Flow Of Viscous Incompressible Fluid Research Articles

A mixed characteristic boundary condition for simulating viscous incompressible fluid flows around a hydrofoil

Smoothed particle hydrodynamics (SPH) is a meshfree method and has been widely used in the field of fluid dynamics. However, there is still a lack of robust approach to implement the far-field boundary condition in the simulation of free stream flow past the rigid body. To solve this problem, on the basis of Lastiwka et al.’s work, an improved non-reflecting boundary condition, called mixed characteristic boundary condition is proposed in this paper. The mixed characteristic boundary condition is tested by two-dimensional incompressible flows with a perturbation at the initial moment. The numerical results show that the mixed characteristic boundary condition can effectively suppress the reflection of waves on far-field boundaries. Finally, flows past a hydrofoil are simulated within the framework of the kernel gradient free SPH in two kinds of non-reflecting boundary condition. The results indicate that the present boundary condition is more robust and suitable for SPH than the one adopted by Lastiwka et al.

A Stable and Convergent Hodge Decomposition Method for Fluid–Solid Interaction

Fluid-solid interaction has been a challenging subject due to their strong nonlinearity and multidisciplinary nature. Many of the numerical methods for solving FSI problems have struggled with non-convergence and numerical instability. In spite of comprehensive studies, it has been still a challenge to develop a method that guarantees both convergence and stability. Our discussion in this work is restricted to the interaction of viscous incompressible fluid flow and a rigid body. We take the monolithic approach by Gibou and Min that results in an extended Hodge projection. The projection updates not only the fluid vector field but also the solid velocities. We derive the equivalence of the extended Hodge projection to the Poisson equation with non-local Robin boundary condition. We prove the existence, uniqueness, and regularity for the weak solution of the Poisson equation, through which the Hodge projection is shown to be unique and orthogonal. Also, we show the stability of the projection in a sense that the projection does not increase the total kinetic energy of fluid and solid. Also, we discusse a numerical method as a discrete analogue to the Hodge projection, then we show that the unique decomposition and orthogonality also hold in the discrete setting. As one of our main results, we prove that the numerical solution is convergent with at least the first order accuracy. We carry out numerical experiments in two and three dimensions, which validate our analysis and arguments.

Navier-Stokes-Oseen flows in the exterior of a rotating and translating obstacle

In this paper, we investigate Navier-Stokes-Oseen equation describing flows of incompressible viscous fluid passing a translating and rotating obstacle. The existence, uniqueness, and polynomial stability of bounded and almost periodic weak mild solutions to Navier-Stokes-Oseen equation in the solenoidal Lorentz space $ L^{3}_{σ, w} $ are shown. Moreover, we also prove the unique existence of time-local mild solutions to this equation in the solenoidal Lorentz spaces $ L^{3,q}_{σ} $.

On hydraulic analysis of the main parameters of longitudinalcirculating flow

Recently in practice of engineering hydraulic structures spillways with a longitudinal-circulating flow are applied. The distinguished properties of longitudinal-circulating flows are a unique example of compatibility of flow type with technological purpose of a spillway structure. The hydraulic characteristics of flow (throughput capacity, velocity distribution, pressure distribution, cavitation analysis, etc.) are determined on the basis of the calculation methods developed in the above studies, namely for: longitudinal flow using the known standard calculation methods [1]; longitudinal-circulating flow interacting with solid boundaries of spillway [1-4]; longitudinal-circulating flow in the form of a swirling stream in the aquatic environment or in the air [2; 3]; the flow arising from the interaction of unidirectional longitudinal-circulating flows [4; 5]; the flow arising from the interaction of oppositely swirling coaxial flows [3]. In this paper, the authors consider the longitudinal-circulating flow of viscous incompressible fluid in a closed channel and in a jet using a velocity wurf linking the three components of velocity U , V and W .

Couette - Hiemenz exact solutions for the steady creeping convective flow of a viscous incompressible fluid, with allowance made for heat recovery

Изучается установившееся ползущее конвективное течение вязкой несжимаемой жидкости в тонком бесконечном слое. Исследование течения жидкости основано на использовании класса точных решений для уравнений Обербека - Буссинеска в приближении Стокса. Поле скоростей описывается точным решением Хименца. Поле температуры и поле давление линейно зависят от горизонтальной (продольной) координаты, что соответствует классу точных решений Остроумова - Бириха. Конвективное движение вязкой несжимаемой жидкости индуцировалось касательными напряжениями на верхней проницаемой (пористой) границе и заданием теплового источника на нижней границе. Кроме того, на верхней границе учитывался теплообмен по закону Ньютона - Рихмана. Полученные точные решения описывают противотечения в жидкости, у которых количество застойных точек не превышает трех. Формирование противотечений в жидкости сопровождается отсосом (sucking) и вдувом (injection) жидкости через проницаемую границу. Наличие большего числа застойных точек формирует ячеистую структуру линий тока. Кроме того, поле скоростей, полученное при решении краевой задачи, характеризуется локализацией течения вблизи границ слоя жидкости (пограничный слой). Полученные в статье точные решения могут использоваться для решения нелинейной системы Обербека - Буссинеска. Показано, что при линеаризации системы Обербека - Буссинеска число Грасгофа может принимать большие значения, зависящие от показателя геометрической анизотропии.

Hydromagnetic chemically reacting and radiating unsteady mixed convection Blasius flow past surface flat in a porous medium

We investigate numerically in this paper, the mutual effects of thermal radiation, magnetic field and buoyancy forces on mixed convection of an electrically conducting chemically reacting incompressible viscous fluid flow over a heated vertical flat surface embedded in a porous medium. Suitable governing equations are obtained and changed to a system of couple nonlinear ordinary differential equations using desirable transformations. Boundary valued problems are therefore solved numerically using the Runge-Kutta-Fehlberg integration procedure coupled with shooting method. The results of the dimensionless velocity, temperature and concentration are then used to compute the skin friction, Nusselt number and Sherwood number. The influences of some of the flow parameters on each of these results are put up graphically and analysed.

Неустойчивость течения в сферическом слое при вращательных колебаниях внутренней границы

AbstractThe instability of viscous incompressible fluid flows caused in a thin spherical layer by torsional oscillations of the inner sphere in a thin spherical layer with respect to the sate of rest is studied numerically. It has been established that an increase in the frequency of torsional oscillations leads to a change in the mode of the instability, with a transition from secondary flows in the form of Taylor vortices to structures not observed earlier. The revealed instability is observed in the frequency range from 0.61 to 2.45 Hz or, if the wavelengths are taken relative to the layer thickness, from 0.67 to 1.33.

Heat and mass transfer with viscous dissipation in horizontal channel partially occupied by porous medium in the presence of oscillatory suction

This paper deals with unsteady oscillatory flow of viscous incompressible fluid with heat & mass transfer in a horizontal channel partially occupied by porous medium following the Darcy-Brinkman model. The interior territory of the channel consists of two regions; one of them is filled with porous material and second is clear fluid. At the porous medium fluid interface, interfacial coupling conditions for the fluid velocity, temperature and concentration were used to derive the analytical solution. The effects of pertinent physical fluid parameter like porosity, viscosity ratio, density ratio etc. on velocity, temperature and concentration distribution are considered and demonstrated through graphs. Also, the non-dimensional Skin-friction coefficient, Nusselt number and Sherwood number have been calculated and reported in tabular form.

Analysis of magnetohydrodynamic flow of a fractional viscous fluid through a porous medium

The aim of this paper is to investigate the exact general solutions of the incompressible viscous fluid flow by using the time-fractional Caputo–Fabrizio derivative. The flow of the fluid is subject to the motion of a plane wall, embedded in a porous medium under the influence of magnetic field. The corresponding non-dimensional governing fractional differential equation with appropriate initial and boundary conditions is solved by means of integral transforms namely, Laplace and Fourier transforms. Solutions are expressed as a sum of steady and transient parts, for the sinusoidal oscillations of the plane wall. The influence of involved physical parameters are discussed graphically. Specifically, it has been observed that the effective permeability Keff reduces the time taken to reach the steady state.

Radiated chemical reaction impacts on natural convective MHD mass transfer flow induced by a vertical cone

Abstract The consequence of thermal radiation in laminar natural convective hydromagnetic flow of viscous incompressible fluid past a vertical cone with mass transfer under the influence of chemical reaction with heat source/sink is presented here. The surface of the cone is focused to a variable wall temperature (VWT) and wall concentration (VWC). The fluid considered here is a gray absorbing and emitting, but non-scattering medium. The boundary layer dimensionless equations governing the flow are solved by an implicit finite-difference scheme of Crank–Nicolson which has speedy convergence and stable. This method converts the dimensionless equations into a system of tri-diagonal equations and which are then solved by using well known Thomas algorithm. Numerical solutions are obtained for momentum, temperature, concentration, local and average shear stress, heat and mass transfer rates for various values of parameters Pr, Sc, λ, Δ, Rd are established with graphical representations. We observed that the liquid velocity decreased for higher values of Prandtl and Schmidt numbers. The temperature is boost up for decreasing values of Schimdt and Prandtl numbers. The enhancement in radiative parameter gives more heat to liquid due to which temperature is enhanced significantly.

Dean instability and secondary flow structure in curved rectangular ducts

The pressure driven, fully developed turbulent flow of incompressible viscous fluid (water) in 120° curved ducts of rectangular cross-section is investigated experimentally and numerically. Three different types of curved duct (A-CL, B-SL and C-IL) with continuously varying curvature conform to blade profile as the inner and outer curvature walls to simplify and guide the impeller design of pumps. After validating the numerical method against Particle Image Velocimetry (PIV) measurements, the flow development in the ducts is analyzed in detail by Computational Fluid Dynamics (CFD) for a wide range of Reynolds numbers (Re = 2.4 × 104–1.4 × 105) and aspect ratios (Ar > 1.0, =1.0 and <1.0). The results clearly depict the existence of multiple Dean vortices along the duct: while the axial velocity profile is more related to an inner Dean vortex (called split base vortex), the wall pressure is more influenced by the Dean vortex attached to the inner curvature wall (called ICW Dean vortex). The induced multiple Dean vortices and the secondary flow patterns in the duct cannot be faithfully predicted by using traditional techniques. Therefore, a new criterion based on the vortex core velocities is proposed. With this approach, the effects of Re, Cr and Ar on the Dean instabilities in curved ducts are carefully studied. Decreasing Re promotes the generation of Dean vortices closer to the duct inlet, a trend that is as opposed to laminar flow. In addition, a new pair of vortices called entrainment Dean vortex occurs near the outlet of the curved duct with Ar = 1.0, which has not been previously reported in the literature.

STAGNATION POINT VISCOUS INCOMPRESSIBLE FLUID FLOW BETWEEN POROUS PLATES – A STUDY USING WAVELET METHOD

The axially symmetric laminar incompressible viscous fluid flow due to uniform blowing through two parallel porous plates is investigated. The governing Navier-Stokes equations are transformed into a nonlinear ordinary differential equation by using similarity transformation. We developed a new elegant approximate scheme based on Haar wavelets coupled with collocation approach for the solution of the problem. Validity of the solution is confirmed by estimating the solution error at various resolution levels. The influence of the Reynolds number on pressure gradient and velocity has been discussed and presented through graphs. We have also analysed the mass transform across the centre plane and a good agreement is found with the available literature results

Numerical solution of inverse problems in hydrodynamics

The paper is devoted to inverse problems for the unsteady viscous incompressible fluid flow. In the problems under consideration we estimate the velocity vector on a part of the boundary using velocity measurements in a certain observation subdomain. Optimal control approach reduces this problem to the constrained minimization. For unsteady flow and the discrete measurement data we use discrete optimization methods to solve this problem. New numerical algorithm based on the finite dimensional minimization is proposed and numerical results are discussed.

Global existence for 3D non-stationary Stokes flows with Coulomb’s type friction boundary conditions

In this paper, we study non-stationary viscous incompressible fluid flows with non-linear boundary slip conditions given by a subdifferential property of friction type. More precisely we assume that the tangential velocity vanishes as long as the shear stress remains below a threshold , that may depend on the time and the position variables but also on the stress tensor, allowing to consider Coulomb’s type friction laws. An existence and uniqueness theorem is obtained first when the threshold is a data and sharp estimates are derived for the velocity and pressure fields as well as for the stress tensor. Then an existence result is proved for the non-local Coulomb’s friction case using a successive approximation technique with respect to the shear stress threshold.

NUMERICAL SOLUTION OF UNSTEADY FLOW BETWEEN PARALLEL PLATES USING HAAR WAVELET-QUASILINEARIZATION METHOD

The present study is concerned with the analysis of unsteady flow of viscous incompressible fluid between parallel rectangular and circular plates. The Navier-Stokes equations modelling the flow are transformed into a fourth order non-linear ordinary differential equation using a similarity transformation. The resulting equation is solved by a new efficient numerical scheme based on Haar wavelet-quasilinearization method. The solution representing pressure gradient is obtained for large values of Reynolds number. A comparison with numerical results generated by MATLAB routine bvp4c demonstrates that the proposed method is more efficient and promising technique for solving highly nonlinear two-point boundary value problems. The absolute error and rate of convergence of numerical results are computed to test the applicability and accuracy of the method

Boundedness, almost periodicity and stability of certain Navier–Stokes flows in unbounded domains

We investigate the existence, uniqueness and stability of bounded and almost periodic mild solutions to several Navier–Stokes flow problems. In our strategy, we propose a general framework for studying the semi-linear evolution equations with certain smoothing properties of the linear part and with the local Lipschitz continuity of the nonlinear operator. Our method is based on interpolation functors combined with differential inequalities. Our abstract results are applied to Navier–Stokes–Oseen equations describing flows of incompressible viscous fluid passing a translating and rotating obstacle and to Navier–Stokes equations on aperture domains and/or in Besov spaces.

The uniform convergence of the eigenfunctions expansions of the biharmonic operator in closed domain

The mathematical models of the various vibrating systems are partial differential equations and finding the solutions of such equations are obtained by developing the theory of eigenfunction expansions of differential operators. The biharmonic equation which is fourth order differential equation is encountered in plane problems of elasticity. It is also used to describe slow flows of viscous incompressible fluids. Many physical process taking place in real space can be described using the spectral theory of differentiable operators, particularly biharmonic operator. In this paper, the problems on the uniform convergence of eigenfunction expansions of the functions from Nikolskii classes corresponding to the biharmonic operator are investigated.

On steady flow of non-Newtonian fluids with frictional boundary conditions in reflexive Orlicz spaces

A stationary viscous incompressible non-Newtonian fluid flow problem is studied with a non-polynomial growth of the extra (viscous) part of the Cauchy stress tensor together with a multivalued nonmonotone frictional boundary condition described by the Clarke subdifferential. We provide an abstract result on existence of solution to a subdifferential operator inclusion and a hemivariational inequality in the reflexive Orlicz–Sobolev space setting modeling the flow phenomenon. We establish the existence result, and under additional conditions, also uniqueness of a weak solution in the Orlicz–Sobolev space to the flow problem.

Influence of Stefan blowing on nanofluid flow submerged in microorganisms with leading edge accretion or ablation

The forced convective boundary layer flow of viscous incompressible time-dependent fluid containing water-based nanofluids and gyrotactic microorganisms simultaneously, from a flat surface with leading edge accretion (or ablation), is theoretically investigated in the present study. In doing so, the governing conservation equations are rendered into a nonlinear system of ordinary differential equations by means of utilizing appropriate coordinates transformations. MAPLE symbolic software is employed to solve these equations, which are subjected to impose boundary conditions using the Runge–Kutta–Fehlberg fourth-fifth order numerical method. It is noteworthy that the results of the present study are in an excellent agreement with previous solutions available in literature. The effect of selected parameters on velocity, temperature, nanoparticle volume fraction and motile microorganism density function is then investigated. Tabular solutions are included for the skin friction, heat transfer rate, nano-particle mass transfer rate and microorganism transfer rate. Applications of the study arise in advanced micro-flow devices to bio-modified nanomaterials processing.

Точные решения для естественной конвекции слоистых течений вязкой несжимаемой жидкости при задании тангенциальных сил и линейного распределения температуры на границах слоя

Точные решения для естественной конвекции слоистых течений вязкой несжимаемой жидкости при задании тангенциальных сил и линейного распределения температуры на границах слоя