Shear Flow Of Fluid Research Articles

A comprehensive assessment of the Reynolds Analogy in predicting heat transfer in turbulent wall-bounded shear flows

Heat transfer modeling plays a major role in design and optimization of modern and efficient thermal-fluid systems. However, currently available models suffer from a fundamental shortcoming: their development is based on the general notion that accurate prediction of the flow field will guarantee an appropriate prediction of the thermal field, known as the Reynolds Analogy. This investigation presents a comprehensive assessment of the capability of the Reynolds Analogy in predicting turbulent heat transfer when applied to turbulent shear flows of fluids with different Prandtl numbers. It turns out that the Reynolds Analogy is able to provide acceptable results for first order statistics only when fluids with Prandtl number close to unity are considered. Further, it is shown that unsteady simulations could provide acceptable results on second order statistics concerning fluids with different Prandtl numbers, if appropriate grid design/resolution is provided that allows to resolve essential dynamics of the thermal field. However, accurate prediction of higher order statistics close to solid surface requires more advanced heat transfer models that can provide accurate information on thermal time scales, in case the grid is too coarse to support accurate resolving of the essential thermal dynamics in these regions.

Entropy Generation Assessment for Wall-Bounded Turbulent Shear Flows Based on Reynolds Analogy Assumptions

Heat transfer modeling plays a major role in design and optimization of modern and efficient thermal-fluid systems. Further, turbulent flows are thermodynamic processes, and thus, the second law of thermodynamics can be used for critical evaluations of such heat transfer models. However, currently available heat transfer models suffer from a fundamental shortcoming: their development is based on the general notion that accurate prediction of the flow field will guarantee an appropriate prediction of the thermal field, known as the. In this work, an assessment of the capability of the in predicting turbulent heat transfer when applied to shear flows of fluids of different Prandtl numbers will be given. Towards this, a detailed analysis of the predictive capabilities of the concerning entropy generation is presented for steady and unsteady state simulations. It turns out that the provides acceptable results only for mean entropy generation, while fails to predict entropy generation at small/sub-grid scales.

Numerical Modelling of the Dynamics of a Cylindrical Turbulent Patch in a Longitudinal Shear Flow

Based on a modified two-equation model of turbulence, the numerical model of the dynamics of a cylindrical localized zone of turbulent mixing in a longitudinal uniform shear flow of homogeneous fluid is constructed. The results of the numerical experiments demonstrate significant turbulent energy generation caused by the effect of the shear flow. The question of the similarity of the flow with respect to the shear Froude number is considered. The results of the numerical experiments show the similarity of the flow for large values of this parameter, which correspond to small values of the velocity gradients of the shear flow.

Migration of spherical particles in a confined shear flow of Giesekus fluid

The lateral migration of a spherical particle in a sheared Giesekus fluid is numerically studied by the direct-forcing fictitious domain method. The model is first validated by comparing the simulation results with the available data in the literature. Effects of the viscosity ratio, shear thinning, Weissenberg number, and wall confinement on the particle migration are examined. Results show that the particle migrates toward the wall, irrespective of whether the fluid is shear thinning. The wall confinement, shear thinning, and high Weissenberg number could respectively facilitate the particle lateral migration. While the effect of viscosity ratio on the particle migration is not monotonic, a separatrix value is found which divides the viscosity ratio into two ranges. Moreover, effects of rheological properties on the particle angular velocity and its variation throughout the migration pathway are also explored, and the position where the angular velocity starts to decrease is affected by fluid rheological properties.

Radial distribution function of Lennard-Jones fluids in shear flows from intermediate asymptotics.

Determining the microstructure of colloidal suspensions under shear flows has been a challenge for theoretical and computational methods due to the singularly perturbed boundary-layer nature of the problem. Previous approaches have been limited to the case of hard-sphere systems and suffer from various limitations in their applicability. We present an alternative analytic scheme based on intermediate asymptotics which solves the Smoluchowski diffusion-convection equation including both intermolecular and hydrodynamic interactions. The method is able to recover previous results for the hard-sphere fluid and to predict the radial distribution function (rdf) of attractive fluids such as the Lennard-Jones (LJ) fluid. In particular, a new depletion effect is predicted in the rdf of the LJ fluid under shear. This method can be used for the theoretical modeling and understanding of real fluids subjected to flow, with applications ranging from chemical systems to colloids, rheology, plasmas, and atmospherical science.

A shear model for unsteady state for viscoelastic fluids, based on the correction of torque transfer lag

In this study, a mathematical model for the magnetic coupling transmission process was set up to solve the problem of torque transfer lag in magnetic-coupled rheological testing systems. This model was developed on the basis of torque balance in a magnetic coupling rotatory rheometer test system, which considered friction loss for the jewel bearing, as well as the inertia of both the motor and fixture. The reliability of the mathematical model was fully confirmed by a constant stress no-load start-up experiment conducted using a HAAKE-MARS60 high pressure rheometer. Based on the mathematical model for simultaneous magnetic coupling transmission and a constitutive equation of viscoelastic thixotropic fluid, a model, put forward for the unsteady mathematical shear of viscoelastic fluids, was designed to correct torque transfer lag. Changes in real stress and strain on the rotator surface were then obtained under the initial unsteady-state shear phase of the rheometer. The results showed that magnetic coupling intensifies the unsteady shear flow of fluids. The bigger the elastic modulus and viscosity of the material, the larger the deviation of test results between rotational rheometers and magnetic couple rheometers will be. The results obtained in this study could facilitate a better understanding of the rheological properties of materials in the transient start-up process under high pressure conditions in later research.

Drag and Lift Forces Acting on a Sphere in Shear Flow of Power-Law Fluid

Laminar flow of a power-law fluid over a sphere is considered for unbounded shear flow. The Navier–Stokes equations with power-law viscosity are solved numerically using an in-house developed CFD package. Vorticities structures downstream of particle are suppressed for powerlaw fluid. The shear rate influence on drag force is negligible for power index close to unit, and the drag force appreciably decreases with falling power index. For small Reynolds numbers, the lift force coefficient monotonically decreases against the power index and exhibits an opposite behavior for moderate values of Reynolds numbers. The results of the parametric studies are used to derive correlations for the drag force and to detect the hydrodynamic differences from uniform flow. The investigation parameters varied within the following ranges: power-law index 0.3 ≤ n ≤ 1, Reynolds number 0 < Re ≤ 150, and dimensionless shear rate 0.05 ≤ s ≤ 0.4.

Pair-particle trajectories in a shear flow of a Bingham fluid

We study numerically the pair trajectories of rigid circular particles in a two dimensional inertialess simple shear flow of a (Binghamian) yield stress fluid. We use a Lagrange multiplier based fictitious domain method, following Glowinski et al. [26, 28, 29], for solving the problem. Contacts between the particles at a finite interparticle distance interpreted as a roughness are taken into account with the da Cunha and Hinch [12] model. Another model, introduced by Glowinski et al. [27], is shown to provide similar results in the limit of infinite contact stiffness. Due to the nonlinear behavior of the suspending fluid, it is found that the trajectories of the particles depend on the shear rate, the relevant dimensionless parameter being here the Bingham number, which compares plastic forces to viscous forces. In absence of interparticle contacts, fore-aft symmetry is observed in all cases; however, the particles are found to come closer to each other as the Bingham number is increased: the plastic behavior of the suspending fluid decreases the range of hydrodynamic interactions. As contacts are introduced, fore-aft asymmetry is observed. Plastic effects are found to enhance surface roughness effects: contacts between particles occur for smaller surface roughness at large Bn. Moreover, the magnitude of the asymmetry is increased as the Bingham number is increased. These observations may explain why the microstructure of suspensions of particles in a yield stress fluid is shear-rate-dependent [45] leading to a complex nonlinear macroscopic behavior.

A 3D DLM/FD method for simulating the motion of spheres in a bounded shear flow of Oldroyd-B fluids

We present a novel distributed Lagrange multiplier/fictitious domain (DLM/FD) method for simulating fluid-particle interaction in Oldroyd-B fluids under creeping conditions. The results concerning two ball interaction in a three dimensional (3D) bounded shear flow are obtained for Weissenberg numbers up to 1. The pass and return trajectories of the two ball mass centers are similar to those in a Newtonian fluid; but they lose the symmetry due to the effect of elastic force arising from viscoelastic fluids. A tumbling chain of two balls (a dipole) may occur, depending on the value of the Weissenberg number and the initial vertical displacement of the ball mass center to the middle plane between two walls.

Newtonian, power law, and infinite shear flow characteristics of concentrated slurries using percolation theory concepts

There is a strong interest today in concentrated particulate-filled dispersion and slurries in both polymeric and Newtonian fluids. This paper reviews and extends theoretical approaches using percolation theory concepts to characterize the rheological behavior of fluids filled with particulate solids. First, a previously proposed limiting, zero shear viscosity model based on percolation theory concepts is reviewed. This model has been primarily tested with rigid fillers in a Newtonian carrier and polymeric fluids. Second, all Newtonian fluid-based slurries that have a high concentration of filler become pseudoplastic, shear-thinning slurries at some threshold shear rate. A new theory is reviewed and new data are evaluated that correlate the power law constant, n, to cluster formation of the fillers suspended in the fluids in shear flow. Slurry systems reported here cover a size range from 58 nm to 200 μm. Third, this cluster percolation-based rheological analysis is then extended to a newly proposed model for the calculation of the ratio of infinite shear, η∞, to the zero shear viscosity, η0. Using literature data, it is demonstrated that measurements of the viscosity ratio, η∞/η0, correlate with the power law through the use of an energy dissipation-based model for Bingham rheological fluids.

Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study.

Hydrodynamic fluctuations in simple fluids under shear flow are demonstrated to be spatially correlated, in contrast to the fluctuations at equilibrium, using mesoscopic hydrodynamic simulations. The simulation results for the equal-time hydrodynamic correlations in a multiparticle collision dynamics (MPC) fluid in shear flow are compared with the explicit expressions obtained from fluctuating hydrodynamics calculations. For large wave vectors k, the nonequilibrium contributions to transverse and longitudinal velocity correlations decay as k^{-4} for wave vectors along the flow direction and as k^{-2} for the off-flow directions. For small wave vectors, a crossover to a slower decay occurs, indicating long-range correlations in real space. The coupling between the transverse velocity components, which vanishes at equilibrium, also exhibits a k^{-2} dependence on the wave vector. In addition, we observe a quadratic dependency on the shear rate of the nonequilibrium contribution to pressure.

Influence of particulate thermophoresis on convection heat and mass transfer in a slip flow of a viscoelasticity-based micropolar fluid

We focus on the intriguing particulate thermophoresis characterized by multi-dependent Soret number in a shear flow of a viscoelasticity-based micropolar fluid (VMF) over a stretching sheet in the existence of the slip condition. The multi-dependent Soret number involving the temperature field and micro-particle size factors is introduced to analyze the critical role of the particulate thermophoresis on the temperature and concentration profiles of a VMF. Such procedure being significant for convection heat and mass transfer has never yet been considered in the transport system of such non-Newtonian fluids. Theoretically, we find the larger particles more susceptible to the actuation of temperature gradient. The local Sherwood number increases linearly with the bulk temperature difference, while the thickness of the concentration boundary layer are decreased. We also find that the flow relaxation and slip behavior can give rise to the obvious reduction of local Nusselt number and Sherwood number in different ways. Moreover, these two behaviors are found to be inherently divergent in varying the local skin friction. A power law expression can fit well the dependence of the local skin friction on the slip parameter. The practical routes of heat and mass transfer in the complex fluids will be implemented by tuning the various physical parameters presented in this paper.

On a criterion of incipient motion and entrainment into suspension of a particle from cuttings bed in shear flow of non-Newtonian fluid

Solids transport is a major issue in high angle wells. Bed-load forms by sediment while transport and accompanied by intermittent contact with stream-bed by rolling, sliding and bouncing. The study presents the results of a numerical simulation of a laminar steady-state flow around a particle at rest and in free motion in a shear flow of Herschel–Bulkley fluid. The simulation was performed using the OpenFOAM open-source CFD package. A criterion for particle incipient motion and entrainment into suspension from cuttings bed (Shields criteria) based on forces and torques balance is discussed. Deflection of the fluid parameters from the ones of Newtonian fluid leads to decreasing of the drag and lift forces and the hydrodynamic moment. Thus, the critical shear stress (Shields parameter) for the considered non-Newtonian fluid must be greater than the one for a Newtonian fluid.

Sedimentation of particles in shear flows of viscoelastic fluids with fibers

We study the effect of fiber additives on rheology and sedimentation of particle suspensions in a base viscoelastic suspending fluid in the case when the suspension is subjected to shear flow. We found experimentally that fiber additives (3–6 mm in length and 8–12 μm in diameter at a mass fraction of 0–0.4%) increase the suspension viscosity and retard the particle sedimentation significantly. At the same mass concentration, long and thin fibers reduce the sedimentation velocity and increase the viscosity to a much greater extent than short and thick fibers. We revealed that both rheology and sedimentation are controlled by a single conformational parameter (overlap parameter) defined as the number of fibers per unit volume multiplied by fiber length cubed.

Apparent slip of shear thinning fluid in a microchannel with a superhydrophobic wall.

The peculiarities of simple shear flow of shear thinning fluids over a superhydrophobic wall consisting of a set of parallel gas-filled grooves and solid stripes (domains with slip and stick boundary conditions) are studied numerically. The Carreau-Yasuda model is used to provide further insight into the problem of the slip behavior of non-Newtonian fluids having a decreasing viscosity with a shear rate increase. This feature is demonstrated to cause a nonlinear velocity profile leading to the apparent slip. The corresponding transverse and longitudinal apparent slip lengths of a striped texture are found to be noticeably larger than the respective effective slip lengths of Newtonian liquids in microchannels of various thicknesses and surface fractions of the slip domains. The viscosity distribution of the shear thinning fluid over the superhydrophobic wall is carefully investigated to describe the mechanism of the apparent slip. Nonmonotonic behavior of the apparent slip length as a function of the applied shear rate is revealed. This important property of shear thinning fluids is considered to be sensitive to the steepness of the viscosity flow curve, thus providing a way to decrease considerably the flow resistance in microchannels.

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle.

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed.This article is part of the themed issue 'Horizons of cybernetical physics'.

Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow

Stratified shear flows occur in many geophysical contexts, from oceanic overflows and river estuaries to wind-driven thermocline layers. We explore a turbulent wall-bounded shear flow of lighter miscible fluid into a quiescent fluid of higher density with a range of Richardson numbers$0.05\lesssim Ri\lesssim 1$. In order to find a stability parameter that allows close comparison with linear theory and with idealized experiments and numerics, we investigate different definitions of$Ri$. We find that a gradient Richardson number defined on fluid interface sections where there is no overturning at or adjacent to the maximum density gradient position provides an excellent stability parameter, which captures the Miles–Howard linear stability criterion. For small$Ri$the flow exhibits robust Kelvin–Helmholtz instability, whereas for larger$Ri$interfacial overturning is more intermittent with less frequent Kelvin–Helmholtz events and emerging Holmboe wave instability consistent with a thicker velocity layer compared with the density layer. We compute the perturbed fraction of interface as a quantitative measure of the flow intermittency, which is approximately 1 for the smallest$Ri$but decreases rapidly as$Ri$increases, consistent with linear theory. For the perturbed regions, we use the Thorpe scale to characterize the overturning properties of these flows. The probability distribution of the non-zero Thorpe length yields a universal exponential form, suggesting that much of the overturning results from increasingly intermittent Kelvin–Helmholtz instability events. The distribution of turbulent kinetic energy, conditioned on the intermittency fraction, has a similar form, suggesting an explanation for the universal scaling collapse of the Thorpe length distribution.

異方性流体のせん断流れの分子動力学シミュレーション

異方性流体のせん断流れの分子動力学シミュレーション

Lift and Drag Forces for a Sphere on a Flat Wall in Non-Newtonian Shear Flow

Parametrical study of perfect steady rolling and steady state freely motion of spherical particle on the wall in shear flow of non-Newtonian fluid was carried out. In the case of perfect rolling the jumps of forces acting on a sphere in the moment of changing particle velocity from zero to positive were observed. Non-Newtonian properties of fluid lead to decreasing of drag force coefficient for low particle's velocity and to opposite effect for high velocity relative to Newtonian fluid. There is no such significant effect for a lift force coefficient. Steady state particle's velocity (Fd (Vpss )=0) increases for non-Newtonian fluid for both considered types of motion. Steady state particle's velocity and lift force coefficient are lower for the case of freely particle motion. Steady state rotational velocity decreases for non-Newtonian fluid.

Dynamic settling of particles in shear flows of shear-thinning fluids

Dynamic settling is the phenomenon whereby a relatively dense particle settles through a sheared flow of a non-Newtonian fluid at a speed that depends on the shear rate of the background flow. This means that due to the nonlinear rheology, the settling velocity may vary spatially and temporally as the background shear rate of the suspending fluid varies, an effect which does not occur in Newtonian fluids. In this contribution, the consequences of this dependency are explored for a dilute suspension of particles released uniformly from a source in a sustained and externally-driven flow of shear-thinning fluid. It is shown theoretically that the concentration field does not remain uniform, but evolves downstream, allowing calculation of the runout length, settling times and distribution of the deposited particles. Flows with a velocity maximum are demonstrated to affect the concentration field very strongly as they develop a ‘kinematic barrier’ over which settling times are considerably lengthened. Flows with bidisperse suspensions are shown to produce deposits that vary non-monotonically in thickness and composition with distance downstream, an effect which is solely due to dynamic settling. Finally flows of viscoplastic fluids which exhibit yielded and unyielded regions may accentuate the role and effects of the kinematic barrier to settling.