To create the most cost-effective package, i.e. one that uses the least possible materials to deliver the highest standards of quality and hygiene, Tetra Pak must achieve the optimum balance between package width, weight and strength. “Complete control over the process is paramount,” said Dr. Mattias Olsson, manager, Virtual Engineering at Tetra Pak. “It requires an in-depth knowledge of the loads and forces involved – both liquid and material.”

The packaging production process poses tremendous engineering challenges. A continuous reel of carton-based packing material – a mainly paper composite strengthened with ultra-thin layers of plastic and aluminum – is fed into a filling machine and sterilized. The material is formed and sealed longitudinally into a tube and filled, causing it to expand. It is then formed into shape and sealed transversely to keep it sterile. Finally, it is cut into the individual packages we recognize on our shop shelves.

“Gravity is driving the liquid down,” Olsson said, “but the folding and the tube deformation are forcing it backward.” A pressure flange (a flat disk with small holes in it) reduces the amount of backflow, but the tube is still subject to deformation under folding and changes in fluid pressure, and it needs to retain its structural integrity without breaking or crimping.

Olsson explained, “The folding and forming of the package are critical. In the past, these have been difficult to predict. What we needed, was a realistic, reliable simulation method that took into account the liquid, the packaging material, and all the major forces acting – and interacting – on them.”

Tetra Pak worked with Abaqus finite element analysis (FEA) software, from Dassault Systèmes’ SIMULIA subsidiary. While Tetra Pak had used Abaqus before, this would be the first time they were to explore the dynamics of the fluid-structure interaction during packaging. 

The engineers analyzed the Tetra Fino Aseptic 500 ml, TFA 500s milk package. “We already had a strong knowledge of production parameters for this application,” Olsson says. 

The packaging material was very thin and flexible, which made for large deformations under pressure changes. The cross-section of the tube rapidly changed from circular to fully closed when folded. Importantly, there was a strong fluid-structure interaction to be modeled that had to take into account the changing pressure waves in the fluid and their effects on the packaging material.

The model for analysis included the composite, packaging, the packaged fluid, the flotation device resting on top of the fluid surface, the packaging folding system, and the pressure flange.

Structural items were modeled in a ‘Lagrangian’ framework, a commonly used method of simplifying the application of forces to objects and quantifying their reactions. The fluid was modeled using a ‘Eulerian’ approach that accurately captures the characteristics of non-viscous fluid flow. This allowed Tetra Pak’s engineers to model the interaction of the packaging tube and the fluid in a single analysis. Abaqus’ strong contact and non-linear capabilities were also essential to the simulation.

The engineers were able to model and define a variety of design parameters:
* Sequencing the folding system action, including any deformation 
* Determining the suitability of the packaging material
* Establishing the correlation between fluid injection rate and formed packaging volume
* Defining the tensile load applied to the material so as to prevent breakage or crimping 

Dr. Anders Magnusson, Technology Specialist at TetraPak says, “In the end, we were able to simulate all the important forces of the process.”

Tetra Pak demonstrated that including the interaction of the fluid and the packaging in the simulation is imperative in order to calculate the degree of package deformation during filling and sealing. “Originally it was believed that modeling the role of the pressure flange would be difficult using our combined methodology, since physical tests had demonstrated turbulence effects,” Olsson observes. 

“But our Abaqus analyses, with and without the flange, proved that this method could capture the fluid behavior well.” 
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