×

Linear stability of particle laden flows: the influence of added mass, fluid acceleration and Basset history force. (English) Zbl 1337.76026

Summary: Both modal and non-modal linear stability analysis of a channel flow laden with particles is presented. The particles are assumed spherical and solid,and their presence is modelled using two-way coupling, with Stokes drag, added mass and fluid acceleration as coupling terms. When the particles considered have a density ratio of order one, all three terms become important. To account for the volume and mass of the particles, a modified Reynolds number is defined. Particles lighter than the fluid decrease the critical Reynolds number for modal stability, whereas heavier particles may increase the critical Reynolds number. Most effect is found when the Stokes number defined with the instability time scale is of order one. Non-modal analysis shows that the generation of streamwise streaks is the most dominant disturbance-growth mechanism also in flows laden with particles: the transient growth of the total system is enhanced proportionally to the particle mass fraction, as observed previously in flows laden with heavy particles. When studying the fluid disturbance energy alone, the optimal growth hardly changes. We also show that the Basset history force has a negligible effect on stability. The inclusion of the extra interaction terms does not show any large modifications of the subcritical instabilities in wall-bounded shear flows.

MSC:

76E05 Parallel shear flows in hydrodynamic stability
76T15 Dusty-gas two-phase flows
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Toschi F, Bodenschatz E (2009) Lagrangian properties of particles in turbulence. Annu Rev Fluid Mech 41:375-404 · Zbl 1157.76020 · doi:10.1146/annurev.fluid.010908.165210
[2] Balachander S, Eaton JohnK (2010) Turbulent dispersed multiphase flow. Annu Rev Fluid Mech 42:111-133 · Zbl 1345.76106 · doi:10.1146/annurev.fluid.010908.165243
[3] Sproull WT (1961) Viscosity of Dusty Gases. Nature 190:976-978 · doi:10.1038/190976a0
[4] Rossetti SJ, Pfeffer R (1972) Drag reduction in dilute flowing gas-solid suspensions. AIChE J 18(1):31-39 · doi:10.1002/aic.690180107
[5] McCormick ME, Bhattacharyya R (1973) Drag reduction of a submersible hull by electrolysis. Naval Eng. J. 85(2):11-16 · doi:10.1111/j.1559-3584.1973.tb04788.x
[6] Jacob B, Olivieri A, Miozzi M, Campana EF, Piva R (2010) Drag reduction by microbubbles in a turbulent boundary layer. Phys Fluids 22(11):115104 · doi:10.1063/1.3492463
[7] Ferrante A, Elghobashi S (2003) On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys Fluids 15:315-329 · Zbl 1185.76126 · doi:10.1063/1.1532731
[8] Xu J, Maxey MR, Karniadakis GEM (2002) Numerical simulation of turbulent drag reduction using micro-bubbles. J Fluid Mech 468:271-281 · Zbl 1035.76052 · doi:10.1017/S0022112002001659
[9] Zhao LH, Andersson HI, Gillissen JJJ (2010) Turbulence modulation and drag reduction by spherical particles. Phys Fluids 22:081702 · doi:10.1063/1.3478308
[10] Klinkenberg J, de Lange HC, Brandt L (2011) Modal and non-modal stability of particle-laden channel flow. Phys Fluids 23:064110 · doi:10.1063/1.3599696
[11] Klinkenberg J, Sardina G, de Lange HC, Brandt L (2013) Numerical study of laminar-turbulent transition in particle-laden channel flow. Phys Rev E 87:043011 · doi:10.1103/PhysRevE.87.043011
[12] Saffman PG (1962) On the stability of laminar flow of a dusty gas. J Fluid Mech 13:120-128 · Zbl 0105.39605 · doi:10.1017/S0022112062000555
[13] Michael DH (1964) The stability of plane Poiseuille flow of a dusty gas. J Fluid Mech 18:19-32 · Zbl 0125.17904 · doi:10.1017/S0022112064000027
[14] Rudyak VYa, Isakov EB, Bord EG (1997) Hydrodynamic stability of the poiseuille flow of dispersed fluid. J Aerosol Sci 82:53-66 · doi:10.1016/S0021-8502(96)00056-0
[15] Asmolov ES, Manuilovich SV (1998) Stability of a dusty-gas laminar boundary layer on a flat plate. J Fluid Mech 365:137-170 · Zbl 0924.76029 · doi:10.1017/S0022112098001256
[16] Ellingsen T, Palm E (1975) Stability of linear flow. Phys Fluids 18:487-488 · Zbl 0308.76030 · doi:10.1063/1.861156
[17] Trefethen LN, Trefethen AE, Reddy SC, Driscoll TA (1993) Hydrodynamic stability without eigenvalues. Science 261:578-584 · Zbl 1226.76013 · doi:10.1126/science.261.5121.578
[18] Reddy SC, Henningson DS (1993) Energy growth in viscous channel flows. J Fluid Mech 252:209-238 · Zbl 0789.76026 · doi:10.1017/S0022112093003738
[19] Schmid PJ, Henningson DS (2001) Stability and transition in shear flows. Springer, Berlin · Zbl 0966.76003 · doi:10.1007/978-1-4613-0185-1
[20] Maxey MR, Riley JJ (1983) Equation of motion for a small rigid sphere in a nonuniform flow. Phys Fluids 26:883-889 · Zbl 0538.76031 · doi:10.1063/1.864230
[21] Tchen CM (1947) Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid. PhD thesis, Delft
[22] Corrsin S, Lumley J (1956) On the equation of motion for a particle in turbulent fluid. Appl Sci Res A 6:114-116 · Zbl 0073.21002
[23] Saffman PG (1992) Vortex dynamics. Cambridge Univ Press, Cambridge · Zbl 0777.76004
[24] Dandy DS, Dwyer HA (1990) A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag, and heat transfer. J Fluid Mech 216:381-400 · doi:10.1017/S0022112090000477
[25] Mei R (1992) An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. Int J Multiph Flow 18:145-147 · Zbl 1144.76419 · doi:10.1016/0301-9322(92)90012-6
[26] McLaughlin JB (1991) Inertial migration of a small sphere in linear shear flows. J Fluid Mech 224:262-274 · Zbl 0721.76029 · doi:10.1017/S0022112091001751
[27] Boronin SA, Osiptsov AN (2008) Stability of a Disperse-Mixture Flow in a Boundary Layer. Fluid Dyn 43:66-76 · Zbl 1210.76064 · doi:10.1134/S0015462808010080
[28] Vreman AW (2007) Macroscopic theory of multicomponent flows: Irreversibility and well-posed equations. Physica D 225:94-111 · Zbl 1111.35041 · doi:10.1016/j.physd.2006.10.002
[29] Boronin SA (2008) Investigation of the stability of a plane-channel suspension flow with account for finite particle volume fraction. Fluid Dyn 43:873-884 · Zbl 1210.76063 · doi:10.1134/S0015462808060069
[30] Calzavarini E, Volk R, Bourgoin M, Lévêque E, Pinton J-F, Toschi F (2009) Acceleration statistics of finite-sized particles in turbulent flow: the role of Faxén forces. J Fluid Mech 630:179-189 · Zbl 1181.76087 · doi:10.1017/S0022112009006880
[31] Matas JP, Morris JF, Guazzelli É (2003) Transition to turubulence in particulate pipe flow. Phys Rev Lett 90:014501 · doi:10.1103/PhysRevLett.90.014501
[32] Matas JP, Morris JF, Guazzelli É (2003) Influence of particles on the transition to turbulence in pipe flow. Philos Trans R Soc Lond A 361:911-919 · Zbl 1134.76306 · doi:10.1098/rsta.2003.1173
[33] Boffetta G, Celani A, De Lillo F, Musacchio S (2007) The Eulerian description of dilute collisionless suspension. Europhys Lett 78:14001 · doi:10.1209/0295-5075/78/14001
[34] Meiburg E, Wallner E, Pagella A, Riaz A, Härtel C, Necker F (2000) Vorticity dynamics of dilute two-way-coupled particle-laden mixing layers. J Fluid Mech 421:185-227 · Zbl 1004.76094 · doi:10.1017/S0022112000001737
[35] Elghobashi S (1994) On predicting particle-laden turbulent flows. Appl Sci Res 52:309-329 · doi:10.1007/BF00936835
[36] Ferry J, Balachander S (2001) A fast Eulerian method for disperse two-phase flow. Int J Multiph Flow 27:1199-1226 · Zbl 1137.76577 · doi:10.1016/S0301-9322(00)00069-0
[37] van der Hoef Van MA, Annaland S, Deen NG, Kuipers JAM (2008) Numerical simulation of dense gas-solid fluidized beds: a multiscale modeling strategy. Annu Rev Fluid Mech 40(1):47-70 · Zbl 1231.76327 · doi:10.1146/annurev.fluid.40.111406.102130
[38] Guazzelli É, Morris JF (2011) A physical introduction to suspension dynamics. Cambridge University Press, Cambridge · Zbl 1426.76003 · doi:10.1017/CBO9780511894671
[39] Reddy SC, Schmid PJ, Baggett JS, Henningson DS (1998) On the stability of streamwise streaks and transition thresholds in plane channel flows. J Fluid Mech 365:269-303 · Zbl 0927.76029 · doi:10.1017/S0022112098001323
[40] van Hinsberg MAT, ten Thije Boonkkamp JHM, Clercx HJH (2011) An efficient, second order method for the approximation of the basset history force. J Comp Physiol 230(4):1465-1478 · Zbl 1391.76593 · doi:10.1016/j.jcp.2010.11.014
[41] Picano F, Breugem W-P, Mitra D, Brandt L (2013) Shear thickening in non-brownian suspensions: an excluded volume effect. Phys Rev Lett 111:098302 · doi:10.1103/PhysRevLett.111.098302
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.