Momentum conservation equation, for

From the momentum conservation equation for the normal flow velocity... 

When considering ordinary diffusion only, the momentum conservation equation for the species i in a multicomponent system can be written as [17]... 

The -component momentum conservation equation for laminar flows is... 

The original VOF model designed for free surface flow simulations constitutes the mass and momentum conservation equations for incompressible fluids in the jump condition form [155, 108[. 

The momentum conservation equation for the cylindrical fluid tube is ... 

The interfacial momentum exchange terms in the momentum conservation equations for each phase consist of drag and virtual mass force terms. The drag force for gas and liquid is modeled, respectively, as... 

Before studying multiple bubble interactions, we must understand the behavior of a single bubble in response to acceleration of the surrounding continuous liquid. Neglecting surface tension effects andp turbulent fluctuations smaller than the scale of the bubble, and assuming incompressible adiabatic flow, Stewart and Crowe [20] derived the averaged momentum conservation equations for dispersed bubbles and the surrounding continuous liquid [20]. These can be expressed, respectively, by ... 

The analysis presented in Chapter 8 was solely in terms of the conservation equations for the particle phase of a fluidized suspension. However, the full one-dimensional description is in terms of the coupled mass and momentum conservation equations for both the particle and fluid phases eqns (8.21)-(8.24). These equations correspond to those derived in Chapter 7, except for the inclusion of the particle-phase elasticity term on the extreme right of eqn (8.22). 

The geometry and mesh arrangement in the fluid region are exactly the same as those of the steady-state subchannel analysis code. Figure 6.60 shows the entire algorithm. The momentum conservation equations for three directions and a mass conservation equation are solved with the Simplified Marker And Cell (SMAC) method [32]. In the SMAC method, a temporary velocity field is calculated, the Poison equation is solved, and then the velocity and pressure fields are calculated as shown in Fig. 6.61. The Successive Over-Relaxation (SOR) method is used to solve a matrix. 

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