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Journal articles on the topic 'Eccentric rotating cylinders'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

de Socio, L. M., and L. Marino. "Flow separation between rotating eccentric cylinders." European Journal of Mechanics - B/Fluids 22, no. 1 (2003): 85–97. http://dx.doi.org/10.1016/s0997-7546(02)00006-7.

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2

Oikawa, Masayuki, Takashi Karasudani, and Mitsuaki Funakoshi. "Stability of Flow between Eccentric Rotating Cylinders." Journal of the Physical Society of Japan 58, no. 7 (1989): 2355–64. http://dx.doi.org/10.1143/jpsj.58.2355.

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3

Szeri, A. Z., and A. Al-Sharif. "Flow between finite, steadily rotating eccentric cylinders." Theoretical and Computational Fluid Dynamics 7, no. 1 (1995): 1–28. http://dx.doi.org/10.1007/bf00312397.

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4

Hird, L. D., and P. F. Siew. "Small reynolds number flow between eccentric rotating cylinders with a permeable sleeve." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 38, no. 2 (1996): 255–73. http://dx.doi.org/10.1017/s0334270000000643.

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AbstractTwo eccentric rotating cylinders together with a permeable membrane surrounding the inner cylinder are used to model the flow around a modified viscometer. A perturbation method is used to solve for the flow between the membrane and the outer cylinder; the flow between the inner rotor and the membrane is assumed to be governed by Stoke's equation, and the two flow regimes are coupled by the through-flow across the membrane. For moderate values of Reynolds number and eccentricity, the permeability of the membrane plays a negligible role, and the flow through the membrane is found to be eccentricity dependent. High eccentricities result in the formation of eddies which, upon increasing the Reynolds number, move in a direction opposite to that of the rotation of the outer bowl.

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5

FAN, YURUN, NHAN PHAN-THIEN, and ROGER I. TANNER. "Tangential flow and advective mixing of viscoplastic fluids between eccentric cylinders." Journal of Fluid Mechanics 431 (March 25, 2001): 65–89. http://dx.doi.org/10.1017/s0022112000002998.

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This is a study on the tangential flow and advective mixing of viscoplastic fluids (Bingham plastics) between two eccentric, alternately rotating cylinders. Two geometrical configurations and various rotation modes are considered for a relatively large range of the yield stress. The hp-type finite element method with the mixed formulation is used to solve for the steady velocity and pressure fields. The bi-viscosity and the Papanastasiou models agree quantitatively with each other in predicting the velocity fields and the practically unyielded zones. However, the Papanastasiou model is more robust and economic than the bi-viscosity model in the computation using Newton iteration. In the steady flows, in addition to the motionless zones, we have discovered some plugs with rigid rotation, including rotating plugs stuck onto the outer cylinder and rotating, even counter-rotating, plugs disconnected from both cylinders. The unsteady, periodic flow is composed of a sequence of the steady flows, which is valid in the creeping flow regime. The characteristics of advective mixing in these flows have been studied by analysing the asymptotic coverages of a passive tracer, the distributions of the lineal stretching in the flow and the variations of the mean stretching of the flow with time. The tracer coverage is intuitive but qualitative and, occasionally, it depends on the initial location of the tracer. On the other hand, the distribution of stretching is quantitative and more reliable in reflecting the mixing characteristics. Interestingly, the zones of the lowest stretching in the distribution graphs are remarkably well matched with the regular zones in the tracer-coverage graphs. Furthermore, the mixing efficiency proposed by Ottino (1989) is used to characterize the advective mixing in the two geometrical configurations with various rotation modes. It is important to realize that, for plastic fluids, a major barrier to effective mixing is the unyielded fluid plugs which are controlled by the yield stress and geometrical configurations. Therefore, when designing an eccentric helical annular mixer it is important to pay attention first to the geometric issues then to the operating issues.

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6

Meena, S., and Prem Kumar Kandaswamy. "The Hydromagnetic Flow between Two Rotating Eccentric Cylinders." International Journal of Fluid Mechanics Research 26, no. 5-6 (1999): 597–617. http://dx.doi.org/10.1615/interjfluidmechres.v26.i5-6.50.

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7

Meena, S., and Prem Kumar Kandaswamy. "The Hydromagnetic Flow between Two Rotating Eccentric Cylinders." International Journal of Fluid Mechanics Research 29, no. 5 (2002): 18. http://dx.doi.org/10.1615/interjfluidmechres.v29.i5.60.

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8

Kuroda, Shigeaki, Ten Min Wang, and Haruno Makioka. "Numerical Analysis of Flow between Eccentric Rotating Cylinders." Transactions of the Japan Society of Mechanical Engineers Series B 61, no. 591 (1995): 3983–88. http://dx.doi.org/10.1299/kikaib.61.3983.

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9

Rui-Xiu, Dai, Q. Dong, and A. Z. Szeri. "Flow between eccentric rotating cylinders: Bifurcation and stability." International Journal of Engineering Science 30, no. 10 (1992): 1323–40. http://dx.doi.org/10.1016/0020-7225(92)90144-6.

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10

Chawda, Amit, and Marios Avgousti. "Stability of visoelastic flow between eccentric rotating cylinders." Journal of Non-Newtonian Fluid Mechanics 63, no. 2-3 (1996): 97–120. http://dx.doi.org/10.1016/0377-0257(96)01425-5.

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11

Hird, L. D., P. F. Siew, and S. Wang. "A numerical solution to the flow between eccentric rotating cylinders with a slotted sleeve." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 41, no. 1 (1999): 129–52. http://dx.doi.org/10.1017/s0334270000011085.

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AbstractThe flow between two eccentric rotating cylinders with a slotted sleeve placed around the inner cylinder is determined numerically using an exponentially fitted finite-volume method. The flow field is determined for various Reynolds numbers, eccentricities and rotational speeds for the cases when the cylinders rotate in the same sense and rotate in opposite senses. The flow field developed when both cylinders rotate in the same sense is characterised, for sufficiently large eccentricity and rotational rate, by two counter-rotating eddies. Only one eddy is observed when the cylinders rotate in opposite senses. The presence of these eddies restricts the flow through the slotted sleeve in the former case but encourages through flow in the latter. For both cases, the eccentricity affects the location of the eddies, while changing the relative rotational rate only affects the eddy location for the case when the cylinders rotate in opposite directions. The change in Reynolds number has little effect on the flow field for the problems considered here. The vorticity generated by the slotted sleeve is convected into the main body of the flow field. No inviscid core within the main body of the flow field is observed for the range of Reynolds number considered.

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12

Kandaswamy, P., K. Murugesan, and L. Debnath. "On the Hydromagnetic Flow between Two Rotating Eccentric Cylinders." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 74, no. 1 (1994): 57–61. http://dx.doi.org/10.1002/zamm.19940740116.

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13

SAATDJIAN, ESTEBAN, and NOEL MIDOUX. "FLOW OF A NEWTONIAN FLUID BETWEEN ECCENTRIC ROTATING CYLINDERS." International Journal of Numerical Methods for Heat & Fluid Flow 2, no. 3 (1992): 261–70. http://dx.doi.org/10.1108/eb017494.

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14

Průša, Vít, and K. R. Rajagopal. "Flow of an electrorheological fluid between eccentric rotating cylinders." Theoretical and Computational Fluid Dynamics 26, no. 1-4 (2011): 1–21. http://dx.doi.org/10.1007/s00162-011-0224-z.

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15

Dai, R. X., Q. Dong, and A. Z. Szeri. "Flow of variable-viscosity fluid between eccentric rotating cylinders." International Journal of Non-Linear Mechanics 27, no. 3 (1992): 367–89. http://dx.doi.org/10.1016/0020-7462(92)90006-s.

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16

Wang, Hua Geng. "The Cutter Head Drive Theoretical Model of a New Multi Dual-Eccentric Axes Tunneling Shield Driven by Hydraulic Cylinders Directly." Applied Mechanics and Materials 741 (March 2015): 586–93. http://dx.doi.org/10.4028/www.scientific.net/amm.741.586.

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Based on work principle analysis of a new multi dual-eccentric axes tunneling shield, the advantages of adapting well to large diameter long distance tunnel and energy saving are showed in detail. Then, the cutter head drive theoretical model driven by a single hydraulic cylinder is analyzed, the expressions of driving force and hydraulic cylinder flow are set up, they all vary with the position changing of the cutter head. On this basis, the multi cylinders drive theoretical model is obtained by superposing the expressions of each cylinder. Subsequently, the relationships between working pressure, system flow and cutter head rotating speed under the working conditions of constant torque, constant flow and constant rotating speed are analyzed. The analysis results show that the working pressure and system flow are fluctuating when the cutter head rotating speed maintains constant, and the cutter head drive system is of constant power, and this is also the actual work condition of the shield. At the same time, each hydraulic cylinder stroke remains determined phase matching relationships. Finally, as the example with five cylinders driving, the matching relationships of the hydraulic cylinder strokes are discussed.

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17

Bryden, Michelle D., and Howard Brenner. "Effect of laminar chaos on reaction and dispersion in eccentric annular flow." Journal of Fluid Mechanics 325 (October 25, 1996): 219–37. http://dx.doi.org/10.1017/s0022112096008099.

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Generalized Taylor dispersion theory is used to study the chaotic laminar transport of a reactive solute between eccentric rotating cylinders in the presence of an inhomogeneous chemical reaction. The circumstance considered is that of laminar axial ‘Poiseuille’ flow in the annular region between the two non-concentric cylinders, accompanied by a secondary, generally chaotic, flow induced via alternate rotation of the cylinders. A Brownian tracer introduced into the flow is assumed to undergo an instantaneous, irreversible reaction on the surface of the outer cylinder. The resulting effective transversely and time-averaged reaction rate, axial solute velocity, and axial convective dispersivity are computed. When chaos is present, the effective reaction rate is increased to a value several times larger than occurs in the absence of chaotic transport. It is found that an optimum alternation frequency exists, and that this frequency decreases with increasing transverse Péclet number (Peq). It is also observed that the maximum achievable reaction rate increases with (Peq). The effect of laminar chaotic mixing on the mean axial solute/solvent velocity ratio is to drive its value towards the perfectly mixed value of 1.0, despite the removal of solute from the slower-moving axial streamlines near the outer (reactive) cylinder wall. Lastly, in the presence of transverse chaotic transport, the convective Taylor contribution to the axial solute dispersivity acquires a value up to several orders of magnitude smaller than that achievable by means of non-chaotic convection.

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18

Meena, S., P. Kandaswamy, and Lokenath Debnath. "Hydrodynamic flow between rotating eccentric cylinders with suction at the porous walls." International Journal of Mathematics and Mathematical Sciences 25, no. 2 (2001): 93–113. http://dx.doi.org/10.1155/s0161171201002563.

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The flow of a viscous, incompressible fluid between two eccentric rotating porous cylinders with suction/injection at both the cylinders, for very small clearance ratio is studied. The expressions for various flow characteristics are obtained using perturbation analysis. Streamlines and pressure plots are shown graphically for various values of flow parameters and discussed.

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19

EKIDA, Takumi, Sadatoshi ARAI, and Yutaka OHTA. "Numerical Simulation of Taylor Vortex Flow between Eccentric Rotating Cylinders." Proceedings of the JSME annual meeting 2003.2 (2003): 397–98. http://dx.doi.org/10.1299/jsmemecjo.2003.2.0_397.

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20

Kamel, M. T. "Flow of a Polar Fluid between Two Eccentric Rotating Cylinders." Journal of Rheology 29, no. 1 (1985): 37–48. http://dx.doi.org/10.1122/1.549785.

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21

de Socio, L. M., and L. Marino. "Numerical experiments on the gas flow between eccentric rotating cylinders." International Journal for Numerical Methods in Fluids 34, no. 3 (2000): 229–40. http://dx.doi.org/10.1002/1097-0363(20001015)34:3<229::aid-fld55>3.0.co;2-5.

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22

Karasudani, Takashi. "Non-Axis-Symmetric Taylor Vortex Flow in Eccentric Rotating Cylinders." Journal of the Physical Society of Japan 56, no. 3 (1987): 855–58. http://dx.doi.org/10.1143/jpsj.56.855.

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23

Christie, I., K. R. Rajagopal, and A. Z. Szeri. "Flow of a non-Newtonian fluid between eccentric rotating cylinders." International Journal of Engineering Science 25, no. 8 (1987): 1029–47. http://dx.doi.org/10.1016/0020-7225(87)90095-4.

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24

Huang, X., N. Phan-Thien, and R. I. Tanner. "Viscoelastic flow between eccentric rotating cylinders: unstructured control volume method." Journal of Non-Newtonian Fluid Mechanics 64, no. 1 (1996): 71–92. http://dx.doi.org/10.1016/0377-0257(96)01429-2.

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25

Teleszewski, Tomasz Janusz. "Effect of viscous dissipation in two-dimensional Stokes flow between rotating cylinders – preliminary numerical investigation." MATEC Web of Conferences 240 (2018): 03015. http://dx.doi.org/10.1051/matecconf/201824003015.

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This paper introduces the modelling of two-dimensional laminar flow of Newtonian fluid in a system of concentric or eccentric rotating cylinders with regards to viscous dissipation. Viscous dissipation is a main part, where the viscosity is large for example in oils. The dependence of the Nusselt number on the ratio of the radius of the inner cylinder to the radius of the external cylinder for the selected distance of the cylinder axes was investigated. In order to determine the velocity fields and the temperature distribution, the boundary element method was used. The results of the calculations were presented in the form of diagrams.

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26

Teleszewski, Tomasz Janusz. "Effect of viscous dissipation in stokes flow between rotating cylinders using BEM." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 4 (2019): 2121–36. http://dx.doi.org/10.1108/hff-11-2018-0622.

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Purpose The purpose of this paper is to apply the boundary element method (BEM) to Stokes flow between eccentric rotating cylinders, considering the case when viscous dissipation plays a significant role and determining the Nusselt number as a function of cylinder geometry parameters. Design/methodology/approach The problem is described by the equation of motion of Stokes flow and an energy equation with a viscous dissipation term. First, the velocity field and the viscous dissipation term were determined from the momentum equation. The determined dissipation of energy and the constant temperature on the cylinder walls are the conditions for the energy equation, from which the temperature distribution and the heat flux at the boundary of the cylinders are determined. Numerical calculations were performed using the author’s own computer program based on BEM. Verification of the model was carried out by comparing the temperature determined by the BEM with the known theoretical solution for the temperature distribution between two rotating concentric cylinders. Findings As the ratio of the inner cylinder diameter to the outer cylinder diameter (r1/r2) increases, the Nusselt number increases. The angle of inclination of the function of the Nusselt number versus r1/r2 increases as the distance between the centers of the inner and outer cylinders increases. Originality/value The computational results may be used for the design of slide bearings and viscometers for viscosity testing of liquids with high viscosity where viscous dissipation is important. In the work, new integral kernels were determined for BEM needed to determine the viscous dissipation component.

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27

TSUJII, Kazunori, Naoyuki TAZAWA, and Yutaka OHTA. "G404 Control of Taylor Vortices Generated between Eccentric Rotating Cylinders(2)." Proceedings of the Fluids engineering conference 2006 (2006): _G404–1_—_G404–4_. http://dx.doi.org/10.1299/jsmefed.2006._g404-1_.

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28

TSUJII, Kazunori, Naoyuki TAZAWA, and Yutaka OHTA. "G404 Control of Taylor Vortices Generated between Eccentric Rotating Cylinders(1)." Proceedings of the Fluids engineering conference 2006 (2006): _G404—a_. http://dx.doi.org/10.1299/jsmefed.2006._g404-a_.

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29

Atobe, Takashi. "Lagrangian Chaos in the Stokes Flow Between Two Eccentric Rotating Cylinders." International Journal of Bifurcation and Chaos 07, no. 05 (1997): 1007–23. http://dx.doi.org/10.1142/s0218127497000820.

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Chaotic motion of the fluid particles in the Stokes flow between two eccentric cylinders rotating alternately is investigated numerically, analytically and experimentally. We examine the dependence of the motion of the fluid particles on the eccentricity ε, focusing on an equilibrium point of the Poincaré plot. When the bifurcation of the equilibrium point from the elliptic to the hyperbolic type occurs at ε = εb, the area of the chaotic region takes a maximum around εb. The results from the perturbation analysis show good agreement with the numerical results. The orbital instability of the motion of the fluid particles is also investigated experimentally. The orbital instability is visualized by injected dye in the "return experiment", in which the two cylinders are rotated alternately by N periods in the first half, and then rotated in its time reversal way for N periods in the second half. The dye starting from the regular region of the numerically computed Poincaré plot of particle positions after every period returns well to its initial position even for large N. However, the deviation of the dye starting from the chaotic region of the Poincaré plot from its initial position is large and rapidly increases with N.

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30

Mori, Noriyasu, Mitsuhiro Yagami, Takaaki Eguchi, Kiyoji Nakamura, and Akira Horikawa. "Pressure Flow of Non-Newtonian Fluids between Eccentric Double Cylinders with the Inner Cylinder Rotating." Journal of the Textile Machinery Society of Japan 33, no. 3 (1987): 73–77. http://dx.doi.org/10.4188/jte1955.33.73.

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31

YAMADA, Takeshi, Jun MIZUSHIMA, Masahiko IIZUKA, and Yutaka OHTA. "K-1118 Unsteady Behavior of Taylor Vortex Flow between Eccentric Rotating Cylinders." Proceedings of the JSME annual meeting II.01.1 (2001): 57–58. http://dx.doi.org/10.1299/jsmemecjo.ii.01.1.0_57.

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32

Kim, E. "A mixed galerkin method for computing the flow between eccentric rotating cylinders." International Journal for Numerical Methods in Fluids 26, no. 8 (1998): 877–85. http://dx.doi.org/10.1002/(sici)1097-0363(19980430)26:8<877::aid-fld628>3.0.co;2-6.

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33

Chou, Mo-Hong. "A multigrid finite difference approach to steady flow between eccentric rotating cylinders." International Journal for Numerical Methods in Fluids 34, no. 6 (2000): 479–94. http://dx.doi.org/10.1002/1097-0363(20001130)34:6<479::aid-fld65>3.0.co;2-v.

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34

Meena, S., and P. Kandaswamy. "Hydromagnetic flow between rotating eccentric cylinders with suction at the porous walls." Forschung im Ingenieurwesen 67, no. 3 (2002): 123–28. http://dx.doi.org/10.1007/s10010-002-0081-4.

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35

Xiang, Junting, Elnaz Hajizadeh, Ronald G. Larson, and Damian Nelson. "Predictions of polymer migration in a dilute solution between rotating eccentric cylinders." Journal of Rheology 65, no. 6 (2021): 1311–25. http://dx.doi.org/10.1122/8.0000330.

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36

Abed, Waleed M., Amer Al-Damook, and Wissam H. Khalil. "Convective Heat Transfer in an Annulus of Concentric and Eccentric Cylinders with an Inner Rotating Cylinder." International Journal of Heat and Technology 39, no. 1 (2021): 61–72. http://dx.doi.org/10.18280/ijht.390107.

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37

Jones, W. M. "The effect of weak elasticity on Couette flow between rotating cylinders: (1) spiral flow; (2) eccentric cylinders." Journal of Non-Newtonian Fluid Mechanics 28, no. 2 (1988): 255–63. http://dx.doi.org/10.1016/0377-0257(88)85043-2.

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38

Phan-Thien, Nhan, Alan L. Graham, Stephen A. Altobelli, James R. Abbott, and Lisa A. Mondy. "Hydrodynamic particle migration in a concentrated suspension undergoing flow between rotating eccentric cylinders." Industrial & Engineering Chemistry Research 34, no. 10 (1995): 3187–94. http://dx.doi.org/10.1021/ie00037a002.

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39

Petrov, A. G. "The mixing of a viscous fluid in a layer between rotating eccentric cylinders." Journal of Applied Mathematics and Mechanics 72, no. 5 (2008): 536–49. http://dx.doi.org/10.1016/j.jappmathmech.2008.11.009.

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40

CHOU, MO-HONG, and HSIU-CHUAN WEI. "AN ANATOMY OF LAGRANGIAN CHAOS IN LOW REYNOLDS NUMBER FLOW BETWEEN TWO ECCENTRIC ROTATING CYLINDERS." International Journal of Bifurcation and Chaos 15, no. 09 (2005): 2833–47. http://dx.doi.org/10.1142/s0218127405013654.

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Chaotic motion of fluid particles in low Reynolds number flow between two eccentric cylinders rotating alternately is studied by investigating the tangling between invariant manifolds of the underlying dynamical system. Such tangles are revealed by a numerical method carrying out the global search of periodic points of the associated Poincaré map and the global tracking of stable and unstable manifolds to the hyperbolic points thus found. Along with such an anatomy the breakup of some elliptic orbits as predicted by Poincaré–Birkhoff theorem is clearly shown. It is found that several drastic changes either in the characteristic of ellipticity and hyperbolicity or in the pattern of homoclinic tangles take place when the cylinders' eccentricity is increased towards its maximum. The results are confirmed either by other numerical approaches or by a rigorous shadowing to a certain extent, and are expected to be of use to some geometric understanding about mixing.

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41

Kacou, A., K. R. Rajagopal, and A. Z. Szeri. "Flow of a Fluid of the Differential Type in a Journal Bearing." Journal of Tribology 109, no. 1 (1987): 100–107. http://dx.doi.org/10.1115/1.3261298.

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The flow of a homogeneous incompressible non-Newtonian fluid of the differential type between infinite eccentric rotating cylinders is discussed within the context of the lubrication approximation. The problem is studied by means of a perturbation and the effects of the non-Newtonian parameters are delineated. It is found that the load carrying capacity of the bearing can be significantly altered by the non-Newtonian character of the fluid.

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42

Rajagopalan, Dilip, Jeffrey A. Byars, Robert C. Armstrong, Robert A. Brown, J. S. Lee, and G. G. Fuller. "Comparison of numerical simulations and birefringence measurements in viscoelastic flow between eccentric rotating cylinders." Journal of Rheology 36, no. 7 (1992): 1349–75. http://dx.doi.org/10.1122/1.550266.

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43

El-Dujaily, M. J., and F. R. Mobbs. "The effect of end walls on subcritical flow between concentric and eccentric rotating cylinders." International Journal of Heat and Fluid Flow 11, no. 1 (1990): 72–78. http://dx.doi.org/10.1016/0142-727x(90)90028-a.

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44

TAZAWA, Naoyuki, and Yutaka OHTA. "G105 Unsteady Behavior and Control of Taylor Vortex Flow Generated between Eccentric Rotating Cylinders." Proceedings of the Fluids engineering conference 2005 (2005): 287. http://dx.doi.org/10.1299/jsmefed.2005.287.

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45

Moghadam, Ali Jabari, and Asghar Baradaran Rahimi. "A singular perturbation solution of viscous incompressible fluid flow between two eccentric rotating cylinders." Arabian Journal of Mathematics 3, no. 1 (2013): 63–78. http://dx.doi.org/10.1007/s40065-013-0081-2.

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46

Ghosh, S., H. C. Chang, and M. Sen. "Heat-transfer enhancement due to slender recirculation and chaotic transport between counter-rotating eccentric cylinders." Journal of Fluid Mechanics 238 (May 1992): 119–54. http://dx.doi.org/10.1017/s0022112092001666.

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Using Stokes flow between eccentric, counter-rotating cylinders as a prototype for bounded, nearly parallel lubrication flow, we investigate the effect of a slender recirculation region within the flow field on cross-stream heat or mass transport in the important limit of high Péclet number Pe where the enhancement over pure conduction heat transfer without recirculation is most pronounced. The steady enhancement is estimated with a matched asymptotic expansion to resolve the diffusive boundary layers at the separatrices which bound the recirculation region. The enhancement over pure conduction is shown to vary as ε½ at infinite Pe, where ε½ is the characteristic width of the recirculation region. The enhancement decays from this asymptote as Pe−½. If one perturbs the steady flow by a time-periodic forcing, fast relative to the convective and diffusive times, the separatrices undergo a homoclinic entanglement which allows fluid elements to cross the separatrices. We establish the existence of this homoclinic entanglement and show that the resulting chaotic particle transport further enhances the cross-stream flux. We estimate the penetration of the fluid elements across the separatrices and their effective diffusivity due to this chaotic transport by a Melnikov analysis for small-amplitude forcing. These and the steady results then provide quantitative estimates of the timeaveraged transport enhancement and allow optimization with respect to system parameters. An optimum forcing frequency which induces maximum heat-transfer enhancement is predicted and numerically verified. The predicted optimum frequency remains valid at strong forcing and large Pe where chaotic transport is as important as the recirculation mechanism. Since most heat and mass transport devices operate at high Pe, our analysis suggests that chaotic enhancement can improve their performance and that a small amplitude theory can be used to optimize its application.

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47

Beris, A. N., R. C. Armstrong, and R. A. Brown. "Spectral/finite-element calculations of the flow of a maxwell fluid between eccentric rotating cylinders." Journal of Non-Newtonian Fluid Mechanics 22, no. 2 (1987): 129–67. http://dx.doi.org/10.1016/0377-0257(87)80033-2.

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48

FAN, YURUN, ROGER I. TANNER, and NHAN PHAN-THIEN. "A numerical study of viscoelastic effects in chaotic mixing between eccentric cylinders." Journal of Fluid Mechanics 412 (June 10, 2000): 197–225. http://dx.doi.org/10.1017/s0022112000008326.

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In this paper, we are concerned with the effect of fluid elasticity and shear-thinning viscosity on the chaotic mixing of the flow between two eccentric, alternately rotating cylinders. We employ the well-developed h-p finite element method to achieve a high accuracy and efficiency in calculating steady solutions, and a full unsteady algorithm for creeping viscoelastic flows to study the transient process in this periodic viscoelastic flow. Since the distribution of periodic points of the viscoelastic flow is not symmetric, we have developed a domain-search algorithm based on Newton iteration for locating the periodic points. With the piecewise-steady approximation, our computation for the upper-convected Maxwell fluid predicts no noticeable changes of the advected coverage of a passive tracer from Newtonian flow, with elasticity levels up to a Deborah number of 1.0. The stretching of the fluid elements, quantified by the geometrical mean of the spatial distribution, remains exponential up to a Deborah number of 6.0, with only slight changes from Newtonian flow. On the other hand, the shear-thinning viscosity, modelled by the Carreau equation, has a large impact on both the advection of a passive tracer and the mean stretching of the fluid elements. The creeping, unsteady computations show that the transient period of the velocity is much shorter than the transient period of the stress, and from a pragmatic point of view, this transient process caused by stress relaxation due to sudden switches of the cylinder rotation can be neglected for predicting the advective mixing in this time- periodic flow. The periodic points found up to second order and their eigenvalues are indeed very informative in understanding the chaotic mixing patterns and the qualitative changes of the mean stretching of the fluid elements. The comparison between our computations and those of Niederkorn & Ottino (1993) reveals the importance of reducing the discretization error in the computation of chaotic mixing. The causes of the discrepancy between our prediction of the tracer advection and Niederkorn & Ottino's (1993) experiment are discussed, in which the influence of the shear-thinning first normal stress difference is carefully examined. The discussion leads to questions on whether small elasticity of the fluid has a large effect on the chaotic mixing in this periodic flow.

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Lee, T. S. "Laminar fluid convection between concentric and eccentric heated horizontal rotating cylinders for low-Prandtl-number fluids." International Journal for Numerical Methods in Fluids 14, no. 9 (1992): 1037–62. http://dx.doi.org/10.1002/fld.1650140904.

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Lee, T. S., Toru Fusegi, Bakhtier Farouk, and Kenneth Ball. "Discussion of the Paper “Numerical Experiments with Laminar Fluid Convection between oncentric and Eccentric Heated Rotating Cylinders”." Numerical Heat Transfer, Part B: Fundamentals 10, no. 1 (1986): 103. http://dx.doi.org/10.1080/10407798608552498.

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