CFD-FLUENT-Multiphase-Eulerian-Model

In the Euler-Euler approach, the different phases are treated mathematically as interpenetrating continua. The concept of phasic volume fraction is introduced. In Fluent 6.1, three different Euler-Euler multiphase models are available: the volume of fluid model, the mixture model, and the Eulerian model.

The Eulerian model solves a set of n energy, momentum and continuity equations for each phase. Coupling is achieved through the pressure and interphase exchange coefficients. Particle tracking (using the Lagrangian dispersed phase model) interacts only with the primary phase. Compressible flow and species transport and reactions are not allowed when using the FLUENT 6.1 Eulerian model [more about the limitation of Eulerian model].

The equations being solved in the Eulerian model are as follows:
1. Continuity equation (void fraction equation) for the q-th phase from total of n phases
2. Momentum equation for the q-the phase
3. Conservation of energy of the qth phase

1. Continuity equation (void fraction equation) for the q-th phase from total of n phases
Properties of Continuity equation:
- the volume fraction of the q-th phase,
- the mass transfer from the p-th to q-th phase.
A similar term appears also in the momentum and enthalpy equations.
The term is zero by default, but can be specified either as a constant, or by a user-defined function (UDF).

2. Momentum equation for the q-the phase
Properties of Continuity equation:
- the qth phase stress-strain tensor equation
- the interphase momentum exchange coefficient (expressed in symmetric form)
- f=CD*Re/24 (Re=Reynold number)
- CD is the drag coefficient or drag factor
# for Re>1000, the drag factor = 0.44
# for other values of Re, the drag factor = (24/Re)*(1+0.15Re^0.687)
- Relative Reynolds number for primary phase, q and secondary phase, p.
- Relative Reynolds number for secondary phase, p and r.
- viscosity of a mixture of phases p and r,
- the diameter of droplets or bubbles of the phase p,
- the diameter of droplets or bubbles of the phase p and r,

- the interphase momentum exchange coefficient (expressed in General form equations(FLUENT)) include:
# a drag function,
# a “particulate relaxation time”,
# an external body force,
# a lift force, and
# a virtual mass force.

3. Conservation of energy of the qth phase
Properties of Conservation of Energy:
- the specific enthalpy of the qth phase
- the heat flux
- a source term that includes sources of enthalpy (e.g. chemical reaction or radiation)
- the intensity of heat exchange between the p-th and q-th phases
- the interphase enthalpy (e.g. the enthalpy of the vapour at the temperature of the droplets, in the case of evaporation).
- The heat transfer coefficient between the p-th and q-th phases is related to the p-th
phase Nusselt number
- the Nusselt number for fluid-fluid multiphase is determined from the Ranz and
Marshall (1952, 1952a) correlation: Nup = 2.0 + 0.6*Rep^(1/2)*Pr^(1/3)
- the q-th phase Prandtl number