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23.4.7 Granular Properties

Since the concentration of particles is an important factor in the calculation of the effective viscosity for the mixture, we may use the granular viscosity (see section on Eulerian granular flows) to get a value for the viscosity of the suspension. The volume weighted averaged for the viscosity would now contain shear viscosity arising from particle momentum exchange due to translation and collision.

The collisional and kinetic parts, and the optional frictional part, are added to give the solids shear viscosity:


 \mu_{s} = \mu_{s,{\rm col}} + \mu_{s,{\rm kin}} + \mu_{s,{\rm fr}} (23.4-18)



Collisional Viscosity


The collisional part of the shear viscosity is modeled as [ 121, 364]


 \mu_{s,{\rm col}} = \frac{4}{5} \alpha_{s} \rho_{s} d_{s} g_{0,ss}(1 + e_{ss}) \left(\frac{\Theta_{s}}{\pi} \right)^{1/2} (23.4-19)



Kinetic Viscosity


FLUENT provides two expressions for the kinetic viscosity.

The default expression is from Syamlal et al. [ 364]:


 \mu_{s,{\rm kin}} = \frac{ \alpha_{s} d_{s} \rho_{s} \sqrt{\... ... \right) \left(3e_{ss} - 1 \right) \alpha_{s} g_{0,ss} \right] (23.4-20)

The following optional expression from Gidaspow et al. [ 121] is also available:


 \mu_{s,{\rm kin}} = \frac{ 10 \rho_{s} d_{s} \sqrt{\Theta_{s... ...{4}{5} g_{0,ss} \alpha_{s} \left( 1 + e_{ss} \right) \right]^2 (23.4-21)


next up previous contents index Previous: 23.4.6 Volume Fraction Equation
Up: 23.4 Mixture Model Theory
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© Fluent Inc. 2006-09-20