Theoretical And Experimental Study For The Dynamic Impedance Match Of The High Efficiency Multi-stage Pulse Tube Cryocooler

Stirling-type pulse tube cryocooler(SPTC)is one of the most competitive candidates for the aerospace cryogenics applications.So the study of the design process and optimization method for this type of cryocooler is always an attractive topic.The impedance match analysis is a powerful method to analyze and optimize the operation of the SPTC.However,facing the rapid development of new cryocooler structures,this impedance match method should be further polished and extended.The four main shortages of this method includes the limitation of only focusing on steady state conditions,the abscense of analytical model for heat exchanging in the regenerator,the limitation of only focusing on single-stage structure and the requirement of mearsuring for oscillation flow rate.In order to fulfill these four demands above,a series of studies are accomplished which are:1.An analytical model for studying the impedance match situation of SPTC during dynamic process is proposed including the method to calculate the temperature distribution along the regenerator and the method to calculate the impedance of the cold finger.According to the study of single stage SPTC during cool down process,the method to calculate the temperature distribution along the regenerator is proposed.The impedance of the cold finger is also studied with the obtained temperature distribution and the impedance match evaluation.It is pointed out that the variation of the impedance of the cold finger is the key parameter which causes the dynamic behavior of the linear compressor and the SPTC.So the dynamic behabvior of the linear compressor and SPTC including the 50%increase of the input power,the 30%increase of the piston movement and the increase of efficiency from 54%to 62%with constant input voltage.The experiments carried out based on a single stage SPTC prove the reliability of the proposed analytical model.This study bordens the application of the impedance match method from steady state to dynamic process.2.An analytical model for studying the heat transfer between the gas and regenerative material in the regenerator is proposed.The lowest temperature can be achieved by single-stage SPTC is analyzed.According to the theoretical study of the energy conservation equations for the gas and solid in the regenerator of the SPTC,the equations which describe the temperature oscillation of the gas solid at the cold end of the regenerator are derived.These equations enable the quantitative study of the amplitude and phase angle of the gas at the cold end.Based on the obtained temperature oscillation,the variation of the enthalpy flow at the cold end is calculated which further leads to the analysis of the loss of the regenerator with different regenerative materials and working conditions.By studying the ratio of the enthalpy flow and the cold end acoustic power,the lowest temperature a single stage SPTC could achieve is discussed and the advantages of multi-stage structure versus single stage structure are analyzed.This study provides important supplement of the regenerator loss analysis to the impedance match analysis method.3.The impedance match analysis is carried out which guides the optimization of a thermal-coupled two-stage SPTC working on 35 K.The relative Carnot efficiency of 5%is achived.A self-developed screen mesh type oscillation flowmeter is applied to measure the oscillation flow rate and acoustic power at the hot end of the SPTC.The impedance match analysis is verified according to the measured flow rate and acoustic power.Appling the impedance match analysis to study the impedance of the two-stage SPTC cold finger and the impedance match situation,the acoustic-mechanicalelectrical coupling relation and the impedance match phasor diagram are proposed.By adjusting the mass of the piston in the linear compressor and the length of the second stage pulse tube guiding by impedance match analysis,the design of the twostage SPTC is improved.The experiments show that with a frequency of 40 Hz and a mean pressure of 2.2 MPa,the developed SPTC could achieve a cooling capacity of 1 W at 35.0 K and 0.1 W at 92.9 K with 150 W input power which means a relative Carnot efficiency of 5%.Using a self-developed screen mesh type oscillation flowmeter,the oscillation flowmeters in the tested SPTC and further verify the impedance analysis.This study demonstrates the application and analysis of impedance match method on two-stage SPTC.