Application of Constrained Optimization Techniques in Optimal Shape Design of a Freezer to Dosing Line Splitter for Ice
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Application of Constrained Optimization Techniques in Optimal Shape Design of a Freezer to Dosing Line Splitter for Ice Cream Production Fabrizio Sarghini1 · Angela De Vivo1 Received: 27 January 2020 / Accepted: 18 September 2020 © The Author(s) 2020
Abstract Design of multiple branches splitting of equal mass flow rate in complex rheological flows like ice cream near melting point temperature can be a challenging task. Pulsations in flow rate due to air pumping process and small fluctuations in temperature affecting flow rheology can determine a consistent difference in internal pipe velocity distribution, resulting in a significant difference in the distribution of ice cream dosage. Computational sciences and engineering techniques have allowed a major change in the way products and equipment can be engineered, as a computational model simulating physical processes can be more easily obtained, rather than making prototypes and performing multiple experiments. Among such techniques, optimal shape design (OSD) represents an interesting approach. In OSD, the essential element with respect to classical numerical simulations in fixed geometrical configurations relays on the introduction a certain amount of geometrical degrees of freedom as a part of the unknowns. This implies that the geometry is not completely defined, but part of it is allowed to move dynamically in order to minimize or maximize an objective function. From a mathematical point of view, OSD is a branch of differentiable optimization and more precisely the application of optimal control for distributed systems. OSD is still today numerically difficult to implement, because it relies on a computer intensive activity and moreover because the concept of “optimal” is a compromise between shapes that are good with respect to several criteria. In this work, the applications of a multivariate constrained optimization algorithm is proposed in the case of a mechanical ice cream 1 to 5 splitting system, required to distribute in an evenly way from one freezer into five dosing valves. Results allowed to design a retro-fitting system on an existing production plant reducing the dosing error down to 3% on the average. Keywords Optimal shape design · Constrained optimization · Ice cream production · Modeling and simulation
Introduction Mass flow rate splitter design in complex rheological flows like ice cream near melting point temperature can be a challenging task. Pulsations in mass flow rate, due to air/ frozen mixture pumping process and small fluctuations in temperature, strongly affect the flow rheology, and they can determine a consistent nonuniformity in final dosing valves, resulting in a significant difference in the distribution of the dosage. Moreover, shortcuts in piping design like the adoption of fully symmetric 3D configurations cannot be easily arranged in existing pilot plants, for example, because an odd number of dosing valves or a direction change in * Fabrizio Sarghini [email protected] 1
Department of Agricultural Sciences,
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