Flow Of Incompressible Newtonian Fluid Research Articles

Limit of the lyne-type vortices of the pulsatile flow in a curved pipe.

The fully developed periodic laminar flows of incompressible Newtonian fluid through a pipe of circular cross section, which is coiled in a circle, have been simulated numerically. The existence of a four-vortex secondary flow system in oscillatory flow was first pointed by Lyne. Even in the pulsating flow, if the amplitude ratio of the volumetric flow rates β is small, the Lyne-type secondary flow patterns appear. The behavior of Lyne-type vortices is investigated for the range 15.07 l De l 176.22, 22.87 l Wo l 50.00, and 0.00 l β l 0.10, and the description of the cause and mechanism of this phenomenon is presented. It is found that the flow patterns are mainly governed by Wo and that the secondary flow in the central core disappears at β g 0.1, unlike in the steady flow.

Flow patterns of the fully developed pulsatile flow in a curved pipe.

The fully developed periodic laminar flows of incompressible Newtonian fluid through a pipe of circular cross section which is coiled in a circle have been simulated numerically. The flow patterns are characterized by three parameters: the Womersley number Wo, the amplitude ratio β, and the Dean number De. The effect of these parameters on the flow has been studied for the range 15.07≤De≤265.49, 2.l9≤Wo≤50.00, and 0.50≤β≤2.00 for the curvature ratio, δ, equal to 0.05. The mannner in which the secondary flows evolve with increasing Womersley number and Dean number is explained. The secondary flow patterns are classified into three groups : the viscous-term-dominated type, the convection-term-dominated type, and the inertia-term-dominated type. It is found that, when the amplitude ratio of the volumetric flow rate, prescribed by a cosine function, is equal to 1.0, 4 - 6 vortices of the secondary flow appear at high Dean number, and that the Lyne-type flow patterns disappear at β≥0.50.

Numerical 3D-simulation of pulsatile wall shear stress in an arterial T-bifurcation model

The structure of pulsatile blood flow and wall shear stress in a 90° T-bifurcation model is analysed numerically. The nonlinear Navier-Stokes equations for time-dependent incompressible Newtonian fluid flow are approximated using a newly developed pressure correction, finite element method. The wall shear stress is calculated from the finite element velocity field. The investigation shows viscous flow phenomena such as flow separation and stagnation and the distribution of high and low wall shear stress during the pulse cycle. Furthermore, the effect of a sharp corner the bifurcation edge on the wall shear stress is analysed. Detailed local flow investigation is required to examine fluid dynamic contribution to the development of arterial diseases such as atherosclerosis and thrombosis.

Analysis of an Oscillatory Oil Squeeze Film Including Effects of Fluid Inertia

This paper presents an analytic solution for the flow of a laminar incompressible Newtonian fluid between two parallel circular plates undergoing oscillatory motion. The solution uses an iterative approximation technique and includes both convective and unsteady fluid inertia terms. The extent to which these terms influence the pressure and load carrying capacity for various flow parameters is analyzed. The results show a significant deviation from the inertialess (viscous) solution at low excursion ratio, e, and moderate modified Reynolds number, Reo. For a purely harmonic (sinusoidal) motion of the plates, a steady-state force is generated in addition to the dynamic transient force. This is due to the inclusion of the inertia terms and is shown to be a function of the excursion ratio, e, and another dimensionless parameter, the squeeze velocity number, N.

Numerical blood flow analysis: Arterial bifurcation with a saccular aneurysm

The flow pattern and the paths of fluid particles in a saccular aneurysm located at the bifurcation of an intracranial arterial segment are investigated with a numerical method. A normal physiological flow pattern was assumed as input to the studied segment. The theoretical study is carried out for two different Reynolds numbers and two different geometries of the aneurysm. The governing equations for incompressible Newtonian fluid flow are solved using the finite element method. The results show the disturbed blood flow in the pathologically altered bifurcation and the flow activity in the aneurysms. It is particularly important that blood particles can circulate in a whirl within the aneurysm for a time which seems long enough to permit the generation of cell aggregates or/and blood clots.

On the paths of fluid particles in an axisymmetrical aneurysm

The aim of this study is the characterization of the pulsatile flow field by demonstration of the paths of single particles in a model of an axisymmetric aneurysm. The detailed analysis of the flow field can give additional information on the flow pattern and the time of transition of blood particles in the segment. The basis of the calculations is the system of the Navier-Stokes equations for incompressible Newtonian fluid flow. To solve these equations numerically the finite element method was used. The trajectory equations for a fluid particle were solved by use of a predictor-corrector procedure. The results of the computer simulation demonstrate the development, shift and disappearance of vortices in the excavation and give references to zones of stasis. This behavior can be an important factor in thrombogenesis.

Application of A pressure gradient method to an FEM flow analysis

AbstractA pressure gradient method employing pressure gradients as dependent variables is applied to a finite‐element‐method flow analysis for a two‐dimensional incompressible Newtonian fluid flow. In a numerical analysis, a triangular element is adopted, a velocity vector and a pressure gradient vector being assigned as dependent variables at the nodal points. Velocity and pressure gradient are interpolated linearly in space, and a discretizing formulation can be made using a suitably selected weighting function. An example of application is shown for an unsteady‐state development of a recirculating circular cavity flow, the numerical results to which are in good agreement with those obtained analytically or by other numerical means.

Behavior and asymptotic stability of thermomechanical processes

Adiabatic shearing flows of incompressible Newtonian fluids with temperature-dependent viscosity under time-dependent inertial force and time periodic or steady boundary velocity are considered. We obtain some results concerning the behavior and the asymptotic stability of these flows for several types of shearing and viscosity functions.

Improvement of a pressure gradient method and its application to an unsteady flow problem

AbstractThe pressure gradient method using velocity components and components of a pressure gradient as dependent variables has been modified to solve incompressible Newtonian fluid flow problems numerically. Applying this modified method to unsteady‐state development of flow in a circular cavity shows that, at least for the case of a low Reynolds number flow, relative errors produced by the proposed method are smaller for most time intervals than those produced by the primitive velocity‐pressure variable method and by the standard pressure gradient method. Also it is found that the modified and standard pressure gradient methods can be applied to the unsteady circular cavity flow at a moderate Reynolds number of at least up to 200.

Transient heat transfer from a wire in a violently fluctuating environment

A closed form perturbation solution is obtained for the problem of transient heat transfer from a constant temperature circular cylinder in a violently fluctuating flow of incompressible Newtonian fluids. The small parameter used in the solution is the ratio of the maximum fluctuation amplitude to the cylinder diameter. The solution is asymptotically valid for any values of the Prandtl and Reynolds numbers. The natural convection is considered as the second-order effect. The solution is also applied to predict the initial transient heat transfer from a wire which starts from rest an arbitrary translational motion. Numerical results in terms of time-dependent local and average Nusselt numbers are used to demonstrate the significant time lag of heat transfer response to the fluctuating velocity. It is shown that an optimum frequency of sinusoidal oscillation exists for the maximum net heat transfer at given flow parameters.

Application of Gyarmati's variational principle to laminar stagnation flow problem

Gyarmati's principle for the evolution of irreversible processes has been applied to construct the variational solutions of laminar stagnation flow of incompressible Newtonian fluid in two dimensions. Variational solutions obtained in three different representations approximate closely the exact numerical result of longitudinal velocity component and the Gyarmati's principle in force representation yield the same result as obtained by Doty and Blick with the help of local potential method of Glansdorff and Prigogine.

Fate of Thermally Polluted Surface Water in Rivers

By means of the time- and space-averaging processes, the general longitudinal thermal energy equation for nonuniform flow is derived from the three-dimensional instantaneous equations of continuity and of thermal energy for flow of incompressible Newtonian fluid. The equation so formulated includes the longitudinal heat dispersion term and can be used to describe mathematically the average temperature distribution in a natural stream at every instant and at all points of the stream after the injection of thermal pollutant. Analytical solution is sought for a typical thermal pollution problem in a natural stream. An accurate evaluation of the longitudinal heat dispersion coefficient that depends on bulk flow parameters and environmental factors is proposed.