×

zbMATH — the first resource for mathematics

Numerical simulations of gas resonant oscillations in a closed tube using lattice Boltzmann method. (English) Zbl 1143.80332
Summary: Numerical studies are presented for gas resonant oscillations in a two-dimensional closed tube using the lattice Boltzmann method. A multi-distribution function model of thermal lattice Boltzmann method is adopted in this work. The oscillating flow of the gas is generated by a plane piston at one end, and reflected by the other closed end. Both isothermal and adiabatic walls of the closed tube are considered. Boundary treatments such as moving adiabatic boundary are given in detail. The time dependent velocity, density and temperature at various locations of the tube for various frequencies and wall boundary conditions are presented. Shock waves with resonant frequency or slightly off-resonant frequencies are numerically captured. From the simulation results, the gas flow and heat transfer characteristics obtained are consistent qualitatively with those from previous simulations using conventional numerical methods.

MSC:
80A20 Heat and mass transfer, heat flow (MSC2010)
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76M28 Particle methods and lattice-gas methods
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Mcnamara, G.; Zanetti, G.: Use of the Boltzmann equation to simulate lattice-gas automata, Phys. rev. Lett. 61, 2235-2332 (1988)
[2] Succi, S.: Lattice Boltzmann equation for fluid dynamics and beyond, (2001) · Zbl 0990.76001
[3] Chen, S. Y.; Doolen, G. D.: Lattice Boltzmann method for fluid flows, Annu. rev. Fluid. mech. 30, 329-364 (1998) · Zbl 1398.76180
[4] Saenger, R. A.; Hudson, G. E.: Periodic shock waves in resonating gas columns, J. acoust. Soc. am. 32, 961-971 (1960)
[5] Alexeev, A.; Gutfinger, C.: Resonance gas oscillations in closed tubes: numerical study and experiments, Phys. fluids 15, No. 11, 3397-3408 (2003) · Zbl 1186.76023 · doi:10.1063/1.1613645
[6] Betchov, R.: Nonlinear oscillations of a column of gas, Phys. fluids 1, 205-212 (1958) · Zbl 0081.41604 · doi:10.1063/1.1724343
[7] Chester, W.: Resonant oscillations in closed tubes, J. fluid mech. 18, 44-64 (1964) · Zbl 0129.19504 · doi:10.1017/S0022112064000040
[8] Ilgamov, M. A.; Zaripov, R. G.; Galiullin, R. G.; Repin, V. B.: Nonlinear oscilltions of a gas in a tube, Appl. mech. Rev. 49, No. 3, 137-154 (1996)
[9] Merkli, P.; Thomann, H.: Transition to turbulence in oscillating pipe flow, J. fluid mech. 68, 567-576 (1975) · Zbl 0309.76060
[10] Merkli, P.; Thomann, H.: Thermoacoustic effects in a resonant tube, J. fluid mech. 70, 161-177 (1975) · Zbl 0309.76060 · doi:10.1017/S0022112075001954
[11] Goldshtein, A.; Vainshtein, P.; Fichman, M.; Gutfinger, C.: Resonance gas oscillations in closed tubes, J. fluid mech. 322, 147-163 (1996) · Zbl 0893.76074 · doi:10.1017/S0022112096002741
[12] Gopinath, A.; Tait, N. L.; Garrett, S. L.: Thermoacoustic streaming in a resonant channel: the time averaged temperature distribution, J. acoust. Soc. am. 103, 1388-1405 (1998)
[13] Lee, C. P.; Wang, T. G.: Nonlinear resonance and viscous dissipation in an acoustic chamber, J. acoust. Soc. am. 92, 2195-2206 (1992)
[14] Elvira-Segura, L.; Sarabia, E.: Numerical and experimental study of finite-amplitude standing waves in a tube at high sonic frequencies, J. acoust. Soc. am. 104, 708-714 (1998)
[15] Aganin, A. A.; Ilgamov, M. A.; Smirnova, E. T.: Development of longitudinal gas oscillations in a closed tube, J. sound vibrat. 195, No. 3, 359-374 (1996)
[16] Tang, H. Z.; Cheng, P.: Numerical simulations of resonant oscillation in a tube, Numer. heat transfer, part A 40, 37-54 (2001)
[17] Buick, J. M.; Greated, C. A.; Campbell, D. M.: Lattice BGK simulation of sound wave, Europhys. lett. 43, No. 3, 235-240 (1998)
[18] Haydock, D.; Yeomans, J. M.: Lattice Boltzmann simulations of acoustic streaming, J. phys. A: math. Gen 34, 5201-5213 (2001) · Zbl 1053.76523 · doi:10.1088/0305-4470/34/25/304
[19] Haydock, D.; Yeomans, J. M.: Lattice Boltzmann simulations of attenuation-driven acoustic streaming, J. phys. A: math. Gen. 36, 5683-5694 (2003) · Zbl 1038.76032 · doi:10.1088/0305-4470/36/20/322
[20] Li, X. M.; Leung, R. C. K.; So, R. M. C.: One-step aeroacoustics simulation using lattice Boltzmann method, Aiaa j. 44, No. 1, 78-89 (2006)
[21] Bartoloni, A.; Battista, C.; Cabasino, S.: LBE simulations of Rayleigh-Bėnard convection on the APE100 parallel processor, Int. J. Mod. phys. C 4, 993-1006 (1993)
[22] He, X. Y.; Chen, S. Y.; Doolen, G. D.: A novel thermal model for the lattice Boltzmann method in incompressible limit, J. comput. Phys. 146, 282-300 (1998) · Zbl 0919.76068 · doi:10.1006/jcph.1998.6057
[23] Guo, Z. L.; Shi, B. C.; Zheng, C. G.: A coupled lattice BGK model for the Boussinesq equations, Int. J. Numer. methods. Fluids 39, 325-342 (2002) · Zbl 1014.76071 · doi:10.1002/fld.337
[24] D’orazio, A.; Succi, S.; Arrighetti, C.: Lattice Boltzmann simulation of open flows with heat transfer, Phys. fluids 15, No. 9, 2778-2781 (2003) · Zbl 1186.76148 · doi:10.1063/1.1597681
[25] Tang, G. H.; Tao, W. Q.; He, Y. L.: Thermal boundary condition for the thermal lattice Boltzmann equation, Phys. rev. E 72, 016703:1-016703:6 (2005)
[26] Wang, Y.; He, Y. L.; Tang, G. H.; Tao, W. Q.: Simulation of two-dimensional oscillating flow using the lattice Boltzmann method, Int. J. Mod. phys. C 17, No. 5, 615-630 (2006) · Zbl 1107.82370 · doi:10.1142/S0129183106009023
[27] Dixit, H. N.; Babu, V.: Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, Int. J. Heat mass transfer 49, 727-739 (2006) · Zbl 1189.76529 · doi:10.1016/j.ijheatmasstransfer.2005.07.046
[28] Chen, C. K.; Yen, T. S.; Yang, Y. T.: Lattice Boltzmann method simulation of backward-facing step on convective heat transfer with field synergy principle, Int. J. Heat mass transfer 49, 1195-1204 (2006) · Zbl 1189.76403 · doi:10.1016/j.ijheatmasstransfer.2005.08.027
[29] Mcnamara, G.; Alder, B.: Analysis of the lattice Boltzmann thermodynamics, Physica A 194, 218-228 (1993) · Zbl 0941.82527
[30] Mcnamara, G.; Alder, B.: A hydrodynamically correct thermal lattice Boltzmann model, J. stat. Phys. 87, 1111-1121 (1997) · Zbl 0939.82038 · doi:10.1007/BF02181274
[31] Chen, Y.; Ohashi, H.; Akiyama, M.: Thermal lattice bhatanagar – Gross – Krook model without nonlinear deviations in macrodynamic equations, Phys. rev. E 50, No. 4, 2776-2783 (1994)
[32] D’orazio, A.; Succi, S.: Simulating two-dimensional thermal channel flows by means of a lattice Boltzmann method with new boundary conditions, Future gener. Comp. sy. 20, 935-944 (2004)
[33] Guo, Z. L.; Zheng, C. G.; Shi, B. C.: Non-equilibrium extrapolation method for velocity and boundary conditions in the lattice Boltzmann method, Chin. phys. Soc. 11, No. 4, 0366-0374 (2002)
[34] Mei, R. W.; Shyy, W.: On the finite difference-based lattice Boltzmann method in curvilinear coordinates, J. comput. Phys. 143, 426-448 (1998) · Zbl 0934.76074 · doi:10.1006/jcph.1998.5984
[35] Shi, Y.; Zhao, T. S.; Guo, Z. L.: Finite difference-based lattice Boltzmann simulation of natural convection heat transfer in a horizontal concentric annulus, Comp. fluids 35, 1-15 (2006) · Zbl 1134.76440 · doi:10.1016/j.compfluid.2004.11.003
[36] Christian, V.; Cleofe, C. P.: Numerical model for nonlinear standing waves and weak shocks in thermoviscous fluids, J. acoust. Soc. am. 109, No. 6, 2660-2667 (2001)
[37] Kataoka, T.; Tsutahara, M.: Lattice Boltzmann model for the compressible Navier – Stokes equations with flexible specific-heat ratio, Phys. E 69, 03570:1-03570:4 (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.