Flow Of Incompressible Newtonian Fluid Research Articles

A variational multiscale stabilized finite element method for double diffusive incompressible flow with application to mixed convection in a heated staggered cavity under magnetic field

In this work, a novel stabilized finite element scheme in a subgrid multiscale variational framework is proposed to efficiently solve double-diffusive incompressible Newtonian fluid flow in a complex geometry occurring in several real-life applications. Here, the fine scale effects are transferred to the course scale problem following algebraic subgrid analysis, and then, the course scale equations are computed and the key stabilization parameters are derived following the Fourier analysis. The influence of flow, heat, and mass transfer parameters such as Reynold’s Number, Hartmann Number, Richardson Number, and Lewis Number are analyzed under a magnetic field, through the streamlines, isotherms, and the local heat fluxes to understand the double-diffusive mixed convective process in a complex staggered cavity, which is relevant to engineering applications such as ventilation and contamination assessment systems. The study finds that maximum species contamination together with the maximum Sherwood Number (12.54) occurs when the Richardson number is 10, and the minimum contamination together with the minimum Sherwood Number (0.71) occurs when the Lewis number is 0.1 when other parameters are varied within the operational range. The results are validated with previously existing literature for simple cases.

Topology optimization of incompressible structures subject to fluid–structure interaction

In this work, an algorithm for topology optimization of incompressible structures is proposed, in both small and finite strain assumptions and in which the loads come from the interaction with a surrounding fluid. The algorithm considers a classical block-iterative scheme, in which the solid and the fluid mechanics problems are solved sequentially to simulate the interaction between them. Several stabilized mixed finite element formulations based on the Variational Multi-Scale approach are considered to be capable of tackling the incompressible limit for the numerical approximation of the solid. The fluid is considered as an incompressible Newtonian fluid flow which is combined with an Arbitrary-Lagrangian Eulerian formulation to account for the moving part of the domain. Several numerical examples are presented and discussed to assess the robustness of the proposed algorithm and its applicability to the topology optimization of incompressible elastic solids subjected to Newtonian incompressible fluid loads.

Endothermic and exothermic chemical reactions’ influences on a nanofluid flow across a permeable microchannel with a porous medium

The compact dimensions and large surface area-to-volume ratio characteristic of microchannel geometries can efficiently utilise endothermic and exothermic chemical reactions to enhance heat transfer, control temperature, adjust reactivity, intensify processes and develop innovative thermal management techniques. Becasue of this, the exothermic and endothermic chemical reaction mechanism is explored by considering the titanium oxide (TiO2) nanoparticles with water (H2O) as the base fluid. An incompressible Newtonian fluid flows through the porous microchannel. The pressure gradient factor assumes the flow in the microchannel. Energy and solutal transportation analyses are made with Robin’s boundary conditions and activated energy phenomena. Similar variables are introduced to convert the model into non-dimensional. A numerical scheme, namely the Runge–Kutta-Fehlberg 45th (RKF-45) scheme, is implemented to execute solutions. The results explore that thermal distribution decreases for elevated activation energy values and Biot number values in the exothermic case while enhanced in the endothermic case. The rate of thermal distribution declines with the addition of solid fractions and chemical reaction parameters in the endothermic case; the opposite trend is observed in the exothermic case.

Regularity for the steady Stokes-type flow of incompressible Newtonian fluids in some generalized function settings

A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving p-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper also provides a relatively complete picture of our main results in two regards: problems with nonlinearity is regular with respect to the gradient variable; and asymptotically regular problems, whose nonlinearity satisfies a particular structure near infinity. For such Stokes-type systems, we derive regularity estimates for both velocity gradient and its associated pressure in two special classes of function spaces: the generalized Lorentz and ψ-generalized Morrey spaces.

Numerical study of Newtonian laminar Flow around circular and square cylinders

In this study, we present a novel algorithm designed to address the computational challenges posed by the governing equations of incompressible Newtonian fluid flow, particularly of bluff bodies of circular and square in a channel. This a significant innovation algorithm is developed based on the Taylor–Galerkin/Pressure-Correction finite element method. Notably, a pivotal element of this approach involves the implementation of the two-step Lax–Wendroff scheme to resolve the momentum equation. To assess the efficacy of our novel algorithm, we conducted a comprehensive analysis using a standard benchmark scenario; the initiation of Poiseuille flow through an axisymmetric rectangular channel encompassing bluff bodies. In this context, our investigation centered on the influence of the Reynolds number (Re) on various pertinent variables. The results obtained from our study underscore the remarkable congruence between the outcomes generated by the new algorithm and established physical principles, as well as findings from prior research, as evidenced through thorough comparisons with the existing body of literature. This research represents a significant stride toward advancing our understanding of fluid dynamics and computational methodologies in this domain.

Direct numerical simulation of fluid/solid particles flow inside a channel

The modeling of moving solid particles in fluid flow has been the focus of many studies and has succeeded to attract significant attention from researchers. However, commonly used modeling approaches such as discrete element modeling (DEM) and direct numerical simulations (DNS) lack simplicity and have been computationally intensive. The aim of this paper is to develop a new approach to simulate solid transport in an incompressible Newtonian fluid flow. This method is based on the Finite element method with penalization of the deformation tensor. The fluid behavior is governed by the Navier-Stokes equations within the investigation domain. To take into account collisions, we present an algorithm which allows us to handle contacts between rigid particles. In this paper, 2D fluid/particles flow simulations are performed; the results are validated by comparison with results from other methods. We attempt to simulate the conveying of solid particles behavior of circular particles in a fluid flow inside a pipe. The numerical tests show that the present method provides a very efficient approach to directly simulate the solid transport inside the channels.

A new computational approach for velocity components analysis of a solid particle in an incompressible fluid flow

In this work, the dynamic motion of a particle in an incompressible Newtonian fluid flow is investigated analytically. The shear and rotation effects on the lift and drag forces of the particle are considered for this problem. Also, the equations governing the motion of a particle are solved using the Temimi–Ansari technique. Analytical solutions for the horizontal and vertical velocities of this particle are obtained and analyzed in terms of time. The corresponding analytical findings are verified in comparison with numerical solutions. The obtained results showed very good accuracy of the solutions and the efficiency of this method in the whole time domain by employing the Padé approximation.

Computational Study of the Flow of Newtonian Fluid Through A Straight Channel and Lid-Driven Cavity

This article aims to introducenumerical study of two different incompressible Newtonian fluid flows. The first type of flow is through the straight channel, while the second flow is enclosed within a square cavity and the fluid is moved by the upper plate at a specific velocity. Numerically, a Taylor-Galerkin\ pressure-correction finite element method (TGPCFEM) is chosen to address the relevant governing equations. The Naiver-Stoke partial differential equations are usually used to describe the activity of fluids. These equations consist of the continuity equation (conservation of mass) and the time-dependent conservation of momentum, which are preserved in Cartesian coordinates. In this study, the effect of Reynolds number (Re) variation is presented for both problems. Here, the influence of Re on the convergence rate and solution behavior is provided. Findings display that, there is a significant impact of Re upon the temporal convergence rates of velocity and pressure. As well, the rate of convergence increases as the values of Re are risen. For the cavity problem, one can infer that, as the Reynolds number rises, the size of the vortex is reduced.

Electroosmotic flow and heat transfer through a polyelectrolyte-grafted microchannel with modulated charged surfaces

In this paper, the electroosmotic flow and heat transfer of incompressible Newtonian fluid through a polyelectrolyte-grafted microchannel with modulated charged surfaces are investigated. The effects of the modulated potential and polyelectrolyte layer on the velocity field and heat transfer properties in the microchannel driven by the axial applied electric field and pressure gradient are discussed. A mathematical model is developed to describe the electroosmotic flow and heat transfer, including the Poisson-Boltzmann equations, the Navier-Stokes equations, and the energy equations. Based on the Debye-Hüchel linearization assumption, the analytical solutions of the potential and velocity are obtained by the superposition principle and the stream function method. The finite difference method is used to obtain the dimensionless temperature in the energy equation. Finally, the results concerning the effects of dimensionless parameters on velocity and temperature are given in graphical form and discussed in detail. The results demonstrate that the velocity distribution exhibits oscillatory characteristics and generates vortices under the influence of the modulated charged potential surfaces. The presence of the Polyelectrolyte layer alters the flow dynamics in the microchannel. The temperature in the fluid changes due to the Joule heating effect under the applied electric field.

Dynamic adaptive moving mesh finite-volume method for the blood flow and coagulation modeling.

In this work, we develop numerical methods for the solution of blood flow and coagulation on dynamic adaptive moving meshes. We consider the blood flow as a flow of incompressible Newtonian fluid governed by the Navier-Stokes equations. The blood coagulation is introduced through the additional Darcy term, with a permeability coefficient dependent on reactions. To this end, we introduce moving mesh collocated finite-volume methods for the Navier-Stokes equations, advection-diffusion equations, and a method for the stiff cascade of reactions. A monolithic nonlinear system is solved to advance the solution in time. The finite volume method for the Navier-Stokes equations features collocated arrangement of pressure and velocity unknowns and a coupled momentum and mass flux. The method is conservative and inf-sup stable despite the saddle point nature of the system. It is verified on a series of analytical problems and applied to the blood flow problem in the deforming domain of the right ventricle, reconstructed from a time series of computed tomography scans. At last, we demonstrate the ability to model the coagulation process in deforming microfluidic capillaries.

A Computational Analysis Unsteady Incompressible Newtonian Fluid Flow and Heat Transfer in a Cylindrical Pipe Filled with Porous Media Via the Collocation Approach

In this study, the problem of unsteady incompressible flow was analyzed using collocation technique to find the most accurate solution for the velocity and energy distribution of the Newtonian fluid flow. The flow experienced a gradual decrease with a retarded flow and afterwards increases but not a steady increase. It is revealed that a little increase in the Darcy number leads to an increase in the velocity of the fluid flow, indicating that porosity increase enhances the fluid flow. Results further show that increase in the Hartman parameter decreases the fluid velocity which is due to the strength the Lorentz force. Temperature decreases with increase in the Prandtl number and the Brinkman parameter.

Couette–Poiseuille Flow in Semi-Elliptic Channels

Abstract We present a novel analytical solution for Couette flows of incompressible Newtonian fluids in channels with a semi-elliptical cross section. The flow is steady, unidirectional, satisfies the no-slip condition at the boundaries, and is driven by the movement of the planar wall at constant velocity. The theoretical approach consists of a mapping function to rewrite the problem in an elliptical coordinate system coupled with Fourier's method for the solution of a Laplace equation with Dirichlet-type boundary conditions in the new domain. We then use our new solution together with available results for Poiseuille flows in a similar geometry (Alassar and Abushoshah, 2012, “Hagen–Poiseuille Flow in Semi-Elliptic Microchannels,” ASME J. Fluids Eng. 134(12), p. 124502) to study the so-called Couette–Poiseuille flows, where both pressure-driven and boundary-driven mechanisms act simultaneously. We present a detailed analysis of the flow field in Couette, Poiseuille, and Couette–Poiseuille flows in semi-elliptical channels with cross sections of different aspect ratios. For the latter case, we also determine the critical values of the axial pressure gradient that (i) increase the maximum flow velocity above that of the moving wall and shift its position toward the center of the channel, (ii) mark the onset of flow reversal with the emergence of a backflow region below the static wall, and (iii) eventually lead to a zero net flow rate through the channel.

Theoretical derivation of Darcy's law for fluid flow in thin porous media

AbstractIn this paper we study stationary incompressible Newtonian fluid flow in a thin porous media. The media under consideration is a bounded perforated 3D domain confined between two parallel plates. The description of the domain includes two small parameters: ε representing the distance between plates and connected to the microstructure of the domain such that . We consider the classical setting of perforated media, i.e. ‐periodically distributed solid (not connected) obstacles of size . The goal of this paper is to introduce a version of the unfolding method, depending on both parameters ε and , and then to derive the corresponding 2D Darcy law.

The Streaming Potential of Fluid through a Microchannel with Modulated Charged Surfaces.

In this paper, the effects of asymmetrically modulated charged surfaces on streaming potential, velocity field and flow rate are investigated under the axial pressure gradient and vertical magnetic field. In a parallel-plate microchannel, modulated charged potentials on the walls are depicted by the cosine function. The flow of incompressible Newtonian fluid is two-dimensional due to the modulated charged surfaces. Considering the Debye–Hückel approximation, the Poisson–Boltzmann (PB) equation and the modified Navier-Stokes (N-S) equation are established. The analytical solutions of the potential and velocities (u and v) are obtained by means of the superposition principle and stream function. The unknown streaming potential is determined by the condition that the net ionic current is zero. Finally, the influences of pertinent dimensionless parameters (modulated potential parameters, Hartmann number and slip length) on the flow field, streaming potential, velocity field and flow rate are discussed graphically. During the flow process and under the impact of the charge-modulated potentials, the velocity profiles present an oscillating characteristic, and vortexes are generated. The results show that the charge-modulated potentials are beneficial for the enhancement of the streaming potential, velocity and flow rate, which also facilitate the mixing of fluids. Meanwhile, the flow rate can be controlled through the use of a low-amplitude magnetic field.

Diffusive terms applied in smoothed particle hydrodynamics simulations of incompressible and isothermal Newtonian fluid flows

Diffusive terms applied in smoothed particle hydrodynamics simulations of incompressible and isothermal Newtonian fluid flows

Cylinder-lamina system fluid–structure interaction problem solved with an original OpenFOAM code

In numerical simulations, the partitioned approach allows treating a multi-physics phenomenon as two different computational fields, which are solved separately with their respective mesh discretisation and algorithms. This is of particular interest to fluid–structure interaction (FSI) problems for their complex resolution. In this respect, through the partitioned approach, ModsFsiFoam (MODalSuperpositionFsiFoam) solver has been developed. It allows the application of two different methods for fluid and solid solutions. In particular, it is based on a theoretical approach, the modal superposition principle, for the structural solution; this method provides a certain result for the linear structural field. The FVM (Finite VolumeMethod), by far the most widely used method for fluid-dynamics and gas-dynamics problems, has been used instead to solve the Navier–Stokes equations for an incompressible laminar flow of Newtonian fluid. The interfacial conditions have been used to pass information between the domains through a coupling algorithm. Implemented in OpenFOAM, a development environment consisting of libraries and applications for Linux distributions, written in the C++ source code, ModsFsiFoam solver has been already applied with satisfactory results to a typical fluid–structure interaction case found in literature, i.e. a system composed by an inverted flag treated as a flexible lamina, clamped to a wind tunnel wall, in which airflow is introduced in the axial direction. In this work, ModsFsiFoam solver outputs are compared with a system, the results of which are known for both fluid-dynamics and structural fields. The configuration consists of a laminar incompressible channel flow around a solid structure with an elastic part.

On the effects of orientation on flow and heat transfer from a semi-circular cylinder near a stationary wall

Numerical analysis of flow and forced convection heat transport from a two-dimensional semi-circular cylinder placed near a stationary wall is presented. The uniformly heated cylinder is within the boundary layer of the plane wall and is subjected to linear shear flow. An unsteady flow of incompressible Newtonian fluid around the cylinder is studied assuming constant properties. Two different orientations of the cylinder, i.e. the curved and flat surfaces exposed to the incoming flow, are considered, and the results are compared with those of a circular cylinder. The cylinder-to-wall gap ratio (G/D.) values are varied between 0.1 and 0.5, and the Reynolds number range of 100 ≤ Re ≤ 200 is considered. Numerical experiments are performed using Ansys Fluent. Results suggest that the presence of a stationary wall influences both the flow and thermal fields significantly. A decrement in the drag coefficient and average Nusselt number values is reported, while the lift coefficient and Strouhal number increase, resulting from shear layers’ interaction in the gap between cylinder and wall. The heat transfer enhancement ratio is higher for the flow past curved forebody than the flat forebody configuration and circular cylinder. Mean Nusselt number correlations for the range of parameters considered in the present study are provided.

Entrance length of oscillatory flows in parallel plate microchannels

This paper presents the numerical investigation of the purely oscillatory laminar flows of incompressible Newtonian fluids, in the entrance region of parallel plate microchannels. Development of the axial velocity profiles and the required entrance length were studied in the low Reynolds number regime (20[Formula: see text] 200) and for the low dimensionless oscillation frequency or the Stokes number (1.08 [Formula: see text] 2.80), which is applicable particularly for microchannel flows. To obtain more realistic and applicable results, the time-dependent parabolic entry conditions were considered for all simulations. The results show that for ([Formula: see text]1.53), the entrance length can be estimated by the steady-state results for corresponding inlet velocity profiles, while for the (1.53 [Formula: see text] 2.80), the deviation from the steady-state condition occurs for the entrance length. Further, according to the obtained numerical data, in this work, a useful correlation is proposed to predict the entrance length for the studied ranges of the purely oscillatory flows through the parallel plate microchannels.

New power-law scaling for friction factor of extreme Reynolds number pipe flows

We report a novel power-law scaling for the friction factor of incompressible Newtonian fluid flows at extreme Reynolds numbers: f = Ce/Re2/13. The formula is based on a new phenomenology for coherent structures that dominate the momentum exchange in meso-layer regions and scales with the geometric mean δδν, where δν is the viscous length scale and δ is the pipe radius. Comparisons with the experimental data from the Princeton Superpipe and the Hi-Reff Facility at the National Metrology Institute of Japan show excellent agreement for a large range of Reynolds numbers. This work, along with the recent empirical evidence, suggests a possible change in the mechanism of turbulent momentum transfer for pipe flows in extreme Reynolds numbers.

Analytical Solutions for a General Mixed Boundary Value Problem Associated with Motions of Fluids with Linear Dependence of Viscosity on the Pressure

An unsteady flow of incompressible Newtonian fluids with linear dependence of viscosity on the pressure between two infinite horizontal parallel plates is analytically studied. The fluid motion is induced by the upper plate that applies an arbitrary time-dependent shear stress to the fluid. General expressions for the dimensionless velocity and shear stress fields are established using a suitable change of independent variable and the finite Hankel transform. These expressions, that satisfy all imposed initial and boundary conditions, can generate exact solutions for any motion of this type of the respective fluids. For illustration, three special cases with technical relevance are considered and some important observations and graphical representations are provided. An interesting relationship is found between the solutions corresponding to motions induced by constant or ramptype shear stresses on the boundary. Furthermore, for validation of the results, the steady-state solutions corresponding to oscillatory motions are presented in different forms whose equivalence is graphically proved.