Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Transient and Steady-periodic Performance Analysis of a Multi-stage Thermoacoustic Pulse Tube Cryocooler

Authors
1 Ph.D., University of Modarres, Faculty of ZMechanical Engineering
2 Professor, faculty of mechanical engineering, Tarbiat Modares University (TMU), Tehran, Iran
Abstract
 
In this paper, the starting and steady-periodic characteristics of a multi-stage looped-branched thermoacoustic cryocooler and its uncertainty with respect to effective parameters are calculated and discussed. In this regard, the start-up and nominal performance of the system are simulated using the numerical solution of Rott's one-dimensional equations. Numerical and experimental results of a similar system confirm the validity of the results of the present article. Simulation outcomes show that the number of stages, mean pressure and loop perimeter can significantly change the system performance. In contrast to previous findings, the results in this paper show that increasing the number of stages or increasing the mean pressure does not necessarily improve thermodynamic performance. Besides, Morris method is implemented to quantify uncertainty of the operating parameters of a four-stage cryocooler in relation to the geometric, modeling and material characteristics. The results reveal that the gas characteristics, solid conductivity and mesh geometry of the engine and refrigerator regenerator have a dominant nonlinear effect on the required hot temperature, exergy efficiency, relative Carnot efficiency, cooling load and temperature. Moreover, by adding additional thermodynamic cores in each stage, the amount of acoustic work and total enthalpy and its uncertainty increase and the effect of solid thermal conductivity decreases. With the developed model and main findings of this paper, one can optimize a reliable thermoacoustic cryocooler based on its onset and steady characteristics.
Keywords

Subjects


[1] Jin, T., Yang, R., Wang, Y., Feng, Y., and Tang, K., “Low Temperature Difference Thermoacoustic Prime Mover with Asymmetric Multi-stage Loop Configuration”, Scientific Reports, Vol. 7(1), Article ID: 7665, DOI: https://doi.org/10.1038/s41598-017-08124-5, (2017).
 
[2] Xu, J., Luo, E., and Hochgreb, S., “Study on a Heat-driven Thermoacoustic Refrigerator for Low-grade Heat Recovery”, Applied Energy, Vol. 271, Article ID: 115167, DOI: https://doi.org/10.1016/j.apenergy.2020.115167, (2020).
 
[3] Xu, J., Zhang, L., Hu, J., Wu, Z., Bi, T., Dai, W., and Luo, E., “An Efficient Looped Multiple-stage Thermoacoustically-driven Cryocooler for Liquefaction and Recondensation of Natural Gas”, Energy, Vol. 101, pp. 427-433, DOI: https://doi.org/10.1016/j.energy.2016.01.085, (2016).
 
[4] Bouramdane, Z., Bah, A., Alaoui, M., and Martaj, N., “Numerical Analysis of Thermoacoustically Driven Thermoacoustic Refrigerator with a Stack of Parallel Plates Having Corrugated Surfaces”, International Journal of Air-conditioning and Refrigeration, Vol. 30, pp. 1-19, DOI: https://doi.org/10.1007/s44189-022-00002-8, (2022).
 
[5] Tijani, M.E.H., and Spoelstra, S., “A High Performance Thermoacoustic Engine”, Journal of Applied Physics, Vol. 110, Article ID:  093519, DOI: https://doi.org/10.1063/1.3658872, (2011).
 
[6] Tartibu, L.K., “Maximum Cooling and Maximum Efficiency of Thermoacoustic Refrigerators”, Heat and Mass Transfer, Vol. 52, pp. 95-102, DOI: https://doi.org/10.1007/s00231-015-1599-y, (2016).
 
[7] Jung, S., and Matveev, K.I., “Study of a Small-scale Standing-wave Thermoacoustic Engine”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 224, pp. 133-141, DOI: https://doi.org/10.1243/09544062JMES1594, (2010).
 
[8] Abd El-Rahman, A.I., Abdelfattah, W.A., Abdelwahed, K.S., Salama, A., Rabie, A., and Hamdy, A., “A Compact Standing-wave Thermoacoustic Refrigerator Driven by a Rotary Drive Mechanism”, Case Studies in Thermal Engineering, Vol. 21, Article ID: 100708, DOI: https://doi.org/10.1016/j.csite.2020.100708, (2020).
[9] Symko, O.G., “Acoustic Approach to Thermal Management: Miniature Thermo Acoustic Engines”, Thermal and Thermomechanical Proceedings 10th Intersociety Conference on Phenomena in Electronics Systems,  May 30-  June 02, San Diego, CA, USA, pp. 6, (2006).
 
[10] Rodriguez, I.A., and Symko, O.G., “Miniature Traveling Wave Thermoacoustic Engine”, The Journal of the Acoustical Society of America, Vol. 125(4), pp. 2562-2562, DOI: https://doi.org/10.1121/1.4783701, (2009).
 
[11] Steiner, T.W., “Looped Thermoacoustic Cryocooler with Self-circulating Large Area Cooling”, International Cryocooler Conference,  June 27-30, Bethlehem, Pennsylvania, USA, pp. 479-487, (2022).
 
[12] Lawn, C.J., and Penelet, G., “Common Features in the Thermoacoustics of Flames and Engines”, International Journal of Spray and Combustion Dynamics, Vol. 10, pp. 3-37, DOI: https://doi.org/10.1177/1756827717743911, (2018).
 
[13] Ceperley, P.H., “A Pistonless Stirling Engine—The Traveling Wave Heat Engine”, The Journal of the Acoustical Society of America, Vol. 66, pp. 1508-1513, DOI: https://doi.org/10.1121/1.383505, (1979).
 
[14] Ceperley, P.H, “Gain and Efficiency of a Short Traveling Wave Heat Engine”, The Journal of the Acoustical Society of America, Vol. 77, pp. 1239-1244, DOI: https://doi.org/10.1121/1.392191, (1985).
 
[15] Yazaki, T., Iwata, A., Maekawa, T., and Tominaga, A., “Traveling Wave Thermoacoustic Engine in a Looped Tube”,  Physical Review Letters, Vol. 81, pp. 3128, DOI: https://doi.org/10.1103/PhysRevLett.81.3128, (1998).
 
[16] Backhaus, S., and Swift, G.W., “A Thermoacoustic-stirling Heat Engine: Detailed Study”, The Journal of the Acoustical Society of America, Vol. 107, pp. 3148-3166, DOI: https://doi.org/10.1121/1.429343, (2000).
 
[17] Pierens, M., Thermeau, J.P., Le Pollès, T., and Duthil, P., “Development of a Thermoacoustic Travelling-wave Refrigerator”, Proceedings of the Acoustics 2012 Nantes Conference, April 23-27, Nantes, France, pp. 3014-3018, (2012).
 
[18] de Blok, K., “Novel 4-stage Traveling Wave Thermoacoustic Power Generator”, Fluids Engineering Division Summer Meeting Collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels, August 1–5, Montreal, Quebec, Canada, pp. 73-79, DOI: https://doi.org/10.1115/FEDSM-ICNMM2010-30527, (2010).
 
[19] de Blok, K., and Systemen, A.T., “Multi-stage Traveling Wave Thermoacoustics in Practice”, 19th International Congress Sound Vibration, July 8-12, Vilnius, Lithuania, (2012).
 
[20] Zhang, X., Chang, J., Cai, S., and Hu, J., “A Multi-stage Travelling Wave Thermoacoustic Engine Driven Refrigerator and Operation Features for Utilizing Low Grade Energy”, Energy Conversion and Management, Vol. 114, pp. 224-233, DOI: https://doi.org/10.1016/j.enconman.2016.02.035, (2016).
 
[21] Yang, R., Wang, Y., Feng, Y., Jin, T., and Tang, K., “Performance of a Looped Thermoacoustic Engine with Multiple Loads Capable of Utilizing Heat Source Below 200° C”, Applied Thermal Engineering, Vol. 148, pp. 516-523, DOI: https://doi.org/10.1016/j.applthermaleng.2018.11.069, (2019).
 
[22] Yang, R., Meir, A., and Ramon, G.Z., “Theoretical Performance Characteristics of a Travelling-wave Phase-change Thermoacoustic Engine for Low-grade Heat Recovery”, Applied Energy, Vol. 261, Article ID: 114377, DOI: https://doi.org/10.1016/j.apenergy.2019.114377, (2020).
 
[23] Tan, J., Luo, J., Wang, Y., Wei, J., and Jin, T., “Performance of an Air‐cooled Looped Thermoacoustic Engine Capable of Recovering Low‐grade Thermal Energy”, International Journal of Energy Research, Vol. 44, pp. 2682-2692, DOI: https://doi.org/10.1002/er.5034, (2020).
 
[24] Xiao, L., Xu, J., Luo, K., Chen, G., and Luo, E., “Numerical Study of a Heat-driven Thermoacoustic Refrigerator Based on a Time-domain Lumped Acoustic–electrical Analogy Model”, Energy Conversion and Management, Vol. 268, Article ID: 115982, DOI: https://doi.org/10.1016/j.enconman.2022.115982, (2022).
 
[25] Urip, T., Setiawan, I., and Utomo, A.B., “Influence of Pressure Variation of Air Working Gas on the Onset Temperature Difference and Electric Power Output of a Standing Wave Thermoacoustic Electricity Generator”, AIP Conference Proceedings (International Conference on Science and Applied Science (ICSAS)), April 6, Surakarta, Indonesia,Vol. 2391, Issue. 1, Article ID: 090028, DOI: https://doi.org/10.1063/5.0072932, (2022).
 
[26] Rahpeima, R., and Ebrahimi, R., “A Numerical Approach for Optimization of the Working Fluid of a Standing-wave Thermo-acoustic Refrigerator”, Engineering with Computers, pp. 1-17, DOI: https://doi.org/10.1007/s00366-022-01646-1, (2022).
 
[27] Xu, J., Yu, G., Zhang, L., Dai, W., Wu, Z., and Luo, E., “Numerical Investigation on a 300 Hz Pulse Tube Cryocooler Driven by a Three-stage Traveling-wave Thermoacoustic Heat Engine”, Cryogenics, Vol. 71, pp. 68-75, DOI: https://doi.org/10.1016/j.cryogenics.2015.06.003, (2015).
 
[28] Ward, B., Clark, J., and Swift, G.W., “Design Environment for Low-amplitude Thermoacoustic Energy Conversion (DeltaEC)”, The Journal of the Acoustical Society of America, Vol. 122, No. 5, DOI: https://doi.org/10.1121/1.2942768, (2007).
 
[29] Bahrami, M., and Ommi, F., “Developing an Augmented Onset Model for a Thermoacoustically-driven, Pulse Tube Cryocooler”, Sustainable Energy Technologies and Assessments, Vol. 47, Article ID:101402, DOI: https://doi.org/10.1016/j.seta.2021.101402, (2021).
 
[30] Wang, K., Sun, D.M., Zhang, J., Zou, J., Wu, K., Qiu, L.M., and Huang, Z.Y., “Numerical Simulation on Onset Characteristics of Traveling-wave Thermoacoustic Engines Based on a Time-domain Network Model”, International Journal of Thermal Sciences, Vol. 94, pp. 61-71, DOI: https://doi.org/10.1016/j.ijthermalsci.2015.02.010, (2015).
[31] Morris, M.D., “Factorial Sampling Plans for Preliminary Computational Experiments”, Technometrics, Vol. 33, pp. 161-174, DOI: https://doi.org/10.1080/00401706.1991.10484804, (1991).
 
[32] Sin, G., and Gernaey, K.V., “Improving the Morris Method for Sensitivity Analysis by Scaling the Elementary Effects”, Computer Aided Chemical Engineering, Vol. 26, pp. 925-930. DOI: https://doi.org/10.1016/S1570-7946(09)70154-3, (2009).
 
[33] Fischer, U., Gomeringer, R., Heinzler, M., Kilgus, R., Naher, F., Oesterle, S., Paetzold, H., and Stephan, A., “Mechanical and Metal Trades Handbook”, 3rd English Edition, Verlag Europa-Lehrmittel Nourney, Vollmer GmbH and Company KG., 42781 Haan-Gruiten, Germany, pp. 444, ISBN: 13 978-3-8085-1914-1, (2012).
 
[34] Soman, K., “Development of Porous Media for Transpiration Cooling”, Master Thesis, Department of Mechanical Engineering, University of Kerala, Kerala, India, (1998).
 
[35] Peterson, H., “The Properties of Helium: Density, Specific Heats, Viscosity, and Thermal Conductivity at Pressures from 1 to 100 Bars from Room Temperature to 1800 K”, Danish Atomic Energy Commission Research Establishment Risö, Roskilde, Denmark, Forskningscenter Risoe, Risoe-R, No. 224, (1970).
 
[36] Mills, “Recommended Values of Thermophysical Properties for Selected Commercial Alloys”, 1st Edition, Woodhead Publishing, Cambridge, England, pp. 246, (2002).
 
[37] https://www.trafag.com/en/nat-8252-industrial-pressure-transmitter.html; [accessed 29 Oct 2022].

  • Receive Date 14 July 2021
  • Revise Date 29 October 2022
  • Accept Date 11 April 2023