Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres

► Drag law for gas–solids flow using particle-resolved simulation of fixed spheres. ► Numerical method PUReIBM based on immersed boundary method with no forcing in fluid. ► PUReIBM is accurate, numerically convergent and consistent with two-fluid theory. ► New drag correlation is proposed that can b...

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Veröffentlicht in:	International journal of multiphase flow Jg. 37; H. 9; S. 1072 - 1092
Hauptverfasser:	Tenneti, S., Garg, R., Subramaniam, S.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Kidlington Elsevier Ltd 01.11.2011 Elsevier
Schlagworte:	Assemblies Computational fluid dynamics Computational methods in fluid dynamics Correlation Drag Drag law Exact sciences and technology Fluid dynamics Fluid flow Fundamental areas of phenomenology (including applications) Gas–solid flow Immersed boundary method Mathematical analysis Mathematical models Multiphase and particle-laden flows Nonhomogeneous flows Particle-resolved direct numerical simulation Physics Simulation Gas–solid flow Immersed boundary method Drag law Particle-resolved direct numerical simulation Gas-solid flow Gas particle flow Particle-resolved direct numerical Digital simulation simulation Velocity distribution Two-phase flow Monodispersed particle Modelling Spherical particle Viscous fluids Drag coefficient
ISSN:	0301-9322, 1879-3533
Online-Zugang:	Volltext
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Abstract	► Drag law for gas–solids flow using particle-resolved simulation of fixed spheres. ► Numerical method PUReIBM based on immersed boundary method with no forcing in fluid. ► PUReIBM is accurate, numerically convergent and consistent with two-fluid theory. ► New drag correlation is proposed that can be used in CFD simulation of fluidized beds. Gas–solid momentum transfer is a fundamental problem that is characterized by the dependence of normalized average fluid–particle force F on solid volume fraction ϕ and the Reynolds number based on the mean slip velocity Re m . In this work we report particle-resolved direct numerical simulation (DNS) results of interphase momentum transfer in flow past fixed random assemblies of monodisperse spheres with finite fluid inertia using a continuum Navier–Stokes solver. This solver is based on a new formulation we refer to as the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PUReIBM). The principal advantage of this formulation is that the fluid stress at the particle surface is calculated directly from the flow solution (velocity and pressure fields), which when integrated over the surfaces of all particles yields the average fluid–particle force. We demonstrate that PUReIBM is a consistent numerical method to study gas–solid flow because it results in a force density on particle surfaces that is reconcilable with the averaged two-fluid theory. The numerical convergence and accuracy of PUReIBM are established through a comprehensive suite of validation tests. The normalized average fluid–particle force F is obtained as a function of solid volume fraction ϕ (0.1 ⩽ ϕ ⩽ 0.5) and mean flow Reynolds number Re m (0.01 ⩽ Re m ⩽ 300) for random assemblies of monodisperse spheres. These results extend previously reported results of Hill et al. (2001a,b) to a wider range of ϕ, Re m , and are more accurate than those reported by Beetstra et al. (2007). Differences between the drag values obtained from PUReIBM and the drag correlation of Beetstra et al. (2007) are as high as 30% for Re m in the range 100–300. We take advantage of PUReIBM’s ability to directly calculate the relative contributions of pressure and viscous stress to the total fluid–particle force, which is useful in developing drag correlations. Using a scaling argument, Hill et al. (2001b) proposed that the viscous contribution is independent of Re m but the pressure contribution is linear in Re m (for Re m > 50). However, from PUReIBM simulations we find that the viscous contribution is not independent of the mean flow Reynolds number, although the pressure contribution does indeed vary linearly with Re m in accord with the analysis of Hill et al. (2001b). An improved correlation for F in terms of ϕ and Re m is proposed that corrects the existing correlations in Re m range 100–300. Since this drag correlation has been inferred from simulations of fixed particle assemblies, it does not include the effect of mobility of the particles. However, the fixed-bed simulation approach is a good approximation for high Stokes number particles, which are encountered in most gas–solid flows. This improved drag correlation can be used in CFD simulations of fluidized beds that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior.
AbstractList	Gas-solid momentum transfer is a fundamental problem that is characterized by the dependence of normalized average fluid-particle force F on solid volume fraction [phi] and the Reynolds number based on the mean slip velocity Re sub(m. In this work we report particle-resolved direct numerical simulation (DNS) results of interphase momentum transfer in flow past fixed random assemblies of monodisperse spheres with finite fluid inertia using a continuum Navier-Stokes solver. This solver is based on a new formulation we refer to as the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PUReIBM). The principal advantage of this formulation is that the fluid stress at the particle surface is calculated directly from the flow solution (velocity and pressure fields), which when integrated over the surfaces of all particles yields the average fluid-particle force. We demonstrate that PUReIBM is a consistent numerical method to study gas-solid flow because it results in a force density on particle surfaces that is reconcilable with the averaged two-fluid theory. The numerical convergence and accuracy of PUReIBM are established through a comprehensive suite of validation tests. The normalized average fluid-particle force F is obtained as a function of solid volume fraction [phi] (0.1 [less-than-or-equals, slant] [phi] [less-than-or-equals, slant] 0.5) and mean flow Reynolds number Re) sub(m) (0.01 [less-than-or-equals, slant] Re sub(m [less-than-or-equals, slant] 300) for random assemblies of monodisperse spheres. These results extend previously reported results of (Hill et al., 2001a) and (Hill et al., 2001b) to a wider range of [phi], Re) sub(m), and are more accurate than those reported by Beetstra et al. (2007). Differences between the drag values obtained from PUReIBM and the drag correlation of Beetstra et al. (2007) are as high as 30% for Re sub(m in the range 100-300. We take advantage of PUReIBM's ability to directly calculate the relative contributions of pressure and viscous stress to the total fluid-particle force, which is useful in developing drag correlations. Using a scaling argument, Hill et al. (2001b) proposed that the viscous contribution is independent of Re) sub(m) but the pressure contribution is linear in Re sub(m (for Re) sub(m) 50). However, from PUReIBM simulations we find that the viscous contribution is not independent of the mean flow Reynolds number, although the pressure contribution does indeed vary linearly with Re sub(m in accord with the analysis of Hill et al. (2001b). An improved correlation for F in terms of [phi] and Re) sub(m) is proposed that corrects the existing correlations in Re sub(m range 100-300. Since this drag correlation has been inferred from simulations of fixed particle assemblies, it does not include the effect of mobility of the particles. However, the fixed-bed simulation approach is a good approximation for high Stokes number particles, which are encountered in most gas-solid flows. This improved drag correlation can be used in CFD simulations of fluidized beds that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior.) ► Drag law for gas–solids flow using particle-resolved simulation of fixed spheres. ► Numerical method PUReIBM based on immersed boundary method with no forcing in fluid. ► PUReIBM is accurate, numerically convergent and consistent with two-fluid theory. ► New drag correlation is proposed that can be used in CFD simulation of fluidized beds. Gas–solid momentum transfer is a fundamental problem that is characterized by the dependence of normalized average fluid–particle force F on solid volume fraction ϕ and the Reynolds number based on the mean slip velocity Re m . In this work we report particle-resolved direct numerical simulation (DNS) results of interphase momentum transfer in flow past fixed random assemblies of monodisperse spheres with finite fluid inertia using a continuum Navier–Stokes solver. This solver is based on a new formulation we refer to as the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PUReIBM). The principal advantage of this formulation is that the fluid stress at the particle surface is calculated directly from the flow solution (velocity and pressure fields), which when integrated over the surfaces of all particles yields the average fluid–particle force. We demonstrate that PUReIBM is a consistent numerical method to study gas–solid flow because it results in a force density on particle surfaces that is reconcilable with the averaged two-fluid theory. The numerical convergence and accuracy of PUReIBM are established through a comprehensive suite of validation tests. The normalized average fluid–particle force F is obtained as a function of solid volume fraction ϕ (0.1 ⩽ ϕ ⩽ 0.5) and mean flow Reynolds number Re m (0.01 ⩽ Re m ⩽ 300) for random assemblies of monodisperse spheres. These results extend previously reported results of Hill et al. (2001a,b) to a wider range of ϕ, Re m , and are more accurate than those reported by Beetstra et al. (2007). Differences between the drag values obtained from PUReIBM and the drag correlation of Beetstra et al. (2007) are as high as 30% for Re m in the range 100–300. We take advantage of PUReIBM’s ability to directly calculate the relative contributions of pressure and viscous stress to the total fluid–particle force, which is useful in developing drag correlations. Using a scaling argument, Hill et al. (2001b) proposed that the viscous contribution is independent of Re m but the pressure contribution is linear in Re m (for Re m > 50). However, from PUReIBM simulations we find that the viscous contribution is not independent of the mean flow Reynolds number, although the pressure contribution does indeed vary linearly with Re m in accord with the analysis of Hill et al. (2001b). An improved correlation for F in terms of ϕ and Re m is proposed that corrects the existing correlations in Re m range 100–300. Since this drag correlation has been inferred from simulations of fixed particle assemblies, it does not include the effect of mobility of the particles. However, the fixed-bed simulation approach is a good approximation for high Stokes number particles, which are encountered in most gas–solid flows. This improved drag correlation can be used in CFD simulations of fluidized beds that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior.
Author	Subramaniam, S. Tenneti, S. Garg, R.
Author_xml	– sequence: 1 givenname: S. surname: Tenneti fullname: Tenneti, S. – sequence: 2 givenname: R. surname: Garg fullname: Garg, R. – sequence: 3 givenname: S. surname: Subramaniam fullname: Subramaniam, S. email: shankar@iastate.edu
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24497605$$DView record in Pascal Francis
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Keywords	Gas–solid flow Immersed boundary method Drag law Particle-resolved direct numerical simulation Gas-solid flow Gas particle flow Particle-resolved direct numerical Digital simulation simulation Velocity distribution Two-phase flow Monodispersed particle Modelling Spherical particle Viscous fluids Drag coefficient
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Snippet	► Drag law for gas–solids flow using particle-resolved simulation of fixed spheres. ► Numerical method PUReIBM based on immersed boundary method with no... Gas-solid momentum transfer is a fundamental problem that is characterized by the dependence of normalized average fluid-particle force F on solid volume...
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SubjectTerms	Assemblies Computational fluid dynamics Computational methods in fluid dynamics Correlation Drag Drag law Exact sciences and technology Fluid dynamics Fluid flow Fundamental areas of phenomenology (including applications) Gas–solid flow Immersed boundary method Mathematical analysis Mathematical models Multiphase and particle-laden flows Nonhomogeneous flows Particle-resolved direct numerical simulation Physics Simulation
Title	Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres
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