# Measurement of Heat Flow Transmitted through a Stacked-Screen Regenerator of Thermoacoustic Engine
## 3 Experiments  
Figure 1 presents the experimental setup, which consists of a stainless steel cylindrical tube with radius \(R=20\) mm and eight loudspeakers (FW168N; Foster Co., Tokyo, Japan). The tube was filled with Ar gas of mean pressure of 0.45 MPa, which is one of the frequently used working fluids of the thermoacoustic engine. It contains a 35-mm-long regenerator and two 20-mm-long heat exchangers with temperatures \(T_{\mathrm{H}}\) and \(T_{\mathrm{R}}\) (=293 K). Regenerators of two kinds were employed: randomly stacked stainless-steel woven wire mesh screens (with mesh number of #20, #30, #50, #60, and #80) and a cylindrical ceramic honeycomb catalyst. Table 1 presents geometrical parameters of the wire meshes and ceramic honeycomb used for this study. The hydraulic diameter of the stacked-screen regenerator described in Table 1 was calculated as \(d_{\mathrm{h}}=\phi d_{\mathrm{w}}/\left(1-\phi\right)\). The cylindrical ceramic honeycomb catalyst possesses regular flow channels made of square pores of \(d_{\mathrm{h}}\times d_{\mathrm{h}}\). Table 1 also includes parameters of the ceramic honeycomb catalyst. The hot heat exchanger with temperature \(T_{\mathrm{H}}\) was heated using three electrical heater rods, whereas the ambient heat exchanger with \(T_{\mathrm{R}}\) was cooled by running water around it. Temperatures \(T_{\mathrm{H}}\) and  
Figure 1: Schematic diagram of the experimental setup. were monitored using Type-K thermocouples placed on the central axis and at the regenerator ends, from which we determined the axial temperature difference \(\Delta T=T_{\rm H}-T_{\rm R}\) across the regenerator. One end of a 50-mm-long thermal buffer tube region, next to the hot heat exchanger, was also cooled by running water. The experimental procedure is explained as follows. First, in the absence of acoustic oscillations, a steady non-oscillating state with \(\Delta T=250\) K was established. The necessary heating power was recorded as \(Q_{\rm OFF}\), which turned out to be 75 W with the change of \(\pm 4\) W at most, depending on the mesh number and ambient temperature. Second, we turned on the loudspeakers at ends of the tube to excite acoustic oscillations in the setup. In the presence of acoustic oscillations, the heat power \(Q_{\rm ON}\), which is necessary to maintain the steady oscillation state with \(\Delta T=250\) K, was increased from \(Q_{\rm OFF}\), which means that the oscillatory flows cause additional heat transport along the regenerator. Therefore, we determined the rate of heat flow passing through the regenerator as  
\[|Q|=Q_{\rm ON}-Q_{\rm OFF}. \tag{12}\]  
Measurements were repeated four times for each experimental condition to obtain the mean value and the standard deviation of the measured \(|Q|\). Because the heat flow \(Q\) is directed in the negative \(x\)-direction, we discuss the heat flow rate \(|Q|\) for brevity. During the measurements, gas oscillations were measured using two pairs of pressure transducers (PD104; JTEKT Corp., Osaka, Japan) mounted on the sidewall of the cylindrical tube at the positions presented in Figure 1. From the pressure amplitudes and phases obtained with a 24 bit fast Fourier transform analyzer (DS-3100; Ono Sokki Co. Ltd., Yokohama, Japan), we evaluated the acoustic pressure field \(p(x)=\mathrm{Re}\left[P(x)\mathrm{exp}\left(i\omega t\right)\right]\) and the velocity field \(\langle u(x)\rangle=\mathrm{Re}\left[\langle U(x)\rangle\mathrm{exp}\left(i \omega t\right)\right]\) in the 40-mm tube using the two-sensor method [26; 27]. The complex amplitude \(\langle V\rangle\) of the cross-sectional average velocity in the hot end of the regenerator was derived as \(\langle V\rangle=\langle U_{\rm H}\rangle\) /\(\phi\) from the continuity of volume velocity, where subscript H denotes the location at the hot end of the tube. Throughout the experiments, the loudspeakers were controlled by voltage signals fed from a two-channel function generator via power amplifiers.