The dependence of residence time distribution on flow in co-axial cylinder devices

Abstract

Numerical simulations are presented showing the effects of operating and geometrical parameters on the transition of laminar to Taylor vortex¯ow for induced rotational-axial¯ow in the gap of a pair of rotating cylinders. These simulations indicate that annular rotational ow becomes more stable in the presence of a small degree of axial¯ow and as gap width increases. The effect of rotational speed on the breakdown of laminar¯ow is more complex and for given radius ratio and axial¯ow rate depends on both the speed ratio and the direction of the rotation of the cylinders, counter-rotating¯ow generally producing a more stable¯ow than co-rotating. Limited experimental data are provided on the residence time distribution for¯ow of Newtonian liquids through the gap of two rotating cylinders. The data include results from experiments in which¯ow transition occurred from laminar to Taylor vortex¯ow. The ®ndings from these experiments are successfully analyzed and assessed using the simulations studies. List of symbolsDimensionless differential operator D m 2 s À1 Axial dispersion coef®cient L m Distance between two measuring points M ± Dimensionless angular velocity, À Xr X 0 Á N rps Rotational speed of cylinder P Pa Pressure P ± Parameter de®ned by Eq. (17) Pe ± Peclet number, À WL D Á Re ± Axial Reynolds number, À WR 2 ÀR 1 m Á R 2 Y R 1 m Radii of outer and inner cylinders R m m Mean radius, À R 1 R 2 2 Á r m Radial coordinate s ± Growth rate of disturbances T c ± Critical Taylor number given by Eq. (15) Ta ± Taylor number, À À 4AX 0 R 2 ÀR 1 4 m 2 Á Ta c ± Critical Taylor number t s Time Ur m s À1 Radial velocity component Vr m s À1 Tangential velocity component W m s À1 Axial¯ow velocity Wr m s À1 Axial velocity component x ± Transformed dimensionless radial coordinate z m Axial coordinateGreek symbols a ± Radius ratio,Wave number l kg m À1 s À1 Viscosity of the working liquid m kg m À1 s À1 Kinematic viscosity of the working liquid r ± Dimensionless growth rate Dr 2 h ± Dimensionless variance difference X 2 , X 1 rad À1

Characterization of Taylor vortex flow in a short liquid column

“…From both experiments and simulation we observe the transition from a pure circulating flow around the inner cylinder to a stable Taylor vortex flow at a Re c of 62 and the data show no sign of wavy vortices up to at least a Re of 519 in the present system. Yim et al21 studied the onset of Taylor vortex for various values of radius ratio with the aspect ratios of 33 and 72. According to their results, a system composed of a rotating inner cylinder and a stationary outer cylinder with a radius ratio of 0.613 has a critical Taylor number of 2500, corresponding to a Re c of 62.9 for our case, which is close to our measured value of 62.…”

Viscosity of blueberry and raspberry juices for processing applications

“…Laminar flow is usually much more stable when the inner cylinder is stationary and the outer cylinder is rotating (Ferguson & Kemblowski, 1991;Steffe, 1996;Yim, Lo, Titchener-Hooker, & Shamlou, 1998). Ferguson and Kemblowski (1991) indicated that formation of Taylor vortices is possible only in fluids of low viscosity.…”

Effect of the rotor shape on the mixing characteristics of a continuous flow Taylor-vortex reactor

“…Mixing in Taylor-vortex devices operated in continuous (axial) flow mode has also been the subject of numerous studies (Kataoka et al, 1975;Kataoka and Takigawa, 1981;Enokida et al, 1989;Pudjiono et al, 1992;Moore and Cooney, 1995;Giordano et al, 1998;Yim et al, 1998;Haut et al, 2003;Judat et al, 2004). In continuous flow mode, not only vortex segregation but also bypass effects and vortex slowdown can be observed.…”