Toward a more perfect freeze-dryer: DSMC simulations of vapor flow and ice dynamics
Arnab Ganguly, Alina Alexeenko, Frank De Marco, Steven Nail
Background and Motivation
Freeze-drying is a low-pressure, low-temperature condensation pumping process used in the manufacture of biological and pharmaceutical products. Freeze-drying is run as a batch process and is both, time and energy intensive. It involves a 3-stage process initiated by freezing (stage A-B), then reducing pressure below the triple point (stage B-C). Heat is then provided for sublimation of the ice in the primary drying (stage C-D). Performance of a freeze-dryer is governed by the vapor and ice dynamics in the low-pressure environment. One of the most important physical processes relevant to the freezedryer design is the formation of ice on the condensing surfaces during the drying stage. A development cycle in a lab-scale freeze-dryer with 100 vials, drying at 0.5 g/hr, leads to the formation of 3.6 kg of ice. If the ice build-up is assumed to be uniform on the coils of the Lyostar condenser, a layer of ice about 1 cm thick is formed. In reality, the coils at the center receive much more ice than those at the periphery. The non-uniform ice growth hinders the vapor trapping capability of the condenser. Understanding and controlling the ice build-up is needed for improved freezedrying systems.
• To develop a comprehensive modeling framework for physics-based modeling of vapor flow and ice dynamics in freeze-drying.
• To compare the model predictions with experimental measurements of freeze-dryer performance for laboratory and production scale.
• To determine the critical design parameters for more efficient freeze-dryer systems and processes.
Numerical Simulations: Direct Simulation Monte Carlo (DSMC) techniques are applied to model the relevant physical processes accompanying low pressure vapor flow in the condenser chamber. Low-temperature water vapor molecular model is used in the DSMC solver SMILE to simulate the flowfield structure. One of the most important physical processes relevant to condenser design is the ice accretion on condensing coils. The developing ice front is tracked based on the mass flux computed at the nodes of the DSMC surface mesh. Experimental Measurements: Ice accretion measurements in laboratory and industrial scale dryer under various loads and cycle parameters.
Effect of the Duct on Non-Uniformity
Simulation Parameters for Lyostar II: Mass Flow rate: 5 g/ hr, Pure water-vapor, reservoir wall temperature: 273 K, surface mesh: 26,654 panels, sticking coefficient of 1 for coils. A uniform velocity was set at the jet source. In case 1 (no duct), setting a uniform velocity profile generates a wider spread in the vapor path. Comparing this to the vapor path taken up in case 2 (with duct), the flux on the second coil away from the duct has a significantly lower flux compared to case 1. While the ratio of the mass flux on the coil nearest to the duct exit to that on the next coil was 1.45 for case 1, it was 2.4 for case 2. Thus, the presence of a duct between the product chamber and condenser increases non-uniformity by 65% at a sublimation rate of 5 g/hr.
Effect of Non-Condensable Gas
Simulation Parameters: Mass Flow rate: 160 g/hr, Multi Species: Water vapor and Nitrogen, reservoir wall temperature: 273 K, Sticking Coefficient of coils: 1 for water-vapor and 0 for N2 , Duct pressure: 120m Torr, Condenser Pressure, 70 mTorr. A typical freeze-drying process is characterized by the presence of both, non-condensable gases in the form of nitrogen or air and condensable water-vapor in the chamber and condenser. The condenser chamber was filled with N2 molecules until the pressure in the chamber reached 70 mTorr. The N2 supply was then stopped and the jet of water-vapor was introduced. The mass flux contours in the condenser chamber are shown in Fig. 6. The flux of vapor is highest on the first coil closest to the duct exit. The flux reduces as we move away from the exit along the same coil or onto the successive coils. Figure 7 shows contours of water vapor fraction in the condenser chamber. It illustrates the importance of the presence of non-condensable gas in the chamber. The presence of the non-condensable gas increases the resistance in the chamber. Thus, as the watervapor enters the condenser chamber, it creates a narrow pocket around the duct exit where the water-vapor number density is highest and decreases away from it.
Tracking Ice Growth
Simulation Parameters: Mass Flow rate: 55 g/hr, Chamber Pressure: 115 mTorr, Condenser Pressure: 70 mTorr, Total drying period: 24 hours Figure 8 presents the non-uniform ice accumulated on the coils over a period of 24 hours. The coils close to the duct exit have a maximum ice accumulation of 3.2 cm while that on the coil farthest away from the duct, drops to a mere 4 mm. The non-uniform ice growth can lead to a significant drop in the vapor trapping capability of the condenser. The predicted icing rates are compared with experimental measurements using time-lapse imaging under typical laboratory drying cycle conditions.
Figure 3: Photograph of the non-uniform ice-buildup: Mass Flow rate: 55 g/hr, Chamber Pressure: 120 mTorr, Condenser Pressure: 70 mTorr, Total drying period: 1hour (left) and 24 hours (right), resulting in 1.1 mm growth rate per hour.
Factors that affect the non-uniformity of mass flux and ice-growth are investigated here. The DSMC simulations reveal that for a typical laboratory scale freeze-dryer, the presence of a duct between the product chamber and condenser increases non-uniformity by 65% at a sublimation rate of 5 g/hr. The presence of non-condensable gases also significantly impacts the non-uniformity in the condenser by reducing the partial pressure of water vapor and increasing the condenser resistance. This leads to a preferential build-up of ice on the coils close to the duct exit.
The financial support from Baxter BioPharma, IMA Life, NSF(CBET/GOALI-0829047) and from Purdue’s Center for Advanced Manufacturing is gratefully acknowledged.