- Email: [email protected]
LES of particle collision and agglomeration in vertical channel flows
Anton Friedl, Jiří J. Klemeš, Stefan Radl, Petar S. Varbanov, Thomas Wallek (Eds.) Proceedings of the 28th European Symposium on Computer Aided Process Engineering June 10th to 13th, 2018, Graz, Austria. © 2018 Elsevier B.V. All rights reserved. https://doi.org/10.1016/B978-0-444-64235-6.50098-X
LES of particle collision and agglomeration in vertical channel flows T. Ogholaja*, D.O. Njobuenwu, M. Fairweather School of Chemical and Process Engineering, University of Leeds, Leeds LS2 9JT, UK *
[email protected]
Abstract Large eddy simulation in a four-way coupled system is used to simulate particle collisions and agglomeration in turbulent vertical channel flows. The particle phase is modelled using Lagrangian particle tracking, ensuring that individual particle behaviour is effectively monitored by solving the particle equation of motion. Particle collisions are described using the hard-sphere collision model, with agglomeration tested based on the pre-collision kinetic energy, restitution coefficient and the van der Waals interactions between particles. The conditions influencing collision and agglomeration are studied for a fluid of Reτ = 300 with 125 µm spherical particles at volume fraction φv ~ O(10-3). Comparing flows in upward and downward directions reveals the influence of the various forces acting on the particles, with the drag and lift forces being dominant in both flows, although the latter is found to govern particle behaviour in downflow, driving the particles towards the wall regions where increased collisions and agglomeration occur. The particle distribution in upflow is more symmetric, with fewer collisions and agglomerations, due to the increased effects of drag. The fluid flow is also slightly modified by the presence of the particles. Keywords: Eulerian-Lagrangian, particles, collision, agglomeration, vertical channel
1. Introduction Particle collision and agglomeration can occur in a wide range of industrial applications where particle-laden flows are being transported. Instances of such behaviour are found in the nuclear industry during the mobilisation and transport of waste materials, in the pharmaceutical industry where fine chemicals are continuously being processed, and in the oil and gas industry during the exploration and processing of crude oil. In these applications, as well as in many others, it is important to gain an understanding of the rheological behaviour of such flows, particularly in terms of the impact of particle agglomeration which can lead to particle deposition and ultimately flow blockage. Numerical models are frequently used in evaluating particle-laden flows since they can generate understanding that is often impossible to gain through experimental means. The Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamic approach is most commonly used in industry due to its relatively modest computational requirements, although large eddy simulation (LES) and direct numerical simulation (DNS) provide far more accurate turbulent flow predictions, and do not require the caseby-case adjustments necessary when using RANS techniques. LES is preferred in this study given that it is a compromise between the more accurate but computationally expensive DNS, and the relatively low computational cost but lower precision RANS approach.
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The current study combines LES with a Lagrangian particle tracking (LPT) approach to improve the accuracy of turbulent two-phase flow predictions over those based on RANS techniques through the time and spatial resolution of the motion of large turbulent eddies, with individual particle motion tracked. Only a few studies of particle agglomeration in wall-bounded flows exist, with most investigations focussing on the dynamics of particles within a flow and their resulting effect on the flow structure. Relevant studies include those of Afkhami et al. (2015) and Njobuenwu et al. (2017) who both used LES as the basis for predicting particle agglomeration, although particle behaviour was modelled using the discrete element method and Lagrangian particle tracking, respectively. Almohammed et al. (2016) compared energy-based and momentum-based agglomeration models, whilst Sommerfeld et al. (2017) introduced a novel agglomerate structure model. Overall, however, our understanding of particle agglomeration remains poor, particularly for the case of wall-bounded flows. Building on previous work (Ogholaja et al., 2017), this study aims at improving our understanding of these flows by extending the investigation to vertical channels, where fluid flow with and against the direction of gravity is expected to lead to contrasting collision and agglomerate formation processes. In particular, the type and number of agglomerates formed in these flows, their local concentrations and their impact on the flow are considered. The understanding gained is of value in improving our ability to predict particle deposition that may lead to flow restrictions.
2. Numerical Simulation Fluid flow predictions were derived based on solutions of the time-dependent NavierStokes equations for an incompressible Newtonian fluid. The BOFFIN-LES simulation code was employed (Bini et al., 2008), which uses a top-hat technique to filter the governing equations of motion. A dynamically calibrated version of the Smagorinsky model was used in computing the resulting sub-grid scale tensor, while the influence of the unresolved velocity fluctuations on particle motion was modelled using a stochastic Markov technique. The code is based on a finite-volume approach, having a co-located grid arrangement and using an implicit low-Mach number formulation. A two-step approximate factorisation pressure correction method is applied to ensure mass conservation, with the time step chosen to ensure the maximum Courant number lies between 0.1 and 0.3. More details of the mathematical model and numerical solution method can be found in Bini et al. (2008) and Ogholaja et al. (2017). Integration of the particle equation of motion was performed within the LPT code, with the particle velocity and location computed using a fourth-order Runge-Kutta integration method, given initially random particle positions and velocities set equal to those of the fluid. The study considered all the significant forces acting on the particles, namely drag, gravity/buoyancy, added mass, shear lift and pressure gradient forces. The simulation was four-way coupled, ensuring particle-particle and particle-fluid interactions. The deterministic hard-sphere collision model (Breuer and Alletto, 2012) was employed in the prediction of particle interactions, with agglomeration modelled using the approach proposed by Breuer and Almohammed (2015). The number of grid nodes used in the x, y and z directions of the channel was 129×128×128, respectively, corresponding to the wall normal, spanwise and streamwise
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directions. For both fluid and particles, periodic boundary conditions were imposed in the y and z directions, whilst in the x direction, fixed boundaries with no-slip conditions for the fluid velocity and elastic particle collisions were assumed. The flow considered was of shear Reynolds number Reτ = uτh/ν = 300, based on the channel half height, h, the shear velocity, uτ, and the kinematic viscosity, ν = 10-6 m2 s-1. The continuous phase density was that of water, ρ = 103 kg m-3. The particles were assumed spherical and of equal diameter, dp = 125 µm, and density, ρ = 2710 kg m-3, with a particle volume fraction φv ~ O(10-3). The minimum particle contact distance δ0 was 3.36×10-10 m, the mean yield stress σ was 3.0×108 Pa, and the Hamaker constant H set to 3.8×10-20 J, with the normal restitution coefficient en = 0.4 being representative of calcite (a frequently used simulant in nuclear waste studies). Simulations were performed for flows in both upward and downward directions, given the anticipated differences in particle behaviour. In order to isolate these effects, a number of assumptions were made: particle-particle collisions are binary; no agglomerate break-up due to turbulence; minimal particle deformation post-collision; and particle agglomeration based on the pre-collision particle energy, restitution coefficient and van der Waals interactions.
3. Results and Discussion Results from both single- and two-phase channel flow simulations were first validated against direct numerical simulation-based predictions, see Ogholaja et al. (2017), with good agreement found. For the upward and downward channel flows, Fig. 1(a) compares the total number of particle collisions, Ncol, and agglomerations, Nagg, for both flows up to a simulation time of t+ = 1000. Both flows show increases in Ncol and Nagg with time, and it is clear that not all collisions result in agglomeration. Both flows initially show a sharp increase in the number of collisions and agglomerations, although with time the rate of increase of both reduces. Unlike for the upflow, however, Ncol and Nagg continue to increase with time in the downflow, and do not asymptote to an approximate steady state. This is as a result of the lift effect which enhances particle migration into regions of high turbulence near the channel walls, consequently increasing particle interactions. This is confirmed by the particle concentration profiles in Fig. 1 which clearly indicate particle migration towards the wall regions in the downflow, whilst the bulk of the particle concentration for the upflow remains evenly distributed across the channel, although depleted in the near-wall regions. Also shown in Fig. 1(b) is the rate of depletion of the primary single particles with time, and the corresponding evolution of multi-sized particle agglomerates, for the two flow cases. In both flows, two-particle agglomerates form fairly rapidly early in the simulation, after which larger agglomerates form through collisions between single primary particles and larger agglomerates, and also between the agglomerates themselves. These results also show that the formation of agglomerates is more prevalent in downflow, with agglomerates consisting of up to five primary particles forming over the time period considered, which contrasts with the upflow case which has a maximum of three particle agglomerates. Again, the increased number of multi-sized particle agglomerates in downflow is a result of more collision events occurring in near-wall regions within the flow where particle concentrations are high due to effect of the lift force on the particles.
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Figure 1. (a) Total number of collisions and agglomerates with time, (b) particle concentration profiles across the channel, and (c, d) agglomerate formation with time for upflow and downflow, respectively. Line numbers: single particle (1), double particle (2), etc.
Figure 2 provides more detail on the collision and agglomeration distribution across the channel width. Results are shown for the cross-stream domain divided into 16 regions in the wall-normal direction at t+ = 1000, although results are averaged over t+ ± 500 about this time to provide a sufficiently large statistical sample. In upflow, the number of collisions and agglomerations are roughly constant, although there are slightly more collisions in the near-wall regions of the flow where turbulence levels are high. In downflow, the trends are noticeably different, with collision and agglomeration reaching maximum levels in the two wall regions due to the migration of particles from the bulk flow towards the walls. As already noted, the lift force is responsible for the continuous increase in particle concentration in the wall regions where turbulence levels are high, consequently promoting more collisions and agglomerations. This is confirmed in the plots that give the forces acting on the particles in the wall-normal direction in the same figure. In these plots, only one half of the channel is shown as the results show identical behaviour in both halves. The lift and drag forces are clearly dominant, and act on the particles in opposite directions, whilst all other forces are insignificant. In upflow, these two forces are almost balanced, explaining why collision and agglomeration events across the channel are nearly symmetric, although there is a slight migration of particles towards the wall owing to the more dominant lift force. In downflow, this imbalance is more pronounced, with the more dominant lift force pushing the particles at a faster rate towards the two wall regions.
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Figure 2. Distribution of particle collisions and agglomerations across the channel for (a) upflow and (b) downflow, and (c, d) forces in (N kg-1) acting on the particles at t+ = 1000 for upflow and downflow, respectively (FSL = shear lift, FAM = added mass, FD = drag, FGB = gravity/buoyancy, FPG = pressure gradient). 20
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Lastly, the effect of particles on the fluid flow is considered in Figs. 3 and 4, again at t+ = 1000, where single-phase flow predictions are compared with liquid phase results for flows including particles. In upflow, the fluid mean streamwise velocity is suppressed due to the increased drag on the fluid, and enhanced in downflow where drag forces are less influential. Additionally, in Fig. 4 a very slight decrease in the upflow stresses is apparent, whilst the opposite is the case in downflow. These differences are, however, almost negligible.
4. Conclusions LES coupled with a Lagrangian particle tracking technique has been employed to predict particle collision and agglomeration in turbulent vertical channel flows. Collision and agglomeration increase with time, although at a much higher rate for a downward flow were particles are observed to migrate towards the wall regions, where turbulence levels are high, owing to the dominant lift force effect on the particles. The particle distribution in upflow is more symmetric, with fewer collisions and agglomerations, due to the increased effect of drag. Only slight changes to the velocity field of the continuous phase are predicted due to the presence of the particles, although some slight enhancement is evident in downflow, with the opposite the case in upflow.
Acknowledgements T.O. would like to thank the Nigerian Government for their financial support of the work described.
References M. Afkhami, A. Hassanpour, M. Fairweather, D.O. Njobuenwu, 2015, Fully coupled LES-DEM of particle interaction and agglomeration in a turbulent channel flow, Comput. Chem. Eng., 78, 24-38. N. Almohammed, M. Breuer, 2016, Modeling and simulation of agglomeration in turbulent particle-laden flows: A comparison between energy-based and momentum-based agglomeration models, Powder Technol., 294, 373-402. M. Bini, W.P. Jones, 2008, Large-eddy simulation of particle-laden turbulent flows, J. Fluid Mech., 614, 207-252. M. Breuer, M. Alletto, 2012, Efficient simulation of particle-laden turbulent flows with high mass loadings using LES, Int. J. Heat Fluid Fl. 35, 2-12. M. Breuer, N. Almohammed, 2015, Modeling and simulation of particle agglomeration in turbulent flows using a hard-sphere model with deterministic collision detection and enhanced structure models, Int. J. Multiphase Flow, 73, 171-206. D.O. Njobuenwu, M. Fairweather, 2017, Simulation of deterministic energy-balance particle agglomeration in turbulent liquid-solid flows, Phys. Fluids, 29, 083301. T. Ogholaja, D.O. Njobuenwu, M. Fairweather, 2017, Particle size effects on collision and agglomeration in turbulent channel flows, 27th European Symposium on Computer Aided Process Engineering, A. Espuña, M. Graells, L. Puigjaner (Eds.), Elsevier, 79-84. M. Sommerfeld, S. Stübing, 2017, A novel Lagrangian agglomerate structure model, Powder Technol., 319, 34-52.
LES of particle collision and agglomeration in vertical channel flows T. Ogholaja*, D.O. Njobuenwu, M. Fairweather School of Chemical and Process Engineering, University of Leeds, Leeds LS2 9JT, UK *
[email protected]
Abstract Large eddy simulation in a four-way coupled system is used to simulate particle collisions and agglomeration in turbulent vertical channel flows. The particle phase is modelled using Lagrangian particle tracking, ensuring that individual particle behaviour is effectively monitored by solving the particle equation of motion. Particle collisions are described using the hard-sphere collision model, with agglomeration tested based on the pre-collision kinetic energy, restitution coefficient and the van der Waals interactions between particles. The conditions influencing collision and agglomeration are studied for a fluid of Reτ = 300 with 125 µm spherical particles at volume fraction φv ~ O(10-3). Comparing flows in upward and downward directions reveals the influence of the various forces acting on the particles, with the drag and lift forces being dominant in both flows, although the latter is found to govern particle behaviour in downflow, driving the particles towards the wall regions where increased collisions and agglomeration occur. The particle distribution in upflow is more symmetric, with fewer collisions and agglomerations, due to the increased effects of drag. The fluid flow is also slightly modified by the presence of the particles. Keywords: Eulerian-Lagrangian, particles, collision, agglomeration, vertical channel
1. Introduction Particle collision and agglomeration can occur in a wide range of industrial applications where particle-laden flows are being transported. Instances of such behaviour are found in the nuclear industry during the mobilisation and transport of waste materials, in the pharmaceutical industry where fine chemicals are continuously being processed, and in the oil and gas industry during the exploration and processing of crude oil. In these applications, as well as in many others, it is important to gain an understanding of the rheological behaviour of such flows, particularly in terms of the impact of particle agglomeration which can lead to particle deposition and ultimately flow blockage. Numerical models are frequently used in evaluating particle-laden flows since they can generate understanding that is often impossible to gain through experimental means. The Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamic approach is most commonly used in industry due to its relatively modest computational requirements, although large eddy simulation (LES) and direct numerical simulation (DNS) provide far more accurate turbulent flow predictions, and do not require the caseby-case adjustments necessary when using RANS techniques. LES is preferred in this study given that it is a compromise between the more accurate but computationally expensive DNS, and the relatively low computational cost but lower precision RANS approach.
556
T. Ogholaja et al.
The current study combines LES with a Lagrangian particle tracking (LPT) approach to improve the accuracy of turbulent two-phase flow predictions over those based on RANS techniques through the time and spatial resolution of the motion of large turbulent eddies, with individual particle motion tracked. Only a few studies of particle agglomeration in wall-bounded flows exist, with most investigations focussing on the dynamics of particles within a flow and their resulting effect on the flow structure. Relevant studies include those of Afkhami et al. (2015) and Njobuenwu et al. (2017) who both used LES as the basis for predicting particle agglomeration, although particle behaviour was modelled using the discrete element method and Lagrangian particle tracking, respectively. Almohammed et al. (2016) compared energy-based and momentum-based agglomeration models, whilst Sommerfeld et al. (2017) introduced a novel agglomerate structure model. Overall, however, our understanding of particle agglomeration remains poor, particularly for the case of wall-bounded flows. Building on previous work (Ogholaja et al., 2017), this study aims at improving our understanding of these flows by extending the investigation to vertical channels, where fluid flow with and against the direction of gravity is expected to lead to contrasting collision and agglomerate formation processes. In particular, the type and number of agglomerates formed in these flows, their local concentrations and their impact on the flow are considered. The understanding gained is of value in improving our ability to predict particle deposition that may lead to flow restrictions.
2. Numerical Simulation Fluid flow predictions were derived based on solutions of the time-dependent NavierStokes equations for an incompressible Newtonian fluid. The BOFFIN-LES simulation code was employed (Bini et al., 2008), which uses a top-hat technique to filter the governing equations of motion. A dynamically calibrated version of the Smagorinsky model was used in computing the resulting sub-grid scale tensor, while the influence of the unresolved velocity fluctuations on particle motion was modelled using a stochastic Markov technique. The code is based on a finite-volume approach, having a co-located grid arrangement and using an implicit low-Mach number formulation. A two-step approximate factorisation pressure correction method is applied to ensure mass conservation, with the time step chosen to ensure the maximum Courant number lies between 0.1 and 0.3. More details of the mathematical model and numerical solution method can be found in Bini et al. (2008) and Ogholaja et al. (2017). Integration of the particle equation of motion was performed within the LPT code, with the particle velocity and location computed using a fourth-order Runge-Kutta integration method, given initially random particle positions and velocities set equal to those of the fluid. The study considered all the significant forces acting on the particles, namely drag, gravity/buoyancy, added mass, shear lift and pressure gradient forces. The simulation was four-way coupled, ensuring particle-particle and particle-fluid interactions. The deterministic hard-sphere collision model (Breuer and Alletto, 2012) was employed in the prediction of particle interactions, with agglomeration modelled using the approach proposed by Breuer and Almohammed (2015). The number of grid nodes used in the x, y and z directions of the channel was 129×128×128, respectively, corresponding to the wall normal, spanwise and streamwise
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directions. For both fluid and particles, periodic boundary conditions were imposed in the y and z directions, whilst in the x direction, fixed boundaries with no-slip conditions for the fluid velocity and elastic particle collisions were assumed. The flow considered was of shear Reynolds number Reτ = uτh/ν = 300, based on the channel half height, h, the shear velocity, uτ, and the kinematic viscosity, ν = 10-6 m2 s-1. The continuous phase density was that of water, ρ = 103 kg m-3. The particles were assumed spherical and of equal diameter, dp = 125 µm, and density, ρ = 2710 kg m-3, with a particle volume fraction φv ~ O(10-3). The minimum particle contact distance δ0 was 3.36×10-10 m, the mean yield stress σ was 3.0×108 Pa, and the Hamaker constant H set to 3.8×10-20 J, with the normal restitution coefficient en = 0.4 being representative of calcite (a frequently used simulant in nuclear waste studies). Simulations were performed for flows in both upward and downward directions, given the anticipated differences in particle behaviour. In order to isolate these effects, a number of assumptions were made: particle-particle collisions are binary; no agglomerate break-up due to turbulence; minimal particle deformation post-collision; and particle agglomeration based on the pre-collision particle energy, restitution coefficient and van der Waals interactions.
3. Results and Discussion Results from both single- and two-phase channel flow simulations were first validated against direct numerical simulation-based predictions, see Ogholaja et al. (2017), with good agreement found. For the upward and downward channel flows, Fig. 1(a) compares the total number of particle collisions, Ncol, and agglomerations, Nagg, for both flows up to a simulation time of t+ = 1000. Both flows show increases in Ncol and Nagg with time, and it is clear that not all collisions result in agglomeration. Both flows initially show a sharp increase in the number of collisions and agglomerations, although with time the rate of increase of both reduces. Unlike for the upflow, however, Ncol and Nagg continue to increase with time in the downflow, and do not asymptote to an approximate steady state. This is as a result of the lift effect which enhances particle migration into regions of high turbulence near the channel walls, consequently increasing particle interactions. This is confirmed by the particle concentration profiles in Fig. 1 which clearly indicate particle migration towards the wall regions in the downflow, whilst the bulk of the particle concentration for the upflow remains evenly distributed across the channel, although depleted in the near-wall regions. Also shown in Fig. 1(b) is the rate of depletion of the primary single particles with time, and the corresponding evolution of multi-sized particle agglomerates, for the two flow cases. In both flows, two-particle agglomerates form fairly rapidly early in the simulation, after which larger agglomerates form through collisions between single primary particles and larger agglomerates, and also between the agglomerates themselves. These results also show that the formation of agglomerates is more prevalent in downflow, with agglomerates consisting of up to five primary particles forming over the time period considered, which contrasts with the upflow case which has a maximum of three particle agglomerates. Again, the increased number of multi-sized particle agglomerates in downflow is a result of more collision events occurring in near-wall regions within the flow where particle concentrations are high due to effect of the lift force on the particles.
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Figure 1. (a) Total number of collisions and agglomerates with time, (b) particle concentration profiles across the channel, and (c, d) agglomerate formation with time for upflow and downflow, respectively. Line numbers: single particle (1), double particle (2), etc.
Figure 2 provides more detail on the collision and agglomeration distribution across the channel width. Results are shown for the cross-stream domain divided into 16 regions in the wall-normal direction at t+ = 1000, although results are averaged over t+ ± 500 about this time to provide a sufficiently large statistical sample. In upflow, the number of collisions and agglomerations are roughly constant, although there are slightly more collisions in the near-wall regions of the flow where turbulence levels are high. In downflow, the trends are noticeably different, with collision and agglomeration reaching maximum levels in the two wall regions due to the migration of particles from the bulk flow towards the walls. As already noted, the lift force is responsible for the continuous increase in particle concentration in the wall regions where turbulence levels are high, consequently promoting more collisions and agglomerations. This is confirmed in the plots that give the forces acting on the particles in the wall-normal direction in the same figure. In these plots, only one half of the channel is shown as the results show identical behaviour in both halves. The lift and drag forces are clearly dominant, and act on the particles in opposite directions, whilst all other forces are insignificant. In upflow, these two forces are almost balanced, explaining why collision and agglomeration events across the channel are nearly symmetric, although there is a slight migration of particles towards the wall owing to the more dominant lift force. In downflow, this imbalance is more pronounced, with the more dominant lift force pushing the particles at a faster rate towards the two wall regions.
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Figure 2. Distribution of particle collisions and agglomerations across the channel for (a) upflow and (b) downflow, and (c, d) forces in (N kg-1) acting on the particles at t+ = 1000 for upflow and downflow, respectively (FSL = shear lift, FAM = added mass, FD = drag, FGB = gravity/buoyancy, FPG = pressure gradient). 20
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Lastly, the effect of particles on the fluid flow is considered in Figs. 3 and 4, again at t+ = 1000, where single-phase flow predictions are compared with liquid phase results for flows including particles. In upflow, the fluid mean streamwise velocity is suppressed due to the increased drag on the fluid, and enhanced in downflow where drag forces are less influential. Additionally, in Fig. 4 a very slight decrease in the upflow stresses is apparent, whilst the opposite is the case in downflow. These differences are, however, almost negligible.
4. Conclusions LES coupled with a Lagrangian particle tracking technique has been employed to predict particle collision and agglomeration in turbulent vertical channel flows. Collision and agglomeration increase with time, although at a much higher rate for a downward flow were particles are observed to migrate towards the wall regions, where turbulence levels are high, owing to the dominant lift force effect on the particles. The particle distribution in upflow is more symmetric, with fewer collisions and agglomerations, due to the increased effect of drag. Only slight changes to the velocity field of the continuous phase are predicted due to the presence of the particles, although some slight enhancement is evident in downflow, with the opposite the case in upflow.
Acknowledgements T.O. would like to thank the Nigerian Government for their financial support of the work described.
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