Couette Poiseuille Flow Research Articles

Shear-induced particle migration and segregation in non-Brownian bidisperse suspensions under planar Poiseuille flow

In our previous work [Chun et al., Phys. Fluids 29, 121605 (2017)], we studied the migration behavior of concentrated monodisperse particles in Couette–Poiseuille flows. Here, we extend this study into an investigation of concentrated ( ϕ0=0.3) bidisperse suspensions undergoing pressure-driven flows at various combinations of volume fraction ratio ( ϕS0/ϕ0=0.13−0.67) and size ratio ( aL/aS=1.4−2.4) between small ( 2aS/H=0.022) and large ( 2aL/H=0.031−0.052) particles in a planar channel of height H. The flow behavior of neutrally buoyant hard spheres suspended in a Newtonian fluid was numerically simulated using the lattice Boltzmann method. The time evolution of the distributions of small and large particles showed segregation under inhomogeneous shear flow, resulting in enrichment of large particles and depletion of small particles near the midplane. Size-dependent particle segregation was more pronounced in these simulations than what was previously observed in the experiment. In bidisperse suspensions, the concentration evolution was markedly slower than in monodisperse situations; the characteristic time to reach a steady state was 5–8 times longer in bidisperse systems. The results of lattice Boltzmann simulation were further analyzed within the framework of a reformulated polydisperse diffusive flux model [Shauly et al., J. Rheol. 42, 1329 (1998)]; four coefficients of the diffusive flux model were adjusted to match steady-state ( KL, KS) and transient ( RL, RS) predictions. The model coefficients showed strong dependence on the particle number density ratio (ϕS0/ϕL0)(aL/aS)3; both KL and RL increased almost linearly with this ratio, whereas KS decreased and RS increased with this ratio.In our previous work [Chun et al., Phys. Fluids 29, 121605 (2017)], we studied the migration behavior of concentrated monodisperse particles in Couette–Poiseuille flows. Here, we extend this study into an investigation of concentrated ( ϕ0=0.3) bidisperse suspensions undergoing pressure-driven flows at various combinations of volume fraction ratio ( ϕS0/ϕ0=0.13−0.67) and size ratio ( aL/aS=1.4−2.4) between small ( 2aS/H=0.022) and large ( 2aL/H=0.031−0.052) particles in a planar channel of height H. The flow behavior of neutrally buoyant hard spheres suspended in a Newtonian fluid was numerically simulated using the lattice Boltzmann method. The time evolution of the distributions of small and large particles showed segregation under inhomogeneous shear flow, resulting in enrichment of large particles and depletion of small particles near the midplane. Size-dependent particle segregation was more pronounced in these simulations than what was previously observed in the experiment. In bidisperse suspension...

Numerical analysis of multiphysical field for independent three-stage magnetorheological damper of double rod during recoil process of artillery

In order to investigate the multiphysics in the recoil process of magnetorheological damper, independent three-stage magnetorheological damper of double rod has been designed. The magnetorheological gel with carbonyl iron powder mass fraction of 70% (MRG-70) has been prepared and the steady-state shear test was carried out for obtaining the consistency coefficient k and the non-Newtonian index n of the Herschel–Bulkley model. MRG-70 has been applied to the damper and the motion analysis of the recoil part has been carried out by combining the law of chancing of the bore resultant force of a certain type of fixed artillery. Results of the theoretical analysis and numerical calculation of multiple physical fields for damper showed: (1) there was a scattered magnetic flux inside the damper. The magnetic field was generated by the combined coil with a high degree of nonlinearity and time variability; (2) the internal energy dissipation of damper comprises five parts, in which Poiseuille pressure flow loss and Couette viscous flow loss were the primary and controllable part of the damper. The temperature of each pole reaches a peak value, and it is different at different times; the pressure drop at the magnetic pole was less than the pressure drop at the coil; (3) the dynamic viscosity of the central axial surface of the effective damping channel shows obvious nonlinearity and time variability from the spatial and time dimension, and varies very sharply at each pole, and the peak value fluctuates with the position.

Analytical solutions of oscillating Couette–Poiseuille flows for the viscoelastic Oldroyd B fluid

This paper deals with the analytical investigation of oscillatory Couette–Poiseuille flows with regard to the viscoelastic Oldroyd B fluid, taking the inertial force into account. The fluid is confined by two infinite horizontal plates under the exertion of a periodic pressure gradient. The upper plate is fixed at rest, and the below plate oscillates in its own plane. The velocity distributions and the stress responses are analytically obtained and graphically presented. The oscillating flow behaviors of the Oldroyd B fluid and its two limiting cases, the Newtonian fluid and the upper-convected Maxwell fluid, are investigated and compared. The inertial, viscous, and elastic effects on the flow behaviors, stress responses, the relation between the shear stress and the shear rate, and the emerging resonance are extensively discussed by reference to the dimensionless parameters, i.e., Reynolds number, Deborah number, and the ratio of the relaxation time to the retardation time.

Self-sustaining dual critical layer states in plane Poiseuille–Couette flow at large Reynolds number

The nonlinear stability of plane Poiseuille–Couette flow subjected to three-dimensional disturbances is studied asymptotically at large Reynolds number R . By analysing the nature of the instability for increasing disturbance size Δ, the scaling Δ = O ( R −1/3 ) is identified at which a strongly nonlinear neutral wave structure emerges, involving the interaction of two inviscid critical layers. The striking feature of this structure is that the travelling wave disturbances have both streamwise and spanwise wavelengths comparable to the channel width, with an associated phase speed of O (1). An alternative method to the classical balancing of phase shifts is proposed, involving vorticity jumps, that uses a global property of the flow-field and enables the amplitude-dependence of the neutral modes to be determined in terms of the wavenumbers and the properties of the basic flow. Numerical computation of the Rayleigh equation which governs the flow outside of the critical layers shows that neutral solutions exist for non-dimensional wall sliding speeds in the range 0 ≤ V < 2. It transpires that the critical layers merge and the asymptotic structure referred to above breaks down both in the large-amplitude limit and the limit V → 2 when the maximum of the basic flow becomes located at the upper wall.

Couette–Poiseuille flow of a Bingham fluid through a channel overlying a porous layer

Couette–Poiseuille flow of a Bingham fluid through a channel overlying a porous layer has been investigated in this study. Such flows are relevant in drilling muds for oil recovery, blood flow in biological systems, etc. An analytical solution of the velocity profile was derived from first principles. Effects of various parameters, like, Couette number (Co), Bingham number (Bn), Darcy number, slip coefficient, depth of porous layer on the velocity profile were studied in detail. The phase space plot of Couette–Bingham number was generated to obtain the region of double shear flow desirable for enhanced convective flow. Effects of other operating parameters on Co–Bn phase space were also investigated in order to identify a feasible region to operate for ensuring double shear flow. Locations of both yield surfaces due to asymmetric flow were obtained and effects of operating conditions on them were investigated. Variation of wall shear stress with operating conditions was also quantified. The present analysis will be beneficial for efficient design of flow channels dealing with viscoplastic fluids in real life applications.

Effect of rough inner wall of nanochannel on fluid flow behavior

Flow system on a nano scale, as an effective and economic system, has been widely employed. While on a macroscopic scale, for the non-slip boundary, the velocity of the fluid at the surface is assumed to be consistent with the surface. This approximation may become invalid on a smaller length scale pertinent to the operation of microfluid devices. The interface slip effect has a significant influence on the flow because of its higher ratio of surface to volume. In this paper, the Poiseuille flow, which is composed of two infinite parallel asymmetric walls, is studied by the molecular dynamics method. The influence of wall roughness and surface wettability of channel on fluid flow in the channel are analyzed. The results show that the asymmetric upper and lower wall can lead to an asymmetric distribution of flow parameters. The change of wall roughness and wettability would affect the flow characteristics of fluid atoms near the wall. Due to the influence of wall grooves, the number density distribution near the rough wall is lower than that on the smooth wall side. As the rib height and wall wettability increase, the number density of fluid atoms in the groove increases gradually, and the change of the rib spacing does not substantially affect the number density distribution of fluid atoms near the rough wall. For different structure types of walls, the real solid-liquid boundary positions are determined by simulating the velocity field distribution in the channel under both Couette flow and Poiseuille flow, which can help us to better analyze the interface slip effect. The variation of wall roughness and wettability can affect the position of the solid-liquid interface. The change of rib height and wettability can greatly influence the velocity distribution in channel, and the position of the solid-liquid boundary as well. Conversely, the rib spacing has a less effect on the boundary position. The difference in boundary position can affect the interface slip effect. We can find the slip velocity and the slip length on one side of the rough wall to be smaller than those on the smooth wall side, and as the rib height and wall wettability increase, the slip velocity and the slip length significantly decrease near the rough wall side. The effect of rib spacing on fluid flow is trivial, and the interface slip velocity and length are relatively stable.

非Newton流体的物质点法模拟研究

Simulation of the non-Newtonian fluid flow is an interesting problem for engineers. As a relatively new particle-based method, the material point method (MPM), combining the advantages of both the Lagrangian algorithm and the Eulerian algorithm, has been widely and effectively used to solve complex engineering problems. The plane Poiseuille flow and Couette flow of the shear thickening and shear thinning cross fluid and power-law fluid were studied with the artificial state equations for the MPM. The results show that, the simulation with the MPM for the Newtonian fluid is in good agreement with the theoretical solution and the MPM simulates the shear thinning and shearing thickening of the non-Newtonian fluid exactly. The results confirm the applicability of the MPM for simulation of the non-Newtonian fluid flow and expand the application field of the MPM.

Experimental observation of heat transfer characteristics in turbulent Couette-Poiseuille flows

Turbulent Couette-Poiseuille flows between horizontal plates heated from below are investigated experimentally at low bulk Reynolds number Reb=1500 and low bulk Richardson number Ri=0.001 using stereo PIV, thermocouple, heat flux sensor and hot-wire thermometer. In the experimental apparatus the flow is driven by a moving plate and a blower. The lower hot plate (seamless belt) moves at several values of speed while the upper cold plate is at rest, and a bulk mean velocity is kept constant. It is found that heat transfer exhibits a local maximum at the lower plate speed for which a wall shear rate is null. In this specific condition turbulence decays in the vicinity of the lower hot plate so that vortical structures stemming from the upper cold plate may attain to the vicinity of the lower plate to carry low-temperature fluids, enhancing heat transfer. In the experiment, this phenomenon is observed by intermittent low-temperature fluctuation in the vicinity of the lower plate.

Dissimilarity between heat and momentum transfer in turbulent plane Couette-Poiseuille flow

Dissimilarity between heat and momentum transfer in turbulent plane Couette-Poiseuille flow

Amplitude–Dependent Three–Dimensional Neutral Modes in Plane Poiseuille–Couette Flow at Large Reynolds Number

Amplitude–Dependent Three–Dimensional Neutral Modes in Plane Poiseuille–Couette Flow at Large Reynolds Number

Аналитическое решение задачи двумерного слоистого напорного течения в прямоугольном канале

Следуя тенденциям и факторам инновационного развития зеленых технологий в пищевой промышленности для эффективной модернизации технологических процессов необходимо более широко использовать теоретический анализ процессов пищевой промышленности. Эксплуатация шнековых экструдеров показывает, что для эффективного отжима растительного масла необходимо, чтобы трение материала по внутренней поверхности корпуса было больше трения его по шнеку. В противном случае материал будет вращаться вместе со шнеком, не продвигаясь в осевом направлении. Нагнетаемый материал оказывается заключенным между движущимися поверхностями (основание и боковые стенки шнекового канала) и неподвижной внутренней поверхностью корпуса. Для адекватного описания процесса экструдирования необходимо перейти к заданию градиента скорости сдвига на трех границах одновременно. Рассмотрено аналитическое решение течения Пуазейля − Куэтта для заданного градиента скорости сдвига на одной из границ прямоугольной области слоистого течения вязкой жидкости. Установлено, что геометрия профиля канала шнека оказывает существенное влияние на расходно-напорные характеристики двумерного потока преодолевающего гидравлическое сопротивление. Построены новые точные решения уравнений движения Навье − Стокса, описывающие двумерные слоистые течения Пуазейля − Куэтта. Рассмотрены граничные условия двух типов: задание градиента скорости сдвига на одной из границ и на трех границах одновременно. Установлено, что при задании градиента скорости сдвига задача является существенно двумерной: не существует линейного преобразования, позволяющего преобразовать исследуемые течения к одномерным. Полученное аналитическое решение задачи позволяет моделировать как безнапорное слоистое течение Куэтта, так и напорное течение Пуазейля с использованием общей математической зависимости для расчета расходно-напорных характеристик экструдеров с прямоугольным в сечении канала шнека в широком диапазоне геометрии витков, как в их поперечном сечении, так и по длине канала.

On the Criterion for Long Wave Stability of Shear Flows

The present paper deals with the stability problem of incompressible, inviscid and density stratified fluid in a channel with arbitrary cross section. For this problem we derive a criterion for long wave stability namely, if the wave number is less than or equal to a critical wave number $$k_{c}$$ then the disturbances is stable. The result is illustrated with plane Poiseuille flow and Couette flow basic flows. Furthermore, we have obtained an upper bound for the growth rate of an unstable mode, which is sharper than the known ones. Moreover, a parabolic instability region which does not depend on any condition and which intersect the known semielliptical instability region is derived under some conditions.

Direct numerical simulation of a turbulent Couette-Poiseuille flow with a rod-roughened wall

A direct numerical simulation of a fully developed turbulent Couette-Poiseuille flow with a rod-roughened wall is performed to investigate the impact of the surface roughness on the flow characteristics compared to the influence of the roughness on a turbulent Poiseuille flow. Transverse rods are periodically arranged on the bottom wall with a streamwise pitch of p = 8k. The roughness height is k = 0.12h, where h is the channel half-height. The mean velocity profile shows that the logarithmic layer of a turbulent Couette-Poiseuille flow is significantly shortened by surface roughness, although that of a turbulent Poiseuille flow with surface roughness is increased. In addition, the Reynolds stresses for the Couette-Poiseuille flow with rod roughness are decreased in the outer layer, contrary to the observation of a turbulent Poiseuille flow with rod roughness. The decomposition of the Reynolds stresses into small- and large-scale motions confirms that the large-scale features dominantly contribute to the decrease of the Reynolds stresses in the outer layer. Although a large-scale counter-rotating roll mode is observed through temporally averaged streamwise fluctuating structures, the roll mode for the Couette-Poiseuille flow over a rough wall is significantly inhibited by the surface roughness due to weakened high- and low-streaky patterns near the centerline. The energy spectrum of the streamwise velocity fluctuations shows that the surface roughness contributes mainly to organizing the entire flow field; thus, the large-scale features observed in a turbulent Couette-Poiseuille flow are significantly suppressed with little interaction between the inner and outer layers.

Limits of one dimensional modeling of rarefied Couette Poiseuille clearance flow in vacuum pumps

Clearance flows are the main loss mechanism in dry running positive displacement vacuum pumps. In order to calculate the operation of those pumps a detailed knowledge of the clearance mass flow rates is crucial. The dimensions of such pumps and the large pressure range of the operating points require a wide range of gas rarefaction to be taken into account. The clearance flow can be described by a combined Couette Poiseuille flow due to the pressure gradient between two chambers and the rotation of the rotary pistons. A clearance of variable cross section is investigated and in order to determine the mass flow rate, the DSMC (direct simulation Monte Carlo) method is used. Results in the slip and transition flow regime are compared to experimental findings and a good agreement can be found. In addition, a one dimensional theory is presented based on a linear superposition of Poiseuille and Couette flow rates. The aim of the present work is to determine the limits of the one dimensional theory concerning the geometry of such clearances. For this, the boundary conditions circumferential speed, inlet and outlet pressure are varied.

Entropy generation of magnetohydrodynamic electroosmotic flow in two-layer systems with a layer of non-conducting viscoelastic fluid

The entropy generation analysis is investigated in two-fluid dragging systems. The bottom layer fluid is considered as electrolyte solution affected by the applied magnetic field and the upper layer fluid is viewed as non-conducting viscoelastic Phan-Thien-Tanner (PTT) fluid. Under the combined influences of electric and magnetic fields, the upper layer non-conducting PTT fluid can be dragged by the bottom layer fluid due to the interfacial shear stress. Firstly, we obtain the analytical velocity expressions for both bottom layer and upper layer fluids under the unidirectional flow assumption. The bottom layer fluid velocity distribution shows a classical M-type velocity profile. The upper layer fluid flow can be viewed as the plate Couette flow or Couette-Poiseuille flow. Subsequently, the thermal transport characteristic and entropy generation analysis are discussed in the present two-fluid dragging system. The results show that magnetic field can enhance the local entropy generation rate, but viscoelastic physical parameter can restrain the local entropy generation rate. The present theoretical research can be used in the design of thermofluidic device. By manipulating the electric and magnetic fields strength and the ratio of fluid rheological properties, the fluid motion and heat transfer characteristics can be manoeuvred efficiently.

Monte Carlo simulation of nonlinear gravity driven Poiseuille–Couette flow in a dilute gas

Abstract Through the direct simulation Monte Carlo, the Boltzmann equation is solved numerically for dilute hard spheres gas between two infinite parallel plates in relative motion and at the same time the particles feel the action of a uniform body force along the same direction as the moving plate. The study is conducted on the effect of the external force on the nonlinear properties of the Poiseuille–Couette flow. We have been interested in the bulk properties, to inhibit the influence of finite-size effects, while ignoring linear effects like Knudsen boundary layer to investigate the generalised transport coefficients depending on the shear rate nonlinearly: the two nonlinear thermal conductivity function of normal heat flux and parallel one, the viscosity function, the tangential friction function, and the thermal curvature. The results indicate that the effect of the external force is significant on the nonlinear functions, where the viscosity function and normal thermal conductivity are increasing functions of this field.

Direct numerical simulation of a turbulent Couette–Poiseuille flow: Turbulent statistics

The direct numerical simulation of a fully developed turbulent Couette–Poiseuille flow is performed to investigate the modification of turbulent statistics on the bottom and top walls compared to those in a pure Poiseuille flow. The streamwise mean velocity profile shows that an extended logarithmic layer for a Couette–Poiseuille flow is developed from each wall to the centerline. In addition, the turbulent intensities and Reynolds shear stress on the bottom wall are found to be larger than those in the Poiseuille flow, whereas it is reversed on the top wall due to reduction of the velocity shear. The quadrant analysis of the Reynolds shear stress reveals that large Q2 and Q4 event motions are continuously created throughout the entire flow near the centerline, leading to active momentum transport between the bottom and top walls for the C-type. Inspection of the pre-multiplied streamwise and spanwise energy spectra shows that distinct secondary outer peaks are created for all velocity components and a plateau, called the kx−1 region, is presented in the logarithmic region. Based on an analysis of the net force spectra, three spectral ranges in the wavelength space, corresponding to small- (λx/δ ≤ 1), large- (1 ≤ λx/δ ≤ 10) and very-large-scale (λx/δ ≥ 10) motions for a Couette–Poiseuille flow, are proposed, and very-large-scale structures are highly energetic and contribute more than half of the streamwise turbulent kinetic energy and Reynolds shear stress, where λx is the streamwise wavelength and δ is the channel half height.

Taylor–Couette–Poiseuille flow with a weakly permeable inner cylinder: absolute instabilities and selection of global modes

Variations in the local stability of the flow in a Taylor–Couette cell can be imposed by adding an axial Poiseuille flow and a radial flow associated with one or both of the cylinders being permeable. At a given rotation rate of the inner cylinder, this results in adjacent regions of the flow that can be simultaneously stable, convectively unstable, and absolutely unstable, making this system fit for studying global modes of instability. To this end, building on the existing stability analysis in absolute modes developing over axially invariant base flows, we consider the case of axially varying base flows in systems for which the outer cylinder is impermeable, and the inner cylinder is a weakly permeable membrane through which the radial flow is governed by Darcy’s law. The frameworks of linear and nonlinear global modes are used to describe the instabilities and assess the results of direct numerical simulations using a dedicated pseudospectral method. Three different axially evolving set-ups are considered. In the first, fluid injection occurs along the full inner cylinder. In the second, fluid extraction occurs along the full inner cylinder. Besides its fundamental interest, this set-up is relevant to filtration devices. In the third, fluid flux through the inner cylinder evolves from extraction to injection as cross-flow reversal occurs. In agreement with the global mode analyses, the numerical simulations develop centrifugal instabilities above the predicted critical rotation rates and downstream of the predicted axial locations. The global mode analyses do not fully explain, however, that the instabilities observed in the numerical simulations take the form of axial stacks of wavepackets characterized by jumps of the temporal frequency.

Electroosmotic Flow of MHD Power Law Al2O3-PVC Nanouid in a Horizontal Channel: Couette-Poiseuille Flow Model

The current manuscript is reported about the electro-osmotic Couette-Poiseuille flow of power law Al2O3-PVC nanofluid through a channel, in which upper wall is moving with constant velocity. The influences of magnetic field, mixed convection, joule heating, and viscous dissipation are also incorporated. The flow is generated because of constant pressure gradient in axial direction. The resulting flow problem is coupled nonlinear ordinary differential equations, which are at first modeled and then transform into dimensionless form through appropriate transformation. Analytical solution of the governing is carried out. The impact of modified Brinkman number, modified Magnetic field, electro-osmotic parameters on velocity and temperature are examined graphically. From the results, it is concluded that the Skin friction at moving isolated wall decreases with the increase of electro-osmotic parameter and reverse behavior for Nusselt number at heated stationary wall occur.

A stable numerical implementation of integral viscoelastic models in the OpenFOAM®computational library

This work presents the implementation and verification of a new solver in the OpenFOAM®open source computational library. The new solver allows the numerical solution of the integral viscoelastic constitutive equations, and their coupling with the continuity and momentum equations. This solver is also more stable when compared to the previous implementation of the group, which was accomplished through the addition of diffusive terms to both sides of the momentum equation, that are discretized using different schemes. The calculation of the Finger tensor follows the ideas presented in the method of deformation fields Peters et al. (2000) together with the modifications proposed by Tomé et al. (2008). We also propose a new approach to optimize the number and distribution of discretization points to be used in the time integration of the constitutive model, and the results obtained are discussed in the light of the recent work by Bollada and Phillips (2009). The solver is verified with three case studies: the steady Poiseuille and transient Couette flows, for a UCM fluid, and the steady 4:1 contraction flow, both for the UCM and K-BKZ fluids.