The influence of the shear-thinning properties on tear dynamics is analyzed using 2D numerical simulations. The simulations were conducted in conditions close to those of the actual tear film dynamics. The paper deals with the spreading of the shear-thinning tear film on a spherical cornea with blinking. The shear-thinning properties are described using Cross’s rheological model, known as the model

The data of Arosemena et al. (2021), consisting of turbulent channel flow simulations of generalized Newtonian (GN) fluids, are considered to study the effects of shear-dependent rheology on the nonzero velocity–vorticity correlations and the mean dynamics. In the near-wall region and compared to Newtonian channel flow, the velocity–vorticity products contributing to the turbulent inertia term decrease/increase

In the present paper, the three dimensional (3D) settlement process of two side-by-side free-falling spheres in a water tank was numerically investigated using coupled Smoothed Particle Hydrodynamics (SPH) - Discrete Element Method (DEM) method. The maximum particle Reynolds number, calculated based on the terminal velocity and sphere diameter, is Rem=2.4 × 104. The accuracy of the model was firstly

Study of the propagation of sound in a single non-ideal fluid originates with Stokes in 1845 and Kirchhoff in 1868. The situation is much more complex in the case of two-fluid flow, both from the physical point of view, as the configuration of the flow matters greatly, and from the analytical point of view. The principle two-fluid models currently in use for CFD are the focus of this article. It is

Understanding the effective viscosity of fiber-filled polymer melts is essential for predicting the local fiber orientation of injection molded short-fiber reinforced components. To circumvent the intrinsic difficulties of experimentally determining the strongly anisotropic viscosity of such particle-reinforced melts, an FFT-based computational homogenization method for computing the effective quasi-static

This paper addresses the analysis and characteristics of submerged underexpanded air jets injected into water by means of single and twin tuyeres (i.e. straight tubes). First, a Computational Fluid Dynamics simulation of a single tuyere is compared with available experimental data found in the literature. In the twin tuyere configuration, spacing is varied and the resultant flow is compared to that

Laminar cross-flow over a circular cylinder with smooth as well as longitudinally grooved surfaces was investigated numerically for low freestream Reynolds number ranging from 50 to 300. Most of the currently published works on similar flow configurations considered high Reynolds number in the turbulent regime. The computations were performed by the ANSYS Fluent code. The numerical results were validated

We consider the ultra-relativistic Euler equations for an ideal gas, which are described in terms of the pressure p and the spatial part u∈R3 of the dimensionless four-velocity. We also numerically investigate the ultra-relativistic Euler equations using the modified Rusanov scheme compared with classical Rusanov scheme. Our scheme consists of predictor and corrector stage. The predictor stage contains

Thermovibrational convection in a water based metallic (Cu-water and Ag-water) or metallic oxide (Al2O3-water and TiO2-water) nanofluid saturated porous medium is addressed incorporating the Brinkman boundary correction. The nanofluid behaves more like a fluid rather than a conventional solid–fluid mixture and is studied through Khanafer–Vafai–Lightstone (KVL) model. A linear stability analysis is

The axisymmetric motion of a spherical particle in the presence of a porous interface is considered in the limit of small Reynolds and capillary numbers where the interface is of negligible deformation. We consider the translation along and the rotation about an axis perpendicular to the interface. The flow through the porous medium is modeled by Brinkman equation with a tangential stress jump condition

In this paper, we employ the boundary integral equation (BIE) to analytically derive the solution of potential flow across a circular cylinder, an elliptical cylinder and a thin airfoil. It is found that the symmetric or antisymmetric potential flow problem can be solved by using the UT or the LM equation alone. Both analytical and numerical approaches were considered. The key tool is using the degenerate

In this paper, the influence of the phase distribution imposed as an inlet boundary condition in a two-phase flow simulation is investigated. Firstly, a new inlet model is proposed which defines a transient inlet boundary condition to be applied in a subsequent Eulerian simulation, more specifically using the Volume-Of-Fluid method. This inlet model is aimed at generating large gas bubbles, making

We revisit the well-known work of K. Masuda in 1984 on the weak–strong uniqueness of L∞L3 Leray–Hopf weak solutions of Navier–Stokes equation. We modify the argument, and extend the uniqueness result to the scaling critical anisotropic Lebesgue space with mixed-norms. As a consequence, our results cover the class of initial data and solutions which may be singular or decay with different rates along

Barenblatt’s hypothesis of incomplete similarity is applied to the turbulent viscosity in a turbulent liquid film flowing under combined action of gravity and gas flow friction. Velocity profile and film thickness are obtained in a closed analytical form. The solution is valid for co-current and counter-current flows.

Diffraction–radiation of regular waves by a body such as an offshore structure or a moored ship is considered within the classical framework of potential-flow theory, which is commonly used because it is realistic and practical. A simple analysis that is based solely on straightforward applications of Green’s classical identity to a ‘free-waterplane’ flow-model and a ‘rigid-waterplane’ flow-model is

In this note, we are concerned with uniform stability for a Leray–Hopf weak solution of the MHD equations and obtain that the Leray–Hopf weak solution is uniformly stable with respect to a small perturbation of initial velocity, magnetic and external forcing. This extends and improves the results given by Gallagher–Planchon and Dong–Jia for Navier–Stokes equations.

This research aims to investigate the behavior of vortex breakdown in vertical annuli filled with a conducting viscous fluid under the axial magnetic field. Three annular gaps and various ratios of annular height to the radius of the outer cylinder are considered. The pumping action of the Ekman boundary layer produced by rotation of the bottom disk sets up a secondary circulation along the meridional

The dynamics of a constrained three-vortex system, a pair of point vortices of arbitrary non-zero circulations in the velocity field of a fixed point vortex, is investigated. The underlying dynamical system is simplified using a coordinate transformation and categorized into two cases based on the zero and non-zero values of the constant of angular impulse. For each case, dynamical features of the

In this study the important aspects of cutting fluid distribution and the chip evacuation during micro twist deep-hole drilling are investigated using 3D multi-physics simulation methods. A coupled particle simulation is performed to analyze the chip transport by combining Smoothed Particle Hydrodynamics and the Discrete Element Method. Therefore, the transient transport of the chips is compared to

The effects of static surface deformations on a spatially developing supersonic boundary layer flow at Mach number M=4 and Reynolds number Reδin≈49300, based on inflow boundary layer thickness (δin), are analyzed by performing large eddy simulations. Two low-order structural modes of a rectangular clamped surface panel of dimensions ≈33δin×48δin are prescribed with modal amplitudes of δin. The effects

The transfer of mass around a spherical double emulsion droplet in a uniform creeping flow and at large Peclet numbers is the subject of this theoretical communication. The double emulsion droplet, submerged in an external fluid (fluid 1), is made from an internal spherical drop (fluid 3) covered by a spherical fluid shell (fluid 2). Four dimensionless numbers describe this situation: two viscosity

Along with the technology development of ocean resources, offshore platforms are gradually becoming larger and more complex. Recent development of the oil and gas field in the deep-water region often involves multiple floating platforms adjacent to each other to perform more complex functions for oil and gas production. This paper describes the investigation carried out on the dynamic responses of

Electroosmotic flows (EOF) in microfluidic devices can be greatly enhanced over superhydrophobic surfaces because the high shear rates within the electrical double layer can drive large slip velocities at the interface. Using the power law fluid model, we derive a novel formulation for the Helmholtz–Smoluchowski (HS) velocity and use it to examine the effect of slip on the hydrodynamics of a coupled

The present investigation centers around a numerical study of the impact of the presence of phototactic microorganisms on the thermo-bioconvection inside a wavy-walled horizontal porous annulus that is saturated with a Newtonian fluid. Consequently, an equation describing the movement of the microorganism cells is added to the mathematical model of natural convection. The thermal equilibrium, Oberbeck–Boussinesq

Lattice Boltzmann (LB) method, which is a mesoscopic numerical method, has been considered as a powerful tool to study microscale gas and liquid flows. Boundary slip phenomenon, which is a significant feature of both microscale gas and liquid flows, has been extensively studied by the LB method in the past decade. However, most of the previous works have focused on the microchannel flows and studies

Storage of liquefied gas in an underground cavity created in hard rocks is a promising new technology that can significantly reduce the dimensions of a storage facility. The intense heat transfer between the cryogenic fluid and the surrounding rocks leads to the formation of an ice ring in water-saturated rocks, which acts as a natural protective barrier. In this paper, we provide a general theoretical

In this paper, we investigate the haemodynamics of a left atrium (LA) by proposing a computational model suitable to provide physically meaningful fluid dynamics indications and detailed blood flow characterization. In particular, we consider the incompressible Navier–Stokes equations in Arbitrary Lagrangian Eulerian (ALE) formulation to deal with the LA domain under prescribed motion. A Variational

An asymptotic solution with double-deck boundary layer structure is constructed for the problem of an incompressible fluid flow over a semi-infinite plate with small localized or periodic (fast-oscillating) irregularities on the surface whose shape depends on time. Numerical simulation of flow in the near-plate region is presented for two types of the shape change: oscillations of the amplitude of

In this numerical study, sediment transport and bed evolution in the surf zone under plunging breakers are investigated; this is a challenging topic that involves complex hydrodynamics coupled with sediment dynamics. Here, a Eulerian–Eulerian multi-phase model for sediment transport, with the capability to capture the free surface, is used. Waves are generated using an open-source toolbox ‘waves2foam’

The effects of particle shape on settling behavior of sand particles under the influence of gravity in an initially quiescent water environment have been studied by a two-dimensional high-resolution numerical experiment. The numerical method is based on an immersed boundary method. The accuracy of the code is well demonstrated against experimental data of a fluttering rectangular plate. The particle

The present article aims to study the suppression of vortex shedding using a passive flow control technique (slit through a circular cylinder) in the laminar regime (Re =100–500). The slit width ratio S/D (slit width/diameter) on the modified cylinder plays an essential role to control the vortex shedding. The additional flow through the slit leads to the suppression of the global instability and vortex

The principle of least action is a variational principle that states an object will always take the path of least action as compared to any other conceivable path. This principle can be used to derive the equations of motion of many systems, and therefore provides a unifying equation that has been applied in many fields of physics and mathematics. Hamilton’s formulation of the principle of least action

Strong wall pressure fluctuations are generated mostly by a high-speed flow passing over a cavity and should be accurately predicted and controlled for the structural design of aircraft. In this work, a spatiotemporal analysis was performed to estimate wall pressure fluctuations and reveal the mechanism of flow control by a sawtooth-like vortex generator installed on the leading edge or by the use

An analytical–numerical method based on collocation techniques is presented to investigate the problem of determining Stokes flow caused by a spherical particle moving perpendicularly to a plane interface separating two semi-infinite immiscible fluid phases. Attention is focused on the case when one of the two fluid phases is of a microstructure nature (micropolar fluid). A linear slip boundary conditions

We propose a numerical study of the evaporation of sessile droplets using a Volume-Of-Fluid (VOF) method in the free-software Basilisk. We consider pure liquid droplets forming a spherical-cap onto a smooth or rough substrate and we investigate two different modes of evaporation: the unpinned mode where the contact angle is constant and the pinned mode where the wetting area is constant. The numerical

The boundary-integral flow-representation associated with the boundary-value problem, commonly called Neumann–Kelvin (NK) problem, that corresponds to linear potential flow around a ship steadily advancing in calm water involves an integral around the mean waterline of the ship. This ‘waterline integral’ is a notorious source of numerical difficulties and has been extensively studied. The waterline

Wave propagation in a system of two arbitrary fluids separated by a contaminated interface in the form of an insoluble monolayer is investigated. The effects of four parameters (density ratio, R; kinematic viscosity ratio, V; Marangoni number, P; and squared wave-Reynolds number, σ) on the solutions of a comprehensive dispersion relation for these waves are analyzed. In the first part of the manuscript

When compound jets are covered with surfactant on both interfaces, the property of those interfaces will be viscoelastic, unlike the Newtonian fluid interface. In this paper, the effects of surface viscoelasticity are principally studied through linear stability analysis and calculated using the Chebyshev spectral collocation method. Both surface elasticity and viscosity have properties to make the

We numerically study the dynamics of axisymmetric compound liquid threads with a phase-field model. Compound threads consist of a middle annular thread enclosing an inner core liquid and surrounded by an outer immiscible liquid. The model is composed of the Navier–Stokes equation, including a surface tension force term, and the convective ternary Cahn–Hilliard system. The finite difference method is

An extension of the Boussinesq-type models to weakly compressible flows is derived in the fully nonlinear case. The dispersive properties are consistent with the linear theory of compressible fluids at the long-wave limit. The particular case of a vanishing Mach number gives a quasi-incompressible model, intended for coastal wave simulations, which is a hyperbolic version of the Serre–Green–Naghdi

Hydrodynamic instability and formation of waves for thin viscous film flowing down a slippery inclined substrate with broken time-reversal-symmetry have been discussed in this present study. The effect of slip on the substrate is modeled using the Navier slip boundary condition. We have derived a nonlinear evolution model in the framework of the long-wave expansion technique. The one equation model

This study investigates the higher order hydrodynamic phenomena of a breaking wave impact on a vertical impermeable wall. During the collision, a small amount of air is entrapped between the water and the wall. Here, we idealize the problem under consideration and we assume that the hydrodynamic pressure in the air-pocket is zero and that the brief collision does not change significantly the volume

The role of leading-edge vortex (LEV) in lift generation for revolving wings is not well-understood. We aim to discern the effect of LEVs and TEVs on revolving flat and twisted wings through a detailed analysis of planar flow in the wing sections. We present a simple quasi-two-dimensional model to estimate the lift distribution over the wingspan by coupling the potential flow and lifting line theory

Over the years, a number of researchers have explored the possibilities of capturing the fantastic Taylor column phenomena numerically. However, comprehensive satisfactory numerical results have not been obtained in spite of the presence of well established experimental and theoretical data. One important blockade in the process is that the existing lower-order schemes cannot capture the phenomena

Most of the flow separation control devices used in the aircraft wing are effective at high angles of attack, and adversely affect the performance of the wing at low angles of attack. In flight mission, the cruise phase takes major portion than the take-off and landing. Therefore, the flow separation control devices installed on wing may reduce the performance of the aircraft in total flight mission

The behavior of falling film over horizontal has significant impacts on the efficiency of heat and mass transfer for the horizontal tube evaporators and absorbers especially for intermittent droplet model at low spray density, which has lower heat and mass transfer resistance. Thus it is critical to illuminate transient and intermittent flow mechanism of droplet dynamic behavior and film thickness

Optimal control of the unsteady, laminar, fully developed flow of a viscous, incompressible and electrically conducting fluid is considered under the effect of a time varying magnetic field B0(t) applied in the direction making an angle with the y–axis. Thus, the coefficients of convection terms in the Magnetohydrodynamics (MHD) equations are also time-dependent. The coupled time-dependent MHD equations

Slip flow in a rectangular cavity is studied. Using slip eigenfunctions, an exact series solution is found for a lid sliding longitudinally. For a transversely sliding lid, the stream function for Stokes flow is determined by a new set of slip eigenfunctions and supplemented by point match on the boundary. It is found that slip has considerable effect on the flow properties. Analyses of the region

We investigate by theoretical means the motion of a gravity current (GC) released from a lock into an ambient fluid in a horizontal channel of non-rectangular cross-section area (CSA) like triangle, trapezoid or semicircle. The lock contains an internal stratification, in particular a layer of density ρL overlain by a layer of density ρU, where ρo<ρU<ρL and ρo is the density of the ambient fluid. Assuming

Natural vortex development in double diffusive confined wall jet flow is firstly analyzed as a basic state. A consecutive vortices production and shedding processes are observed at moderated Reynolds numbers. The influence of these phenomena on combined transfers is then discussed. Strouhal number evolution was determined by spectral analysis conducted in the near-field region of the laminar wall jet

Spatially damped continental shelf waves (CSWs) with diurnal tidal frequency outside Lofoten–Vesterålen in north-west Norway are studied theoretically for an idealized shelf topography. Wave damping is caused by the exchange of fluid on the shelf with an inner archipelago through a permeable coastline. This exchange is modelled by the application of a Robin condition at the coastal boundary. It is

Numerical simulations of flow-induced vibration on isolated and tandem elliptic cylinders with varying reduced velocities are carried out. Immersed boundary multi-relaxation-time lattice Boltzmann flux solver is used as numerical solution method so that the solution procedure can be conducted in a Cartesian grid. The accuracy and rationality of this method are verified by comparison with previous numerical

Poisson equation lies in the heart of the numerical solutions of incompressible Navier–Stokes equations (NSEs) based on the popular projection methods, which decouple the pressure and velocities fields. This paper presents enhanced numerical solutions of the 2D incompressible NSEs inspired by a newly-developed Generalized Harmonic Polynomial Cell (GHPC) method for the Poisson equation, which has a

The present outbreak enables the researchers from fluid mechanics to widen the understanding of expelling respiratory liquids from a unique perspective to diminish the persistence of COVID-19. This article focuses on uncovering the instability mechanism responsible for forming droplets and aerosols during respiratory events such as breathing, talking, coughing and sneezing. We illustrate a mathematical

We study the linear stability of the Poiseuille flow of a viscoelastic upper convected Maxwell fluid in which the rheological parameters depend on the concentration of particles suspended in the fluid (dense suspension with negligible diffusion). After determining the basic flow and basic concentration profile we consider a temporal three dimensional perturbation in the form of a stream-wise and span-wise

The behavior of an offshore structure in regular waves – and the related (linear and nonlinear) wave loads, added-mass and wave-damping coefficients, and body-motions – are commonly analyzed via the Green-function and boundary-integral method associated with potential-flow theory. This realistic, widely-used method requires accurate and efficient numerical evaluation of flows created by distributions

The Lattice Boltzmann Method (LBM) is promising for studies on Tsunami inundation. In this work, a Lattice Boltzmann Model for non-linear Shallow-Water Equations with a Turbulence Modeling​ (LABSWETM) was developed to consider the turbulence and non-Newtonian fluid behavior of tsunami flow. This involves incorporating the Sisko viscosity model into the lattice Boltzmann equation. By using the LABSWETM

The problem of the free streamline solutions of the Falkner–Skan equation is revisited in this paper. Until now, such solutions were found for negative values of the pressure gradient parameter β only. All of them are associated with slip velocities −1