Thermopneumatic Analysis and Process Design of Closed Cycle Cryocoolers

Abstract

The cryocooler is a tabletop size machine, which extracts heat from an object to decrease its temperature below the cryogenic temperature limit. Cryocoolers are used in the cooling of high-temperature superconducting (HTS) magnets, HTS motors, HTS generators, and HTS transformers, etc. to retain their superconductivity state. Furthermore, they are used in liquefaction of permanent gases, cooling of space satellites, night vision camera, infrared sensors, cryosurgical probes, magnetic resonance imaging (MRI), etc. to name a few. It is believed that with the development of compact, efficient, miniature, and portable cryocoolers, its application domain will further increase in other fields of modern science and technology. In this research, numerical simulation is conducted to illustrate the thermo-fluidic processes occurring inside the regenerative cryocoolers. The heat transfer and fluid flow processes of regenerative cryocoolers are governed by a set of non-linear, coupled partial differential equations. The governing equations of the compressible working fluid are conservation of mass, momentum, and energy. Moreover, the conservation of the solid/ matrix energy equation is coupled with the fluid energy equation by means of film heat transfer. By adopting the finite volume discretization method, the partial differential equations are converted into algebraic equations. The first and second-order implicit schemes are used for the discretization of time coordinate, and a combination of first and second-order upwind schemes are used for the discretization of space coordinates. The first-order implicit scheme is used for the first time step, and the second-order implicit scheme is used for the remaining time steps in a cycle. The boundary nodes of the computational domain are discretized by the first-order upwind scheme and internal nodes are discretized by the second-order upwind scheme. By applying the ideal gas equation-of-state, both continuity and momentum equations are converted into a single equation, which upon solution yields pressure distribution. Therefore, one discretized algebraic equation is circumvented in the iterative solution process and thereby increases the computational speed. The resulting set of algebraic equations are solved iteratively by Tri-diagonal and Penta-diagonal matrix algorithm. After completion of the first time step, the final computed values are used as initial conditions for successive time steps, and this process is continued until a cyclic steady state is achieved. Once a cyclic steady state is achieved, the performance parameters of the cryocooler like work input, cooling capacity, enthalpy flow, energy flow, exergy flow, entropy generation, etc. can be computed from the physical quantities like pressure, mass flow rate, temperature, density, fluid properties, and matrix properties, etc. In this work, the one-dimensional model is extended by introducing the influence of turbulent conduction, eddy mixing and thermal dispersion with the help of a gas axial- conduction enhancement factor in the fluid energy equation. The effect of zero gas conductivity, molecular conductivity, and both molecular conductivity and eddy conductivity on the oscillating flow processes have been examined for an inline inertance pulse tube cryocooler. Subsequently, simulation is conducted to study the effect of zero conductivity and corrected conductivity on the gas flow and heat transfer processes of a coaxial pulse tube cryocooler. After considering the influence of the gas axial-conduction enhancement factor in the numerical model, it is noticed that the phase angle of each physical quantity like flow rate, pressure, temperature, density changes at every location of the cryocooler. Multi-dimensional CFD simulation of inertance pulse tube cryocooler is conducted to visualize various second-order loss mechanisms inside the pulse tube, which cannot be usually analyzed by the one-dimensional model. The one-dimensional numerical model is further modified for a GM cryocooler by modifying the boundary conditions and neglecting the influence of inertia term in the one-dimensional momentum equation. By using the numerical model, the effect of waiting period, and opening angle difference between intake and exhaust valves on the thermodynamic processes of mechanical drive GM cryocooler is studied. Then, a previously established first-order thermodynamic model for mechanical drive GM cryocooler is extended for a pneumatic drive GM cryocooler by implementing the complex displacer dynamics in its governing equations. The thermodynamic processes happening within the cold heads of both mechanical drive GM cryocooler and pneumatic drive GM cryocooler is examined. Subsequently, the effect of opening-closing intervals of drive chamber intake and exhaust valves of pneumatic drive GM cryocooler on the thermodynamic processes have been studied. The simulation results will be useful for a better understanding of the thermo-fluidic processes of GM cryocooler and design of an efficient rotary valve. It is noticed that, with an increase in the waiting period, the P-V power in the expansion chamber and compression chamber reduces due to the decrease in an enclosed area of the P-V diagram of both gas chambers. Multi-dimensional CFD simulation of a mechanical drive GM cryocooler is carried out by commercial code Fluent®, to identify the second-order loss mechanism and formation of recirculation patterns inside the individual gas chambers. The influence of uniform mesh regenerator and multi-mesh regenerator on the cooling rate is examined. In addition, the basic configuration of the displacer is modified by making an annular extruded portion at its cold end so as to construct a multiplex structure. It is noticed that, the extruded portion has an adverse effect on the cooling performance due to the compression of gas parcels in the slots of the extruded portion. One-dimensional numerical simulation is conducted for a GM-type pulse tube cryocooler. By using the one-dimensional numerical model, the effect of geometrical parameters (i.e., regenerator length and diameter, pulse tube length and diameter, orifice and double inlet valve flow coefficients), and operating parameters (i.e., mean pressure and pressure ratio) on the cooling capacity and no load temperature is studied. It is seen that, an increase in mean pressure increases the cooling capacity. It is also noticed that the optimum value of orifice valve opening and double inlet valve opening to attain a minimum no load temperature and a maximum cooling capacity varies with the geometrical parameters of the cryocooler. An experimental investigation is carried out to validate the results of the one-dimensional numerical model. CFD simulation is carried out for a GM-type orifice pulse tube cryocooler to visualize the oscillating gas flow behavior. The process of vortex street formation in an orifice pulse tube cryocooler is also explained. Multi-objective optimization of input parameters of GM pulse tube cryocooler is also carried out using response surface methodology to maximize the cooling capacity and percentage Carnot efficiency.