HYBRID PERTURBATION-GALERKIN SOLUTION OFTHE FLOW IN A CIRCULAR CROSS-SECTIONTUBE WITH CONSTRICTION~

Using hybrid perturbatin- Galerkin technique, a circular cross-section tube model with sinusoidal wall is studied. This technique can remove the limitation of small parametersfor perturbation and the difficulty of selecting good coordinate functions about Galerkintechnique. The effects caused by the boundary conditions and the Reynolds number on theflow were discussed. The position of the separate and reattachment points was obtained. The tendency of the variation about the shear stress on the wall and friction factor along the axisdirection were also analyzed, The results at a small parameter have good agreements withthe perturbation ones.     

剧变截面圆管内渗流的数值计算方法

对于剧变截面圆管的渗流问题写出不可压缩渗流的基本方程组,对直接求解原始变量(速度和压力)的数值计算方法作出改进。先由非主流方向的运动方程计算压力,后由主流方向的运动方程计算主流方向的速度分量,再由连续性方程计算非主流方向的速度分量。这样可以避免在一般的求解原始变量方法中由连续性方程计算压力时出现的困难和麻烦。根据本方法和剧变截面圆管的特点,采用半交错不等距非正交贴体混合网格系。本文详细写出差分方程和迭代计算公式,对剧变截面圆管内的渗流算例进行数值计算。本方法的优点是简单和实用,在工程上具有较大的应用价值。     

Calculation of the stability of the flow in a circular pipe with injection

An experimental investigation of the transition of a laminar flow regime into a turbulent one has been carried out in [1] for a flow in a circular pipe which is organized due to injection through the porous lateral surface with a jammed leading end of the pipe. It was established as a result that injection leads to an increase in stability of the laminar flow regime and increases the Reynolds number of the transition to 10,000 instead of the value 2300 which is characteristic of flow in a circular pipe with impenetrable walls. A similar effect was discovered in [2], in which it was also obtained that the Reynolds number of stability loss under the action of injection can take values significantly larger than in pipes with impenetrable walls. The phenomenon of relaminarization of a turbulent flow in the initial section of a circular pipe under the action of injection has been experimentally detected at the entrance for relatively low Reynolds numbers in [3, 4]. Theoretical investigations of stability of flow with injection have been performed only for a plane channel [5, 6]. A calculation is made in this paper of the stability of a hydrodynamically developed flow in a circular pipe with injection through a porous lateral surface.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 82–86, May–June, 1984.     

Heat transfer to air–water annular flow in a horizontal pipe

Two-phase air–water flow and heat transfer in a 25 mm internal diameter horizontal pipe were investigated experimentally. The water superficial velocity varied from 24.2 m/s to 41.5 m/s and the air superficial velocity varied from 0.02 m/s to 0.09 m/s. The aim of the study was to determine the heat transfer coefficient and its connection to flow pattern and liquid film thickness. The flow patterns were visualized using a high speed video camera, and the film thickness was measured by the conductive tomography technique. The heat transfer coefficient was calculated from the temperature measurements using the infrared thermography method. It was found that the heat transfer coefficient at the bottom of the pipe is up to three times higher than that at the top, and becomes more uniform around the pipe for higher air flow-rates. Correlations on local and average Nusselt number were obtained and compared to results reported in the literature. The behavior of local heat transfer coefficient was analyzed and the role of film thickness and flow pattern was clarified.     

Pulsatile flow in a straight circular pipe with reabsorption across the wall

Summary Velocity-, stress- und pressure distribution has been investigated for the flow of a Newtonian liquid in a circular cylindrical tube with reabsorption across the wall. For constant reabsorption the nonlinear steady flow case has been treated for small cross flow Reynoldsnumbers, while for pulsatile flow the flow behavior is presented for constant and exponentially decaying reabsorption across the wall.

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Übersicht Für die pulsierende Strömung einer Newtonschen Flüssigkeit mit Absaugung längs der kreiszylindrischen Wand werden Geschwindigkeits-, Druck- und Spannungsverteilungen bestimmt. Dabei wird sowohl lineares als auch exponentiell abnehmendes Absaugevolumen behandelt. Für konstantes Absaugen längs der Wand wird die nichtlineare Lösung für kleine Querstrom-Reynoldszahlen angegeben.

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Awardee of the U. S. Special Program of the Alexander von Humboldt-Stiftung.     

Bubbly-to-cap bubbly flow transition in a long-26 m vertical large diameter pipe at low liquid flow rate

The concurrent upward two-phase flow of air and water in a long vertical large diameter pipe with an inner diameter (D) of 200 mm and a height (z) of 26 m (z/D = 130) was investigated experimentally at low superficial liquid velocities from 0.05009 to 0.3121 m/s and the superficial gas velocities from 0.01779 to 0.5069 m/s. The resultant void fractions range from 0.03579 to 0.4059. According to the observations using a high speed video camera, the flow regimes of bubbly, developing cap bubbly and fully-developed cap bubbly flows prevailed in the flows. The developing cap bubbly flow appeared as a flow regime transition from bubbly to fully-developed cap bubble flow in the vertical large diameter pipe. The developing cap bubbly flow changes gradually and lasts for a long time period and a wide axial region in the flow direction, in contrast to a sudden transition from bubbly to slug flows in a small diameter pipe. The analysis in this study showed that the flow regime transition depends not only on the void fraction but also on the axial distance in the flow and the pipe diameter. The axial flow development brings about the transition to happen in a lower void fraction flow and the increase of pipe diameter causes the transition to happen in a higher void fraction flow. The measured void fraction showed an N-shaped axial changing manner that the void fraction increases monotonously with axial position in the bubbly flow, decreases non-monotonously with axial position in the developing cap bubbly flow, and increases monotonously again with axial position in the fully-developed cap bubbly flow. The temporary void fraction decrease phenomenon in the transition region from bubbly to cap bubbly flow can be attributed to the formation of medium to large cap bubbles and their gradual growth into the maximum size of cap bubble and/or cluster of large cap bubbles in the developing cap bubbly flow. In order to predict the N-shaped axial void fraction changing behaviors in the flow regime transition from bubbly to cap bubbly flow, the existing 12 drift flux correlation sets for large diameter pipes are reviewed and their predictabilities are studied against the present experimental data. Although some drift flux correlation sets, such as those of Clark and Flemmer (1986) and Hibiki and Ishii (2003), can predict the present experimental data with reasonable average relative deviations, no drift flux correlation set for distribution parameter and drift velocity can give a reliable prediction for the observed N-shaped axial void fraction changing behaviors in the region from bubbly to cap bubbly flow in a vertical large diameter pipe.     

Control of the aerodynamic characteristics of a profile oscillating with respect to the incidence angle in subsonic viscous flow

The results of a numerical simulation of the unsteady subsonic viscous gas flow around a two-dimensional profile oscillating with respect to the incidence angle are presented and the possibility of controlling the nonstationary aerodynamic characteristics is considered. The hysteresis phenomena typical of oscillatory profile motions are investigated, the dependence of the lift force and drag is found for various laws of periodic variation of the incidence angle with time, and the effect of the frequency and amplitude of the angular profile oscillations on the shape of the hysteresis curves is studied. The calculations were based on the numerical solution of the nonstationary Navier-Stokes equations averaged in the Reynolds sense (Reynolds equations) which were closed using the k-ω turbulence model with modeling of the laminar/turbulent transition.     

A numerical study of bingham turbulent flow in sudden-expansion straight circular pipe

I.IntroductionBinghamfluidisonebranchofnon-Newtonianfluid,suchascrudeparaffinoil,highsediment--ladenwaterflow,highconcentrationmudandthelikewhicharetransportedinpipelinesinmanyindustries,soit'sofgreatsignificancetostudytheflowmechanismsofBinghamfluid.Tsaietal.II]studiedthelinkagebetweenBinghamfluidandpluggedflow.Wangetal.I2]measuredtheturbulencestructureofBinghammud.Mengetal.[3]researchedthekineticenergycorrectionfactorofBinghamfluidinacircularpipe.However,thestudyofBinghamfluidsofarisn't…     

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.     

Theoretic expression of flow rate for a single fracture with linearly varying width

By means of reasonable assumption and mathematical derivation, a theoretic expression of flow rate for a single fracture with linearly varying width was obtained. The mathematical derivation was based on the cubic law and the new theoretic expression was an extention of traditional parallel plate model. This study may help to analyze seepage in fractured rock mass.     

Magnetohydrodynamic pipe flow in ducts with partial circular ring cross section and annular cross section

In this paper we use the Green function method to solve the problem of steady one dimensional flow of an incompressible viscous, electrically conducting fluid through a pipe with partial circular ring cross section and one with annular cross section, in the presence of an applied transverse uniform magnetic field. We obtain analytic solutions and carry out some numerical calculations of the velocity distribution and induced magnetic field.     

Justification of the drift-flux model for two-phase flow in a circular pipe

A flow of a gas-liquid dispersed mixture in a circular pipe with a variable inclination to the horizon, as applied to oil and gas flows in wells, is considered. Within the framework of a multi- fluid approach, the equations of an asymptotic drift-flux model, which contains an algebraic relation between the phase velocities and one momentum equation for the volume-averaged velocity of the mixture, are derived. It is shown that the drift-flux model in this formulation strictly follows from the balance laws under assumption of inertialess velocity slip of the phases in case of validity of one of the following conditions: (i) the dispersed-phase volume fraction is small; (ii) the phase velocity slip may be neglected; or (iii) the flow regime is inertialess and the acceleration of the mixture can be neglected. A numerical algorithm based on the SIMPLE method is implemented for solving the obtained equations of the drift-flux model. The possibility of modeling the gravitational segregation and the pressure buildup in a shut-in well and transient slug flows is demonstrated.     

Experimental investigation of the effect of entry conditions and rotation on flow resistance in circular tubes rotating about a parallel axis

Results are presented of an experimental investigation into the influence on flow resistance of flow conditioning prior to the entry region of a circular sectioned tube rotating about an axis parallel to its central axis of symmetry. This investigation is part of a long term study into the effect of rotation on pressure loss and heat transfer characteristics in rotating coolant channels. It is shown that for fully developed flow, rotation has little significant effect on flow resistance in the normal laminar and turbulent zones. The transition region is, however, affected; the usual ‘dip’ in friction factor is replaced by a smoother transition from laminar to turbulent flow. For developing flow, however, it has been shown that rotation can significantly increase the flow resistance above the normal stationary correlations. This increase can be reduced by smoothing the flow with gauzes and flow straightening honeycombs prior to the entry region of the tube.     

Investigation of the specific mass flow rate distribution in pipes supplied with a pulsating flow

A pulsating flow is typical of inlet and exhaust pipes of internal combustion engines and piston compressors. Unsteady flow phenomena are especially important in the case of turbocharged engines, because dynamic effects occurring in the exhaust pipe can affect turbine operation conditions and performance.One of the basic parameters describing the unsteady flow is a transient mass flow rate related to the instantaneous flow velocity, which is usually measured by means of hot-wire anemometers. For the flowing gas, it is more appropriate to analyze the specific mass flow rate φ_m = ρv, which takes into account also variations in the gas density. In order to minimize the volume occupied by measuring devices in the control section, special double-wire sensors for the specific mass flow rate (CTA) and temperature (CCT) measurement were applied. The article describes procedures of their calibration and measurement. Different forms of calibration curves are analyzed as well in order to match the approximation function to calibration points. Special attention is paid to dynamic phenomena related to the resonance occurring in a pipe for characteristic frequencies depending on the pipe length. One of these phenomena is a reverse flow, which makes it difficult to interpret properly the recorded CTA signal. Procedures of signal correction are described in detail. To verify the measurements, a flow field investigation was carried out by displacing probes radially and determining the profiles of the specific mass flow rate under the conditions of a steady and pulsating flow. The presence and general features of a reverse flow, which was identified experimentally, were confirmed by 1-D unsteady flow calculations.     

On the flow in a uniformly porous pipe

This article considers fully laminar flow of an incompressible viscous fluid in a uniformly porous pipe with suction and injection. An exact solution of the Navier–Stokes equations is given. The velocity filed can be expressed in a series form in terms of the modified Bessel function of the first kind of order n. The volume flux across a plane normal to the flow, the vorticity and the stress on the boundary are presented. The flow properties depend on the cross-Reynolds number, Ua/ν, where U is the suction velocity, a is the radius of the pipe and ν is the kinematic viscosity of the fluid. It is found that for large values of the cross-Reynolds number, the flow near the region of the suction shows a boundary layer character. In this region the velocity and the vorticity vary sharply. Outside the boundary layer, the velocity and the vorticity do not show an appreciable change.     

Numerical study of a piston-driven unsteady flow in a pipe with sudden expansion

This paper presents results of the numerical study of a piston-driven unsteady flow in a pipe with sudden expansion. The piston closes the larger-diameter pipe and moves between two limiting positions with strong acceleration or deceleration at the beginning and end of each stroke and constant velocity in between. The piston velocity in the exhaust stroke is about four times higher than in the intake stroke. Periodic piston movement in this fashion creates a complex unsteady flow between the piston head and the plane of sudden expansion. The numerical method is implicit and of finite volume type, using a moving grid and a collocated arrangement of variables. Second-order spatial discretization, fine grids and a multigrid solution method were used to ensure high accuracy and good efficiency. Spatial and temporal discretization errors were of the order of 1% and 0.1% respectively. The features of the flow are discussed and the velocity profiles are compared with experimental data, showing good qualitative and quantitative agreement.     

Particle behavior in a turbulent pipe flow with a flat bed

Particle behavior in a turbulent flow in a circular pipe with a bed height h = 0.5R is studied at Re_b = 40,000 and for two sizes of particles (5 μm and 50 μm) using large eddy simulation, one-way coupled with a Lagrangian particle tracking technique. Turbulent secondary flows are found within the pipe, with the curved upper wall affecting the secondary flow formation giving rise to a pair of large upper vortices above two smaller vortices close to the pipe floor. The behavior of the two sizes of particle is found to be quite different. The 50 μm particles deposit forming irregular elongated particle streaks close to the pipe floor, particularly at the center of the flow and the pipe corners due to the impact of the secondary flows. The deposition and resuspension rate of the 5 μm particles is high near the center of the floor and at the pipe corners, while values for the 50 μm particles are greatest near the corners. Near the curved upper wall of the pipe, the deposition rate of the 5 μm particles increases in moving from the wall center to the corners, and is greater than that for the larger particles due to the effects of the secondary flow. The maximum resuspension rate of the smaller particles occurs above the pipe corners, with the 50 μm particles showing their highest resuspension rate above and at the corners of the pipe.     

An analytical model for plug flow in microcapillaries with circular cross section

Plug flow in microcapillaries or microchannels offers significant advantages for the development of microfluidic applications and recently triggers many interests and studies. Recirculation is formed within liquid plugs due to the presence of interfaces. This paper presents an analytical model to investigate the recirculation flow and the flow resistance in microcapillaries with circular cross section. A fourth order partial differential equation is used to model the Stokes flow within the liquid plug. The results of the flow field show that the flow pattern is affected by the plug length. The flow resistance is determined through the force balance of the liquid plug. The comparison of the flow field and the flow resistance from the analytical model and the experiments shows good agreement.     

Stokes flow of a rotating sphere around the axis of a circular orifice or a circular disk

This paper presents an infinite series solution to the creeping flow equations for the axisymmetric motion of a sphere of arbitrary size rotating in a quiescent fluid around the axis of a circular orifice or a circular disk whose diameters are either larger or smaller than that of the sphere. Numerical tests of the convergence are passed and the comparison with the exact solution and other computational results shows an agreement to five significant figures for the torque coefficients in both cases. The torque coefficients are obtained for the sphere located up to a position tangent to the wall plane containing either the orifice or the disk. It is concluded that the torque coefficients of the sphere and the disk are monotonically increasing with the decrease of the distance from the disk or the orifice plane in both cases.     

Unsteady flow of an elastico-viscous fluid between two coaxial circular cylinders

Unsteady flow of an Oldroyd fluid between two coaxial circular cylinders is investigated, the fluid being set in motion as the inner cylinder moves from rest for a certain period with linearly growing speed and then stops suddenly. The Laplace transform technique is used to derive the solution. For the case when the gap between the cylinders is small, a simplified solution is obtained. The expression for the shear stress on the wall of the outer cylinder is obtained and particular cases are discussed.