Results from direct numerical simulations of laminar bubbly flow in a vertical channel are compar... more Results from direct numerical simulations of laminar bubbly flow in a vertical channel are compared with predictions of a two-fluid model for steady-state flow. The simulations are done assuming a twodimensional system and the model coefficients are adjusted slightly to match the data for upflow. The model is then tested by comparisons with different values of flow rate and gravity, as well as downflow. In all cases the results agree reasonably well, even though the simulated void fraction is considerably higher than what is assumed in the derivation of the model. The results do, however, suggest a need to understand the lift and the wall repulsion force on bubbles better, particularly in dense flows.
Direct numerical simulations of bubbly flows are reviewed and recent progress is discussed. Simul... more Direct numerical simulations of bubbly flows are reviewed and recent progress is discussed. Simulations of homogeneous bubble distribution in fully periodic domains at relatively low Reynolds numbers have already yielded 9 considerable insight into the dynamics of such flows. Many aspects of the evolution converge rapidly with the size of the systems and results for the rise velocity, the velocity fluctuations, as well as the average relative orientation 11 have been obtained. The challenge now is to examine bubbles at higher Reynolds numbers, bubbles in channels and confined geometry, and bubble interactions with turbulent flows. We briefly review numerical simulations used 13 for direct numerical methods of multiphase flows, with a particular emphasis on methods that use the so-called "one-field" formulation of the governing equations, and then discuss studies of bubble in periodic domains, along 15 with recent work on wobbly bubbles, bubbles in laminar and turbulent channel flows, and bubble formation in boiling.
Direct numerical simulations of nearly spherical bubbles rising in a laminar flow in vertical cha... more Direct numerical simulations of nearly spherical bubbles rising in a laminar flow in vertical channels have shown that for upflow the bubbles are pushed to the walls, until the fluid mixture in the center of the channel is in hydrostatic equilibrium. The excess bubbles hug the channel wall, forming a wall-layer, one bubble diameter thick. The upward velocity of the core flow depends entirely on the velocity increase across the wall layer. Here we examine how the bubbles in the wall layer rise and how their rise velocity, as well as the velocity in the center of the channel, depends on the governing parameters of the flow. The study is done using direct numerical simulations where the flow around the bubbles is fully resolved and the uniform flow outside the wall layer is generated by a properly adjusted body force. The behavior of the flow is studied for a range of parameters using a regular periodic array and the results then compared with results from simulations of freely evolving and interacting bubbles for one case, as well as with results of simulations of the full channel. The average properties of the flow in the wall layer are examined and compared with a simple two-fluid model.
Direct numerical simulations are used to examine laminar bubbly flows in vertical channels. For e... more Direct numerical simulations are used to examine laminar bubbly flows in vertical channels. For equal size nearly spherical bubbles the results show that at steady state the number density of bubbles in the center of the channel is always such that the fluid mixture there is in hydrostatic equilibrium. For upflow, excess bubbles are pushed to the walls, forming a bubble rich wall-layer, one bubble diameter thick. For downflow, bubbles are drawn into the channel center, leading to a wall-layer devoid of bubbles, of a thickness determined by how much the void fraction in the center of the channel must be increased to reach hydrostatic equilibrium. The void fraction profile can be predicted analytically using a very simple model and the model also gives the velocity profile for the downflow case. For the upflow, however, the velocity increase across the wall-layer must be obtained from the simulations. The slip velocity of the bubbles in the channel core and the velocity fluctuations are predicted reasonably well by results for homogeneous flows.
Recent DNS studies of buoyant bubbly flows in vertical channels are discussed. Simulations of nea... more Recent DNS studies of buoyant bubbly flows in vertical channels are discussed. Simulations of nearly spherical bubbly flows in vertical channels show that the bubbles move towards the wall for upflow and away from the wall for downflow in such a way that the core is in hydrostatic equilibrium. For downflow the wall layer is free of bubbles but for upflow there is an excess of bubbles in the wall layer. The liquid velocity in the core is uniform. For laminar downflow the velocity in the wall layer can be computed analytically and for turbulent flow the velocity is given (almost) by the law of the wall. For upflow the velocity is strongly influenced by the presence of the bubbles. Results from several simulations, fully resolving the flow around each bubble, are used to discuss the effect of void fraction and bubble size for turbulent downflow.
The status of direct numerical simulations of bubbly flows is reviewd and a few recent results ar... more The status of direct numerical simulations of bubbly flows is reviewd and a few recent results are presented. The development of numerical methods based on the one-field formulation has made it possible to follow the evolution of a large number of bubbles for a sufficiently long time so that converged statistics for the averaged properties of the flow can be obtained. In addition to extensive studies of homogeneous bubbly flows, recent investigations have helped give insight into drag reduction due to the injection of bubbles into turbulent flows and two-fluid modeling of laminar multiphase flows in channels.
Recent stuies of bubbly flows, using direct numerical simulations, are discussed. The goal of thi... more Recent stuies of bubbly flows, using direct numerical simulations, are discussed. The goal of this study is to examine the collective behavior of many bubbles as the rise Reynolds number is increased and and a single bubble rises unsteadily, as well as to examine the motion of bubbles in channels. A front-tracking/finite volume method is used to fully resolve all flow scales, including the bubbles and the flow around them. Two cases are simulated, for one the bubbles remain nearly spherical and for the other case the bubbles are deformable and wobble. The wobbly bubbles remains relatively uniformly distributed and are not susceptible to the streaming instability found by Bunner and Tryggvason (2003) for deformable bubbles at lower rise Reynolds numbers. The more spherical bubbles, on the other hand, form transients ``rafts'' somewhat similar to those seen in potential flow simulation of many bubbles. For channel flow we compare results from direct numerical simulations of bubbly flow with prediction of the steady-state two-fluid model of Antal, Lahey, and Flaherty (1991). The simulations are done assuming a two-dimensional system and the model coefficients are adjusted slightly to match the data for upflow. The results generally agree reasonably well, even though the simulated void fraction is considerably higher than the one assumed in the derivation of the model. Research supported by DOE.
The transient buoyancy driven motion of two-dimensional bubbles across a domain bounded by two ho... more The transient buoyancy driven motion of two-dimensional bubbles across a domain bounded by two horizontal walls is studied by direct numerical simulations. The bubbles are initially released next to the lower wall and as they rise, they disperse. Eventually all the bubbles collect at the top wall. The goal of the study is to examine how a simple one-dimensional model for the averaged void fraction captures the unsteady bubble motion. By using void fraction dependent velocities, where the exact dependency is obtained from simulations of homogeneous bubbly flows, the overall dispersion of the bubbles is predicted. Significant differences remain, however. We suggest that bubble dispersion by the bubble induced liquid velocity must be included, and by using a simple model for the bubble dispersion we show improved agreement.
Considerable effort has been devoted to the study of the turbulent dispersion of small bubbles an... more Considerable effort has been devoted to the study of the turbulent dispersion of small bubbles and particles by turbulent flows. While the bubbles and particles may modify the flow somewhat, the primary effect is a one-way coupling from the fluid to the particles. When the response time of the particles is comparable to the time scales of the fluid motion the effect of the bubbles on the fluid cannot be ignored. Here we examine, using direct numerical simulations, the dispersion of buoyant bubbles rising in quiescent flow, or simple horizontal shear, where every continuum length and time scale are fully resolved. The fluid motion disperses the bubbles, but the bubbles are responsible for the fluid motion, as they rise. At the moment most of our results are for two-dimensional flows and we examine the dispersion by following the motion of several tens of bubbles as they rise across a horizontal channel. The results show that the dispersion is reasonably insensitive to the initial distribution of the bubbles and the length of the channel. Weak shear has essentially no effect on the dispersion.
Results from direct numerical simulations of laminar bubbly flow in a vertical channel are compar... more Results from direct numerical simulations of laminar bubbly flow in a vertical channel are compared with predictions of a two-fluid model for steady-state flow. The simulations are done assuming a twodimensional system and the model coefficients are adjusted slightly to match the data for upflow. The model is then tested by comparisons with different values of flow rate and gravity, as well as downflow. In all cases the results agree reasonably well, even though the simulated void fraction is considerably higher than what is assumed in the derivation of the model. The results do, however, suggest a need to understand the lift and the wall repulsion force on bubbles better, particularly in dense flows.
Direct numerical simulations of bubbly flows are reviewed and recent progress is discussed. Simul... more Direct numerical simulations of bubbly flows are reviewed and recent progress is discussed. Simulations of homogeneous bubble distribution in fully periodic domains at relatively low Reynolds numbers have already yielded 9 considerable insight into the dynamics of such flows. Many aspects of the evolution converge rapidly with the size of the systems and results for the rise velocity, the velocity fluctuations, as well as the average relative orientation 11 have been obtained. The challenge now is to examine bubbles at higher Reynolds numbers, bubbles in channels and confined geometry, and bubble interactions with turbulent flows. We briefly review numerical simulations used 13 for direct numerical methods of multiphase flows, with a particular emphasis on methods that use the so-called "one-field" formulation of the governing equations, and then discuss studies of bubble in periodic domains, along 15 with recent work on wobbly bubbles, bubbles in laminar and turbulent channel flows, and bubble formation in boiling.
Direct numerical simulations of nearly spherical bubbles rising in a laminar flow in vertical cha... more Direct numerical simulations of nearly spherical bubbles rising in a laminar flow in vertical channels have shown that for upflow the bubbles are pushed to the walls, until the fluid mixture in the center of the channel is in hydrostatic equilibrium. The excess bubbles hug the channel wall, forming a wall-layer, one bubble diameter thick. The upward velocity of the core flow depends entirely on the velocity increase across the wall layer. Here we examine how the bubbles in the wall layer rise and how their rise velocity, as well as the velocity in the center of the channel, depends on the governing parameters of the flow. The study is done using direct numerical simulations where the flow around the bubbles is fully resolved and the uniform flow outside the wall layer is generated by a properly adjusted body force. The behavior of the flow is studied for a range of parameters using a regular periodic array and the results then compared with results from simulations of freely evolving and interacting bubbles for one case, as well as with results of simulations of the full channel. The average properties of the flow in the wall layer are examined and compared with a simple two-fluid model.
Direct numerical simulations are used to examine laminar bubbly flows in vertical channels. For e... more Direct numerical simulations are used to examine laminar bubbly flows in vertical channels. For equal size nearly spherical bubbles the results show that at steady state the number density of bubbles in the center of the channel is always such that the fluid mixture there is in hydrostatic equilibrium. For upflow, excess bubbles are pushed to the walls, forming a bubble rich wall-layer, one bubble diameter thick. For downflow, bubbles are drawn into the channel center, leading to a wall-layer devoid of bubbles, of a thickness determined by how much the void fraction in the center of the channel must be increased to reach hydrostatic equilibrium. The void fraction profile can be predicted analytically using a very simple model and the model also gives the velocity profile for the downflow case. For the upflow, however, the velocity increase across the wall-layer must be obtained from the simulations. The slip velocity of the bubbles in the channel core and the velocity fluctuations are predicted reasonably well by results for homogeneous flows.
Recent DNS studies of buoyant bubbly flows in vertical channels are discussed. Simulations of nea... more Recent DNS studies of buoyant bubbly flows in vertical channels are discussed. Simulations of nearly spherical bubbly flows in vertical channels show that the bubbles move towards the wall for upflow and away from the wall for downflow in such a way that the core is in hydrostatic equilibrium. For downflow the wall layer is free of bubbles but for upflow there is an excess of bubbles in the wall layer. The liquid velocity in the core is uniform. For laminar downflow the velocity in the wall layer can be computed analytically and for turbulent flow the velocity is given (almost) by the law of the wall. For upflow the velocity is strongly influenced by the presence of the bubbles. Results from several simulations, fully resolving the flow around each bubble, are used to discuss the effect of void fraction and bubble size for turbulent downflow.
The status of direct numerical simulations of bubbly flows is reviewd and a few recent results ar... more The status of direct numerical simulations of bubbly flows is reviewd and a few recent results are presented. The development of numerical methods based on the one-field formulation has made it possible to follow the evolution of a large number of bubbles for a sufficiently long time so that converged statistics for the averaged properties of the flow can be obtained. In addition to extensive studies of homogeneous bubbly flows, recent investigations have helped give insight into drag reduction due to the injection of bubbles into turbulent flows and two-fluid modeling of laminar multiphase flows in channels.
Recent stuies of bubbly flows, using direct numerical simulations, are discussed. The goal of thi... more Recent stuies of bubbly flows, using direct numerical simulations, are discussed. The goal of this study is to examine the collective behavior of many bubbles as the rise Reynolds number is increased and and a single bubble rises unsteadily, as well as to examine the motion of bubbles in channels. A front-tracking/finite volume method is used to fully resolve all flow scales, including the bubbles and the flow around them. Two cases are simulated, for one the bubbles remain nearly spherical and for the other case the bubbles are deformable and wobble. The wobbly bubbles remains relatively uniformly distributed and are not susceptible to the streaming instability found by Bunner and Tryggvason (2003) for deformable bubbles at lower rise Reynolds numbers. The more spherical bubbles, on the other hand, form transients ``rafts'' somewhat similar to those seen in potential flow simulation of many bubbles. For channel flow we compare results from direct numerical simulations of bubbly flow with prediction of the steady-state two-fluid model of Antal, Lahey, and Flaherty (1991). The simulations are done assuming a two-dimensional system and the model coefficients are adjusted slightly to match the data for upflow. The results generally agree reasonably well, even though the simulated void fraction is considerably higher than the one assumed in the derivation of the model. Research supported by DOE.
The transient buoyancy driven motion of two-dimensional bubbles across a domain bounded by two ho... more The transient buoyancy driven motion of two-dimensional bubbles across a domain bounded by two horizontal walls is studied by direct numerical simulations. The bubbles are initially released next to the lower wall and as they rise, they disperse. Eventually all the bubbles collect at the top wall. The goal of the study is to examine how a simple one-dimensional model for the averaged void fraction captures the unsteady bubble motion. By using void fraction dependent velocities, where the exact dependency is obtained from simulations of homogeneous bubbly flows, the overall dispersion of the bubbles is predicted. Significant differences remain, however. We suggest that bubble dispersion by the bubble induced liquid velocity must be included, and by using a simple model for the bubble dispersion we show improved agreement.
Considerable effort has been devoted to the study of the turbulent dispersion of small bubbles an... more Considerable effort has been devoted to the study of the turbulent dispersion of small bubbles and particles by turbulent flows. While the bubbles and particles may modify the flow somewhat, the primary effect is a one-way coupling from the fluid to the particles. When the response time of the particles is comparable to the time scales of the fluid motion the effect of the bubbles on the fluid cannot be ignored. Here we examine, using direct numerical simulations, the dispersion of buoyant bubbles rising in quiescent flow, or simple horizontal shear, where every continuum length and time scale are fully resolved. The fluid motion disperses the bubbles, but the bubbles are responsible for the fluid motion, as they rise. At the moment most of our results are for two-dimensional flows and we examine the dispersion by following the motion of several tens of bubbles as they rise across a horizontal channel. The results show that the dispersion is reasonably insensitive to the initial distribution of the bubbles and the length of the channel. Weak shear has essentially no effect on the dispersion.
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