## 2 The Experimental Set-Up  
The test rig considered for this research is a home-made standing wave thermoacoustic engine using air at atmospheric pressure as working fluid. A schematic of the engine is shown in Figure 1. The engine comprises four basic elements, namely an acoustic resonator filled with air at atmospheric pressure, a stack, an ambient heat exchanger and an electric heater. The engine works by heating one edge of the stack by the heater while anchoring the other edge to ambient temperature by the ambient HX. Acoustic waves will spontaneously generate in the device when the temperature gradient across the stack overcomes an onset level (depending mainly on the length and position of the stack inside the resonator).  
* The stack is a honeycomb stack made of a ceramic material (Celcor) characterized by a low thermal conductivity and a high specific heat. These properties enhance the stack performance in converting heat to acoustic power [15]. It fits the stack holder and is 8 cm long in the direction of the resonator axis (the longitudinal direction of acoustic vibration). The pores have a squared shape and are characterized by a hydraulic radius of around 0.28 mm. The cell density is near 400 cpsi. The stack placed inside the stack-holder and a magnified view of a portion of it are shown in Figure 2.
- The heater is fabricated by passing about 4 m of a Ni-Cr wire (30 \(\Omega\)/m) uniformly through the pores of a honeycomb ceramic slice 1 cm long along the resonator axis (and made of the same material of the stack) that served as a support. The slice is inserted on one side of a stainless steel ring, 2 cm long along the resonator axis, equipped with feedthroughs for power cables. The heater is placed between the \"hot\" duct and the stack holder. It is fed through a variable voltage autotransformer and is able to dissipate up to 600 W of electric power. A picture of the heater is shown in Figure 3.
- The HXs under test (widely described in the next section) function in this arrangement as ambient HXs (i.e., subtract heat from the gas oscillating at the ambient side of the stack) and are placed between the stack holder and the conical shape section at a distance of about 20 cm from the closed end of the \"hot\" duct. This location is around midway the velocity node and antinode and allows a wide range of velocity amplitudes (or, equivalently, gas displacement amplitudes) to be selected by varying the heat input to the system. This information has been deduced by simulating the engine behavior by highly specialized design tools of thermoacoustics systems, namely the DelatEC computer code (Design Environment for Low-Amplitude ThermoAcoustic Engines) [16], developed at the Los Alamos National Laboratory (see Section 5). Note that the test-rig arrangement above described do not correspond to a requirement of performance optimization but, rather, to the need of guaranteeing that the HXs under test (1) be interested by substantial heat transfer rates (and associated temperature changes in the cooling water) and (2) by values of the local acoustic particle displacement ranging around (both below and above) the axial length of the HXs, as it will be more exhaustively explained in Section 5.  
Figure 1: Schematic of the standing wave test engine. Labels “T” indicate thermocouple locations. Label “P” indicates microphone location.