The present research analyzes random porous thermoacoustic stack systems analytically, experimentally, and numerically with a primary objective to develop a comprehensive analytical porous media modeling for random porous (such as Reticulated Vitreous Carbon (RVC) foams) environment. Mathematical models are developed for flow, thermal, and energy fields within the random porous medium stack. Initially, the Darcy model is used for modeling the momentum equation and local thermal equilibrium assumption between the porous matrix and trapped fluid in the void space for energy equation. The expressions of temperature, energy flux density, and acoustic work absorbed or produced by a thermoacoustic device are compared with existing literature and observed good agreements. After obtaining the flow and thermal fields’ information, the present study examines the entropy generation distribution within the stack. One important item revealed in this study is that entropy generation inside the porous medium completely follows the trend of the imaginary part of ~f_k profile. Another major contribution of this research is to identify the location of maximum entropy generation which is identical to the location of maximum thermoacoustic heat and work transport. The expression of Nusselt number for steady flow cannot be used in oscillatory random porous medium because of the phase difference between the temperature gradient at the wall and the temperature difference between the wall and the space averaged temperature.

The present study then extends the Darcy model by considering Brinkman-Forchheimer-extended Darcy model for the modeling of momentum equation. The reason for considering Brinkman-Forchheimer extended Darcy model is to consider the presence of high velocity and high porosity porous medium which are typical in thermoacoustic devices. Therefore, this model is applicable in practical thermoacoustic devices. Mathematical models are developed for flow, thermal, and energy fields within the random porous media. To verify the present study, the temperature difference obtained across the stack ends is compared with the experimental results. A very good agreement is obtained between the modeling and the experimental results thus strengthening confidence in the newly developed model.

The present research experimentally examines novel stack configuration by considering “alternating conducting and insulating materials” as stack in thermoacoustic devices. The objective of considering such stack arrangement is to reduce the conduction heat transfer loss from the hot end of the stack to the cold end, thereby increasing the performance of the stack. Eight different heterogeneous (alternating conducting and insulating materials) stack arrangements are studied in this research. The performance (temperature difference generated across the stack ends at steady state and stack hot end temperature for a thermoacoustic heat pump) of the heterogeneous stack arrangement is compared with the typical homogeneous stacks. It is observed that heterogeneous stack arrangements of smaller length (0.02λ, where λ is the wavelength of the acoustic wave) show comparable performance to that of longer (0.04λ) homogeneous regular stack (Corning Celcor ceramic stack). This research shows that heterogeneous stacks can be used in thermoacoustic devices particularly in small (millimeter) scale thermoacoustic devices.

Numerically the present study investigates the influence of working fluid, geometric, and operating conditions on stack performance by solving the full Navier-Stokes, mass, energy equation, and equation of state. The drive ratio (DR) is varied from 1.7 to 10%, Prandtl number (Pr) is varied between 0.7 and 0.28, stack plate spacing (y₀) is varied from 3.33δ k to 1.0δ_k , and mean pressure (p_m) is varied from 10 kPa to 1000 kPa in these simulations. Results are presented in terms of velocity, temperature, cooling power, acoustic power, COP, and entropy generation contours. It is found that, lowering the Pr of the working fluid at a low mean pressure (for example, 10 pm = kPa), low DR (DR=1.7%), and at a stack plate spacing of k y0 = 3.33δ_k shows the best performance regarding the COP. An important finding of this study is that cooling power and acoustic power absorbed by a thermoacoustic refrigerator increase as the p_m and DR increase, but the increase of acoustic power is more significant than the cooling power at higher DR and p_m. Therefore, COP decreases at higher DR and pm .