Bubbly Flow Model Research Articles

CFD Modeling of Gas-Liquid Bubbly Flow in Horizontal Pipes: Influence of Bubble Coalescence and Breakup

Modelling of gas-liquid bubbly flows is achieved by coupling a population balance equation with the three-dimensional, two-fluid, hydrodynamic model. For gas-liquid bubbly flows, an average bubble number density transport equation has been incorporated in the CFD code CFX 5.7 to describe the temporal and spatial evolution of the gas bubbles population. The coalescence and breakage effects of the gas bubbles are modeled. The coalescence by the random collision driven by turbulence and wake entrainment is considered, while for bubble breakage, the impact of turbulent eddies is considered. Local spatial variations of the gas volume fraction, interfacial area concentration, Sauter mean bubble diameter, and liquid velocity are compared against experimental data in a horizontal pipe, covering a range of gas (0.25 to 1.34 m/s) and liquid (3.74 to 5.1 m/s) superficial velocities and average volume fractions (4% to 21%). The predicted local variations are in good agreement with the experimental measurements reported in the literature. Furthermore, the development of the flow pattern was examined at three different axial locations ofL/D= 25, 148, and 253. The first location is close to the entrance region where the flow is still developing, while the second and the third represent nearly fully developed bubbly flow patterns.

Two-fluid modeling of bubbly flows around surface ships using a phenomenological subgrid air entrainment model

The quantitative prediction of bubbly flow around a maneuvering surface ship is critical in determining its hydrodynamic performance and its acoustic and optical signatures. It is a challenging multiscale problem that relies heavily on subgrid models of turbulence and air entrainment. In this manuscript we analyze this problem using a phenomenological air entrainment model that predicts the location and rate of air entrainment around a surface ship. This subgrid model was coupled with a two-fluid Reynolds averaged Navier Stokes (RaNS) bubbly flow model and used to evaluate the flow field around a naval surface ship in straight ahead and turning motions. For straight ahead motion the predicted void fraction distributions aft of the stern were compared with experiments at three different ship speeds and good agreement was found. The qualitative differences in the location of the air entrainment and the resulting bubbly flow between straight ahead and steady turning motions were discussed and compared with experimental observations at sea. To our knowledge this study presents the first quantitative numerical prediction of void fraction distributions around a full-scale surface ship, well matching the experimental measurements.

CO2 Mass Transfer Induced through an Airlift Loop by a Microbubble Cloud Generated by Fluidic Oscillation

Carbon dioxide is one of the most common gases produced from biological processes. Removal of carbon dioxide from these processes can influence the direction of biological reactions as well as the pH of the medium, which affects bacterial metabolism. Kinetics of carbon dioxide transfer mechanisms are investigated by sparging with conventional fine bubbles and microbubbles. The estimate of the concentrations of CO2(aq), H2CO3, HCO3 –, and CO32– from pH measurement in an airlift loop sparged mixer is derived. The canonical estimate of overall mass transfer coefficient of CO2 has been estimated as 0.092 min–1 for a microbubble size of 550 m compared with 0.0712 min–1 for a fine bubble (mean bubble size of 1.3 mm) sparging. It is observed that the efficiency of CO2 removal has increased up to 29% by microbubble sparging compared with fine bubble sparging. Laminar bubbly flow modeling of the airlift loop configuration correctly predicts the trend of the change in overall mass transfer in both gas stripping with nitrogen and gas scrubbing for CO2 exchange, while demonstrating the expected separated flow structure. The models indicate that the macroscale flow structure is transient and pseudoperiodic. This latter feature should be tested by flow visualization, as preferential frequencies in the flow can be exploited for enhanced mixing.

Modeling air entrainment and transport in a hydraulic jump using two-fluid RANS and DES turbulence models

Both RaNS (Reynolds-averaged Navier–Stokes) and DES (Detached Eddy Simulation) type turbulence models were used in conjunction with a two-fluid model of bubbly flow and a new subgrid air entrainment model to predict air entrainment and transport in a hydraulic jump. It was found that the void fraction profiles predicted by both methods are in agreement with the experimental data in the lower shear layer region, which contains the air bubbles entrained at the so-called toe of the hydraulic jump. In contrast, in the upper roller region behind the toe, the averaged results of the DES turbulence model gives accurate predictions while a RaNS turbulence model does not. This is because the DES turbulence model successfully captures the strong fluctuations on the free surface which allows it to entrain air near the top of the roller region. In contrast, RaNS type turbulence model results in a steady, smooth interface which fails to capture the wave-induced bubble sources in that region. To our knowledge, this study is the first successful quantitative numerical simulation of the overall void fraction profiles in a hydraulic jump.

The effect of the VOF–CSF static contact angle boundary condition on the dynamics of sliding and bouncing ellipsoidal bubbles

The static contact angle is the only empiricism introduced in a Volume of Fluid–Continuum Surface Force (VOF–CSF) model of bubbly flow. Although it has previously been shown to have a relatively limited effect on the accuracy of velocity and shape predictions in the case of large gas bubbles sliding under inclined walls (e.g. Cook and Behnia, 2001), it may have a more determining influence on the numerical prediction of the dynamics of smaller ellipsoidal bubbles which were shown by Tsao and Koch (1997) to bounce repeatedly when sliding under inclined walls at certain wall inclinations. The present paper reports on the influence of surface tension and the static contact angle on the dynamics of an ellipsoidal air bubble of equivalent diameter D e = 3.4 mm. The bubble Eötvös and Morton numbers are Eo = 1.56 and Mo = 2 × 10 −11 respectively. The computational results are achieved with a Piecewise Linear Construction (PLIC) of the interface and are reviewed with reference to experimental measurements of bubble velocity and interface shape oscillations recorded using a high speed digital camera. Tests are performed at plate inclination angles θ ∈ {10°, 20°, 30°, 45°} to the horizontal and computational models consider three static contact angles θ c ∈ {10°, 20°, 30°}. The static contact angle has been found to have a significant effect on the bubble dynamics but to varying degree depending on the plate inclination. It is shown to promote lift off and bouncing when the plate inclination angle reaches 30° in a way that does not necessarily reflect experimental observations.

A polydisperse two-fluid model for surf zone bubble simulation

[1] Wave breaking in the surf zone entrains large volumes of air bubbles into the water column, forming a two-phase bubbly flow field. Numerical study of bubbly flow is largely restricted by the lack of robust and comprehensive bubble entrainment models. In this paper, we propose a new model that connects bubble entrainment with turbulent dissipation rate at the air-water interface. The entrainment model as well as a polydisperse two-fluid model are incorporated into a 3-D volume of fluid code TRUCHAS. The bubbly flow model is first tested against laboratory experimental data for an oscillatory bubble plume. The calculated time-averaged liquid velocities and their fluctuations agree well with measurements, indicating that the model correctly reproduces dynamic interactions between the liquid phase and the continuum representation of the gas phase. Then, it is employed to study the bubbly flow under a laboratory surf zone breaking wave. Through the comparisons with experimental data, it is demonstrated that the model describes bubble entrainment and void fraction evolution reasonably well. The exponential decay of void fraction observed in the laboratory experiments is captured by the model. The kinematics of bubble plume as well as the vertical evolution of bubble size spectrum at any depth are investigated. Studies of bubble effects on liquid phase turbulence show that the presence of bubbles could suppress a large amount of turbulence under breaking waves.

Computational modeling of bubbly flows in differential pressure flow meters

This paper addresses bubbly flow modeling within Venturi tubes and nozzles using the two-fluid model. The effects of non-drag forces as virtual mass and the so-called “transversal forces” such as lift and wall lubrication are investigated in the context of the two-fluid model. As expected, the transversal forces have an important influence on void distribution as long as the virtual mass affects the pressure drop along the contraction, which is the main parameter for the flow rate measurement. Models for the virtual mass and lift forces were implemented via user routines in commercial computational fluid dynamics (CFD) software, as the models embedded within these packages, specifically for virtual mass, were found not to be adequate for the purpose of this study. The models are validated against results from the literature and pressure drop measurements along a Venturi tube, developed in this work. Additionally, some experimental visualizations were used to make a qualitative comparison with predicted void distribution.

A Comprehensive Sub-Grid Air Entrainment Model for RaNS Modeling of Free-Surface Bubbly Flows

The simulation of free surface bubbly flows using a two-fluid model remains a challenging problem in part due to the lack of a comprehensive air entrainment model that can predict the rate and location of air entrainment for a wide range of flows. In this study we derive a sub-grid model and implement it in a computational multiphase fluid dynamics (CMFD) framework to solve the Reynolds-averaged two-fluid equations. We assess the performance of our model in simulating bubbly flows underneath a plunging liquid jet and a hydraulic jump while varying the characteristic velocity. We compare the void fraction predictions with their experimental counterparts and conclude that the air entrainment model and the two-fluid modeling approach yield accurate results everywhere for the plunging jet and in the turbulent shear layer for the hydraulic jump. The inability of the proposed approach to recover the high void fraction in the roller region of the hydraulic jump is attributed to the failure of RaNS model to resolve the large coherent vortices observed in this region.

ICONE19-43877 Prediction of Residual Stress Improvement by Water Jet Peening (WJP) Using Cavitating Jet and Residual Stress Simulations

We have developed a new method for predicting the distribution of compressive residual stress on and under the weld surface after Water Jet Peeing (WJP). WJP is a practical technology for the preventive maintenance of nuclear power plants. The welds of internal structures of nuclear reactors are subjected to tensile residual stress without any surface treatment. WJP utilizes a cavitating jet to mitigate the generation of Stress Corrosion Cracking (SCC) by changing the residual stress from tensile to compressive. The prediction and confirmation tests of the compressive residual stress are therefore important. We predicted the residual stress improvement by WJP using a combination of a cavitating jet simulation and a residual stress simulation. Impulsive bubble pressure that varied in microseconds in the cavitating jet was numerically simulated with 'bubble flow model'. The distribution of the impulsive bubble pressure was verified with a measurement of bubble collapse location by using multi Acoustic Emission (AE) sensors. The cavitation intensity was estimated by the bubble pressure. The residual stress simulation was conducted on the basis of the input condition obtained from the cavitation intensity. The residual stress distributions on and under the material surface were predicted. The distributions were compared with measured data, and the results confirmed the developed method for predicting the compressive residual stress after WJP was valid.

CFD MODELING OF ADIABATIC BUBBLY FLOW

CFD MODELING OF ADIABATIC BUBBLY FLOW

Research on Two Phase Waterjet Nozzles

Air-augmented waterjets derive their propulsion from compressed gas mixed directly into the main flow. The gas bubbles expand as the mixture passes through the pressure gradient of the convergent nozzle, and energy is imparted to the water from the air in a complex fashion. This experiment measures the exchange of air and water energy for three nozzles over a range of flowrates and void fractions using compressed air injected and mixed upstream of the nozzle entrance. Pressures and nozzle thrust are measured to examine flow changes. The results are compared with predictions from a one-dimensional bubbly flow model. The measured efficiencies are lower than or comparable to predicted values.

Prediction of Cavitation Intensity and Erosion Area in Centrifugal Pump by Using Cavitating Flow Simulation with Bubble Flow Model

We developed a numerical simulation code and a method of estimation for predicting the cavitation erosion in pumps. Cavitation erosion is closely related to cavitation intensity based on bubble dynamics. A “bubble flow model” simulates detailed bubble behavior in a cavitating flow. Cavitation intensity was estimated by analyzing the bubble pressure and bubble nuclei distribution in a centrifugal pump. We simulated the impulsive bubble pressure that varied in microseconds. The impulsive pressure was considered to be related to actual bubble collapse, which caused cavitation erosion. The erosion area was experimentally detected using a paint method. The predicted high cavitation intensity area agreed well with the experimental erosion area, since the predicted and experimental areas were both located between the shroud and mid-point of the blade near the leading edge. Our code was thus effective for estimating the cavitation intensity and predicting the erosion area around the impeller of a centrifugal pump.

Comparison of several models for multi-size bubbly flows on an adiabatic experiment

This paper deals with the modelling and numerical simulation of isothermal bubbly flows with multi-size bubbles. The study of isothermal bubbly flows without phase change is a first step towards the more general study of boiling bubbly flows. Here, we are interested in taking into account the features of such isothermal flow associated to the multiple sizes of the different bubbles simultaneously present inside the flow. With this aim, several approaches have been developed. In this paper, two of these approaches are described and their results are compared to experimental data, as well as to those of an older approach assuming a single average size of bubbles. These two approaches are (i) the moment density approach for which two different expressions for the bubble diameter distribution function are proposed and (ii) the multi-field approach. All the models are implemented into the NEPTUNE_CFD code and are compared to a test performed on the MTLOOP facility. These comparisons show their respective merits and shortcomings in their available state of development.

CFD modelling of polydispersed bubbly two-phase flow around an obstacle

A population balance model (the Inhomogeneous MUSIG model) has recently been developed in close cooperation between ANSYS-CFX and Forschungszentrum Dresden-Rossendorf and implemented into the CFD-Code CFX [Krepper, E., Lucas, D., Prasser, H.-M, 2005. On the modelling of bubbly flow in vertical pipes. Nucl. Eng. Des. 235, 597–611; Frank, T., Zwart, P.J., Shi, J.-M., Krepper, E., Rohde, U., 2005. Inhomogeneous MUSIG Model—a population balance approach for polydispersed bubbly flows, International Conference “Nuclear Energy for New Europe 2005”, Bled, Slovenia, September 5–8, 2005; Krepper, E., Beyer, M., Frank, Th., Lucas, D., Prasser, H.-M., 2007. Application of a population balance approach for polydispersed bubbly flows, 6th Int. Conf. on Multiphase Flow Leipzig 2007, (paper 378)]. The current paper presents a brief description of the model principles. The capabilities of this model are discussed via the example of a bubbly flow around a half-moon shaped obstacle arranged in a 200 mm pipe. In applying the Inhomogeneous MUSIG approach, a deeper understanding of the flow structures is possible and the model allows effects of polydispersion to be investigated. For the complex flow around the obstacle, the general structure of the flow was well reproduced in the simulations. This test case demonstrates the complicated interplay between size dependent bubble migration and the effects of bubble coalescence and breakup on real flows. The closure models that characterize the bubble forces responsible for the simulation of bubble migration show agreement with the experimental observations. However, clear deviations occur for bubble coalescence and fragmentation. The models applied here, which describe bubble fragmentation and coalescence could be proved as a weakness in the validity of numerous CFD analyses of vertical upward two-phase pipe flow. Further work on this topic is under way.

Modeling of isothermal bubbly flow with ınterfacial area transport equation and bubble number density approach

In this study, isothermal turbulent bubbly flow is mechanistically modeled. For the modeling, Fluent version 6.3.26 is used as the computational fluid dynamics solver. First, the mechanistic models that simulate the interphase momentum transfer between the gas (bubbles) and liquid (continuous) phases are investigated, and proper models for the known flow conditions are selected. Second, an interfacial area transport equation (IATE) solution is added to Fluent’s solution scheme in order to model the interphase momentum transfer mechanisms. In addition to solving IATE, bubble number density (BND) approach is also added to Fluent and this approach is also used in the simulations. Different source/sink models derived for the IATE and BND models are also investigated. The simulations of experiments based on the available data in literature are performed by using IATE and BND models in two and three-dimensions. The results show that the simulations performed by using IATE and BND models agree with each other and with the experimental data. The simulations performed in three-dimensions give better agreement with the experimental data.

Experimental Investigation and Modeling of the Effects of Rising Gas Bubbles in a Closed Pipe

Summary Transient multiphase flow in the wellbore causes problems in well-test interpretation when the well is shut in at surface and the pressure is measured downhole. Pressure-buildup data recorded during a test can be dominated by transient wellbore effects (i.e., phase change, flow reversal, and re-entry of the denser phase into the producing zone), making it difficult to distinguish between true reservoir features and transient wellbore artifacts (Gringarten et al. 2000). This paper is a follow-up to paper SPE 96587 (Ali et al. 2005), which presented experimental results of phase redistribution effects on pressure-buildup data. Though the results of the experiments were revealing, they are complex because they reflect the real well situation. To obtain results in which the phase redistribution in the well is studied independently of the interaction with the reservoir, a further set of experiments was carried out. In these experiments, the tube (simulating the well) was isolated at both the top and the bottom at the same time. The pressure distribution was measured during the transient following shut-in and for the steady-state final condition, in which there was a liquid-filled zone at the bottom of the test section and a gas-filled zone at the top. A substantial number of tests were conducted in the bubbly-flow region and could therefore be analyzed by a simple 1D model for bubbly flow. The results of the comparison between the model and the experimental data are presented in this paper.

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.

Turbulent cascade modeling of single and bubbly two-phase turbulent flows

The analysis of turbulent two-phase flows requires closure models in order to perform reliable computational multiphase fluid dynamics (CMFD) analyses. A spectral turbulence cascade-transport model, which tracks the evolution of the turbulent kinetic energy from large to small liquid eddies, has been developed for the analysis of the homogeneous decay of isotropic single and bubbly two-phase turbulence. This model has been validated for the decay of homogeneous, isotropic single and two-phase bubbly flow turbulence for data having a 5 mm mean bubble diameter. The Reynolds number of the data based on bubble diameter and relative velocity is approximately 1400.

Population balance modeling of bubbly flows considering the hydrodynamics and thermomechanical processes

AbstractThree‐dimensional two‐fluid model and population balance equation is presented to treat the complex hydrodynamics and thermomechanical processes under various bubbly flow conditions. The class method, realized by the MUSIG model, alongside with suitable bubble coalescence and bubble breakage kernels is adopted. Homogeneous MUSIG model predictions have shown to yield good agreement against isothermal bubbly flow measurements. Subcooled boiling flow is further modeled through the use of class method with an improved wall heat partition model. Against experimental data, numerical results also showed good agreement for the local Sauter mean bubble diameter, void fraction, and interfacial area concentration profiles. Inhomogeneous MUSIG model is applied to investigate transition bubbly‐to‐slug flow. Better prediction of bubble diameter is accomplished, especially capturing separation of small and large bubbles. Weakness exists nonetheless in the interfacial forces model. Work is in progress through the consideration of swarm and cluster bubbles instead of isolated spherical bubble calibration. © 2008 American Institute of Chemical Engineers AIChE J, 2008

The inhomogeneous MUSIG model for the simulation of polydispersed flows

A generalized inhomogeneous multiple size group (MUSIG) model based on the Eulerian modeling framework was developed in close cooperation of ANSYS-CFX and Forschungszentrum Dresden-Rossendorf and implemented into the CFD code CFX. The model enables the subdivision of the dispersed phase into a number of size groups regarding the mass balance as well as regarding the momentum balance. In this work, the special case of polydispersed bubbly flow is considered. By simulating such flows, the mass exchanged between bubble size classes by bubble coalescence and bubble fragmentation, as well as the momentum transfer between the bubbles and the surrounding liquid due to bubble size dependent interfacial forces have to be considered. Particularly the lift force has been proven to play an important role in establishing a certain bubble size distribution dependent flow regime. In a previous study [Krepper, E., Lucas, D., Prasser, H.-M., 2005. On the modeling of bubbly flow in vertical pipes. Nucl. Eng. Des. 235, 597–611] the application of such effects were considered and justified and a general outline of such a model concept was given. In this paper the model and its validation for several vertical pipe flow situations is presented. The experimental data were obtained from the TOPFLOW test facility at the Forschungszentrum Dresden-Rossendorf (FZD). The wire-mesh technology measuring local gas volume fractions, bubble size distributions and velocities of gas and liquid phases were employed. The inhomogeneous MUSIG model approach was shown as capable of describing bubbly flows with higher gas content. Particularly the separation phenomenon of small and large bubbles is well described. This separation has been proven as a key phenomenon in the establishment of the corresponding flow regime. Weaknesses in this approach can be attributed to the characterization of bubble coalescence and bubble fragmentation, which must be further investigated.