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Thermal Response of Thermoacoustic Refrigerating System to Variable Loading

Emmanuel C. Nsofor1 and Azrai Ali2

Department of Mechanical Engineering and Energy Processes Southern Illinois University, Carbondale, IL 62901

[Abstract] In this study, an experimental research was conducted on the thermal response of the thermoacoustic refrigeration system subjected to varying cooling load. The setup consists mainly of the thermoacoustic refrigeration system with appropriate valves for the desired controls, instrumentation and the electronic data acquisition system. An acoustic driver connected to an amplifier and an audio generator produced the required power and acoustic waves in the resonator. The stack used in this system is the parallel plate type made from a thermoplastic material. Each plate was lined with aluminum perpendicular to its thickness to reduce the heat transfer in the direction opposite to the heat pumping in the resonator tube. The temperature difference between the two ends of the stack ranged from 0ºC to 15ºC. The cooling load was controlled using resistance heating in place of the cold side heat exchanger. Significant factors that influence the performance of the thermoacoustic refrigerating system were identified. The cooling load increases with the temperature difference between the two ends of the stack. High pressure alone does not necessarily result in a higher cooling load in the system. There exists an optimum pressure and an optimum frequency for which the system should be operated so as to obtain maximum cooling load. There should be a compromise between pressure, frequency and cooling for best performance of the system.

Nomenclature a = sound velocity B = blockage ratio cp = isobaric specific heat COP = coefficient of performance D = drive ratio d = diameter f = frequency k = thermal conductivity Lsn = normalized stack length M = Mach number

HeM = molecular mass of Helium Pm= = mean pressure Qc = cooling power Qcn = normalized cooling power R = gas constant Re = Reynolds number T = temperature Th = hot side temperature of the stack Tm = mean temperature u = velocity _______________________________ 1 Associate Professor, Department of Mechanical Engineering and Energy Processes, Mail Stop 6603, Member. 2 Graduate Student, Department of Mechanical Engineering and Energy Processes, Mail Stop 6603, Nonmember.

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5th International Energy Conversion Engineering Conference and Exhibit (IECEC) 25 - 27 June 2007, St. Louis, Missouri

AIAA 2007-4775

Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

W = acoustic power Wtotal = total acoustic power xn = normalized stack center position α = thermal diffusivity

kδ = thermal penetration depth

knδ = normalized thermal penetration depth

vδ = viscous penetration depth γ = ratio of specific heats

Heγ = adiabatic constant for Helium µ = dynamic viscosity coefficient ν = kinematic viscosity coefficient ρ = density

mρ = mean density σ = Prandtl number ω = angular frequency

mT∆ = temperature difference between hot end and cold end of the stack

mnT∆ = normalized temperature difference

I. Introduction Orefo

NCERN for the environment has become increasingly important in the design and development of frigerating systems. To eliminate the use of environmentally hazardous refrigerants, research efforts have cused partly on the development of alternative refrigerants and partly on alternative refrigeration

technologies. An approach in the category of alternative technologies is thermoacoustic refrigeration, a process by which cooling is produced from sound. Fluid inside the resonance tube of the system interacts thermally with the stack plates aligned parallel to the direction of vibration of the standing waves supported by the fluid. The two major effects resulting from communication between the sound waves and the solid boundary of the stack plates are the absorption of acoustic power very close to the surface of the plates and a heat flux at the surface of the plates in the direction of acoustic vibration.

C

Previous related studies include Jebali et al. [1] where the performance of a thermoacoustic refrigerator subjected to variable loading was studied. The hot heat exchanger of the system was maintained at ambient temperature while the temperature of the cold heat exchanger was varied to achieve temperature differences of between 0 and 10ºC along the stack. The cooling load was measured for these temperature differences while varying the driving frequency between 30 and 65 Hz. The contribution of the progressive and stationary waves and the losses on the thermoacoustic heat flow was calculated. Results from the study show that the cooling power is dependent on the working frequency and on the temperature difference between the stack ends. Also, the maximum refrigeration power occurs around the resonance frequency for a non-zero temperature span.

Bai et al. [2] studied and reported on the performance of a thermoacoustic prime mover. The study investigated the effect of the working fluid, resonator length, charging pressure and heating temperature on the performance of the prime mover. Zhou [3] performed experiments on a thermoacoustic prime mover with stacks made of copper wire mesh. The influence of gas properties, frequency, mean pressure, mesh size and stack length on overall performance were measured and expressed in terms of normalized input power, heater temperature and pressure amplitude. Wetzel and Herman [4, 5] investigated the thermal interaction between a heated solid plate and the working fluid by visualizing and quantifying the temperature fields in the neighborhood of the solid plate. A combination of holographic interferometry and high-speed cinematography was used in the experiments. The study was more on the thermoacoustic effects on a single stack plate. An evaluation procedure that accounts for the influence of acoustic pressure variations on the refractive index was applied to reconstruct the high speed, two-dimensional oscillating temperature distributions. The reports summarized the design steps, gave guidelines and pointed out areas where more research is required.

Worlikar et al [6, 7, and 8] performed numerical studies on a thermoacoustic refrigeration system with emphasis on thermally stratified flow in the neighborhood of an idealized thermoacoustic stack, using a low-Mach-number model. Energy flux density around the heat exchangers was visualized and implications on the heat exchanger

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design were examined. Belcher et al [9] reported that the best working gases for thermoacoustic refrigeration should have high ratios of specific heats and low Prandtl numbers. This was based on studies related to working gases suitable for use in thermoacoustic systems. Swift [10] documented the early history of thermoacoustics and provided the basic equations and concepts for the thermoacoustic theory in a book [11].

The purpose of the present work is to study the thermal response of the thermoacoustic refrigerating system subjected to variable loading. Since limited studies have been made on the response of this system when subjected to variable loading, further research such as this is necessary for better understanding of the thermoacoustic system. The experimental setup consists mainly of the thermoacoustic refrigeration system with appropriate valves for the desired controls, instrumentation and the electronic data acquisition system. The stack used in the resonator is the parallel plate type made from a thermoplastic material and each plate was lined with aluminum perpendicular to the plate the plate thickness to reduce the heat transfer in the direction opposite to the heat pumping. The experimental study is on the systems’ response to various working pressures, frequencies, and refrigerant loading to understand the performance of the system better. Helium was used as the working fluid in the system.

II. Summary on the System Design and Basic Equations The stack of the system used in this study was fabricated from a thermoplastic material to reduce conduction in

the direction opposite to heat pumping. For design of the resonator tube, a length parameter of λ/4 with open-end criteria [12] was used. The ratio of the small diameter tube portion to the large diameter tube portion was 0.54 for minimum energy losses. The auxiliary components of the system include the audio frequency generator, power amplifier, pressure transducers and gauges, thermocouples, an oscilloscope and the data acquisition system. The desired cooling power, temperature difference between the hot heat exchanger and the cold heat exchanger and the operating frequency of the system were some of the items selected for the design of the system. The acoustic Mach number M was limited to approximately 0.1 to eliminate nonlinear effects [13]. The Reynolds number defined as

υδ v

u=Re (1)

was also limited to less than 500 to avoid turbulence [13]. The drive ratio, defined as

essureMeanAmplitudeessureDynamicD

PrPr

= (2)

of 0.02 was selected to satisfy M < 0.1 and Re < 500. Thermal penetration depth kδ was calculated using the equation

ωδ

ρ pm

k ck2

= (3)

and the viscous penetration depth vδ was calculated using the equation

ωµδ

ρm

v2

= (4)

where u is axial particle velocity, ν is kinematic viscosity, k is thermal conductivity, ρm is mean density, cp is isobaric specific heat, ω is angular frequency and µ is dynamic viscosity. The angular frequency ω of the sound wave is defined as

fπω 2= (5)

The normalized cooling power, and acoustic power, was expressed [12] as cnQ nW

⎟⎟⎠

⎞⎜⎜⎝

⎛−+−

+++

−∆

Λ+−= )1(

11

)1()tan(

)1(82sin2

knsn

nmnnkncn BL

xTxDQ δσσσσσ

γσγδ

(6)

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Λ−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

Λ+−∆

−=B

xDLBL

xTxBDLW nsnkn

sn

nmnn

snknn

222

2 sin4

1)1)(1(

)tan(cos)1(4

σγ

δσγ

γγ

δ (7)

where is expressed as Λ2

211 knkn σδδσ +−=Λ (8)

From equation 6, the normalized cooling power is seen to be affected by several parameters. However, some of these parameters are constant such as the blockage ratio and some geometrical parameters since the stack has been fabricated. The equation for sound velocity in Helium is given by [11]

He

mHe

MRTa γ

= (9)

where is the gas constant and is the molecular mass of the gas. When the system parameters and relevant information are substituted into equation (6) and the equation is simplified, it can be shown that the cooling load is a function of mean pressure, mean temperature, hot side temperature, oscillating frequency and drive ratio. Thus

R HeM

),,,,( DfTTPFQ hmmc = (10)

The Drive ratio defined in equation (2) is also a function of mean pressure. Therefore, the main parameters that

affect the cooling load are pressure, temperature and frequency. Experiments were performed to study the response of the system to frequency, cooling load and pressure. The performance of the system can be calculated using the expression for the coefficient of performance

total

c

WQ

COP = (11)

where is the total input power to the system. totalW

III. Experimental Setup and Procedure Figure 1 shows an outline or schematic illustrating the arrangement of the experimental setup. The data

acquisition system includes thermocouples, pressure transducer, oscilloscope, flow meter, data acquisition board and a personal computer for the data display. In the figure T, M and P stand for temperature, mass flow and pressure connections respectively. Water was used to cool the hot heat exchanger and reject heat from the system to the outside. An electrical resistance heater arrangement was located at the cold side of the resonator to supply the variable load for the refrigerating system. An audio generator with frequency range from 10Hz to 1MHz was used to produce the sound that was transferred to the amplifier. The amplified sound is transferred to the acoustic driver which powers the thermoacoustic system.

Two thermocouples were installed at each end of the stack. One thermocouple was installed near the electric heater, one was installed at the surface of the acoustic driver, two were each installed at the inlet and outlet of the cooling water; and one was installed at the middle of the resonator tube. All the thermocouples used inside the vacuum vessel, were type-T Teflon insulated. The thermocouples used are capable of measuring both low temperatures and high temperatures encountered in the system. Outside the vacuum vessel, the thermocouples used were type-T Nylon insulated with a diameter of 0.024 inches. All the thermocouples were connected to the data acquisition board. The pressure transducer used to measure the pressure has a range of 0 to 100 psig. An oscilloscope was used to analyze the pressure waves. It can measure at a maximum sampling rate of 200Msa/s with the highest frequency it can detect being 100MHz. The flow-meter was also connected to the data acquisition board that has 16 input channels. Although the thermocouples, pressure transducers and flow meters were calibrated by the manufacturers, they were also calibrated before the measurements were made using suitable calibrators.

Experiments were conducted to find the thermal response of the system under various operating conditions. The mean pressure was set initially at the lowest pressure of 3 bars to begin the experiments. The desired frequency was selected and increased slowly from minimum to the maximum in the course of each of these experiments. The cooling load which was controlled using the resistance heating in place of the cold side heat exchanger was initially

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set at a constant load. For each experiment, the data readings were taken from the initial time until conditions became stable. The frequency was then set at the next level and the experiment was repeated. After completing the

Figure 1 Schematic of the experimental setup experiments for the desired frequency range, the pressure was adjusted to the next level and the experiment was repeated for the same set of frequencies and cooling load. The experiments were also repeated for various values of the cooling load setting from the lowest cooling load to the highest.

IV. Results and Discussion Figure 2 shows the history of the temperature (at the hot end of the stack) for various frequencies at constant mean pressure and cooling load. This shows how the frequency affects the temperature in the system. The graph shows

2021222324252627282930

0 200 400 600 800 1000 1200 1400

time (sec)

tem

pera

ture

(°C

) 250Hz300Hz350Hz400Hz450Hz500Hz

Figure 2. Temperature (at the hot end of the stack) -time history for a constant cooling load and mean pressure for various frequencies.

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that for each frequency, the temperature increased at the beginning and then stabilized after a time. The experiment was performed for various constant pressure and cooling load. It was found that the stabilization time increased as the pressure was increased. This could be because the thermoacoustic process increased with pressure in the system and therefore it took more time for the temperature to stabilize.

Figure 3 shows the history of the temperature at the hot end of the stack when the cooling load was varied at constant pressure and frequency. It can also be seen that the temperature increased at the beginning and stabilized after a time. The maximum temperature occurred for the maximum power tested and the lowest temperature occurred at the lowest power confirming that the maximum temperature increased with the cooling load. This is good for the system since higher temperatures are likely to result in higher temperature differences between the two ends of the stack and therefore better performance of the system. Also, the stabilization time increased as the cooling load increased. This might be because the working temperature in the system increased as the cooling load increased. More time is needed to reach equilibrium in the system.

20.000

25.000

30.000

35.000

40.000

45.000

0 200 400 600 800 1000

time (sec)

tem

pera

ture

(°C

)

1W2W3W4W

Figure 3. Temperature at the hot end of the stack-time history at constant mean pressure and frequency.

Figure 4 shows variation of the temperature at the hot end of the stack with frequency when the cooling load was varied at constant pressure. This looks sinusoidal which is likely due to the oscillating nature for the gas in the thermoacoustic process. Each cooling load has a different maximum temperature for the range of the frequency

20.000

25.000

30.000

35.000

40.000

45.000

250 300 350 400 450 500

frequency (Hz)

tem

pera

ture

(°C

)

1W2W3W4W

Figure 4. Temperature at the end of the stack versus frequency at constant mean pressure for various cooling loads.

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studied. The results also confirm that the higher the cooling load required, the higher the hot side temperature should be at the resonator.

12.500

13.000

13.500

14.000

14.500

15.000

3 4 5 6

pressure (bars)

Tem

pera

ture

diff

eren

ce (°

C)

Figure 5. Temperature difference between the two ends of the stack versus mean pressure at constant frequency.

Figure 5 shows the variation of the temperature difference between the hot end and the cold end of the stack with pressure for a constant cooling load and frequency. The results show that for the system and the range of pressure used in this study, a maximum value of temperature difference occurs at a pressure of about 4 bars. At higher pressures, the temperature difference decreases. Thus increasing the pressure in the system further wouldn’t result in a better temperature difference and thus cooling load. It can be concluded that for the thermoacoustic system, there is an optimum pressure that gives the maximum temperature difference.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

Temperature difference (°C)

Coo

ling

Load

(W)

Figure 6. Cooling load versus temperature difference between the two ends of the stack for constant pressure and

frequency.

Figure 6 shows the cooling load versus temperature difference between the hot end and the cold end of the stack for constant pressure and frequency. The temperature difference varies linearly with the cooling load. Therefore, a

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high temperature difference between the hot end and the cold end of the stack is synonymous with high cooling load in the system.

Figure 7 shows the temperature difference between the hot end and cold end of the stack as it varies with frequency for constant cooling load and pressure. The graph looks sinusoidal which could be due to the oscillating process of the gas in the system. Also, within the limits of the study, there exists a maximum frequency that gives the maximum temperature difference between the hot end and the cold end of the stack. Thus in order to achieve maximum hot side temperature for a possible maximum cooling load, careful consideration needs to be made in choosing the operating pressure and frequency for the system.

12.500

13.000

13.500

14.000

250 300 350 400 450 500

Frequency (Hz)

Tem

pera

ture

Diff

eren

ce (°

C)

Figure 7. Temperature difference between the two ends of the stack versus frequency for a constant cooling load

and pressure.

V.Conclusion An experimental research was conducted to study the thermal response of the thermoacoustic refrigerating system

to variable loading. The temperature difference between the hot end and the cold end of the stack ranged from 0ºC to 15ºC. The cooling load was controlled using resistance heating in place of the cold side heat exchanger. Results from this study show that the cooling load increases with the temperature difference between the two ends of the stack which confirms the results of the study by Jebali et al. [1]. It was also found that high pressure alone in the system does not necessarily result in a higher cooling temperature difference and thus a higher cooling load. For the thermoacoustic refrigerating system, there exists for a given frequency, an optimum pressure that results in the maximum temperature difference that is expected to result in the possible maximum cooling load. Thus, careful consideration should be taken in choosing the operating pressure and frequency for the system.

Acknowledgments The authors are grateful to Serdar Celik and Hans Bank for valuable advice and contributions in the development

of the experimental system and experimentation.

References 1Jebali, F., Lubiez, J. V., and Francois, M. X., “Response of a Thermoacoustic Refrigerator to the Variation of the

Driving Frequency and Loading”, International Journal of Refrigeration, Vol. 27, pp. 165-175. 2Bai, X., Jin, T., and Chen, G. B., “Experimental Study on a Thermoacoustic Prime Mover,” Proceedings of the Conference on Cryogenics and Refrigeration, ICCR, Hangzhou, China, pp. 522 – 525. 3Zhou, S and Matsubara, Y, “Experimental research of the thermoacoustic prime mover”, Cryogenics, Vol.38; Aug 1998.

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4Herman, C and Wetzel, M, “Experimental study of thermoacoustic effects on a single plate-Part 2”, Heat and Mass Transfer, Vol.35; No.6; p 433-441. 5Herman, C and Wetzel, M, “Experimental study of thermoacoustic effects on a single plate-Part 1”, Heat and Mass Transfer, Vol.36; No.1; p 7-20.

6Worlikar, A. S., and Knio, O. M., “Numerical Simulation of a Thermoacoustic Refrigerator I – Unsteady Adiabatic Flow around the Stack,” Journal of Computational Physics, Vol. 127 pp. 424 – 451.

7Worlikar, A. S., Knio, O. M., and Klein, R., “Numerical Simulation of a Thermoacoustic Refrigerator II – Stratified Flow around the Stack,” Journal of Computational Physics, Vol. 144, No. 2 pp. 299 – 324. 8Worlikar, A. S., and Knio, O. M., “Numerical Study of Oscillatory Flow and Heat Transfer in a Loaded Thermoacoustic Stack,” Numerical Heat Transfer, Part A: Applications, Vol. 35, No.1, pp. 49 – 65. 9Belcher, J. R., Slaton, W. V., Raspet, R., Bass, H. F., and Lightfoot, J., “Working Gases in Thermoacoustic Engines,” Journal of the Acoustical Society of America, Vol. 105, No. 5, pp. 2677 – 2684. 10Swift, G. W., “Thermoacoustic Engines”, Journal of the Acoustical Society of America, Vol. 84, No. 4, 1988, pp. 1145 – 1180. 11Swift, G. W., Thermoacoustics: A Unifying Perspective for some Engines and Refrigerators, New York: Acoustical Society of America: 2002. 12Tijani, M. E. H., Zeegers, J. C. H. and de Waele, A. T. A. M., “Design of thermoacoustic refrigerators”, Journal of Cryogenics, Vol. 42, pp.49 - 57. 13Merkli, P. and Thomann, H., “Transition to Turbulence in Oscillating Pipe Flow”, Journal of Fluid Mechanics, Vol. 68, pp. 567 – 575. 14Hofler, T. J., “Thermoacoustic Refrigerator Design and Performance”, Ph.D. Dissertation, Physics Department, University of California at San Diego, USA, 1986.

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