Abstract
The mean square of particle velocity fluctuations, \(\delta v^{2}\) , which is directly related to the so-called granular temperature, plays an important role in the flow, mixing, segregation and attrition phenomena of particulate systems and associated theories. It is, therefore, important to be able to measure this quantity. We report here in detail our use of diffusing wave spectroscopy (DWS) to measure the mean square particle velocity fluctuations for a 2D non-circulating gas fluidized bed of hollow glass particles whose mean diameter and effective density are 60 \(\upmu\) m and 200 kg/m3, respectively. Mean square particle velocity fluctuations were observed to increase with superficial velocity, U s, beyond the minimum fluidization velocity. Following the uniform fluidization theory of Batchelor (1988), the function \(f{\left(\phi \right)}\) in the expression \(\delta v^{2} = f{\left(\phi \right)}U^{2}_{\rm s}\) was also determined and shown to increase from zero at a solids loading of \(\phi \approx 0.33\) to a maximum at \(\phi \approx 0.4\) before decreasing again to zero at \(\phi \approx 0.53\) . The spatial variation of the mean square particle velocity fluctuations was also determined and shown to be approximately symmetrical about the centreline where it is also maximal, and to increase with height above the distributor.
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References
Ogawa S. (1978). Multitemperature theory of granular materials. In: Cowin, S.C. and Satake, M. (eds) Proceedings of the US-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp 208–217. Gakujutsu Bunken Fukyukai, Tokyo
Ogawa S., Umemura A. and Oshima N. (1980). On the equations of fully fluidized granular materials. J. Appl. Math. Phys. 31: 483–493
Jenkins J.T. and Savage S.B. (1983). Theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130: 187–202
Lun C.K.K., Savage S.B., Jeffrey D.J. and Chepurniy N. (1984). Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 140: 223–256
Chapman S. and Cowling T. (1970). The Mathematical Theory of Non-Uniform Gases. Cambridge University Press, Cambridge
Grad H. (1949). On the kinetic theory of rarefied gases. Comm. Pure Appl. Math. 2(4): 331–407
Campbell C.S. (1990). Rapid granular flows. Ann. Rev. Fluid Mech. 22: 57–92
Natarajan V.V.R. and Hunt M.L. (1998). Kinetic theory analysis of heat transfer in granular flows. Int. J. Heat Mass Trasfer 41(13): 1929–1944
Tan H.S., Goldschmidt M.J.V., Boerefijn R., Hounslow M.J., Salman A.D. and Kuipers J.A.M. (2005). Population balance modelling of fluidized bed melt granulation. Trans. IChemE 83(A7): 871–880
Ding J. and Lyczkowski R.W. (1992). Three-dimensional kinetic theory modelling of hydrodynamics and erosion in fluidized beds. Powder Technol. 73(2): 127–138
Ahn H., Brennen C.E. and Sabersky R.H. (1991). Measurements of velocity, velocity fluctuation, density, and stresses in chute flows of granular materials. ASME J. Appl. Mech. 58(3): 792–803
Hsiau S.S. and Hunt M.L. (1993). Shear-induced particle diffusion and longitudinal velocity fluctuations in a granular-flow mixing layer. J. Fluid. Mech. 251: 299–313
Boateng A.A. and Barr P.V. (1997). Granular flow behaviour in the transverse plane of a partially filled rotating cylinder. J. Fluid Mech. 330: 233–249
Drake T.G. (1991). Granular flow: Physical experiments and their implications for microstructural theories. J. Fluid Mech. 225: 121–152
Natarajan V.V.R., Hunt M.L. and Taylor E.D. (1995). Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow. J. Fluid Mech. 304: 1–25
Azanza E., Chevoir F. and Moucheront P. (1999). Experimental study of collisional granular flows down an inclined plane. J. Fluid Mech. 400: 199–227
Bi W., Delannay R., Richard P. and Valance A. (2006). Experimental study of two-dimensional, monodisperse, frictional–collisional granular flows down an inclined chute. Phys. Fluids 18(12): 123302–123314
Hanes D.M. and Walton O.R. (2000). Simulations and physical measurements of glass spheres flowing down a bumpy incline. Powder Technol. 109: 133–144
Armanini A., Capart H., Fraccarollo L. and Larcher M. (2005). Rheological stratification in experimental free-surface flows of granular-liquid mixtures. J. Fluid Mech. 532: 269–319
Hsiau S.S. and Jang H.W. (1998). Measurements of velocity fluctuations of granular materials in a shear cell. Expt. Thermal Fluid Sci. 17(3): 202–209
Hsiau S.S. and Shieh Y.M. (2000). Effect of solid fraction of fluctuations and self-diffusion of sheared granular flows. Chem. Eng. Sci. 55(11): 1969–1979
Hsiau S.S, Yang W.L. Stresses and transport phenomena in sheared granular flows with different wall conditions. Phys. Fluids 14(2): 612–621
Hsiau S.S. and Yang W.L. (2005). Transport property measurements in sheared granular flows. Chem. Eng. Sci. 60(1): 187–199
Yang W.L. and Hsiau S.S. (2005). Wet granular materials in sheared flows. Chem. Engng. Sci. 60(15): 4265–4274
Hsiau W.L., Lu L.S., Chen J.C. and Yang W.L. (2005). Particle mixing in a sheared granular flow. Int. J. Multiph. Flow 31(7): 793–808
Perng A.T.H., Capart H. and Chou H.T. (2006). Granular configurations, motions, and correlations in slow uniform flows driven by an inclined conveyer belt. Granul. Matter 8(1): 5–17
Warr S., Huntley J.M. and Jacques G.T.H. (1995). Fluidization of a two-dimensional granular system: experimental study and scaling behavior. Phys. Rev. E 52(5): 5583–5595
Wildman R.D., Huntley J.M. and Hansen J.-P. (1999). Self-diffusion of grains in a two-dimensional vibrofluidized bed. Phys. Rev. E 60(6): 7066–7075
Losert W., Cooper D.G.W, Delour J., Kudrolli A. and Gollub J.P. (1999). Velocity statistics in excited granular media. Chaos 9(3): 682–690
Blair D.L. and Kudrolli A. (2003). Collision statistics of driven granular materials. Phys. Rev. E 67(41): 413011–4130112
Tai C.H. and Hsiau S.S. (2004). Dynamic behaviours of powders in a vibrated bed. Powder Technol. 139(3): 221–232
Baxter G.W. and Olafsen J.S. (2007). The temperature of a vibrated granular gas. Granul. Material 9(1–2): 135–139
Spinewine B., Capart H., Larcher M. and Zech Y. (2003). Three-dimensional Voronoi imaging methods for the measurement of near-wall particulate flows. Exp. Fluids 34(2): 227–241
Jung J., Gidaspow D. and Gamwo I.K. (2005). Measurement of two kinds of granular temperatures, stresses, and dispersion in bubbling beds. Ind. Eng. Chem. Res. 44(5): 1329–1341
Gidaspow D. and Huilin L. (1996). Collisional viscosity of FCC particles in a CFB. AIChE J. 42(9): 2503–2510
Gidaspow D. and Huilin L. (1998). Equation of state and radial distribution functions of FCC particles in a CFB. AIChE J. 44(2): 279–291
Tartan M. and Gidaspow D. (2004). Measurement of granular temperature and stresses in risers. AIChE J. 50(8): 1760–1775
Longo S. and Lamberti A. (2002). Grain shear flow in a rotating drum. Exp. Fluids 32(3): 313–325
Wildman, R.D., Huntley, J.M., Hansen, J.P., Parker, D.J., Allen, D.A.: Single-particle motion in three-dimensional vibrofluidized granular beds. Phys. Rev. E 62(3), 3826–3835 (2000)
Wildman R.D., Huntley J.M. and Parker D.J. (2001). Granular temperature profiles in three-dimensional vibrofluidized granular beds. Phys. Rev. E 63: 061311–061321
Wildman R.D. and Parker D.J. (2002). Coexistance of two granular temperatures in binary vibrofluidized beds. Phys. Rev. Lett. 88(6): 064201–064205
Wildman R.D. and Huntley J.M. (2003). Scaling exponents for energy transport and dissipation in binary vibro-fluidized granular beds. Phys. Fluids 15(10): 3090–3098
Bhusarapu S., Al-Dahhan M.H. and Dudukovic M.P. (2006). Solids flow mapping in a gas–solid riser: mean holdup and velocity fields. Powder Technol. 163(1–2): 98–123
Yang X., Huan C., Candela D., Mair R.W. and Walsworth R.L. (2002). Measurements of grain motion in a dense, three-dimensional granular fluid. Phys. Rev. Lett. 88(4): 443011–443014
Huan C., Yang X., Candela D., Mair R.W. and Walsworth R.L. (2004). NMR experiments on a three-dimensional vibrofluidized granular media. Phys. Rev. E 69(41): 041302–0413115
Cody G.D., Goldfarb D.J., Storch G.V. and Norris A.N. (1996). Particle granular temperature in gas fluidized beds. Powder Technol. 87(3): 211–232
Menon N. and Durian D.J. (1997). Diffusing wave spectroscopy of dynamics in a three-dimensional granular flow. Science 275: 1920–1922
Menon N. and Durian D.J. (1997). Particle motions in a gas-fluidized bed of sand. Phys. Rev. Lett. 79(18): 3407–3410
Kim K., Park J.J., Moon J.K., Kim H.K. and Pak H.K. (2002). Solid–liquid transition in a highly dense 3D vibro-fluidized granular system. J. Korean Phys. Soc. 40(6): 983–986
Xie, L.: Study of granular temperatures in gas-fluidized beds by diffusing wave spectroscopy (The University of Edinburgh), PhD Thesis (2005)
Xie L., Biggs M.J., Glass D., McLeod A.S., Egelhaaf S.U. and Petekidis G. (2006). Granular temperature distribution in a gas fluidized bed of hollow microparticles prior to onset of bubbling. Europhys. Lett. 74(2): 268–274
Polashenski W. and Chen J.C. (1997). Normal solid stress in fluidized beds. Powder Technol. 90(1): 13–23
Louge M.Y. and Keast S.C. (2001). On dense granular flows down flat frictional inclines. Phys. Fluids 13(5): 1213–1233
Falcon E., Aumaître S., Évesque P., Palencia F., Lecoutre-Chabot C., Fauve S., Beysens D. and Garrabos Y. (2006). Collision statistics in a dilute granular gas fluidized by vibrations in low gravity. Europhys. Lett. 74(5): 830–836
D’Anna G., Mayor P., Barrat A., Loreto V. and Nori F. (2003). Observing Brownian motion in vibration-fluidized granular matter. Nature 424: 909–912
Mayor P., D’Anna G., Barrat A. and Loreto V. (2005). ObservingBrownian motion and measuring temperatures in vibration-fluidized granular matter. New J. Phys. 7: 28
Mayor P., D’Anna G., Gremaud G., Barrat A. and Loreto V. (2006). Mechanical spectroscopy of vibrated granular matter. Mat. Sci. Eng. A 442(1–2): 256–262
Valverde J.M., Castellanos A. and Quintanilla M.A.S. (2001). Self-diffusion in a gas-fluidized bed of fine powder. Phys. Rev. Lett. 86(14): 3020–3023
Weitz D.A. and Pine D.J. (1993). Diffusing wave spectroscopy. In: Brown, W. (eds) Dynamic Light Scattering, pp 652–719. OUP, Oxford
Li J.H., Lisyansky A.A., Cheung T.D., Livdan D. and Genack A.Z. (1993). Transmission and surface intensity profiles in random-media. Europhys. Lett. 22(9): 675–680
Leutz W. and Rička J. (1996). On light propagation through glass bead packings. Opt. Commun. 126(4–6): 260–268
Ishimaru A. (1999). Wave Propagation and Scattering in Random Media. Wiley, IEEE, London
Geldart D. and Wong A.C.Y. (1984). Fluidization of powders showing degrees of cohesiveness I. Bed Expans. Chem. Eng. Sci. 39(10): 1481–1488
Lemieux P.A. and Durian D.J. (1999). Investigating non-Gaussian scattering processes by using n-th order intensity correlation functions. J. Opt. Soc. Am. A 16(7): 1651–1664
Abate A.R. and Durian D.J. (2006). Approach to jamming in an air-fluidized granular bed. Phys. Rev. E 74(3): 031308
Biggs M. and Agarwal P. (1992). Mass diffusion of atomic fluids in random micropore spaces using equilibrium molecular-dynamics. Phys. Rev. A 46(6): 3312–3318
Biggs M. and Agarwal P. (1994). Mass diffusion of diatomic fluids in random micropore spaces using equilibrium molecular-dynamics. Phys. Rev. E 49(1): 531–537
Batchelor G.K. (1988). A new theory of the instability of a uniform fluidized bed. J. Fluid Mech. 193: 75–110
Wong, Y.S.: Experimental and numerical investigation of fluidisation behaviour with and without the presence of immersed tubes. PhD Thesis, pp. 75 (The University of Birmingham) (2003)
Morooka S., Kusakabe K., Kobata A. and Kato Y. (1988). Fluidization state of ultrafine powders. J. Chem. Eng. Jpn. 21(1): 41–46
Zhao G.Y., Zhu C.W. and Hlavacek V. (1994). Fluidization of micron-sized ceramic powders in a small-diameter fluidized bed. Powder Technol. 79(3): 227–235
Wang Z., Kwauk M. and Li H. (1998). Fluidization of fine particles. Chem. Eng. Sci. 53(3): 377–395
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Biggs, M.J., Glass, D., Xie, L. et al. Granular temperature in a gas fluidized bed. Granular Matter 10, 63–73 (2008). https://doi.org/10.1007/s10035-007-0077-8
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DOI: https://doi.org/10.1007/s10035-007-0077-8