The granular temperature for the solids phase is proportional to the kinetic energy of the random motion of the particles. The transport equation derived from kinetic theory takes the form [ 81]
|=||the generation of energy by the solid stress tensor|
|=||the diffusion of energy ( is the diffusion coefficient)|
|=||the collisional dissipation of energy|
|=||the energy exchange between the|
|fluid or solid phase and the solid phase|
Equation 23.5-75 contains the term describing the diffusive flux of granular energy. When the default Syamlal et al. model [ 364] is used, the diffusion coefficient for granular energy, is given by
FLUENT uses the following expression if the optional model of Gidaspow et al. [ 121] is enabled:
The collisional dissipation of energy, , represents the rate of energy dissipation within the solids phase due to collisions between particles. This term is represented by the expression derived by Lun et al. [ 222]
The transfer of the kinetic energy of random fluctuations in particle velocity from the solids phase to the fluid or solid phase is represented by [ 121]:
FLUENT allows the user to solve for the granular temperature with the following options:
This is given by Equation 23.5-75 and it is allowed to choose different options for it properties.
This is useful in very dense situations where the random fluctuations are small.
For a granular phase
, we may write the shear force at the wall in the following form:
The general boundary condition for granular temperature at the wall takes the form [ 166]