Showing papers on "Pipe flow published in 1982"

Calculation of Secondary Currents in Channel Flow

Abstract: A model is presented for calculating the flow in channels with turbulence-driven secondary motion, with an emphasis on open channel flow. Algebraic expressions are derived for the Reynolds stresses in the momentum equations for the secondary motion by simplifying modelled Reynolds stress equations. A simple eddy viscosity model is used for the shear stresses in the logitudinal momentum equation. The kinetic energy k, and the dissipation rate ϵ of the turbulent motion appearing in the algebraic and eddy viscosity expressions are determined from transport equations for these quantities. The restricting influence of a free surface on the length scale of turbulence is accounted for by a special free surface boundary condition for ϵ. The resulting set of equations is solved with a marching forward numerical procedure for three-dimensional boundary layers. The model is tested by application to developed two-dimensional closed and open channel flow, closed square duct flow, and flow in open channels of various width-to-depth-ratios. Most features of these flows are simulated well by the model, including the reduction of the eddy viscosity near the free surface and the depression of the velocity maximum below the surface.

On the structure of turbulent channel flow

Abstract: Hot-film measurements of the streamwise velocity component were carried out in a fully developed turbulent water-channel flow for three different Reynolds numbers (13800, 34600 and 48900). The results for the first four statistical moments complement and extend the results from previous studies of turbulent channel flow. The VITA variance technique waa employed to detect deterministic events in the streamwise velocity. It waa demonstrated that the VITA technique has a band-pass-filter character. The number of events detected was found to decrerrae exponentially with the threshold level and the events occupy a wide range of timescales. This makes it impossible to define one unique frequency of occurrence or one unique duration of the events. However, by using this technique information was obtained on the amplitude and timescale distributions of the events. The chmacteristic features of the conditional iverages were found to be related to the skewness and flatness factors.

On the effect of torsion on a helical pipe flow

Abstract: An orthogonal coordinate system along a generic spatial curve has been introduced, and the Navier-Stokes equations for a steady incompressible viscous flow have been explicitly written in this frame of reference. As an application the flow in a helical pipe has been studied, and, formdii 5f curvature and torsion small compared with the radius of the pipe, the flow has been considered as a perturbed Poiseuille flow. The result is that for curvatures and torsions of the same order and for low Reynolds number the curvature induces on the flow a first-order effect on the parameter e =κa, where κ is the curvature and a the radius of the pipe, while the effect of the torsion on the flow is of the second order in E. This last result disagrees with those of Wang (1981), who, adopting a non-orthogonal coordinate system, found a first-order effect of torsion on the flow.

Acoustic streaming in swirling flow and the Ranque—Hilsch (vortex-tube) effect

Abstract: The Ranque–Hilsch effect, observed in swirling flow within a single tube, is a spontaneous separation of total temperature, with the colder stream near the tube centreline and the hotter air near its periphery. Despite its simplicity, the mechanism of the Ranque–Hilsch effect has been a matter of long-standing dispute. Here we demonstrate, through analysis and experiment, that the acoustic streaming, induced by orderly disturbances within the swirling flow is, to a substantial degree, a cause of the Ranque–Hilsch effect. The analysis predicts that the streaming induced by the pure tone, a spinning wave corresponding to the first tangential mode, deforms the base Rankine vortex into a forced vortex, resulting in total temperature separation in the radial direction. This is confirmed by experiments, where, in the Ranque–Hilsch tube of uniflow arrangement, we install acoustic suppressors of organ-pipe type, tuned to the discrete frequency of the first tangential mode, attenuate its amplitude, and show that this does indeed reduce the total temperature separation.

Turbulence in two-phase dispersed flows

Abstract: Turbulence measurements in dispersed-bubble two-phase pipe flow, using laser velocimetry techniques, are presented. The turbulence-intensity measurements show a strong dependence on the quality of the flow. A theoretical basis for the prediction of turbulence levels in two-phase flows is proposed. The approach is applied to dispersed-gas/liquid (bubbly) and solid/gas (particulate) two-phase flows, for which experimental data are available, with excellent results.

Non-Newtonian Fluids in Circular Pipe Flow

Abstract: Publisher Summary This chapter focuses on heat transfer behavior of viscoelastic fluid in turbulent pipe flow Although the asymptotic values of the heat transfer and friction factor can be calculated, there exist no firm criteria for determining whether asymptotic conditions exist Predictions of the intermediate values of the friction and heat transfer are not yet possible, even if the rheology and the thermal properties of the aqueous polymer solution are known To deals with the problems, the Weissenberg or Deborah number has to be taken into account The behavior of viscoelastic fluids flowing turbulently in noncircular channels or over external surfaces represents a relatively unexplored area of fluid mechanics Open channel flow of viscoelastic fluid is another interesting field currently being investigated The chapter concludes that to approach turbulent heat transfer behavior analytically, the usual and simplest method is to solve the uncoupled energy equation using the empirically determined velocity profile Hence, it is essential to understand the fluid mechanics of non-Newtonian fluids as well as the rheology

Fully Developed Turbulent Flow in a Pipe: An Intermediate Layer

Abstract: The fully developed mean turbulent pipe flow is analysed at large Reynolds number by the method of matched asymptotic expansions. From the study of various limiting processes, in the sense of Kaplun, a crucial intermediate limit is identified whose transverse dimension is of the order of geometric mean of the transverse dimensions of the classical inner and outer layers. The asymptotic expansions in the three layers (inner, intermediate and outer) are matched by the Millikan's argument leading to two overlap domains where velocity distribution is logarithmic but their slopes could be different. The measurements show that the sustantial log regions do in fact exist in the two overlap domains and the ratio of their slopes is 2.03. The present theory describes the velocity profile over a greater range when compared to the classical theory. The predictions of Reynolds stress and turbulent energy production are in remarkably good argreement with the data for almost entire turbulent flow region from the beginning of the buffer layer to the axis oj pipe.

Relation Between Mass Transfer and Corrosion in a Turbulent Pipe Flow

Abstract: Electrochemical measurements of mass transfer in a turbulent pipe flow are presented. In particular the effect of flow obstacles, such as orifices and circumferential slots with varying diameter and axial length, has been studied. The results also include measurements of mass transfer downstream, a sudden expansion or reduction of the tube diameter. The experiments were performed at a Schmidt number of 1460 and Reynolds numbers ranging between and . The work presented in this paper is a part of a project aiming to study the relation between corrosion and mass transfer at high flow rates with particular emphasis on disturbed turbulent pipe flow.

Transition to Turbulence and Velocity Distribution in an Oscillating Pipe Flow

Abstract: Experiments on transition to turbulence in an oscillating pipe flow were made by using a hot wire anemometer over ranges of Reynolds numbers Re os = |μm, os, l| D/ν(|μm, os, l|is the cross-sectional mean velocity amplitude, D = 2R the pipe diameter, ν the kinematic viscosity) from 600 to 65000 and of dimensionless frequencies √(ω') = R√(ω/ν) (ω is the angular frequency) from 2.6 to 41. Critical Reynolds numbers from laminar to transitional and from transitional to turbulent flows agreed well with published experimental results. In the turbulent regime turbulent bursts follow by relaminarization in the same cycle. It is observed that the instantaneous velocity profile in every phase when a turbulence with higher frequency appears is represented by the well-known Blasius 1/7 power law, but in the laminar-like phase it does not follow the laminar theoretical solutions for a steady oscillating pipe flow.

Theory for electric charging in turbulent pipe flow

Abstract: Basec on somewhat simplified profiles of turbulent eddy diffusivity and mean vcLacity in turbulent flow, an expression is derived for the convection current in a pipe where electrification occurs at the wall. The expression is in explicit analytic form, and applies for all turbulent Reynolds numbers and all fluid conductivities, from conditions where the Debye length is small compared with the diffusion sublayer (typical aqueous solutions) to conditions where the Debye length is large compared with the sublayer (typical liquid hydrocarbons).

Phase-distribution mechanisms in turbulent low-quality two-phase flow in a circular pipe

Abstract: The radial distribution of the volumetric vapour (or void) fraction in steady, fully developed turbulent two-phase flow is described for vertical low-quality bubbly flows in a circular pipe The analysis is based on the phasic equations of conservation of momentum in the axial and radial directions Mixing-length theory is used to model the turbulent stresses in the continuous phase The predicted flow structure shows three distinct regions The ‘outer’ region, that is, the region away from the wall and the centre-line, has a uniform void distribution For upflow, a bubble layer is predicted near the wall, while for downflow, vapour coring is predicted, with a peak in void fraction at the centre-line These predictions are in agreement with observed void profiles

A new numerical method for the simulation of three dimensional flow in a pipe

Abstract: A new numerical method has been developed to investigate three-dimensional, unsteady pipe flows using a new velocity-vector expansion method. Each vector function in the expansion set is divergence-free and satisfies the boundary conditions for viscous flow. Other features of the general technique are as follows: (1) pressure is eliminated from the dynamics; (2) only two unknowns per “mesh point” are required; (3) there is rapid convergence of spectral methods; (4) there is implicit treatment of the viscous term at no extra computational cost; and (5) no fractional time-steps are required. In the present application of the method to flow in a pipe, the behavior of each flow variable near the computational singular point is treated rigorously and expansions in Jacobi polynomials have been shown to be particularly advantageous. The method has been tested on the linear stability problem for Poiseuille flow and has demonstrated rapid convergence of the eigenvalues and eigenfunctions as the number of radial modes is increased.

Low-frequency sound radiation and generation due to the interaction of unsteady flow with a jet pipe

Abstract: In this paper we examine the low-frequency sound radiated when various types of unsteady flow interact with a jet pipe. In each case we solve the problem exactly by the Wiener-Hopf technique, producing results valid for arbitrary internal and ex- ternal Mach numbers and temperatures, discuss the importance of a Kutta condition at the duct exit, and provide an interpretation, in elementary terms, of the radiated sound field using the Lighthill acoustic analogy. A central feature is that the solutions are always obtained subject to a causality requirement, regardless of whether or not a Kutta condition is imposed at the pipe lip. When low-frequency sound propagates down the jet pipe, little of it reaches the far field, and the major disturbance outside the pipe is that associated with the jet instability waves. At subsonic jet speeds and low-enough Strouhal number these waves transport kinetic energy at a rate precisely balancing the loss of acoustic energy from the pipe, resulting in a net attenuation of the sound power. For supersonic jet condi- tions a further wave motion, the unsteady-flow counterpart of the steady wave struc- ture of an imperfectly expanded jet, is present in addition to the instability wave. We use the Lighthill acoustic analogy to show that, for high-enough jet Mach number and temperature, the sound radiation is caused largely by quadrupole sources arising from the jet instability waves. An alternative interpretation uses the acoustic analogy incorporating a mean flow due to Dowling, Ffowcs Williams and Goldstein, and expresses the far-field sound as the sum of contributions from monopoles and dipoles distributed over the duct exit. The directivity and power of the calculated far-field sound are in good agreement with experiments. We also calculate the sound scattered by the jet pipe when there is an incident external sound field, and show a previously published result to be in error. In general, the flbw phenomena produced by internal and external incident sound fields are similar. Finally, we discuss the effects of nozzle contraction. We find that the radiated sound field is little changed in character, but that the reflection properties of the nozzle may be drastically altered.

Study on correction coefficients of liminar and turbulent entrance region effect in round pipe

Abstract: In this paper, a universal method for calculation of the inlet length and correction coefficient for the pressure losses and the flow in the case of laminar and turbulent flow in a smooth round pipe is put forward.

Numerical solutions for the spin-up of a stratified fluid

Abstract: The model of Warn-Varnas et al. (1978) is used to numerically examine the spin-up flow of a thermally stratified fluid in a cylinder with an insulating side wall, and comparison of the results with the laser-Doppler measurements of Lee (1975) shows excellent agreement. It is shown that flow gradients are created in the interior of the fluid during the meridional circulation spin-up phase, and that the azimuthal flow decayed faster than has been predicted by Wallin (1969). It is established that viscous diffusion in the interior, arising from the interior-flow gradients, is the cause of the discrepancy with Wallin's theory.

Flow Patterns and Frictional Losses in an Oscillating Pipe Flow

Abstract: Velocity distribution and pressure gradient in an oscillating pipe flow are measured over wide ranges of Reynolds numbers and dimensionless frequencies. Wall shear stress is determined by substituting experimental values of cross-sectional mean velocity and pressure gradient into an unsteady momentum integral equation. From these experimental quantities frictional losses and four characteristic parameters describing the flow pattern are calculated. They are well represented by the known laminar theory in a laminar regime and by the turbulent quasi-steady relations in a turbulent regime. Here, turbulent quasi-steady state is defined as the state in which relationship between cross-sectional mean velocity and wall shear stress for steady turbulent pipe flow holds at any moment in a cycle.

Measurements and predictions of fully developed turbulent flow in a simulated rod bundle

Abstract: Fully developed air flow has been investigated over a Reynolds-number range of 82800-346700 in a duct that simulates two interconnected subchannels of a rod bundle with a pitchldiameter ratio of 1.20. Based on equivalent hydraulic diameter, friction factors were found to be 2% lower than for pipe flow. Detailed measurements were made at a Reynolds number of 200000 of axial velocities, secondary velocities, and the Reynolds stresses. The distribution of axial velocity near the walls (normalized with the local friction velocity) could be expressed by an inner law of the wall for y + up to 1500. Distributions of the normal Reynolds stresses and the mean turbulence kinetic energy were similar to those observed in a number of pipe and two-dimensional channel flows and could be correlated using the axial-velocity fluct,uations normalized with the local friction velocity. Maximum secondary velocities were about 1.5 % of the bulk axial velocity. The ‘ k -e’ turbulence model and an algebraic vorticity source for generating secondary velocities enabled the computation of axial velocities, secondary velocities, and mean turbulence kinetic energies that are in satisfactory agreement with those measured.

Characteristics of Countercurrent Gas-Liquid Two-Phase Flow in Vertical Tubes

Abstract: Investigations into the flow pattern and the void fraction for countercurrent air-water flow in vertical tubes of diameter D = 40 and 80 mm were reported. The flow maps were presented and showed slug flow regime occupied larger portion on them. The void fraction was measured by the quick-closing valve technique, in bubbly and slug flow regime. The void fraction data available in the literatures as well as present work for counter- current flow in vertical tubes were correlated in terms of dimensionless groups. The experimental results of the present work were also compared with the drift flux model.

Local drag reduction due to injection of polymer solutions into turbulent flow in a pipe. Part II: Laser‐doppler measurements of turbulent structure

Abstract: Aqueous solutions of polyethyleneoxide (Polyox WSR-301) were injected into a pipe flow through either a small tube at the center line or an annular slot in the wall. The solution contained polymer at an injection concentration of 1,000 wppm. Injection into water flow with a Reynolds number Re = 3.5 X 10/sup 4/ was at a rate which gave a mean polymer concentration of 5.0 wppm in the water flow. A laser-Doppler anemometer (LDA) was used to measure the streamwise turbulent velocity at various radial positions and at several stations downstream from the injection point. Results were obtained for mean velocity and intensity profiles; autocorrelations; and one-dimensional energy spectra. The mean bursting period was determined using the ''short-sampling-time'' autocorrelation method. Changes in all these quantities due to polymer injection were found to depend on the amount of local drag reduction at that particular downstream station but were independent of the local polymer concentration at the measuring point.

Transition to Turbulence in a Pulsatile Pipe Flow : Part 2, Characteristics of Reversing Flow Accompanied by Relaminarization

Abstract: The instantaneous velocity distributions and pressure gradients in a reversing pulsatile flow and an oscillatory flow in which turbulent bursts follow by relaminarization in the same cycle are investigated. They are predicted with sufficient accuracy by the theory for a transient pulsatile laminar flow in the laminar phase. Meanwhile, in the phase where turbulence with higher frequency appears, they are well approximated by the well-known 1/7 power law and the turbulent quasi-steady friction law respectively.

Closed-cavity laminar flows at moderate Reynolds numbers

Abstract: The paradox reported by Brady & Acrivos (1981) of the non-existence of similarity solutions in the Reynolds-number range 10·25 < R < 147 for the flow in a tube with an accelerated surface velocity is resolved. It is shown that the source of the difficulty lies in the assumption that the tube is infinite in extent. For a finite tube, it is demonstrated that the presence of the closed end, even though far removed from the origin, affects in a fundamental way the structure of the flow throughout the entire tube. The change in the flow structure that occurs in a finite tube at R = 10·25 is caused by the fluid which is returning from the downstream end; it is shown further that the problem of determining the motion in a long finite tube is equivalent to that of selecting the initial condition for the boundary-layer equations that properly takes into account the presence of the reverse flow. By applying a method originally developed by Klemp & Acrivos (1976) for selecting this condition, the flow in a finite tube is determined numerically for Reynolds numbers up to 70. In addition, it is shown that the same change in structure brought about by the returning fluid occurs in a finite two-dimensional channel at R = 57, even though the corresponding similarity solutions exist for all values of R. The results suggest that similarity solutions should be viewed with caution because they may not represent a real flow once a critical Reynolds number is exceeded.