Evaluation of standing-wave thermoacoustic cycles for cooling applications

Abstract

The most promising applications for standing-wave thermoacoustic cooling were investigated from the perspective of the ratio of coefficient of performance (COP) to the reversible COP or COPR. A design optimization program based on the thermoacoustic simulation program known as DELTAE was developed. The program was applied to two standing-wave thermoacoustic cooler configurations in order to determine the best possible COPRs for various temperature spans between hot-side and cold-side stack-end temperatures. It was found that the COPR of standing-wave thermoacoustic coolers increases with temperature span and reaches a maximum for temperature lifts around 80 °C. Analysis of the results and the losses clearly shows that the efficiency of these systems may be good for refrigeration, but not for air-conditioning and cryogenic cooling. The COPRs determined from measurements for various thermoacoustic coolers developed so far show similar trends, and generally support the optimization results.

Introduction

Thermoacoustic cooling is a recent technology that has been proposed to obtain cooling energy from high amplitude sound waves. Periodic compression and expansion of gas particles, combined with heat transfer within regions near boundaries, result in heat pumping cycles with environmentally benign working fluids [1]. There is significant interest in thermoacoustic cooling systems because they possess a few possible advantages over other technologies. These advantages include the use of environmentally benign working fluids, simple design, continuous cooling capacity control, and possible quiet operation. There are, however, noteworthy technical challenges related to the design and construction of efficient, robust, economical thermoacoustic cooling systems. Most of the systems conceived to date require a stack and two sets of heat exchangers between the primary and the conditioned working fluids, which increases complexity and irreversibility [1]. For standing-wave thermoacoustic coolers, it is difficult to achieve very large cooling capacities with a single device. Furthermore, thermoacoustic system performance is very sensitive to the choice of design parameters and should be optimized to achieve a reasonable efficiency [2].

Many thermoacoustic cooler prototypes have been developed since the success of Hofler's thermoacoustic cooler in 1986 [3]. Early prototypes achieved relatively low operating temperatures with cooling capacities lower than 20 W [4], [5]. Subsequently, more efforts have been made on the development of thermoacoustic coolers with larger cooling capacities through the use of more powerful and better tuned electroacoustic transducers [6], [7]. Heat-driven thermoacoustic systems for applications at operating temperatures greater or lower than general refrigeration applications were investigated [8], [9]. The largest thermoacoustic cooler built to date has a maximum cooling capacity of 10 kW and was designed for air conditioning [10].

Efforts have been made to optimize the design of thermoacoustic coolers by improving stack geometry, gas mixture, thermal insulation, duct and cone diameters, and other parameters. An optimization scheme to achieve the best electroacoustic driver efficiency was developed by Wakeland using equivalent electrical circuit theory [11]. An equation was derived to calculate electroacoustic efficiency from known driver parameters. Optimization of the stack spacing for maximum COP or for maximum cooling power was experimentally investigated by Tijani et al. [12]. It was observed that a stack spacing of about 3 times larger than the thermal penetration depth (see next section) is optimal for thermoacoustic refrigeration. Systematic investigations of the effects of the Prandtl number of the gas mixture used in thermoacoustic cooling were also performed [13]. It was observed that the COPR, defined as the ratio of coefficient of performance (COP) to Carnot COP [14], increases with decreasing Prandtl number.

There also have been studies aimed at the systematic design optimization of thermoacoustic coolers. Wetzel and Herman used a model based on the boundary layer approximation, and the short stack assumption to calculate the work flux and heat flux [15]; they optimized the system by adjusting 19 design variables to achieve the best COP. A similar design optimization method was used by Tijani to design the stack of a thermoacoustic cooler [16]. Instead of using simplified work flux and heat flux equations, Minner et al. developed a design optimization program that interacts with DELTAE using a C⁺⁺ computer program [2]. From a parametric study, they observed that the efficiency of thermoacoustic coolers is sensitive to stack length, position, mean pressure and gas mixture (Prandtl number), and less sensitive to the stack spacing.

The COPR of prototypes developed so far has varied between about 10% and 20% for different prototypes and for different cooling temperatures [3], [5], [6], [8], [16]. Thermoacoustic coolers with a relatively small temperature span have poor COPR, lower than 10% [7], [9], [10]. This implies that there may be a relationship between the best achievable COPR and the temperature span.

The objective of the present study was to identify the most promising application area for standing-wave thermoacoustic cooling in terms of operating temperatures. In order to accomplish this goal, an optimization tool was built to identify the designs that result in the best efficiency for a range of imposed operating temperatures. Results from the optimization study allowed the identification of the major loss mechanisms, which may help to improve component design.