CFD-DEM Simulation of Propagation of Sound Waves in Fluid Particles Fluidised Medium
DOI:
https://doi.org/10.1260/1750-9548.5.1.47Abstract
In this work, speed of sound in 2 phase mixture has been explored using CFD-DEM (Computational Fluid Dynamcis - Discrete Element Modelling). In this method volume averaged Navier Stokes, continuity and energy equations are solved for fluid. Particles are simulated as individual entities; their behaviour is captured by Newton's laws of motion and classical contact mechanics. Particle-fluid interaction is captured using drag laws given in literature.
The speed of sound in a medium depends on physical properties. It has been found experimentally that speed of sound drops significantly in 2 phase mixture of fluidised particles because of its increased density relative to gas while maintaining its compressibility. Due to the high rate of heat transfer within 2 phase medium as given in Roy et al. (1990), it has been assumed that the fluidised gas-particle medium is isothermal.
The similar phenomenon has been tried to be captured using CFD-DEM numerical simulation. The disturbance is introduced and fundamental frequency in the medium is noted to measure the speed of sound for e.g. organ pipe. It has been found that speed of sound is in agreement with the relationship given in Roy et al. (1990). Their assumption that the system is isothermal also appears to be valid.
References
Anderson T.B, Jackson R. (1967). Industrial and Engineering Chemistry Fundamentals, 6, 4 527-539.
Anderson J.D. (1995). Computational fluid dynamics, McGraw-Hill. pp 237-239.
Beetstra R., Van der Hoef, M.A., Kuipers J.A.M. (2007). Numerical study of segregation using a new drag force correlation for polydisperse systems derived from latticeBoltzmann simulations. Chemical Engineering Science, 62, 246-255. https://doi.org/10.1016/j.ces.2006.08.054
Bi H.T, Grace J.R, and Zhu J. (1994) Propagation of pressure waves and forced oscillations in gas-solid fluidised beds and their influence on diagnostics of local hydrodynamics, Powder Technology, 82, 239-253. https://doi.org/10.1016/0032-5910(94)02929-i
Cambell I.J & Pitcher A.S. (1958) Shock wave in a liquid containing gas bubbles, Proceeding of Royal Society, A-243, 534-554.
Chung T.J. (2002). Computational fluid dynamics, Cambridge University Press, pp 195-205.
Courant R, Friedrichs K, Lewy H. (1967) On the partial difference equations of mathematical physics, IBM Journal, 215-234. https://doi.org/10.1147/rd.112.0215
Cundall P, & Strack O. (1979) A discrete element model for granular assemblies, Geotechnique, 29, 47. https://doi.org/10.1680/geot.1979.29.1.47
Hairer, Nørsett, Wanner, Gerhard (1993) Solving ordinary differential equations I: Nonstiff problems, Springer Verlag. https://doi.org/10.1137/1032091
Hertz H. (1882) Uber die Beruhrang fester elastischer Korper (On the contact of elastic solids), Journal der rennin und angewandeten Mathematik. 92, S. 156-171. https://doi.org/10.1515/crll.1882.92.156
Hoef M, Ye M, & Kuipers J. (2005) The effects of particle and gas properties on the fluidisation of Geldart A particles, Chemical Engineering Science, 60, 4567-4580. https://doi.org/10.1016/j.ces.2005.03.017
Kundt (1868) From dust figures to the kinetic theory of gases, Annalen der Physik. 85, 337.
Kunii D. and Levenspiel O. (1991). Fluidisation Engineering. Butterworth-Heinemann, Stoneham, USA
Lamb H. (1963) Hydrodynamics, Cambridge University Press, Cambridge.
Mallock A. (1910) The damping of sound by frothy liquids, Proceeding of Royal Society, A-84, 391-395.
Mindlin R. D. & Deresiewicz H. (1953) Elastic Spheres in Contact under Varying Oblique Forces, Journal of Applied Mechanics, 20, 327. https://doi.org/10.1007/978-1-4613-8865-4_35
Roy R, Davidson J.F, & Tuponogov V.G. (1990) The velocity of sound in fluidised beds, Chemical Engineering Science, 45, 11, 3233-3245. https://doi.org/10.1016/0009-2509(90)80216-2
Tangren R.F, Dodge C.H, & Seifert H.S. (1949) Compressibility Effects in Two_Phase Flow, Journal of Applied Physics, 20, 637-645. https://doi.org/10.1063/1.1698449
Tsuji Y, Kawaguchi T, & Tanaka T. (1992) Discrete particle simulation of two-dimensional fluidised bed, Powder Technology, 77, 79-87. https://doi.org/10.1016/0032-5910(93)85010-7
Turton R, Fitzgerald T.J, & Levenspiel O. (1989) An experimental method to determine the heat transfer coefficient between fine fluidised particles and air via changes in magnetic properties, International Journal of Heat and Mass Transfer, 32, 289-296. https://doi.org/10.1016/0017-9310(89)90176-2
Published
How to Cite
Issue
Section
Copyright (c) 2011 H Khawaja, S Scott
This work is licensed under a Creative Commons Attribution 4.0 International License.