PHARMABIO TRANSPORT: Bringing Cold Chain Shippers to Market Faster with Thermal Modeling
FEA container design promotes savings.
Cold Chain Technologies Inc.
Figure 1. Creating a GTS-5420 model helped determine the relative contribution of conduction (heat transfer via solid) versus convection (heat transfer via flow over solid body) in the shipperï¿½s design over a period of nine hours, through a symmetric, ï¿½-size model, shown at right.
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Predictive, or mathematical, modeling is the process whereby a set of mathematical relationships (the model) represents a real-life system based on certain approximations and assumptions. Finite Element Analysis (FEA) is one well-suited method of predictive modeling for complex modeling tasks requiring high accuracy.
Using FEA, container developers can simulate many possibilities to arrive at an optimal design for testing. This efficient development process saves time and money by avoiding the need to build and test multiple packages.
Normally a commercial computer program is used, whereby the user passes through a number of required steps before program execution, including analysis selection, geometry creation, element selection, and boundary condition application. Geometry meshing is performed, by which the solid geometry is divided into discrete (finite) volumes, also called “elements.”
Differential equations are linearized to allow solution with applied boundary conditions. As a result, more (and smaller) elements allow increased accuracy (at the expense of increased computing time). Care must be exercised to use the correct elements and boundary conditions for a given problem. However, a well-meshed, continuous geometry with the correct element type and realistic boundary conditions will allow for very accurate solutions.
Figure 2. This figure compares actual test data over 10 hours, versus a simulation. Although not shown, similar results were seen on the top layer of the product load. Overall, the model was validated at the center of the payload.
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For modeling Cold Chain Technologies’ (CCT) KoolTemp GTS-5420 universal pallet shipper using FEA, the relative contribution of conduction (heat transfer via solid) versus convection (heat transfer via flow over solid body) in the shipper’s design were examined.
The GTS-5420 pallet shipper is designed to hold a 2º to 8ºC payload temperature over 120 hours for both winter and summer ambient air temperature profiles. The shipper sits on a 70 × 60-in. pallet and accepts a payload of dimensions 48 × 40 × 33.25 in. Temperature is passively controlled by frozen (–20ºC) and liquid (5ºC) preconditioned Koolit refrigerant sleeves in combination with molded polyurethane (PUR) foam-corrugate container walls.
In a first pass analysis, the shipper was modeled via conduction heat transfer alone, to isolate the impact of conduction on the system. Although this shipper is also designed to use convection as a means of controlling payload temperature profile, initial (chamber) test data results for convection could not easily be categorized. By modeling thermal transfer in the GTS-5420 using conduction, it was anticipated that the root cause of convection data anomalies could be identified. Specifically, the model results from conductive heat transfer were compared to actual thermal test data. This allowed corresponding conclusions to be made about convection performance.
All mathematical models are idealizations to some degree, and place certain limitations on the validity of the solution. For the model to be useful, all approximations and assumptions must be stated along with the results.
The geometry of the shipper was constructed using the actual components, which were generated via solid modeling software (SolidWorks). For each part, the thermal properties—such as density, specific heat, and thermal conductivity—were input into the FEA program and assumed to be constant with both direction and temperature. Once the type of element was selected, the geometry was inspected and corrected to eliminate any interferences and/or discontinuities between parts. The majority of the geometry was meshed using solid elements with a constant global feature size, although some localized meshing was utilized for smaller and thinner parts. Only conduction heat transfer was modeled for the initial analysis; all air gaps were modeled as solids without the possibility of convection.
As we are most interested in temperature of the payload over time, the type of analysis run was selected as a 3-D transient thermal model [T = T(x,y,z,t)], with a predetermined ambient temperature profile. The transient model was run for 120 hours with 40 time steps. The results were used to validate and further compound the model.
Comparison of the simulation results and actual test data at the bottom layer of the product load showed that the bottom corner point temperatures were not the same (ranging from 2.5º to 3ºC). Also, one of the bottom corner thermocouples started increasing significantly at 7.5 hours into the test (without any ambient temperature changes).
Overall, the model was validated for conduction at the center of the payload. The differences in test data versus simulation results allowed CCT to draw several conclusions:
- Using a ¼ model (¼ of the symmetrical package), and simulating conduction only, does not accurately simulate test chamber data.
- As expected, conduction is clearly not the only method of thermal transfer in the 5420.
- The effects of internal convection must be taken into account in the 5420 design.
Given that CCT only had to run the actual test for less than one day to reach the above conclusions, we saved four days (80%) in test time in the chamber, with a corresponding amount of labor hours. This freed up the chamber for customer product testing. In the meantime, the team compounded the model by modifying the shipper design and preparing another set of tests to account for the convective effect.
Recent test results have shown that, with the given ambient temperature profile, the modified design is now able to pass both summer and winter profiles at maximum/minimum payload by holding 2º to 8ºC for 120 hours. This passing solution was demonstrated on the next iteration, where previous attempts had been unsuccessful. In total, it is estimated that predictive modeling on the GTS-5420 has saved at least 35% of total development time, allowing the product to be launched faster and for less money, saving three months and $60,000. Other cold chain supply providers are using these types of tools as well. Certainly, this simple case study shows that predictive modeling can save both time and money, with the overall result of reaching the market faster.
Cold Chain Technologies (CCT), headquartered in Holliston, MA, offers a global one-stop source for the design, qualification, R&D, and manufacture of cold chain shipping containers.