DIRECT SIMULATIONS OF THERMOACOUSTIC HEAT EXCHANGERS O. M. Knio † , E. Besnoin Department of Mechanical Engineering, The Johns Hopkins University, USA † Email: knio@jhu.edu Abstract The performance of an idealized thermoacoustic re- frigerator is analyzed using direct numerical simula- tions. The model is based on a combination of quasi-1D resonant tube acoustics with multi-dimensional tran- sient simulations of the flow and temperature fields in the neighborhood of the thermoacoustic stack and heat exchangers. The latter are described using a vorticity- based model that simulates the compressible conserva- tion equations in the low-Mach-number limit. Model predictions are validated by comparing computed re- sults with corresponding PIV measurements of the ve- locity and vorticity distributions around the plate edges. Computations are then applied to analyze the effects of heat exchanger length and position on the performance of the device and on the flow behavior. The results indi- cate that the cooling load peaks at a well-defined combi- nation of heat exchanger length and gap width between the heat exchangers and the stack plates. At high drive ratio, the flow exhibits sustained unsteady behavior and is characterized by the appearance of a large-amplitude wavy motion within the gap, between the plates and in the vicinity of the thermoacoustic stack. It is also found that this phenomenon leads to enhancement of the cool- ing load and affects optimal heat exchanger parameters. Introduction As schematically illustrated in figure 1, a thermoa- coustic refrigerator typically comprises a resonance tube that houses a stack of parallel plates, an acous- tic source, and heat exchangers. The operating princi- ple of the device is the well-known thermoacoustic ef- fect [1], [2], which results in transport of heat from one end of the stack to the other. By placing hot and cold heat exchangers close to the ends of the stack plates, the thermo-acoustically generated heat flux can be ex- ploited to drive a refrigeration cycle. The mechanics of the mean energy transport between the stack plates is relatively well understood, and is in most cases ade- quately described using the well-known linearized the- ory [2]. In contrast, the behavior of thermoacoustic heat exchangers is far more challenging, in large part due to presence of concentrated eddy structures in the neighborhood of plate ends [3], [4], [5], [6], [7], [8], [9], [10]. Consequently, effective design and optimiza- tion of thermoacoustic refrigerators necessitates a fun- damental understanding of these vortical motions, and their dependence on geometric parameters and operat- ing conditions. Domain Acoustic Driver Resonance Tube Stack of Cold Heat Exchangers Rigid End of the Tube Quasi 1-D Flow Multidimensional Flow Computational Thermoacoustic Plates Stack of Heat Exchangers Field Stack of Hot Measurement Figure 1: Schematic illustration of the thermoacoustic refrigerator (top) with a magnified view of the computational domain (bottom) This paper discusses recent results of a computa- tional effort [7], [10], [11] that aims at investigating the flow features around, and heat transfer behavior of thermoacoustic heat exchangers. The model is based on a simplified representation of resonance tube acous- tics and on detailed (2D) representation of the unsteady flow in a neighborhood of the stack and heat exchang- ers. Earlier versions of the numerical model [4], [8] were validated after comparison with linear theory pre- dictions, experimental data for a thermoacoustic cou- ple [12] and numerical results obtained using a finite- volume model [8]. Recent improvements account for finite plate thickness, where the stack and heat exchang- ers plates are no longer treated as vanishingly thin, and the effect of a gap between the stack and heat exchanger plates. Numericaly obtained visualizations of the un- steady flow field around the edges of a thermoacoustic stack are first compared with time-resolved PIV mea- surements [7] of the velocity and vorticity fields [9] ob- tained at similar conditions. We focus on stacks oper- ating at low drive ratios, and present results obtained with two stack configurations that are characterized by disparate ratios of the plate thickness to the viscous pen- etration depth. This enables us to contrast experimental and computational predictions in distinct flow regimes. The simulations are then used to analyze the combined WCU 2003, Paris, september 7-10, 2003 1063