Momentum source terms

Typically, the interface obtained with the versions of the VOF method described above is smeared over a few grid cells, which, on sufficiently fine grids, allows one to identify uniquely the simply connected volumes belonging to the different phases. Instead of regarding the dynamic conditions of Eqs. (132)-(134) as boundary conditions, surface tension can be implemented as a volume force in those cells where c lies between 0 and 1. In the method developed by Brackbill et al. [176], a momentum source term of the form... 

The diffusion of the gaseous species in the porous electrodes is considered by specifying the molecular diffusivity for each specimen and specifying the momentum source term in a linearized form. The calculation for the diffusion of the gaseous species in porous electrodes is reported in details in Chapter 3. 

The porous media model (8) is used to simulate flows through the biomass in a packed bed where biomass is the porous media. In this model, a momentum source term S, is added to the standard fluid flow equation ... 

Mti Momentum source term due to interaction between phase k and phase /,... 

These cases would suggest that the best averaged velocity to use depends on which internal coordinates are held constant. However, because conservation of momentum is of fundamental importance, it is always best to use the mass-average velocity in Eq. (4.85). For this reason, Eq. (4.85) should always be included in the set of moment-transport equations used to model the disperse phase. The disperse-phase momentum source terms appearing on the right-hand side of Eq. (4.85) are defined as follows. The first term. 

As in many other areas of CFD, advances in impeller treatment are occurring rapidly, both in developing new treatments and in making the established treatments more accurate and more efficient computationally. For example, Derksen and Van den Akker (1999) have applied an adaptive force field technique in a model of Rushton turbine flow. VanderHeyden et al. (private communication) at Los Alamos have developed a technique of switching a momentum source term at certain mesh node points on and off in a pattern that simulates the effect of a rotating impeller. These and other approaches promise increased fidelity with greater computational efficiency. 

In this equation, Sf is the the momentum source term, which can be obtained by the following equation. That is ... 

In this equation, is the coefficient of linear impedance and is the coefficient of secondary impedance contains other momentum source term U, U are aU apparent velocity. 

The last term may be regarded as a momentum source term S and can be decomposed into several contributions according to Eq. (2.32)... 

Neglecting the second part, the momentum source term Eq. (4.356) becomes ... 

In the CFD modelling of membrane filtration process, membranes are usually modelled as a porous wall while the flow within a membrane is usually solved using both Navier-Stokes and Darqr equations (Ghidossi et al, 2006). A porous media model is widely used for determining the pressure loss during flow through packed beds, filter papers, perforated plates, flow distributors and tube banks (ANSYS, 2010). A momentum source term is added to the governing momentum equations, which creates a pressure drop that is proportional to the fluid velocity ... 

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