Flow Of Viscous Incompressible Fluid Research Articles

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.

The influence of noises with different spectra on viscous incompressible fluid flows

The results of an experimental study of the effects of noises on flows in a rotating spherical layer are presented. Noise is introduced into the flow in the form of random fluctuations of the inner sphere rotational rate relative to a time constant mean value. The flow velocity was measured with a laser Doppler anemometer. It was found that the noises of the equal amplitude, but with different spectra cause the generation of mean flows of different intensity. It is shown that the increase in the average velocities under the action of the noise is larger for the stable flows compared to unstable ones Keywords: noise, flows with rotation, spherical Couette flow.

Dynamics of incompressible viscous fluid flow in an elastic tube of varying cross-section

Dynamics of incompressible viscous fluid flow in an elastic tube of varying cross-section

The structure of viscous liquid internal flows in tanks with damping baffles

Modern moving objects containing large volumes of liquid need to ensure stability on the movement trajectory, reliability of control during maneuvers, as well as the ability to predict and prevent extreme movement conditions. The presented article provides review materials devoted to the research results into inertial flows of viscous incompressible fluid in tanks with internal damping baffles. In order to exert force on resonant excitations from the liquid side and to compensate for the instabilities of moving objects, the analysis and design of rational structures of influence means on currents is carried out. Among the most effective means of damping should be noted rigid internal baffles of various designs installed in tanks in the most likely areas where instabilities and sources of excitation of resonant fluid movements may occur. Flat rigid partitions, profiled permeable damping surfaces, perforated and retaining elements, enslavers of liquid due to surface tension forces, etc., require comprehensive and detailed study and analysis.

On the Regularity of Weak Solutions to Time-Periodic Navier–Stokes Equations in Exterior Domains

Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not have finite kinetic energy in general, the well-known regularity results for weak solutions to the corresponding initial-value problem cannot be transferred directly. The established regularity criterion demands a certain integrability of the purely periodic part of the velocity field or its gradient, but it does not concern the time mean of these quantities.

N-Side Cell-Based Smoothed Finite Element Method for Incompressible Flow with Heat Transfer Problems

In this paper, an n-sided cell-based smoothed finite element method (nCS-FEM) is presented to solve the convective heat transfer in incompressible viscous fluid flow. The Characteristic-based-split (CBS) scheme is used to stabilize the spatial and pressure oscillations of CS-FEM that occur during the process of solving incompressible Navier-Stokes equations. Meanwhile, the characteristic-Galerkin method in CBS is adopted as the convective stabilization in the heat transfer equation. In order to verify the proposed method, typical numerical examples are used to test the computational accuracy of CS-FEM. Meanwhile, the investigation of the robustness of highly distorted element is conducted in a natural convection test case. The calculation results of numerical examples show that CS-FEM is qualified to solve the steady and unsteady convective heat transfer problems for incompressible laminar flow with high reliability. The flow across tube banks with complex geometry in the heat sinks is also simulated to prove the capabilities of the proposed method. Well agreed comparison with the results of CFD software, Fluent, proves that the present method can effectively simulate realistic and complex flow with heat transfer problems.

Three-Dimensional Simulations of Viscous Incompressible Fluid Flows on Grids with Unmatched Grid Interfaces

The paper describes a numerical method that considers specific computational fluid dynamics (CFD) aspects of viscous incompressible flow simulations in the vicinity of interfaces between unmatched fragments of unstructured grids. The method is based on the general grid interface (GGI) principle, which involves conservative flux interpolation and does not require original grid modification at unmatched interfaces. A method is presented which combines adjacent unmatched fragments of an unstructured grid into a single domain by means of virtual interfaces considering connections between adjacent cells through virtual faces. The performance of the method is illustrated by the finite-volume discretization of the transport equation in the region of matched interfaces and its modification for the case of unmatched interfaces. The efficiency of the proposed method is demonstrated by three-dimensional CFD simulations with grid models composed of unmatched unstructured grid fragments. The simulation results are compared with equivalent simulations on matched grids. The influence of unmatched interfaces on the convergence rate and accuracy of the solution is assessed.

Analytical investigation of an incompressible viscous laminar Casson fluid flow past a stretching/shrinking sheet

This paper presents an analytical approach on capturing the effect of incompressible, non-Newtonian, viscous, Casson nanofluid flow past a stretching/shrinking surface, under the influence of heat radiation and mass transfer parameter. The governing nonlinear partial differential equations are first transformed into a series of associated nonlinear ordinary differential equations with aid of predictable transformation, while numerical computations follow. The implied nanofluid here is aluminum oxide (Al_{2} O_{3}). The analytical solution is exploited to reveal the accompanying non-dimensional boundary value problem and output results are employed to verify the method's reliability, where it is shown that they agree with current findings in the field. An incomplete gamma function is used to solve temperature equation analytically. We present various instances of the solution, depicting effects of the essential flow factor, the stretching/shrinking parameter, the mass transfer parameter, radiation parameter, and Prandtl number.

Random vortex dynamics via functional stochastic differential equations

In this paper, we present a novel, closed, three-dimensional random vortex dynamics system, which is equivalent to the Navier–Stokes equations for incompressible viscous fluid flows. The new random vortex dynamics system consists of a stochastic differential equation which is, in contrast with the two-dimensional random vortex dynamics equations, coupled to a finite-dimensional ordinary functional differential equation. This new random vortex system paves the way for devising new numerical schemes (random vortex methods) for solving three-dimensional incompressible fluid flow equations by Monte Carlo simulations. In order to derive the three-dimensional random vortex dynamics equations, we have developed two powerful tools: the first is the duality of the conditional distributions of a couple of Taylor diffusions, which provides a path space version of integration by parts; the second is a forward type Feynman–Kac formula representing solutions to nonlinear parabolic equations in terms of functional integration. These technical tools and the underlying ideas are likely to be useful in treating other nonlinear problems.

Transient natural convective flow of a radiative viscous incompressible fluid past an exponentially accelerated porous plate with chemical reaction species

AbstractThe present study deals with an unsteady magnetohydrodynamic natural convective flow of a viscous, incompressible fluid past an exponentially accelerated porous plate surrounded by a porous medium with suction or injection. The novelty of the current research is to analyze the behavior of the flow due to mass transfer with first‐order chemical reaction in the presence of a heat source in the energy equation. The existence of suction/injection and radiation parameters in the flow enhances the utility of the research as they are an integral part of nuclear reactors, thermal and chemical engineering processes, and many more. The Laplace transform technique (via Bromwich contour) is applied to solve exactly the governing equations. The nature of the flow velocity, temperature, and concentration profiles due to the impact of pertinent flow parameters are presented graphically. The numerical outcomes of coefficient of skin friction, rate of heat transfer, and mass transfer are obtained in tabular form. The results indicate that the skin friction increases slowly with the reaction parameter and largely with the suction parameter, whereas the concentration gradient increases at a much higher rate with the reaction parameter. The fluid injection has a negative impact on the velocity gradient. It is seen that the heat source enhances both velocity and temperature profiles throughout the flow field, whereas the first‐order chemical reaction acts reversely on the velocity and mass transfer process. The current research can be applied to identify the cause behind the drag force produced in seepage flow due to the heated or cooled accelerated plate.

Drag and heat transfer of metal and oxide agglomerates in flow of combustion products of solid propellant

Modeling and simulation of the motion of agglomerates with a complex composition and shape in the flow of combustion products is of interest for problems related to design and optimization of solid propellant rocket motors. An approach is developed for modeling of unsteady processes that occur when a particle consisting of an aluminum droplet and a condensed oxide particle attached to it (aluminum droplet with oxide cap) is transported by a viscous incompressible fluid flow. Methods are proposed to take into account the sliding of an attached oxide particle over the surface of the aluminum droplet. The results of numerical computations are used to find the drag and heat transfer coefficients of a non-spherical particle at flow velocities corresponding to the formation of separation zones. The constructed model is one of the components of a more general mathematical model designed to calculate two-phase flows of combustion products based on a multi-scale approach to the simulation of two-phase flows in a complex environment.

The Combined Impact of Thermal Radiation and Thermophoresis on Buoyancy-Driven Flow Near an Inclined Porous Plate

Abstract This report presents a similarity solution for the buoyancy-driven flow of viscous incompressible fluid past an inclined porous plate influenced by nonlinear thermal radiation and thermophoresis. The boundary layer equations are reduced to some set of ODEs through similarity variables. Furthermore, the ODEs are converted to IVP through the shooting technique. The numerical solution is obtained through the Runge–Kutta algorithm in Maple software. The impact of the emergence parameters present in the mathematical model is explained through graphs and tables. Results obtained showed that with combined effects of suction/injection and nonlinear thermal radiation, the heat transfer rate is directly proportional to the angle of inclination but inversely proportional to plate shear stress and mass transfer rate. Furthermore, it was observed that the heat transfer rate declines with higher buoyancy force but enhances the plate shear stress. Also, the mass transfer rate could be enhanced with a higher thermophoresis effect. Suction propagates the velocity and temperature profiles whereas it decreases the rate of particle concentration, while the contrast is true for injection. In addition, nonlinear thermal radiation complements the fluid temperature, particle concentration, and fluid transport.

Instabilities, Bifurcations, and Nonlinear Dynamics in Two-Dimensional Generalizations of Kolmogorov Flow

A family of two-dimensional flows of viscous incompressible fluid in a plane rectangular region with periodic boundary conditions (two-dimensional torus) is considered. The flows are induced by a force, periodic in the two spatial variables and independent of time. In the particular case of the harmonic dependence of the force on one coordinate and in the absence of average flow the well-known Kolmogorov flow is realized. In the general two-dimensional case restructurings of the stationary solutions of the Navier–Stokes equations are investigated numerically and the stability domains are determined in the space of governing physical and geometric parameters, namely, Reynolds numbers, force amplitudes, and spatial dimensions of periodicity cells. It is found that in a square region, whose side is equal to the spatial period of the external force, the main stationary flow preserves its stability against variation in the force amplitude and the Reynolds number. Contrariwise, in the cells, whose sides include several force periods, the variation in the parameters destabilizes the stationary flow. Stationary and self-oscillatory nonlinear secondary flows are considered. The effect of nonstationarity on the Lagrangian dynamics is discussed: the mechanisms of transition to the chaotic advection of passive particles depend on the commensurability of the Reynolds numbers characterizing the average flow in mutually perpendicular directions.

Deep reinforcement learning of viscous incompressible flow

We develop a new computational method to solve viscous incompressible fluid flow. This method is an extension of the Derivative-Free Loss Method, which solves elliptic and parabolic partial differential equations using Brownian motion, the Feynman-Kac formula, and reinforcement learning. Herein we derive a martingale condition and directly incorporate a projection of the velocity to solve the incompressible Navier-Stokes equations. Our method is mesh-free, scalable, and flexible, as demonstrated with several test cases.

Ab initio method of calculating invariant measure for turbulent flow

We present a method of calculating the invariant measure (IM) of hydrodynamical systems describing incompressible viscous fluid flow in bounded 3D volume V. Using a basis { w I } of zero-divergence vector functions on V satisfying boundary conditions we transform the Navier–Stokes equations (NSE) for the velocity field v ( x , t) = ∑ I v I (t) w I ( x ) into a simple system of ordinary differential equations for v I (t). The fact that fluid consists of a finite number of molecules in thermal motion implies that the number N of variables v I is finite too and that the system of equations for v I (t) contains a white-noise term. We prove that all solutions of this system are global, the IM exists and is unique. Its density ψ(v) defined on the phase space satisfies an elliptic partial differential equation (PDE). Expanding into Hermite functions He μ (v) φ ε (v) (where φ ε is a Gaussian function on , He μ are Hermite polynomials orthonormal with the weight φ ε and are IM mean values of He μ ) we transform this PDE into an infinite system of linear algebraic equations for and suggest some methods for solving it numerically. From known first- and second-order we could easily calculate mean turbulent velocity and Reynolds stress at any point x . Cylindrical pipe flow is used to illustrate the method everywhere in the paper. All conclusions are derived from the mathematical model by rigorous mathematics, with no further assumptions. All approximations can be arbitrarily improved.

Characteristic-Based Fluid Flow Modeling between Two Eccentric Cylinders in Laminar and Turbulent Regimes

Determining the flow between eccentric cylinders is crucial in a wide range of industries. The governing equations for the flow between eccentric cylinders cannot be solved analytically. Therefore, three-dimensional incompressible viscous fluid flow between eccentric and concentric cylinders has numerically been simulated in this paper to investigate them using a characteristic-based approach. The first-order characteristic-based scheme is used to calculate convective terms, whereas the second-order averaging technique is used to calculate viscous fluxes. The Taylor number, eccentricity distance, Reynolds number, and radius ratio are considered the controlling parameters of fluid flow between the cylinders. The influence of flow between cylinders on flow patterns is presented in terms of velocity, pressure, and flow contours. It is found that at a constant Taylor number, the asymmetric centrifugal forces produce the Taylor vortices on the right of the internal rotating cylinder as the eccentric distance increases. When the eccentric distance increases, the magnitude of shear stress and its fluctuation on the cylinder wall, as well as the pressure on the cylinder wall, rise. The numerical results obtained were validated by comparing them to previously published experimental results, which showed a high level of agreement.

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.