Flow Of Viscous Incompressible Fluid Research Articles

On well-posedness of Navier–Stokes variational inequalities

In this paper, well-posedness is carried out on variational inequalities in a general form for the stationary Navier–Stokes equations modeling viscous incompressible fluid flows with a nonsmooth slip boundary condition of friction type. For a special form of the variational inequality commonly studied in existing literature, our proof technique leads to a substantial improvement on the well-posedness condition.

Numerical study of transitions in lid-driven flows in shallow cavities

In this article, three dimensional (3D) lid-driven flow in shallow cavities with a unit square base are studied. The numerical solution of the Navier–Stokes equations modeling incompressible viscous fluid flow in a cavity is obtained via a methodology combining a first order accurate operator-splitting scheme, a L 2 -projection Stokes solver, a wave-like equation treatment of the advection and finite element space approximations. Numerical results of a lid-driven flow in a cubic cavity show a good agreement with those reported in literature. The critical Reynolds numbers (Re cr ) for having flow with increasing of oscillating amplitude (a Hopf bifurcation) in different shallow cavities are obtained and associated oscillating modes are studied.

Optimization of mass and heat flux of MHD viscous fluid flow with constant proportional Caputo derivative by using response surface methodology: Sensitivity analysis

The study of viscous dissipation in the context of unsteady incompressible magnetohydrodynamic viscous fluid flow over a moving plate is a complex and important topic in fluid dynamics and heat transfer. This scenario combines several physical phenomena and has practical applications in various engineering and scientific fields. The fractional mathematical model is proposed by considering the effect of viscous dissipation force of the flowing fluid. For this purpose, fluid is assumed to be lying over a vertical plate that is moving in its own plane. The governing equations are transformed into the dimensionless form and developed fractional model with a new operator Constant Proportional Caputo Derivative. We used the Laplace transform technique to find the solution of the dimensionless governing equation analytically. The transformed solutions for energy and momentum balances developed in terms of series. The validation of the present model comparison graphs is plotted for temperature. The sensitivity of different input parameters on output response are analyzed and displayed the sensitivity results in tabular and graphical form and found that the permeable parameter is most sensitive to skin friction coefficient, and the Eckert number is most sensitive parameter among others to Nusselt Number. The novelty of present work is to develop a correlation between input parameters and output responses by using Response Surface Methodology (RSM). As no such correlation has been developed for optimization of mass and heat flux of MHD viscous fluid flow with Constant Proportional Caputo derivative by using RSM. By using this correlation, we have performed sensitivity analysis for output responses.

A Hermite-type collocation mesh-free approach for simulating incompressible viscous fluid flows

In this work, a novel Hermite-type mesh-free model for incompressible viscous fluid flows is proposed, as a way, to overcome the numerical difficulties experienced by solving under weak or strong formulation the pure stream-function Navier–Stokes equation. In this model a dimensionless virtual domain is utilized, in order to make an accurate dimensionless shape-functions of the recently developed Hermite-type collocation Weighted Least Square approximation, by using dimensionless scale parameters. Then, a Jacobian transformation matrix is built to express the shape-functions spatial derivatives from the virtual to the considered domain. The resolution of the obtained nonlinear algebraic system is performed by the High Order Continuation Method. Numerical tests were investigated on incompressible viscous isothermal fluid flows in lid-driven cavity, backward-facing step, sudden expansions and around various obstacle shapes. They show the advantages of the proposed model compared to the reference Hermite-type collocation models used for pure stream-function equation and the weak Galerkin procedures as Finite Element Method and Element Free Galerkin method, in term of computation accuracy, number of degree of freedom, implementation simplicity and computation time. The numerical and experimental results of literature confirm the validity and capability of the proposed dimensionless model to simulate fluid flows in a expended-lengths inflow–outflow geometry and around obstacles of circular, inclined elliptical and Joukowski airfoil shapes.

Effect of the Non-Linear Radiative Unsteady Mixed Convective Flow over a Curved Stretching Surface with Soret and Dufour Effects: A Numerical Study

The subject of unsteady convective flow with non-linear thermal radiation has become an important issue of research, due to its implications in advanced energy conversion systems operating at high temperature, solar energy technology and chemical process at high operation temperature. Due to the importance of this issue, a time dependent incompressible viscous fluid flow, heat and mass transfer over a curved stretching surface has been numerically analysed by taking into account the heat flux due to concentration gradient and mass flux due to temperature gradient. Together with this the Rosseland approximation is being employed for the nonlinear thermal radiation impact in presence of thermal slip. With the aid of non-dimensional variables and the corresponding physical boundary conditions, the leading nonlinear momentum, energy, and species equations are converted into a set of coupled ordinary differential equations. These equations are then resolved using the MATLAB bvp4c solver. The stability of the numerical technique has been verified and compared with available literatures. The resultant parameters of engineering interest and the boundary layer flow field parameters and have been presented using tables and graphically plots. The study concludes that for lesser curvature parameter (0.5≤K≤0.7) the surface drag force, heat and mass transfer rates can improve by about 9.59%, 2.87% and 1.67% each respectively. The presence of the temperature ratio parameter and the non-linear thermal radiation are found to greatly influence the temperature profile and the heat transfer rate of the system. Results show that the heat transfer rate improves by about 24.39% and 16.66% for varying non-linear thermal radiation (1≤Rd≤1.5) and temperature ratio parameter (1.2≤θw≤1.4) respectively. Results obtained also show that improving the thermal slip parameter (0.4≤L≤0.6) can reduce heat transfer rate by about 13.62% and reduce the surface temperature profile.

Dissipation in nonequilibrium thermodynamics and its connection to the Rayleighian functional

We examine quantitatively the role of dissipation in nonequilibrium thermodynamics and its connection to variational principles and the Rayleighian functional. The extremum of the Rayleighian is sometimes used to describe the inertialess (dissipation-dominated) dynamics of continuum systems, and it has been applied recently for the modeling of soft matter dynamics. We discuss how dissipation is considered within one of the modern complete descriptions of nonequilibrium thermodynamics, namely the single generator bracket formalism. Within this formalism, dissipation is introduced through the use of the dissipation bracket, describing irreversible dynamics, which is added to a Poisson bracket that describes the reversible dynamics of the system. A possible connection with the Rayleighian functional is then demonstrated that in all cases considered herein, the Rayleighian is equal to minus one half of the effective dissipation rate of the Lagrangian functional. The effective dissipation rate is obtained starting with an inertial (i.e., flux-based or velocity-based) system description, involving the Poisson bracket and the primitive part (i.e., without the entropy correction term) of the dissipative bracket. Several examples are discussed in detail, ranging from an algebraic model (damped oscillator) to continuum ones: modeling of fluid flow in porous particle media, viscous Newtonian compressible and incompressible fluid flows, and more interestingly, flow of a nematic liquid-crystalline material.

Зарождение вихреобразования на границе кругового цилиндра при его обтекании потоком вязкой жидкости

The paper considers the problem of the generation of vortex formation on the surface of a circular cylinder placed in a flow of incompressible viscous fluid. To study this process, a new time-iterative approach is formu-lated for solving the 2D problem of flow around the circle based on the BIE method with Green's functions for the outer part of the cylinder with the Dirichlet boundary condition on its surface. A new approach, based on the transient Navier-Stokes equation in the variables stream function - vortex, using classical methods of potential theory and the boundary element method, allows us to obtain a complete system of three integral equations that determine the fields of stream functions and vorticity at a new time step, if these fields are known from the previous step. The assumption about the initial unexcited state of the flow (the vorticity function in the entire flow region is zero) allows us to obtain an analytical solution at the first time iteration step. The analysis of the obtained solution depending on the time step allows us to formulate a hypothesis about the nature of the generation of vortex formation on the surface of the circular cylinder in a flow of incompressible viscous fluid. The results obtained describe the appearance on the surface of the cylinder of two generalized vortices, having infinitely high intensity and infinitely small localization near the surface of the cylinder, which “instantly” break away from the surface of the cylinder, with a significant decrease in intensity, but with a large coverage of the flow around the cylinder.

Analysis of incompressible viscous fluid flow in convergent and divergent channels with a hybrid meta-heuristic optimization techniques in ANN: An intelligent approach

Analysis of incompressible viscous fluid flow in convergent and divergent channels with a hybrid meta-heuristic optimization techniques in ANN: An intelligent approach

Exact solutions for the description of nonuniform unidirectional flows of magnetic fluids in the Lin–Sidorov–Aristov class

The paper considers the exact integration of magnetic hydrodynamic equations for describing nonuniform unidirectional flows of viscous incompressible fluids. The construction of an exact solution is based on the well-known representation of hydrodynamic fields as the Lin–Sidorov–Aristov class. The 3d magnetic field is described by linear forms with respect to two spatial coordinates (longitudinal, or horizontal). The coefficients of the linear forms depend on the third coordinate and time. In view of the incompressibility condition, the 1D velocity field depends on two coordinates and time. The pressure is shown to be determined by a quadratic form with constant coefficients. These coefficients are determined by pressure distribution on the known (free) boundary. The exact solution is illustrated by the integration of non-1D hydrodynamic fields in the case of the steady motion of a conducting viscous incompressible fluid. This solution is polynomial, and it will be useful for the formulation of new problems of hydrodynamic stability.

Weakly viscous two-dimensional incompressible fluid flows using efficient isogeometric finite element method

This paper presents a straightforward and efficient numerical simulation method for solving the Navier–Stokes equations for weakly viscous incompressible fluids describing steady flow. Our approach utilizes isogeometric finite elements to handle higher-order partial differential operators associated with weakly viscous incompressible flow problems. Specifically, our numerical formulation employs a principle of virtual power (PVP)-based weak formulation that utilizes a stream-function field, which distinguishes it from the more commonly used bi-harmonic type formulations. The usage of a stream-function field ensures a pointwise divergence-free velocity condition, making the present method suitable for low to moderately high Reynolds number flow problems. In contrast to the bi-harmonic formulation, which is typically used for describing internal flow and requires special treatment of outflow boundary conditions, the PVP-based formulation is more general and does not require special treatment at the outflow boundary. It is also demonstrated that both bi-harmonic and PVP-based weak formulations yield identical results for internal flow problems. Our method employs non-uniform rational B-spline basis functions, and we present a simple stitching technique for imposing no-slip Dirichlet boundary conditions. Finally, we solve Poisson's equation to recover the pressure field. Furthermore, we use an appropriate Gaussian quadrature that is exact for splines to speed up the computation of various element matrices, especially for high polynomial degrees. The proposed formulation is evaluated by solving a set of numerical problems, including internal flow and channel flow problems.

Analysis of Fluid Flows in Bounded Domain with Particular Shape of a Cavity using Lattice Boltzmann Method

Background: The present work numerically models the incompressible, continuous phase, viscous flow of Newtonian fluid flow in a bounded domain of two-dimensional cavity that is driven by walls and contains grooves in the shape of squares on the lower wall. With the help of the mesoscopic lattice Boltzmann method (LBM) and D2Q9 square lattice model, simulation results are found stable and reliable. The flow physics of the problem by varying Reynolds number, the height and quantity of lower wall grooves, and other fluid flow characteristics within the bounded domain are studied in detail. It is seen that the effects of the groove heights and wavelengths on the fluid flow are structured within the bounded domain. The study is performed from low Re = 100 to high Re = 3200, with minimum two and maximum four-wavelength grooves evaluated on the bottom surface, each having a height of low 0.25 and high 0.75. Additionally, a thorough discussion of complicated vortex dynamics is provided regarding the input parameters and geometry. Objective: The current study aims to use mesoscopic LBM to analyze incompressible viscous fluid flows on complex geometries other than rectangular shapes. Methods: Mesoscopic approach of kinetic theory-based Lattice Boltzmann method (LBM) is implemented in the current work. The popular Single Relaxation Time Lattice Boltzmann method with D2Q9 square lattice model and second-order accurate boundary condition is adopted for the current study. Results: The numerical approach of LBM is used to simulate fluid flows in a 2D bounded domain with grooved bottom surfaces. The influence of different factors, such as the height of bottom-wall surface grooves, flow Reynolds number, and wavelength of these grooves on flow patterns, is then investigated. Conclusion: The numerical study of the bounded domain is considered, and the Reynolds number is varied from 100 to 3200, with two and four-wavelength grooves evaluated on the bottom surface, each having a height of 0.25 and 0.75. The impacts on the flow pattern both within and slightly above the grooves of the computational findings for different Reynolds numbers, groove heights, and groove wavelengths are evaluated. As the Reynolds number rises, the mixing phenomenon of fluid is shown to flow more quickly in the wall-driven enclosures.

On Exact Solutions to Problems of Steady Flow of Incompressible Viscous Fluid in a Channel and in a Circular Pipe

Turning to the well-known Couette flow, we again, but now in a new formulation, consider the steady motion of an incompressible viscous fluid in a channel with two parallel flat walls, one of which is stationary while the other moves at a constant speed in its plane. In the classical formulation of this problem on a layered (laminar) fluid flow in a channel, the wall velocity and the constant pressure drop along the channel are independent quantities and are considered predetermined. However, when a solid body moves along the fluid surface, the fluid particles are set in motion. This occurs due to the arising pressure generated in the fluid caused by the movement of the solid body. Therefore, here the pressure or pressure drop is not predetermined but is determined as a result of solving the corresponding two-dimensional boundary value problem of a steady flow of a viscous fluid in a channel. For this, the corresponding boundary value problem of a fluid flow in the channel is formulated based on the linearized Navier-Stokes equations obtained from the general nonlinear Navier-Stokes equations for a steady flow of a viscous fluid neglecting the convective terms, which is true for small Reynolds numbers. Using the Fourier integral transform method, an exact (closed) solution to this boundary value problem is constructed; the velocity and pressure components are determined. Then it is shown that the resulting solution, different from the known Couette flow solution, also satisfies the original nonlinear Navier-Stokes equations, the continuity equation, and boundary conditions. A comparative analysis of the new solution with the Couette flow solution is carried out. The well-known Hagen-Poiseuille problem is also discussed from the point of view of establishing the conditions for the laminar axisymmetric and steady flow of an incompressible viscous fluid in a straight circular pipe According to the study's results, to implement laminar flow under the indicated conditions, the pressure drop along the pipe must be constant. The study demonstrates that this condition is simultaneously sufficient, and therefore, the necessary and sufficient condition is established for a laminar flow in a straight circular pipe.

The heat transfer effects of MHD slip flow with suction and injection and radiation over a shrinking sheet by optimal homotopy analysis method

The current study investigates the laminar flow of boundary layer using a porous surface shrinking exponentially under varying magnetic field, suction/injection, radiation on velocity and thermal slips. The dimensionless nonlinear differential equations were also defined in terms of governing partial differential equations and applying similarity transformations. The equations were analytically solved following the homotopy analysis method (HAM). An excellent agreement is observed in comparison with theavailable literature in special case (Skin friction coefficient). In the current study, an analytic solution is obtained for the laminar incompressible MHD boundary layer viscous fluid flow problem on the exponentially electrically conducting porous shrinking surface. The impact of different parameters like injection/suction, Prandtl number, radiation, velocity slip, thermal slip, as well as the magnetic field on different velocity and temperature values have been presented graphically, and have been discussed in detail. The f″(0) skin friction rises with higher suction parameter s(>0) values, magnetic parameter M but it decreases when the slip parameter value is increased. Whereas heat transfer rate −θ′(0) rises with an increasing M, s and λ..

Physics-Informed Neural Network for Flow Prediction Based on Flow Visualization in Bridge Engineering

Wind loads can endanger the safety and stability of bridges, especially long-span cable-supported bridges. Therefore, it is important to evaluate the potential wind loads during the bridge design stage. Traditionally, wind load evaluation is performed by wind tunnel testing, which is relatively expensive. With the development of computational fluid dynamics and high-performance computing, numerical simulations are becoming more accessible for designers. However, the costs required for accurate numerical results are still high, especially for high-fidelity simulations. Under this condition, searching for a more efficient method to evaluate the wind loads in bridge wind engineering has become a new goal. It seems that flow visualization is a good entry point. Although flow visualization techniques have been developed in recent years, it remains difficult to extract velocity and pressure fields from images. To address this problem, physics-informed neural networks (PINNs) have been developed and validated. This study establishes a PINN to investigate the two-dimensional viscous incompressible fluid flow passing a generic bridge deck section. Two cases with different Reynolds numbers are tested. After careful training, it is found that the PINN can accurately extract the velocity and pressure fields from the concentration field and predict the drag and lift coefficients. The results demonstrate that PINNs are a promising method for extracting useful flow information from flow visualization data in engineering applications.

Unsteady Magnetohydrodynamic (MHD) Cu–Al2O3/Water Hybrid Nanofluid Flow and Heat Transfer from an Exponentially Accelerated Plate

The present study intends to explore heat transfer characteristics of the unsteady natural convective flow of Cu–Al2O3/water hybrid nanofluid due to exponentially accelerated vertical plate. 2D Laminar viscous incompressible boundary layer fluid flow is considered in the presence of MHD and accelerating parameter. The governing partial differential equations with appropriate boundary conditions are solved using the Crank-Nicolson numerical technique. Plots for skin friction coefficient, velocity, temperature, Nusselt number concerning Magnetic parameter (M), Accelerating parameter (a), Grashof number (Gr), Volume fraction (Φ2), and time are disclosed. The study imparted that Cu–Al2O3 hybrid nanoparticles with water as base fluid facilitate a higher heat transfer rate and soaring Nusselt number compared to nanofluid Cu/water. Furthermore, we found an elevated skin friction coefficient in nanofluid Cu/water than in hybrid nanofluid Cu–Al2O3/water in all non-dimensional parameters.

An analytical method for the drag force of a thin flat plate in a flow of viscous fluid

In the problem of classical hydrodynamics about a thin finite-length flat plate in a uniform flow of viscous incompressible fluid we propose a new analytical method to develop an explicit representation for the drag force. The approach proposed is based on a certain integral equation of the first kind which is valid in the case of small Reynolds numbers (strong viscosity, or slow stream). The constructed asymptotic solution coincides with the classical Harrison–Filon formula, developed by absolutely different technique, as a particular case of the Oseen slow flow around an elliptical cylinder.

Analysis of Von Kármán Swirling Flows Due to a Porous Rotating Disk Electrode

The study of Von Kármán swirling flow is a subject of active interest due to its applications in a wide range of fields, including biofuel manufacturing, rotating heat exchangers, rotating disc reactors, liquid metal pumping engines, food processing, electric power generating systems, designs of multi-pore distributors, and many others. This paper focusses on investigating Von Kármán swirling flows of viscous incompressible fluid due to a rotating disk electrode. The model is based on a system of four coupled second-order non-linear differential equations. The purpose of the present communication is to derive analytical expressions of velocity components by solving the non-linear equations using the homotopy analysis method. Combined effects of the slip λ and porosity γ parameters are studied in detail. If either parameter is increased, all velocity components are reduced, as both have the same effect on the mean velocity profiles. The porosity parameter γ increases the moment coefficient at the disk surface, which monotonically decreases with the slip parameter λ. The analytical results are also compared with numerical solutions, which are in satisfactory agreement. Furthermore, the effects of porosity and slip parameters on velocity profiles are discussed.

Space-time spectral method for the Stokes problem

The Stokes equations are a linearized version of the Navier-Stokes equations and model incompressible viscous fluid flow with low Reynolds numbers. Several spectral methods, exhibiting exponential decay in error when the solution is analytic, are known to solve the steady-state Stokes problem numerically. A common strategy to solve such a problem in the time-dependent case involves extending the spectral scheme in spatial derivatives by implementing a low-order finite difference scheme for the time derivatives. Instead, we implement and analyze a space-time spectral method for the Stokes problem, which converges exponentially in both space and time. This numerical scheme imposes spectral collocation in time and PN−PN−2 spectral Galerkin scheme in space by using a recombined Legendre polynomial basis, resulting in a global spectral operator that is a saddle point matrix. The main objectives of the research are estimating the condition number of the global spectral operators and proving the spectral convergence of this scheme in space and time. The analysis is not quite complete because two of the estimates are based on numerical evidence. However, throughout the project, some intermediate results-such as the 2-norm of the pseudospectral derivative matrix for Chebyshev-Gauss-Lobatto nodes as well as the condition number of the mass matrix and discrete Laplacian for a recombined Legendre basis-were proved to obtain the aforementioned findings. Numerical experiments of this scheme verify the theoretical results. Also, the numerical result of applying this scheme to the Navier-Stokes equations is presented.

On numerical simulation of fluid - structure interaction problems using variational multiscale methods

This paper focus on the numerical approximation of a simplified two dimensional aeroelastic problem, where the flexibly supported airfoil with a control section is considered. In this case the coupling of the control section with other mode can cause a decrease of the flutter velocity. The problem is mathematically described using the fully coupled formulation of the incompressible viscous fluid flow over a flexibly structure, whose motion is modeled by system of ordinary differential equations. The incompressible flow is described by the system of Navier–Stokes equations written in the Arbitrary Lagrangian Eulerian form in order to treat the motion of the computational domain. The numerical approximation is treated using the variational multiscale approach using the algebraic subgrid scale model. The construction of the ALE mapping is based on a robust mesh deformation method. The numerical results are presented.

On numerical solution of boundary layer flow of viscous incompressible fluid past an inclined stretching sheet in porous medium and heat transfer using spline technique

In this paper, the boundary layer flow of viscous incompressible fluid over an inclined stretching plate in porous media with body force and heat transfer has been studied. To solve this problem, we develop a suitable spline method which is used to calculate the velocity function of the flow problem. We proceed as follows:•With a suitable stream function, the concerned boundary layer equation is converted into non-linear third order ordinary differential equation together with appropriate boundary conditions in an infinite domain which has been further linearized by using quasi-linearization method.•Then, we develop a non polynomial quintic spline technique which has been used to find the numerical values of the velocity function of the flow problem. The convergence analysis of the developed spline technique has been discussed.•Later, the method developed so far has been applied to solve nonlinear boundary value problem for different angles of inclination and Froude number. The values obtained so far have been used to study heat flow problem. Finally, skin friction has been discussed.