1/4波长驻波型热声发动机的非线性模型

doi:10.7527/S1000-6893.2015.0207

Abstract

Abstract:

A quasi-one-dimensional nonlinear model of a standing-wave thermoacoustic engine with a quarter-wavelength resonator is presented. The model is based on cross-sectional averaged equations and is solved by high-order low-dispersion numerical schemes. Considering the acoustic reflection and radiation at the open end, broadband time-domain impedance boundary conditions are employed so that oscillation frequency can be self-adaptive. The impedance is expressed in the mathematical form of partial fraction expansion with complex-conjugate residues and poles, so that the convolution of the impedance with the velocity can be calculated by efficient and causal recursive convolution. Pole-residue pairs of the impedance can be optimized in the frequency domain. Critical temperature difference of an open-ended standing-wave thermoacoustic engine can be predicted and the time-domain simulation shows that the pressure oscillation undergoes a nonlinear amplifying process and eventually reaches saturation amplitude. Numerical results agree very well with the experiment for a small-scale thermoacoustic engine. The simulation results for different stack geometries are included.

Key words: thermoacoustic engines, nonlinear, model, broadband, time-domain impedance boundary condition

CLC Number:

HOU Wei, WANG Xiaoyu, JING Xiaodong, SUN Xiaofeng. A quasi-one-dimensional nonlinear model of an open-closed standing-wave thermoacoustic engine[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(7): 2091-2101.

References

[1] GARRETT S L, ADEFF J A, HOFLER T J. Thermoacoustic refrigerator for space applications[J]. Journal of Thermophysics and Heat Transfer, 1993, 7(4):595-599.
[2] GARIMELLA S V, JOSHI Y K, BAR-COHEN A, et al. Thermal challenges in next generation electronic systems-Summary of panel presentations and discussions[J]. IEEE Transactions on Components and Packaging Technologies, 2003, 25(4):569-575.
[3] MATVEEV K I, WEKIN A, RICHARDS C D, et al. On the coupling between standing-wave thermoacoustic engine and piezoelectric transducer[C]//International Mechanical Engineering Congress and Exposition. Seattle, WA:ASME, 2007:765-769.
[4] HOFLER T J, ADEFF J A. An optimized miniature Hofler tube[J]. Acoustics Research Letters Online, 2001, 2(1):37-42.
[5] SYMKO O G, ABDEL-RAHMAN E, KWON Y S, et al. Design and development of high-frequency thermoacoustic engines for thermal management in microelectronics[J]. Microelectronics Journal, 2004, 35(2):185-191.
[6] JIN T, ZHANG B S, TANG K, et al. Experimental observation on a small-scale thermoacoustic prime mover[J]. Journal of Zhejiang University SCIENCE A, 2007, 8(2):205-209.
[7] HARIHARAN N M, SIVASHANMUGAM P, KASTHURIRENGAN S. Influence of stack geometry and resonator length on the performance of thermoacoustic engine[J]. Applied Acoustics, 2012, 73(10):1052-1058.
[8] JUNG S, MATVEEV K I. Study of a small-scale standing-wave thermoacoustic engine[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2010, 224(1):133-141.
[9] ROTT N. Damped and thermally driven acoustic oscillations in wide and narrow tubes[J]. Zeitschrift Für Angewandte Mathematik und Physik ZAMP, 1969, 20(2):230-243.
[10] SWIFT G W. Thermoacoustic engines[J]. The Journal of the Acoustical Society of America, 1988, 84(4):1145-1180.
[11] WATANABE M, PROSPERETTI A, YUAN H. A simplified model for linear and nonlinear processes in thermoacoustic prime movers. Part I. Model and linear theory[J]. The Journal of the Acoustical Society of America, 1997, 102(6):3484-3496.
[12] YUAN H, KARPOV S, PROSPERETTI A. A simplified model for linear and nonlinear processes in thermoacoustic prime movers. Part Ⅱ. Nonlinear oscillations[J]. The Journal of the Acoustical Society of America, 1997, 102(6):3497-3506.
[13] KARPOV S, PROSPERETTI A. A nonlinear model of thermoacoustic devices[J]. The Journal of the Acoustical Society of America, 2002, 112(4):1431-1444.
[14] HAMILTON M F, ILINSKⅡ Y A, ZABOLOTSKAYA E A. Nonlinear two-dimensional model for thermoacoustic engines[J]. The Journal of the Acoustical Society of America, 2002, 111(5):2076-2086.
[15] HIRECHE O, WEISMAN C, BALTEAN-CARLES D, et al. Low Mach number analysis of idealized thermoacoustic engines with numerical solution[J]. The Journal of the Acoustical Society of America, 2010, 128(6):3438-3448.
[16] HIRECHE O, WEISMAN C, BALTEAN-CARLES D, et al. Numerical model of a thermoacoustic engine[J]. Comptes Rendus Mécanique, 2010, 338(1):18-23.
[17] DOWLING A P, FFOWCS WILLIAMS J E, WRIGHT W M. Sound and sources of sound[J]. American Journal of Physics, 1983, 53(6):320.
[18] CHESTER W. Resonant oscillations of a gas in an open-ended tube[J]. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1981, 377(1771):449-467.
[19] KARPOV S, PROSPERETTI A. Nonlinear saturation of the thermoacoustic instability[J]. The Journal of the Acoustical Society of America, 2000, 107(6):3130-3147.
[20] 侯薇, 潘浩然, 宋卫华, 等. 有限长号筒中非线性声传播的数值模拟研究[J]. 声学学报, 2015(4):569-578. HOU W, PAN H R, SONG W H, et al. Numerical simulation of nonlinear propagation of sound waves in a finite horn[J]. Acta Acustica, 2015(4):569-578(in Chinese).
[21] RIENSTRA S W. Impedance models in time domain, including the extended Helmholtz resonator model:AIAA-2006-2686[R]. Reston:AIAA, 2006.
[22] REYMEN Y, BAELMANS M, DESMET W. Time-domain impedance formulation based on recursive convolution:AIAA-2006-2685[R]. Reston:AIAA, 2006.
[23] FUNG K Y, JU H. Broadband time-domain impedance models[J]. AIAA Journal, 2001, 39(8):1449-1454.
[24] FUNG K Y, JU H. Time-domain impedance boundary conditions for computational acoustics and aeroacoustics[J]. International Journal of Computational Fluid Dynamics, 2004, 18(6):503-511.
[25] COTTE B, BLANC-BENON P, BOGEY C, et al. Time-domain impedance boundary conditions for simulations of outdoor sound propagation[J]. AIAA Journal, 2009, 47(10):2391-2403.
[26] BOX M J. A comparison of several current optimization methods, and the use of transformations in constrained problems[J]. The Computer Journal, 1966, 9(1):67-77.
[27] TAM C K W. Computational aeroacoustics-issues and methods[J]. AIAA Journal, 1995, 33(10):1788-1796.
[28] STANESCU D, HABASHI W G. 2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics[J]. Journal of Computational Physics, 1998, 143(2):674-681.
[29] LEVINE H, SCHWINGER J. On the radiation of sound from an unflanged circular pipe[J]. Physical Review, 1948, 73(4):383-406.
[30] HANTSCHK C C, VORTMEYER D. Numerical simulation of self-excited thermoacoustic instabilities in a Rijke tube[J]. Journal of Sound and Vibration, 1999, 227(3):511-522.
[31] YU G, DAI W, LUO E. CFD simulation of a 300Hz thermoacoustic standing wave engine[J]. Cryogenics, 2010, 50(9):615-622.
[32] SWIFT G W. Thermoacoustic:A unifying perspective for some engines and refrigerators[J]. The Journal of the Acoustical Society of America, 2003, 113(5):2379-2381.

A quasi-one-dimensional nonlinear model of an open-closed standing-wave thermoacoustic engine

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Shanjie XU, Hongqiang LYU, Zhongchen LIU, Yan LENG, Xuejun LIU. Data analysis of sonic boom test based on probability model [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(2): 626269-626269.
[2]	Gongye YU, Weidong CAI, Minghui HU, Wencai LIU, Bo MA. Intelligent migration diagnosis of mechanical faults driven by hybrid fault mechanism and domain adaptation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(2): 426800-426800.
[3]	Feng JIANG, Huacong LI, Jiangfeng FU, Linxiong HONG. A RBF and active learning combined method for structural non-probabilistic reliability analysis [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(2): 226667-226667.
[4]	Qian YANG, Xiaofeng GUO, Qin LI, Wei DONG. Hot air anti-icing performance estimation method based on POD and surrogate model [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 626992-626992.
[5]	Feng ZHENG, Wei HUANG, Hongli JI, Jinhao QIU. Acoustic black hole effect of composite sheet structures [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 426453-426453.
[6]	Qilei GUO, Weimin SANG, Junjie NIU, Ye YUAN. UAV flight strategy considering icing risk under complex meteorological conditions [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 627518-627518.
[7]	Junjie NIU, Weimin SANG, Dong LI, Lian HAO, Zelin WANG. Icing test flight area determination method based on surrogated model of water droplet collection [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 627697-627697.
[8]	Shouchao HU, Yu ZHUANG, Xian LI, Tao JIANG. Hypersonic aero-heating environment research model HyHERM-I: Experiment [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S2): 233-248.
[9]	Deyang TIAN, Yi PING, Yesi CHEN, Weifang CHEN. Influence of physical and chemical models on electromagnetic wave propagation characteristics of flow field [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S2): 214-224.
[10]	Shaobo YAO, Lijian JIANG, Wenwen ZHAO, Zheng LU, Changju WU, Weifang CHEN. Numerical method of data-driven rarefied nonlinear constitutive relations coupled with clustering [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S2): 40-53.
[11]	ZHANG Yu, DENG Xinyang, LI Mingda, LI Xinyu, JIANG Wen. Air target intention recognition based on evidence-network causal analysis [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S1): 726896-726896.
[12]	LIU Chuang, YU Xiaojun, ZHANG Ting, ZHU Haokun. Research status and trend of key technologies for simulation test of unmanned swarm equipment [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S1): 726919-726919.
[13]	WEN Qian, YANG Jiawei, WU Zeping, YANG Xixiang, ZHAO Hailong, WANG Zhixiang. An approximation modeling method of launch vehicles improved by fast cross-validation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 225967-225967.
[14]	WANG Xinguang, MAO Meiliang, HE Kun, CHEN Qi, WAN Zhao. Application of wall function to supersonic turbulence simulation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 126153-126153.
[15]	ZHANG Ziyu, HAO Lin. Application of X-FEM in a phase-field model for crack propagation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 225976-225976.