Reduced models for the packaging industry

Model reduction techniques based on either geometrical multi-scale modeling (coupling of differential models operating at different spatial dimensions) or reduced order modeling (e.g. Proper Orthogonal Decomposition or Reduced Basis) have proved very successful for the simulation of complex integrated systems, such as the human cardiovascular system.

The long-lasting experience at MOX in such type of modeling has been exploited during the past few years in a new industrial context, in the framework of an industrial collaboration with MOXOFF s.p.a. (Spinoff of Politecnico di Milano) and a world-leading company in the packaging of liquid food.

The packages are assembled by collapsing a papertube which, at the same time, is filled by the liquid product in a very fast and complex process. The design and control of this system, which has to be carried out in an aseptic environment at very high speed (up to 50000 packages per hours), is extremely difficult. In order to simulate the propagation of pressure waves through the liquid-filled carton tube produced by the tube collapse, a set of reduced geometrical multi-scale fluid-structure interaction models have been developed. Each component of the system has been described by a reduced (either 0D or 1D) model and the different models have been integrated in the control system which governs the process.

Sketch of the coupled reduced FSI models for two filling systems

 

Other reduction strategies are currently being explored in order to obtain fast and reliable simulations of the complex 3D fluid-dynamics in some specific part of the system (such as the counter pressure flange). To this end a reduced order model based on the POD approach has been developed that will allows efficient parametric analysis in the design process.

Pressure field across the counter pressure flange: high fidelity FEM solution (left), reduced order POD solution (middle) and absolute error (right)

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