Learning Forum

[KeFon]

Good Morning,

I have a two rather theoretical questions concerning the equations solved using the Multiphase Eulerian model in Fluent.

Ansys Fluent Theory Guide gives us equation 14-181 (section 14.5.4.2.2.)

When using a turbulence model such as the k - ω SST model, the momentum equation becomes a time averaged of the original equation in which quantities (velocities, pressure) are decomposed into a time - averaged component and a fluctuation component. The result of such a treatment for a single phase is given in Equation 4.4 (section 4.1.1). For a two-phase flow, however, another quantity is introduced, which is the mass transferred from one fluid to the other (in kg/s). I would assume that this quantity is also decomposed into its time-averaged component and fluctuation component. Therefore, if we denote the time averaged components using an upper-case letter and the fluctuations components using italics, the term

m_pq*v_pq should become (M_pq+m_pq)(V_pq+v_pq) which yields, after taking the time averaged, to:

M_pq*V_pq + time_average(m_pq*v_pq)

(the same applies to m_qp*v_qp)

As m_pq and v_pq are unknown, how does Fluent solve this ? Or is the term m_pq not decomposed at all?

My second question concerns the phase stress-strain tensor described in equation 14-177 (Section 14.5.4.1.2) Indeed, the tensor uses the bulk viscosity which is only defined in the theory guide for solids. In case of fluids, am I right to assume that the Stokes' hypothesis is taken and therefore, the bulk viscosity λ_q is 0? (Although I guess this should not matter on my current case as it is an incompressible flow and the divergence of the velocity should give 0 so the term with the bulk viscosity should become 0 as well but I would like to understand anyway.)

Thank you very much for your time and answers .

[Surya Deb]

Hello,
If I understand correctly, then the contributions due to mass transfer are added as source terms to the continuity and momentum equations, respectively. They are not filtered in that case. The relative velocity V_pq or V_qp is simply the difference between the phase velocities like Vp - Vq. Vp and Vq already get decomposed from the momentum equations.
Regards SD

[KeFon]

I see,
Thank you very much for your answer.
Regards FK