Theoretical And Experimental Investigations On Scaling Laws For The Linear Compressor And 20K High Frequency Pulse Tube Cryocoolers

The Stirling-type pulse tube cryocooler(SPTC) has no moving part at the cold end, which brings many outstanding advantages such as simple structure, low vibration, low electromagnetic interference, high reliability and long operation life. Due to these advantages, the SPTC has found many important applications, especially in some special fields such as aerospace. This paper makes the systemic theoretical analyses and experimental verifications on the scaling laws for the Oxford-type linear compressor, and then carries out the theoretical and experimental investigations on the 20 K two-stage SPTCs. The main contents are given as follows:1) The theoretical analyses on the scaling laws are carried out. Firstly, the governing equations of the linear compressor are deduced and the integral scaling laws are summarized. The partial scaling methods are then put forward in which only several selected dimensional parameters are scaled, and both capacity and efficiency of the scaled compressor are equal to or similar to those achieved by the integral scaling laws. The specific procedures of the partial scaling methods are given.2) Experimental investigations on the scaling laws are made. Firstly, for the partial scaling methods, the scaled compressor's maximum input electric power increases from 236.7 W to 370.0 W, and the cooling power is enhanced from 10.0 W to 15.0 W. The motor efficiency comes to be 73%, and the average cooling efficiency is 12% of Carnot efficiency. Secondly, for the integral scaling laws method, the scaled compressor's maximum input electric power is 481.5 W with 19.0 W of cooling capacity at 80 K. The average motor efficiency reaches 71%, and the average cooling efficiency achieves 11.5% of Carnot efficiency. An input electric power of 505.0 W is achieved and thus the above theoretical analyses are verified.3) Theoretical analyses and modeling are conducted on dynamic and thermodynamic characteristics of the SPTC. Governing equations are deduced, and ? and ?P are found to be two key parameters connecting compressor to pulse tube cold finger. An improved ECA model is developed to investigate the cold finger characteristics and their influences on ?, ?P. Systematic simulations based on a specific case are performed to provide elaborate explanations about the theoretical analyses with the frequency varying from 30 Hz to 100 Hz at 60 K, 80 K and 100 K, respectively. The variations of four important parameters of ?, ?P, I and ?, the compressor thermodynamic performances, and the cryocooler cooling performances, with the frequency at above temperatures are simulated and analyzed, respectively. The effects of compressor geometrical parameters on ?motor are also simulated.4) Experimental investigations are carried out to verify the theoretical analyses and modeling. Some empirical corrections are made and two sets of experiments are arranged based on the same compressor coupled with two different coaxial cold fingers typically operating at 80 K and 60 K, respectively. The variations of ?, ?P, I, ?, the input electric power, ?motor, the cooling capacity and ?Carnot with the operating frequency at the given cooling temperatures are tested and compared with the simulation results, and fairly good agreements are found in both cases. The effects of the cooling temperature on these characteristics are also tested and discussed. Experimental results verify the validity of the theoretical investigations. The results also indicate that the proposed theoretical model can apply to wide ranges of both the operating frequency and the cooling temperature.5) The theoretical investigations on the 20 K two-stage SPTC are carried out. Based on the dynamic and thermodynamic characteristics of the SPTC, the ECA model of two-stage SPTC are put forward, and the governing equations of each components and the cooling performances of each stage are deduced. The main problems caused by the very low cooling temperature are discussed, such as the power loss, the regenerator matrix, the phase shifter. The gas distribution of the two-stage SPTC is analyzed, which is influenced by the dimensions and operating parameters of the cold fingers. A 20 K two-stage coaxial SPTC is designed and the performances are simulated. The second stage can achieve 0.69 W/20 K together with 1.0 W/80 K, or 0.08 W/15 K with 0.8 W/80 K.6) The experimental investigations on the 20 K two-stage SPTC are carried out. The experiments achieves a no-load temperature of 17.4 K, and several typical cooling capacities of 59 m W/18 K, 159 m W/19 K or 258 m W/20 K. The above theoretical analyses and optimizations have thus been experimently verified.