# Influence of the Water-Cooled Heat Exchanger on the Performance of a Pulse Tube Refrigerator
## 2 Experimental Apparatus and WCHXs  
### Experimental Apparatus  
The experimental apparatus is schematically shown in Figure 2. It mainly consisted of a linear compressor and an in-line pulse-tube cooler. The main geometric parameters of the cooler and its operating conditions are listed in Table 1. The water-cooled heat exchanger was replaceable, so that different heat exchangers could be tested. The heat exchangers were cooled by circulating water with a temperature of 293 K. Because the hydraulic diameter of the heat exchanger was quite small, it was difficult to place thermometers inside it, in order to measure the gas or the wall temperatures. Subsequently, only a calibrated K-type sheathed thermocouple (\(T_{0}\)) was installed close to the inlet of the heat exchanger, to measure the gas temperature.  
The regenerator housing was filled with a 300-mesh stainless-steel screen with a porosity of 0.7. Four calibrated PT-100 resistance thermometers (\(T_{1}\)-\(T_{4}\)) with an accuracy of \(\pm\)0.1 K were placed on the outer wall of the regenerator, distributed with equal spacing. If the wall temperature equals the screen temperature in the same cross-section, then the temperature in the regenerator can be obtained from the four thermometers. The temperature of the cold head was measured with another PT-100 (\(T_{\rm S}\)). Three constanta wires heated by a direct voltage source were mounted on the cold head, to simulate cooled loads. The voltage was adjusted to keep the temperature of the cold head at 80 K. The heat power was read from the direct voltage source, which had an accuracy of \(\pm\)0.3%. The regenerator, cold head, and pulse tube, were enclosed in a vacuum chamber. The flow straightener was made of 5-mm long 40-mesh copper screens. The inertance tube was cooled with a water jacket. The linear compressor was used to provide acoustic power for the pulse-tube cooler. The efficiency of the compressor was not important in this study, so the match between the compressor and the refrigerator was not optimized. The output acoustic power of the compressor was calculated from the pressures (\(\rm P_{f}\) and \(\rm P_{b}\), respectively) in its front and back spaces. \(\rm P_{f}\) and \(\rm P_{b}\) were measured using high-precision dynamic pressure sensors, supplied by PCB Piezotronics shown in Figure 2. The input acoustic power, \(W_{a}\), was calculated as:  
\[W_{a}=\frac{1}{2}\Big{|}P_{f}\Big{|}\left|\frac{i\omega V_{b}}{\gamma P_{0}}P_{ b}\right|\cos\theta_{PU} \tag{1}\]  
where \(\theta_{PU}\) is the phase difference between the pressure wave and the volume flow rate, \(\omega\) is the angular frequency, \(V_{b}\) is the back space volume of the compressor, \(P_{0}\) is the mean pressure, and \(\gamma\) is the specific heat ratio [25]. The accuracy of the pressure sensor measuring \(P_{0}\) was 0.2%. The non-linearity of the pressure sensors measuring \(P_{f}\) and \(P_{b}\) was 1%.  
Figure 2: Schematic of the experimental apparatus. 1 Liner compressor; 2 WCHX; 3 Regenerator; 4 Clod head; 5 Pulse-tube; 6 Flow straightener; 7 Inertance tube; 8 Gas reservoir.