Shear Flow Model Research Articles

Numerical study on the effect of gravity levels on apparent viscosity of bubbly suspensions

Based on the Couette parallel plate shear flow model, it was investigated on the effects of the gravity level and the liquid-gas viscosity ratio (λ) on the bubble deformation and the apparent viscosity of the bubbly suspension with the volume of fluid method. The results show that, for a given bubbly suspension, the effect of gravity on the bubble deformation and the relative viscosity is great when the shear action is relatively weak. However, the gravity effect can be neglected when the shear action is relatively strong. Additionally, when the gravity level and the shear action are definite, for the bubbly suspension with a small viscosity ratio (i.e., the influence of gravity is far greater than the viscous force), the relative viscosity is related to gravity because gravity has a great effect on the bubble deformation. In this situation, the bubble is stretched in the direction perpendicular to gravity, leading to the decrease of the obstruction of the bubble to the flow and the increase of the area of the free slip surface. Therefore, the relative viscosity is relatively small. On the contrary, when the viscosity ratio is large (i.e., the influence of the viscous force is much larger than that of gravity), the relative viscosity is less affected by gravity due to the weak effect of gravity on the bubble deformation. The large viscous force decreases the bubble deformation, leading to the increase of the obstruction of the bubble to the flow and the decrease of the area of the free slip surface. Thus the relative viscosity is relatively larger than that when the liquid-gas viscosity ratio is small. When the liquid-gas viscosity ratio is larger than 103, the bubble deformation is dominated by the viscous force, and the effect of gravity on the bubble deformation is negligible. Correspondingly, the effect of gravity on the relative viscosity is also negligible when λ ≥ 103.

Molecular Dynamics Study of Lubrication Model of Quasi-steady Shear Flow of Poly-alpha-olefin Liquid

Molecular Dynamics Study of Lubrication Model of Quasi-steady Shear Flow of Poly-alpha-olefin Liquid

Finding Extremal Periodic Orbits with Polynomial Optimization, with Application to a Nine-Mode Model of Shear Flow

Tobasco et al. [Physics Letters A, 382:382-386, 2018; see https://doi.org/10.1016/j.physleta.2017.12.023] recently suggested that trajectories of ODE systems that optimize the infinite-time average of a certain observable can be localized using sublevel sets of a function that arise when bounding such averages using so-called auxiliary functions. In this paper we demonstrate that this idea is viable and allows for the computation of extremal unstable periodic orbits (UPOs) for polynomial ODE systems. First, we prove that polynomial optimization is guaranteed to produce auxiliary functions that yield near-sharp bounds on time averages, which is required in order to localize the extremal orbit accurately. Second, we show that points inside the relevant sublevel sets can be computed efficiently through direct nonlinear optimization. Such points provide good initial conditions for UPO computations. As a proof of concept, we then combine these methods with a single-shooting Newton-Raphson algorithm to study extremal UPOs for a nine-dimensional model of sinusoidally forced shear flow. We discover three previously unknown families of UPOs, one of which simultaneously minimizes the mean energy dissipation rate and maximizes the mean perturbation energy relative to the laminar state for Reynolds numbers approximately between 81.24 and 125.

Solitary waves, breathers, and rogue waves modulated by long waves for a model of a baroclinic shear flow.

Investigated in this paper is a quasigeostrophic two-layer model for the wave packets in a marginally stable or unstable baroclinic shear flow. We find that the wave packets can be modulated by certain long waves, resulting in different behaviors from those in the existing literature. Via the bilinear method, we construct the modulated Nth-order (N=1,2,...) solitary waves, breathers, and rogue waves for the wave-packet equations. Based on the modulation effects of the long waves, the solitary waves are classified into three types, i.e., Type-I, Type-II, and Type-III solitary waves. Type-I solitary waves, without the modulations, are the bell shaped and propagate with constant velocities; Type-II solitary waves, with the weak modulations, are shape changing within a short time and subsequently return to the bell-shaped state; and Type-III solitary waves, with the strong modulations, show not only the variations of shapes but also the appearances, splits, combinations, and disappearances of certain bulges in the evolution. For the interaction between the two unmodulated solitary waves, two Type-I solitary waves can bring about the oscillations in the interaction zone when they possess different velocities, and bring into being the bound-state, oscillation-state, and bi-oscillation-state solitary waves when they possess the same velocity. For the two interactive modulated solitary waves, bound-state, oscillation-state, and bi-oscillation-state solitary waves with the short-time variations of shapes or appearances of bulges can occur. Due to the modulations of the long waves, breathers and rogue waves are distorted and stretched, mainly in two aspects: one is the evolution trajectories for the breathers; the other is the shape variations for each element of the breathers and rogue waves. Numbers of the peaks and valleys for the rogue waves are adjustable via the modulations. In addition, modulated breathers and rogue waves can degenerate into the M- or W-shaped or multipeak solitary waves under certain conditions.

A framework for input–output analysis of wall-bounded shear flows

We propose a new framework to evaluate input–output amplification properties of nonlinear models of wall-bounded shear flows, subject to both square integrable and persistent disturbances. We focus on flows that are spatially invariant in one direction and whose base flow can be described by a polynomial, e.g. streamwise-constant channel, Couette and pipe flows. Our methodology is based on the notion of dissipation inequalities in control theory and provides a single unified approach for examining flow properties such as energy growth, worst-case disturbance amplification and stability to persistent excitations (i.e. input-to-state stability). It also enables direct analysis of the nonlinear partial differential equation rather than of a discretized form of the equations, thereby removing the possibility of truncation errors. We demonstrate how to numerically compute the input–output properties of the flow as the solution of a (convex) optimization problem. We apply our theoretical and computational tools to plane Couette, channel and pipe flows. Our results demonstrate that the proposed framework leads to results that are consistent with theoretical and experimental amplification scalings obtained in the literature.

Hyperbolic model for free surface shallow water flows with effects of dispersion, vorticity and topography

We derive a hyperbolic system of equations approximating the two-layer dispersive shallow water model for shear flows recently proposed by Gavrilyuk et al. (2016). The use of this system for modelling the evolution of surface waves makes it possible to avoid the major numerical challenges in solving dispersive shallow water equations, which are connected with the resolution of an elliptic problem at each time instant and realization of non-reflecting conditions at the boundary of the calculation domain. It also allows one to reduce the computation time. The velocities of the characteristics of the obtained model are determined and the linear analysis is performed. Stationary solutions of the model are constructed and studied. Numerical solutions of the hyperbolic system are compared with solutions of the original dispersive model. It is shown that they almost coincide for large time intervals. The system obtained is applied to study non-stationary undular bores produced after interaction of a uniform flow with an immobile wall, non-hydrostatic shear flows over a local obstacle and the evolution of breaking solitary wave on a sloping beach.

Blood-Contacting Biomaterials: In Vitro Evaluation of the Hemocompatibility.

Hemocompatibility of blood-contacting biomaterials is one of the most important criteria for their successful in vivo applicability. Thus, extensive in vitro analyses according to ISO 10993-4 are required prior to clinical applications. In this review, we summarize essential aspects regarding the evaluation of the hemocompatibility of biomaterials and the required in vitro analyses for determining the blood compatibility. Static, agitated, or shear flow models are used to perform hemocompatibility studies. Before and after the incubation of the test material with fresh human blood, hemolysis, cell counts, and the activation of platelets, leukocytes, coagulation and complement system are analyzed. Furthermore, the surface of biomaterials are evaluated concerning attachment of blood cells, adsorption of proteins, and generation of thrombus and fibrin networks.

Padé approximant for normal stress differences in large-amplitude oscillatory shear flow

Analytical solutions for the normal stress differences in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the inexact form of the first few terms of a series expansion in the shear rate amplitude. Here, we improve the accuracy of these truncated expansions by replacing them with rational functions called Padé approximants. The recent advent of exact solutions in LAOS presents an opportunity to identify accurate and useful Padé approximants. For this identification, we replace the truncated expansion for the corotational Jeffreys fluid with its Padé approximants for the normal stress differences. We uncover the most accurate and useful approximant, the [3,4] approximant, and then test its accuracy against the exact solution [C. Saengow and A. J. Giacomin, “Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow,” Phys. Fluids 29, 121601 (2017)]. We use Ewoldt grids to show the stunning accuracy of our [3,4] approximant in LAOS. We quantify this accuracy with an objective function and then map it onto the Pipkin space. Our two applications illustrate how to use our new approximant reliably. For this, we use the Spriggs relations to generalize our best approximant to multimode, and then, we compare with measurements on molten high-density polyethylene and on dissolved polyisobutylene in isobutylene oligomer.

Large eddy simulations of wall‐bounded flows using a simplified immersed boundary method and high‐order compact schemes

SummaryThis paper presents a solution algorithm based on an immersed boundary (IB) method that can be easily implemented in high‐order codes for incompressible flows. The time integration is performed using a predictor‐corrector approach, and the projection method is used for pressure‐velocity coupling. Spatial discretization is based on compact difference schemes and is performed on half‐staggered meshes. A basic algorithm for body‐fitted meshes using the aforementioned solution method was developed by A. Tyliszczak (see article “A high‐order compact difference algorithm for half‐staggered grids for laminar and turbulent incompressible flows” in Journal of Computational Physics) and proved to be very accurate. In this paper, the formulated algorithm is adapted for use with the IB method in the framework of large eddy simulations. The IB method is implemented using its simplified variant without the interpolation (stepwise approach). The computations are performed for a laminar flow around a 2D cylinder, a turbulent flow in a channel with a wavy wall, and around a sphere. Comparisons with literature data confirm that the proposed method can be successfully applied for complex flow problems. The results are verified using the classical approach with body‐fitted meshes and show very good agreement both in laminar and turbulent regimes. The mean (velocity and turbulent kinetic energy profiles and drag coefficients) and time‐dependent (Strouhal number based on the drag coefficient) quantities are analyzed, and they agree well with reference solutions. Two subfilter models are compared, ie, the model of Vreman (see article “An eddy‐viscosity subgrid‐scale model for turbulent shear flow: algebraic theory and applications” in Physics and Fluids) and σ model (Nicoud et al, see article “Using singular values to build a subgrid‐scale model for large eddy simulations” in Physics and Fluids). The tests did not reveal evident advantages of any of these models, and from the point of view of solution accuracy, the quality of the computational meshes turned out to be much more important than the subfilter modeling.

A constitutive model for simple shear of dense frictional suspensions

Discrete particle simulations are used to study the shear rheology of dense, stabilized, frictional particulate suspensions in a viscous liquid, toward development of a constitutive model for steady shear flows at arbitrary stress. These suspensions undergo increasingly strong continuous shear thickening (CST) as the solid volume fraction [Formula: see text] increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed in a range of [Formula: see text]. When studied at controlled stress, the DST behavior is associated with nonmonotonic flow curves of the steady-state shear rate as a function of stress. Recent studies have related shear thickening to a transition from mostly lubricated to predominantly frictional contacts with the increase in stress. In this study, the behavior is simulated over wide ranges of concentration, dimensionless shear stress, and coefficient of interparticle friction. The simulation data have been used to populate the lubricated-to-frictional rheology model of Wyart and Cates [Phys. Rev. Lett. 112, 098302 (2014)], which is based on the concept of two viscosity divergences or “jamming” points at volume fraction [Formula: see text] (random close packing) for the low-stress lubricated state, and at [Formula: see text] for any nonzero μ in the frictional state; a generalization provides the normal stress response as well as the shear stress, allowing a description of the full stress tensor. A flow state map of this material is developed based on the simulation results. At low stress and/or intermediate [Formula: see text], the system exhibits CST, and DST appear at volume fractions below but approaching the frictional jamming point. For [Formula: see text], DST is associated with a material transition from one stress-independent rheology to another, while for [Formula: see text], the system exhibits DST to shear jamming as the stress increases.

Model-data comparison of high frequency compressional wave attenuation in water-saturated granular medium with bimodal grain size distribution

Several acoustic models, such as the poro-elastic model, visco-elastic model, and multiple scattering model, have been used for describing the dispersion relation in a porous granular medium. However, these models are based on continuum or scattering theory, and therefore cannot explain the broadband measurements in cases where scattering and non-scattering losses co-exist. Additionally, since the models assume that the porous granular medium consists of grains of identical size (unimodal size distribution), the models does not account for the behavior of wave dispersion in a medium that has a distribution of differing grain sizes. As an alternative approach, this study proposes a new broadband attenuation model that describes the high frequency dispersion relation for the p-wave in the case of elastic grain scatterers existing in the background fluid medium. The broadband model combines the Biot-Stoll plus grain contact squirt and shear flow (BICSQS) model and the quasicrystalline approximation (QCA) multiple scattering model. Additionally, distribution of grain size effect is examined rudimentarily through consideration of bimodal grain size distribution. Through the quantitative analysis of the broadband model and measured data, it is shown that the model can explain the attenuation dependencies of frequency and grain size distribution for a water-saturated granular medium in the frequency range from 350kHz to 1.1MHz. This study can be applied to the high frequency acoustic SONAR modeling and design in the water-saturated environment.

Mean velocity and suspended sediment concentration profile model of turbulent shear flow with probability density function

This work purposes a general mean velocity and a suspended sediment concentration (SSC) model to express distribution at every point of the cross section of turbulent shear flow by using a probability density function method. The probability density function method was used to describe the velocity and concentration profiles interacted on directly by fluid particles in the turbulent shear flow to solve turbulent flow and avoid different dynamical mechanics. The velocity profile model was obtained by solving for the profile integral with the product of the laminar velocity and probability density, through adopting an exponential probability density function to express probability distribution of velocity alteration of a fluid particle in turbulent shear flow. An SSC profile model was also created following a method similar to the above and based on the Schmidt diffusion equation. Different velocity and SSC profiles were created while changing the parameters of the models. The models were verified by comparing the calculated results with traditional models. It was shown that the probability density function model was superior to log-law in predicting stream-wise velocity profiles in coastal currents, and the probability density function SSC profile model was superior to the Rouse equation for predicting average SSC profiles in rivers and estuaries. Outlooks for precision investigation are stated at the end of this article.

Advection of nematic liquid crystals by chaotic flow

Consideration is given to the effects of inhomogeneous shear flow (both regular and chaotic) on nematic liquid crystals in a planar geometry. The Landau–de Gennes equation coupled to an externally prescribed flow field is the basis for the study: this is solved numerically in a periodic spatial domain. The focus is on a limiting case where the advection is passive, such that variations in the liquid-crystal properties do not feed back into the equation for the fluid velocity. The main tool for analyzing the results (both with and without flow) is the identification of the fixed points of the dynamical equations without flow, which are relevant (to varying degrees) when flow is introduced. The fixed points are classified as stable/unstable and further as either uniaxial or biaxial. Various models of passive shear flow are investigated. When tumbling is present, the flow is shown to have a strong effect on the liquid-crystal morphology; however, the main focus herein is on the case without tumbling. Accordingly, the main result of the work is that only the biaxial fixed point survives as a solution of the Q-tensor dynamics under the imposition of a general flow field. This is because the Q-tensor experiences not only transport due to advection but also co-rotation relative to the local vorticity field. A second result is that all families of fixed points survive for certain specific velocity fields, which we classify. We single out for close study those velocity fields for which the influence of co-rotation effectively vanishes along the Lagrangian trajectories of the imposed velocity field. In this scenario, the system exhibits coarsening arrest, whereby the liquid-crystal domains are “frozen in” to the flow structures, and the growth in their size is thus limited.

Modified kinetic theory applied to the shear flows of granular materials

Granular materials are characterized by large collections of discrete particles, where the particle-particle interactions are significantly more important than the particle-fluid interactions. The current kinetic theory captures fairly accurately the granular flow behavior in the dilute case, when only binary interactions are significant, but is not accurate at all in the dense flow regime, where multi-particle interactions and contacts must be modeled. To improve the kinetic theory results for granular flows in the dense flow regime, we propose a Modified Kinetic Theory (MKT) model that utilizes the contact duration or cutoff time to account for the complex particle-particle interactions in the dense regime. The contact duration model, also called TC model, was originally proposed by Luding and McNamara [“How to handle the inelastic collapse of a dissipative hard-sphere gas with the TC model,” Granular Matter 1, 113 (1998)] to solve the inelastic collapse issue existing in the inelastic hard sphere model. This model defines a cutoff time tc such that dissipation is not counted if the time between two consecutive contacts is less than tc. As shown in their study, the use of a cutoff time tc can also reduce the dissipation during multi-particle contacts. In this paper we relate the TC model with the Discrete Element Method (DEM) by choosing the cutoff time tc to be the duration of contact calculated from the linear-spring-dashpot soft-sphere model of the DEM. We examine two types of granular flows, simple shear flow and the plane shear flow, and compare the results of the classical kinetic theory model, the present MKT model, and the DEM model. We show that the MKT model entails a significant improvement over the kinetic theory model for simple shear flows at inertial regimes. With the MKT model the calculations are close to the DEM results at solid fractions as high as 0.57. Even for the plane shear flows, where shear rate and solid fraction are inhomogeneous, the results of the MKT model agree very well with the DEM results.

Space-Time Correlations and Dynamic Coupling in Turbulent Flows

Space-time correlation is a staple method for investigating the dynamic coupling of spatial and temporal scales of motion in turbulent flows. In this article, we review the space-time correlation models in both the Eulerian and Lagrangian frames of reference, which include the random sweeping and local straining models for isotropic and homogeneous turbulence, Taylor's frozen-flow model and the elliptic approximation model for turbulent shear flows, and the linear-wave propagation model and swept-wave model for compressible turbulence. We then focus on how space-time correlations are used to develop time-accurate turbulence models for the large-eddy simulation of turbulence-generated noise and particle-laden turbulence. We briefly discuss their applications to two-point closures for Kolmogorov's universal scaling of energy spectra and to the reconstruction of space-time energy spectra from a subset of spatial and temporal signals in experimental measurements. Finally, we summarize the current understanding of space-time correlations and conclude with future issues for the field.

Absence of dissipation in trajectory ensembles biased by currents

We consider biased ensembles of trajectories associated with large deviations of currents in equilibrium systems. The biased ensembles are characterised by non-zero currents and lack the time-reversal symmetry of the equilibrium state. In cases where the equilibrium system has an inversion symmetry which is broken by the bias, we show that the biased ensembles retain a generalised time-reversal symmetry, involving a spatial transformation that inverts the current. This means that these ensembles lack dissipation. Hence, they differ significantly from non-equilibrium steady states where currents are induced by external forces. One consequence of this result is that maximum entropy assumptions (MaxEnt/MaxCal), widely used for modelling thermal systems away from equilibrium, have quite unexpected implications, including apparent superfluid behaviour in a classical model of shear flow.

Modulated patterns in a reduced model of a transitional shear flow

We consider a close relative of plane Couette flow called Waleffe flow in which the fluid is confined between two free-slip walls and the flow driven by a sinusoidal force. We use a reduced model of such flows constructed elsewhere to compute stationary exact coherent structures in this flow in periodic domains with a large spanwise period. The computations reveal the emergence of stationary states exhibiting strong amplitude and wavelength modulation in the spanwise direction. These modulated states lie on branches exhibiting complex dependence on the Reynolds number but no homoclinic snaking.

Padé approximants for large-amplitude oscillatory shear flow

Analytical solutions for either the shear stress or the normal stress differences in large-amplitude oscillatory shear flow, both for continuum or molecular models, often take the form of the first few terms of a power series in the shear rate amplitude. Here, we explore improving the accuracy of these truncated series by replacing them with ratios of polynomials. Specifically, we examine replacing the truncated series solution for the corotational Maxwell model with its Pade approximants for the shear stress response and for the normal stress differences. We find these Pade approximants to agree closely with the corresponding exact solution, and we learn that with the right approximants, one can nearly eliminate the inaccuracies of the truncated expansions.

Geometry of the edge of chaos in a low-dimensional turbulent shear flow model.

We investigate the geometry of the edge of chaos for a nine-dimensional sinusoidal shear flow model and show how the shape of the edge of chaos changes with increasing Reynolds number. Furthermore, we numerically compute the scaling of the minimum perturbation required to drive the laminar attracting state into the turbulent region. We find this minimum perturbation to scale with the Reynolds number as Re(-2).

Three-dimensional physics-based cellular automata model for granular shear flow

Granular flows continue to be a complex problem in nature and industry where solid particles exhibit solid, liquid, and gaseous behavior in a manner which is often difficult to predict both locally and globally. In solids processing applications such as pharmaceutical production, food processing, and coal processing, the ability to accurately predict particle flows can improve process efficiency and product effectiveness. The “gold standard” for the modeling and prediction of granular flows is the discrete element method (DEM), which provides a rigorous physical treatment of particle interactions. One possible supplement to DEM-based analysis is lattice-based cellular automata (CA). CA provides a platform for obtaining fast predictions by pairing rule-based mathematics with high-fidelity physics to rapidly model physical processes, such as granular flows. The present work develops a novel three-dimensional (3D) physics-based CA framework for modeling granular shear flows. This 3D CA model extends the framework's modeling capabilities beyond the granular kinetic regime, includes treatments for force chains, and provides reasonably high accuracy in terms of predicting fundamental granular flow experiments. The predictive capabilities and quantitative accuracy of this CA model have been tested and validated against experimental shear flow results from an annular shear cell. Results from this validation work suggest that the model accurately predicts local flow properties. A parametric study varying the particle–particle coefficient of restitution demonstrated the ability of the 3D CA model to capture nonlinear trends in the local solid fraction profiles. A time study was also performed to highlight the computational efficiency of the 3D CA framework developed in this work. Results of this study showed that even at relatively low particle counts (104), the 3D CA model provides for considerable computational savings, with run times of two orders of magnitude less than a 2D DEM model.