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Nasibullayev I.Sh. Two-Dimensional numerical parametric modeling of the capillary microgripper cooling system with unsteady fluid flow. Multiphase Systems. 17 (2022) 3–4. 153–166 (in Russian).
2022. Vol. 17. Issue 3–4, Pp. 153–166
URL: http://mfs.uimech.org/mfs2022.3.014,en
DOI: 10.21662/mfs2022.3.014
Two-Dimensional numerical parametric modeling of the capillary microgripper cooling system with unsteady fluid flow
Nasibullayev I.Sh.
Mavlyutov Institute of Mechanics UFRC RAS, Ufa, Russia

Abstract

The paper presents a parametric analysis of a 2D model of a fluid cooling system for the hot side of a Peltier element of a capillary microgripper. An unsteady flow of coolant in the cooling chamber is considered. The cooling efficiency is studied for three chamber geometries with different radiator locations: monolithic, located on the Peltier element; with one or three ribs. Mathematical models are built: fluid flow through the microgripper chamber; heating the radiator with the hot side of the Peltier element; heat transfer from the radiator to fluid and the removal of the heated fluid from the chamber. The simulation is carried out in the FreeFem++ program until the average change in the temperature of the radiator over the period of fluid oscillations reaches saturation (microgripper operating mode). Using the method of orthogonal central compositional planning, analytical dependences of response functions (maximum temperature on the radiator, amplitude of temperature change on the radiator, and time to establish the operating mode) on model factors (average coolant velocity, heat transfer coefficient, frequency and amplitude of fluid velocity oscillations) are obtained. For each considered geometry and response function, leading and insignificant factors are determined. A parametric analysis of the influence of the physical parameters of the system on the operation of the cooling system was carried out. The simulation results show that the geometry that provides a high degree of cooling and a faster exit to the operating mode (radiator with three fins) has a large amplitude of temperature fluctuations on the radiator and can be used in technical devices that are less sensitive to temperature fluctuations on the radiator. The single fin radiator geometry provides the least radiator temperature fluctuation and can be used to cool capillary microgripper.

Keywords

hydrodynamics,
heat transfer,
capillary microgripper,
fluid cooling system,
finite element method,
orthogonal central composition plan

Article outline

The paper presents a parametric analysis of a two-dimensional model of a liquid cooling system for the hot side of a Peltier element of a capillary microcapture. An unsteady flow of coolant in the cooling chamber is considered. The cooling efficiency is studied for three chamber geometries with different radiator locations: monolithic, located on the Peltier element; with one or three ribs. The first geometry is a vertical section of the cooling chamber and does not take into account the fluid flow around the radiator along the front and rear walls of the chamber, as well as the flow between the radiator fins. The next two geometries represent a horizontal section and do not take into account the flow of fluid along the top wall of the chamber. Mathematical models are built: fluid flow through the microgripper chamber; heating the radiator with the hot side of the Peltier element; heat transfer from the radiator to the fluid and the removal of the heated fluid from the chamber.

Equations of hydrodynamics and thermal conductivity with the corresponding boundary conditions were written in variational form and solved numerically by the finite element method in the FreeFem++ numerical simulation package. Discretization in time was carried out according to the implicit first order Euler’s scheme. Every five time steps, the computational mesh was rebuilt with the density of the finite elements proportional to the fluid velocity gradient. The simulation was carried out until the change in the temperature of the radiator, averaged over the period of flow oscillations, reaches saturation (the operating mode of microgripper). All physical parameters of the coolant (bulk density, dynamic viscosity, isobaric specific heat and thermal conductivity) were considered as temperature-dependent finite element functions with an approximation obtained from tabular data.

For each considered geometry, a series of computational experiments was carried out using the orthogonal central compositional planning method for the following ranges of parameters (factors): average coolant velocity, heat transfer coefficient, frequency and amplitude of fluid velocity oscillations. The following output parameters (response functions) were determined: the maximum temperature on the radiator, the amplitude of the temperature change on the radiator, and the operating mode settling time).

For each considered geometry and response functions, leading and insignificant factors are determined. A parametric analysis of the influence of the physical parameters of the system on the operation of the cooling system was carried out. It was found that, on average, the third geometry, compared to the second, provides better cooling (by 1.8 times) and less time to reach the operating mode (by 1.7 times), but has large temperature fluctuations on the radiator (by 2 times), which can lead to to premature failure of the held object. The simulation results show that the geometry that provides a high degree of cooling and a faster exit to the operating mode (radiator with three fins) has a large amplitude of temperature fluctuations on the radiator and can be used in technical devices that are less sensitive to temperature fluctuations on the radiator. The single fin radiator geometry provides the least radiator temperature fluctuation and can be used to cool capillary micro grippers.

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