Effect of Mean Operating Pressure on the Performance of Stack-Based Thermoacoustic Refrigerator

Transcription

1 Int. J. of Thermal & Environmental Engineering Volume 5, No. 1 (2013) Effect of Mean Operating Pressure on the Performance of Stack-Based Thermoacoustic Refrigerator B.G. Prashantha a, *, M.S. Govinde Gowda b c, S. Seetharamu a JSS Academy of Technical Education, Uttarahalli-Kengeri Road, Bangalore , India b Principal, Alwa s Institute of Engg. & Technology, Mijar, Moodbidri, D.K , India c Additional Director, MTD, Central Power Research Institute, Bangalore , India Abstract This paper describes the basic design procedures for designing a laboratory scale stack-based thermoacoustic refrigerator model and the effect of varying the mean operating pressure on its performance. The objective of the present work is to reduce the length of the resonator so as to make the device compact and hence there is a scope for increasing the performance of the refrigerator. In the present design, the dry air is used as working substance through spiral stack and heat exchangers on either side of the stack within the resonator. The loud speaker attached to one end of the resonator tube, generates acoustic pressure amplitude, which is closed at the other end. The device is tested for 1 to 10 bar mean operating pressure with the cooling load capacity varying from 1 to 10 Watts. The power density and hence the cooling capacity of the thermoacoustic refrigerator model can be increased by increasing the mean operating pressure and is found to be correct from design and analysis results using DeltaEC software. Keywords: Stack, Thermoacoustic, Quarter-wavelength resonator 1. Introduction Thermoacoustics, in its most general sense, is the study of the interaction between heat and sound. Thermoacoustic refrigeration is an emerging green technology based upon the purposeful use of high-pressure sound waves to provide cooling. These devices can be made with indigenous materials with no moving parts, no sliding seals or lubrication, are mechanically simpler than traditional vapour compression refrigerators. The loudspeaker driven thermoacoustic refrigerator is arguably the easiest form to implement successfully as an initial step and is intrinsically suited to proportional control depending on load conditions. This allows improved overall efficiency by doing rapid cool-down at a lower COP and then maintaining heat leak losses at higher COP, whereas the vapour compression units uses binary control for domestic fridges, it comes on for a while and then it goes off. The stack-based refrigeration technology for domestic cooling has not been effectively applied at room temperature so far due to limitations of current techniques and hence there is a lot of scope for improving the performance of the device by varying the various design and operational parameters. Because of its many advantages, thermoacoustic refrigeration is becoming more important in the research community and may * Corresponding author. Tel.: , Fax: ; bshosalli@rediffmail.com 2013 International Association for Sharing Knowledge and Sustainability DOI: /ijtee soon reach a point in its development when it can replace the predominant technology for air conditioning, the vapour compression cycle. The theoretical model analysis of the laboratory scale model for its optimized performance is done using DeltaEC software which is a computer programme that integrates one-dimensional wave equation and energy flow equations in a gas, for the complex geometry given by the user to validate its performance. 2. Literature Review A large amount of literature is available on thermoacoustic effect covering various aspects of thermoacoustic devices. From the literature survey, it is observed that the following parameters need attention in the design and analysis of stackbased thermoacoustic refrigerator system driven at low amplitude in which the drive ratio (which is the ratio of acoustic pressure amplitude to mean pressure), D 3% so as to avoid nonlinearities. 1. Analysis of thermoacoustic refrigerator performance for different stack geometry viz. spiral stack, parallel plate stack & pin array stack subjected to various thermoacoustic refrigerator working fluids viz. dry air, humid air, helium, neon, He-Xe mixture, He-Ar 83

2 mixture, Ne-Xe mixtures, hydrogen, carbon dioxide, natural gas, and flue gas. nitrogen, 2. In addition to the above, selection of the optimal solid materials viz. Kapton, Mylar, Stainless steel, Molybdenum, tungsten, copper, nickel and celcor for the construction of stack, heat exchangers and resonator part to build optimal model is required for the better performance with various operating conditions. 3. The power density, and hence cooling capacity, in thermoacoustic devices can be increased by increasing the mean operating pressure, P m and the diameter of the resonator [6]. It is favorable to choose P m as large as possible and is depends on the mechanical strength of the resonator. But, the thermal penetration depth, δ k is inversely proportional to square root of P m, so high value for P m, results in a small value for δ k and small stack plate spacing. This makes the construction difficult. The increase in resonator diameter influences resonator energy losses, since the total dissipated energy is proportional to the resonator wall surface area. Hence the selection of optimum mean operating pressure and resonator diameter for various working substances is needed for better performance. 4. Also the power density of the thermoacoustic refrigerator is a linear function of the frequency, and hence high value of frequency is desirable. But, high frequency results in a small stack plate spacing and that makes construction difficult. Hence the selection of optimum frequency is needed using suitable loudspeaker [5]. 5. The optimum stack center position from the driver end which depends on the highest temperature difference between the hot and cold heat exchangers, the stack length which depends on the linear acoustic displacement amplitude of the gas and the pore size of the stack in the resonator fluid is not clearly defined in the literature for optimum performance. 6. Many researchers from literature review suggested to use quarter-wavelength (λ/4) resonator over halfwavelength (λ/2) resonator [1] because it dissipates only half the energy dissipated by a half-wavelength resonator and hence there is a scope to reduce resonator length further to minimize the energy loss to environment so as to make the device compact and efficient. 7. Relatively less amount of development work is done in respect of the crucial component like in heat exchangers which determines the performance of the refrigerator. 3. Basic Design Procedures Some of the outlines of the basic design procedure for the stack-based thermoacoustic refrigerator model are summarized in the following lines. There are many parameters to be considered, which includes the stack length and position, pore size and geometry, resonator dimensions, heat exchanger dimensions, driver parameters, working gas properties, and operating conditions. To begin a design, few choices must be made to reduce the number of variables. Often the first step is selecting a working gas because it is much easier to design other parameters around the physical properties of a fluid. The working gas should be chosen to have a large thermal penetration depth and a small viscous penetration depth to avoid irreversibility. The second step will be the selection of average pressure, frequency and drive ratio. The average operating pressure should be chosen as it is fairly independent of other parameters and can be easily adjusted as needed. Average pressure is proportional to the power density of a thermoacoustic refrigerator and hence for this reason, it is desirable to choose a large average pressure up to 10 bar [2]. However, other factors limit the pressure is the mechanical strength of the resonator and the thermal penetration depth, which is inversely proportional to square root of mean pressure, so a high pressure results in a small stack plate spacing which is undesirable. The operating frequency of the thermoacoustic devices is usually high, because its power density is a linear function of the acoustic resonance frequency. Also, thermal penetration depth is inversely proportional to square root of the frequency which implies a stack with very small plate spacing which makes the construction difficult. The drive ratio of the device is kept sufficiently low so as to avoid acoustic nonlinearities such as turbulence. The next step is the design and optimization of the stack which is often made of expensive materials and also difficult to machine and construct so as to meet predetermined specifications. The stack must be able to efficiently convert the acoustic pressure oscillations into a temperature gradient. It is desirable for the stack material to have a low thermal conductivity and greater heat capacity than the working gas. The size of the stack pores is dependent upon the thermal penetration depth. The pores should be designed so that the working gas and stack/heat-exchanger walls can transfer heat as effectively as possible. The pores should be as small as possible (0.3 mm) [3], so that more gas is within a thermal penetration depth of a stack/heat exchanger walls, thus makes good thermal contact. On the other hand, small pores create more surface area where losses occur and may cause turbulence, disrupting the acoustic field. These factors may affect the efficiency of the device significantly and need to be balanced. Once the operating pressure, frequency, and stack parameters are chosen, the resonator can be designed. The resonator should be made of an acoustically reflective material that is sufficiently strong for the desired operating pressure. The possibilities of working fluid and thermal leakage should also be considered. For overall thermal considerations, the resonator material should have very low thermal conductivity to prevent heat leak in the cold side with atmosphere and also from the hot side of the resonator back to the cold side. It is better to insulate the entire resonator tube except at the heat exchangers. Next, the design of heat exchangers is done which is a critical task in thermoacoustics. The heat exchanger material should have high thermal conductivity. The heat exchangers are designed such that the porosity of the heat exchanger should match the porosity of the stack preferably using micro-channel heat exchanger to exchange heat with the gas lies within thermal penetration depth. The porosity of stack/heat-exchanger is likely to be about %. Lastly, the driver of a thermoacoustic refrigerator must be able to supply sufficient acoustic pressure and frequency to develop an appreciable temperature difference across the stack. Most drivers have been custom made or modified electroacoustic transducers, but any form of acoustic power production can be used. 84

3 4. Designing a model using DeltaEC Software The stack-based laboratory scale thermoacoustic refrigerator model is designed considering dry air as working substance with an ideal solid material based on the design knowledge mentioned above using DeltaEC (Design Environment for Low amplitude Thermoacoustic Energy Conversion) software as shown in Fig.1, which solves the exact thermoacoustic equations in a geometry given by the user, using the boundary conditions for the different variables. The latest version 6.2 is freely available for noncommercial, educational, and evaluation use, and can be downloaded from Los Alamos National Laboratory website, US, which is under continuous development. In the present design, loud speaker with 13 Watts capacity is selected, spiral stack length is 7.85 cm and the stack center position is 8.8 cm is chosen from the loud speaker [4]. The porosity of the stack, hot (ambient) heat exchanger and cold heat exchanger is 0.724, 0.6 & 0.67 respectively. The hot heat exchanger temperature (300 K) is assumed to be kept constant by circulating cooling water. Fig. 1 Stack-based thermoacoustic refrigerator model designed using DeltaEC software Considering the Mach number, M as 0.02 to avoid nonlinearities of the system, and for air, sound velocity a is 345 m/s, gas constant R as 287 J/Kg-K and T m, is the mean temperature of the gas across hot and cold heat exchangers, the driving ratio, D is calculated using the following formula (eq. 1) and is found to be less than 3 % for all the mean operating pressure, which is desirable for low amplitude thermoacoustic devices: 2 Ma D = (1) RT m In the present design, the BEGIN segment is counted as the zeroth segment of the file. It is used to initialize variables like mean pressure, frequency etc. that are shared among subsequent segments. Segment 1 is VESPEAKER, the voltage driven loudspeaker. Segment 4 is the duct of length 4.3 cm. Segment 5 is hot heat exchanger having length 6.4 mm. Segment 6 is the spiral stack. The segment 7 is cold heat exchanger having length 2.5 mm. The large and small diameter tube is taken as 3.8 cm and 2.2 cm respectively. The segment 8 is the cone having length 2 cm. The length of the segment 9 is 14.7 cm. The length of the segment 10 is 6.7 cm having diameter 3.8 cm at the exit. The segment 11 is end spherical bulb having the volume m 3. The segment 12 is HARDEND, which is a logistical final segment used to enforce complex volume flow rate somewhere to be zero. The segments 2, 3, and 13 to 18 are Reverse Polish Notation (RPN) segments used to create nonstandard guesses, targets, and simple algebraic calculations in a DeltaEC model file. 5. Analysis and Results The analysis of thermoacoustic refrigerator model is done by varying mean operating pressure and fine-tuning DeltaEC software [8] for the optimized performance. The results are tabulated for the mean operating pressure from 1 bar to 10 bar with a cooling load capacity varying from 1 to 10 Watts. The performance evaluation of the model is done using RPN segments of the software, by calculating COP, Carnot COP and relative COP from the following formulae: Q C QC COP = (2) W where is the gross cooling power which is the sum of net cooling at cold heat exchanger and tail dissipation near cold heat exchanger within the resonator tube and W is the acoustic power used to pump heat Q C. The quantity (COPC) is called the Carnot coefficient of performance which is the maximal performance for all refrigerators. It is given in eq. (3) 85

4 Fig. 2 DeltaEC calculations as functions of the cooling load at the cold heat exchanger and for different mean operating pressures: Variation of speaker voltage Fig. 3 DeltaEC calculations as functions of the cooling load at the cold heat exchanger and for different mean operating pressures: Variation of operating frequency 86

5 Fig.4 DeltaEC calculations as functions of the cooling load at the cold heat exchanger and for different mean operating pressures: Variation of cold heat exchanger temperature Fig. 5 DeltaEC calculations as functions of the cooling load at the cold heat exchanger and for different mean operating pressures: Variation of temperature difference across heat exchangers 87

6 Fig. 6 DeltaEC calculations as functions of the cooling load at the cold heat exchanger and for different mean operating pressures: variation of COP Fig. 7 DeltaEC calculations as functions of the cooling load at the cold heat exchanger and for different mean operating pressures: Variation of relative COP 88

7 COPC T T T c = (3) h c The coefficient of performance relative to Carnot s coefficient of performance is defined as COP COPR = (4) COPC From the analysis results, the total resonator length L is found to be 48.5 cm and the operating frequency range for this resonator length is Hz. Using dry air as working substance with sound velocity a is 345 m/s, the type of resonator is identified using the following formula. a f = (5) λ For the quarter wavelength resonator design, i.e., λ = 4 L the operating frequency is found to be Hz, which is nearly equal to the above frequency range, and hence the resonator is quarter-wavelength type [7] in which the energy loss is half of the half-wavelength counterpart. The refrigerator geometry given in Fig. 1 is used in DeltaEC software and the results of computations are shown in Fig. 2. The voltage input for acoustic driver decrease as mean operating pressure increase and at the same time we need to operate the device at higher frequency as observed in Figures 2 and 3. The temperature of the cold heat exchanger increases whereas the temperature difference across heat exchangers decreases as mean operating pressure increases as shown in Figures 4 and 5 by keeping hot heat exchanger temperature constant by circulating cooling water. The COP and the performance relative to Carnot COPR as function of the heat load at the cold heat exchanger Q C is shown in Figures 6 and 7 is increases as mean operating pressure increases which determine the performance of the device. 6. Conclusion For the atmospheric pressure (1bar) model with dry air as working substance, a low COP of 0.26 is obtained at 10 Watt cooling load capacity and comparatively a very high voltage and frequency is required for the loud speaker that demands more power. For the high pressure model, maximum COP of 2.95 is found at 10 Watt cooling load capacity with 10 bar mean operating pressure. Hence it is concluded that the performance of stack-based thermoacoustic refrigerator improves if we operate the device at higher mean operating pressure. Acknowledgments The authors would like to thank Bill Ward, John Clark, and Greg Swift, Los Alamos National Laboratory for developing DeltaEC software and to make it freely available for noncommercial, educational, and evaluation use of thermoacoustic devices. References [1] M.E.H. Tijani, J.C.H. Zeegers, A.T.A.M. de Waele, Design of ThermoAcoustic Refrigerators, Cryogenics 42, 2002, [2] M.E.H. Tijani, J.C.H. Zeegers, and A.T.A.M. de Waele, Construction and Performance of a Thermoacoustic Refrigerator, Cryogenics 42, 2002, [3] M.E.H. Tijani, J.C.H. Zeegers, and A.T.A.M. de Waele, The optimal stack spacing for thermoacoustic refrigeration, J. Acoust. Soc. Am. 112 (1), [4] Yong Tae Kim and Min Gon Kim, Optimum positions of a stack in a thermoacoustic heat pump, Journal of the Korean Physical Society, Vol. 36, No. 5, 2000 pp [5] G.W. Swift, Thermoacoustics: A Unifying Perspective for Some Engines and Refrigerators, Acoustical Society of America, New York, ISBN [6] Luke Zoontjens, Carl Q. Howard, Anthony C. Zander and Ben S. Cazzolato, Development of a Low-Cost Loudspeaker-Driven ThermoAcoustic refrigerator, Proceedings of Acoustics, Busselton, Western Australia, November [7] G.S. V. L. Narasimham & Prof. M.V. Krishnamurthy, Thermoacoustic Refrigeration an Overview, Workshop on Cryocooler Technology- Emerging Trends, Applications and Curriculum Development, Indian Institute of Science, Bangalore, December [8] Bill Ward, John Clark, and Greg Swift, Design Environment for Low-amplitude Thermoacoustic Energy Conversion, Version 6.2, December 2008, 89