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23.4.8 Granular Temperature

The viscosities need the specification of the granular temperature for the $s^{\rm th}$ solids phase. Here we use an algebraic equation derived from the transport equation by neglecting convection and diffusion and takes the form [ 364]

 0 = (-p_s \overline{\overline{I}} + \overline{\overline{\tau}}_s):\nabla \vec v_s - \gamma_{\Theta_s} + \phi_{ls} (23.4-22)

  $(-p_s \overline{\overline{I}}+\overline{\overline{\tau}}_s):\nabla \vec v_s$ = the generation of energy by the solid stress tensor
  $\gamma_{\Theta_s}$ = the collisional dissipation of energy
  $\phi_{ls}$ = the energy exchange between the $l^{\rm th}$
      fluid or solid phase and the $s^{\rm th}$ solid phase

The collisional dissipation of energy, $\gamma_{\Theta_s}$, represents the rate of energy dissipation within the $s^{\rm th}$ solids phase due to collisions between particles. This term is represented by the expression derived by Lun et al. [ 222]

 \gamma_{\Theta m} = \frac{12(1-e_{ss}^2) g_{0,ss}}{d_{s} \sqrt{\pi}} \rho_{s} \alpha_{s}^2 \Theta_{s}^{3/2} (23.4-23)

The transfer of the kinetic energy of random fluctuations in particle velocity from the $s^{\rm th}$ solids phase to the $l^{\rm th}$ fluid or solid phase is represented by $\phi_{ls}$ [ 121]:

 \phi_{ls} = - 3 K_{ls} \Theta_s (23.4-24)

FLUENT allows you to solve for the granular temperature with the following options:

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