Flow Of Viscous Incompressible Fluid Research Articles

Origin of enhanced skin friction at the onset of boundary-layer transition

Boundary-layer transition is accompanied by a significant increase in skin friction whose origin is rigorously explained using the stochastic Lagrangian formulation of the Navier–Stokes equations. This formulation permits the exact analysis of vorticity dynamics in individual realizations of a viscous incompressible fluid flow. The Lagrangian reconstruction formula for vorticity is here extended for the first time to Neumann boundary conditions (Lighthill source). We can thus express the wall vorticity, and, therefore, the wall stress, as the expectation of a stochastic Cauchy invariant in backward time, with contributions from (a) wall vorticity flux (Lighthill source) and (b) interior vorticity that has been evolved by nonlinear advection, viscous diffusion, vortex stretching and tilting. We consider the origin of stress maxima in the transitional region, examining a sufficient number of events to represent the increased skin friction. The stochastic Cauchy analysis is applied to each event to trace the origin of the wall vorticity. We find that the Lighthill source, vortex tilting, diffusion and advection of the outer vorticity make minor contributions. They are less important than spanwise stretching of near-wall spanwise vorticity, which is the dominant source of skin-friction increase during laminar-to-turbulent transition. Our analysis should assist more generally in understanding drag generation and reduction strategies and flow separation in terms of near-wall vorticity dynamics.

The Effect of Variable Magnetic Field on Viscous Fluid between 3-D Rotatory Vertical Squeezing Plates: A Computational Investigation

In this paper, the 3-D squeezing flow of viscous incompressible fluid between two parallel plates rotating at the same rate is investigated. The flow is observed under the influence of the varying magnetic field. The flow phenomena are modeled by utilizing the basic governing equations, i.e., equation of continuity, coupled Navier Stokes, and Magnetic Field equations. Using appropriate similarity transformations, the resultant partial differential equations are then transformed into a system of ordinary differential equations. The computational technique is developed via the Homotopy Analysis Method (HAM) to obtain the solution of transformed systems of ordinary differential equations. The influence of several engineering fluid parameters, such as squeeze Reynolds number, magnetic field strength parameter, and magnetic Reynolds number, on velocity and magnetic field components, are observed from different graphs. It has been investigated that by increasing the squeeze Reynolds number, fluid velocity in the y and z directions will be increased as well. On the magnetic field component along the y-axis, an increasing influence of squeezing Reynolds number is also noticed. Similarly, raising the magnetic Reynolds number increases the velocity along the y-axis, whereas the inverse relationship is found for magnetic field components. Furthermore, for each flow phenomenon, an error analysis is also presented.

Linear stability of flow in a 90° bend

This paper considers two-dimensional flow in a channel that consists of straight inlet and outlet branches and a circular 90° curved bend. An incompressible viscous fluid flows through the elbow under the action of a constant pressure gradient between the inlet and outlet. Navier–Stokes equations were solved numerically using a high-fidelity spectral/hp element method. In a range of Reynolds numbers, an adaptive selective frequency damping method was used to obtain steady-state flow. It was found that three separation bubbles and vortex shedding can exist in the bend. The modal stability of two- and three-dimensional perturbations was investigated. The critical Reynolds number of two-dimensional disturbances was found by extrapolation from lower Reynolds number results. It is much greater than the three-dimensional one, but the two-dimensional flow could be subcritically unstable with respect to the externally imposed small-amplitude white noise. For three-dimensional perturbations, the dependence of critical Reynolds numbers on the bending radius was obtained. For the case of a moderate bending radius, a neutral curve is provided and eigenfunctions are studied in detail. Three-dimensional instability can be caused by a periodic or monotonically growing mode, and these unstable modes relate to recirculation bubbles that occur after the bend.

Magnetized dissipative Soret effect on nonlinear radiative Maxwell nanofluid flow with porosity, chemical reaction and Joule heating

The present research paper deals with the study of magnetized dissipative Soret of steady viscous incompressible two-dimensional Maxwell fluid flow in a porous medium over a stretching sheet with chemical reaction and Joule heating. Maxwell nanofluid flow model using to differentiate it from the Newtonian fluids. Nonlinear coupled partial differential equations model has been not applicable to any of the direct methods. A Von-Karman similarity transformations are used to convert the nonlinear system of differential equations and are solved numerically via the bvp4c MATLAB function. The simulated results are shown for various values of physical parameters in the flow regime. In addition to, the numerical results of magnetized dissipative Soret, chemical reaction and Joule heating are calculated and tabularized. The effects of various parameters like Maxwell fluid, magnetic parameter, chemical reaction parameter, wall temperature, etc. on normal velocity profile, axial velocity profile, temperature profile and concentration profile. Comparison of current similarity solutions with available results indicates the accuracy and guarantee of the present numerical results and the used method. The results indicate that the effects of the Maxwell fluid, magnetic parameter, chemical reaction parameter, wall temperature are very pronounced.

Смещение предела устойчивости течений при наличии случайных флуктуаций скорости вращения

Nonlinear stability of the isothermal three-dimensional flows of viscous incompressible fluid in the rotational spherical layer with the noise presence was studied numerically. Transition between stable non-stationary flow and unstable flow in the form of travelling azimuthal waves is under consideration. Small-amplitude noise inserted to the flow by random broadband disturbances of the inner sphere rotational rate about constant at time averaged value, outer sphere is fixed. An approach is proposed to simplify finding the critical Reynolds number, corresponding to the stability limit in the presence of noise. The results obtained by the proposed and well known methods are compared.

Shifting the flow stability limit in the presence of random fluctuation of the rotational velocity

Nonlinear stability of the isothermal three-dimensional flows of viscous incompressible fluid in the rotational spherical layer with the noise presence was studied numerically. Transition between stable non-stationary flow and unstable flow in the form of travelling azimuthal waves is under consideration. Small-amplitude noise inserted to the flow by random broadband disturbances of the inner sphere rotational rate about constant at time averaged value, outer sphere is fixed. An approach is proposed to simplify finding the critical Reynolds number, corresponding to the stability limit in the presence of noise. The results obtained by the proposed and well known methods are compared. Keywords: noise, rotational flows, spherical Couette flow, instability control.

A study of free convective heat and mass transmission in the presence of heat source, variable viscosity, chemical reaction, and Soret effects via a porous medium

This manuscript addresses the impressions of Darcy-Forchheimer flow of hydromagnetic viscous incompressible fluid in a vertical infinite porous channel. The governing equations in dimensionless form is considered to the analysis. Implicit-finite difference scheme is employed to obtain the numerical solutions of the non-linear differential equations governing the flow. Relevance fluid flow quantities are found and portrayed graphically. Also, skin-friction, Nusselt number, and Sherwood number are numerically examined. It is understood that velocity, temperature, and concentration of the fluid change substantially with Forchheimer parameter, variable viscosity parameter, thermal conductivity parameter, and chemical reaction parameter.

Stagnation point flow of a viscous incompressible fluid

A steady two-dimensional incompressible viscous fluid flow in the vicinity of a stagnation point has been discussed. The reduced third order nonlinear ordinary differential equation of velocity has been solved using fourth order Runge-Kutta method with shooting technique. The qualitative (graphical) as well as quantitative (tabular) analysis of the velocity distribution has been made. Some of the important findings are (i) The viscous effect are confined in the boundary layer for fluids with very small viscosity. (ii) Outside the boundary layer, the viscous effect is negligible and the fluid is considered as inviscid. (iii) The difference in velocity between adjacent layers is decreasing for less viscous fluids.

A numerical approach for solving one nonlinear problem of hydrodynamics in a non-convex polygonal domain

The paper considers the two-dimensional stationary problem obtained as a result of time discretization of the nonlinear Navier-Stokes equations in rotation form, which describe the incompressible viscous fluid flow in a non-convex polygonal domain. In order to solve a nonlinear problem, it is necessary to find solutions to a sequence of approximate linear problems. For linear problems, the concept of an Rv-generalized solution in weighted sets obeying the weighted analogue of the Ladyzhenskaya-Babuška-Brezzi condition is introduced. A scheme of the weighted finite element method is constructed which suppresses the error arising in the neighborhood of the vertex of the reentrant angle and does not allow it to propagate into the inner part of the computational domain. The mass conservation law is valid directly at the grid nodes, and not only in the (weak) integral sense. Numerical experiments are carried out and a comparative analysis is made in polygonal domains with different values of reentrant angles. The advantage of the proposed approach over the classical finite element method is the order of convergence with respect to the grid step. A set of optimal parameters of the method is determined to obtain the required order of convergence. In this case, the exponent of the weight function depends on the value of the reentrant angle, and the parameters determining the Rv-generalized solution are independent on its value. In contrast to the classical approach, the order of convergence of the proposed approximate method to the exact solution of a nonlinear problem does not depend on the value of the reentrant angle. The constructed approximate method can be used without geometric mesh refinement in the vicinity of the singularity point.

THE IMPACT OF SELECTED PARAMETERS ON PRESSURE DISTRIBUTION IN THE FACE THROTTLE OF A CENTRIFUGAL PUMP AUTOMATIC BALANCING DEVICE

Face throttles are a necessary functional element of non-contact face seals and automatic balancing devices of centrifugal pumps of different constructions. To calculate the hydrodynamic forces and moments acting on the rotor and fluid flow through the automatic balancing device, it is necessary to know the pressure distribution in the cylindrical and face throttle when considering all important factors which predetermine fluid flow. The face throttle surfaces are moving, which leads to unsteady fluid flow. The movement of the walls of the face throttle causes an additional circumferential and radial flow, which subsequently leads to the additional hydrodynamic pressure components. The paper analyses viscous incompressible fluid flow in the face throttle of an automatic balancing device taking into account the axial and angular displacements of throttle’s surfaces and the inertia component of the fluid. The effect of local hydraulic losses as well as random changes in the coefficients of local hydraulic resistance at the inlet and outlet of the throttle is analysed.

Estimation of the value of leaks through a through defect of the pipeline when using in-pipe repair elements

The loss of hydrocarbons when using in-pipe repair elements is determined by the nature of the fluid flow in the gap between the pipe and the repair sleeve. An accurate analytical calculation of the flow parameters for a real sleeve, taking into account its length, the asymmetry of the defect and other design features, is very difficult. In this article, the problem of accurate calculation of the radial flow of a viscous incompressible fluid in a thin layer between two annular plates simulating a circular region with a center coincide with a pipeline defect is solved. The area consists of two circles formed by the pipeline wall with a through defect and the surface of the internal repair element. The results obtained will allow us for accurate calculations in the area adjacent to the defect of the pipe and approximate calculations for the whole repair element.

Comparative study of aerodynamic properties of ichthyosaur bodies

The flow of viscous incompressible fluid around the geometric shapes corresponding to the bodies of ichthyosaurs of different evolutionary ages has been studied. The static pressure and flow velocity distributions around the bodies have been computed with the help of AnSys Fluent 2021 R2 software. It is shown that at some ‘angles of attack’ of the body to the flow there are vortices, pairs of vortices or vortex wakes, which lead to changes in the shear stress distribution along the body, that can be used by aquatic animals for purposes of sensing their environment and communicating. The hydrodynamic properties of the ichthyosaur bodies have been compared with dolphins and whales of a similar size. It is shown that in terms of aerodynamic indices there are no obvious differences between body forms of different evolutionary ages. Different species are most likely to have adapted the specifics of swimming, such as speed, angles of attack, habitation in the upper or lower layers, and others to their living conditions. The obtained results allow us to understand better the adaptational mechanisms and direction of evolution of aquatic animals.

Mathematical Modelling of Electrophysical Water Treatment

The problem of mathematical modeling the processes of water treatment from charged particles by electric field is considered. The problem is relevant due to the mass use of cleaning technologies in industry, medicine or the national economy. At the present stage, a significant improvement of purification system quality and the introduction of the technologies for the regeneration of their filtration components are required. Mathematical simulation using computer and supercomputer calculations helps to accelerate the development of new devices and cleaning technologies. On the basis of the chosen purification technology, it is important to create a numerical simulation apparatus with a controlled high accuracy of the calculations. For this purpose, we use a quasi-hydrodynamic (QHD) model of a viscous incompressible fluid flow, a system of convection-diffusion equations taking into account the action of the Lorentz force to describe the propagation of harmful impurities in aqueous medium, and an equation for the electric field potential [1, 2]. The numerical algorithm is based on the finite volume method. It is applied in the case of irregular unstructured meshes. This is important for problems of real two-dimensional (2D) and three-dimensional (3D) geometry. Time integration is performed according to an explicit scheme, which simplifies the procedure for parallelizing the algorithm. The proposed approach was tested on the examples of 2D and 3D geometry with various locations of the electrodes and various values of the potentials. The obtained results of the concentration of the ionic impurities show the possibility of this method to purify water from 10 to 40 percent. A design of a water purifier based on electrophysical purification technology can be developed on the base of this study.

How Does the Creep Stress Regulate Void Formation at the Lithium‐Solid Electrolyte Interface during Stripping?

AbstractInterfacial instability from void formation at the solid–solid interface is one of the crucial challenges in solid‐state batteries. However, the fundamental mechanism as to how stress is generated in lithium and thus impacts void formation has not been established. A general creep/contact electro‐chemo‐mechanical model is herein developed to reveal the mechanisms of void formation at the Li/solid electrolyte (SE) interface during stripping. Li stress calculation is achieved by presuming that the strain‐rate‐dependent creep deformation of Li metal acts like that of an incompressible viscous fluid flow. The results demonstrate that the dominant mechanism that impedes void formation is the creep‐induced flux enhancement of vacancies, which are transported into Li metal for a non‐ideal Li/SE interface with pre‐existing interfacial defects. This contrasts with previous simulations on an ideal flat Li/SE interface in which the vacancy diffusion away from the interface is shown to govern whether voids are formed.

An entropy flow analysis by means of new similarity approach

In this paper, we present the entropy generation for an incompressible viscous fluid flow over a heated stretching surface. Liquid and gas type fluids are taken for the boundary layer problem. The energy equation is discussed under the effect of Rosseland approximation. The variable fluid properties depends on temperature. Temperature-dependent liquid viscosity is investigated to convert the base flow velocity profiles the base flow and temperature profile. In this study, the fluid viscosity is assumed to be variable. The governing equations are converted into ordinary differential equations by new similarity approach. Numerical solution of the ordinary differential equations are then calculated by using a shooting method. The obtained results are discussed for the base flow and entropy. The physical interpretation has given through graphs and tables. Correlation in terms of base flow and entropy solutions are plotted graphically.

Investigation of boundary stresses on MHD flow in a convergent/divergent channel: An analytical and numerical study

This study investigates the boundary stresses prescribed by the traction boundary condition on an incompressible magnetohydrodynamic Jeffery-Hamel flow of viscous fluid. The governing partial differential equations are transformed to a nonlinear ordinary differential equation (ODE) by the transformation obtained from continuity equation. We have modeled traction boundary conditions to solve the problem. We have not imposed flow symmetry condition and applied prescribed flow rate condition. We have computed analytical and numerical solutions of the problem. We have developed modified Adomian decomposition method based on Daun-Rach Approach (DRA) for general nonlinear third order ODE subject to Robin’s and integral boundary conditions. The governing equation is solved using the developed scheme. The Mathematica routine, NDSolve, is used to obtain numerical solution by first approximating the constant flow rate condition by Gauss-Lobatto integration formula of four and five points as well as by trapezoidal rule. Analytical and numerical results are compared and found in good agreement. The slip and no-slip scenarios are observed both for inertial and non-inertial flows. The back flow occurs both for convergent and divergent channel geometries. Flow bifurcations and boundary layer get strengthened due to presence of boundary stresses. The symmetric and asymmetric natures of flow are also captured due to presence of boundary stresses.

A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow

The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of the fluid density on the phase-field order parameter. Driven by applications in biomembrane studies, the model is written for tangential flows of fluids constrained to a surface and consists of (surface) Navier–Stokes–Cahn–Hilliard type equations. We apply an unfitted finite element method to discretize the system and introduce a fully discrete time-stepping scheme with the following properties: (i) the scheme decouples the fluid and phase-field equation solvers at each time step, (ii) the resulting two algebraic systems are linear, and (iii) the numerical solution satisfies the same stability bound as the solution of the original system under some restrictions on the discretization parameters. Numerical examples are provided to demonstrate the stability, accuracy, and overall efficiency of the approach. Our computational study of several two-phase surface flows reveals some interesting dependencies of flow statistics on the geometry.

Description of Nonlinear Vortical Flows of Incompressible Fluid in Terms of a Quasi-Potential

As it was shown earlier, a wide class of nonlinear 3-dimensional (3D) fluid flows of incompressible viscous fluid can be described by only one scalar function dubbed the quasi-potential. This class of fluid flows is characterized by a three-component velocity field having a two-component vorticity field. Both these fields may, in general, depend on all three spatial variables and time. In this paper, the governing equations for the quasi-potential are derived and simple illustrative examples of 3D flows in the Cartesian coordinates are presented. The generalisation of the developed approach to the fluid flows in the cylindrical and spherical coordinate frames represents a nontrivial problem that has not been solved yet. In this paper, this gap is filled and the concept of a quasi-potential to the cylindrical and spherical coordinate frames is further developed. A few illustrative examples are presented which can be of interest for practical applications.

Characteristics of MHD Casson fluid past an inclined vertical porous plate

This paper addresses the effects of Soret on unsteady free convection flow of viscous incompressible fluid through a porous medium with high porosity bounded by a vertical infinite moving plate under the influence of thermal diffusion, chemical reaction, and heat source. The fluid is considered to be gray, absorbing, and emitting but non-scattering medium. Rosseland approximation is considered to describe the radiative heat flux in the energy equation. The dimensionless governing equations for this investigation are solved analytically using perturbation technique. The effects of various governing parameters on the velocity, temperature, concentration, skin-friction coefficient, Nusselt number and Sherwood number are shown in figures and tables and analyzed in detail. It was noticed that velocity distribution increased with increasing buoyancy parameters; temperature decreased with increasing Prandtl number, and concentration decreased with increasing the Schmidt number and chemical reaction parameter.

Recovery of radial-axial velocity in axisymmetric swirling flows of a viscous incompressible fluid in the Lagrangian consideration of vorticity evolution

Swirling laminar axisymmetric flows of viscous incompressible fluids in a potential field of body forces are considered. The study of flows is carried out in a cylindrical coordinate system. In the flows, the regions in which the axial derivative of the circumferential velocity cannot take on zero value in some open neighborhood (essentially swirling flows) and the regions in which this derivative is equal to zero (the region with layered swirl) are considered separately. It is shown that a well-known method (the method of viscous vortex domains) developed for non-swirling flows can be used for regions with layered swirling. For substantially swirling flows, a formula is obtained for calculating the radial-axial velocity of an imaginary fluid through the circumferential vorticity component, the circumferential circulation of a real fluid, and the partial derivatives of these functions. The particles of this imaginary fluid “transfer” vortex tubes of the radial-axial vorticity component while maintaining the intensity of these tubes, and also “transfer” the circumferential circulation and the product of the circular vorticity component by some function of the distance to the axis of symmetry. A non-integral method for reconstructing the velocity field from the vorticity field is proposed. It is reduced to solving a system of linear algebraic equations in two variables. The obtained result is proposed to be used to extend the method of viscous vortex domains to swirling axisymmetric flows.