes simulation in a reduced computational domain including the region of interaction of the two vortices. Initial and boundary conditions in the reduced domain were provided by the RANS solution of the full ducted propulsor flow. Bubble nuclei were released in this flow field, and spherical and nonspherical bubble dynamics models were exercised to investigate cavitation inception. This resulted in a solution in much better agreement with the experimental measurements than the original RANS solution. Both the value of the cavitation inception index and the location of the cavitation inception were very well captured. The characteristics of the emitted acoustic signals and of the bubble shapes during a cavitation event were also computed.

The acoustic pressure generated by cavitation inception in a tip vortex flow was simulated in water containing a realistic bubble nuclei size distribution using a surface-averaged pressure (SAP) spherical bubble dynamics model. The flow field was obtained by the Reynolds-averaged Navier–Stokes computations for three geometrically similar scales of a finite-span elliptic hydrofoil. An “acoustic” criterion, which defines cavitation inception as the flow condition at which the number of acoustical “peaks” above a pre-selected pressure level exceeds a reference number per unit time, was applied to the three scales. It was found that the scaling of cavitation inception depended on the reference values (pressure amplitude and number of peaks) selected. Scaling effects (i.e., deviation from the classical σi∝Re0.4) increase as the reference inception criteria become more stringent (lower threshold pressures and less number of peaks). Larger scales tend to detect more cavitation inception events per unit time than obtained by classical scaling because a relatively larger number of nuclei are excited by the tip vortex at the larger scale due to simultaneous increase of the nuclei capture area and of the size of the vortex core. The average nuclei size in the nuclei distribution was also found to have an important impact on cavitation inception number. Scaling effects (i.e., deviation from classical expressions) become more important as the average nuclei size decreases.

A spherical and a nonspherical bubble dynamics models were developed to study cavitation inception, scaling, and dynamics in a vortex flow. The spherical model is a modified Rayleigh–Plesset model to account for bubble slip velocity and for nonuniform pressures around the bubble. The nonspherical model is embedded in an unsteady Reynolds-averaged Navier–Stokes code with appropriate free-surface boundary conditions and a moving chimera grid scheme around the bubble. The effect of nonspherical deformation and bubble/flow interaction on bubble dynamics is illustrated by comparing spherical and nonspherical models. It is shown that nonspherical deformations and bubble/flow interactions are important for an accurate prediction of cavitation inception. The surface-averaged pressure-modified Rayleigh–Plesset scheme is a significant improvement over the conventional spherical model, and is able to capture the volume changes of a bubble during its capture. It is also a fast scheme for studying scaling. In a preliminary study, the scaling effects on cavitation inception were examined using two different Reynolds numbers owing to two different chord lengths. The nuclei-size effect on the prediction of cavitation inception was also studied, and its important effects are highlighted.

The current study considers the prediction of tip vortex cavitation inception at a fundamental physics based level. Starting form the observation that cavitation inception detection is based on the “monitoring” of the interaction between bubble nuclei and the flow field, the bubble dynamics is investigated in detail. A spherical model coupled with a bubble motion equation is used to study numerically the dynamics of a nucleus in an imposed flow field. The code provides bubble size and position versus time as well as the resulting pressure at any selected monitoring position. This model is used to conduct a parametric study. Bubble size and emitted sound versus time are presented for various nuclei sizes and flow field scales in the case of an ideal Rankine vortex to which a longitudinal viscous core size diffusion model is imposed. Based on the results, one can deduce cavitation inception with the help of either an “optical inception criterion” (maximum bubble size larger than a given value) or an “acoustical inception criterion” (maximum detected noise higher than a given background value). We use here such criteria and conclude that scaling effects can be inherent to the way in which these criteria are exercised if the bubble dynamics knowledge is not taken into account.

The uniform flow past a rotating marine propeller was studied using incompressible Reynolds-averaged Navier-Stokes computations with the Baldwin-Barth turbulence model. Extensive comparison with the experimental data was made to validate the numerical results. The general characteristics of the propeller flow were well predicted. The current numerical method, however, produced an overly diffusive and dissipative tip vortex core. Modification of the Baldwin-Barth model to better predict the Reynolds stress measurements also improved the prediction of the mean velocity field. A modified tip geometry was also tested to show that an appropriate cross section design can delay cavitation inception in the tip vortex without reducing the propeller performance.

The tip-vortex flow over a finite-span hydrofoil with laminar separation on the hydrofoil surface was numerically studied by computing the three-dimensional unsteady Navier-Stokes equations. The computations were direct numerical simulations of all resolvable structures without adding a turbulence model. The topological structure of unsteady separated flow and the influence of the unsteady laminar separated flow on the tip vortex for both swept and unswept hydrofoils were qualitatively investigated. The secondary flow induced by the swept planform played an important role in the unsteadiness of the tip vortex. The interaction between the tip vortex and the unsteady laminar separated flow became stronger as the sweep angle was increased

The Rayleigh-Plesset bubble dynamics equation coupled with the bubble motion equation developed by Johnson and Hsieh was applied to study the real flow effects on the prediction of cavitation inception in tip vortex flows. A three-dimensional steady-state tip vortex flow obtained from a Reynolds-Averaged Navier-Stokes computation was used as a prescribed flow field through which the bubble was passively convected. A “window of opportunity” through which a candidate bubble must pass in order to be drawn into the tip-vortex core and cavitate was determined for different initial bubble sizes. It was found that bubbles with larger initial size can be entrained into the tip-vortex core from a larger window size and also had a higher cavitation inception number.

The flow over a finite-span hydrofoil creating a tip vortex was numerically studied by computing the full Navier-Stokes equations. A good agreement in pressure distribution and oil flow pattern was achieved between the numerical solution and available experimental data. The steady-state roll-up process of the tip vortex was described in detail from the numerical results. The effect of the angle of attack, the Reynolds number, and the hydrofoil planform on the tip vortex was investigated. The axial and tangential velocities within the tip-vortex core in the near-field wake region were greatly influenced by the angle of attack. A jet-like profile in the axial velocity was found within the tip-vortex core at high angle of attack, while a wake-like profile in the axial velocity was found at low angle of attack. Increasing the Reynolds number was found to increase the maximum axial velocity, but only had a slight impact on the tangential velocity. Finally, a swept hydrofoil planform was found to attenuate the strength of the tip vortex due to the low-momentum boundary layer traveling into the tip vortex on the suction side.

An Eulerian/Lagrangian multi-scale two-phase flow model is developed to simulate the various types of cavitation including bubble, sheet, and tip vortex cavitation. Sheet cavitation inception, unsteady breakup, and cloud shedding on a hydrofoil are used as an example here. No assumptions are needed on mass transfer between phases; instead, the method tracks bubble nuclei, which are in the bulk of the liquid and those generated by nucleation from solid boundaries and this is- sufficient to accurately capture the sheet dynamics. The multi-scale model includes a micro-scale model for tracking the bubbles, a macro-scale model for describing large cavity dynamics and a transition scheme to bridge the micro and macro scales. Nuclei are treated as flow singularities until they grow into large bubbles, which eventually merge to form a large scale discretised sheet cavity. The sheet performs large scale oscillations with a periodic reentrant jet forming under the sheet cavity, traveling upstream, and breaking the cavity. This results in bubble cloud formation and in high pressure peaks as the broken pockets shrink and collapse while travelling downstream. The results for a NACA0015 foil are in good agreement with the experimental data.

A Surface-Averaged Pressure (SAP) spherical bubble dynamics model accounting for a statistical nuclei size distribution was used to model the acoustic signals generated by cavitating bubbles near inception in a tip vortex flow. The flow field generated by finite-span elliptic hydrofoils is obtained by Reynolds-Averaged Navier-Stokes computations. An “acoustic” criterion which defines the cavitation inception by counting the number of acoustical signal peaks that exceed a certain level per unit time was applied to deduce the cavitation inception number for different scales. It was found that the larger scale results in more cavitation inception events per unite time because more nuclei are excited by the tip vortex at the larger scale. The nuclei size was seen to have an important effect on cavitation inception number with scaling effects due to nuclei increasing as nuclei sizes decreases.Copyright © 2003 by ASME