Turbulent Bubbly Flow Research Articles

Two-phase flow effect on methane conversion in pyrolysis reactors embedding molten salts or metals

In this work, we numerically investigate the impact of flowrate, sparger and reactor geometry on methane conversion in lab-scale cylindrical pyrolysis reactors embedding molten salts or metals. A multiscale approach is enforced, where a diffusion-reaction model yielding the conversion vs time within a single rising bubble is combined with the average residence time of gas bubbles obtained through the two-phase turbulent bubbly flow model. We find that the relative size of the sparger and the height-to-diameter ratio of the molten medium are key parameters for controlling the average residence time of the bubbles, which always results lower than that predicted by the terminal velocity of a single bubble rising in an overall static melt. The highest relative discrepancy (order 300%) between the single-bubble estimate and the CFD-based residence time is found in the case of molten salts in low-aspect ratio reactors fed by small spargers. The physical mechanism underpinning the influence of geometric parameters on the overall conversion is addressed in detail, together with the impact of two-phase flow effects on the estimation of bubble size in laboratory scale bubble reactors.

A numerical study on the turbulence characteristics in an air–water upward bubbly pipe flow

A high-resolution numerical simulation of an air–water turbulent upward bubbly flow in a pipe is performed to investigate the turbulence characteristics and bubble interaction with the wall. We consider three bubble equivalent diameters and three total bubble volume fractions. The bulk and bubble Reynolds numbers are $Re_{bulk}= u_{bulk} D/\nu _w = 5300$ and $Re_{bub}= (\langle u_{bub}\rangle - u_{bulk}) d_{eq}/\nu _w = 533\unicode{x2013}1000$ , respectively, where $u_{bulk}$ is the water bulk velocity, $\langle u_{bub}\rangle$ is the overall bubble mean velocity, $D$ is the pipe diameter and $\nu _w$ is the water kinematic viscosity. The mean water velocity near the wall significantly increases due to bubble interaction with the wall, and the root-mean-square water velocity fluctuations are proportional to $\bar {\psi }(r)^{0.4}$ , where $\bar {\psi } (r)$ is the mean bubble volume fraction. For the cases considered, the bubble-induced turbulence suppresses the shear-induced turbulence and becomes the dominant flow characteristic at all radial locations including near the wall. Rising bubbles near the wall mostly bounce against the wall rather than slide along the wall or hang around the wall without collision. Low-speed streaks observed in the near-wall region in the absence of bubbles nearly disappear due to the bouncing bubbles. These bouncing bubbles generate counter-rotating vortices in their wake, and increase the skin friction by sweeping high-speed water towards the wall. We also suggest an algebraic Reynolds-averaged Navier–Stokes model considering the interaction between shear-induced and bubble-induced turbulence. This model provides accurate predictions for a wide range of liquid bulk Reynolds numbers.

Experimental study on modulation of homogeneous isotropic turbulence by bubbles of different sizes

The mechanism of turbulence modulation by bubbles is crucial for understanding and predicting turbulent bubbly flow. In this study, we conducted an experimental investigation of turbulence modulation by bubbles of different sizes in homogeneous isotropic turbulence using two-phase stereo-particle image velocimetry measurement techniques. Two bubble generation methods, electrolysis and porous medium, were employed to generate bubbles in micrometer and millimeter sizes, respectively. The oscillating grid system was utilized to generate homogeneous isotropic turbulence, allowing precise control of turbulent boundary conditions. The ratio of the fluctuating velocities and the comparison between turbulent kinetic energy and average kinetic energy indicated that the generated turbulence was nearly homogeneous and isotropic. With increasing turbulence intensity, micron-sized bubbles transition from suppressing turbulence to enhancing it, while millimeter-sized bubbles exhibit the opposite behavior. Turbulence modulation by millimeter-sized bubbles appears to be nearly isotropic, whereas micrometer-sized bubbles do not exhibit isotropy.

Enforcing accurate volume conservation in VOF‐based long‐term simulations of turbulent bubble‐laden flows on coarse grids

AbstractThis study proposes two different strategies to enforce accurate volume conservation in volume‐of‐fluid (VOF)‐based simulations of turbulent bubble‐laden flows on coarse grids. It is demonstrated that, without a correction, minimal volume errors on a time‐step level, caused by the under‐resolution of the interface, can accumulate to significant deviations from the intended flow conditions despite the comparably good volume conservation properties of the geometric VOF method. In particular, large volume errors are observed for challenging setups combining coarse grid resolutions and comparably high Reynolds and Eötvös numbers. The problem is reinforced for long‐term simulations in periodic domains, which are often performed to collect flow statistics of bubbly flows. The first proposed volume conservation method simply corrects the volume error of a bubble by uniformly adding or removing the respective amount of gas volume in the interface cells. The second proposed method performs an additional reconstruction and advection step of the VOF field using a non‐divergence‐free velocity field, which can be interpreted as a slight dilatation or contraction of the bubble. A comparison between the global flow statistics as well as the individual bubble dynamics for both volume conservation methods reveals that the results are quasi‐identical for a number of challenging test cases, while the gas volume is accurately conserved. The proposed methods allow to perform numerical simulations of freely deformable bubbles in turbulent flows for setups that have previously been out of reach for this numerical framework.

Wall shear stress measurement of turbulent bubbly flows using laser Doppler displacement sensor

A novel wall shear stress meter is developed to promote studies of frictional drag reduction by injecting air bubbles into a turbulent boundary layer. Such studies require a tool having a time resolution sufficiently high to capture the unsteady effect of turbulent characteristics due to various bubble passage patterns. The present study adopts the principle of the heterodyne interferometer to capture of time variation of wall shear stress in turbulent flow up to 500 Hz in sampling frequency. We demonstrate the performance of the tool by applying it to bubbly flows beneath a flat-bottom model ship running at 3 m/s in a towing water reservoir, where bubbles experience wavy passage around a few Hz in frequency. The data obtained by the proposed shear stress meter agree well with Dean's formula for single-phase turbulent channel flow. The scattering of the data across three trials is sufficiently small, at approximately 3 %. This high reproducibility is a great advantage over conventional direct measurements, which have low reproducibility and a large scatter of the data of approximately 15 %. The obtained results represent reasonable drag reductions by injecting bubbles with different void fractions. We also evaluate histogram of the wall shear stress fluctuation to characterize the effect of drag reduction by unsteady passage of bubbles.

Enhancing thermal mixing in turbulent bubbly flow by inhibiting bubble coalescence

The presence of bubbles in a turbulent flow changes the flow drastically and enhances the mixing. Adding salt to the bubbly aqueous flow changes the bubble coalescence properties as compared to regular demineralized water. Here we provide direct experimental evidence that also the turbulent thermal energy spectra are strongly changed. Experiments were performed in the Twente Mass and Heat Transfer water tunnel, in which we can measure the thermal spectra in bubbly turbulence in salty water. We find that the mean bubble diameter decreases with increasing concentration of salt (NaCl), due to the inhibition of bubble coalescence. With increasing salinity, the transition frequency from the classical −5/3 scaling of the thermal energy spectrum to the bubble induced −3 scaling shifts to higher frequencies, thus enhancing the overall thermal energy. We relate this frequency shift to the smaller size of the bubbles for the salty bubbly flow. Finally we measure the heat transport in the bubbly flow, and show how it varies with changing void fraction and salinity: Increases in both result into increases in the number of extreme events.

Bubble flow analysis using multi-phase field method

In simulations of gas-liquid two-phase flows using conventional interface capture methods, we observed that when bubbles come close to each other, they tend to merge numerically, despite experimental evidence indicating that they would repel each other. Given the significant impact of sequential numerical coalescence on flow patterns, it is necessary to regulate the merging behavior of close bubbles. To address this issue, we introduced the Multi-Phase Field (MPF) method, which mitigates bubble coalescence by applying an independent fluid fraction function to each bubble. In this study, we employed the MPF based on the N-phase model [7] to minimize numerical errors associated with surface interactions at triple junction points. Additionally, we implemented the Ordered Active Parameter Tracking (OAPT) method [9] to efficiently store several hundreds of fluid fraction functions. To validate the MPF method, we conducted analysis of turbulent bubbly pipe flows and compared the results against experimental data from Colin et al [12]. The validation results showed reasonable agreements with respect to the bubble distribution and the flow velocity profiles.

Improvement of the two-fluid momentum equation for turbulent bubbly flows

A two-fluid model is widely employed to predict gas–liquid two-phase flows. Conventional two-fluid equations, derived by assuming that all phases are interpenetrating continua, occasionally yield impractical results. For example, the bubble velocity is predicted to be higher than the water velocity for a horizontal fully developed bubbly flow. One solution for this irrational result is two-fluid momentum equations based on the motion of fluid particles. This study revisits the particle-motion-based two-fluid equations. Previously, it was validated only with respect to the difference between the bubble and liquid velocities. Recently, we observed an erroneous prediction of the void fraction distribution by the existing particle-motion-based momentum equations. This study, through rigorous analysis, discovered that this error could be resolved by neglecting the turbulent kinetic energy term in the particle-motion-based equation for the gas phase. Subsequently, the revised momentum equations were applied to the vertical and horizontal air–water bubbly flows. The conventional and revised momentum equations produced similar results for upward bubbly flows because the relative velocity between the bubble and water phases was mainly governed by buoyancy. For horizontal bubbly flows, the revised momentum equations led to a downward shift in the liquid velocity distributions, which was attributed to the modified momentum diffusion term. At a higher modification factor of turbulent dispersion, the velocity distributions exhibited an upward shift. We conclude that the optimization of physical models should be based on the revised two-fluid momentum equations.

Large eddy simulations of bubbly flows and breaking waves with smoothed particle hydrodynamics

For turbulent bubbly flows, multi-phase simulations resolving both the liquid and bubbles are prohibitively expensive in the context of different natural phenomena. One example is breaking waves, where bubbles strongly influence wave impact loads, acoustic emissions and atmospheric-ocean transfer, but detailed simulations in all but the simplest settings are infeasible. An alternative approach is to resolve only large scales, and model small-scale bubbles adopting sub-resolution closures. Here, we introduce a large eddy simulation smoothed particle hydrodynamics (SPH) scheme for simulations of bubbly flows. The continuous liquid phase is resolved with a semi-implicit isothermally compressible SPH framework. This is coupled with a discrete Lagrangian bubble model. Bubbles and liquid interact via exchanges of volume and momentum, through turbulent closures, bubble breakup and entrainment, and free-surface interaction models. By representing bubbles as individual particles, they can be tracked over their lifetimes, allowing closure models for sub-resolution fluctuations, bubble deformation, breakup and free-surface interaction in integral form, accounting for the finite time scales over which these events occur. We investigate two flows: bubble plumes and breaking waves, and find close quantitative agreement with published experimental and numerical data. In particular, for plunging breaking waves, our framework accurately predicts the Hinze scale, bubble size distribution, and growth rate of the entrained bubble population. This is the first coupling of an SPH framework with a discrete bubble model, with potential for cost-effective simulations of wave–structure interactions and more accurate predictions of wave impact loads.

Development of machine learning framework for interface force closures based on bubble tracking data

Interfacial force closures in the two-fluid model play a critical role for the predictive capabilities of void fraction distribution. However, the practices of interfacial force modeling have long been challenged by the inherent physical complexity of the two-phase flows. The rapidly expanding computational capabilities in the recent years have made high-fidelity data from the interface-captured direct numerical simulation become more available, and hence potential for data-driven interfacial force modeling has prevailed.In this work, we established a data-driven modeling framework integrated to the HZDR multiphase Eulerian-Eulerian framework for computational fluid dynamics simulations. The data-driven framework is verified in a benchmark problem, where a feedforward neural network managed to capture the non-linear mapping between bubble Reynolds number and drag coefficient and reproduce the void distribution resulting from the baseline model in the test case.The second focus is on utilizing the bubble tracking data set to form a closure for the bubble drag in the turbulent bubbly flow, in which the drag coefficient is set to be correlated with the bubble Reynolds number and the Eötvös number. Pseudo-steady state filtering in the Frenet Frame was carried out to obtain the drag coefficient from the turbulent bubbly flow data. The performance of the data-driven drag model is also examined through a case study, where improvement of model’s prediction near-wall is regarded necessary. Discussion and further plans of investigation are provided.

Experimental Study of Turbulent Bubbly Flow in 180-Degree Elbow by PIV-PS Technique

The curvature effect and bubbles are the key factors that affect the gas-liquid two-phase flow and turbulent characteristics in the 180-degree elbow. Limited by the difficulty of experimental measurement and numerical investigation, little is known about the two-phase flow evolution and turbulent modulation in 180-degree elbow. In this paper, a gas-liquid two-phase measurement technique, simultaneous Particle Image Velocimetry and Pulsed Shadowgraphy (PIV-PS) has been developed by combining two cameras through a spectroscope and optical filters and was applied to explore the two-phase characteristics in 180-degree elbow. In addition, an image post-processing method, based on bubble area detection and remaining particles estimation, was proposed. The characteristics of velocity and turbulent fields in the 180-degree elbow are experimentally studied in different conditions, and the evolution of the flow field in the elbow was also explored in detail. The results show that the horizontal velocity on the centerline of the elbow increases linearly with the liquid flow rates. However, with the introduction of bubbles, the linear feature is eliminated. The turbulent fields show that the introduction of bubbles suppresses turbulence at the low void fraction condition, and enhances at the high void fraction in bubble accumulation areas.

Euler-Euler numerical simulations of upward turbulent bubbly flows in vertical pipes with low-Reynolds-number model

In this work, numerical simulations of upward turbulent bubbly flows in vertical pipes are conducted in the Euler-Euler framework with a low-Reynolds-number (LRN) model for liquid. It is found that the existing correlation for the drag coefficient of a single bubble in a shear flow, which has been successfully used along with the high-Reynolds-number (HRN) models, cannot be used with the LRN model. The reason is that drag forces of bubbles calculated using such correlation are enormous in near-wall cells (order of [Formula: see text]), which causes a divergence of numerical simulations with LRN. Therefore, a modified correlation for the drag coefficient of a single bubble in shear flow, that can be used successfully with the LRN model, has been proposed. The results of numerical simulations, performed with a new correlation for the drag coefficient, are analysed and compared to selected experimental measurements for different pipe diameters and different flow conditions of gas and liquid. It is shown that the largest effect of the application of the new correlation for the drag coefficient of a single bubble in shear flow in numerical simulations can be achieved on the reduction of the relative velocity between gas and liquid. The degree of this reduction depends on the pipe diameter and liquid volumetric flux.

Combined Effects of the Turbulence and Interfacial Momentum Transfer on Two-Phase Turbulent Bubbly Flows

Abstract The paper studies one-way and two-way coupling interactions between the liquid turbulence and bubbles' presence in bubbly jets. One-way coupling focuses on jet with low void fraction in which the bubbles have no significant effect on the hydrodynamic liquid fields in comparison to the single-phase jet. It sets out to model the interfacial momentum transfer identifying the turbulent contribution and its effect on the bubbles' dynamics and phase distribution. Two-way coupling considers jets with high void fractions where the liquid turbulence is altered by the bubbles which in turn influence the interfacial momentum transfers. This paper aims to improve the two-fluid model closures by implementing in computational fluid dynamics code a three-equation turbulence model and new interfacial momentum transfer closures. A benchmark of turbulence models combined with different interfacial exchange modeling is achieved to highlight the strong couplings between the interfacial forces, the phase distribution and the hydrodynamic fields of both phases.

水平二次元拡大チャネル内の気液二相流に現れるボイド波の周波数特性

Void wave, which is a spatio-temporal fluctuation of the void fraction of air bubbles in turbulent flow of water, appears beneath the bottom of a ship with an air-lubrication system when the frictional drag is reduced. Controlling the void wave has a potential to improve the drag reduction rate by air-lubrication. However, it is hard to generate the void wave in a normal channel facility generally used for laboratory-scale experiments on air lubrication. As the reason for this, it is expected that there is the boundary layer without spatially development in such channel flow. We, hence, designed an expanded channel facility where the boundary layer thickness developed and realized the generation of the void wave. To estimate the spatial development of the generated void wave in our channel, we observed the void wave at several positions in the streamwise direction by a high-speed camera and then, analyzed the frequency spectrum of the void fraction by Walsh transformation. Two dominant frequencies of the void wave were revealed at the midstreamposition regardless of the superficial velocity of gas phase, and the frequencies decreased in the downstream-position.

On turbulence and interfacial momentum transfer in dispersed gas-liquid flows: Contribution of bubbly flow experiments under microgravity conditions

The major focus of the present work is to develop an adequate closure model for the turbulent contribution of the interfacial momentum transfer term in turbulent bubbly flow. For this purpose, numerical simulations have been conducted on bubbly pipe flows under microgravity conditions. With no buoyancy effect, the average interfacial forces are negligible due to the small interphase relative motion. In these conditions, the distribution and the dynamics of bubbles are mainly controlled by the turbulence effects. Based on a phenomenological approach, a new closure for the turbulent interfacial momentum transfer is developed within Eulerian two-fluid modelling based on the averaging of the added mass force. The turbulent terms thus obtained comprises a non-linear term and a convective acceleration term associated with the drift velocity. The two-fluid model with the proposed interfacial momentum transfer closure and an original three-equation turbulence model for bubbly flows has been implemented in a 3D CFD code and applied to pipe bubbly flow under microgravity conditions. When compared to conventional two-fluid closures, the turbulent contribution of the added mass force proved to be a relevant closure that provides a substantial improvement in predicting the void fraction distribution and the bubbles’ dynamics.

Polymer drag reduction in surfactant-contaminated turbulent bubbly channel flows

Polymer additives are commonly utilized to manipulate bubbly flows in various applications. Here, we investigate the effects of clean and contaminated bubbles driven upwards (upflow) in Newtonian and viscoelastic turbulent channel flows. Interface-resolved direct numerical simulations are performed to examine sole and combined effects of soluble surfactant and viscoelasticity using an efficient 3D finite-difference/front-tracking method. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant concentrations. The latter coupling is accomplished by a non-linear equation of state that relates the surface tension to the surfactant concentration. For Newtonian turbulent bubbly flows, the effects of Triton X-100 and 1-Pentanol surfactant are examined. It is observed that the sorption kinetics highly affect the dynamics of bubbly flow. A minute amount of Triton X-100 is found to be sufficient to prevent the formation of bubble clusters restoring the single-phase behavior while even two orders of magnitude more 1-Pentanol surfactant is not adequate to prevent the formation of layers. For viscoelastic turbulent flows, it is found that the viscoelasticity promotes formation of the bubble-wall layers and thus the polymer drag reduction is completely lost for the surfactant-free bubbly flows, while the addition of small amount of surfactant (Triton X-100) in this system restores the polymer drag reduction resulting in $25\%$ drag reduction for the $Wi=4$ case.

Nonlinear scattering of crossed ultrasonic beams in the presence of a turbulent bubbly jet flow in water

Experiments involve the nonlinear scattering of mutually perpendicular crossed ultrasonic beams of primary CW frequency components: f1 = 2.240 MHz, f2 = 2.293 MHz; interacting nonlinearly with turbulent bubbly shear flow generated by a circular water jet (nozzle exit diameter D = 1.6 mm and volume flow rate 32 cc/s). The jet axis is perpendicular to the crossed beam axes. The nozzle exit is downward (5 mm above the surface). The water pump’s suction port was at the bottom center of the 10 cm cubic acrylic water tank (wall thickness 4.8 mm). Identical 1.27 cm diameter quartz transducers (T1 and T2) were epoxied at the centers of adjacent vertical tank sidewalls generate the primary beams (in the i or j directions). Identical 4.5MHz receiving transducers (6.35 mm diam PZT-4) measure nonlinear scattering in the forward or backscattered directions. Receiver Rf located in the plane formed by the primary acoustic beam axes) detects in the i cos 45 + j sin 45 direction. Receiver Rb was located in the opposite direction. In the absence of turbulence virtually no radiated sum frequency component exists. Doppler shift, frequency broadening, skewness and kurtosis from the received sum frequency power spectrum were measured.

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.

Scale-wise analysis of upward turbulent bubbly flows: An experimental study

In this work, we investigate the upward turbulent bubbly pipe flow according to relevant length scales, to understand the bubble-induced turbulence modulation of the liquid-phase flow. Using two-phase particle image velocimetry, the bubbly flow fields in a vertical pipe (diameter of 40 mm) were obtained for Reynolds numbers (ReD) of 5300 and 44 000, while increasing the volume void fraction (bubble size of 2.5–4.5 mm) to 1.8% and 1.5%, respectively. The turbulent bubbly flow is visualized and further quantified from the decomposed flow fields (according to the length scales) using the discrete wavelet transform. At ReD = 5300, flow structures of the energy-containing scales (larger than the Taylor microscale) are energized by the disturbance from bubble surface deformation and near wake (whose scales are located close to the integral scale), resulting in the turbulence enhancement across the entire pipe. The interaction between wake vortices, sized between the integral scale and Taylor microscale, apart from the near wake also contributes to the turbulence enhancement. At higher ReD, despite the similar bubble size and void fraction, the scales of flow agitation owing to the bubble surface and the shed wake vortices become smaller, having a negligible effect on turbulence modification. However, the scale of the near wake is still large enough to enhance the turbulence at the pipe center (although it is significantly reduced toward the wall). With the highest void fraction among tested, on the other hand, the mean liquid velocity gradient becomes milder near the pipe wall, which causes a turbulence suppression locally near the wall.

Radial pressure forces in Euler-Euler simulations of turbulent bubbly pipe flows

Two-equation turbulence models based on the Boussinesq eddy viscosity hypothesis that have been used in the vast majority of previous simulation studies on bubbly pipe flows contain a term which renders the radial pressure distribution non-constant. In single phase simulations this effect is invariably absorbed in the definition of a modified pressure, from which the real pressure may be recovered if necessary. For bubbly multiphase flows however, this is not possible since the bubbles experience a force which depends, of course, on the real pressure rather than the modified one. As it turns out, most software codes by default rely on the approximation of neglecting the difference between modified and real pressure for bubbly flows. The purpose of the present study is to assess the influence of this approximation on the final simulations results. Fortunately it turns out that at least for the conditions considered in this study, the error is small.