Numerical and Experimental Study of an Annular Pulse Tube Used In The Pulse Tube Cooler Xiaomin Pang, Yanyan Chen, Xiaotao Wang, Wei Dai, Ercang Luo Key Laboratory of Cryogenic Engineering, Technical Institute of Physics and Chemistry of CAS , China

Contents Introduction Physical model and CFD simulation Experimental setup and results Conclusions

INTRODUCTION Single stage Stirling type pulse tube cooler configuration In-line U-type Co-axial The stirling type pulse tube coolers have become the research hot in recent years due to the advantage of no moving part in low temperature. Compactness is one of the research focus of pulse tube cooler system. For single stage pulse tube cooler, there are three configurations, in-line, U-type and co-axial. The co-axial is the most compact configuration. most compact

INTRODUCTION Two-stage Stirling type pulse tube cooler configuration Thermal-coupled Gas-coupled For thermal-coupled configuration, the thermal-bridge working in low temperature make the configuration more complicate. For gas-coupled configuration, most of them are U-type configuration, however the completely co-axial configuration is more compact than others. There are few studies about this configuration. Co-axial U-type Co-axial Completely co-axial two-stage configuration is the most compact configuration

INTRODUCTION Co-axial configuration for two stage G-M type pulse tube cooler In 2006 T.Koettig has made some study on two stage co-axial G-M pulse tube cooler. They obtain a no-load temperature of 6.6 K with 6 kW input power. However they did not compare the performance with U-type or in-line type. T. Koettig, S. Moldenhauer, R. Nawrodt. et.al. Two-stage pulse tube refrigerator in an entire coaxial configuration. Cryogenics, 2006, 46: 888-891

INTRODUCTION Co-axial configuration for two stage Stirling type pulse tube cooler In 2012 I. Charles developed a Stirling type co-axial pulse tube cooler. The solid line is the results with co-axial configuration, the dot line is the results with U-type configuration. As we can see, with co-axial configuration, the second stage reached a lower temperature, however the temperature of the first stage is arised. The author attributes this to the annular pulse tube of the first stage but not give detailed analysis. I. Charles, E. Ercolani, C. Daniel. Preliminary thermal testing of a high frequency two stage coaxial tube for earth observation missions. [c]//Proceedings of ICEC24-ICMC 2012

INTRODUCTION Annular pulse tube is inevitable in the completely two stage co-axial configuration Comparison of Circular pulse tube and Annular pulse tube is present in this paper based on a single stage in-line type pulse tube cooler working in liquid nitrogen temperature. Annular pulse tube is inevitable in the two stage co-axial configuration. This presentation focus on the performance of annular pulse tube. And make comparison with circular pulse tube.

Contents Introduction Physical model and CFD simulation Experimental setup and results Conclusions Based on Fluent software, we made some simulation study. Then let’s begin the second part, physical model and CFD simulation.

Physical model Configuration and details of the model. 9.5 54 10 Cold end heat exchanger Pulse tube(thin Stainless pipe) Ambient heat exchanger Φ 8 Φ 12.8 Φ10 Rod (PEEK) 0.25 Circular pulse tube Annular pulse tube This picture shows configuration of the model, It includes cold end heat exchanger, pulse tube and ambient heat exchanger. For annular pulse tube, a rod made of PEEK is inserted inside the thin stainless pipe. The gap between the outer pipe and the PEEK rod serves as the annular pulse tube. The cross-sectional flow area and the length are kept the same as the circular pulse tube.

Physical model Two dimensional axisymmetric model Grids and Boundary condition Inlet 77K Outlet 300K Axis Inlet Outlet Axis Two dimensional axisymmetric models are set up. Quadrilateral cells are adopted in all the regions including gas, wall and rod area. For the gas flow area, boundary layer mesh is used near the wall. The initial temperature of the cold end heat exchanger is set as 77K, and for the ambient heat exchanger is set as 300K. Linear temperature distribution is set in the pulse tube. The model has a mass flow inlet boundary at the cold end heat exchanger, and a pressure outlet boundary at the ambient heat exchanger. The average pressure is 3.5 MPa, the frequency is 100 Hz. After the calculation reached steady, The results have been present. Inlet : Mean Pressure: 3.5 MPa Outlet : Frequency: 100 Hz

Simulation results Influence of the pulse tube shape on the pulse tube impedance is small Firstly, the flow characteristics are investigated. This Figure presents the distribution of the pressure amplitude and axial velocity amplitude along the X axis. The changing trend is similar and the difference between them is minor. The right picture shows the phase difference between the pressure and velocity. The difference between the two pulse tubes is also small. Table listed the impedances at the cold end of the pulse tube. The impedance amplitude and phase angle are close to each other. This validates that the influence of the tube shape on the impedance is small.   Circular pulse tube Annular pulse tube Impedance amplitude (Pa.s/m2) 1.612E+9 Impedance angle (Deg) 41.5 41.4

Simulation results The skin effect influencing area occupies a larger fraction of the total flow area in the annular pulse tube To further study the effect on the flow and temperature field. Figure shows the radial distributions of velocity in the middle of pulse tube at four moments during a cycle. We can see the maximum velocity occurs near the pulse tube wall, which is well-known as the skin effect. Compared with the circular pulse tube, the skin effect influencing area occupies a larger fraction of the total flow area in the annular pulse tube, which may lead to different performance. Radial distributions of velocity at X=36 mm (middle of the pulse tube) at four moments

Simulation results The skin effect influencing area occupies a larger fraction of the total flow area in the annular pulse tube The radial temperature distribution has a similar skin effect, and the larger temperature inhomogeneity may contribute to more thermal losses in the annular pulse tube. Radial distributions of temperature at X=36 mm (middle of the pulse tube) at four moments

Simulation results The enthalpy flow in the annular pulse tube is lower by about 1.6 W (11%) compared to that in the circular pulse tube. The expansion efficiency of the circular pulse tube is 88% The expansion efficiency of the annular pulse tube is 78% We also investigate the energy flow along X axis in the pulse tube. The curves of the acoustic power distributions almost overlap each other. However, the enthalpy flow is different. The enthalpy flow in the annular pulse tube is lower by about 1.6 W compared to that in the circular pulse tube. The performance difference between the two type pulse tubes is about 11%. Expansion efficiency can also be calculated. For the circular pulse tube, the expansion efficiency is 88% , for annular pulse tube it is only 78% . The distribution of energy flow in the pulse tube

Contents Introduction Physical model and CFD simulation Experimental setup and results Conclusions Based on the simulation results, various experiments are carried out. Then introduce the experimental set up and results.

5. Pulse tube 6. Ambient heat exchanger 7. Inertance tube Experimental setup Schematic of the experimental setup Figure shows the schematic of the system. It consists of a linear compressor and an in-line type pulse tube cooler. The components of the pulse tube cooler are the same except for the cold end heat exchanger and the pulse tube. compressor 2. Main ambient heat exchanger 3. Regenerator 4. Cold end heat exchanger 5. Pulse tube 6. Ambient heat exchanger 7. Inertance tube

Experimental results The no-load temperature increases by about 5.5 K when the pulse tube changes from circular shape to annular shape. Mean pressure: 3.5 MPa Frequency: 100 Hz The average pressure and frequency is kept the same as the simulation. 3.5MPa and 100Hz. With the input acoustic power increasing, the no-load temperature decreases. The no-load temperature of annular pulse tube is about 5.5 K higher than the circular pulse tube. No-load temperature vs. Input acoustic power

Experimental results Cooling power difference is about 0.9 W (11.4%). Figure presents the dependence of cooling power at 77K and relative Carnot efficiency on input acoustic power. With acoustic power increasing, Cooling power and efficiency are also increase. With maximum acoustic power of 105 W, the cooling powers the circular pulse tube is 7.9 W, and 7.0 W for annular pulse tube. The difference is about 11%. The changing trend is consistent with the simulation results. Cooling power & efficiency at 77 K vs. input acoustic power

Contents Introduction Physical model and CFD simulation Experimental setup and results Conclusions

Conclusions Simulation results show that inhomogeneity of the velocity and temperature are stronger in the annular pulse tube. Simulation results show that the expansion efficiency: Annular pulse tube 78% vs. Circular pulse tube 88%. Experimental results show that the cooling power at 77 K: Annular pulse tube 7.0 W vs. Circular pulse tube 7.9 W. Set the basis for building a completely co-axial two-stage pulse tube cooler system Simulation and experimental results show that the influence of the annular pulse tube is acceptable(about 11%).

Conclusions A Two stage completely co-axial pulse tube system has been set up.

THANKS This work is financially supported by the National Natural Science Foundation of China under contract number of [51376187] and [51576205]