Explicit Sweep Distribution Simulations

To explicitly calculate the shell and lumen flow distributions, the shell-side and Inmen-side spaces are treated as bi-continuous porous media. Volume averaging the conservation 

For low Reynolds number flows, volume average of the conservation of mass equations yields Darcy s law as the relationship between superficial velocity and pressure  

The steady-state volume average conservation of mass equation for component i is given by Equation (16.16) 

Summing Equation (16.16) over all of the components yields the continuity equation for the porous media. 

The shell and lumen velocity fields are obtained by substituting Darcy s law. Equation (16.15) for the velocity and applying appropriate boundary conditions. An appropriate equation of state also is required to calculate density from pressure. The ideal gas law is used for the relatively low pressure dehydration process considered here. 

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The explicit sweep distribution simulations were performed with increasingly refined meshes until the results did not change by more than 5%. Typical meshes contained 5000 elements. 

This work reports simulations of sweep distribution within the shell and its effect on module performance. Two types of simulations are considered (1) simulations that assume the sweep flow around each fibre is distributed in a Gaussian manner and (2) simulations that explicitly predict flow fields within the shell based on how the sweep gas is introduced. 

Figure 16.2 Boundary conditions used in explicit simulations of sweep distribution to evaluate module performance (a) lumen-side boundary conditions and (b) shell-side boundary conditions. Note that the boundary conditions for the shell correspond to one of the configurations used to simulate shell flows. Similar boundary conditions apply for the others. The shell extensions allow establishment of uniform velocity and concentration fields as described previously 124 ...

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