Use of Computational Fluid Dynamics for improving freeze-dryers design and process understanding. Part 2: Condenser duct and valve modelling

This manuscript shows how computational models, mainly based on Computational Fluid Dynamics (CFD), can be used to simulate different parts of an industrial freeze-drying equipment and to properly design them; in particular in this part the duct connecting the chamber with the condenser, with its valves, is considered, while the chamber design and its effect on drying kinetics have been investigated in Part 1. Such an approach allows a much deeper process understanding and assessment of the critical aspects of lyophilisation. This methodology will be demonstrated on freeze-drying equipment of different sizes, investigating influence of valve type (butterfly and mushroom) and shape on duct conductance and critical flow conditions. The role of the inlet and boundary conditions considered has been assessed, also by modelling the whole apparatus including chamber and condenser, and the influence of the duct diameter has been discussed; the results show a little dependence of the relationship between critical mass flux and chamber pressure on the duct size. Results concerning the fluid dynamics of a simple disk valve, a profiled butterfly valve and a mushroom valve installed in a medium size horizontal condenser are presented. Also in these cases the maximum allowable flow when sonic flow conditions are reached can be described by a correlation similar to that found valid for empty ducts; for the mushroom valve the parameters are dependent on the valve opening length. The possibility to use the equivalent length concept, and to extend the validity of the results obtained for empty ducts will be also discussed. Finally the presence of the inert gas modifies the conductance of the duct, reducing the maximum flow rate of water that can be removed through it before the flow is choked; this also requires a proper over-sizing of the duct (or duct-butterfly valve system).