Pipe Of Circular Cross-section Research Articles

The axisymmetric non-linear steady flow of a rarefied gas in a pipe of circular cross-section

The axisymmetric non-linear steady flow of a rarefied gas in a pipe of circular cross-section

Classification of Pulsating Flow Patterns in Curved Pipes

The fully developed periodic laminar flow of incompressible Newtonian fluids through a pipe of circular cross section, which is coiled in a circle, was simulated numerically. The flow patterns are characterized by three parameters: the Womersley number Wo, the Dean number De, and the amplitude ratio beta. The effect of these parameters on the flow was studied in the range 2.19 < or = Wo < or = 50.00, 15.07 < or = De < or = 265.49 and 0.50 < or = beta < or = 2.00, with the curvature ratio delta fixed to be 0.05. The way the secondary flow evolved with increasing Womersley number and Dean number is explained. The secondary flow patterns are classified into three main groups: the viscosity-dominated type, the inertia-dominated type, and the convection-dominated type. It was found that when the amplitude ratio of the volumetric flow rate is equal to 1.0, four to six vortices of the secondary flow appear at high Dean numbers, and the Lyne-type flow patterns disappear at beta > or = 0.50.

A steady-state model for heat pipes of circular or rectangular cross-sections

The objective of this paper is to present a generalized analytical-numerical model of the internal flow in heat pipes. The model formulation is based on two-dimensional formulation of the energy and momentum equations in the vapour and liquid regions and also in the metallic tube. The numerical solution of the model is obtained by using the descretization scheme LOAD and the SIMPLE numerical code. The flow fields, as well as the pressure fields, for different geometries were obtained and discussed.

Flow of Oldroyd-B fluids in curved pipes of circular and annular cross-section

Perturbation methods are used to study steady, fully developed flow of Oldroyd-B fluids through curved pipes for both pipes of circular and annular cross-section. The perturbation parameter is the curvature ratio, given by the cross-sectional radius of the pipe divided by the constant radius of the pipe centerline. We compare results for creeping and non-creeping flows for both viscoelastic and Newtonian fluids. In pipes of circular cross-section, the velocity field for creeping flows of Oldroyd-B fluids is qualitatively similar to that found for non-creeping flows of Newtonian fluids. Namely, in addition to the primary flow, there is a secondary motion consisting of counter-rotating vortices. In curved annular pipes, two pairs of counter-rotating vortices are generated by either inertial or elastic effects. In this geometry, the differences between creeping flow of viscoelastic fluids and non-creeping flow of Newtonian fluids are dramatically accentuated at small values of inner to outer pipe radius, r i r o . For Newtonian fluids, as r i r o approaches zero, the magnitude and size of the vortices adjacent to the inner cylinder shrink to zero. However, for creeping flow of Oldroyd-B fluids, the inner vortex pair is comparable to the outer vortex pair in both size and strength, even for values of r i r o as small as 0.01. For pipes of circular cross-section, the effect of elasticity on the drag is considered and earlier predictions by Bowen et al. for the upper convected Maxwell fluid are extended to the Oldroyd-B fluid for non-zero Reynolds number.

Measurements of Turbulent Flow Downstream from Elbow Pipe.

Measurements of the longitudinal mean and fluctuating velocities downstream from a 90° elbow pipe of circular cross section were obtained using a laser-Doppler velocimeter at a Reynolds number of 5×104 and radius ratio of 1.1, 2, 4 and 8 in order to clarify the effect of the radius of curvature and the distance from the elbow exit on the behavior of turbulent flow. The turbulence intensity is large near the inner-radius wall of the elbow where flow separation occurs, and in the center of the pipe where velocity gradient is high. The increase of the cross-sectionally averaged value of the longitudinal component of the turbulent energy in the region more than 2 times the pipe diameter downstream from the elbow exit compared with that for fully developed turbulent flow is proporional to the -1.6 power of the radius ratio and decreases as an exponential function of the distance from the elbow exit.

Unsteady axial viscoelastic pipe flows

The main objective of this work is to examine in detail basic unsteady pipe flows and to investigate any new physical phenomena. We take the viscoelastic upper-convected Maxwell fluid as our non-Newtonian model and consider the flow of such a fluid in pipes of uniform circular cross-section in the following three cases: 1. (a) when the pressure gradient varies exponentially with time; 2. (b) when the pressure gradient is pulsating; 3. (c) a starting flow under a constant pressure gradient. In the first problem we looked separately at the pressure gradient rising exponentially with time and falling exponentially with time, i.e. the pressure gradient is proportional to e ± α 2 τ . The behaviour of the flow field depends to a large extent on β where β 2 = α 2(1 ± Hα 2) with H being the quotient of the Weissenberg and Reynolds numbers. In both cases for small | βη|, η being the radial distance from the axis, the velocity profiles are seen to be parabolic. However, for large | βη| the flows are vastly different. In the case of increasing pressure gradient the flow depicts boundary-layer characteristics while for decreasing pressure gradient the velocity depends on the wall distance. The case of a pulsating pressure gradient is investigated in the second problem. Here the pressure gradient is proportional to cos nτ. Again the flow depends to a large extent on a parameter β ( β 2 = i n − n 2 H). For small values of | βη| the velocity profile is parabolic. However, it is found that, unlike Newtonian fluids, the velocity distribution for the upper-convected Maxwell fluid is not in phase with the exciting pressure distribution. In the case of large | βη| the solution displays a boundary-layer characteristic and the phase of the motion far from the wall is shifted by half a period. The final problem examines a flow that is initially at rest and then set in motion by a constant pressure gradient. A closed form solution has been obtained with the aid of a Fourier-Bessel series. The variation of the velocity across the pipe has been sketched and comparison made with the classical solution.

Direct numerical modeling of three-dimensional turbulent flows in pipes of circular cross section

Turbulent viscous incompressible flows in pipes of circular cross section are subjected to a detailed numerical investigation on the Reynolds number interval from 2000 to 10 000. The evolution of the motion and the distribution of the average characteristics in the limiting regimes are studied. A detailed comparison shows good general agreement between the results of the calculations and the known experimental data. Possible causes of the differences are discussed.

Torsion effect on the flow in a helical pipe

The effect of curvature and torsion on the flow in a helical pipe of circular cross-section is studied numerically by the spectral method. The calculations are carried out for 0 ⩽ δ ⩽ 0.6, 0 ⩽ β0 ⩽ 1.4 and 500 ⩽ Dn ⩽ 2000, where δ is the non-dimensional curvature, β0 the ratio of torsion to square root of curvature, and Dn the Dean number. The results obtained indicate large effects of torsion on the flow: The conventional two-vortex secondary flow is distorted to become almost one single recirculating cell when β0 ≳ 0.8. The flux through the pipe at the given Dean number and curvature first decreases from that of the toroidally curved pipe as β0 increases from zero, reaches a minimum at β0 ≈ 0.8, and then increases to values larger than that of the toroidally curved pipe. The minimum value decreases as δ increases.

An experimental study of pressure drop in helical pipes

Pressure drops of fully-developed incompressible laminar newtonian flows in helical pipes of constant circular cross-section having a finite pitch are experimentally investigated. For the case of loosely coiled pipes of 0 &lt; η/λ &lt; 41.22, f Re ( f is the Fanning friction factor and Re is the Reynolds number) is found to be proportional to the square root of the flow Dean number, Dn = Re λ ½ . Here λ and η are the normalized curvature ratio and torsion which incorporate both the coil radius and its pitch. In all cases studied, the experimental results for f Re are in excellent agreement with the theoretical prediction of Liu &amp; Masliyah.

Effects of Bingham Viscosity on Flow in Curved Pipes.

Bingham plastic fluid flows through coiled pipes of circular cross section were experimentally studied. In the investigations, kaolin clay slurries were used as the Bingham plastic fluid. The effects of the Reynolds number Re or the Dean number De on the friction factor λc in the laminar steady flow of the Bingham plastic fluid flowing through coiled pipes were clarified. The apparent Reynolds number Reap, expected to play the equivalent role of Re in Newtonian fluids, was introduced using the similarity law of energy dissipation which was derived from a generalized equation of non-Newtonian fluid. It was clarified that the effects of the curvature of the pipes are greater in the case of greater concentration of the slurry, and that there exists a good correlation between the friction factor and the apparent Dean number Deap(defined according to Reap).

Experimental Observations of Flow Instability in a Helical Coil (Data Bank Contribution)

Experimental observations were made for the nominally fully developed flow through a helically coiled pipe of circular cross-section with a curvature radius to pipe radius ratio Rc/a = 18.2. Laser-Doppler measurements of the instantaneous streamwise velocity, uθ, and the cross-stream circumferential velocity, uφ, components were obtained along the midplane of the pipe cross-section. The Reynolds number range explored was 3800 &lt; Re &lt; 10500 (890 &lt; De &lt; 2460) and spans the laminar and turbulent flow regimes. Time integration of the velocity records has yielded previously unavailable mean and rms velocity profiles. In the range 5060 &lt; Re &lt; 6330, the time records of the velocity components reveal periodic flow oscillations with St ≈ 0.25 in the inner half of the pipe cross-section while the flow near the outer wall remains steady. A frequency doubling (St ≈ 0.5) is also observed at some midplane locations. This low frequency unsteadiness is distinct from the shear-induced turbulent fluctuations produced with increasing Re first at the outer wall and later at the inner wall of the coiled pipe. Simple considerations suggest that the midplane jet in the recirculating cross-stream flow is the source of instability.

Axially invariant laminar flow in helical pipes with a finite pitch

Steady axially invariant (fully developed) incompressible laminar flow of a Newtonian fluid in helical pipes of constant circular cross-section with arbitrary pitch and arbitrary radius of coil is studied. A loose-coiling analysis leads to two dominant parameters, namely Dean number, Dn = Reλ½, and Germano number, Gn = Reη, where Re is the Reynolds number, λ is the normalized curvature ratio and η is the normalized torsion. The Germano number is embedded in the body-centred azimuthal velocity which appears as a group in the governing equations. When studying Gn effects on the helical flow in terms of the secondary flow pattern or the secondary flow structure viewed in the generic (non-orthogonal) coordinate system of large Dn, a third dimensionless group emerges, γ = η/(λDn)½. For Dn &lt; 20, the group γ* = Gn Dn-2 = η/(λRe) takes the place of γ.Numerical simulations with the full Navier-Stokes equations confirmed the theoretical findings. It is revealed that the effect of torsion on the helical flow can be neglected when γ ≤ 0.01 for moderate Dn. The critical value for which the secondary flow pattern changes from two vortices to one vortex is γ* &gt; 0.039 for Dn &lt; 20 and γ &gt; 0.2 for Dn ≥ 20. For flows with fixed high Dean number and A, increasing the torsion has the effect of changing the relative position of the secondary flow vortices and the eventual formation of a flow having a Poiseuille-type axial velocity with a superimposed swirling flow. In the orthogonal coordinate system, however, the secondary flow generally has two vortices with sources and sinks. In the small-γ limit or when Dn is very small, the secondary flow is of the usual two-vortex type when viewed in the orthogonal coordinate system. In the large-γ limit, the appearance of the secondary flow in the orthogonal coordinate system is also two-vortex like but its orientation is inclined towards the upper wall. The flow friction factor is correlated to account for Dn, A and γ effects for Dn ≤ 5000 and γ &lt; 0.1.

Round incompressible jets with asymmetric initial velocity distributions

THE near-field development of turbulent air jets with asymmetric initial velocity distributions is investigated experimentally. The jets emerge from pipes of circular cross section into a still environment. The level of asymmetry of the exit plane mean velocity distribution is controlled by the angle of pipe bend upstream of the exit. Jets with two levels of initial streamwise velocity asymmetry are studied in addition to an axisymmetric jet emerging from a straight pipe. The-Reynolds number based on exit bulk velocity and pipe diameter is 13,500. Streamwise velocity measurements, using hot-wire anemometry, indicate that the near-field turbulence structure is significantly modified by the skewed velocity distribution. On the plane of symmetry, higher levels of initial velocity skewness lead to increased disparity of turbulence intensity and unequal rate of growth on the two sides of the jet. Furthermore, higher rates of maximum velocity decay and jet growth are attained with the initially asymmetric jets. The increase in jet spread rate on the symmetry plane is found to distort the initially round cross-sectional shape of the jets beyond 10 pipe diameters from the exit plane.

A direct theory of viscous fluid flow in pipes II. Flow of incompressible viscous fluid in curved pipes

This paper is a companion to Part I under the same title and is concerned with the development of an analytical solution (via a direct formulation) for flow of an incompressible viscous fluid in curved pipes. Although a major portion of the analysis is presented for circular pipes of elliptical cross section, detailed calculations are carried out only for pipes of circular cross section. These calculations include the friction loss factor and the velocity contours, both of which are presented over a range of Dean number th a t significantly goes beyond the corresponding range of recent numerical solutions and the available experimental data. The results obtained show very favourable agreements with existing experimental data and several recent numerical solutions of the same problem based on the Navier—Stokes equations. Also included (for pipes of circular cross section) is a comparison of the multiple solutions and bifurcation points, as predicted by the present analytical solution, with corresponding available inform ation from several recent num erical solutions of the problem.

Flow of an elastico-viscous liquid in a curved pipe of slowly varying curvature

Curvature forms an important feature of thoracic aorta and this paper deals with the flow of an idealized elastico-viscous liquid in a curved pipe of circular cross-section and slowly varying curvature, under a pressure gradient. The flow is assumed to be steady and at low Reynolds numbers. By using the series expansion method of Dean ( Phil Mag 4 (1927) 208–223; Phil Mag 5 (1928) 673–693) in powers of a parameter L, which can be considered as the square of ratio of the centrifugal force induced by the circular motion of the fluid to the viscous force, it is shown that in a tube of increasing curvature, there will be delay in setting up of the secondary motion. The wall shear stress, an important parameter in physiological flows, is calculated. The flow of Newtonian fluid in a tube of circular cross section is discussed, as a particular case.

Characteristics of a Pulsating Bingham Plastic Fluid Flow in a Curved Pipe. Experimental and Numerical Study.

The fully developed pulsating laminar flows of an incompressible Bingham plastic fluid through a pipe of circular cross section coiled in a circle were investigated experimentaly and numerically. The flow fields were characterized by the Dean number De, Hedstrom number He, the Womersley number Wo and the curvature ratio δ. The friction factors were measured experimentaly for various volumetric ratio in the case of Wo=4. The calculations were carried out for a fixed He. The flow patterns and the axial velocity profiles were required in the calculations. It was clarified that the effects of the curvature of the pipes appeared easily for Newtonians compared with the plastic fluids. That is, the values of the amplitudes of the friction factor λac of the plastic fluid were smaller than that of Newtonians for a range of high Dean number, especially in the case of lower curvature ratio. In the calculations, it was found in the case of a plastic fluids that, in the axial velocity distributions a typical plug flow area appeared near the outer side of the vent in all of a period, and that the strength of the secondary flows were greater than that of Newtonians especially within the period the volumetric rates increased.

Monoharmonic self-excited oscillations bifurcating from Poiseuille flow in a compliant pipe of circular cross section

The bifurcation problem near the neutral curves constructed for Poiseuille flow in a compliant pipe is investigated. The existence of stable self-excited oscillatory regimes branching from the noses of the neutral curves in the region of linear instability is established both for Re 2000, which corresponds to a soft excitation regime. The bifurcated self-excited oscillation modes are determined, and the effect on the branching of the Reynolds numbers Re and, moreover, the compliance and internal viscosity of the pipe material is analyzed. The data obtained can be used in medicine and for designing stabilizing elements for flows in circular pipes.

Characteristics of a Palsating Bingham Plastic Fluid Flow in a Curved Pipe. Analysis Using Power-Law Model.

Pulsating laminar flows of a purely viscous non-Newtonian fluid in a curved pipe of circular cross section in the high Dean number region were investigated analytically by using boundary layer approximations. The governing equations were formulated for a Power-Law fluid. The momentum integral approach and Pohlhausen's approximate method were used to analyze the flow in some detail, and the governing equations were solved by the successive approximation. In the case of steady flow, the present theory was in good agreement with previous experimental data, and the friction factor becomes greater as the pseudoplasticity index n decreases. In the case of Palsatile flow, the phase lag of the mean sectional velocity from the wave of pressure gradient, Γ, and the amplitude of the friction factor, λ^^∼ac, diminishes with increasing Dean number, and Γ diminishes with increasing n. The phase lag Γ and the amplitude of the friction factor λ^^∼ac derived in this work are in qualitative agreement with available experimental data.

The motion of a viscous fluid in a pipe of finite length

A solution is obtained of a linearized, initial-boundary-value problem of the unsteady motion of a viscous fluid in a cylindrical pipe of circular cross-section with a horizontal axis, under the assumption that the pressure at one end of the pipe is constant, and at the other end a device is set up which changes the flow rate of the fluid. It is shown that, depending on the relations between the defining parameters of the problem, the solution tends asymptotically either to a periodic solution, or to one of the two stable steady-state solutions. These results are obtained using methods similar to those developed in [1–3], where the unsteady motions of ground waters during the irrigation were considered, taking into account the evaporation from the regions between the channels. It was assumed there that the irrigation, which was carried out at a constant rate, was switched on and off depending on the level of ground waters in the inspection well.

A characteristics model of transient friction in pipes

A quasi two-dimensional model of transient flows in pipes of circular cross-section is developed, using the one dimensional method of characteristics in concentric cylindrical annuli. Lateral velocity components are permitted between adjacent cylinders. The model can nominally incorporate any desired relationship between shear stresses and local velocities. In this paper, it is applied to laminar flows and to a five-region model of turbulent flows. The accuracy of Zielke's (1969) one-dimensional expression for transient wall-shear stresses in laminar flows is verified, and it is shown that his expression is also a reasonable approximation for smooth-wall, turbulent flows, at least at low Reynolds numbers. Quasi-steady relationships are shown to be highly inaccurate in transient laminar or turbulent flows.