CFD modelling of condensers for freeze-drying processes

Abstract

The aim of the present research is the development of a computational tool for investigating condensation processes and equipment with particular attention to freeze-dryers. These condensers in fact are usually operated at very low pressures, making it difficult to experimentally acquire quantitative knowledge of all the variables involved. Mathematical modelling and CFD (Computational Fluid Dynamics) simulations are used here to achieve a better comprehension of the flow dynamics and of the process of ice condensation and deposition in the condenser, in order to evaluate condenser efficiency and gain deeper insights of the process to be used for the improvement of its design. Both a complete laboratory-scale freeze-drying apparatus and an industrial-scale condenser have been investigated in this work, modelling the process of water vapour deposition. Different operating conditions have been considered and the influence exerted by the inert gas as well as other parameters has been investigated.

Appendices

Nomenclature

J _i :

diffusive flux of the generic chemical species i, kg m⁻² s⁻¹

k :

kinetic constant of water deposition process, m s⁻¹

Kn :

Knudsen number,-

L :

characteristic length scale of the system, m

n :

normal versor to wall surface

R _s,w :

rate of water deposition process, kg m⁻² s⁻¹

t :

time, s

T :

temperature of the gas, K

T _c :

temperature of the gas in the centre of the computational cell close to the wall, K

T _g :

temperature of the gas near the wall, K

T _w :

temperature of the wall, K

U :

gas velocity vector, ms⁻¹

U _c,p :

component parallel to the wall of the velocity of the gas in the centre of the computational cell close to the wall, ms⁻¹

U _g,n :

component normal to the wall of the velocity of the gas near the wall, ms⁻¹

U _g,p :

component parallel to the wall of the velocity of the gas near the wall, ms⁻¹

U _p :

component parallel to the wall of the gas velocity, ms⁻¹

$U_{\textit{w},n}$ :

component normal to the wall of the wall velocity , ms⁻¹

$U_{\textit{w},p}$ :

component parallel to the wall of the wall velocity, ms⁻¹

v_z :

axial velocity component, ms⁻¹

Y _i :

mass fraction of the generic chemical species i, -

$Y_{\textit{w}}$ :

water mass fraction, -

Greek Symbols

α _T :

thermal accomodation coefficient of the gas mixture, -

α _v :

momentum accomodation coefficient of the gas mixture, -

δ :

distance of the cell centre from the wall, m

λ :

mean free path of the gas molecules, m

ρ :

fluid density, kg m^− 3