Turbulent Bubbly Flow Research Articles

Simulation of turbulent bubbly pipe flow with high density ratio and high reynolds number by using the lattice boltzmann method and a multi-phase field model

Direct numerical simulation (DNS) has been widely employed to study the dynamics of turbulent bubbly flows; however, it is used in a limited setting, namely, turbulent bubbly channel flows with low density ratio and low Reynolds number. The present study aims to overcome these limitations and simulate turbulent bubbly pipe flow of a water-air system, a common experimental setting, with high density ratio and Reynolds number. Recently, we developed a cumulant lattice Boltzmann method for two-phase flows and simulated violent two-phase flows with high density ratio and high Reynolds number (Sitompul and Aoki, 2019). In this study, that method is extended by incorporating a multi-phase field model for simulating dispersed bubbles. The proposed method was evaluated by using several cases, namely, 3D bubble rising, turbulent single-phase channel and pipe flows with friction Reynolds number (Reτ≈180,550), turbulent bubbly channel flows with (Reτ≈180) and void fraction (α=1.5%,19.4%), and turbulent bubbly pipe flow with (Reτ=550,α=9.5%). The proposed method can stably simulate the cases, and the results obtained by the proposed method agree well with numerical and experimental results given in the references for given computational domain and grid sizes.

One-equation model to assess population balance kernels in turbulent bubbly flows

A simplified population balance model has been developed to predict the Sauter mean diameter, and to optimize any breakage and coalescence kernel. Firstly, the shortcut model is detailed, and the simplifying assumptions are argued. Then the model is applied in a comparison of 60 combinations of a selection of classical breakage, collision frequency and coalescence efficiency kernels. The models are fitted and then compared with an experimental dataset measured in two different technologies of interest for biotechnology: bubble columns (Gemello et al., 2018), and stirred tanks (Cappello et al., 2020). The best kernels are identified for each flow configuration separately, and some kernels are identified as giving acceptable predictions simultaneously of both flows (average error on bubble size less than 20%).

Structure of a turbulent bubbly flow and heat transfer in a vertical tube

The results of numerical simulation of the flow structure and heat transfer in a vertical polydispersed bubbly flow are presented. The mathematical model is based on the Euler approach taking into account the effect of bubbles on the mean characteristics and turbulence of the carrier phase. The polydispersed distribution of bubbles size in a two-phase flow is modeled by the method of delta approximation considering the process of bubble break-up and coalescence. Carrier phase (fluid) turbulence is predicted using the Reynolds stress transport model. The simulation results showed good agreement with the experimental data presented in the literature. The measured and predicted thermal-hydraulic parameter distribution indicates that in a turbulent bubbly flow, the wall friction increase is greater than heat transfer enhancement.

Bubbles in turbulent flows: Data-driven, kinematic models with history terms

We present data driven kinematic models for the motion of bubbles in high-Re turbulent fluid flows based on recurrent neural networks with long-short term memory enhancements. The models extend empirical relations, such as Maxey-Riley (MR) and its variants, whose applicability is limited when either the bubble size is large or the flow is very complex. The recurrent neural networks are trained on the trajectories of bubbles obtained by Direct Numerical Simulations (DNS) of the Navier Stokes equations for a two-component incompressible flow model. Long short term memory components exploit the time history of the flow field that the bubbles have encountered along their trajectories and the networks are further augmented by imposing rotational invariance to their structure. We first train and validate the formulated model using DNS data for a turbulent Taylor-Green vortex. Then we examine the model predictive capabilities and its generalization to Reynolds numbers that are different from those of the training data on benchmark problems, including a steady (Hill’s spherical vortex) and an unsteady (Gaussian vortex ring) flow field. We find that the predictions of the developed model are significantly improved compared with those obtained by the MR equation. Our results indicate that data-driven models with history terms are well suited in capturing the trajectories of bubbles in turbulent flows.

Modelling of the laminar dispersion force in bubbly flows from direct numerical simulations

In a previous study, we have shown that the momentum transfer between phases, which requires modeling in two-fluid models, is partly comprised of a laminar dispersion force connected to surface tension and pressure effects. This dispersion force, which is obtained by stepping away from the particle hypothesis, is important for the prediction of the void fraction distribution and therefore requires modeling. In this article, based on five direct numerical simulations of turbulent bubbly flows in a vertical channel, a model is proposed by using, inter alia, the structure of the pressure field in the vicinity of bubbles. The resulting model shows very positive results. It is expected to be valid through a wide range of flow regimes for spherical and deformable bubbles as long as the drag force closure is accurate. It is ready for use and can be integrated into an Euler-Euler calculation code.

Development and evaluation of data-driven modeling for bubble size in turbulent air-water bubbly flows using artificial multi-layer neural networks

In the present study, we consider a new reliable model of the bubble size based on multi-layer artificial neural networks (ANN). A multi-layer ANN is used to establish a function for the bubble size without any assumption on the form. In the training procedure, the proposed ANN is trained using data sets collected from open literature and experiments performed in the present study. An excellent agreement was obtained between the trained ANN and experimental data in the bubble size. Also, sensitivity analyses along with principal component analysis and random forest method provide important physical parameters for the bubble size. Next, in order to rigorously evaluate the prediction capability of the present model, flow simulations were conducted for turbulent bubbly flows, for which experimental data are available. The present validation results show that a regime-adaptive data-driven model for the bubble size achieves successful estimation for both wall and core peaking regimes.

First and Second Order Turbulence Closures Applied to Homogeneous Turbulent Bubbly Flows

First and second turbulence models for turbulent bubbly flows are implemented in the CFD code. In the second order turbulence closure, the Reynolds stress tensor of the continuous phase is split into two parts: a turbulent part produced by the gradient of the mean velocity and a pseudo-turbulent part induced by the bubbles displacements; each part is predetermined by a transport equation. The turbulent viscosity issued from this modeling takes into account the excess of the agitation and the supplementary eddies stretching due to the bubbles displacements. First order turbulence closure based on this turbulent viscosity is deduced and a three-equation turbulence model (k, ks, epsilon) is developed. We present the most prominent steps of the modeling and of its implementation in the CFD code then we comment the application of the model in the two homogeneous turbulent flows (uniform and uniformly sheared bubbly flows).

Flow structure and heat transfer in a turbulent vertical bubbly flow downstream of a sudden duct expansion

The flow structure and heat transfer in bubbly flows in a sudden duct expansion were studied. The data was obtained both in a pipe and a flat channel with a sudden expansion. Measurements are performed using shadow photography and PIV/LIF system. For modelling two-phase bubbly flow the set of RANS equations is used. Reynolds stress transport model is used to predict the turbulence of the liquid phase. The influence of sudden channel expansion on the distribution of bubbles and it`s velocity is shown. It is shown, that in the pipe with sudden expansion there are not a strong influence of bubbles on the hydrodynamical structure and heat transfer in the flow recirculation zone. In a contrast, in the vertical channel with back facing step the strong increasement of void fraction were found in similar region. It can result in increasement of heat transfer.

Modeling of Flow Structure, Bubble Distribution, and Heat Transfer in Polydispersed Turbulent Bubbly Flow Using the Method of Delta Function Approximation

The results of modeling of flow structure, air bubble distribution over the pipe cross section, and heat transfer in a vertical polydispersed gas-liquid flow are presented. Themathematical model is based on the Euler description with allowance for the back effect of bubbles on the averaged characteristics and turbulence of the carrier phase. The polydispersity of two-phase flow is described by the delta approximation method with consideration of bubble break-up and coalescence. The turbulence of the carrier phase is predicted using the Reynolds stress transport equations. The results of the modeling showed good agreement with experimental and numerical data of other works.

Eulerian-Eulerian large eddy simulation of two-phase dilute bubbly flows

An efficient mathematical model is presented for conducting large eddy simulation (LES) of turbulent bubbly flows at low gas hold-ups. The mathematical model is based on the filtered multi-fluid equations derived by application of the component-weighted volume-averaging process of each phase. A two-fluid model is applied to the filtered set of equations, yielding a more computationally tractable set of filtered equations. The filtered equations are formulated in generalized curvilinear coordinates to simulate turbulent gas-liquid bubbly flows in complex geometries. The Germano model is used to account for sub-grid turbulent stresses. The gas and liquid momentum equations are discretized with the hybrid staggered/non-staggered method. The performance of the developed mathematical model is demonstrated by simulating the benchmark test case of a turbulent gas-liquid bubbly flow in a rectangular bubble column. The accuracy of the proposed method is assessed via comparison with the experimental data and other numerical results in the literature.

Evaluation of Hydrodynamic Closures for Bubbly Regime CFD Simulations in Developing Pipe Flow

AbstractThe effect of interfacial forces and relevant closures, particularly the lift and wall lubrication forces, on the predictions of Eulerian‐Eulerian computational fluid dynamics simulations of bubbly flows was studied. The test case under study was a developing turbulent bubbly pipe flow, simulated by using OpenFOAM. The results show that the geometric approach to consider the wall effect leads to better agreement than a standard relation assuming asymmetric drainage around the bubble near the wall. Furthermore, the results verify the need for employing negative lift coefficients in cases with large bubbles. A sensitivity analysis on the lift coefficient highlighted the importance of investigating spatially developing flows to draw general conclusions on the applicability of closure relations.

Mixing induced by a bubble swarm rising through incident turbulence

This work describes an experimental investigation on the mixing induced by a swarm of high Reynolds number air bubbles rising through a nearly homogeneous and isotropic turbulent flow. The gas volume fraction α and the velocity fluctuations u0′ of the carrier flow before bubble injection are varied, respectively, in the ranges 0 ≤ α ≤ 0.93% and 2.3 cm/s ≤u0′≤5.5 cm/s, resulting in a variation of the bubblance parameter b in the range [0, 1.3] (b=Vr2αu′02, where Vr is the relative rising velocity). Mixing in the horizontal direction can be modelled as a diffusive process, with an effective diffusivity Dxx. Two different diffusion regimes are observed experimentally, depending on the turbulence intensity. At low turbulence levels, Dxx increases with gas volume fraction α, while at high turbulence levels the enhancement in Dxx is negligible. When normalizing by the time scale of successive bubble passage, the effective diffusivity can be modelled as a sole function of the gas volume fraction α* ≡ α/αc, where αc is a theoretically estimated critical gas volume fraction. The present explorative study provides insights into modeling the mixing induced by high Reynolds number bubbles in turbulent flows.

Application of a novel model for bubble-induced turbulence to bubbly flows in containers and vertical pipes

The baseline model for the CFD-simulation of turbulent bubbly flows in the Euler-Euler framework was proposed several years ago. It defines a fixed set of closures including all constants to avoid case by case tuning and to have a basis for sustainable model development. The present paper extends the baseline model by improving the modelling of bubble-induced turbulence. The closure terms in the transport equations of the k-ω SST model are revisited and replaced with the model recently proposed by Ma et al. (Ma et al., 2017. Physical Review Fluids 2, 034301) which is based on an analysis of the turbulent kinetic energy budget obtained from direct numerical simulation data. Detailed validation results for various flow configurations with a wide range of gas and liquid volumetric fluxes are presented. In case of vertical pipe flow significant improvements in the predicted gas volume fraction and velocity profiles are obtained, especially in high gas volume fraction cases where bubble-induced turbulence is dominant. Simulations of other configurations, such as uniform and non-uniform bubble columns, show that the model of Ma et al. (2017) results in an also for these cases overall improvement. Therefore, the baseline model is now updated to include the new model for bubble-induced turbulence.

수평 파이프 내 난류기포류 수치해석을 위한 이상유동 모델

이상유동은 자연현상이나 산업적 응용에서 많이 발견된다. 그러나 이상유동은 액체와 기체의 지속적인 상호작용으로 인하여 유동이 복잡하고 해석하기 쉽지 않다. 특히 거대 유체 시스템 내 이상유동해석에 적합한 2유체 방정식은 많은 모델링 항을 가지고 있다. 본 연구에서는 2유체 방정식을 이용하여 수평 난류 기포류를 해석할 때, 최적의 계면운동량 모델을 찾고 모델 값을 제시하고자 한다. 이를 위해 7개의 실험 데이터에 대해 수치해석을 수행하였다. 본 연구에서 제시된 모델들과 그 값들은 수평 난류기포류를 해석하는데 있어 유용한 정보가 될 것이다.

Methodology for pressure drop of bubbly flow based on energy dissipation

Abstract Pressure drop of bubbly flow is a widely used parameter in petroleum industry. The energy dissipation rate is induced by three factors, including wall resistance, bubble breakup and coalescence, which is studied here from the perspective of the macroscopic flow and microscopic bubbles. This work details a model using the principle of energy conservation to clarify the mechanism of the pressure drop for turbulent bubbly flow in horizontal pipes. The model was validated via a comparison with experimental data of horizontal bubbly flow collected from nine previous studies with 200 points. Most of the errors are within ±20%. The proportions of pressure drop induced by wall resistance, bubble breakup and coalescence were calculated by the model. The results indicate that the largest proportion is from wall resistance, followed by bubble coalescence, with bubble breakup having the smallest proportion. In addition, the trends of proportion induced by the three factors above are analyzed by increasing gas volume fraction and mixture viscosity. The results show that the proportion induced by wall resistance decreases with the increasing volume fraction of the gas, and increases with the increasing mixture viscosity. The proportions induced by the bubble breakup and coalescence in the opposite case.

LES of turbulent non-isothermal two-phase flows within a multifield approach

Safety issues in nuclear power plant involve complex turbulent bubbly flows. To predict the behavior of these flows, the two-fluid approach is often used. Nevertheless, this model has been developed for the simulation of small spherical bubbles, considered as a dispersed field. To deal with bubbles with a large range of sizes, a multifield approach based on this two-fluid model has been proposed. A special treatment, called the Large Bubble Model (LBMo), has been implemented and coupled to the dispersed model. However, only laminar and isothermal flows were considered in previous papers. Thus, here, Large Eddy Simulations (LES) are investigated to model turbulence effects. For this purpose, the two-fluid model equations are filtered to highlight the specific subgrid terms. Then, an a priori LES study using filtered Direct Numerical Simulation (DNS) results is detailed. This analysis allows classifying these terms according to their relative weight and then concentrating the modelling efforts on the predominant ones. Five different turbulence models are compared. These results are finally used to perform true LES on a turbulent two-phase flow. Moreover, in order to tackle non-isothermal flows occurring in industrial studies, a new heat transfer model is implemented and validated to deal with phase change at large interfaces using the Large Bubble Model.

Modelling bubble induced turbulence for gas-liquid bubbly flow in a vertical pipe

A two-fluid model in the Eulerian-Eulerian framework has been implemented for the turbulent gas-liquid bubbly upward flow in a vertical pipe. The transport equations, i.e. Reynolds-Averaged Navier-Stokes equations for the two-fluid model, are discretized using the finite volume method. The effect of the disperse gas phase on the liquid phase turbulence, referred to as turbulence modulation, was accounted for through source terms in the transport equations for a low Reynolds number k-ε turbulence closure. The model was used to predict the turbulence kinetic energy and its dissipation rate, mean phasic velocities and volume fraction distribution for a set of test cases selected from the available literature. The focus of the present study was on assessing the model predictions using measurements of the turbulence kinetic energy of the liquid phase. A relatively novel aspect of the present analysis is the use of the budgets of the transport equations for the turbulence kinetic energy and dissipation rate to assess the effect of the turbulence modulation on the liquid turbulence field. Although the present model formulation is shown to adequately predict the effect of bubbles in some flows and perform better than some of the other model formulations, the overall conclusion is that the present approaches for incorporating turbulence modulation are at best partially successful and still need further development.

Validation of a closure model framework for turbulent bubbly two-phase flow in different flow situations

Abstract In the present paper a set of closure relations for interphase momentum exchange and for bubble-induced turbulence within the Euler-Euler framework is presented and validated against a set of tests performed at the HZDR-facility MT-Loop. The facility was equipped with wire-mesh sensors that allow cross sectional distributions of gas fraction, gas velocity, and bubble sizes to be measured at different distances from the gas injection. The here applied models were derived for the simulation of fully developed turbulent vertical upward bubbly flow in a pipe. The radial gas fraction profile for this kind of flow is the result of the ratio of the radial force components of the so-called non-drag forces and can be used for model validation. However, only the ratio, not the absolute value of the bubble forces can be tested in this way. In the present paper more detailed information from the experiment is exploited by consideration of the evolution of gas fraction distribution particularly after the gas injection region. The change of cross sectional gas volume fraction distribution is the result of the action of non-drag forces. In addition to vertical pipe flow tests further insight is obtained from the investigation of the effect of a slight tube inclination which shifts the gas distribution. Here the disturbance of the cylindrical symmetry of a vertical pipe gives hints on the absolute value of the non-drag force components. The results show that the presented model framework at least is able to describe the phenomena qualitatively. Possible reasons for quantitative deviations are discussed and require further investigations.

Interface Tracking Investigation of Geometric Effects on the Bubbly Flow in PWR Subchannels

Absorbing heat from the fuel rod surface, water as coolant can undergo subcooled boiling within a pressurized water reactor (PWR) fuel rod bundle. Because of the buoyancy effect, the vapor bubbles generated will then rise along and interact with the subchannel geometries. Reliable prediction of bubble behavior is of immense importance to ensure safe and stable reactor operation. However, given a complex engineering system like a nuclear reactor, it is very challenging (if not impossible) to conduct high-resolution measurements to study bubbly flows under reactor operation conditions. The lack of a fundamental two-phase-flow database is hindering the development of accurate two-phase-flow models required in more advanced reactor designs. In response to this challenge, first-principles–based numerical simulations are emerging as an attractive alternative to produce a complementary data source along with experiments. Leveraged by the unprecedented computing power offered by state-of-the-art supercomputers, direct numerical simulation (DNS), coupled with interface tracking methods, is becoming a practical tool to investigate some of the most challenging engineering flow problems. In the presented research, turbulent bubbly flow is simulated via DNS in single PWR subchannel geometries with auxiliary structures (e.g., supporting spacer grid and mixing vanes). The geometric effects these structures exert on the bubbly flow are studied with both a conventional time-averaging approach and a novel dynamic bubble tracking method. The new insights obtained will help inform better two-phase models that can contribute to safer and more efficient nuclear reactor systems.

Dispersion of Air Bubbles in Isotropic Turbulence.

Bubbles play an important role in the transport of chemicals and nutrients in many natural and industrial flows. Their dispersion is crucial to understanding the mixing processes in these flows. Here we report on the dispersion of millimetric air bubbles in a homogeneous and isotropic turbulent flow with a Taylor Reynolds number from 110 to 310. We find that the mean squared displacement (MSD) of the bubbles far exceeds that of fluid tracers in turbulence. The MSD shows two regimes. At short times, it grows ballistically (∝τ^{2}), while at larger times, it approaches the diffusive regime where the MSD∝τ. Strikingly, for the bubbles, the ballistic-to-diffusive transition occurs one decade earlier than for the fluid. We reveal that both the enhanced dispersion and the early transition to the diffusive regime can be traced back to the unsteady wake-induced motion of the bubbles. Further, the diffusion transition for bubbles is not set by the integral timescale of the turbulence (as it is for fluid tracers and microbubbles), but instead, by a timescale of eddy crossing of the rising bubbles. The present findings provide a Lagrangian perspective towards understanding mixing in turbulent bubbly flows.