A numerical approach for optimization of the working fluid of a standing-wave thermo-acoustic refrigerator

Impact of stack length on performance of standing wave thermoacoustic refrigerator

“…The oscillatory boundaries utilised in thermoacoustic as low amplitudes have been expounded and summarised by [17]. The pressure (𝑃𝑃), velocity (𝑢𝑢) and temperature (𝑇𝑇) illustrated below have been applied at the inlet of computational domain, which expressed in terms of mean component and first order component were adapted from [6]:…”

“…Where: 𝑃𝑃 𝑚𝑚 and 𝑇𝑇 𝑚𝑚 are mean pressure and mean temperature respectively, 𝑧𝑧 = is the geometric direction of 2D axisymmetric model of computational domain, 𝑅𝑅 𝑒𝑒 { } is the real part, 𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖 is the time dependency of a particular variable, 𝜔𝜔 is the angular frequency, and 𝑃𝑃 1 , 𝑢𝑢 1 and 𝑇𝑇 1 are oscillating amplitude pressure, velocity, and temperature respectively of the standing wave adapted from [6], which expressed as follows :…”

“…Where: 𝑃𝑃 𝐴𝐴 = is the amplitude pressure at pressure antinode, a = is the speed of sound, 𝑘𝑘 1 = is the wave number, 𝜌𝜌 𝑚𝑚 = is the mean density and 𝐶𝐶 𝑝𝑝 = is the gas specific heat capacity at constant pressure. Then substituted equations ( 1) to (3) into equations ( 4) to (6), yielded three final equations ( 7) to (9) illustrated below, which were adapted from [6]:…”

“…The stack plate thickness (𝑡𝑡ℎ) was of 0.5 mm, and a hot copper heat exchanger of approximately, L copper /𝜆𝜆 = 0.02625 embedded in the tube thickness, which positioned at the upper end of each stack length to absorb the exhausting heat and dissipating it to the environment. A cold heat exchanger omitted in the computational domain reason being that no heat generated would be utilised externally ( [6]. The total length of the computational domain was set to 0.012𝜆𝜆+0.0238𝜆𝜆 m. The lower edge of the stack positioned at 0.012𝜆𝜆 m away from the inlet boundary of computational domain while the distance of the lower edge of the stack to the upper closed end of computational domain was set to 0.0238𝜆𝜆 m.…”

“…To optimize thermoacoustic effects, it is essential for the stack to feature a large surface area and short distances between surfaces within the flow channels [5]. This paper aims to numerically investigate the effects of seven stack length using COMSOL Multiphysics on the performance of the standing wave thermoacoustic refrigerator [6]. It is significant to investigate the impact of stack length to enable the optimisation of TAR.…”