Choked flow and importance of Mach I in freeze-drying process design

Occasionally the freeze drying cycle conditions are developed on a small scale dryer that result in a water vapor flux during primary drying that the full-scale equipment cannot handle, resulting in loss of the ability to control chamber pressure. A primary cause of loss of pressure control is a phenomenon commonly described as “choked flow”, where the required mass transfer through the duct connecting the drying and condenser chamber cannot be maintained at the control pressure. Water vapor flow rate increases as the condenser pressure decreases, but it can continue to do so only until the velocity of water vapor reaches speed of sound (i.e., Mach I) at the duct exit. The flow is then said to be choked, and any further increase in water vapor flow rate results in an increase in chamber pressure (i.e., loss in chamber pressure control). Sublimation tests were carried out in Lyostar II freeze-dryer (SP Industries, NY) to predict the occurrence of choked flow. A capacitance manometer was installed in the “condenser chamber” and differential pressure (Pc−Pcd) was measured as a function of sublimation rate (Pc=chamber pressure and Pcd=condenser pressure). Water vapor flow rate was measured by Tunable Diode Laser Absorption Spectroscopy (TDLAS) methodology, with a check by gravimetric data. Flow of water vapor in the duct connecting chamber and the condenser was modeled using computational fluid dynamics software (Fluent 6.3). The critical pressure ratio (K⁎=Pc/Pcd) has been identified as an important variable that determines the onset of choked flow during primary drying. This ratio can be calculated given the mass flux. For our freeze-dryer, K* greater than 2.5 (for Pc<150 mTorr) resulted in choked flow. The gas velocity indeed reaches Mach I limit at the duct exit under the choked flow conditions, as modeled by Fluent. Using the differential pressure measurements, the throat connecting the chamber and the condenser can be used as an “in process” mass flow meter to measure sublimation rate under non-choked flow conditions during primary drying without interrupting the process. Also, TDLAS is a useful tool for determination of sublimation rate even at very high mass flux.