Application of Constrained Optimization Techniques in Optimal Shape Design of a Freezer to Dosing Line Splitter for Ice Cream Production

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.

Measurement of Magnetic Field Properties of a 3.0 T/m Air-Core HTS Quadrupole Magnet and Optimal Shape Design to Increase the Critical Current Reduced by the Incident Magnetic Field

Air-core high-temperature superconducting quadrupole magnets (AHQMs) differ from conventional iron-core quadrupole magnets, in that their iron cores are removed, and instead high-temperature superconductors (HTSs) are applied. The high operating temperature and high thermal stability of HTS magnets can improve their thermodynamic cooling efficiency. Thus, HTS magnets are more suitable than low temperature superconducting magnets for withstanding radiation and high heat loads in the hot cells of accelerators. AHQMs are advantageous because they are compact, light, and free from the hysteresis of ferromagnetic materials, due to the removal of the iron-core. To verify the feasibility of the use of AHQMs, we designed and fabricated a 3.0 T/m AHQM. The magnetic field properties of the fabricated AHQM were evaluated. Additionally, the characteristics of the air-core model and iron-core model of 9.0 T/m were compared in the scale for practical operation. In comparison with the iron-core model, AHQM significantly reduces the critical current (IC) due to the strong magnetic field inside the coil. In this study, a method for the accurate calculation of IC is introduced, and the calculated results are compared with measured results. Furthermore, the optimal shape design of the AHQM to increase the critical current is introduced.