[ASME 2010 14th International Heat Transfer Conference - Washington, DC, USA (August 8–13, 2010)] 2010 14th International Heat Transfer Conference, Volume 4 - Quantitative Visualization

1 Copyright © 2010 by ASME

Proceedings of the 14th International Heat Transfer Conference IHTC-14

August 8-13, 2010, Washington D.C., USA

IHTC14-23286

QUANTITATIVE VISUALIZATION OF THE THERMOACOUSTIC EFFECT

Cila Herman Department of Mechanical Engineering

Johns Hopkins University Baltimore, MD, USA [email protected]

ABSTRACT Thermoacoustic energy conversion was introduced into engineering systems during the past three decades as a new, alternative, environmentally safe energy conversion technology. It uses noble gases and mixtures of noble gases as working fluids rather than hazardous refrigerants required for the vapor compression cycle. A thermoacoustic system can operate both as a prime mover/engine (a temperature gradient and heat flow imposed across the stack lead to the generation of acoustic work/sound in the resonator) and, when reversing the thermodynamic cycle, as a refrigerator (acoustic work is used to pump heat from the low temperature reservoir and release it into a higher temperature ambient). Energy transport in thermoacoustic systems is based on the thermoacoustic effect. Using an acoustic driver, the working fluid in the resonance tube is excited to generate an acoustic standing wave. When introducing a stack of parallel plates of length ∆x into the acoustic field at a suitable location, a temperature difference ∆T develops along the stack plates. This temperature difference is caused by the thermoacoustic effect. In this paper the thermoacoustic effect is visualized using real-time holographic interferometry combined with high-speed cinematography. In holographic interferometry both temperature and pressure variations impact the refractive index and both of these variations are present in our thermoacoustic system. In our analysis temperature variations are uncoupled from pressure variations to quantitatively visualize the oscillating temperature fields around the stack plate.

INTRODUCTION Over the past decades environmental concerns have become an increasingly important issue in the design and development of energy conversion and refrigeration systems. Thermoacoustic refrigeration is one promising approach in the class of alternative refrigeration technologies. It is attractive because it

does not rely on hazardous refrigerants. Properly designed and optimized thermoacoustic refrigerators can achieve a substantial fraction of Carnot’s efficiency (upper thermodynamic limit is 40-50%, depending on the working fluid used and the temperature ranges), and the progress in the development of the technology over the past 40 years has been remarkable. The basic physics and thermodynamics processes responsible for thermoacoustic energy conversion are quite well understood (Rott, 1980) and several commercial thermoacoustic energy conversion systems (for example, an ice cream refrigerator for Ben and Jerry’s and a system for the liquefaction of gases) have been developed over the past two decades. The potential for commercial applications is far from being fully exploited. In the top portion of Figure 1, a schematic of a thermoacoustic refrigerator is shown. The working fluid within the resonance tube is excited with an acoustic driver to form an acoustic standing wave in the resonator. The length of the resonance tube in our study corresponds to half the wavelength of the standing wave, λac/2. The corresponding pressure and velocity distributions are displayed in the middle image in Figure 1. A densely spaced stack of parallel plates of length ∆x is introduced at a location specified by the stack center position xc into the acoustic field. The optimum position of the stack center xc is determined by optimizing the coefficient of performance or the cooling load of the system and it is not the center of the resonance tube. During the operation of the refrigerator a temperature difference ∆T develops along the stack plates (bottom image in Figure 1). By attaching heat exchangers to the cold and hot ends of the stack, heat can be removed from a low temperature reservoir, pumped along the stack plate to be delivered into the high temperature heat exchanger and ambient. The temperature difference along the stack is caused by the thermoacoustic effect. It should be noted that the velocity in this system is a dependent parameter, a function of pressure and fluid properties – the relationship between them is given in the formula in Figure 1. This paper

Proceedings of the 14th International Heat Transfer Conference IHTC14

August 8-13, 2010, Washington, DC, USA

IHTC14-23286

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2

focuses on the visualization of the oscillating temperature fields in the thermoacoustic stack near the edge of the stack plates, which allows the visualization of the thermoacoustic effect.

The mechanism of thermoacoustic heat pumping (Swift, 1988) is illustrated in the schematic in Figure 2, by considering the oscillation of a single gas parcel of the working fluid along a stack plate. The gas parcel begins the cycle at a temperature T (1). In the first step the gas parcel is moved to the left towards the pressure antinode by the acoustic standing wave. During this displacement it experiences adiabatic compression which causes its temperature to rise by two arbitrary units to T++( Step 1 in Figure 2). In this state the gas parcel is warmer than the stack plate and irreversible heat transfer from the parcel towards the stack plate takes place (Step 2 in Figure 2). The resulting temperature of the gas parcel after this step is T + . On its way back to the initial location, during the expansion phase of the acoustic cycle, the gas parcel experiences adiabatic expansion and cools down by two arbitrary units to the temperature T – (Step 3 in Figure 2). At this state the gas parcel is colder than the stack plate and irreversible heat transfer from the stack plate

towards the gas parcel takes place (Step 4 in Figure 2). After these four steps the gas parcel has completed one thermodynamic cycle and reached its initial location and temperature T. At this point the cycle can start again. In this paper we visualize the oscillating temperature distributions near the edge of two stack plates to visualize the thermoacoustic effect. There are many gas parcels subjected to this thermodynamic cycle along each stack plate: the heat that is delivered to the plate by one gas parcel is picked up and transported further by the adjacent parcel, as illustrated in the bottom portion of the magnified region of Figure 2. The result of this transport is a temperature gradient that develops along the stack plates. The described cycle can also be reversed by imposing a temperature gradient ∆T along the stack plates. In this situation the directions of irreversible heat transfer and work flux in are reversed and the thermoacoustic device operates as a prime mover, also known as the thermoacoustic engine. Thermoacoustic prime movers can be used to generate acoustic work that can drive a thermoacoustic refrigerator, a pulse tube or a Stirling refrigerator.

Holographic Interferometry (HI) is a well-established measurement and visualization technique widely used in engineering sciences (Vest, 1979, Herman et al., 1998). In transparent fluids it visualizes refractive index fields, which are related to fluid properties, such as temperature, pressure, species concentration, as well as density in compressible flows. Optical measurement techniques have virtually no “inertia”;

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pressure distribution

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U(x)=-P /( c)sin(2 x/ )A m acρ π λ

p(x)=P cos(2 x/ )A acπ λ

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Figure 1. a) Schematic of the thermoacoustic refrigerator, b) pressure and velocity distributions in the resonance tube and c) temperature distribution along the stack and in the resonator.

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igure 2. Heat pumping cycle along a stack plate by onsidering the oscillation of one gas parcel. The four steps f the cycle are: 1: ++→T T adiabatic compression, 2: ++ +→T irreversible heat transfer, 3: + −→T T adiabatic

xpansion and 4: − →T T irreversible heat transfer. Bottom rame: bucket brigade model illustrating the thermoacoustic eat pumping process along the stack plate.

Copyright © 2010 by ASME

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therefore they are ideal tools for investigation of high-speed, unsteady processes, such as the thermoacoustic heat pumping process. The combination of HI and high-speed cinematography (that allows high spatial resolutions) is used in the present study to visualize the thermoacoustic effect at the edge of thermoacoustic stack plates. In the thermoacoustic resonator the temperature fields oscillate with a frequency of 337Hz. Therefore sampling rates of the order of 5000 frames per second were needed to accurately resolve the temporal evolution of the physical process. No phase locking was needed in the measurements. At the same time high spatial resolutions of up to 2700 dpi were achieved by individually scanning the interferometric images recorded on 16mm high-speed film.

When applying HI to the visualization of temperature fields in a thermoacoustic refrigerator, the experimenter faces the challenge that the changes in the refractive index cannot be directly related to temperature changes. This is the case because, as we will show in the present paper, the acoustic pressure variations and compressibility effects cannot be neglected in the evaluation. Therefore, it was necessary to develop a new interpretation and evaluation procedure for the interferometric fringe pattern that allows accurate measurements of oscillating temperature fields by accounting for the effect of periodic pressure variations. For a complete description of the unsteady temperature distribution it was also necessary to include frequency and phase measurements into the evaluation procedure. The holographic recording is used to reconstruct the reference (old) state of the object and compare it to the measurement state (current) - rather than for capturing 3D information, which is common in holography.

EXPERIMENTAL SETUP AND METHOD

In Figure 3, the photograph of the thermoacoustic refrigerator model used in the visualization experiments described in this paper is shown. The loudspeaker (Electro Voice EVM-10M) was used to generate an acoustic standing wave in the resonance tube. The 337Hz input signal for the loudspeaker was generated by an HP 8116A function generator and amplified using a Crown DC-300A Series II amplifier, before being led to the loudspeaker. A dynamic pressure transducer (Sensym SX01) was mounted at the entrance of the resonance tube to measure acoustic pressures. At this location the transducer measures the dynamic peak pressure amplitude AP . The drive ratio in the

system is defined as the ratio of peak pressure amplitude AP to

the mean pressure mp within the working fluid, A mDR P p≡ ,

and it is determined from this measurement. Experiments were conducted for drive ratios ranging from 1% to 3% to avoid nonlinear effects.

The length of the resonance tube (510mm) matches half the wavelength of the acoustic standing wave 2acλ , as indicated

Figure 4. Photograph of the optical arrangement for holographic interferometry and the thermoacoustic refrigerator model.

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rectangular, and the experimental setup represents a two dimensional model of the physical situation in the Cartesian coordinate system. The width of the resonance tube is 157mm and this is also the length of the path of the measurement laser beam past the heated stack plate in the measurement volume L. Its height is 4cm.

Visualization experiments were carried out on two stack plates. The temperature gradient that naturally develops along the stack plates during the operation of the thermoacoustic refrigerator was enhanced by additional heating accomplished with heater foils embedded into the stack plates. This modeling can be considered as using temperature as a tracer to better resolve the small temperature fluctuations generated by the acoustic field. The dimensions of the stack plates are: plate

odel used in the e optical table with terferometry in the

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spacing 3mm, plate thickness 4mm, stack length 76mm and stack center position 127mm measured from the driver end of the resonance tube, as shown in Figure 1.

In Figure 4, the photograph of the optical arrangement for HI is presented. Laser light is used as information carrier to obtain qualitative as well as quantitative data on the investigated refractive index field, that is, after accounting for pressure variations, related to the time dependent temperature field. The light source is an argon-ion laser operating at a wavelength of λ=514.5nm. The laser beam is split into a reference beam and a measurement beam by a beam splitter. Both beams are then expanded by beam expanders and bundled into 50 mm diameter parallel rays by a collimating lens. The measuring beam (also termed the object wave) passes through the transparent side walls of the thermoacoustic refrigerator model and the working fluid, as shown in Figure 4, and falls on the holographic plate. The reference beam falls directly on the holographic plate. More details about the optical arrangement and the measurement technique are available in Herman et al., 1998 and Wetzel and Herman, 1998.

Interferometric measurements are conducted in two steps. The reference state of the fluid in the thermoacoustic refrigerator model at ambient temperature is recorded first on

the holographic plate. This reference state is later reconstructed by illuminating the holographic plate with the reference beam only. At the same time the stack plates are heated, the acoustic driver is activated, and the oscillating temperature field in the stack region and its neighborhood develops. Changes in the refractive index, caused by the heating of air as well as the acoustic field within the stack region, cause the object wave to experience a phase change on its way through the thermoacoustic refrigerator model. The difference between the reference and the measurement states is visualized in the second step in the form of an interference fringe pattern. In unsteady processes, as we will show in this paper, the fringe pattern moves following the refractive index variations in the working fluid. To capture details of the movements and to resolve the unsteady temperature fields as a function of time, we use a high-speed film camera, which is capable of recording speeds up to 10,000 picture frames per second. This speed corresponds to a temporal resolution of 0.1ms. A film camera is used rather than a digital camera to allow the high spatial resolutions needed to resolve dense and thin fringes in thin thermal boundary layers.

In conventional applications of HI in heat transfer, the evaluation of the interferometric fringes is based on the following three equations (Hauf and Grigull, 1970): (i) the

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igure 5. a-h) Oscillating temperature fields around two stack plates of the thermoacoustic refrigerator at a drive ratio DR=1%. mages were recorded at a rate of 5,000 picture frames per second. Fringes of the order 0, 0.5 and 1 are indicated in the images nd the measured temperature as well as the shape and motion of the fringe of the order of 0.5 is displayed under the image. It hould be noted that the temperature of this fringe changes periodically with the change of the acoustic pressure.


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equation of ideal interferometry

( , , ) ( ( , , ) )S x y t n x y t n Lλ ∞⋅ = − ⋅ , (1)

that applies in the present form when the experiment is designed to represent a two dimensional model of the physical situation in the Cartesian coordinate system, (ii) the Gladstone-Dale equation,

2 1( ) ( ( , , ) 1)

3 ( , , )r n x y t

x y tλ

ρ= − , (2)

that holds when gases with a refractive index close to one are used as working fluids, and (iii) the ideal gas law

( , , )( , , )

( , , )p x y t

R T x y tx y tρ

= ⋅ . (3)

The parameters of interest for interferometric measurements in this set of equations are the refractive index ( , , )n x y t ,

density ( , , )x y tρ , temperature ( , , )T x y t , pressure ( , , )p x y t

and interference order ( , , )S x y t , which are all functions of the spatial coordinates x and y and time t . In an experiment the

interference order ( , , )S x y t is measured, so that we are left

with four unknowns ( , , )n x y t , ( , , )x y tρ , ( , , )T x y t and

( , , )p x y t , related by only three equations. In conventional applications of HI in heat transfer this problem is resolved by maintaining the pressures of the reference state and the measurement state constant and equal. In the present study the approach of maintaining constant pressure is not feasible, since acoustic pressure variations that cannot be neglected in the evaluation process are present in the measurement volume. Therefore, additional information is needed to be able to extract temperature data from the interferometric fringe pattern.

In the evaluations the interference order ( , , )S x y t is represented as a linear combination of a time independent mean value ( , )mS x y and a harmonic, time dependent fluctuation

( , , )S x y tδ , similar to the representation of the pressure in an acoustic field. Substituting the expansions for the density (Eqs. 2-3) and the interference order (Eq. 1) into the equations for the reconstruction of temperature fields, and collecting the time independent and time dependent terms, we obtain the following two equations

2( , ) ( , )

3 ( )m mx y S x y

L r

λρ ρ

λ ∞= + (4)

and 2

( , ) ( , )3 ( )

A Ax y S x yL r

λρ

λ= . (5)

The notable feature of Equations 4 and 5 is that the mean interference order ( , )mS x y as well as the amplitude ( , )AS x y

of the fluctuation ( , , )S x y tδ are not necessarily multiples of 1

or 1 2 , as in conventional applications of HI. Since the pressure distribution in the resonance tube is known, it was possible to remove the influence of temperature fluctuations from the pressure measurement. More details about the reconstruction procedure can be found in Wetzel and Herman, 1998. RESULTS The temperature fields visualized by HI were analyzed and reconstructed quantitatively by first identifying a sequence of interferometric images that describe a complete period of acoustic oscillations in the movie segment of interest. A sequence of 8 interferometric images, representative of one period of oscillations for a drive ratio of 1%, is presented in Figure 5. The changes the fringe pattern undergoes during one period of oscillations are analyzed by following the motion of the fringes tagged with the order 0.5. The changes of temperature of the fringe tagged with interference order 0.5 from 77.3ºC to 71.4ºC - obtained by taking advantage of the concept of quasi isotherms - are indicated in the schematic for the time instants illustrated in Figure 5.

Prior to the quantitative evaluation, an image specific coordinate system was defined, and image processing as well as

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m]

Figure 6. Time-averaged visualized temperature fields (left: color coded reconstructions from interferometric fringe patterns and right: corresponding interferometric fringe patterns) at the hot end of the two stack plates for drive ratios DR of 1%, 2% and 3%.



curve fit algorithms were applied to determine the spatially and temporally continuous interference order ( , , )S x y t . Details regarding the image processing procedure are available in the literature (Wetzel and Herman, 1998). From the continuous interference order, the time averaged interference order

( , )mS x y and the interference order amplitude ( , )AS x y were recovered. The latter two quantities were then used to determine the time averaged temperature fields ( , )mT x y , shown in Figure 6.

An examination of the time averaged temperature field and interferometric image in Figure 6a shows that for the drive ratio DR=1% the working fluid along the axis of the channel is colder than at the stack plates. This trend is confirmed by considering the interferometric image on the right hand side of Figure 6a. This image demonstrates that the colder fringe of order 0 bends over the warmer fringe of order 0.5. Such a temperature distribution and fringe pattern indicate that heat is being transferred from the stack plates to the working fluid. This behavior is expected, since heat is generated in the stack plates by resistive heaters.

The shape of the isotherms in Figures 6b and c, representing the time averaged temperature fields for the drive ratio DR=2% and 3%, becomes more complicated than for DR=1%, with the shape of the isotherms reflecting vortex shedding in the region 0 1ξ≤ ≤ , which is the edge of the stack plate. The temperature of the working fluid is higher than that of the lower stack plate close to the edge of the plate ( ~ 0ξ ). Both fringe pattern and temperature distribution indicate that heat is transferred into the lower stack plate at ~ 0ξ .

Time dependent temperature distributions ( , , )T x y t in the upper half of the channel between the two investigated stack plates for the drive ratio DR=3% are shown in Figure 7. The flow direction is also indicated in Figure 7, and the length of the arrow is proportional to the flow velocity. The instanteneous temperature distributions correspond to four time instants of one half of the acoustic cycle, 0, 6 , / 3 and / 2t τ τ τ= , steps 2 through 4, described by the gas parcel model (Swift, 1988). At t=0 (top left) the working fluid is fully compressed and hotter than the stack plate in the region 0 3ξ< < . This is indicative of heat being transferred into the stack plate. This time instant displayed therefore corresponds to the second step in the gas parcel model with the working fluid at the temperature T ++ (Figure 2). As time progresses, at

6 and / 3 t τ τ= (top right and bottom left), the working fluid

gradually expands and cools down to the temperature T − . This time sequence corresponds to the third step in the gas parcel model. The fourth step in the gas parcel model is represented by the last temperature field image (bottom right) in Figure 7. At this time instant the working fluid is fully expanded, it is colder than the stack plate, and heat is being transferred from the stack plate to the working fluid, illustrated as cdQ . During the second half of the cycle the working fluid is being compressed, and the temperature distribution goes through the phases displayed in Figure 7 in reversed order. The temperature gradient changes sign and therefore heat is being transferred from the stack plate into the working fluid at 0ξ = .

distance =ξtdx/x

td

0

-1.5

625672

[ C]o

10-1 2 3

t= /2τ

distance =ξtdx/x

td

flow

0

-1.5

625650

[ C]o

10-1 2 3

t= /3τ

distance =ξtdx/x

td

flow

0

-1.5

625752

[ C]o

10-1 2 3

t= /6τ

distance =ξtdx/x

td

0

-1.5

645852

[ C]o

10-1 2 3

t=0

Figure 7. Visualization of the thermoacoutic effect through the reconstructed temperature distributions during one half of the acoustic cycle. The first image illustrates full compression and the last one full expansion with the associated reversal of the direction of the heat flow, which is the characteristic of the thermoacoutic effect.



CONCLUSIONS The results shown in the paper illustrate that holographic interferometry is suitable for the visualization and accurate measurement of the high-speed, unsteady, oscillating temperature fields. The reversal of the heat flow direction during the acoustic cycle is shown and the thermoacoustic effect was successfully visualized. These experiments represent the first visualization of the thermoacoustic effect. From the temperature measurements discussed in this paper the values of the local heat transfer coefficients can be determined. Heat transfer coefficients are needed to optimize the design heat exchangers for this system

ACKNOWLEDGMENTS The contribution of Martin Wetzel to the visualization experiments is gratefully acknowledged.

REFERENCES Hauf, W., Grigull, U., 1970, "Optical methods in heat

transfer", Advances in Heat Transfer, Vol. 6, Academic Press, New York.

Herman, C., Kang, E., Wetzel, M., 1998, "Expanding the

application of holographic interferometry to the quantitative visualization of oscillatory thermofluid processes using temperature as tracer", Exp. Fluids, Vol. 24 5/6, pp. 431-446. Rott, N., 1980, "Thermoacoustics", Adv. Appl. Mech., Vol. 20, pp. 135-175. Swift, G.W., 1988, "Thermoacoustic engines", J. Acoust. Soc. Am. 84(4), pp. 1145-1180.

Vest, C. M., 1979, "Holographic interferometry", John Wiley

& Sons, New York. Wetzel, M., Herman C., 1998, "Accurate measurements of

high-speed, unsteady temperature fields by holographic interferometry in the presence of periodic pressure variations", Meas. Sci. Technol., Vol. 9, No. 6, pp. 939-9.


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[ASME 2010 14th International Heat Transfer Conference - Washington, DC, USA (August 8–13, 2010)] 2010 14th International Heat Transfer Conference, Volume 4 - Quantitative Visualization