Evaluation of bubble-induced turbulence using direct numerical simulation

The presented research evaluates the interaction between a single bubble and homogeneous turbulent flow using direct numerical simulation (DNS) approach. The homogeneous single-phase turbulence is numerically generated by passing a uniform flow through grid planes. The turbulence decay rate is compared with experiment-based correlation. The single phase turbulence is then used as an inflow boundary condition for a set of single bubble studies. By estimating the turbulent field around the fully resolved bubble, the effects of bubble deformability, turbulent intensity and relative velocity on the bubble-induced turbulence are investigated. The existence of bubble creates new vortices in the wake region and the enhancement of turbulence is observed in the region behind the bubble. The results show that the magnitude of the turbulence enhancement would increase as the bubble encounters larger liquid turbulent intensity or higher relative velocity. Set of bubble Weber numbers from 0.34 to 3.39 are used to investigate the effect of bubble deformability. The more deformable bubble is the higher the increase in the magnitude of the turbulence enhancement behind the bubble. This research provides systematic insight on the bubble-induced turbulence (BIT) mechanism and is important for multiphase computational fluid dynamics (M-CFD) closure model development.     

Modeling of bubble behaviors and size distribution in a slab continuous casting mold

Population balance equations combined with Eulerian–Eulerian two-phase model are employed to predict the polydispersed bubbly flow inside the slab continuous-casting mold. The class method, realized by the MUltiple-SIze- Group (MUSIG) model, alongside with suitable bubble breakage and coalescence kernels is adopted. A two-way momentum transfer mechanism model combines the bubble induced turbulence model and various interfacial forces including drag, lift, virtual mass, wall lubrication, and turbulent dispersion are incorporated in the model. A 1/4th scaled water model of the slab continuous-casting mold was built to measure and investigate the bubble behavior and size distribution. A high speed video system was used to visualize the bubble behavior, and a digital image processing technique was used to measure the mean bubble diameter along the width of the mold. Predictions by previous mono-size model and MUSIG model are compared and validated against experimental data obtained from the water model. Effects of the water flow rate and gas flow rate on the mean bubble size were also investigated. Close agreements by MUSIG model were achieved for the gas volume fraction, liquid flow pattern, bubble breakage and coalescence, and local bubble Sauter mean diameter against observations and measurements of water model experiments.     

Turbulence structure of air-water bubbly flow—I. measuring techniques

This paper, the first in a series describing our work on the turbulence structure of air-water bubbly flow, describes the principles of measurement and specially developed electronic instrumentation for determining various important local parameters, and the rates of turbulent transport of heat and bubbles in air-water two-phase bubbly flow. These instruments indicate the phase distribution, the bubble velocity and its spectrum, the water velocity and the turbulent intensity, and the turbulent dispersion coefficient of bubbles. Brief discussions are also presented on the accuracy of these techniques.     

Mathematical modelling of bubble driven flows in metallurgical processes

The complex fluid dynamics of two-phase bubbly flows in metallurgical reactors is modelled numerically by using a k–e turbulence model for the liquid phase, with a driving force determined by considering the motion of the bubbles. The latter are affected by the buoyancy forces and the drag caused by their relative motion with the mean and turbulent motions of the liquid, the turbulent component being obtained by random sampling to give an ensemble of bubble trajectories. The two-way coupling between the two phases is resolved by an iterative procedure which converges on a stable overall solution. The results are compared with measurements carried out on an air-water model and show good overall agreement.     

Effect of particles suspended in a fluid flow on the decay of isotropic turbulence

Dynamic equations have been obtained for the two-point double correlations of the fluctuation velocities of a fluid and the particles suspended in it at low volume concentrations of the solid phase. In the case of uniform isotropic turbulence these equations can be considerably simplified. The final period of decay of isotropic turbulence has been studied in detail. At this stage in the case of high-inertia particles the inhomogeneous-fluid turbulence is similar to the turbulence of a homogeneous fluid (without particles) in the sense that the presence of the particles affects only the fluctuation energy but leaves unchanged the spatial scales of turbulence and the spatial energy spectrum function. The suspended particles lead to exponential damping of the turbulent pulsations.Little theoretical information is available on the hydrodynamics of a suspension of fine particles in a turbulent liquid or gas. Research has been mainly confined to the behavior of the individual particles in a given turbulence field [1]. The problem of the turbulent motion of the mixture as a whole has been examined by Barenblatt [2], who derived the equations of motion of the mixture, using Kolmogorov's hypothesis to close them. Hinze [3] has also attempted to derive equations for turbulent pulsations of the mixture. However, as Murray showed [4], Hinze' s equations contradict Newton' s third law.The effect of suspended particles on the turbulence of a two-phase flow is governed by the noncorrespondence of the local velocities of the particles and the medium. The forces of resistance to the motion of the particles relative to the fluid lead to additional dissipation of fluctuation energy and decay of turbulence [2]. On the other hand, if the averaged velocities of particles and medium do not correspond, the suspended particles may also have a destabilizing effect [5, 6], causing energy transfer from the averaged to the pulsating motion. Below we shall consider the case where the averaged velocities of the two phases coincide, i.e., we shall deal only with the first of the two above-mentioned effects.The authors thank G.I. Barenblatt for his useful advice.     

Water entrainment due to spillway surface jets

Strong flow entrainment has been observed downstream of spillways constructed with flow deflectors. This water entrainment has important environmental and ecological impacts because it improves the mixing of powerhouse and spillway flows, but may negatively impact fish migration or create adverse flow conditions.

Most studies found in the literature attempt to explain this entrainment with turbulent mixing. Both reduced-scale hydraulic models and single-phase, isotropic RANS models grossly under-predict the degree of entrainment observed in prototypes. In this paper, an anisotropic model that accounts for the bubble volume fraction and attenuation of the normal velocity fluctuations at the free surface is presented. The model adequately predicts the main mechanisms causing water entrainment and compares well against experimental data for a round surface jet and for Brownlee Dam at model scale. It is shown that appropriate entrainment can only be captured if the turbulence anisotropy and the two-phase nature of the flow are modelled.     

Interfacial area concentration in gas–liquid bubbly to churn flow regimes in large diameter pipes

This study performed a survey on existing correlations for interfacial area concentration (IAC) prediction and collected an IAC experimental database of two-phase flows taken under various flow conditions in large diameter pipes. Although some of these existing correlations were developed by partly using the IAC databases taken in the low-void-fraction two-phase flows in large diameter pipes, no correlation can satisfactorily predict the IAC in the two-phase flows changing from bubbly, cap bubbly to churn flow in the collected database of large diameter pipes. So this study presented a systematic way to predict the IAC for the bubbly-to-churn flows in large diameter pipes by categorizing bubbles into two groups (group 1: spherical or distorted bubble, group 2: cap bubble). A correlation was developed to predict the group 1 void fraction by using the void fraction for all bubble. The group 1 bubble IAC and bubble diameter were modeled by using the key parameters such as group 1 void fraction and bubble Reynolds number based on the analysis of Hibiki and Ishii (2001, 2002) using one-dimensional bubble number density and interfacial area transport equations. The correlations of IAC and bubble diameter for group 2 cap bubbles were developed by taking into account the characteristics of the representative bubbles among the group 2 bubbles and the comparison between a newly-derived drift velocity correlation for large diameter pipes and the existing drift velocity correlation of Kataoka and Ishii (1987) for large diameter pipes. The predictions from the newly-developed two-group IAC correlation were compared with the collected experimental data in gas–liquid bubbly to churn flow regimes in large diameter pipes and their mean absolute relative deviations were obtained to be 28.1%, 54.4% and 29.6% for group 1, group 2 and all bubbles respectively.     

Turbulent shear stress profiles in a bubbly channel flow assessed by particle tracking velocimetry

Particle tracking velocimetry (PTV) is applied to a bubbly two-phase turbulent flow in a horizontal channel at Re = 2 × 10⁴ to investigate the turbulent shear stress profile which had been altered by the presence of bubbles. Streamwise and vertical velocity components of liquid phase are obtained using a shallow focus imaging method under backlight photography. The size of bubbles injected through a porous plate in the channel ranged from 0.3 to 1.5 mm diameter, and the bubbles show a significant backward slip velocity relative to liquid flow. After bubbles and tracer particles are identified by binarizing the image, velocity of each phase and void fraction are profiled in a downstream region. The turbulent shear stress, which consists of three components in the bubbly two-phase flow, is computed by analysis of PTV data. The result shows that the fluctuation correlation between local void fraction and vertical liquid velocity provides a negative shear stress component which promotes frictional drag reduction in the bubbly two-phase layer. The paper also deals with the source of the negative shear stress considering bubble’s relative motion to liquid.     

Study of two-phase flows in reduced gravity using ground based experiments

Experimental studies have been carried out to support the development of a framework of the two-fluid model along with an interfacial area transport equation applicable to reduced gravity two-phase flows. The experimental study simulates the reduced gravity condition in ground based facilities by using two immiscible liquids of similar density namely, water as the continuous phase and Therminol 59^® as the dispersed phase. We have acquired a total of eleven data sets in the bubbly flow and bubbly to slug flow transition regimes. These flow conditions have area-averaged void (volume) fractions ranging from 3 to 30% and channel Reynolds number for the continuous phase between 2,900 and 8,800. Flow visualization has been performed and a flow regime map developed which is compared with relevant bubbly to slug flow regime transition criteria. The comparison shows that the transition boundary is well predicted by the criterion based on critical void fraction. The value of the critical void fraction at transition was experimentally determined to be approximately 25%. In addition, important two-phase flow local parameters, including the void fraction, interfacial area concentration, droplet number frequency and droplet velocity, have been acquired at two axial locations using state-of-the-art multi-sensor conductivity probe. The radial profiles and axial development of the two-phase flow parameters show that the coalescence mechanism is enhanced by either increasing the continuous or dispersed phase Reynolds number. Evidence of turbulence induced particle interaction mechanism is highlighted. The data presented in this paper clearly show the marked differences in terms of bubble (droplet) size, phase distribution and phase interaction in two-phase flow between normal and reduced gravity conditions.     

Modeling of bubble coalescence and break-up considering turbulent suppression phenomena in bubbly two-phase flow

New mechanistic bubble coalescence and break-up models considering turbulent suppression phenomena, which can possibly occur in the high liquid velocity condition of turbulent bubbly two-phase flow, are presented. The energy exchange mechanism between a turbulent eddy and interfacial structure was taken into account in the efficiency terms. Numerical simulations of turbulent bubbly flow were conducted in a CFD code to evaluate the newly developed models, in comparison with other advanced models coupled with a bubble-induced turbulent effect for one-group interfacial area transport equation. Local measurements of the bubble characteristics on the bubble size evolution along a vertical pipe flow were performed at KAERI-VAWL test facility using the five-sensor conductivity probe method to provide database for models validation. Results from the calculation clearly show the improvements of the newly developed models.     

Direct numerical simulation of a freely decaying turbulent interfacial flow

Whereas Large Eddy Simulation (LES) of single-phase flows is already widely used in the CFD world, even for industrial applications, LES of two-phase interfacial flows, i.e. two-phase flows where an interface separates liquid and gas phases, still remains a challenging task. The main issue is the development of subgrid scale models well suited for two-phase interfacial flows. The aim of this work is to generate a detailed data base from direct numerical simulation (DNS) of two-phase interfacial flows in order to clearly understand interactions between small turbulent scales and the interface separating the two phases. This work is a first contribution in the study of the interface/turbulence interaction in the configuration where the interface is widely deformed and where both phases are resolved by DNS. To do this, the interaction between an initially plane interface and a freely decaying homogeneous isotropic turbulence (HIT) is studied. The densities and viscosities are the same for both phases in order to focus on the effect of the surface tension coefficient. Comparisons with existing theories built on wall-bounded or free-surface turbulence are carried out. To understand energy transfers between the interfacial energy and the turbulent one, PDFs of the droplet sizes distribution are calculated. An energy budget is carried out and turbulent statistics are performed including the distance to the interface as a parameter. A spectral analysis is achieved to highlight the energy transfer between turbulent scales of different sizes. The originality of this work is the study of the interface/turbulence interactions in the case of a widely deformed interface evolving in a turbulent flow.     

Creating homogeneous and isotropic turbulence without a mean flow

A novel method of creating homogeneous and isotropic turbulence with small mean flow has been developed. Eight synthetic jet actuators on the corners of a cubic chamber can create energetic turbulence with root-mean-square (rms) velocities as large as 0.87 m/s, corresponding to a Taylor microscale Reynolds number, Re , of 218. Stationary turbulence results show that the turbulence was isotropic, with the rms velocity ratio equal to 1.03, and also homogeneous within the region of interest. Natural decaying turbulence measurements confirmed the power-law decay of the turbulent kinetic energy, with the decay exponent n equal to 1.86 for an initial Re of 224.     

Assessment of the validity of a log-law for wall-bounded turbulent bubbly flows

There has been considerable discussion in recent years concerning whether a log-law exists for wall-bounded, turbulent bubbly flows. Previous studies have argued for the existence of such a log-law, with a modified von Kármán constant, and this is used in various modelling studies. We provide a critique of this idea, and present several theoretical reasons why a log-law need not be expected in general for wall-bounded, turbulent bubbly flows. We then demonstrate using recent data from interface-resolving Direct Numerical Simulations that when the bubbles make a significant contribution to the channel flow dynamics, the mean flow profile of the fluid can deviate significantly from the log-law behaviour that approximately holds for the single-phase case. The departures are not surprising and the basic reason for them is simple, namely that for bubbly flows, the mean flow is affected by a number of additional dynamical parameters, such as the void fraction, that do not play a role for the single-phase case. As a result, the inner/outer asymptotic regimes that form the basis of the derivation of the log-law for single-phase flow do not exist in general for bubbly turbulent flows. Nevertheless, we do find that for some cases, the bubbles do not cause significant departures from the unladen log-law behaviour. Moreover, we show that if departures occur these cannot be understood simply in terms of the averaged void fraction, but that more subtle effects such as the bubble Reynolds number and the competition between the wall-induced turbulence and the bubble-induced turbulence must play a role.     

Investigation of turbulence modification in a non-reactive two-phase flow

In a two-phase flow the influence of a dispersed phase on the turbulence properties of a continuous phase, known as turbulence modification, is investigated. An experimental approach is discussed that is suitable for studying the decay of grid-generated turbulence in a vertically orientated wind tunnel with a cross-section large enough to avoid influences from walls. Phase Doppler anemometry is used to characterize both single and two-phase flow by measuring mean axial and radial velocity components, velocity fluctuations, turbulent kinetic energy, and integral time scales. By direct comparison of results from single- and two-phase flows, the feedback of the dispersed phase on the continuous phase can be isolated. The data is used to deduce a source term for particle-induced turbulence production appropriate for a numerical simulation of the flow, based on the Reynolds-averaged Navier-Stokes equations. Although of special importance for a detailed understanding of turbulent two-phase combustion, additional complexity introduced by evaporation and chemical reactions is avoided by using glass beads as dispersed phase.     

Evaporation of polydispersed droplets in a highly turbulent channel flow

A model experiment for the study of evaporating turbulent two-phase flows is presented here. The study focuses on a situation where pre-atomized and dispersed droplets vaporize and mix in a heated turbulent flow. The test bench consists in a channel flow with characteristics of homogeneous and isotropic turbulence where fluctuations levels reach very high values (25% in the established zone). An ultrasonic atomizer allows the injection of a mist of small droplets of acetone in the carrier flow. The large range diameters ensure that every kind of droplet behavior with regards to turbulence is possible. Instantaneous concentration fields of the vaporized phase are extracted from fluorescent images (PLIF) of the two phase flow. The evolution of the mixing of the acetone vapor is analyzed for two different liquid mass loadings. Despite the high turbulence levels, concentration fluctuations remain significant, indicating that air and acetone vapor are not fully mixed far from the injector.     

Objective tensorial representation of the pressure–strain correlations of turbulence

An explicit algebraic model for the fluctuating pressure–strain rate correlations of turbulence is developed by the use of representation theorems for tensor-valued isotropic tensors, and by invoking the principle of objectivity. The resulting model differs from others by the absence of the vorticity tensor from its formulation. The new model is calibrated by reference to data from homogeneous shear flows, and its potential as a practical tool for the analysis of turbulent flows is demonstrated by numerical simulations of a benchmark two-dimensional shear layer.     

A scattering light probe for the measurement of oceanic air bubble sizes

A new optical probe has been designed, tested, calibrated and used in a bubbly two-phase flow. The probe is based on the principle of light scattering at an angle of ninety degrees from an incident laser beam. The errors inherent in such a technique are reviewed and evaluated. The calibration curve shows that the output voltage is proportional to the square of the bubble diameter. A first test is presented in a real bubbly flow produced by the action of wave-breaking in an air-sea interaction simulating facility.     

Numerical Simulation of Isotropic Turbulence Dynamics

The Karman-Howarth closed equation is used to describe the behavior of homogeneous isotropic turbulence. A numerical solution is obtained by the collocation-grid and finite-difference methods using moving grids. The predicted results are compared with experimental data on the decay of fully developed and weak turbulence. The numerical realization of the Loitsiansky-MilHonshtchikov asymptotic solution has been made.     

Numerical Study and Lagrangian Modelling of Turbulent Heat Transport

A stochastic Lagrangian model for both fluid velocities and temperature fluctuations is evaluated from Direct Numerical Simulation of heat transport in homogeneous isotropic turbulence submitted to a linear mean temperature gradient. The first stage lies on the study of the Lagrangian fluid turbulence statistics (Lagrangian correlations functions) computed from predictions of DNS. They are crucial for the analysis and the modelling of the fluid turbulent properties along discrete particle trajectories. In the second stage, a velocity-scalar Lagrangian stochastic model is proposed and evaluated from the DNS data. The coefficients of the drift and diffusion terms of the model are determined by only Lagrangian timescales, temperature variance and turbulent flux. The shapes of correlation functions present a good agreement between DNS results and stochastic modelling approach.