Abstract
The lattice Boltzman method (LBM) and the finite difference-based lattice Boltzmann method (FDLBM) are quite recent approaches for simulating fluid flow, which have been proven as valid and efficient tools in a variety of complex flow problems. They are considered attractive alternatives to conventional finite-difference schemes because they recover the Navier-Stokes equations and are computationally more stable, and easily parallelizable. However, most models of theLBM orFDLBM are for incompressible fluids because of the simplicity of the structure of the model. Although some models for compressible thermal fluids have been introduced, these models are for monatomic gases, and suffer from the instability in calculations. A lattice BGK model based on a finite difference scheme with an internal degree of freedom is employed and it is shown that a diatomic gas such as air is successfully simulated. In this research we present a 2-dimensional edge tone to predict the frequency characteristics of discrete oscillations of a jet-edge feedback cycle by theFDLBM in which any specific heat ratio γ can be chosen freely. The jet is chosen long enough in order to guarantee the parabolic velocity profile of a jet at the outlet, and the edge is of an angle of α=23°. At a stand-off distancew, the edge is inserted along the centerline of the jet, and a sinuous instability wave with real frequency is assumed to be created in the vicinity of the nozzle exit and to propagate towards the downstream. We have succeeded in capturing very small pressure fluctuations resulting from periodic oscillation of the jet around the edge.
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References
Alexander, F. J., Chen, S. and Sterling, D. J., 1993, “Lattice Boltzmann Thermodynamics,”Physical Review E, Vol. 47, pp. 2249–2252.
Bamber, A., Bansch, E. and Siebert, K.G., 2004, “Experimental and Numerical Investigation of Edge Tones,”ZAMM. Angew. Math. Mech., Vol. 84, No. 9, pp. 632–646.
Cao, N., Chen, S., Jin, S. and Martinez, D., 1997, “Physical Symmetry and Lattice Symmetry in the Lattice Boltzmann Method,”Physical Review E, 55, pp. R21-R24.
Chen, Y. and Doolen, G. D., 1998, “Lattice Boltzmann Method for Fluid Flows,”Annual Review Fluid Mechanics, Vol. 30, pp. 329–364.
Crighton, D. G., 1992, “The Jet Edge-Tone Feedback Cycle; Linear Theory for the Operating Stages,”Journal of Fluid Mechanics, Vol. 234, pp. 361–391.
Holger, D. K., Wilson, T. A. and Beavers, G. S., 1977, “Fluid Mechanics of the Edgetone,”Journal of Acoustical Society of America, Vol. 62(5), pp. 1116–1128.
Kang, H. K., Tsutahara, M., Ro, K. D. and Lee, Y. H., 2002, “Numerical Simulation of Shock Wave Propagation Using the Finite Difference Lattice Boltzmann Method,”KSME International Journal, Vol. 16, No. 10, pp. 1327–1335.
Kaykayoglu, R. and Rockwell, D., 1986, “Unstable Jet-Edge Interaction. Part 1. Instantaneous Pressure Fields at a Single Frequency,”Journal of Fluid Mechanics, Vol. 169, pp. 125–149.
Ohring, S., 1988, “Calculations Pertaining to the Dipole Nature of the Edge Tone,”Journal of Acoustical Society of America, Vol. 83, pp. 2047–2085.
Peng, G., Xi, H., Duncan, C. and Chou, S. H., 1999, “Finite Volume Scheme for the Lattice Boltzmann Method on Unstructured Meshes,”Physical Review E, Vol. 59, pp. 4675–4681.
Powell, A., 1961, “On the Edge Tone,”Journal of Acoustical Society of America, Vol. 33, pp. 395–409.
Takada, N. and Tsutahara, M., 1999, “Proposal of Lattice BGK Model with Internal Degrees of Freedom in Lattice Boltzmann Method,”Trans. JSME Journal, B, Vol. 65, No. 629, pp. 92–99.
Tsutahara, M., Takada, N. and Kataoka, T., 1999, Lattice Gas and Lattice Boltzmann Methods.Corona-sha; in Japanese.
Wolfram, S., 1986, “Cellular Automaton Fluids 1; Basic Theory, ”Journal of Statistical Physics, Vol.45, pp. 471–526.
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Hokeun, K., Eunra, K. On implementation of the finite difference lattice boltzmann method with internal degree of freedom to edgetone. J Mech Sci Technol 19, 2032–2039 (2005). https://doi.org/10.1007/BF02916496
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DOI: https://doi.org/10.1007/BF02916496