DOCSLIB.ORG

Taylor-Couette Instability of Giesekus Fluids

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Taylor-Couette Instability of Giesekus Fluids ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 20, 2012 Taylor-Couette Instability of Giesekus Fluids Mohammad Pourjafar1, and Kayvan Sadeghy2 1 University of Tehran, College of Engineering, School of Mechanical Engineering, Tehran, Iran. 2 University of Tehran, College of Engineering School of Mechanical Engineering, Tehran, Iran. ABSTRACT inner cylinder). The fact that the critical Taylor-Couette instability of Giesekus Taylor number obtained by Taylor2 closely fluids is investigated at large gaps using a matched the experimental value was temporal, linear instability analysis regarded by many as one of the greatest assuming that the perturbations are achievements of the linear instability axisymmetric. Using normal-mode concept, analysis. In ensuing works, other aspects of an eigenvalue problem is obtained which is the flow (e.g., the effect of the gap size, and solved numerically using pseudo-spectral the effect of the cylinders eccentricity) has collocation method. A fluid’s elasticity is been investigated3. There are also many predicted to have a stabilizing or works addressing the effects of a fluid’s destabilizing effect on the Couette flow non-Newtonian behavior on the instability depending on the Weissenberg number picture of the circular Couette flow4-9. being smaller or larger than a critical value. The interest in studying Taylor-Couette instability for non-Newtonian fluids stems INTRODUCTION mainly from the fact that Couette Tangential flow between two infinitely- rheometers are widely used for long concentric cylinders rotating at characterizing non-Newtonian fluids. But, different angular velocities (the circular the rheological data obtained in Couette Couette flow) loses its stability and switches rheometers are useful only if the gap is free to more complicated laminar flow patterns from secondary flow. Therefore, depending on the Reynolds number1. The determining conditions under which first mode of instability exhibits itself as a secondary flow occurs in the gap is very secondary flow comprising a pair of important in shear rheometry. This is stationary-mode, axisymmetric, counter- perhaps why the literature is so rich when it rotating, toroidal roll cells stacked in the comes to the Taylor-Couette instability of gap. Taylor2 relied on a normal-mode, linear viscoelastic fluids5-9. One can notably instability analysis to show that for mention the numerical work carried out by Newtonian fluids, when the gap spacing is Beris10 in which the critical Taylor number narrow, the secondary flow should emerge has been calculated for the Giesekus fluid under narrow-gap restriction. whenever the parameter Re d R1 (the so- In the present work, we are going to called Taylor number) exceeds 41, where d extend Beris’ work10 to the large-gap is the gap spacing, R is the radius of the 1 situation, to the best of our knowledge, for inner cylinder, and Re is the Reynolds the first time. The case of large gap is more number (based on the angular velocity of the 91 common in shear rheometry, particularly 1 v (rv ) z 0 (1d) when dealing with fluids containing solid rr r z particles, or for highly-viscous fluids. To that end, we superimpose an infinitesimal perturbation, represented by normal modes, where it has tacitly been assumed that the to the base flow and see what happens to its flow is axisymmetric (i.e., 0 ). In these amplitude in the course of time. An equations, is the density, vi represents the eigenvalue problem will be obtained this velocity components, and ij are the way in which terms nonlinear in the components of the stress tensor. The stress perturbation quantities will be dropped. To components appearing in these equations ensure high degree of accuracy, spectral need a constitutive equation to be related to method will be used to find the critical the velocity field. In the present work, we conditions for the onset of instability. assume that the fluid of interest obeys the Giesekus model as its constitutive equation. MATHEMATICAL FORMULATIONS In this viscoelastic fluid model, the extra Taylor-Couette geometry basically stress tensor is given by11, consists of two infinitely long, concentric cylinders of radii R1 and R 2 with the fluid confined in the annulus between them. In (.) V. t general, the cylinders are rotating (2) independently with an angular velocity 1 .V V.T 2D and either in the same direction or in 2 opposite direction. For non-Newtonian where 2D is the deformation-rate tensor, fluids, the equations to start with are the is the mobility, is the longest relaxation Cauchy equations of motion together with time of the fluid, and is the fluid’s zero- the continuity equation. Assuming that the shear viscosity. It needs to be mentioned fluid is incompressible, in polar coordinate that, for 0 the Giesekus model reduces system, we have, simply to the upper-convected Maxwell (UCM) model. On the other hand for vvv 2 v rr r 0 the Giesekus model reduces to (vrz v) trrz (1a) the Newtonian fluid model. 1p rz The Giesekus model is widely regarded (rrr ) rr r z r as one of the best rheological models for representing polymeric liquids (i.e., polymer melts and concentrated polymer solutions). vvvvv The mobility factor, which accounts for (v r v) rz anisotropic relaxation of polymer trrz (1b) 2 macromolecules, profoundly affects the 1 (rrz ) ( ) 2 shear- and extensional-flow behaviour of the rr z fluid. In fact, by increasing (starting from zero) shear-thinning starts at lower shear rates, and the asymptotic value of the vvvzzz (vrz v) extensional viscosity is decreased. This fluid trz (1c) model also correctly predicts the first and 1p(rrz ) ( zz ) second normal stress differences for rr z z polymeric liquids provided that the mobility factor is selected in the range of 00.5 . 92 BASIC FLOW Figure 1 shows that the velocity profiles As the first step in our instability deviate more from a linear one by an analysis, we need the basic (i.e., steady) increase in the Weissenberg number. flow velocity and stress fields. Porjafar12 has recently shown that for Giesekus fluids, the INSTABILITY ANALYSIS governing equations can be simplified to the Having calculated the basic-flow following ordinary differential equations as velocity and stress fields for the Giesekus 0 fluid, we are now ready to investigate their far as the basic-flow velocity profiles, v , is concerned, vulnerability to instability when perturbed slightly. The perturbations are assumed to be axisymmetric and two-dimensional, so 0 0000 d v rrrrWe r (3) that we have. 0 dr r 1(1We) rr 0 ˆ V(r,z,t) v (r) V(r,z,t), (4) where We R11 d is the Weissenberg 12 number. Porjafar has also shown that in 0 0 (r,z,t) (r)ˆ (r,z,t), (5) this ODE, the basic-flow stress terms rr and 0 0 can be related to r by simple algebraic where Vˆ , and ˆ represent the perturbation equations. As such, a shooting scheme in 0 velocity and stress fields. Assuming that the which r is guessed at the inner wall and perturbations can be represented by normal the velocity profile so-obtained is checked modes we have, to see if it satisfies the no-slip condition at the outer wall can easily be used to find v0 . ikz t Vˆ A(r) B(r) C(r) e , (6) Figure 1 shows typical basic-flow velocity profiles obtained this way at a mobility D(r) E(r) F(r) factor of 0.2 for a large-gap radii ratio ikz t RR 0.65 ˆ E(r) G(r) H(r) e . of 12 when the cylinders are (7) rotating in the opposite directions. F(r) H(r) Q(r) 1 We=0 1.25 In these equations, k is the 0.5 2.25 (dimensionless) real wavenumber, and RI i is the (dimensionless) complex 0 phase velocity with R 0 signalling the -0.5 occurrence of instability. V Using continuity equation, C(r) can be -1 related to A(r) by, -1.5 11d Cr rAr . (8a) -2 ik r dr -2.5 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0 r rB r Re 1 A r 1 rD v r Figure 1. Effect of the Weissenberg number 12rDErr1ikHr on the basic-flow velocity profiles obtained (8b) 0.65, 0.2 1 at when 21 . 93 00 11 1 e 2We r Dr 2We rEr DD D rr r r 2 1Ar r 2 00 k (1 ) 2 1 We rr r D WeD rr r A r (8g) vr0 Gr 2Re B r D Q r 1e Wer 00 Fr WerHr rr rr r 0 1 1Werrr 11 1DDr (1 )ik 1 D D D A r r 22 krr 11 DD D (8h) r 2 ik 1 r F r k2 1e Wer 0 Hr (8c) 0 1 Wer r (1 ) D F r r 1e We 00 r r Er rr We0 11 1 (1 )ik B r r D D D A r 00 22 We(1 ) D rr r r D A r krr r 0 (8i) r r We0 r G r We D r * ** 2 2 r 1 0 where Dddr and DD d dr. From the (1 ) D v r r boundary conditions, one can conclude that: * 0 1 ADA0,andB0. (1 ) 1 We rr r D B r r (8d) NUMERICAL METHOD For solving the instability problem as posed by Eqs. 8a-i, we have decided to rely on the pseudo-spectral, Chebeshev-based, 1e 2We 0 r Gr collocation method13. The basic idea in all 0 r spectral methods is to assume that the r 2We E r unknown function(s) can be approximated 1 0 (1 ) D v r by a sum of certain number of base r functions; that is, 0 1 2We(1 ) r r D B r r N1 0 r 120 A(y) ann (y) 1WeDrWeAr (9a) rrr n1 N1 (8e) B(y) bnn (y) (9b) n1 1 1e Q(r)2(1) D Ar N1 r D(y) dnn (y) (9c) (8f) n1 N1 E(y) enn (y) (9d) n1 94 N1 fast propagation of the boundary errors into F(y) fnn (y) (9e) the integration domain.
Load more

Recommended publications
  • Experimental and Numerical Characterization of the Thermal and Hydraulic Performance of a Canned Motor Pump Operating with Two-P
    EXPERIMENTAL AND NUMERICAL CHARACTERIZATION OF THE THERMAL AND HYDRAULIC PERFORMANCE OF A CANNED MOTOR PUMP OPERATING WITH TWO-PHASE FLOW A Dissertation by YINTAO WANG Submitted to the Office of Graduate and Professional Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Chair of Committee, Adolfo Delgado Committee Members, Karen Vierow Kirkland Michael Pate Je-Chin Han Head of Department, Andreas A. Polycarpou May 2019 Major Subject: Mechanical Engineering Copyright 2019 Yintao Wang ABSTRACT Canned motor pump (CMP), as one kind of sealless pump, has been utilized in industry for many years to handle hazards or toxic product and to minimize leakage to the environment. In a canned motor pump, the impeller is directly mounted on the motor shaft and the pump bearing is usually cooled and lubricated by the pump process liquid. To be employed in oil field, CMP must have the ability to work under multiphase flow conditions, which is a common situation for artificial lift. In this study, we studied the performance and reliability of a vertical CMP from Curtiss-Wright Corporation in oil and air two-phase flow condition. Part of the process liquid in this CMP is recirculated to cool the motor and lubricate the thrust bearing. The pump went through varying flow rates and different gas volume fractions (GVFs). In the test, three important parameters, including the hydraulic performance, the pump inside temperature and the thrust bearing load were monitored, recorded and analyzed. The CMP has a second recirculation loop inside the pump to lubricate the thrust bearing as well as to cool down the motor windings.
    [Show full text]
  • Concentric Cylinder Viscometer Flows of Herschel-Bulkley Fluids Received Sep 09, 2019; Accepted Nov 28, 2019
    Appl. Rheol. 2019; 29 (1):173–181 Research Article Hans Joakim Skadsem* and Arild Saasen Concentric cylinder viscometer flows of Herschel-Bulkley fluids https://doi.org/10.1515/arh-2019-0015 Received Sep 09, 2019; accepted Nov 28, 2019 Abstract: Drilling fluids and well cements are example τ non-Newtonian fluids that are used for geothermal and Cement slurry petroleum well construction. Measurement of the non- Spacer Newtonian fluid viscosities are normally performed using a concentric cylinder Couette geometry, where one of the Shear stress, Drilling fluid cylinders rotates at a controlled speed or under a con- trolled torque. In this paper we address Couette flow of yield stress shear thinning fluids in concentric cylinder geometries. We focus Chemical wash on typical oilfield viscometers and discuss effects of yield Shear rate,γ ˙ stress and shear thinning on fluid yielding at low viscome- ter rotational speeds and errors caused by the Newtonian Figure 1: Example of typical flow curves for fluids involved in well shear rate assumption. We relate these errors to possible construction. implications for typical wellbore flows. Keywords: Drilling fluids, Herschel-Bulkley, Viscometry The operation schedule involves drilling, where the drilling fluid transports out drilled cuttings, displacement PACS: 83.85.Jn, 83.60.La, 83.10.Gr, 47.57.Qk of the drilling fluid from the narrow annular space be- tween the casing string and the formation and replace it by a cement slurry to create a total zonal isolation in the well. 1 Introduction Once in place, the cement slurry is allowed to harden into a cement sheath.
    [Show full text]
  • Friction Losses and Heat Transfer in High-Speed Electrical Machines
    XK'Sj Friction losses and heat transfer in high-speed electrical machines Juha Saari DJSTR10UTK)N OF THI6 DOCUMENT IS UNLIMITED Teknillinen korkeakoulu Helsinki University of Technology Sahkotekniikan osasto Faculty of Electrical Engineering Sahkomekaniikan laboratorio Laboratory of Electromechanics Otaniemi 1996 1 50 2 Saari J. 1996. Friction losses and heat transfer in high-speed electrical machines. Helsinki University of Technology, Laboratory of Electromechanics, Report 50, Espoo, Finland, p. 34. Keywords: Friction loss, heat transfer, high-speed electrical machine Abstract High-speed electrical machines usually rotate between 20 000 and 100 000 rpm and the peripheral speed of the rotor exceeds 150 m/s. In addition to high power density, these figures mean high friction losses, especially in the air gap. In order to design good electrical machines, one should be able to predict accurately enough the friction losses and heat-transfer rates in the air gap. This report reviews earlier investigations concerning frictional drag and heat transfer between two concentric cylinders with inner cylinder. rotating. The aim was to find out whether these studies cover the operation range of high-speed electrical machines. Friction coefficients have been measured at very high Reynolds numbers. If the air-gap surfaces are smooth, the equations developed can be applied into high-speed machines. The effect of stator slots and axial cooling flows, however, should be studied in more detail. Heat-transfer rates from rotor and stator are controlled mainly by the Taylor vortices in the air-gap flow. Their appearance is affected by the flow rate of the cooling gas. The papers published do not cover flows with both high rotation speed and flow rate.
    [Show full text]
  • Couette and Planar Poiseuille Flow
    An Internet Book on Fluid Dynamics COUETTE AND PLANAR POISEUILLE FLOW Couette and planar Poiseuille flow are both steady flows between two infinitely long, parallel plates a fixed distance, h, apart as sketched in Figures 1 and 2. The difference is that in Couette flow one of the plates Figure 1: Couette flow. Figure 2: Planar Poiseuille flow. has a velocity U in its own plane (the other plate is at rest) as a result of the application of a shear stress, τ, and there is no pressure gradient in the fluid. In contrast in planar Poiseuille flow both plates are at rest and the flow is caused by a pressure gradient, dp/dx, in the direction, x, parallel to the plates. It is however, convenient, to begin the analysis of these flows together. We will omit any conservative body forces like gravity since their effects are can be simply added to the final solutions. Then, assuming that the only non-zero component of the velocity is ux and that the velocity and pressure are independent of time the resulting planar continuity equation for an incompressible fluid yields ∂ux ∂x =0 (Bib1) so that ux(y) is a function only of y, the coordinate perpendicular to the plates. Using this the planar Navier-Stokes equations for an incompressible fluid of constant and uniform viscosity reduce to 2 ∂p ∂ ux = μ (Bib2) ∂x ∂y2 ∂p ∂y =0 (Bib3) The second of these shows that the pressure, p(x), is a function only of x and hence the gradient, dp/dx, is well defined and a parameter of the problem.
    [Show full text]
  • Rayleigh-Bernard Convection Without Rotation and Magnetic Field
    Nonlinear Convection of Electrically Conducting Fluid in a Rotating Magnetic System H.P. Rani Department of Mathematics, National Institute of Technology, Warangal. India. Y. Rameshwar Department of Mathematics, Osmania University, Hyderabad. India. J. Brestensky and Enrico Filippi Faculty of Mathematics, Physics, Informatics, Comenius University, Slovakia. Session: GD3.1 Core Dynamics Earth's core structure, dynamics and evolution: observations, models, experiments. Online EGU General Assembly May 2-8 2020 1 Abstract • Nonlinear analysis in a rotating Rayleigh-Bernard system of electrical conducting fluid is studied numerically in the presence of externally applied horizontal magnetic field with rigid-rigid boundary conditions. • This research model is also studied for stress free boundary conditions in the absence of Lorentz and Coriolis forces. • This DNS approach is carried near the onset of convection to study the flow behaviour in the limiting case of Prandtl number. • The fluid flow is visualized in terms of streamlines, limiting streamlines and isotherms. The dependence of Nusselt number on the Rayleigh number, Ekman number, Elasser number is examined. 2 Outline • Introduction • Physical model • Governing equations • Methodology • Validation – RBC – 2D – RBC – 3D • Results – RBC – RBC with magnetic field (MC) – Plane layer dynamo (RMC) 3 Introduction • Nonlinear interaction between convection and magnetic fields (Magnetoconvection) may explain certain prominent features on the solar surface. • Yet we are far from a real understanding of the dynamical coupling between convection and magnetic fields in stars and magnetically confined high-temperature plasmas etc. Therefore it is of great importance to understand how energy transport and convection are affected by an imposed magnetic field: i.e., how the Lorentz force affects convection patterns in sunspots and magnetically confined, high-temperature plasmas.
    [Show full text]
  • Transition to Turbulence in Plane Poiseuille and Plane Couette Flow by STEVEN A
    J. Fluid Mech. (1980), vol. 96, part 1, pp. 159-205 169 Printed in Great Britain Transition to turbulence in plane Poiseuille and plane Couette flow By STEVEN A. ORSZAG AND LAWRENCE C. KELLST Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 [Received 8 June 1978 and in revised form 2 October 1978) Direct numerical solutions of the three-dimensional time-dependent Navier-Stokes equations are presented for the evolution of three-dimensional finite-amplitude disturbances of plane Poiseuille and plane Couette flows. Spectral methods using Fourier series and Chebyshev polynomial series are used. It is found that plane Poiseuille flow can sustain neutrally stable two-dimensional finite-amplitude dis- turbances at Reynolds numbers larger than about 2800. No neutrally stable two- dimensional finite-amplitude disturbances of plane Couette flow were found. Three-dimensional disturbances are shown to have a strongly destabilizing effect. It is shown that finite-amplitude disturbances can drive transition to turbulence in both plane Poiseuille flow and plane Couette flow at Reynolds numbers of order 1000. Details of the resulting flow fields are presented. It is also shown that plane Poiseuille flow cannot sustain turbulence at Reynolds numbers below about 500. I. Introduction One of the oldest unsolved problems of fluid mechanics is the theoretical description of the inception and growth of instabilities in laminar shear flows that lead to trans- ition to turbulence. The behaviour of small-amplitude disturbances on a laminar flow is reasonably well understood, but understanding of the behaviour of finite-amplitude disturbances is in a much less satisfactory state.
    [Show full text]
  • A Numerical and Experimental Investigation of Taylor Flow Instabilities in Narrow Gaps and Their Relationship to Turbulent Flow
    A NUMERICAL AND EXPERIMENTAL INVESTIGATION OF TAYLOR FLOW INSTABILITIES IN NARROW GAPS AND THEIR RELATIONSHIP TO TURBULENT FLOW IN BEARINGS A Dissertation Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Dingfeng Deng August, 2007 A NUMERICAL AND EXPERIMENTAL INVESTIGATION OF TAYLOR FLOW INSTABILITIES IN NARROW GAPS AND THEIR RELATIONSHIP TO TURBULENT FLOW IN BEARINGS Dingfeng Deng Dissertation Approved: Accepted: _______________________________ _______________________________ Advisor Department Chair Dr. M. J. Braun Dr. C. Batur _______________________________ _______________________________ Committee Member Dean of the College Dr. J. Drummond Dr. G. K. Haritos _______________________________ _______________________________ Committee Member Dean of the Graduate School Dr. S. I. Hariharan Dr. G. R. Newkome _______________________________ _______________________________ Committee Member Date R. C. Hendricks _______________________________ Committee Member Dr. A. Povitsky _______________________________ Committee Member Dr. G. Young ii ABSTRACT The relationship between the onset of Taylor instability and appearance of what is commonly known as “turbulence” in narrow gaps between two cylinders is investigated. A question open to debate is whether the flow formations observed during Taylor instability regimes are, or are related to the actual “turbulence” as it is presently modeled in micro-scale clearance flows. This question is approached by considering the viscous fluid flow in narrow gaps between two cylinders with various eccentricity ratios. The computational engine is provided by CFD-ACE+, a commercial multi-physics software. The flow patterns, velocity profiles and torques on the outer cylinder are determined when the speed of the inner cylinder, clearance and eccentricity ratio are changed on a parametric basis.
    [Show full text]
  • Simulation of Taylor-Couette Flow. Part 2. Numerical Results for Wavy-Vortex Flow with One Travelling Wave
    J. E’l~idM(&. (1984),FOI. 146, pp. 65-113 65 Printed in Chat Britain Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave By PHILIP S. MARCUS Division of Applied Sciences and Department of Astronomy, Harvard University (Received 26 July 1983 and in revised form 23 March 1984) We use a numerical method that was described in Part 1 (Marcus 1984a) to solve the time-dependent Navier-Stokes equation and boundary conditions that govern Taylor-Couette flow. We compute several stable axisymmetric Taylor-vortex equi- libria and several stable non-axisymmetric wavy-vortex flows that correspond to one travelling wave. For each flow we compute the energy, angular momentum, torque, wave speed, energy dissipation rate, enstrophy, and energy and enstrophy spectra. We also plot several 2-dimensional projections of the velocity field. Using the results of the numerical calculations, we conjecture that the travelling waves are a secondary instability caused by the strong radial motion in the outflow boundaries of the Taylor vortices and are not shear instabilities associated with inflection points of the azimuthal flow. We demonstrate numerically that, at the critical Reynolds number where Taylor-vortex flow becomes unstable to wavy-vortex flow, the speed of the travelling wave is equal to the azimuthal angular velocity of the fluid at the centre of the Taylor vortices. For Reynolds numbers larger than the critical value, the travelling waves have their maximum amplitude at the comoving surface, where the comoving surface is defined to be the surface of fluid that has the same azimuthal velocity as the velocity of the travelling wave.
    [Show full text]
  • Experimental and Numerical Study of Taylor-Couette Flow" (2015)
    Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2015 Experimental and numerical study of Taylor- Couette flow Haoyu Wang Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Mechanical Engineering Commons Recommended Citation Wang, Haoyu, "Experimental and numerical study of Taylor-Couette flow" (2015). Graduate Theses and Dissertations. 14462. https://lib.dr.iastate.edu/etd/14462 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Experimental and numerical study of Taylor-Couette flow by Haoyu Wang A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Mechanical Engineering Program of Study Committee: Michael G. Olsen, Major Professor Terry Meyer Shankar Subramaniam James Christian Hill Richard Dennis Vigil Iowa State University Ames, Iowa 2015 Copyright c Haoyu Wang, 2015. All rights reserved. ii TABLE OF CONTENTS LIST OF TABLES . iv LIST OF FIGURES . v ACKNOWLEDGEMENTS . xv ABSTRACT . xvi CHAPTER 1. INTRODUCTION . 1 General Introduction . .1 Dissertation Organization . .8 CHAPTER 2. POWER SPECTRUM ANALYSIS IN TAYLOR-COUETTE FLOW ......................................... 9 Abstract . .9 Introduction . 10 Experiment Apparatus and Procedure . 13 Data analysis . 17 Results and Discussion . 20 Summary and Conclusion . 28 CHAPTER 3. NUMERICAL INVESTIGATION OF TAYLOR-COUETTE FLOW WITH k − " MODEL . 43 Abstract . 43 Introduction .
    [Show full text]
  • Computational Study of Couette Flow Between Parallel Plates for Steady and Unsteady Cases Y
    EG0800331 Computational Study of Couette Flow Between Parallel Plates for Steady and Unsteady Cases Y. Rihan Atomic Energy Authority, Hot Lab. Centre, Egypt ABSTRACT Couette flow between parallel plates is a classical problem that has important applications in various industrial processing. In this investigation an analytical solution was obtained to predict the steady and unsteady Couette flow between parallel plates. One of the plates was stationary and the other plate moved with constant velocity. The governing partial differential equations were solved numerically using Crank-Nicolson implicit method to represent the flow behavior of the fluid. Key Words: Couette flow/ modeling/ parallel plates/ steady/ unsteady. INTRODUCTION Couette flow is a classical problem of primary importance in the history of fluid mechanics (1-4), which is a typical example of exact solutions for Navier-Stokes equation. Couette flow is perhaps the simplest of all viscous flows, while at the same time retaining much of the same physical characteristics of a more complicated boundary-layer flow. One of the most important process in industry is extrusion. Since the gap between the barrel and the screw of extruder is small, assuming a fluid flowing between parallel plates leads to representative results. There exist a large number of parameters in extrusion process which influence significantly the production rate and the quality of the final product. Couette flow between parallel plates is a classical problem that has important applications in power generators and pumps, etc. Several investigations have been done in this type of flow (5- 10). Etemad et al. (11) solved the simultaneously developed case of the motion and energy equation for power law fluid between parallel stationary plates when the variation of viscosity with temperature and viscous dissipation could not be neglected.
    [Show full text]
  • Numerical Modeling of Fluid Flow and Heat Transfer in a Narrow Taylor-Couette-Poiseuille System
    Numerical modeling of fluid flow and heat transfer ina narrow Taylor-Couette-Poiseuille system Sébastien Poncet, Sofia Haddadi, Stéphane Viazzo To cite this version: Sébastien Poncet, Sofia Haddadi, Stéphane Viazzo. Numerical modeling of fluid flow and heat transfer in a narrow Taylor-Couette-Poiseuille system. International Journal of Heat and Fluid Flow, Elsevier, 2010, 32, pp.128-144. 10.1016/j.ijheatfluidflow.2010.08.003. hal-00678877 HAL Id: hal-00678877 https://hal.archives-ouvertes.fr/hal-00678877 Submitted on 14 Mar 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Numerical modeling of fluid flow and heat transfer in a narrow Taylor-Couette-Poiseuille system S¶ebastienPoncet,¤ So¯a Haddadi,y and St¶ephaneViazzoz Laboratoire M2P2, UMR 6181 CNRS - Universit¶ed'Aix-Marseille - Ecole Centrale Marseille, IMT la Jet¶ee,38 rue Joliot-Curie, 13451 Marseille (France) (Dated: February 17, 2010) We consider turbulent flows in a di®erentially heated Taylor-Couette system with an axial Poiseuille flow. The numerical approach is based on the Reynolds Stress Modeling (RSM) of Elena and Schiestel [1, 2] widely validated in various rotor-stator cavities with throughflow [3{5] and heat transfer [6].
    [Show full text]
  • Electro-Osmotic Couette Flow with Joule Heating Effect
    The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/2634-2499.htm Flow control in Flow control in microfluidics microfluidics devices: electro-osmotic Couette devices flow with joule heating effect C. Ahamed Saleel and Saad Ayed Alshahrani Mechanical Engineering Department, College of Engineering, King Khalid University, Abha, Saudi Arabia Received 30 March 2021 Revised 27 May 2021 Asif Afzal Accepted 9 June 2021 Mechanical Engineering, PA College of Engineering, Mangalore, India Maughal Ahmed Ali Baig Mechanical Engineering, CMR Technical Campus, Secunderabad, India, and Sarfaraz Kamangar and T.M. Yunus Khan Mechanical Engineering Department, College of Engineering, King Khalid University, Abha, Saudi Arabia Abstract Purpose – Joule heating effect is a pervasive phenomenon in electro-osmotic flow because of the applied electric field and fluid electrical resistivity across the microchannels. Its effect in electro-osmotic flow field is an important mechanism to control the flow inside the microchannels and it includes numerous applications. Design/methodology/approach – This research article details the numerical investigation on alterations in the profile of stream wise velocity of simple Couette-electroosmotic flow and pressure driven electro-osmotic Couette flow by the dynamic viscosity variations happened due to the Joule heating effect throughout the dielectric fluid usually observed in various microfluidic devices. Findings – The advantages of the Joule heating effect are not only to control the velocity in microchannels but also to act as an active method to enhance the mixing efficiency. The results of numerical investigations reveal that the thermal field due to Joule heating effect causes considerable variation of dynamic viscosity across the microchannel to initiate a shear flow when EDL (Electrical Double Layer) thickness is increased and is being varied across the channel.
    [Show full text]