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Vinay Kumaran - One of the best experts on this subject based on the ideXlab platform.
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particle dynamics in the channel flow of a turbulent particle gas suspension at high Stokes Number part 1 dns and fluctuating force model
Journal of Fluid Mechanics, 2011Co-Authors: Partha S. Goswami, Vinay KumaranAbstract:The fluctuating force model is developed and applied to the turbulent flow of a gas-particle suspension in a channel in the limit of high Stokes Number, where the particle relaxation time is large compared to the fluid correlation time, and low particle Reynolds Number where the Stokes drag law can be used to describe the interaction between the particles and fluid. In contrast to the Couette flow, the fluid velocity variances in the different directions in the channel are highly non-homogeneous, and they exhibit significant variation across the channel. First, we analyse the fluctuating particle velocity and acceleration distributions at different locations across the channel. The distributions are found to be non-Gaussian near the centre of the channel, and they exhibit significant skewness and flatness. However, acceleration distributions are closer to Gaussian at locations away from the channel centre, especially in regions where the variances of the fluid velocity fluctuations are at a maximum. The time correlations for the fluid velocity fluctuations and particle acceleration fluctuations are evaluated, and it is found that the time correlation of the particle acceleration fluctuations is close to the time correlations of the fluid velocity in a `moving Eulerian' reference, moving with the mean fluid velocity. The variances of the fluctuating force distributions in the Langevin simulations are determined from the time correlations of the fluid velocity fluctuations and the results are compared with direct numerical simulations. Quantitative agreement between the two simulations are obtained provided the particle viscous relaxation time is at least five times larger than the fluid integral time.
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Particle dynamics in the channel flow of a turbulent particle–gas suspension at high Stokes Number. Part 1. DNS and fluctuating force model
Journal of Fluid Mechanics, 2011Co-Authors: Partha S. Goswami, Vinay KumaranAbstract:The fluctuating force model is developed and applied to the turbulent flow of a gas-particle suspension in a channel in the limit of high Stokes Number, where the particle relaxation time is large compared to the fluid correlation time, and low particle Reynolds Number where the Stokes drag law can be used to describe the interaction between the particles and fluid. In contrast to the Couette flow, the fluid velocity variances in the different directions in the channel are highly non-homogeneous, and they exhibit significant variation across the channel. First, we analyse the fluctuating particle velocity and acceleration distributions at different locations across the channel. The distributions are found to be non-Gaussian near the centre of the channel, and they exhibit significant skewness and flatness. However, acceleration distributions are closer to Gaussian at locations away from the channel centre, especially in regions where the variances of the fluid velocity fluctuations are at a maximum. The time correlations for the fluid velocity fluctuations and particle acceleration fluctuations are evaluated, and it is found that the time correlation of the particle acceleration fluctuations is close to the time correlations of the fluid velocity in a `moving Eulerian' reference, moving with the mean fluid velocity. The variances of the fluctuating force distributions in the Langevin simulations are determined from the time correlations of the fluid velocity fluctuations and the results are compared with direct numerical simulations. Quantitative agreement between the two simulations are obtained provided the particle viscous relaxation time is at least five times larger than the fluid integral time.
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Particle dynamics in a turbulent particle–gas suspension at high Stokes Number. Part 2. The fluctuating-force model
Journal of Fluid Mechanics, 2010Co-Authors: Partha S. Goswami, Vinay KumaranAbstract:A fluctuating-force model is developed for representing the effect of the turbulent fluid velocity fluctuations on the particle phase in a turbulent gas–solid suspension in the limit of high Stokes Number, where the particle relaxation time is large compared with the correlation time for the fluid velocity fluctuations. In the model, a fluctuating force is incorporated in the equation of motion for the particles, and the force distribution is assumed to be an anisotropic Gaussian white noise. It is shown that this is equivalent to incorporating a diffusion term in the Boltzmann equation for the particle velocity distribution functions. The variance of the force distribution, or equivalently the diffusion coefficient in the Boltzmann equation, is related to the time correlation functions for the fluid velocity fluctuations. The fluctuating-force model is applied to the specific case of a Couette flow of a turbulent particle–gas suspension, for which both the fluid and particle velocity distributions were evaluated using direct numerical simulations by Goswami & Kumaran (2010). It is found that the fluctuating-force simulation is able to quantitatively predict the concentration, mean velocity profiles and the mean square velocities, both at relatively low volume fractions, where the viscous relaxation time is small compared with the time between collisions, and at higher volume fractions, where the time between collisions is small compared with the viscous relaxation time. The simulations are also able to predict the velocity distributions in the centre of the Couette, even in cases in which the velocity distribution is very different from a Gaussian distribution.
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Particle dynamics in a turbulent particle–gas suspension at high Stokes Number. Part 1. Velocity and acceleration distributions
Journal of Fluid Mechanics, 2010Co-Authors: Partha S. Goswami, Vinay KumaranAbstract:The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-Number and high Stokes Number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.
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particle dynamics in a turbulent particle gas suspension at high Stokes Number part 2 the fluctuating force model
Journal of Fluid Mechanics, 2010Co-Authors: Partha S. Goswami, Vinay KumaranAbstract:A fluctuating-force model is developed for representing the effect of the turbulent fluid velocity fluctuations on the particle phase in a turbulent gas–solid suspension in the limit of high Stokes Number, where the particle relaxation time is large compared with the correlation time for the fluid velocity fluctuations. In the model, a fluctuating force is incorporated in the equation of motion for the particles, and the force distribution is assumed to be an anisotropic Gaussian white noise. It is shown that this is equivalent to incorporating a diffusion term in the Boltzmann equation for the particle velocity distribution functions. The variance of the force distribution, or equivalently the diffusion coefficient in the Boltzmann equation, is related to the time correlation functions for the fluid velocity fluctuations. The fluctuating-force model is applied to the specific case of a Couette flow of a turbulent particle–gas suspension, for which both the fluid and particle velocity distributions were evaluated using direct numerical simulations by Goswami & Kumaran (2010). It is found that the fluctuating-force simulation is able to quantitatively predict the concentration, mean velocity profiles and the mean square velocities, both at relatively low volume fractions, where the viscous relaxation time is small compared with the time between collisions, and at higher volume fractions, where the time between collisions is small compared with the viscous relaxation time. The simulations are also able to predict the velocity distributions in the centre of the Couette, even in cases in which the velocity distribution is very different from a Gaussian distribution.
Partha S. Goswami - One of the best experts on this subject based on the ideXlab platform.
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particle dynamics in the channel flow of a turbulent particle gas suspension at high Stokes Number part 1 dns and fluctuating force model
Journal of Fluid Mechanics, 2011Co-Authors: Partha S. Goswami, Vinay KumaranAbstract:The fluctuating force model is developed and applied to the turbulent flow of a gas-particle suspension in a channel in the limit of high Stokes Number, where the particle relaxation time is large compared to the fluid correlation time, and low particle Reynolds Number where the Stokes drag law can be used to describe the interaction between the particles and fluid. In contrast to the Couette flow, the fluid velocity variances in the different directions in the channel are highly non-homogeneous, and they exhibit significant variation across the channel. First, we analyse the fluctuating particle velocity and acceleration distributions at different locations across the channel. The distributions are found to be non-Gaussian near the centre of the channel, and they exhibit significant skewness and flatness. However, acceleration distributions are closer to Gaussian at locations away from the channel centre, especially in regions where the variances of the fluid velocity fluctuations are at a maximum. The time correlations for the fluid velocity fluctuations and particle acceleration fluctuations are evaluated, and it is found that the time correlation of the particle acceleration fluctuations is close to the time correlations of the fluid velocity in a `moving Eulerian' reference, moving with the mean fluid velocity. The variances of the fluctuating force distributions in the Langevin simulations are determined from the time correlations of the fluid velocity fluctuations and the results are compared with direct numerical simulations. Quantitative agreement between the two simulations are obtained provided the particle viscous relaxation time is at least five times larger than the fluid integral time.
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Particle dynamics in the channel flow of a turbulent particle–gas suspension at high Stokes Number. Part 1. DNS and fluctuating force model
Journal of Fluid Mechanics, 2011Co-Authors: Partha S. Goswami, Vinay KumaranAbstract:The fluctuating force model is developed and applied to the turbulent flow of a gas-particle suspension in a channel in the limit of high Stokes Number, where the particle relaxation time is large compared to the fluid correlation time, and low particle Reynolds Number where the Stokes drag law can be used to describe the interaction between the particles and fluid. In contrast to the Couette flow, the fluid velocity variances in the different directions in the channel are highly non-homogeneous, and they exhibit significant variation across the channel. First, we analyse the fluctuating particle velocity and acceleration distributions at different locations across the channel. The distributions are found to be non-Gaussian near the centre of the channel, and they exhibit significant skewness and flatness. However, acceleration distributions are closer to Gaussian at locations away from the channel centre, especially in regions where the variances of the fluid velocity fluctuations are at a maximum. The time correlations for the fluid velocity fluctuations and particle acceleration fluctuations are evaluated, and it is found that the time correlation of the particle acceleration fluctuations is close to the time correlations of the fluid velocity in a `moving Eulerian' reference, moving with the mean fluid velocity. The variances of the fluctuating force distributions in the Langevin simulations are determined from the time correlations of the fluid velocity fluctuations and the results are compared with direct numerical simulations. Quantitative agreement between the two simulations are obtained provided the particle viscous relaxation time is at least five times larger than the fluid integral time.
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Particle dynamics in a turbulent particle–gas suspension at high Stokes Number. Part 2. The fluctuating-force model
Journal of Fluid Mechanics, 2010Co-Authors: Partha S. Goswami, Vinay KumaranAbstract:A fluctuating-force model is developed for representing the effect of the turbulent fluid velocity fluctuations on the particle phase in a turbulent gas–solid suspension in the limit of high Stokes Number, where the particle relaxation time is large compared with the correlation time for the fluid velocity fluctuations. In the model, a fluctuating force is incorporated in the equation of motion for the particles, and the force distribution is assumed to be an anisotropic Gaussian white noise. It is shown that this is equivalent to incorporating a diffusion term in the Boltzmann equation for the particle velocity distribution functions. The variance of the force distribution, or equivalently the diffusion coefficient in the Boltzmann equation, is related to the time correlation functions for the fluid velocity fluctuations. The fluctuating-force model is applied to the specific case of a Couette flow of a turbulent particle–gas suspension, for which both the fluid and particle velocity distributions were evaluated using direct numerical simulations by Goswami & Kumaran (2010). It is found that the fluctuating-force simulation is able to quantitatively predict the concentration, mean velocity profiles and the mean square velocities, both at relatively low volume fractions, where the viscous relaxation time is small compared with the time between collisions, and at higher volume fractions, where the time between collisions is small compared with the viscous relaxation time. The simulations are also able to predict the velocity distributions in the centre of the Couette, even in cases in which the velocity distribution is very different from a Gaussian distribution.
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Particle dynamics in a turbulent particle–gas suspension at high Stokes Number. Part 1. Velocity and acceleration distributions
Journal of Fluid Mechanics, 2010Co-Authors: Partha S. Goswami, Vinay KumaranAbstract:The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-Number and high Stokes Number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.
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particle dynamics in a turbulent particle gas suspension at high Stokes Number part 2 the fluctuating force model
Journal of Fluid Mechanics, 2010Co-Authors: Partha S. Goswami, Vinay KumaranAbstract:A fluctuating-force model is developed for representing the effect of the turbulent fluid velocity fluctuations on the particle phase in a turbulent gas–solid suspension in the limit of high Stokes Number, where the particle relaxation time is large compared with the correlation time for the fluid velocity fluctuations. In the model, a fluctuating force is incorporated in the equation of motion for the particles, and the force distribution is assumed to be an anisotropic Gaussian white noise. It is shown that this is equivalent to incorporating a diffusion term in the Boltzmann equation for the particle velocity distribution functions. The variance of the force distribution, or equivalently the diffusion coefficient in the Boltzmann equation, is related to the time correlation functions for the fluid velocity fluctuations. The fluctuating-force model is applied to the specific case of a Couette flow of a turbulent particle–gas suspension, for which both the fluid and particle velocity distributions were evaluated using direct numerical simulations by Goswami & Kumaran (2010). It is found that the fluctuating-force simulation is able to quantitatively predict the concentration, mean velocity profiles and the mean square velocities, both at relatively low volume fractions, where the viscous relaxation time is small compared with the time between collisions, and at higher volume fractions, where the time between collisions is small compared with the viscous relaxation time. The simulations are also able to predict the velocity distributions in the centre of the Couette, even in cases in which the velocity distribution is very different from a Gaussian distribution.
Alejandro J. Souza - One of the best experts on this subject based on the ideXlab platform.
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On the use of the Stokes Number to explain frictional tidal dynamics and water column structure in shelf seas
Ocean Science, 2013Co-Authors: Alejandro J. SouzaAbstract:Abstract. In recent years coastal oceanographers have suggested using the "Strouhal" Number or its inverse, the "Stokes" Number, to describe the effect of bottom boundary layer turbulence on the vertical structure of both density and currents. These are defined as the ratios of the frictional depth (δ) to the water column depth (h) or vice versa. Although many researchers have mentioned that the effects of the earth's rotation should be important, they have tended to omit it. Rotation may have an important influence on tidal currents, as the frictional depth from a fully cyclonic to a fully anticyclonic tidal ellipse can vary by up to an order of magnitude at mid latitudes. The Stokes Number might appear smaller for cyclonic current ellipses (larger for anticyclonic) than it is without rotation, resulting in frictional effects being underestimated (overestimated). Here, a way to calculate a Stokes Number is proposed, in which the effect of the earth's rotation is taken into account. The standard Stokes and the rotational Stokes Numbers are used as predictors for the position of the tidal mixing fronts in the Irish Sea. Results show that use of the rotational Number improves the predictions of fronts in shallow cyclonic areas of the eastern Irish Sea. This suggests that the effect of rotation on the water column structure will be more important in shallow shelf seas and estuaries with strong rotational currents.
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On the use of the Strouhal/Stokes Number to explain the dynamics and water column structure on shelf seas
2012Co-Authors: Alejandro J. SouzaAbstract:Abstract. In recent years coastal oceanographers have suggested the use of the "Strouhal" Number or it's inverse the "Stokes" Number, which have been defined as the ratios of the frictional depth (δ) to the water column depth (h) or vice versa, to describe the effect of bottom boundary layer turbulence on the vertical structure of both density and currents. Although they have mention that the effects of rotation should be important, they have tended to omit it. This omission may be important when talking about tidal currents as the frictional depth from a fully cyclonic to a fully anticyclonic tidal ellipse can vary up to an order of magnitude in the mid latitudes; so that the Stokes Number might appear smaller (larger) than it is resulting in frictional effects being underestimated (overestimated). Here a way to calculate a Stokes Number, in which the effect of the Earth's rotation is taken into account, is suggested. Then the standard Stokes and the rotational Stokes Numbers are used as predictors for the position of the tidal mixing fronts in the Irish Sea. Results show that the rotational Number improves prediction of the front in shallow cyclonic areas of the eastern Irish Sea. This suggest that the effect of rotation on the water column structure will be more important in shallow shelf seas and estuaries with strong rotational currents.
John Abraham - One of the best experts on this subject based on the ideXlab platform.
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lattice boltzmann method simulations of Stokes Number effects on particle motion in a channel flow
Physics of Fluids, 2016Co-Authors: Lenan Zhang, Anand Samuel Jebakumar, John AbrahamAbstract:In a recent experimental study by Lau and Nathan [“Influence of Stokes Number on the velocity and concentration distributions in particle-laden jets,” J. Fluid Mech. 757, 432 (2014)], it was found that particles in a turbulent pipe flow tend to migrate preferentially toward the wall or the axis depending on their Stokes Number (St). Particles with a higher St (>10) are concentrated near the axis while those with lower St (<1) move toward the walls. Jebakumar et al. [“Lattice Boltzmann method simulations of Stokes Number effects on particle trajectories in a wall-bounded flow,” Comput. Fluids 124, 208 (2016)] have carried out simulations of a particle in a laminar channel flow to investigate this behavior. In their work, they report a similar behavior where particles with low St migrate toward the wall and oscillate about a mean position near the wall while those with high St oscillate about the channel center plane. They have explained this behavior in terms of the Saffman lift, Magnus lift, and wall repulsion forces acting on the particle. The present work extends the previous work done by Jebakumar et al. and aims to study the behavior of particles at intermediate St ranging from 10 to 20. It is in this range where the equilibrium position of the particle changes from near the wall to the axis and the particle starts oscillating about the axis. The Lattice Boltzmann method is employed to carry out this study. It is shown that the change in mean equilibrium position is related to increasing oscillations of the particle with mean position near the wall which results in the particle moving past the center plane to the opposite side. The responsible mechanisms are explained in detail.
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Lattice Boltzmann method simulations of Stokes Number effects on particle motion in a channel flow
Physics of Fluids, 2016Co-Authors: Lenan Zhang, Anand Samuel Jebakumar, John AbrahamAbstract:In a recent experimental study by Lau and Nathan [“Influence of Stokes Number on the velocity and concentration distributions in particle-laden jets,” J. Fluid Mech. 757, 432 (2014)], it was found that particles in a turbulent pipe flow tend to migrate preferentially toward the wall or the axis depending on their Stokes Number (St). Particles with a higher St (>10) are concentrated near the axis while those with lower St (
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Lattice Boltzmann method simulations of Stokes Number effects on particle trajectories in a wall-bounded flow
Computers & Fluids, 2016Co-Authors: Anand Samuel Jebakumar, Kannan N. Premnath, John AbrahamAbstract:Abstract Experimental studies of particle-laden flows in a pipe show that the spatial distribution of the particles across the radius of the pipe is dependent on the Stokes Number [Timothy C. W. Lau & Graham J. Nathan, J. Fluid Mech. 2014]. It has been suggested that the Saffman lift effect [Saffman, 1965] makes a significant contribution to this spatial distribution. The Saffman lift effect has been studied in prior works by several authors and the relative contribution of the lift force has been studied within the context of various forces acting on particles in a flow. The lift force depends on the particle size and the velocity of the particle relative to the gas phase. In this study, the lattice Boltzmann method is employed to study the mechanism of particle migration of an isolated particle moving in a wall-bounded flow. The boundary condition proposed by Bouzidi et al. [2001][23], which involves the bounce-back scheme modified to account for fractional link distances between the wall and the fluid node, is used for the particles. The force acting on the particle is found by adding the momentum lost by all the fluid molecules as they bounce back from the particle surface along the link joining the particle and the fluid boundary nodes. This force is used to update the position of the particle after every streaming step. The torque acting on the particle is determined similarly and is used to update the angular velocity of the particle. It is found that at low Stokes Number the particle behaves like a neutrally buoyant particle and exhibits the Segre–Silberberg effect. With increasing Stokes Number, the particle exhibits an oscillatory behavior about its mean position. For large Stokes Number, the particle oscillations are significant. If the ratio of channel height to particle diameter is increased, the particle moves closer to the wall and the oscillatory behavior is evident at lower Stokes Number.
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Comparison of the structure of computed and measured particle-laden jets for a wide range of Stokes Numbers
International Journal of Heat and Mass Transfer, 2016Co-Authors: Anand Samuel Jebakumar, John AbrahamAbstract:Abstract Turbulent particle-laden jets have been the subject of interest for many years on account of their relevance to several practical devices like engines, combustors and gasifiers. While prior experimental studies have examined particle-laden flows at high Stokes Number, experimental data on particle-laden jets with particle Stokes Number of the order of one and lower have not been available until recently. This study presents results from computations of particle-laden jets for Stokes Number ranging from 0.3 to 500 and their comparison with measured results. The mean gas-phase velocity is found by solving RANS equations with a k – ∊ model for turbulence. The particles are solved in a Lagrangian framework with the coupling between the carrier and dispersed phase modeled using a drag coefficient with a high-Reynolds Number correction. Particle–turbulence interactions are modeled using a random-walk dispersion model. The influence of Stokes Number on the spreading rate of the carrier and dispersed phase is examined. It is shown that for the range of Stokes Numbers considered, the computed results agree with measured particle centerline velocities within about 20%. The changes in particle velocities predicted as Stokes Number varies are consistent with measured changes in these variables. While no specific trends can be identified in the differences between computed and measured results that would relate the differences to Stokes Number, several parametric studies are carried out to investigate the effect of jet inlet gas phase turbulence intensity, fluctuating particle velocity at the jet inlet, turbulence modulation and the dispersion model employed on jet spreading and centerline velocities.
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Development of a parallel multiphase Lattice-Boltzmann solver to study Stokes Number effects on particle trajectories
2015Co-Authors: Lenan Zhang, Anand Samuel Jebakumar, John AbrahamAbstract:Particle-laden flows are important owing to their relevance to many engineering devices such as coal combustors, gasifiers and solar thermochemical reactors. In a recent experimental study by Lau and Nathan [1], it was found that particles in a turbulent pipe flow tend to migrate preferentially depending on their Stokes Number (St). Particles with a high St (>10) are concentrated near the axis while those with low St (
Ronak Gupta - One of the best experts on this subject based on the ideXlab platform.
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Unified theory for a sheared gas-solid suspension: from rapid granular suspension to its small-Stokes-Number limit
Journal of Fluid Mechanics, 2019Co-Authors: Meheboob Alam, Saikat Saha, Ronak GuptaAbstract:A non-perturbative nonlinear theory for moderately dense gas–solid suspensions is outlined within the framework of the Boltzmann–Enskog equation by extending the work of Saha & Alam (J. Fluid Mech., vol. 833, 2017, pp. 206–246). A linear Stokes’ drag law is adopted for gas–particle interactions, and the viscous dissipation due to hydrodynamic interactions is incorporated in the second-moment equation via a density-corrected Stokes Number. For the homogeneous shear flow, the present theory provides a unified treatment of dilute to dense suspensions of highly inelastic particles, encompassing the high-Stokes-Number rapid granular regime ($St\rightarrow \infty$) and its small-Stokes-Number counterpart, with quantitative agreement for all transport coefficients. It is shown that the predictions of the shear viscosity and normal-stress differences based on existing theories deteriorate markedly with increasing density as well as with decreasing Stokes Number and restitution coefficient.