Abstract
In a rotating filter separator a suspension is introduced at one end of the annulus between a rotating porous inner cylinder and a fixed impermeable outer cylinder. The filtrate is removed through the inner cylinder and the concentrate is removed from the opposite end of the annulus from which the suspension entered. The flow in a rotating filter separator is circular Couette flow with a pressure-driven axial flow and a suction boundary condition at the inner cylinder. Flow visualization was used to determine the effect of the Taylor number, axial Reynolds number, and radial Reynolds number on the types of flows present in the annulus. A rich variety of secondary vortical flows appear, depending upon the flow parameters. The radial inflow at the inner cylinder delays the appearance of supercritical circular Couette flow and prevents the appearance of certain flow regimes that have a helical vortex structure. Nevertheless, the average azimuthal velocity measured using laser Doppler velocimetry indicates that the velocity profile is nearly the same for all supercritical flow regimes.
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References
Andereck CD; Liu SS; Swinney HL (1986) Flow regimes in a circular Couette system with independently rotating cylinders. J Fluid Mech 164: 155–183
Bahl SK (1970) Stability of viscous flow between two concentric rotating porous cylinders. Def Sci J 20: 89–96
Beaudoin G; Jaffrin MY (1989) Plasma filtration in Couette flow membrane devices. Artif Organs 13: 43–51
Bühler K (1992) Taylor vortex flow with superimposed radial mass flux. In: Ordered and turbulent patterns in Taylor-Couette flow (ed. Andereck CD; Hayot F) pp 197–203. New York: Plenum Press
Bühler K; Polifke N (1990) Dynamical behaviour of Taylor vortices with superimposed axial flow. In: Nonlinear evolution of spatio-temporal structures in dissipative continuous systems (ed. Busse FH; Kramer L) pp 21–29. New York: Plenum Press
Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. pp 272–342. Oxford University Press
Chang TS; Sartory WK (1967) Hydromagnetic stability of dissipative flow between rotating permeable cylinders: Part 1. Stationary critical modes. J Fluid Mech 27: 65–79 with corrections noted in: Chang TS; Sartory WK (1969) Hydromagnetic stability of dissipative flow between rotating permeable cylinders: Part 2. Oscillatory critical modes and asymptotic results. J Fluid Mech 36: 193–206
Chung KC; Astill KN (1977) Hydrodynamic instability of viscous flow between rotating coaxial cylinders with fully developed axial flow. J Fluid Mech 81: 641–655
Coughlin, KT; Marcus PS (1992) Modulated waves in Taylor-Couette flow. Part 2. Numerical simulation. J Fluid Mech 234: 19–46
DiPrima RC (1960) The stability of a viscous fluid between rotating cylinders with an axial flow. J Fluid Mech 9: 621–631
DiPrima RC; Pridor A (1979) The stability of viscous flow between rotating concentric cylinders with an axial flow. Proc R Soc Lond A 366: 555–573
DiPrima RC; Swinney HL (1985) Instabilities and transition in flow between concentric rotating cylinders. In: Topics in applied physics, hydrodynamic instabilities and the transition to turbulence (ed. Swinney HL; Gollub JP) PP 139–180. Berlin: Springer Verlag
Fenstermacher PR; Swinney HL; Gollub JP (1979) Dynamical instabilities and the transition to chaotic Taylor vortex flow. J Fluid Mech 94: 103–128
Fishel RJ; Fishel H; Shatzel A; Lange WP; Cahill D; Gervais D; Ascher NL (1988) Couette membrane filtration with constant shear stress. Trans Am Soc Artif Intern Organs 34: 375–385
Gorman M; Swinney HL (1982) Spatial and temporal characteristics of modulated waves in the circular Couette system. J Fluid Mech 117: 123–142
Gravas N; Martin BW (1978) Instability of viscous axial flow in annuli having a rotating inner cylinder. J Fluid Mech 86: 385–394
Hallström B; Lopez-Leiva M (1978) Description of a rotating ultrafiltration module. Desalination 24: 273–279
Hasoon MA; Martin BW (1977) The stability of viscous axial flow in an annulus with a rotating inner cylinder. Proc R Soc Lond A 352: 351–380
Hildebrandt JR; Saxton JB (1987) The use of Taylor vortices in protein processing to enhance membrane filtration performance. Bioprocess Engineering Colloquium (ed. Dean RC; Nerem RM) pp 93–96, ASME Book No. G00422
Jaffrin M; Beaudoin G; Ding LH; Djennaoui N (1989) Effect of membrane characteristics on the performance of Couette rotating plasma separation devices. Trans Am Soc Artif Intern Organs 35: 690–693
Kataoka K; Doi H; Komai T (1977) Heat/mass transfer in Taylor vortex flow with constant axial flow rates. Int J Heat Mass Trans 20: 57–63
Kaye J; Elgar EC (1958) Modes of adiabatic and diabatic fluid flow in an annulus with an inner rotating cylinder. Trans ASME 80: 753–765
Koschmieder EL (1993) Benard cells and Taylor vortices, pp 197–308. Cambridge University Press
Lopez-Leiva M (1980) Ultrafiltration at low degrees of concentration polarization: technical possibilities. Desalination 35: 115–128
Lueptow RM; Docter A; Min K (1992) Stability of axial flow in an annulus with a rotating inner cylinder. Phys Fluids A 4: 2446–2455
Lueptow RM; Hajiloo A (1994) Flow in a rotating membrane separator. Submitted to ASAIO Trans
Marcus PS (1984) Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave. J Fluid Mech 146: 65–113
Min K; Lueptow RM (1994) Hydrodynamic stability of viscous flow between rotating porous cylinders with radial flow. Phys Fluids 6: 144–151
Ng BS; Turner ER (1982) On the linear stability of spiral flow between rotating cylinders. Proc R Soc Lond A 382: 83–102
Ohashi K; Tashiro K; Kushiya F; Matsumoto T; Yoshida S; Endo M; Horio T; Ozawa K; Sakai K (1988) Rotation-induced Taylor vortex enhances filtrate flux in plasma separation. Trans Am Soc Artif Organs 34: 300–307
Roberts PH (1965) The solution of the characteristic value problem. Proc R Soc Lond A 283: 550–556
Schwarz KW; Springett BE; Donnelly RJ (1964) Modes of instability in spiral flow between rotating cylinders. J Fluid Mech 20: 281–289
Snyder HA (1962) Experiments on the stability of spiral flow at low axial Reynolds numbers. Proc R Soc Lond A 265: 198–213
Takeuchi DI; Jankowski DF (1981) A numerical and experimental investigation of the stability of spiral Poiseuille flow. J Fluid Mech 102: 101–126
Taylor GI (1923) Stability of a viscous liquid contained between two rotating cylinders. Phil Trans Roy Soc A 223: 289–343
Vigo F: Uliana C (1986) Influence of the vortices at the membrane surface on the performances of the ultrafiltration rotating module. Separation Science and Technology 21: 367–381
Vigo F; Uliana C; Lupino P (1985) The performance of a rotating module in oily emulsions ultrafiltration. Separation Science and Technology 20: 213–230
Wereley ST; Lueptow RM (1994) Azimuthal velocity in supercritical circular Couette flow. Submitted to Exp Fluids
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This work was supported by a grant from The Whitaker Foundation
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Min, K., Lueptow, R.M. Circular Couette flow with pressure-driven axial flow and a porous inner cylinder. Experiments in Fluids 17, 190–197 (1994). https://doi.org/10.1007/BF00190916
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DOI: https://doi.org/10.1007/BF00190916