×

Flow instability and transitions in Taylor-Couette flow of a semidilute non-colloidal suspension. (English) Zbl 07346848

Summary: Flow of a semidilute neutrally buoyant and non-colloidal suspension is numerically studied in the Taylor-Couette geometry where the inner cylinder is rotating and the outer one is stationary. We consider a suspension with bulk particle volume fraction \(\phi_b = 0.1\), the radius ratio \((\eta = r_i/r_o = 0.877)\) and two particle size ratios \(\epsilon (=d/a) = 60\), \(200\), where \(d\) is the gap width \((= r_o-r_i)\) between cylinders, \(a\) is the suspended particles’ radius and \(r_i\) and \(r_o\) are the inner and outer radii of the cylinder, respectively. Numerical simulations are conducted using the suspension balance model (SBM) and rheological constitutive laws. We predict the critical Reynolds number in which counter-rotating vortices arise in the annulus. It turns out that the primary instability appears through a supercritical bifurcation. For the suspension of \(\epsilon =200\), the circular Couette flow (CCF) transitions via Taylor vortex flow (TVF) to wavy vortex flow (WVF). Additional flow states of non-axisymmetric vortices, namely spiral vortex flow (SVF) and wavy spiral vortex flow (WSVF) are observed between CCF and WVF for the suspension of \(\epsilon =60\); thus, the transitions occur following the sequence of CCF \(\rightarrow\) SVF \(\rightarrow\) WSVF \(\rightarrow\) WVF. Furthermore, we estimate the friction and torque coefficients of the suspension. Suspended particles substantially enhance the torque on the inner cylinder, and the axial travelling wave of spiral vortices reduces the friction and torque coefficients. However, the coefficients are practically the same in the WVF regime where particles are almost uniformly distributed in the annulus by the axial oscillating flow.

MSC:

76-XX Fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ali, M.E., Mitra, D., Schwille, J.A. & Lueptow, R.M.2002Hydrodynamic stability of a suspension in cylindrical Couette flow. Phys. Fluids14, 1236-1243. · Zbl 1185.76894
[2] Andereck, C.D., Liu, S.S. & Swinney, H.L.1986Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech.164, 155-183.
[3] Asmolov, E.S.1999The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number. J. Fluid Mech.381, 63-87. · Zbl 0935.76025
[4] Baroudi, L., Majji, M.V. & Morris, J.F.2020Effect of inertial migration of particles on flow transitions of a suspension Taylor-Couette flow. Phys. Rev. Fluids5, 114303.
[5] Boubnov, B.M., Gledzer, E.B. & Hopfinger, E.J.1995Stratified circular Couette flow: instability and flow regimes. J. Fluid Mech.292, 333-358. · Zbl 0850.76207
[6] Caton, F., Janiaud, B. & Hopfinger, E.J.1999Primary and secondary Hopf bifurcations in stratified Taylor-Couette flow. Phys. Rev. Lett.82, 4647-4650. · Zbl 0956.76504
[7] Chan, P.C.-H. & Leal, L.G.1981An experimental study of drop migration in shear flow between concentric cylinders. Intl J. Multiphase Flow7, 83-99.
[8] Climent, E., Simonnet, M. & Magnaudet, J.2007Preferential accumulation of bubbles in Couette-Taylor flow patterns. Phys. Fluids19, 083301. · Zbl 1182.76157
[9] Coles, D.1965Transition in circular Couette flow. J. Fluid Mech.21, 385-425. · Zbl 0134.21705
[10] Cox, R.G. & Brenner, H.1968The lateral migration of solid particles in Poiseuille flow: I. Theory. Chem. Engng Sci.23, 147-173.
[11] Dherbécourt, D., Charton, S., Lamadie, F., Cazin, S. & Climent, E.2016Experimental study of enhanced mixing induced by particles in Taylor-Couette flows. Chem. Engng Res. Des.108, 109-117.
[12] Diprima, R.C., Eagles, P.M. & Ng, B.S.1984The effect of radius ratio on the stability of Couette flow and Taylor vortex flow. Phys. Fluids27, 2403-2411. · Zbl 0567.76047
[13] Drew, D.A. & Lahey, R.T.1993Analytical modeling of multiphase flow. In Particular Two-Phase Flow (ed. Roco, M.), pp. 509. Butterworths.
[14] Eckhardt, B., Grossmann, S. & Lohse, D.2007Torque scaling in turbulent Taylor-Couette flow between independently rotating cylinders. J. Fluid Mech.581, 221-250. · Zbl 1165.76342
[15] Eckstein, E.C., Bailey, D.G. & Shapiro, A.H.1977Self-diffusion of particles in shear flow of a suspension. J. Fluid Mech.79, 191-208.
[16] Fang, Z., Mammoli, A.A., Brady, J.F., Ingber, M.S., Mondy, L.A. & Graham, A.L.2002Flow-aligned tensor models for suspension flows. Int. J. Multiphase Flow28, 137-166. · Zbl 1136.76500
[17] Gillissen, J.J.J. & Wilson, H.J.2019Taylor-Couette instability in sphere suspensions. Phys. Rev. Fluids4, 043301.
[18] Grossmann, S., Lohse, D. & Sun, C.2016High-Reynolds number Taylor-Couette turbulence. Annu. Rev. Fluid Mech.48, 53-80. · Zbl 1356.76106
[19] Guillerm, R., Kang, C., Savaro, C., Lepiller, V., Prigent, A., Yang, K.-S. & Mutabazi, I.2015Flow regimes in a vertical Taylor-Couette system with a radial thermal gradient. Phys. Fluids27, 094101.
[20] Guckenheimer, J. & Holmes, P.1983Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag. · Zbl 0515.34001
[21] Ho, B.P. & Leal, L.G.1974Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech.65, 365-400. · Zbl 0284.76076
[22] Hogg, A.J.1994The inertial migration of non-neutrally buoyant spherical particles in two-dimensional shear flows. J. Fluid Mech.272, 285-318. · Zbl 0823.76086
[23] Hristova, H., Roch, S., Schmid, P. & Tuckerman, L.S.2002Transient growth in Taylor-Couette flow. Phys. Fluids14, 3475-3484. · Zbl 1185.76173
[24] Huisman, S.G., Van Gils, D.P.M., Grossmann, S., Sun, C. & Lohse, D.2012Ultimate turbulent Taylor-Couette flow. Phys. Rev. Lett.108, 024501. · Zbl 1275.76034
[25] Jeong, J. & Hussain, F.1995On the identification of a vortex. J. Fluid Mech.285, 69-94. · Zbl 0847.76007
[26] Kang, C., Meyer, A., Mutabazi, I. & Yoshikawa, H.N.2017aRadial buoyancy effects on momentum and heat transfer in a circular Couette flow. Phys. Rev. Fluids2, 053901.
[27] Kang, C., Meyer, A., Yoshikawa, H.N. & Mutabazi, I.2017bNumerical simulation of circular Couette flow under a radial thermo-electric body force. Phys. Fluids29, 114105.
[28] Kang, C., Meyer, A., Yoshikawa, H.N. & Mutabazi, I.2019Thermoelectric convection in a dielectric liquid inside a cylindrical annulus with a solid-body rotation. Phys. Rev. Fluids4, 093502.
[29] Kang, C. & Mirbod, P.2020Shear-induced particle migration of semi-dilute and concentrated Brownian suspensions in both Poiseuille and circular Couette flow. Intl J. Multiphase Flow126, 103239.
[30] Kang, C., Yang, K.-S. & Mutabazi, I.2015Thermal effect on large-aspect-ratio Couette-Taylor system: Numerical simulation. J. Fluid Mech.771, 57-78.
[31] Kim, J. & Moin, P.1985Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comp. Phys59, 308-323. · Zbl 0582.76038
[32] Krieger, I.M.1972Rheology of monodisperse lattices. Adv. Colloid Interface Sci.3, 111-136.
[33] Landau, L.D. & Lifshitz, E.M.1976Mechanics, 3rd edn. Elsevier Butterworth-Heinemann.
[34] Lathrop, D.P., Fineberg, J. & Swinney, H.S.1992aTransition to shear-driven turbulence in Couette-Taylor flow. Phys. Rev. A46, 6390-6405.
[35] Lathrop, D.P., Fineberg, J. & Swinney, H.S.1992bTurbulent flow between concentric rotating cylinders at large Reynolds numbers. Phys. Rev. Lett.68, 1515-1518.
[36] Leighton, D. & Acrivos, A.1987The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech.181, 415-439.
[37] Lim, T.T., Chew, Y.T. & Xiao, Q.1998A new flow regime in a Taylor-Couette flow. Phys. Fluids10, 3233-3235. · Zbl 1185.76902
[38] Majji, M.V., Banerjee, S. & Morris, J.F.2018Inertial flow transitions of a suspension in Taylor-Couette geometry. J. Fluid Mech.835, 936-969.
[39] Majji, M.V. & Morris, J.F.2018Inertial migration of particles in Taylor-Couette flows. Phys. Fluids30, 033303.
[40] Marques, F. & Lopez, J.1997Taylor-Couette flow with axial oscillations of the inner cylinder: Floquet analysis of the basic flow. J. Fluid Mech.348, 153-175. · Zbl 0897.76027
[41] Mclaughlin, J.B.1993The lift on a small sphere in wall-bounded linear shear flows. J. Fluid Mech.226, 249-265. · Zbl 0765.76027
[42] Miller, R.M. & Morris, J.F.2006Normal stress-driven migration and axial development in pressure-driven flow of concentrated suspensions. J. Non-Newtonian Fluid135, 149-165. · Zbl 1195.76406
[43] Morris, J.F. & Brady, J.F.1998Pressure-driven flow of a suspension: buoyancy effects. Int. J. Multiphase Flow24, 105-130. · Zbl 1121.76462
[44] Morris, J.F. & Boulay, F.1999Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol.43, 1213-1237.
[45] Mullin, T., Cliffe, K.A. & Pfister, G.1987Unusual time-dependent phenomena in Taylor-Couette flow at moderately low Reynolds numbers. Phys. Rev. Lett.58, 2212-2215.
[46] Nott, P.R. & Brady, J.F.1994Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech.275, 157-199. · Zbl 0925.76835
[47] Pfister, G. & Rehberg, I.1981Space dependent order parameter in circular Couette flow transitions. Phys. Lett. A83, 19-22.
[48] Phillips, R.J., Armstrong, R.C. & Brown, R.A.1992A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys. Fluids A4, 30-40. · Zbl 0742.76009
[49] Ramesh, P. & Alam, M.2020Interpenetrating spiral vortices and other coexisting states in suspension Taylor-Couette flow. Phys. Rev. Fluids5, 042301(R).
[50] Ramesh, P., Bharadwaj, S. & Alam, M.2019Suspension Taylor-Couette flow: co-existence of stationary and travelling waves, and the characteristics of Taylor vortices and spirals. J. Fluid Mech.870, 901-940. · Zbl 1419.76664
[51] Resende, M.M., Tardioli, P.W., Fernandez, V.M., Ferreira, A.L.O., Giordano, R.L.C. & Giordano, R.C.2001Distribution of suspended particles in a Taylor-Poiseuille vortex flow reactor. Chem. Engng Sci.56, 755-761.
[52] Richardson, J.F. & Zaki, W.N.1954Sedimentation and fluidization: part 1. Trans. Inst. Chem. Engrs32, 35-53.
[53] Rida, Z., Cazin, S., Lamadie, F., Dherbécourt, D., Charton, S. & Climent, E.2019Experimental investigation of mixing efficiency in particle-laden Taylor-Couette flows. Exp. Fluids60, 61.
[54] Rudman, M.2004Mixing and particle dispersion in the wavy vortex regime of Taylor-Couette flow. AIChE J.44, 1015-1026.
[55] Sierou, A. & Brady, J.F.2004Shear-induced self-diffusion in non-colloidal suspensions. J. Fluid Mech.506, 285-314. · Zbl 1062.76049
[56] Tetlow, N., Graham, A.L., Ingber, M.S., Subia, S.R., Mondy, L.A. & Altobelli, S.A.1998Particle migration in a Couette apparatus: Experiment and modeling. J. Rheol.42, 307-327.
[57] Vasseur, P. & Cox, R.G.1976The lateral migration of a spherical particle in two-dimensional shear flows. J. Fluid Mech.78, 385-413. · Zbl 0342.76039
[58] Wereley, S.T. & Lueptow, R.M.1999Inertial particle motion in a Taylor-Couette rotating filter. Phys. Fluids11, 325-333. · Zbl 1147.76534
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.