Fluid flow in a helical pipe

Without simplifying the N-S equations of Germano's^[5], we study the flow in a helical circular pipe employing perturbation method. A third perturbation solution is fully presented. The first- second- and third-order effects of curvature κ and torsion τ on the secondary flow and axial velocity are discussed in detail. The first-order effect of curvature is to form two counter-rotating cells of the secondary flow and to push the maximum axial velocity to the outer bend. The two cells are pushed to the outer bend by the pure second-order effect of curvature. The combined higher-order (second-, third-) effects of curvature and torsion, are found to be an enlargement of the lower vortex of the secondary flow at expense of the upper one and a clockwise shift of the centers of the secondary vortices and the location of maximum axial velocity. When the axial pressure gradient is small enough or the torsion is sufficiently larger than the curvature, the location of the maximal axial velocity is near the inner bend. The equation of the volume flux is obtained from integrating the perturbation solutions of axial velocity. From the equation the validity range of the perturbation solutions in this paper can be obtained and the conclusion that the three terms of torsion have no effect on the volume flux can easily be drawn. When the axial pressure gradient is less than 22.67, the volume flux in a helical pipe is larger than that in a straight pipe.     

Viscous flow in a cylindrical vessel in the presence of a rotating disk

Viscous flows in the cylinder-disk system have been investigated theoretically and experimentally, over a broad range of Reynolds numbers Re, H/R_T, and R_k/R_T in order to explore the characteristics of the flow, which is a function of time, the depth of the liquid, the Reynolds number, the radii of the disk and the cylinder, and their geometry (flat, convex or concave disk). The results of comparing the data of numerical and laboratory simulations are presented. The appearance of secondary eddies in the axial region at large Reynolds numbers has been detected and diagrams of flows of different spatial configuration constructed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 33–40, September–October, 1985.     

Pulsatile blood flow in a resistance vessel

The quasi-one-dimensional Newtonian fluid flow in an active vessel in which the inlet pressure oscillates about a mean value is considered. The vascular wall is assumed to display the Bayliss effect and a reaction to changes in blood flow. The first is characterized by the dependence of the contractility of the vascular smooth-muscle cells on the intravascular pressure and the second by the sensitivity of the endothelial cells to the wall shear stress. The dependence of the period-average radius and blood flow rate on the mean value and pulsation amplitude and frequency of the inlet pressure is investigated numerically. The characteristics are compared for the passive vessel, the vessel with the Bayliss effect, and the vessel with both reactions.     

Potential flow in helical pipes

Summary In this paper we studied the potential flow in a helical pipe using an orthogonal system of coordinates fixed to the helical axis. The analysis was conducted both analitically by applying perturbative methods and numerically. Results show that the torsion of the helical axis has little effect on axial velocity in a torus provided with the same curvature of the helix. At the same time it induces a large secondary flow that is expected to have a relevant effect on the boundary layer on the walls of the helical pipe.

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Sommario In questo lavoro si è studiato il flusso potenziale in un tubo ad asse elicoidale per mezzo di un sistema di coordinate ortogonali fisse all'asse del tubo. Il flusso è stato studiato sia analiticamente con metodi perturbativi che numericamente. I risultati ottenuti mostrano che la torsione dell'asse elicoidale ha piccoli effetti sulla velocitá assiale, approssimativamente data da quella che si avrebbe in un toro di uguale curvatura, mentre produce forti flussi secondari nel piano normale all'asse. Questi flussi secondari possono avere un'effetto rilevante per quel che riguarda lo strato limite sulle pareti del tubo.

     

Effective flow of a viscous liquid through a helical pipe

We study the flow of a viscous fluid through a pipe with helical shape parameterized with , where the small parameter stands for the distance between two coils of the helix. The pipe has small cross-section of size . Using the asymptotic analysis of the microscopic flow described by the Navier–Stokes system, with respect to the small parameter that tends to zero, we find the effective fluid flow described by an explicit formula of the Poisseuile type including a small distorsion due to the particular geometry of the pipe. To cite this article: E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).

Résumé

On considère un écoulement dans un tube de section circulaire et de forme hélicoïdale paramétré par , où est la distance entre deux tours de la spirale. Le rayon de la section du tube est lui aussi supposé égal à . A partir de l'écoulement microscopique décrit par le système de Navier–Stokes et en utilisant l'analyse asymptotique par rapport à ce petit paramètre on obtient l'écoulemment effectif décrit par une formule explicite de type Poiseuille associée à une petite déviation due à la géometrie du tube. Pour citer cet article : E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).     

Fluid outflow from an orifice in a plane wall in the presence of a variable-strength source on the symmetry plane of flow

The unsteady jet outflow of an ideal incompressible weightless fluid from an orifice in a wall is considered in the presence of a variable-strength point source on the symmetry plane of flow. It is assumed that the velocity of the perturbed flow induced by the change of the source discharge is small compared to the velocity of the steady flow. The Gurevich–Haskind method is used to solve the problem. A boundary value problem for the complex potential of the perturbed flow is formulated and solved. The pressure distribution on hard walls is determined for the harmonic law of the source discharge variation. The evolution of the shape of the jet’s free boundary is studied.     

A study on the unsteady flow in a helical pipe

IntroductionRecently ,theresearchofunsteadyflowincurvedpipesmaintainsclosetiewiththatofbloodflowinbio_mechanics.Sothecharacteristicsofbloodflowinvesselscanbestudiedthroughtheresearchofflowincurvedpipesandthelocationthattheatherosclerosistakeplacecanbeprejudged[1].Theessentialcauseofatherosclerosiscanbeprobedinto ,too .In 1 971 ,Lyne[2 ]successfullysolvedtheproblemofflowinacircularcross_sectioncurvedpipeundertheconditionthattheaxialpressuregradientvariedinaccordwiththecosinelawusingthemethodof…     

Characterizing fluid structure interactions of a helical coil in cross flow

Mechanical vibrations compromise the integrity of key components of thermal power plants. Without careful design, strong resonances during steady state operation can wear these components to the point of failure, leading to an unsafe situation that may force a plant to shut down. The purpose of this research is to further the understanding of the vibrations induced in a helical coil subject to steady fluid flow. A helical coil steam generator, such as that found in most integral pressurized water reactors, appears to eliminate many flow-induced vibration concerns when compared to traditional steam generators; however this has yet to be clearly demonstrated experimentally. The objective of this study is to detail and demonstrate a new method to quantify the motion of a helical coil in an annulus subject to external axial flow of water and further characterizing the influence of pitch-to-diameter ratio on the fluidelastic instability of a helical coil. This is accomplished by observing the motion of a helical coil mounted to an inner opaque cylinder through an outer glass tube using a high speed video camera. A mirrored image-pair is used to observe this structure from two perspectives simultaneously, allowing for three-dimensional characterization of the coil motion. The experimental facility is described in detail. The method developed herein for identifying specific points on the coil from images and mapping them to the coil location using the law of refraction is described. An uncertainty analysis of the coil position measurement is conducted based on geometry and refractive index which can be readily applied to measurements obtained using this method. The outcome of empirical observations shows these helical coils to hold a slightly higher resonance frequency than that of cylinders in cross flow, their mechanical stiffness approximated through analytical means shows to produce relatively accurate natural frequencies when compared to the empirical data – 14.1 Hz and 12.5 Hz, respectively for first mode vibration. This study”s contributions present a new method for metering fluid structure interactions with high-fidelity, provide new empirical data which has not previously been produced, and make observations to the response of a helical coil which are new to the field of fluid-structure interactions.     

Fluid flow in a rotating curved rectangular duct

The fluid flowing in a rotating curved duct is subjected to both the Coriolis force due to a rotation and the centrifugal force due to a curvature. In this paper, the combined effects of the two forces on the flows in rotating curved rectangular ducts are examined numerically. According to the aspect ratio of the cross-section, the rectangular ducts are divided into three types: η>1, η=1, η<1, where η is the aspect ratio. The variations of the flow structures with the force ratio F (the ratio of the Corislis force to the centrifugal force) are studied in detail and many hitherto unknown flow patterns are found. The effects of the force ratio and the aspect ratio of the cross-section on the friction factor are also examined. Present results show both the characteristics of the secondary flow, axial flow and the natures of the friction factor.     

Fluid flow in a rotating channel of square section

Laminar flow in a channel rotating about a transverse axis has been studied numerically [1–3] and analytically [4–7] at small Reynolds numbers. The drag coefficient of rotating channels with straight and curvilinear axes has been measured [4, 8, 9]. The present paper gives the results of an experimental investigation into the kinematics of water flow in a channel rotating with different intensities. The flow was visualized by means of hydrogen bubbles and a dye. A study was made of the process of flow separation in a rapidly rotating channel into a core with homogeneous velocity distribution in the direction parallel to the rotation axis and thin shear layers on the walls normal to this axis. The values of the dimensionless numbers were found that correspond to flow rearrangement accompanied by formation of longitudinally oriented vortex structures in the region of higher pressure, and also the values of the rotation parameter needed for the almost complete suppression of turbulence in the region of lower pressure. A general analysis is made of the forms of instability in the different regions of the flow and of the possible flow regimes in a rotating channel.     

On the helical pipe flow with a pressure-dependent viscosity

We address the flow of incompressible fluid with a pressure-dependent viscosity through a pipe with helical shape. The viscosity-pressure relation is defined by the Barus law. The thickness of the pipe and the helix step are assumed to be of the same order and considered as the small parameter. After transforming the starting problem, we compute the asymptotic solution using curvilinear coordinates and standard perturbation technique. The solution is provided in the explicit form clearly showing the influence of viscosity-pressure dependence and pipe's geometry on the effective flow.     

Fluid flow through a partially filled cylinder

The laminar flow of viscous incompressible fluid through a partially filled circular cylinder is studied. The governing equations reduce to Laplace's equation, and the region of solution is the union of two intersecting circles. This region is mapped onto the unit circle by a conformal transformation, so that the problem may be solved by the Poisson integral formula. The integration is performed by a combination of residues and numerical integration. The results agree very well with exact analytic solutions at 50%, 85.4%, and 100% depth to diameter ratios. It is found that by not filling the cylinder completely, the flow rate can be increased by a significant 27.3%.     

Boundary layer development of pulsatile blood flow in a tapered vessel

Assuming that the tapered angle is small,the problems of developing flow under unsteady oscillatory condition are studied in this paper.The formula of velocity distribution is obtained.The analyses for the results show that the blood flow in a converging tapered vessel remains a developing flow throughout the length,and the effects of tapered angle on the developing flow are increased with the increment of the tapered angle.     

Bifurcation of flow and mass transport in a curved blood vessel

A numerical analysis of flow and concentration fields of macromolecules in a, slightly curved blood vessel was carried out. Based on these results, the effect of the bifurcation of a flow on the mass transport in a curved blood vessel was discussed. The macromolecules turned out to be easier to deposit in the inner part of the curved blood vessel near the critical Dean number. Once the Dean number is higher than the critical number, the bifurcation of the flow appears. This bifurcation can prevent macromolecules from concentrating in the inner part of the curved blood vessel. This result is helpful for understanding the possible correlations between the blood dynamics and atherosclerosis. The project supported by National Natural Science Foundation of China (10002003), JSPS Postdoctoral Fellowship for Foreign Researcher and Foundation for University Teachers, the Ministry of Education     

Fluid flow through a network of thin pipes

We study the fluid flow through a network of intersected thin pipes with prescribed pressure at their ends. Pipes are either thin or long and the ratio between the length and the cross-section is considered as the small parameter. Using the asymptotic analysis with respect to that small parameter the effective behaviour of the flow is found. At each junction an explicit formula for computing the value of the pressure is found. The interior layer phenomenon in vicinity of the junction is studied. We generalize the junction formula on the case of adiabatic compressible flow.     

Experimental and numerical investigation a bubble-driven laminar flow in a axisymmetric vessel

Measurements have been obtained, by laser-Doppler anemometry (LDA), of the axisymetric, recirculating liquid flow caused by a column of air bubbles ($\text{5–6}\text{1}\text{2}\text{mm dia.}$) rising through caster oil in a cylindrical enclosure (100 mm dia.). The liquid velocities correspond to creeping flow. Axial and radial liquid velocity profiles are reported at eight axial stations and, close to within the bubble column, as a function of time. The maximum liquid velocity found outside the bubble column is about 0.5 of that of the bubbles and a very rapid radical decay from this value is noted. The temporal variation of the velocity field, due to the passage of the air bubbles, is undetectable at radial locations greater than about $\text{1}\text{1}\text{2}$ bubble radii from the centreline.The variation of bubble velocity with axial distance was aise measured by LDA for liquid height to enclosure diámeter ratios of 0.98 and 2.78. The maximum bubble velocities were about 0.1–0.2 higher than the Strokes law terminal velocity. The increase is due to the convection of the bubble column by the liquid flow. The maximum bubble velocity is established within approximately three bubble diameters of the air inlet.The motion of the liquid has been calculated by the numerical solution of the steady form of the equations of motion, with the inner boundary of the area of integration lying 1.3 bubble radii from the centerline. The boundary conditions at this surface are assumed to be steady and are taken from measurements of the time-averaged velocity components. The assumption of steady flow at this boundary is supported by experimental observation and results in calculations which are generally in close agreement with the measurements. Discrepancies are confined to the immediate vicinity of the bubble column near to the top and bottom of the enclosure. These are ascribed to a combination of small asymmetries in the experiment and inadequate numerical resolution in these regions.     

Wavy flow of a liquid film in the presence of a cocurrent turbulent gas flow

Wavy downflow of viscous liquid films in the presence of a cocurrent turbulent gas flow is analyzed theoretically. The parameters of two-dimensional steady-state traveling waves are calculated for wide ranges of liquid Reynolds number and gas flow velocity. The hydrodynamic characteristics of the liquid flow are computed using the full Navier-Stokes equations. The wavy interface is regarded as a small perturbation, and the equations for the gas are linearized in the vicinity of the main turbulent flow. Various optimal film flow regimes are obtained for the calculated nonlinear waves branching from the plane-parallel flow. It is shown that for high velocities of the cocurrent gas flow, the calculated wave characteristics correspond to those of ripple waves observed in experiments.     

Fluid flow in charged nanotubes

The dynamics of fluid flow through nanochannels is different from those in macroscopic systems. By using the molecular dynamics simulations, we investigate the influence of surface polarity of nanotube on the transport properties of the water fluid. The nanotube used here resembles the carbon nanotube, but carries charges of q on some atoms; overall, the nanotube is charge-neutral. Our simulation results show that water flux decreases sharply with the increasing of q for q < 1.6 e; however, the water flux for shells far away from nanotube wall increases slightly when q > 1.6 e. The mechanism behind the interesting phenomenon is discussed. Our findings may have implications for development of nano-fluidic devices and for understanding the movement of confined fluid inside the hydrophilic nanochannel.     

Fluid flow in curved ducts

The advent of standard algorithms for the numerical solution of partial differential equations has given researchers a new tool for fluid flow calculations. In this paper, single-phase flow in curved ducts is numerically simulated by imposing a spatially varying centrifugal force on a fluid flowing in a straight tube. The resulting set of partial differential equations is solved using the HARWELL-FLOW3D computer program. Comparison with other numerical and experimental results shows that this simplified formulation gives accurate results. The model neglects certain geometric terms of the order d/D, the duct-to-coil diameter ratio. The effect of these terms is investigated by considering the flow in a 90° bend for large d/D. It is shown that while there may be significant error in the prediction of the local variables for large d/D, the circumference-averaged quantities are well predicted.     

Experimental investigations of the unsteady rotating flow field in a cylindrical vessel

The rotating flow field in a cylindrical vessel — the so-called whirlpool — is widely used in food engineering as a method for separating particles out of a suspension (Cup-of-tea-method). However many of these whirlpools do not operate adequately or fail entirely. In order to solve this problem, the first step was to investigate the flow field and its time dependency which has not been sufficiently understood until now.The rotating flow in a cylindrical vessel — induced by a fluid jet during the filling period of this vessel — is slowed down by fluid friction after the closing of the inlet valve. The velocity fields to be found mainly near, and pressure distributions at the bottom of the vessel, are measured during this unsteady flow. The results, especially those which describe vortex systems, are used to improve the separation system. This paper is restricted to the hydrodynamic aspect. Therefore success in industrial applications can only be indicated.