System 1 Flow Dynamics of Gas-Liquid-Solid Fluidized Beds

System 1 Flow Dynamics of Gas-Liquid-Solid Fluidized Beds 

The level-set technique described in Section II.A is employed to capture the motion of 3-D gas liquid interfaces. The numerical procedures for solving the gas-liquid interface include finding the solution for the time-dependent Eqs. (3), (5), and (6). Given r/jnand Fndefined at cell centers at one time instant tn, fin+, and Vn i i can be solved over a time increment at a new time instant tn+i — tn + At following the procedures given below  

Solve Eqs. (5) and (6) to obtain the velocity distribution in the flow field Vn+1 using the Arbitrary-Lagrangian-Eulerian (ALE) scheme (Kashiwa et al., 1994). 

Solve Eq. (3) to obtain / B+1 using the second-order TVD-Runge-Kutta method presented as follows  

Although, in principle, Eq. (12) would not alter the location of the zero-level set of 4 , in practice, with numerical computation it may not be true. A redistance operation is needed to maintain the volume conservation. Therefore, Eq. (12) is modified to (Sussman et al., 1998)  

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