Experimental study of the stack geometric parameters effect on the resonance frequency of a standing wave thermoacoustic refrigerator

ABSTRACT

Thermoacoustic refrigeration is an emerging technology that makes use of acoustic power to pump heat. The resonance frequency is important for the performance of thermoacoustic refrigerators, as it affects the temperature difference across the stack. This paper aims to optimize the performance of thermoacoustic refrigerators by experimentally investigating the effect of the stack geometric parameters (i.e. stack position, stack length, and the stack size) on the resonance frequency of a standing wave loudspeaker driven thermoacoustic refrigerator. Celcor Ceramic stacks of normalized positions of 0.764, 1.05, 1.43, and 1.72, normalized lengths of 0.076, 0.114, 0.153, and 0.191, and two porosities of 0.8 and 0.85 are used. The clarification of the relationship between the stack geometric parameters and the resonance frequency of the thermoacoustic refrigerator is presented. Moreover, the coefficient of performance of the thermoacoustic refrigerator is observed to increase at the resonance frequency of each stack configuration.

KEYWORDS:

• Frequency
• performance
• refrigeration
• resonance
• thermoacoustics

Nomenclature

Latin Letters

$\mathrm{A}$	=	Area, $\left[{\mathrm{m}}^2\right]$
$\mathrm{a}$	=	Sound velocity, $\left[\mathrm{m}/\mathrm{s}\right]$
$\mathrm{B}$	=	Porosity
C	=	Compliance, $\left[\mathrm{m}/\mathrm{N}\right]$
c	=	Specific heat, $\left[\mathrm{k}\mathrm{J}/\left(\mathrm{k}\mathrm{g}.\mathrm{K}\right)\right]$
$\mathrm{D}$	=	Drive ratio
$\mathrm{f}$	=	Frequency,$\left[\mathrm{H}\mathrm{z}\right]$
I	=	Inertance, $\left[\mathrm{k}\mathrm{g}/{\mathrm{m}}^4\right]$
J	=	Imaginary unit,
$\mathrm{K}$	=	Thermal conductivity $\left[\mathrm{W}/\left(\mathrm{m}.\mathrm{K}\right)\right]$
$\mathrm{L}$	=	Length, $\left[\mathrm{m}\right]$
$\mathrm{l}$	=	The half plate thickness, $\left[\mathrm{m}\mathrm{m}\right]$
$\mathrm{M}$	=	Mass, $\left[\mathrm{k}\mathrm{g}\right]$
$\mathrm{P}$	=	Pressure,$\left[\mathrm{P}\mathrm{a}\right]$
$\mathrm{Q}$	=	Thermal power, $\left[\mathrm{k}\mathrm{W}\right]$
$\mathrm{R}$	=	Individual gas constant, $\left[\mathrm{k}\mathrm{J}/\left(\mathrm{k}\mathrm{g}.\mathrm{K}\right)\right]$
$\mathrm{r}$	=	Resistance, $\left[\mathrm{k}\mathrm{g}/\left({\mathrm{m}}^4.\mathrm{s}\right)\right]$
$\mathrm{T}$	=	Temperature, $\left[\mathrm{K}\right]$
$\mathrm{V}$	=	Volume, $\left[{\mathrm{m}}^3\right]$
$\dot{\mathrm{W}}$	=	Acoustic power, $\left[\mathrm{k}\mathrm{W}\right]$
X	=	Stack position, $\left[\mathrm{m}\right]$
$\mathrm{y}$	=	Half stack spacing, $\left[\mathrm{m}\mathrm{m}\right]$
$\mathrm{Z}$	=	Impedance, $\left[\mathrm{k}\mathrm{g}/\left({\mathrm{m}}^4.\mathrm{s}\right)\right]$

Greek Letters

${\epsilon }_{\mathrm{s}}$	=	Stack heat capacity ratio
$\gamma$	=	Ratio of specific heats
${\delta }_{\mathrm{k}}$	=	Thermal penetration depth, $\left[\mathrm{m}\right]$
${\delta }_{\mathrm{v}}$	=	Viscous penetration depth, $\left[\mathrm{m}\right]$
$\lambda$	=	Wavelength, $\left[\mathrm{m}\right]$
$\mu$	=	Dynamic viscosity, $\left[\mathrm{P}\mathrm{a}.\mathrm{s}\right]$
$\rho$	=	Fluid density, $\left[\mathrm{k}\mathrm{g}/{\mathrm{m}}^3\right]$
$\sigma$	=	Prandtl number
$\omega$	=	Angular frequency, $\left[\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}\right]$
$\mathrm{\Delta }\mathrm{T}$	=	Temperature Difference, $\left[\mathrm{K}\right]$

Subscripts

$\mathrm{o}$	=	Oscillating
$\mathrm{c}$	=	Cold
$\mathrm{g}$	=	Gas
h	=	Hot
$\mathrm{h}\mathrm{e}\mathrm{x}$	=	Heat exchanger
$\mathrm{k}$	=	Thermal
$\mathrm{m}$	=	Mean
$\mathrm{n}$	=	Normalized
$\mathrm{p}$	=	At constant pressure
$\mathrm{r}\mathrm{e}\mathrm{s}$	=	Resonator
$\mathrm{s}$	=	Stack
$\mathrm{t}\mathrm{o}\mathrm{t}$	=	Total
$\mathrm{v}$	=	Viscous

Highlights

• A test rig of a standing wave thermoacoustic refrigerator is built.

• Eight Celcor Ceramic stacks with different lengths, positions, and porosities are tested.

• The effect of the stack geometric parameters on the resonance frequency is investigated.

• The effect of the resonance frequency on the performance and the temperature difference across the stack is discussed.

Acknowledgements

Generous advice given by Dr Ahmed Elamer, a senior lecturer at Brunel University London, has been a great help in this work. My special thanks are also extended to the staff of engineering workshops and electronic labs at Mansoura University for their help in setting up the experiments.