Table 1: Summary of governing and constitutive equations for Eulerian approach.

Gas-solid Eulerian flow model

Governing equations

Continuity equations:
 Gas-phase: (A)
 Solid-phase: (B)
Momentum equations:
 Gas-phase:
(C)
 Solid-phase:
(D)
Energy equations:
 Gas-phase:
(E)
 Solid-phase: (F)
Species conservation: (G)
Reynolds stresses:
(H)

Constitutive equations

Gas-solid momentum exchange 
(Gidaspow drag model):
 when , (I)
 when , (J)
  for , (K)
  for , (L)
Gas-solid heat exchange: (M)
Kinetic theory of granular flow:
 Solids pressure: (N)
 Radial distribution: (O)
 Granular temperature: (P)
   where, (Q)
(R)
(S)
(T)