Jingsen Ma

Numerical and experimental study of bubble entrainment due to a horizontal plunging jet

Free surface disruption, bubble entrainment, and resulting bubbly wake due to a stationary and moving horizontal jets plunging into a quiescent liquid were studied both numerically and experimentally. The moving jet wake showed significantly different flow characteristics than the stationary jet wake. High speed videos revealed that large vortical structures with entrapped air were generated periodically from the horizontal plunging jet. Each vortical air pocket broke up into multiple bubbles due to local shear flows as it returned toward the free surface and moved downstream. The frequency of the air pocket occurrence was analyzed and found to scale with the plunging jet flow and geometry conditions. The plunging dynamics was simulated with an Eulerian/Lagrangian one-way coupled two-phase flow model, which included a Level-Set method and a sub-grid bubble entrainment model. These captured free surface dynamics and predicted the bubble generation and entrainment. The flow structures, velocity field, and overall bubble spreading region near the plunging region were well captured by the numerical model. Further improvement on downstream wake flow is being sought through two-way coupling between the two phases since the one-way coupling does not account properly for the effective density.

A physics based multiscale modeling of cavitating flows

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.

Euler–Lagrange Simulations of Bubble Cloud Dynamics Near a Wall

We present in this paper a two-way coupled EulerianLagrangian model to study the dynamics of microbubble clouds exposed to incoming pressure waves and the resulting pressure loads on a nearby rigid wall. The model simulates the twophase medium as a continuum and solves the N-S equations using Eulerian grids with a time and space varying density. The microbubbles are modeled as interacting spherical bubbles, which follow a modified Rayleigh-Plesset-Keller-Herring equation and are tracked in a Lagrangian fashion. A two-way coupling between the Euler and Lagrange components is realized through the local mixture density associated with the bubbles volume change and motion. Using this numerical framework, simulations involving a large number of bubbles were conducted under driving pressures of different frequencies. The results show that the frequency of the driving pressure is critical in determining the overall dynamics: either a collective strongly coupled cluster behavior or non-synchronized weaker multiple bubble oscillations. The former creates extremely high pressures with peak values orders of magnitudes higher than that of the excitation pressures. This occurs when the driving frequency matches the natural frequency of the bubble cloud. The initial distance between the bubble cloud and the wall is also critical on the resulting pressure loads. A bubble cloud collapsing very close to the wall exhibits a cascading collapse with the bubbles farthest from the wall collapsing first and the nearest ones collapsing last, thus the energy accumulates and then results in very violent pressure peaks at the wall. Farther from the wall, the bubble cloud collapses quasi spherically with the cloud center collapsing last.

Modelling Cavitating Flows using an Eulerian-Lagrangian Approach and a Nucleation Model

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.

Shared-Memory Parallelization for Two-Way Coupled Euler–Lagrange Modeling of Cavitating Bubbly Flows

Cavitating and bubbly flows are encountered in many engineering problems involving propellers, pumps, valves, ultrasonic biomedical applications, etc. In this contribution, an openmp parallelized Euler–Lagrange model of two-phase flow problems and cavitation is presented. The two-phase medium is treated as a continuum and solved on an Eulerian grid, while the discrete bubbles are tracked in a Lagrangian fashion with their dynamics computed. The intimate coupling between the two description levels is realized through the local void fraction, which is computed from the instantaneous bubble volumes and locations, and provides the continuum properties. Since, in practice, any such flows will involve large numbers of bubbles, schemes for significant speedup are needed to reduce computation times. We present here a shared-memory parallelization scheme combining domain decomposition for the continuum domain and number decomposition for the bubbles; both selected to realize maximum speedup and good load balance. The Eulerian computational domain is subdivided based on geometry into several subdomains, while for the Lagrangian computations, the bubbles are subdivided based on their indices into several subsets. The number of fluid subdomains and bubble subsets matches with the number of central processing unit (CPU) cores available in a shared-memory system. Computation of the continuum solution and the bubble dynamics proceeds sequentially. During each computation time step, all selected openmp threads are first used to evolve the fluid solution, with each handling one subdomain. Upon completion, the openmp threads selected for the Lagrangian solution are then used to execute the bubble computations. All data exchanges are executed through the shared memory. Extra steps are taken to localize the memory access pattern to minimize nonlocal data fetch latency, since severe performance penalty may occur on a nonuniform memory architecture (NUMA) multiprocessing system where thread access to nonlocal memory is much slower than to local memory. This parallelization scheme is illustrated on a typical nonuniform bubbly flow problem, cloud bubble dynamics near a rigid wall driven by an imposed pressure function (Ma et al., 2013, “Euler–Lagrange Simulations of Bubble Cloud Dynamics Near a Wall,” International Mechanical Engineering Congress and Exposition, San Diego, CA, Nov. 15–21, Paper No. IMECE2013-65191 and Ma et al., 2015, “Euler–Lagrange Simulations of Bubble Cloud Dynamics Near a Wall,” ASME J. Fluids Eng., 137(4), p. 041301).

Modeling Separation and Cavitation Behind a Blunt Body

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.

Euler-Lagrange Simulations of Bubble Cloud Dynamics Near a Wall

We present in this paper a two-way coupled EulerianLagrangian model to study the dynamics of microbubble clouds exposed to incoming pressure waves and the resulting pressure loads on a nearby rigid wall. The model simulates the twophase medium as a continuum and solves the N-S equations using Eulerian grids with a time and space varying density. The microbubbles are modeled as interacting spherical bubbles, which follow a modified Rayleigh-Plesset-Keller-Herring equation and are tracked in a Lagrangian fashion. A two-way coupling between the Euler and Lagrange components is realized through the local mixture density associated with the bubbles volume change and motion. Using this numerical framework, simulations involving a large number of bubbles were conducted under driving pressures of different frequencies. The results show that the frequency of the driving pressure is critical in determining the overall dynamics: either a collective strongly coupled cluster behavior or non-synchronized weaker multiple bubble oscillations. The former creates extremely high pressures with peak values orders of magnitudes higher than that of the excitation pressures. This occurs when the driving frequency matches the natural frequency of the bubble cloud. The initial distance between the bubble cloud and the wall is also critical on the resulting pressure loads. A bubble cloud collapsing very close to the wall exhibits a cascading collapse with the bubbles farthest from the wall collapsing first and the nearest ones collapsing last, thus the energy accumulates and then results in very violent pressure peaks at the wall. Farther from the wall, the bubble cloud collapses quasi spherically with the cloud center collapsing last. INTRODUCTION Collapse of clouds of bubbles near boundaries occur in various engineering applications such as in ultrasonic cavitation, cavitating jets, unsteady sheet cavities on propeller blades, etc. [1,2,3]. Numerical modeling of such a problem is very challenging, since it involves bubble-bubble, bubble-flow, and bubble-wall interactions. In addition the problem involves multi-scale physics ranging from micron-scale individual bubbles to meterscale flow field (e.g., propeller blade). In between, there are very rich and complex meso-scale phenomena at the scale of the bubble cloud, where the bubbles can act collectively [4-8]. The Boundary Element Method (BEM) or Direct Numerical Simulation (DNS) which can fully resolve individual bubbles’ behavior provide details at several scales of interest with impressive progress reported [e.g.,8-11]. However, due to the computational cost these methods are mostly limited to small scale problems addressed for fundamental study purposes, such as developing subgrid relationships for larger scale models. For real applications, twophase bubbly flows are usually modeled using one of several approaches: equivalent homogeneous continuum models, Eulerian two-fluid models, or Eulerian-Lagrangian approaches wherein the bubbles are treated as discrete particles.

An Eulerian-Lagrangian study of cloud dynamics near a wall

The dynamics of bubble clouds is studied using an Eulerian-Lagrangian model treating the two-phase medium as a continuum and modeling the microbubbles as discrete sources and dipoles tracked in a Lagrangian fashion. These two are coupled through the local void fractions associated with the instantaneous bubble volumes and locations. Resonance of the bubble cloud, resulting in the highest pressure at the nearby rigid wall, is deduced from simulations with the same initial bubble distribution while varying the excitation frequency and amplitude. This resonance frequency deviates significantly from the classical linearized solution as the relative amplitude of driving pressure increases. It gradually drops as the excitation amplitude increases until reaching a limit value. In the high amplitude driving pressure regime, the peak pressure generated at the wall has a maximum for an optimum value of the initial bubble radius for the same cloud radius. This occurs when the ratio of maximum over initial bubble siz...

Numerical Study of Gravity Effects on Phase Separation in a Swirl Chamber

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.

SHARED-MEMORY PARALLELIZATION FOR TWO-WAY COUPLED EULER-LAGRANGE MODELING OF BUBBLY FLOWS

Cavitating bubbly flows are encountered in many engineering problems involving propellers, pumps, valves, ultrasonic biomedical applications, … etc. In this contribution an OpenMP parallelized Euler-Lagrange model of two-phase flow problems and cavitation is presented. The two-phase medium is treated as a continuum and solved on an Eulerian grid, while the discrete bubbles are tracked in a Lagrangian fashion with their dynamics computed. The intimate coupling between the two description levels is realized through the local void fraction, which is computed from the instantaneous bubble volumes and locations, and provides the continuum properties. Since, in practice, any such flows will involve large numbers of bubbles, schemes for significant speedup are needed to reduce computation times. We present here a shared-memory parallelization scheme combining domain decomposition for the continuum domain and number decomposition for the bubbles; both selected to realize maximum speed up and good load balance. The Eulerian computational domain is subdivided based on geometry into several subdomains, while for the Lagrangian computations, the bubbles are subdivided based on their indices into several subsets. The number of fluid subdomains and bubble subsets are matched with the number of CPU cores available in a share-memory system. Computation of the continuum solution and the bubble dynamics proceeds sequentially. During each computation time step, all selected OpenMP threads are first used to evolve the fluid solution, with each handling one subdomain. Upon completion, the OpenMP threads selected for the Lagrangian solution are then used to execute the bubble computations. All data exchanges are executed through the shared memory. Extra steps are taken to localize the memory access pattern to minimize non-local data fetch latency, since severe performance penalty may occur on a Non-Uniform Memory Architecture multiprocessing system where thread access to non-local memory is much slower than to local memory.This parallelization scheme is illustrated on a typical non-uniform bubbly flow problem, cloud bubble dynamics near a rigid wall driven by an imposed pressure function.Copyright