Couette Poiseuille Research Articles

Computational study on the internal layer in a diffuser

We report an internal layer found in the turbulent flow through an asymmetric planar diffuser using large-eddy simulation; we discuss five issues relevant to the internal layer: definition and identification, conditions for occurrence, connection with its outer flow, similarity with other equilibrium flows, and growth. The present internal layer exists in a region with stabilized positive skin friction downstream of a sharp reduction. The streamwise pressure gradient changes suddenly from slightly favourable to strongly adverse at the diffuser throat, and relaxes in a prolonged mildly adverse region corresponding to the skin friction plateau. Development of the internal layer into the outer region is slow, in contrast to the internal layers previously identified from certain external boundary-layer flows where the sudden change in streamwise pressure gradient is from strongly adverse to mildly favourable. Signatures of the internal layer include an inflectional point in the wall-normal profiles of streamwise turbulence intensity, and a well-defined logarithmic slope in the mean streamwise velocity underneath a linear distribution extending to the core region of the diffuser. Some of these characteristics bear a certain resemblance to those existing in the C-type of Couette–Poiseuille turbulent flows. Frequency spectrum results indicate that application of strong adverse pressure gradient at the diffuser throat enhances the low-frequency content of streamwise turbulent fluctuations. Inside the internal layer, the frequency energy spectra at different streamwise locations, but with the same wall-normal coordinate, nearly collapse. Two-point correlations with streamwise, wall-normal and temporal separations were used to examine connections between fluctuations inside the internal layer and those in the core region of the diffuser where the mean streamwise velocity varies linearly with distance from the wall. Galilean decomposition of instantaneous velocity vectors reveals a string of well-defined spanwise vortices outside the internal layer. The internal layer discovered from this study provides qualified support for a conjecture advanced by Azad & Kassab some years ago (Phys. Fluids A, vol. 1, 1989, p. 564).

Laminar forced convection with viscous dissipation in a Couette–Poiseuille flow between parallel plates

In this study, analytical solutions are obtained to predict laminar heat-convection in a Couette–Poiseuille flow between two plane parallel plates with a simultaneous pressure gradient and an axial movement of the upper plate. A Newtonian fluid with constant properties is considered with an emphasis on the viscous-dissipation effect. Both hydrodynamically and thermally fully-developed flow cases are investigated. The axial heat-conduction in the fluid is neglected. Two different orientations of the thermal boundary-conditions are considered: the constant heat-flux at the upper plate with an adiabatic lower plate (Case A) and the constant heat-flux at the lower plate with an adiabatic upper plate (Case B). For different values of the relative velocity of the upper plate, the effect of the modified Brinkman number on the temperature distribution and the Nusselt number are discussed. Comparison of the present analytical results for a special case with those available in the literature indicates an excellent agreement.

On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

Films and molds of nematic polymer materials are notorious for heterogeneity in the orientational distribution of the rigid rod or platelet macromolecules. Predictive tools for structure length scales generated by shear-dominated processing are vitally important: both during processing because of flow feedback phenomena such as shear thinning or thickening, and postprocessing since gradients in the rod or platelet ensemble translate to nonuniform composite properties and to residual stresses in the material. These issues motivate our analysis of two prototypes for planar shear processing: drag-driven Couette and pressure-driven Poiseuille flows. Hydrodynamic theories for high aspect ratio rod and platelet macromolecules in viscous solvents are well developed, which we apply in this paper to model the coupling between short-range excluded volume interactions, anisotropic distortional elasticity (unequal elasticity constants), wall anchoring conditions, and hydrodynamics. The goal of this paper is to generalize scaling properties of steady flow molecular structures in slow Couette flows with equal elasticity constants (M. G. Forest et al., J. Rheol., 48 (2004), pp. 175-192) in several ways: to contrast isotropic and anisotropic elasticity; to compare Couette versus Poiseuille flow; and to consider dynamics and stability of these steady states within the asymptotic model equations.

Navier–Stokes Analysis of a Regular Two-Dimensional Roughness Pattern Under Turbulent Flow Regime

The present work deals with the flow characteristics induced by a two-dimensional textured surface. The texture consists of identical and equally spaced rectangles with characteristic lengths at least one order of magnitude larger than the clearance of the thin film. Periodic boundary conditions enable the analysis of a single groove and the complete Navier–Stokes analysis is carried on for turbulent flow Reynolds numbers. The analysis is performed for shear driven flows (Couette), pressure driven flows (Poiseuille), and combined Couette–Poiseuille flows. First, the presence of inertial forces generated by the groove is emphasized by the momentum balance performed for the computational cell. The peculiar effect of the groove is also shown by the rotor and the stator shear stresses variations. Finally, it is shown that despite the presence of fluid inertia forces, cell-averaged rotor, and stator shear stresses obtained for pure Couette or Poiseuille flows can be added or subtracted to obtain with good accuracy the characteristics of combined shear and pressure driven flows.

Wind effect in turbulence parametrization

The action of wind blowing over a closed basin ultimately results in a steady shear-induced circulation pattern and in a leeward rising of the free surface—and a corresponding windward lowering—known as wind set-up. If the horizontal dimensions of the basin are large with respect to the average flow depth, the occurrence of local quasi-equilibrium conditions can be expected, i.e. the flow can be assumed to be locally driven only by the wind stress and by the opposing free surface gradient due to set-up. This wind-induced flow configuration shows a strong similarity with turbulent Couette–Poiseuille flow, the one dimensional flow between parallel plates generated by the simultaneous action of a constant pressure gradient and of the shear induced by the relative motion of the plates. A two-equation turbulence closure is then employed to perform a numerical study of turbulent Couette–Poiseuille flows for different values of the ratio of the shear stresses at the two walls. The resulting eddy viscosity vertical distributions are analyzed in order to devise analytical profiles of eddy viscosity that account for the effect of wind. The results of this study, beside allowing for a physical insight on the turbulence process of this class of flows, will allow for a more accurate description of the wind effect to be included in the formulation of quasi-3D and 3D models of lagoon hydrodynamics.

Stability of pressure-driven creeping flows in channels lined with a nonlinear elastic solid

The effect of pressure gradients on the stability of creeping flows of Newtonian fluids in channels lined with an incompressible and impermeable neo-Hookean material is examined in this work. Three different configurations are considered: (i) pressure-driven flow between a rigid wall and a wall lined with a neo-Hookean material; (ii) pressure-driven flow between neo-Hookean-lined walls; and (iii) combined Couette–Poiseuille flow between a rigid wall and a neo-Hookean-lined wall. In each case, a first normal stress difference whose magnitude depends on depth arises in the base state for the solid, and linear stability analysis reveals that this leads to a short-wave instability which is removed by the presence of interfacial tension. For sufficiently thick solids, low-wavenumber modes become unstable first as the applied strain increases above a critical value, whereas for sufficiently thin solids, high-wavenumber modes becomes unstable first. Comparison of the dimensionless critical strains shows that configurations (i) and (ii) are more difficult to destabilize than Couette flow past a neo-Hookean solid. For configuration (iii), the nonlinear elasticity of the solid leads to two physically distinct critical conditions, in contrast to what happens when a linear elastic material is used. The mechanisms underlying the behaviour of the critical strains are explained through an analysis of the interfacial boundary conditions.

Multiscaling in the Presence of Indeterminacy: Wall-Induced Turbulence

This paper provides a multiscale analytical study of steady incompressible turbulent flow through a channel of either Couette or pressure-driven Poiseuille type. Mathematically, the paper’s two most novel features are that (1) the analysis begins with an underdetermined singular perturbation problem, namely the Reynolds averaged mean momentum balance equation, and (2) it leads to the existence of an infinite number of length scales. (These two features are probably linked, but the linkage will not be pursued.) The paper develops a credible assumption of a mathematical nature which, when added to the initial underdetermined problem, results in a knowledge of almost the complete layer (scaling) structure of the mean velocity and Reynolds stress profiles. This structure in turn provides a lot of other important information about those profiles. The possibility of almost-logarithmic sections of the mean velocity profile is given special attention. The sense in which the length scales are asymptotically proportional to the distance from the wall is determined. Most traditional theoretical analyses of these wall-bounded flows are based ultimately on either the classical overlap hypothesis, mixing length concepts, or similarity arguments. The present paper avoids those approaches and their attendant assumptions. Empirical data are also not used, except that the Reynolds stress takes on positive values. Instead, reasonable criteria are proposed for recognizing scaling layers in the flow, and they are then used to determine the scaling structure and much more information.

Enzymatic tailor‐made proteolysis of whey in a vortex flow reactor

AbstractEnzymatic hydrolysis of cheese whey proteins with immobilized enzymes, providing a tailor‐made pool of peptides, within narrow ranges of molecular weight, might be an advantageous alternative for this by‐product of the dairy industry. In this work, Alcalase® was immobilized in agarose–glyoxyl gel beads and the proteolysis reaction was run in a continuous Taylor–Couette–Poiseuille reactor [or vortex flow reactor (VFR)], which presented efficient stirring without damaging the fragile beads. VFR mass transfer parameters were estimated after residence time distribution assays. Artificial neural networks were used to predict reaction rates of five ranges of peptide molecular weights. Using this hybrid model, a detailed description of the system was achieved. A bench‐scale VFR (radius ratio η = 0.48 and aspect ratio Γ = 11.9) was used to validate the model. © 2004 American Institute of Chemical Engineers AIChE J, 21: 314–322, 2005

Nonmodal growth of three-dimensional disturbances on plane Couette–Poiseuille flows

The time development of three-dimensional disturbances superimposed on a variety of mean flow profiles representing plane Couette–Poiseuille flow is investigated numerically. Specifically, with y representing the wall normal coordinate, the mean flow profiles U(y) are represented by U(y)=A(1−y2)+By, where B=1 when 0⩽A⩽1∕2 and B=2A(1−A) when 1∕2⩽A⩽1. For streamwise independent disturbances, which are the most amplified ones, there is an increase of the disturbance peak amplification when the parameter A increases in the interval 1∕10⩽A⩽1∕2. In the interval 1∕2⩽A⩽9∕10, and especially for 9∕10⩽A⩽1, the disturbance peak amplification decreases rapidly when A is increased. For A close to 1, a slight reduction of A will therefore cause a strong increase of the disturbance amplification.

Kinematics of the stationary helical vortex mode in Taylor–Couette–Poiseuille Flow

We reconstruct a kinematically admissible (volume-preserving) three-dimensional velocity field corresponding to the stationary helical vortex (SHV) mode which is observed in the Taylor–Couette–Poiseuille (TCP) system with a ratio of inner to outer cylinder radii of 0.5 and a length to annulus gap ratio of 16, starting from experimental data obtained via magnetic resonance imaging (MRI) for , and the reconstruction method is directly applicable to three-dimensional incompressible flows that possess a continuous volume-preserving symmetry. The SHV flow structure consists of a pair of asymmetric counter-rotating helical cells in a double helix structure, foliated with invariant helically symmetric surfaces containing fibre-like fluid particle orbits wrapped around the inner cylinder. Imposing general topological constraints, juxtaposing SHV with neighbouring hydrodynamic modes such as the propagating Taylor vortex flow and direct numerical simulation help corroborate the validity of the reconstruction of the SHV flow field. The kinematically admissible flow field obeys the Navier–Stokes equations with 10% accuracy, which is consistent with experimental error, and has the same flow portrait as the numerically computed flow. Global analysis of the SHV mode indicates that it corresponds to a minimum in dissipation and mixing in comparison with a wide class of perturbed neighbouring modes; hence it is a candidate for the study of particle segregation. To our knowledge, the present study reports the first synthesis of a physically realizable complex open flow that can be represented by an integrable Hamiltonian system starting from point-wise experimental data and using solely kinematic constraints.

Multidimensional flow modeling of the compression test of a Gaede pump stage in the viscous regime

Two-dimensional and three-dimensional models for a Gaede pump, based on the Navier–Stokes equations, are developed and a commercial Computational Fluid Dynamics code is used to solve them. We simulate a compression test in an outlet pressure range (30–2500 Pa) corresponding to the viscous laminar regime for an experimental pump. Experimental data are collected in order to validate the developed model. The pump tested is the high pressure stage of a commercial hybrid turbomolecular vacuum pump and can work in both transition and viscous regime, according to the operating pressure. The data show that the standard Couette–Poiseuille one-dimensional analytic model, developed by Helmer and Levi to describe the Gaede pump behavior and operating principle, has a limited accuracy when it is used as a design tool and not just as a physical model. The two-dimensional and the three-dimensional model results are compared with the experimental data showing an increasing level of agreement, with only a 10% maximum difference for the three-dimensional model in terms of compression ratio. The different flow structures shown by the models are critically analyzed to explain the different level of agreement.

A continuum model for pumping performance of turbomolecular pumps in all flow regimes

In the present study a continuum model for one-dimensional plane Couette–Poiseuille flow is implemented to turbomolecular pumps in different flow regimes. Pumping performance of various turbomolecular pumps including 6 single rotors, a rotor–stator row, a rotor–stator–rotor row, and a multi-row with 13 alternative rotor–stator rows is considered here. The obtained results show that the model provides good quantitative values for pumping performance of turbomolecular pumps over the whole regimes ranging from molecular flow to transition to slip flow.

Forced convection heat transfer of Couette–Poiseuille flow of nonlinear viscoelastic fluids between parallel plates

Heat transfer to viscoelastic fluids is frequently encountered in various industrial processing. In this investigation an analytical solution was obtained to predict the fully developed, steady and laminar heat transfer of viscoelastic fluids between parallel plates. One of the plates was stationary and was subjected to a constant heat flux. The other plate moved with constant velocity and was insulated. The simplified Phan-Thien–Tanner (SPTT) model, believed to be a more realistic model for viscoelastic fluids, was used to represent the rheological behavior of the fluid. The energy equation was solved for a wide range of Brinkman number, dimensionless viscoelastic group, and dimensionless pressure drop. Results highlight the strong effects of these parameters on the heat transfer rate.

Similarity laws of velocity profiles and turbulence characteristics of CouettePoiseuille turbulent flows

Similarity laws of mean velocity profiles and turbulence characteristics of Couette–Poiseuille turbulent flow (C-P flow) have been studied experimentally. The global parameters of C-P flow are the Reynolds number with a small absolute value.

Axial Couette–Poiseuille flow of power-law viscoplastic fluids in concentric annuli

The laminar axial flow of non-Newtonian fluids obeying Robertson–Stiff model in concentric annuli is analysed. Fluid flow is produced by the inner cylinder moving along its axis and by the pressure gradient imposed in the axial direction. Both cases (where pressure gradient either assists the moving cylinder or opposes the moving cylinder) are considered. All possible cases with respect to the positions of the plug flow regions are uniquely diversified by the derived semi-analytical criteria using the entry (geometric, kinematic, and rheologic) parameters. The explicit semi-analytical expression is derived for each possible case of the volumetric flow rate.

Continuous rheometry for industrial slurries

Mineral solids are usually processed, produced or handled in the form of two-phase slurries. Accurate and reliable measurements of the rheological properties of settling slurries using conventional viscometric instruments can be difficult, if not impossible, since the solid particles settle rapidly under the influence of gravity. In this paper we report on the development of an on-line flow rheometer specially designed and constructed for characterising the rheological behaviour of settling slurries. The instrument design is based on the principles of helical flow, which is the combination of tangential Couette and axial Poiseuille flows. The data reduction procedure developed is firmly based on the theory of helical flow and has been extensively tested and validated with fluids of different rheological behaviour. Good results have been obtained using the rheometer for various Newtonian liquids, pseudoplastic polymeric solutions and mineral slurries.

Poiseuille, thermal creep and Couette flow: results based on the CES model of the linearized Boltzmann equation

A synthetic-kernel model (CES model) of the linearized Boltzmann equation is used along with an analytical discrete-ordinates method (ADO) to solve three fundamental problems concerning flow of a rarefied gas in a plane channel. More specifically, the problems of Couette flow, Poiseuille flow and thermal-creep flow are solved in terms of the CES model equation for an arbitrary mixture of specular and diffuse reflection at the walls confining the flow, and numerical results for the basic quantities of interest are reported. The comparisons made with results derived from solutions based on computationally intensive methods applied to the linearized Boltzmann equation are used to conclude that the CES model can be employed with confidence to improve the accuracy of results available from simpler approximations such as the BGK model or the S model.

On the nonlinear stability in anisotropic MHD with application to Couette–Poiseuille flows

Nonlinear stability of the hydromagnetic Couette–Poiseuille flows in L 2-norm, to 3-D perturbations, in presence of MHD anisotropic Hall and ion-slip currents with transport parameters β H and β I is investigated by the direct Lyapunov functional method. It is proved that high levels of the anisotropic currents can assure asymptotic stability, according with the conditions β I> β H>1.

Numerical simulation of incompressible flows through granular porous media

The primitive equations of incompressible flows through isotropic granular porous media have been deduced by DuPlessis and Masliyah in the form of generalized Navier–Stokes equations. We first derive some analytical solutions of these equations in the form of generalized Hagen–Poiseuille, Couette–Poiseuille and Beltrami type flows. The respective classic flows are the limit cases of generalized solutions as porosity approaches zero. Then we develop a finite difference semi-implicit scheme, which is applied to numerical simulation of 3D flows in granular porous medium. The theoretical properties of accuracy and stability of this scheme are investigated and a method of specifying boundary conditions is suggested. The constructed scheme is applied to simulation of the obtained analytical solutions as well as to test problems of the lid-driven cavity flow.

BEM-NN computation of generalised Newtonian flows

This paper presents a boundary-element-only method (BEM) for the calculation of generalised Newtonian fluid (GNF) flows. The volume integral arising from non-linear effects is approximated via a particular solution technique. Multilayer perceptron networks (MLPN) and radial basis function networks (RBFN) are used for global approximation of field variables and hence volume discretisation is not required. The iterative numerical formulation is achieved by viewing the material as being composed of a Newtonian base (artificially assigned with a constant, but maybe different from subdomain to subdomain, viscosity) and the remaining component, which is accordingly defined from the original constitutive equation. This decoupling of the non-linear effects allows a Picard-type iterative procedure to be employed by treating the non-linear term as a known forcing function. However, convergence is sensitive to the estimate of this forcing function and an adaptive subregioning of the domain is adopted to control the accuracy of the estimate of this non-linear term. The criterion for subregioning is that the velocity gradient should not vary significantly in each subdomain. This strategy enables convergence of the present method (BEM-NN) at power-law index as low as 0.2 for the difficult power law fluid. The use of MLPNs (instead of single layer perceptrons) and RBFNs is another contributing factor to the improved convergence performance. The overall scheme is very suitable for coarse-grain parallelisation as each subdomain can be independently analysed within an iteration. Furthermore, within each subdomain process, there are other parallelisable computations. The present method is verified with circular Couette and planar Poiseuille flows of the power-law, Carreau–Yasuda and Cross fluids.