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ICR07-A1-156

PARAMETRIC STUDIES OF THERMOACOUSTIC REFREIGERATORS

DRIVEN BY SOLAR ENERGY

Guozhong DING, Xiaoqing ZHANG, Fangzhong GUO, Suyi HUANG

School of Energy and Power Engineering,Huazhong University of Science and

Technology,Wuhan,Hubei,430074,P.R.China

Fax:86-27-87540724 email:ding_guo_zhong@https://www.sodocs.net/doc/632521905.html,

ABSTRACT

The article discusses the technical feasibility of thermoacoustic refrigerator driven by solar energy. A concept of a thermoacoustic stack (TARS)is proposed and the thermoacoutic Stirling scheme is adopted as a basic system for parametric study of a refrigeration energy transducer driven by solor energy. The relationships between pressures of input pressure, resonator pressure and output pressure and between working frequency and buffer volume are discussed, and a series of problems have been investigated by computation modeling . The main problems are the limitation of specific cold capacity in unit volume, the preferred resonance frequency and the required thermal properties of working medium in TA system. Based on the presented study an experimental prototype of the proposed system is being established.

INTRODUCTION

Over the last three decades, with the fast development of the thermoacoustic technology, thermoacousic engines(refrigerators and prime movers) reached a great benefit in terms of simplicity, reliability and cost. Moreover, the employment of nonpollution working fluids makes thermoacoustic devices being very attracitive from an environmental point of view. A comprehensive review of the principles of thermoacoustic heat transport can be found in the tutorial article of Swift[1,2].Usually solar energy power density is about 800W/m 2。For a 20m 2 air-conditioning room, 3000W refrigeration capacity supply is required. Suppose the temperatures of two heat source of a refrigerator is 400K and 300K and the effective absorb coefficient is 0.5, 400W/m 2 power can be absorbed, then Carnot efficiency is 25.0=η, the required solar energy area is 30m 2 under the condition of Carnot efficiency. The best efficiency of thermoacoustic engines is 0.4 of Carnot efficiency reported by G . Swift reported[3]. It is obvious that the refrigeration capacity is insufficient if supplied only by solar energy. Whether is there a technical feasibility of thermoacoustic refrigerator driven by solar energy? In order to solve the problem, the power density for application has to be estimated. According to current thermoacoutic refrigerator ’s levels and there are being some problems, such as power density, critical temperature and feasibility, effectiveness. A original scheme of thermoacoustic refrigerators stacks(TARS) can be exploited, it can be assembled by a lot of TARS chips according to the requirement of target objects.

The most significant problem with prior thermoacoustic engines and refrigerators is that they have a very low power density. They are typically much larger and more massive for the amount of output work they produce, than other types of engines and refrigerators. A compound engine by coupling Ceperley ’s

torus-shaped traveling-wave engine with a cylindrical standing-wave resonator, made by Greg Swift[3], in an effort to produce greater output power from the traveling-wave component, without damping the standing-wave oscillator. But the engine develops low energy density because the design still relies mainly on geometry to produce an engine that is acoustically resonant.H. Sugita et al. [4] reported an experimental study on thermally actuated pressure wave generator for space cryocooler, the maximum work amplification ratio of 1.6 was obtained in the work amplifier with solid displacers. It is the best level in thermoacoustic refrigetators so far. The paper will adopt Sugita model and the analysis of the influence of buffer volume on working frequency will be also discussed. According to the prototype, the power density of thermoacoutic refrigerator that is estimatly compared with that of target objects to decide the numbers of TARS chips. Another key problem of thermoacoustic refrigeration driven by solar energy is that the influence of temperature difference of heat sources on the performance of thermoacoustic refrigeration, which decides the technical feasibility of thermoacustic refrigerator. This will be also discussed in the paper.

1. SCHEME STUDY OF THE TECHNICAL FEASIBILITY OF THERMOACOUSTIC

REFRIGERATOR DRIVEN BY SOLAR ENERGY

The paper proposes a conceptual scheme that the key component is a thermoacoustic stacks(TARS) with resonator and buffer volume. Its optimistic target is unit volume refrigeration capacity, which decides the number of TARS in one square meter. In terms of required refrigeration, the number of TARS calculated can be compared with the maximum number TARS that can be laid in one square meter. According to the compared results, the scheme of thermoacoustic refrigerator driven by solar energy whether is with reason can be verdicted.

Power output of the TARS depends on the physical dimensions of the pistons and heat exchangers in the device, the static pressure of the working fluid and the thermal gradient across the device. The frequency of operation is determined by the engineering properties of all the heat exchangers, and to a less extent, by the geometry of the acoustic cavity. When affixed to a blackened metal absorber panel, or other radiant-energy absorbing material, and to a cooling means on its opposite face, the TAR can convert heat from radiant energy, such as sunlight, into electrical energy. In this respect, the TAR responds to a wider bandwidth of radiant energy than photovoltaic cells. It can absorb and use wavelengths that are below the photovoltaic threshold for most materials.Energy conversion efficiencies are directly related to the temperature gradient across the TAR. According to above said description, key parameters of thermoacoustic refrigerator driven by solar energy, which decided by optimistic target of unit volume refrigeration capacity, are the relationship between input pressures, resonator pressure and output pressure, and the relationship between working frequency and buffer volume,and the location of stack and wire mesh have an important effect on performance of TARS.

The calculation scheme of thermoacoutic Stirling amplifer is shown below[4]:

Fig. 1 Schematic diagram of work amplifer

1.1 Basic equation of thermoacoustic systems

The network scheme figure of resonator of Stirling engine is shown below[5]:

Fig.2 the network scheme of variation volume resonator for Stirling engine

s R is the sum of dissipation of the engine system, s p m m + is the total mass of vibration, s k is strain coefficient of spring systems, TA R is the actual load of the Stirling engine system.

It is obvious that the characteristic frequency of the system is as follows: s s m k f π21

0=

(1) where dr m ech gas s k k k k ++=, dr p s m m m m ++=0s .

This is a optimation frequency of the system for the design of thermoacousitc Stirling engine.In fact, the length ,geometry and diameter of resonator and void volume have an important effect on the resonance frequency.

The network model of resonator is expressed as follows[6]:

??

????''??????-=??????''in in end end J p a V i J p 1/012ρω (2) The network transport equation of thermoacoustic components is expressed as follows[6]:

???????????

???????+++-+-++++=??????----in in x x

x x x x x x J p e e e e z e e z e e J p 21212121212211212121211212)()(1)(γγγγγγγγγγγγγγγγγγγγγγγγγγ (3) yz 4212121++-=ααγ, yz 4212122++=ααγ

The equation is suitable for all kinds of stacks such as parallel plates, circular pores, meshes, and pin-array . the work flux is then given by[7,8]

t r u p x I ?????=11)( (4)

The symbol t >?

written as follows:

?c o s ||||5.0)(11q p x W = (5)

For modeling the output work and pressure variation of TARS, momentum equation and pressure equations respect to thermoacoustic components need to be established according to Fig. 1[11].

1.2 Influence of buffer volume on working frequency

As shown in Fig.1, the equations of continuity and mass conservation lead to

04030201P P P P ===

004030201=+++Q Q Q Q

where P is gas pressure and Q is volume flow rate.

In terms of the fluid network principle, for a pipe with length L and flow area A, when the gas viscosity is ignored, the relation between the input impedance and output impedance of the system, is given[9]

L

C L L C Z a L Z Z i a L Z Z i

Z ωωt a n 1t a n 10++= (6) where a is acoustic speed, C Z is characteristic impedance which is equal to A a /ρ to an idealized pipe, ρ is fluid density, ω is angular frequency, 0Z is input impedance, L Z is output impedance. In terms of the definition of impedance, we get:

0111104

030201=+++Z Z Z Z (7) Using Eq.(6), the frequency equation can be expressed as

011t a n 1t a n 1t a n 1t a n 10403222222

2221111111=+++++++Z Z a V i a L Z Z i a L Z Z i a V i a L Z Z i a L Z Z i

L C C L L C C L ρωωωρωωω (8) 1.3 Influence of temperature difference on performance of TARS

The thermoacoustic refrigerator driven by solar energy has a low temperature difference between the hot end and the cold ends of the regenerator (stack), a gamma-configuration engine requireds a normal 90 degree phase angle between the displacer and the power piston. Some characteristics of the low temperature difference Stirling refrigerator are as follows:(1)Displacer to power piston swept volume ratio is large;(2)Diameter of displacer cylinder and displacer is large;(3)Displacer is short;(4)Displacer stroke is small;(5)Working frequency is low.The characteristics are the same with external actuacted thermoacoustic Stirling engine.

1.4 Influence of kinds and location of stacks(regenerator) on performance of TARS

Work gain has a peak with the length of stacks under the condition of different wire mesh. The influence of

stack can be calculated by DeltaE and the result show that an optimistic length of stacks(regenerator) must be choosed.

2 THE CALCULATION RESULT AND DISCUSSION OF A PROTOTYPE SCHEME 2.1 The input work and loss of TARS

Fig. 3 Input work at an actuator

PV work is shown in Fig.3 under the condition of different working frequency。This is the input work at the compressor piston. It tells us that a larger input work under the condition of the same amplification ratio is more benificial. Fig.4 is the dissipated work at the displacer. The narrow PV shape indicates the high quality factor of the resonator to generate the standing wave.

Fig. 4 Lost work at buffer volumes

2.2 The relationship between pressures of TARS

Fig.5 Pressure variation with time

The pressure variation is shown in Fig.5. It is obvious that there are a phase angle difference between the compression piston and displacer and buffer volume. It tells us that the three components need optimistic design to produce resonant working frequency under the condition of three inherent charcteristic frequency. From Fig.5, a difference of the amplification between pressures can be found. It tells us that a larger input pressure can reach a larger output work at the condition of the same pressure ratio.

2.3 influence of buffer volume on working frequency

The computed result of the dependence of specific buffer volume on resonance frequency with helium as the working fluid is shown in Fig.6. The resonance frequency of the resonator can be decreased by means of increasing the buffer volume in each arrangement[10]. The arrangement of Fig.1 is the best for the frequency reduction.

Fig. 6 Relationship between resonance frequency and buffer volume

From Fig.6 we can find that an optimical buffer volume is coincided with the design resonance frequency.

2.4 Influence of kinds and location of stacks on performance of TARS

Fig.7 Influence of the length of stacks and wire mesh on performance of TARS

From Fig.7 the length of stack and wire mesh must be an optimistic choice.

CONCLUSION

In this paper, we proposed a prototype scheme of a thermoacoustic refrigerator driven by solar energy. The relationships between input pressure, resonator pressure and output pressure and between working frequency and buffer volume indicate the conditions of technical feasibility of a thermoacoustic refrigerator. By discussing the parameters, a Stirling scheme of thermoacoustic refrigerator driven by solar energy must adopte work amplifier and buffer volume, and correspongding to a certain resonance frequency, there is an optimical buffer volume and a stack(regenerator). By stacking the modules of the thermoacoustic stacks, a required refrigeration capacity can be capable of satisfaction.

ACKNOWLEDGEMENT

The projects is sponsored by natural science foundation of China(50676068).

REFERENCES

1. G.W.Swift, 1988,Thermoacoustic engines,J.Acoust. Soc.Amer.84(8): 1145-1180.

2. S.Backhaus and G.W. Swift, 2000,A thermoacoustic-Stirling heat engine:Detailed study, J.Acoust.

Soc.Amer.107(6):3148-3166.

3. S. Backhaus and,G..W. Swift, 1999,A thermoacoustic Stirling heat engine, Nature 399:335-338.

4. H. Sugita et al., 2004,Experimental study on thermally actuated pressure wave generator for space

cryocooler, Cryogenics 44:431-437.

5. Qiu Tu et al., 2003, Influence of temperature gradient on acoustic characteristic parameters of stack in

TAE , Int. J. Engineering Science 41(12):1337-1349.

6. Q. Tu et al., 2003,Network model approach for calculating oscillating frequency of thermoacoustic prime

mover, Cryogenics 43(6):351-357.

7. Arnott WP, Bass HE, Raspet R. 1991,General formulation of thermoacoustics for stacks having arbitrarily

shaped pore cross sections, J.Acoust. Soc.Amer. 90(6):3228-37

8. A.Tominaga, 1995,Thermodynamic aspects of thermoacoustic theory, Cryogenics 35(7):427-440.

9. J.M. Kirshner, S. Katz, 1975,Design theory of fluidic components. New York:Academic Press.

10. G.B. Chen et al., 2002,Influence of buffer on resonance frequency of thermoacoustic engine, Cryogenics

42:223-227.

11. Y. Matsubara et al., 2003,Pressure wave generator for a pulse tube cooler, Cryocoolers 12:343-348.

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模具毕业设计外文翻译(英文+译文)

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建筑-外文翻译

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