## Abstract

A general two-fluid model is derived and applied in CFD computations to various test cases of important industrial multiphase flows. It is general in the sense of its applicability to dilute and dense dispersed fluid-particle flows. The model is limited to isothermal flow without mass transfer and only one particle phase is described. The instantaneous fluid phase equations, including the phase interaction terms, are derived from a volume averaging technique, and the instantaneous particle phase equations are derived from the kinetic theory of granular material. Whereas the averaging procedure, the treatment of the interaction terms, and the kinetic theory approach have been reported in literature prior to this work the combination of the approaches is new. The resulting equations are derived without ambiguity in the interpretation of the particle phase pressure (equation-of-state of particle phase). The basic modeling for the particle phase is improved in two steps. Because in the basic modeling only stresses due to kinetic and collisional interactions are included, a simple model for an effective viscosity is developed in order to allow also frictional stresses within the particle phase. Moreover, turbulent stresses and turbulent dispersion of particles play often an important role for the transport processes. Therefore
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## Citation Formats

Laux, Harald.
Modeling of dilute and dense dispersed fluid-particle flow.
Norway: N. p.,
1998.
Web.

Laux, Harald.
Modeling of dilute and dense dispersed fluid-particle flow.
Norway.

Laux, Harald.
1998.
"Modeling of dilute and dense dispersed fluid-particle flow."
Norway.

@misc{etde_20185889,

title = {Modeling of dilute and dense dispersed fluid-particle flow}

author = {Laux, Harald}

abstractNote = {A general two-fluid model is derived and applied in CFD computations to various test cases of important industrial multiphase flows. It is general in the sense of its applicability to dilute and dense dispersed fluid-particle flows. The model is limited to isothermal flow without mass transfer and only one particle phase is described. The instantaneous fluid phase equations, including the phase interaction terms, are derived from a volume averaging technique, and the instantaneous particle phase equations are derived from the kinetic theory of granular material. Whereas the averaging procedure, the treatment of the interaction terms, and the kinetic theory approach have been reported in literature prior to this work the combination of the approaches is new. The resulting equations are derived without ambiguity in the interpretation of the particle phase pressure (equation-of-state of particle phase). The basic modeling for the particle phase is improved in two steps. Because in the basic modeling only stresses due to kinetic and collisional interactions are included, a simple model for an effective viscosity is developed in order to allow also frictional stresses within the particle phase. Moreover, turbulent stresses and turbulent dispersion of particles play often an important role for the transport processes. Therefore in a second step, a two-equation turbulence model for both fluid and particle phase turbulence is derived by applying the phasic average to the instantaneous equations. The resulting k-{epsilon}-k{sup d}-{epsilon}{sup d} model is new. Mathematical closure is attempted such that the resulting set of equations is valid for both dilute arid dense flows. During the development of the closure relations a clear distinction is made between granular or ''viscous'' microscale fluctuations and turbulent macro scale fluctuations (true particle turbulence) within the particle phase. The set of governing equations is discretized by using a finite volume method. For the numerical solution of the discretized equations a new algorithm that is based on the SIMPLE algorithm is developed. The new algorithm treats the particle phase as fully compressible. The algorithm is therefore referred to as compressible dispersed phase method (CDP). The CDP method solves the particle volume fraction from the equation-of-state of the particle phase, and both the equation-of-state and the particle continuity equation are always fulfilled simultaneously. Several types of industrial multiphase flows are studied and it is demonstrated that the two-fluid model solved with the CDP method produces stable and physically reliable solutions. First, the flow of sand and the heap building in an hourglass is computed. By means of an comprehensive parameter study it is shown that whereas the instantaneous equations without frictional stress modeling predict mass flow rates in the hourglass orifice that are in good agreement with the empirical Beverloo correlation, only with the frictional stress model realistic shapes of the heap of sand are obtained. A similar effect on the shape of the bulk particles is shown for the sediment bed in a sedimentation column. Second, the flow in two cold gas-fluidized beds is computed. It is shown that the predicted motion and characteristics of large scale bubbles in a bed with a central jet are in good agreement with classical analytical results and available experimental results. It is also shown that the model predicts spontaneous bubble formation in an uniformly fluidized bed. Third, a liquid-particle system is studied, that is, the settling convection in an inclined parallel plate settler. The computations are in excellent agreement with measurements carried out in our laboratory and analytical theories. However, the results suggest that the kinetic theory of granular material needs modification if applied to liquid-particle suspensions. Finally, the turbulence model is applied to three test cases. The particle dispersion in a dilute particle-laden air jet is studied and the dense flow in a plane shear cell. Experimental results were not available for these two cases. However, for the particle-laden jet the computations show correctly the increased dispersion width when the turbulence model is used, and that kinetic energy is transferred from the fluid to the particle phase. For the dense shear cell on the other hand, especially close to the moving bottom plate turbulent kinetic energy is transferred from the particle to the fluid phase, indicating the existence of true particle turbulence. The last turbulent test case, a riser flow, is compared to selected experimental data. In this case it is obvious that the turbulence model gives more realistic velocity profiles and good agreement with the measured rms fluctuations in the particle phase. A flux boundary condition which allows collisional dissipation of particle phase kinetic energy at the riser walls seems crucial for an accurate solution.}

place = {Norway}

year = {1998}

month = {Aug}

}

title = {Modeling of dilute and dense dispersed fluid-particle flow}

author = {Laux, Harald}

abstractNote = {A general two-fluid model is derived and applied in CFD computations to various test cases of important industrial multiphase flows. It is general in the sense of its applicability to dilute and dense dispersed fluid-particle flows. The model is limited to isothermal flow without mass transfer and only one particle phase is described. The instantaneous fluid phase equations, including the phase interaction terms, are derived from a volume averaging technique, and the instantaneous particle phase equations are derived from the kinetic theory of granular material. Whereas the averaging procedure, the treatment of the interaction terms, and the kinetic theory approach have been reported in literature prior to this work the combination of the approaches is new. The resulting equations are derived without ambiguity in the interpretation of the particle phase pressure (equation-of-state of particle phase). The basic modeling for the particle phase is improved in two steps. Because in the basic modeling only stresses due to kinetic and collisional interactions are included, a simple model for an effective viscosity is developed in order to allow also frictional stresses within the particle phase. Moreover, turbulent stresses and turbulent dispersion of particles play often an important role for the transport processes. Therefore in a second step, a two-equation turbulence model for both fluid and particle phase turbulence is derived by applying the phasic average to the instantaneous equations. The resulting k-{epsilon}-k{sup d}-{epsilon}{sup d} model is new. Mathematical closure is attempted such that the resulting set of equations is valid for both dilute arid dense flows. During the development of the closure relations a clear distinction is made between granular or ''viscous'' microscale fluctuations and turbulent macro scale fluctuations (true particle turbulence) within the particle phase. The set of governing equations is discretized by using a finite volume method. For the numerical solution of the discretized equations a new algorithm that is based on the SIMPLE algorithm is developed. The new algorithm treats the particle phase as fully compressible. The algorithm is therefore referred to as compressible dispersed phase method (CDP). The CDP method solves the particle volume fraction from the equation-of-state of the particle phase, and both the equation-of-state and the particle continuity equation are always fulfilled simultaneously. Several types of industrial multiphase flows are studied and it is demonstrated that the two-fluid model solved with the CDP method produces stable and physically reliable solutions. First, the flow of sand and the heap building in an hourglass is computed. By means of an comprehensive parameter study it is shown that whereas the instantaneous equations without frictional stress modeling predict mass flow rates in the hourglass orifice that are in good agreement with the empirical Beverloo correlation, only with the frictional stress model realistic shapes of the heap of sand are obtained. A similar effect on the shape of the bulk particles is shown for the sediment bed in a sedimentation column. Second, the flow in two cold gas-fluidized beds is computed. It is shown that the predicted motion and characteristics of large scale bubbles in a bed with a central jet are in good agreement with classical analytical results and available experimental results. It is also shown that the model predicts spontaneous bubble formation in an uniformly fluidized bed. Third, a liquid-particle system is studied, that is, the settling convection in an inclined parallel plate settler. The computations are in excellent agreement with measurements carried out in our laboratory and analytical theories. However, the results suggest that the kinetic theory of granular material needs modification if applied to liquid-particle suspensions. Finally, the turbulence model is applied to three test cases. The particle dispersion in a dilute particle-laden air jet is studied and the dense flow in a plane shear cell. Experimental results were not available for these two cases. However, for the particle-laden jet the computations show correctly the increased dispersion width when the turbulence model is used, and that kinetic energy is transferred from the fluid to the particle phase. For the dense shear cell on the other hand, especially close to the moving bottom plate turbulent kinetic energy is transferred from the particle to the fluid phase, indicating the existence of true particle turbulence. The last turbulent test case, a riser flow, is compared to selected experimental data. In this case it is obvious that the turbulence model gives more realistic velocity profiles and good agreement with the measured rms fluctuations in the particle phase. A flux boundary condition which allows collisional dissipation of particle phase kinetic energy at the riser walls seems crucial for an accurate solution.}

place = {Norway}

year = {1998}

month = {Aug}

}