Couette Poiseuille Research Articles

Decay of streaks and rolls in plane Couette–Poiseuille flow

We report the results of an experimental investigation into the decay of turbulence in plane Couette–Poiseuille flow using ‘quench’ experiments where the flow laminarises after a sudden reduction in Reynolds number $Re$ . Specifically, we study the velocity field in the streamwise–spanwise plane. We show that the spanwise velocity containing rolls decays faster than the streamwise velocity, which displays elongated regions of higher or lower velocity called streaks. At final Reynolds numbers above $425$ , the decay of streaks displays two stages: first a slow decay when rolls are present and secondly a more rapid decay of streaks alone. The difference in behaviour results from the regeneration of streaks by rolls, called the lift-up effect. We define the turbulent fraction as the portion of the flow containing turbulence and this is estimated by thresholding the spanwise velocity component. It decreases linearly with time in the whole range of final $Re$ . The corresponding decay slope increases linearly with final $Re$ . The extrapolated value at which this decay slope vanishes is $Re_{a_z}\approx 656\pm 10$ , close to $Re_g\approx 670$ at which turbulence is self-sustained. The decay of the energy computed from the spanwise velocity component is found to be exponential. The corresponding decay rate increases linearly with $Re$ , with an extrapolated vanishing value at $Re_{A_z}\approx 688\pm 10$ . This value is also close to the value at which the turbulence is self-sustained, showing that valuable information on the transition can be obtained over a wide range of $Re$ .

Energy budget analysis and neutral curve characteristics for the linear instability of Couette–Poiseuille flow

Here, we present some interesting new results on the linear modal stability of the Couette–Poiseuille flow (CPF), by numerically solving the Orr–Sommerfeld equation within the temporal framework. We provide a mechanistic explanation to the well-known result that the upper plate movement causes progressive stabilization of the CPF. The temporal energy budget reveals appearance of a region of negative energy production with plate movement, which is located near the plate that has a higher relative velocity in the direction of the bulk flow. This has a negative contribution to the integral production term, which, along with the expectation that energy dissipation is nominally constant (to leading order) at a given Reynolds number (Re), reduces the growth rate of kinetic energy, thereby causing flow stabilization with an increase in plate speed. Next, we compare the linear stability portrait of the CPF for positive and negative plate speeds and find that the upper and lower neutral branches in the frequency-Re plane cross over each other (to form a “loop”) for a certain range of negative plate speeds. Interestingly, this behavior is not seen for positive plate speeds. At high Re and small plate speeds (positive/negative), we observe that the CPF supports an additional unstable mode manifested in the neutral curves as a bifurcation of the unstable region into primary and secondary regions. The secondary unstable mode is found to be sufficiently distinct in character from the primary mode. These results contribute to the contemporary efforts to better understand the stability of the CPF.

Experimental measurements in plane Couette–Poiseuille flow: dynamics of the large- and small-scale flow

Abstract

The effect of temperature-dependent viscosity and thermal conductivity on velocity and temperature field: an analytical solution using the perturbation technique

This paper proposes a general form of the perturbation expansion method for the governing equations of viscous flow coupled to the temperature evolution. The effect of the variations of viscosity and thermal conductivity with temperature on the temperature and velocity fields in a steady two-dimensional Couette–Poiseuille flow is examined. The presented analytical solution by the perturbation method is validated against a finite difference solution of the governing equations. The numerical and analytical solutions are in good agreement.

Laminar–Turbulent Intermittency in Annular Couette–Poiseuille Flow: Whether a Puff Splits or Not

Direct numerical simulations were carried out with an emphasis on the intermittency and localized turbulence structure occurring within the subcritical transitional regime of a concentric annular Couette–Poiseuille flow. In the annular system, the ratio of the inner to outer cylinder radius is an important geometrical parameter affecting the large-scale nature of the intermittency. We chose a low radius ratio of 0.1 and imposed a constant pressure gradient providing practically zero shear on the inner cylinder such that the base flow was approximated to that of a circular pipe flow. Localized turbulent puffs, that is, axial uni-directional intermittencies similar to those observed in the transitional circular pipe flow, were observed in the annular Couette–Poiseuille flow. Puff splitting events were clearly observed rather far from the global critical Reynolds number, near which given puffs survived without a splitting event throughout the observation period, which was as long as outer time units. The characterization as a directed-percolation universal class was also discussed.

Annular Couette–Poiseuille flow and heat transfer of a power-law fluid – analytical solutions

Analytical solutions involving hypergeometric functions are presented for the fully developed laminar flow of a Non-Newtonian fluid in an annulus with a stationary or a moving inner boundary. The solutions are valid for arbitrary values of the power law index in the Couette–Poiseuille flow under consideration, and consider scenarios with and without extrema in the velocity profile, in addition to flow against adverse pressure gradients. Criteria are identified for the disappearance and reappearance of an extreme point, development of flow reversal, and occurrence of an adverse pressure gradient. Fully developed Heat Transfer is also analysed with three different types of boundary conditions and analytical solutions are presented for the case of both inner and outer annulus boundaries maintained at constant but possibly different heat fluxes. A non-homogeneous Cauchy-Euler ODE is solved numerically for the case in which both annulus boundaries are at the same temperature. Correlations for the friction factor and for the Nusselt numbers at the inner and outer walls are presented in terms of the annulus radius ratio, the power law index and the ratio of the wall-to-bulk velocities. It is shown how a multiplicative correction can be used to extend the applicability of the API-RP-13D prescription for the friction factor to flow scenarios involving a moving inner wall as is common in many oil well circulating scenarios. Results of a parametric sensitivity analysis are presented and indicate that the influence of the power law index on the friction factor is significant only in conjunction with the inner wall velocity, and that its influence on the Nusselt numbers is largely minimal. The methodology is validated with exact closed form solutions for limiting cases, and with results in the literature. From a practical perspective, the results will prove useful in the context of hydraulics and heat transfer in complex oilfield wellbores, as well as in the process industry.

Impact of Hall effect, nonlinear radiation and heat source on MHD Couette–Poiseuille flow of nanoliquid through a rotating channel

PurposeThis report offers the detailed investigation of Couette–Poiseuille flow of nanoliquid with varying viscosity. The analysis is carried out by considering flow between two parallel plates in a rotating permeable channel with the aid of nonlinear thermal radiation and Hall effect. The predominant equations governing the physical phenomenon are demonstrated using the Buongiorno model.Design/methodology/approachNumerical computation for the demonstrated physical problem is achieved through the implementation of the Runge–Kutta–Fehlberg fourth–fifth-order method along with shooting technique.FindingsThe theoretical view of Brownian motion, nonlinear radiation, Hall effect and thermophoresis parameter is presented graphically.Originality/valueIt is revealed that flow velocity increases with the upper wall motion parameter and magnetic field. Also, it is established that an increase in the Nusselt number is achieved for increasing values of nonlinear radiation parameter.

Simple criterion for vortex formation in the channel flow of power-law fluids

Vortices can have negative effects on the processing of various flows in industrial engineering. Thus, there have been many attempts to seek vortex-free operating conditions. This study explores the feasibility of applying the flow reversal condition in the Couette–Poiseuille (C–P) flow of power-law fluid to the prediction of vortex birth. In previous studies, flow reversal conditions are explicitly expressed only in terms of the pressure gradient. In certain industrial flows, which involve various traits of C–P flows such as slot coating, the flow rate is the key operating parameter, which needs to be precisely controlled. Therefore, in this work, we analytically derived a critical flow-rate condition for the flow reversal to occur in planar C–P flows. The critical condition was compared with the computationally-predicted vortex formation conditions in the slot coating flow. The flow reversal condition, despite its simplicity, successfully predicted the onset of vortex birth in the downstream slot coating flow for power-law fluids. Moreover, the result suggested that stronger shear-thinning effect allows a wider range of vortex-free operating conditions.

Explicit flow velocity modelling of yield power-law fluid in concentric annulus to predict surge and swab pressure gradient for petroleum drilling applications

Exact prediction and controlling of surge/swab pressure are required during drilling of hydrocarbon reservoirs and other geological formations that often leads to well control challenges. The existing methods to predict the surge/swab pressure gradient in the wellbore are much implicitly developed, which further reduces the model accuracy. Therefore, the present research aims to develop a novel analytical model by incorporating the explicit flow velocity equations to further improve the efficiency in predicting the surge pressure gradient. The governing flow velocity equations are developed for a concentric annulus exhibiting Couette–Poiseuille flow phenomenon that subsequently used in designing a new analytical model for yield power-law fluids to predict surge pressure gradient. Detailed analysis for the validation of a newly developed model is performed using existing predictive models and experimental data of surge pressure. The statistical analysis exhibits satisfactory outcomes with a maximum error of 5.61% and R2 of 0.988. A detailed analysis on the effect of relevant parameters on surge/swab pressure is also presented. The impact of fluid behaviour index and diameter ratio is found to be highly dependent on surge pressure under varying tripping speeds compared to other drilling parameters such as fluid yield point and consistency index.

Orientation of inertial spheroids in turbulent Couette–Poiseuille flow with a shear-free wall

The role of mean shear on the orientational behavior of aspherical particles is studied by Lagrangian tracking of inertial spheroids in a directly simulated turbulent Couette–Poiseuille flow. The effects of particle inertia and shape in the conventional wall-turbulence near the stationary wall closely resemble observations made earlier in turbulent channel flows. The particles’ orientational behavior in the anisotropic turbulence field near the shear-free wall is qualitatively different. Direct comparisons between the orientation statistics near the sheared and the shear-free wall provide an insight into the role played by the mean shear. We observed that disks (rods) with low inertia preferentially oriented in the directions of Lagrangian compression (stretching) of the fluid elements, similarly as already reported for tracer spheroids. Spheroids with intermediate inertia exhibited similar orientations as the low-inertia particles near the shear-free wall, although the behavior of such spheroids was greatly affected by inertia near the sheared wall. This is explained by a six-fold increase of the Kolmogorov time scale across the flow, which leads to a corresponding reduction of the local Stokes number near the shear-free wall. The most inertial spheroids, however, oriented almost randomly near the shear-free wall, a finding we ascribe to the absence of mean shear and inertial filtering of the anisotropic vorticity field. It can therefore be inferred that the presence of mean shear is essential for forming the preferential orientation of inertial spheroids in near-wall turbulence and the particle inertia alone merely randomizes particle alignment due to the inertia-filtering.

One-dimensional simulation of Couette–Poiseuille flow with variable cross section for the full range of gas rarefaction

Clearance mass flows are a major loss mechanism in dry running rotatory positive displacement vacuum pumps. Therefore, a detailed knowledge of the clearance mass flow is crucial to calculate the operation of those pumps. The small clearance heights and the large pressure range of such pumps require a wide range of gas rarefaction parameters to be taken into account. The flow in the clearance can be described as a combined Couette–Poiseuille flow with variable cross section. This is typically done by solving the Stokes equation, but especially at high gas rarefaction parameters, the inertia cannot be neglected any more, which can lead to choking of the flow. A one-dimensional approach for the compressible fluid flow was provided by Shapiro. It is shown that this approach can be carried over for the rarefied gas flow. The problem is solved in bounds for the constant total temperature and compared to experimental investigations by varying the pressure ratio and the circumferential speed of the clearance boundary in a wide range of gas rarefaction parameters.

Effects of magnetization relaxation in ferrofluid film flows under a uniform magnetic field

We analyze the magnetization relaxation effects of a ferrofluid film flow governed by the ferrohydrodynamics encompassing the Fokker–Planck magnetization equation in a Couette–Poiseuille configuration subject to an applied uniform stationary magnetic field perpendicular to the boundaries. A solver based on OpenFOAM is programmed to find solutions numerically for the velocity, spin velocity, and magnetization in ferrofluid films under the combined pressure gradient, boundary flow, and magnetic field forcing. The solver is validated by comparison with the classical Couette–Poiseuille flows and the analytic solutions of the magnetization relaxation problem when the product of flow vorticity and relaxation time is much smaller than unit, ΩτB≪1. We compare the effects of magnetization relaxation obtained from the phenomenological magnetization equation with those from the equation derived microscopically. The results obtained from the former equation are not suitable for the description of ferrofluid film flows. Due to the magnetization relaxation effects, a misalignment between the local magnetization and the local magnetic field is observed. The net effects are that the flow is hampered by magnetic fields and it manifests as diminished slopes of vorticity profiles and reduced volumetric flow rates. The magnetization relaxation effects also slow down the spin velocity of particles or change their direction, which leads to an enhanced effective viscosity. The total tangential stress exerted on the moving boundary is higher than that of the classical Couette–Poiseuille flow owing to the addition of a magnetic stress. The magnetization relaxation effect is more significant in cases of ferrofluids with higher relaxation times.

Effect of Couette component on the stability of Poiseuille flow of a Bingham fluid–porous system: Modal and non-modal approaches

In this study, both modal and non-modal stability analyses are attempted in case of Couette–Poiseuille flow of a Bingham fluid overlying a porous layer. Such a flow configuration is widely encountered in the geophysical context in case of oil drilling. The solution of the modal problem yields no unstable eigenvalue, similar to the flow of a viscoplastic fluid in a non-porous channel configuration. Thus, non-modal analysis is performed to throw light on the short-time characteristics. The primary goal is to unveil the complex interplay between the upper plate velocity (Couette component) and the parameters characterizing the porous layer in dictating the flow transition characteristics. The current study is possibly the first attempt at investigating the effect of the Couette flow on the stability of a fluid–porous system for any kind of non-Newtonian fluid and reveals marked departure from the results reported in the literature for a similar flow configuration involving Newtonian rheology. The reason for the deviation is attributed to the role of yield stress, quantified by the Bingham number, and its complex interaction with the Couette number and porous layer parameters (depth, permeability, anisotropy, inhomogeneity, etc.). The relative interaction between fluid and porous modes in an environment of non-linear viscosity variation (owing to the rheology of the viscoplastic fluid), coupled with enhanced shearing (imparted by the Couette component), is found to demonstrate unique, non-monotonic flow transition characteristics. The possible physical mechanism governing short-time (non-modal) amplifications via interaction between the mean shear flow and the perturbation waves is also explored in detail.

Flow Resistance Modeling for Coolant Distribution within Canned Motor Cooling Loops

Taylor–Couette–Poiseuille (TCP) flow dominates the inner water-cooling circulation of canned motor reactor coolant pumps. Current research on TCP flow focuses on torque behaviors and flow regime transitions through experiments and simulations. However, research on axial flow resistance in a large Reynolds number turbulent state is not sufficient, especially for the various flow patterns. This study is devoted to investigating the influence of annular flow on the axial flow resistance of liquid in the coaxial cylinders of the stator and rotor in canned motor reactor coolant pumps, and predicting the coolant flow distribution between the upper coil cooling loop and lower bearing lubricating loop for safe operation. The axial flow resistance, coupled with the annular rotation, is experimentally investigated at a flow rate with an axial Reynolds number, Rea, from 2.6 × 103 to 6.0 × 103 and rotational Reynolds number, Ret, from 1.6 × 104 to 4.0 × 104. It is revealed that the axial flow frictional coefficient varies against the axial flow rate in linear relation sets with logarithmic coordinates, which shift up when the flow has a higher Ret. Further examination of the axial flow resistance, with the Rea extending to 3.5 × 105 and Ret up to 1.6 × 105, by simulation shows gentle variation rates in the axial flow frictional coefficients against the Rea. The relation curves with different Ret values converge when the Rea exceeds 3.5 × 105. A prediction model for TCP flow consisting of a polygonal approximation with logarithmic coordinates is developed to estimate the axial flow resistance against different axial and rotational Reynolds numbers for the evaluation of heat and mass transfer during transition states and the engineering design of the canned motor chamber structure.

Effect of radial injection on heat transfer of a Taylor–Couette–Poiseuille flow

The effect of radial flow injection on the heat transfer characteristics of a Taylor–Couette–Poiseuille flow in an annulus is numerically investigated using the SST k-ω turbulence model. The ranges of the axial Reynolds number (ReA) and the rotational Reynolds number (ReΩ) are and respectively. For every combination of axial and rotational Reynolds number, flow is injected radially into the air gap through a rectangular duct located on the inner cylinder with the injection rate which varies from 0.02 to 0.14. Airflow in the air gap, before the injection, is in a fully developed condition and the effect of radial injection on the heat transfer of inner and outer cylinder is investigated in terms of the Nusselt number. In the studied range, radial injection increases the averaged Nusselt number up to 24% on the inner cylinder and up to 27% on the outer cylinder. In order to compare the heat transfer increase due to the radial injection, Nu* is defined as the difference between local Nusselt and Nusselt number of the fully developed flow happening at the same configuration without injection, and it is shown that though the trend of local Nusselt on the inner and outer cylinder is different, the averaged Nu* on both surfaces follows the same trend.

Energy redistribution dynamics in coupled Couette–Poiseuille flows using large-Eddy simulation

The problem of turbulent Couette flow driven by a statistically steady external wind is studied in the framework of spatially filtered Navier–Stokes equations. The phenomenon of wind-driven flow of water is represented by a layer of air modeled as Poiseuille flow (air sub-domain), coupled to a layer of water modeled as Couette flow (water sub-domain). We focus on changes in the statistics in either the air or the water sub-domain, due to the coupling with the other sub-domain. We also highlight dynamic flow structures forming near the air-water interface. Simulations based on different Reynolds numbers in the air and the water sub-domains are compared to computationally less demanding simulations with equal Reynolds numbers. Results of these simulations indicate strong similarities, i.e., the flow is well approximated by simulating air and water at the same Reynolds numbers. Further analysis shows that the flow in the water domain shares important features with classical Couette flows. The horizontal turbulent mixing renders a thinner boundary layer in the water sub-domain. Moreover, an increased intermittency in the flow velocities is observed, which may be linked to so-called splat events near the air-water interface. These splats characterize the interaction of coherent structures across the interface, being stronger in the water phase. An analysis of the pressure-strain correlation near the air-water interface on the water side shows that such splats are responsible for redistributing energy from the streamwise and spanwise directions, to the vertical direction. This behavior, although qualitatively similar to wall-bounded flows, differ mainly on the fact that most of the energy drained comes from the streamwise direction: in wall-bounded the main contributor is the spanwise direction. The boundary layers near the air-water interface show inclined vortical structures. Unlike in coupled Couette–Couette flow, the peak in the Reynolds stress is displaced from the channel’s center into the buffer region of the water sub-domain.

Linear stability of a plane Couette–Poiseuille flow overlying a porous layer

The modal and non-modal linear stability analyses of a three-dimensional plane Couette–Poiseuille flow through a porous channel are studied based on the two-domain approach, where fluid and porous layers are treated as distinct layers separated by an interface. The unsteady Darcy–Brinkman equations are used to describe the flow in the porous layer rather than the unsteady Darcy’s equations. In fact, the Brinkman viscous diffusion terms are necessary to capture the momentum boundary layer developed close to the fluid-porous interface. The modal stability analysis is performed under the framework of the Orr–Sommerfeld boundary value problem. On the other hand, the non-modal stability analysis is performed under the framework of the time-dependent initial value problem in terms of normal velocity and normal vorticity components. The Chebyshev spectral collocation method along with the QZ algorithm is implemented to solve the boundary value problem numerically for disturbances of arbitrary wavenumbers. The convergence test of spectrum demonstrates that more Chebyshev polynomials are required to arrest the flow dynamics in the momentum boundary layer once the Couette flow component is turned on. Two different types of modes, so-called the fluid layer mode and the porous layer mode are identified in the modal stability analysis. The most unstable fluid layer mode intensifies while the most unstable porous layer mode attenuates in the presence of the Couette flow component. Further, the mechanism of modal instability is deciphered by using the method of the energy budget. It is found that the energy production term supplies energy from the base flow to the disturbance via the Reynolds stress, and boosts the disturbance kinetic energies for the fluid layer and the porous layer. Moreover, the non-modal stability analysis demonstrates that short time energy growth exists in the parameter space and becomes significant in the presence of the Couette flow component and the permeability of the porous medium.

Magneto-rheological damper modeling by using dissipative particle dynamics method

A mesoscale modeling of magneto-rheological damper is performed by using dissipative particle dynamics method. Bounce-back and periodic boundary conditions are used, and the model is validated by Couette flow, Poiseuille flow and flow through a micro-tube. Shear stress and damping behavior are probed with considering hysteresis condition. Three electrical coils are placed inside MR damper, control damping force by applying magnetic strength distribution as step function pattern. Results show that by increasing both of average strength of magnetic field and shear rate, shear stress increases. The effects of different parameters such as frequency and amplitude of piston velocity, magnetic field strength, diameter of magnetic particles and strength of dissipative forces on damping force and hysteresis condition are investigated by using Bouc–Wen model. Results show by increasing frequency and decreasing amplitude and magnetic field strength, hysteresis range and strength of damping force reduce. Sensitivity analysis performed on MR fluid parameters reveals that the weight of magnetic particles and the dissipative force have the most effect on strength of damping force so that, by increasing dissipative force, damping force increases linearly, but enhancement in the weight of magnetic particles leads to damping force firstly increases and then reduces.

Numerical Simulation and Mathematical Modeling of Electro-Osmotic Couette–Poiseuille Flow of MHD Power-Law Nanofluid with Entropy Generation

The basic motivation of this investigation is to develop an innovative mathematical model for electro-osmotic flow of Couette–Poiseuille nanofluids. The power-law model is treated as the base fluid suspended with nano-sized particles of aluminum oxide (Al2O3). The uniform speed of the upper wall in the axial path generates flow, whereas the lower wall is kept fixed. An analytic solution for nonlinear flow dynamics is obtained. The ramifications of entropy generation, magnetic field, and a constant pressure gradient are appraised. Moreover, the physical features of most noteworthy substantial factors such as the electro-osmotic parameter, magnetic parameter, power law fluid parameter, skin friction, Nusselt number, Brinkman number, volume fraction, and concentration are adequately delineated through various graphs and tables. The convergence analysis of the obtained solutions has been discussed explicitly. Recurrence formulae in each case are also presented.

Shear stress-driven flow: the state space of near-wall turbulence as

An inner-scaled, shear stress-driven flow is considered as a model of independent near-wall turbulence as the friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\rightarrow \infty$. In this limit, the model is applicable to the near-wall region and the lower part of the logarithmic layer of various parallel shear flows, including turbulent Couette flow, Poiseuille flow and Hagen–Poiseuille flow. The model is validated against damped Couette flow and there is excellent agreement between the velocity statistics and spectra for the wall-normal height $y^{+}<40$. A near-wall flow domain of similar size to the minimal unit is analysed from a dynamical systems perspective. The edge and fifteen invariant solutions are computed, the first discovered for this flow configuration. Through continuation in the spanwise width $L_{z}^{+}$, the bifurcation behaviour of the solutions over the domain size is investigated. The physical properties of the solutions are explored through phase portraits, including the energy input and dissipation plane, and streak, roll and wave energy space. Finally, a Reynolds number is defined in outer units and the high-$Re$ asymptotic behaviour of the equilibria is studied. Three lower branch solutions are found to scale consistently with vortex–wave interaction (VWI) theory, with wave forcing localising around the critical layer.