Showing papers on "Pipe flow published in 1979"

Calculation of strongly curved open channel flow

Abstract: The paper describes the application of a finite-difference calculation procedure to the problem of simulating the three-dimensional, turbulent flow in a strongly curved, open, 180° bend with straight inlet and outlet reaches. The configuration can be considered to represent an element of a model meander, and the work presented here forms an important stage in efforts to simulate the flow in successive reverse-curvature bends. No restrictions other than the absence of flow separation and hydraulic jumps are imposed. Full account is taken of non-linear fluid-inertia and of turbulent diffusion terms. Effects of turbulence are represented by an eddy viscosity related to two parameters— the turbulent kinetic energy k and its rate of dissipation ϵ\N— for which related differential transport equations are solved. Predictions are presented for the transverse surface slope and velocity field in a configuration experimentally examined by Rozovskii. Agreement between predictions and experimental data is judged to be satisfactory on all major flow phenomena.

Flow structure of the free round turbulent jet in the initial region

Abstract: This note presents measurements of radial and axial distributions of mean velocity, turbulent intensities and kinetic energy as well as radial distributions of the turbulent shear stress in the initial region of a turbulent air jet issuing from a long round pipe into still air. The pipe flow is transformed relatively smoothly into a jet flow. In the core subregion the mean centre-line velocity decreases slightly. The highest turbulence occurs at an axial distance of about 6d and radius of (0·7 to 0·8)d. On the axis the highest turbulent kinetic energy appears at a distance of (7·5 to 8·5)d. Normalized distributions of the turbulent quantities are in good agreement with known data on the developed region of jets issuing from short nozzles.

Attenuation of Sound in a Low Mach Number Nozzle Flow

Abstract: This paper examines the energy conversion mechanisms which govern the emission of low frequency sound from an axisymmetric jet pipe of arbitrary nozzle contraction ratio in the case of low Mach number nozzle flow. The incident acoustic energy which escapes from the nozzle is partitioned between two distinct disturbances in the exterior fluid. The first of these is the free-space radiation, whose directivity is equivalent to that produced by monopole and dipole sources. Second, essentially incompressible vortex waves are excited by the shedding of vorticity from the nozzle lip, and may be associated with the large-scale instabilities of the jet. Two linearized theoretical models are discussed. One of these is an exact linear theory in which the boundary of the jet is treated as an unstable vortex sheet. The second assumes that the finite width of the mean shear layer of the real jet cannot be neglected. The analytical results are shown to compare favourably with recent attenuation measurements.

The separating flow through a severely constricted symmetric tube

Abstract: The axisymmetric flow of an incompressible fluid through a pipe (of radius a) suffering a severe constriction is studied for large Reynolds numbers R, the features of symmetric channel flows being virtually the same. Here ‘severe’ refers to a constriction whose typical dimensions are finite, and the oncoming velocity profile is taken to be of a realistic type, i.e. with no slip at the wall. The study adopts (Kirchhoff) free-streamline theory, which, for the mostly inviscid description, affords a rational basis consistent with viscous separation. The major (triple-deck) separation takes place on the constriction surface and is followed by a downstream eddy of length O(aR). Another, less familiar, separation is predicted to occur at a distance 0.087a In R + O(a) ahead of the finite obstacle. Free-streamline solutions are found in the two main extremes of moderately severe and very severe constriction. In both extremes, and in any slowly varying constriction, the major separation is sited near the maximum constriction point. The upstream separation point is also derived, to O(a) accuracy in each case. The upstream separation can be suppressed, however, if the constriction has no definite starting point and decaysslowly upstream, but then the upstream flow response extends over a much increased distance. Comparisons with Navier-Stokes solutions and with experiments tend to favour the predictions of the free-streamline theory.

Bifurcation from Infinity

Abstract: Poiseuille flow in a pipe and plane Couette flow of a viscous incompressible fluid are stable in the linear approximation at all Reynolds numbers, yet these flows certainly do not remain laminar as the Reynolds number is increased indefinitely. In this paper a study is made of some nonlinear differential equations, containing a parameter, which model this aspect of the fluid-mechanical problems. In the model equations there is no finite value of the parameter at which bifurcation occurs, but there are solutions whose norm tends to zero as the parameter tends to infinity. It is shown that these small-norm bifurcating solutions are characterized by strongly-nonlinear balances. In the fluid-mechanical context the viscous and inertial terms would be comparable.

Laminar flow in the entrance region of a smooth pipe

Abstract: The entrance region has been divided into two parts, the inlet region and the filled region. At the end of the inlet region, the boundary layers meet at the pipe axis but the velocity profiles are not yet similar. In the filled region, adjustment of the completely viscous profile takes place until the Poiseuille similar profile is attained at the end of it. The boundary-layer equations in the inlet region and the Navier-Stokes equations with order-of-magnitude analysis in the filled region are solved using fourth-degree velocity profiles. The total length of the entrance region so obtained is ξ = x/R Re = 0·150, whereas the boundary layers are observed to meet at approximately one-quarter of the entrance length, i.e. at ξ = 0·036. Experiments reported in the paper corroborate the analytical results.

The Effect of Gaseous Cavitation on Fluid Transients

Abstract: Gaseous cavitation (alternately termed gas release) is investigated for turbulent pipe flows subjected to transient wave motion. Experimental data are presented that exhibit developing 2-component flow (air or carbon dioxide and water mixtures) in a 295-m laboratory pipeline; the flow is characterized by wave dispersion due to the increase in void fraction. An analytical model based on the method of characteristics yields simultaneous solutions for pressure, velocity, and void fraction. The greatest uncertainty in the formulation is the rate of gas release; in this instance, it is allowed to depend upon the difference between saturation and instataneous line pressures. 28 references.

Channel flow with temperature-dependent viscosity and internal viscous dissipation

Abstract: This paper uses asymptotic methods to analyse the flow in a narrow channel of a fluid with temperature-dependent viscosity and internal viscous dissipation. When the Nahme–Griffith number is large we show how the flow evolves from Poiseuille flow with a uniform temperature distribution to a plug flow with hot boundary layers on the walls. An asymptotic solution is obtained for the flow in the region of transition from Poiseuille to plug flow and an explicit equation is derived for the pressure gradient in terms of the local downstream co-ordinate in this transition region.

The influence of suction on the structure of turbulence in fully developed pipe flow

Abstract: The effect of uniform wall suction on the structure of turbulence in a fully established turbulent pipe flow has been measured, with special attention to the critical layers close to the wall. Uniform suction was introduced into a pipe flow with a Reynolds number of 17250 by means of a porous-walled section 2·2 diameters in length with very fine perforations. The effect of suction on the turbulent energy balance was then measured over the entire cross-section at four axial locations. The results indicate the following. The amplitudes of the three principal velocity fluctuation components are reduced by suction, but to differing degrees. Moreover, the effects of suction on the amplitudes of these fluctuations develop at differing rates such that the x-wise components are first affected, then the r-wise and lastly the ϕ-wise components.The suction-induced perturbation in the turbulent structure propagates from the wall to the pipe centre-line with a velocity approximately equal to the friction velocity Uτ.Even with very small rates of fluid extraction the maxima of the terms in the turbulent energy balance occurring close to the wall are drastically reduced. Nevertheless there is no tendency for the location of these maxima to move towards the wall.The general reduction of the level of turbulent energy across the entire section is due to transport of this energy by the augmented mean radial velocity towards the wall, where it is dissipated since the boundary condition inhibits the passage of turbulent energy through the wall.

The dispersion of discrete particles in a turbulent fluid field

Abstract: The degree of radial dispersion of medium size particles (ηK < dp < lf) emanating from a point source, is measured photographically in the turbulent core of a fully developed vertical pipe flow of water. From the classical theoretical results of G. Taylor, it was then possible to calculate statistical parameters which characterize the turbulent particle motion. A comparison is made between a tracer and neutrally dense, buoyant and heavy particles. Results indicate that the effect of particle intertia is negligible, and that the crossing trajectories effect dominates the dispersion process. A “wake effect” causes a buoyant particle to disperse to a greater degree than an equivalent heavy particle. An exponential-cosine form of the Lagrangian autocorrelation coefficient provides a best fit for the dispersion data, although a purely exponential form is equally adequate for practical calculations.

The effect of turbulence on premixed flame noise

Abstract: The effects of turbulence intensity and integral length scale on combustion noise have been investigated in cylindrical burners with fully developed pipe flow and in a nozzle burner with grid induced turbulence. Mean velocity and turbulence intensity measurements in flames over a wide range of Reynolds numbers have been made by laser anemometry and the results for equivalent air jets have been verified by hot-wire anemometry. Semi-empirical relationships for combustion noise have been tested over a wide range of flow conditions and equivalence ratios and it has been confirmed that these expressions give accurate predictions for fuel lean and stoichiometric flames on cylindrical burners. Grids producing higher turbulence levels in flames give rise to higher values of turbulent burning velocity and combustion noise, indicating that the upstream turbulence is also responsible for the increase in amplitude of combustion noise. Integral length scale measurements by auto-correlation indicate that the magnitude of the macro-scale is independent of the grid gemetry. Assuming that the integral scale in equivalent air jets is identical to that in flames, it appears to have no effect on combustion noise.

Study on the Tubular Pinch Effect in a Pipe Flow : I. Lateral migration of a single particle in laminar poiseuille flow

Abstract: In laminar flow of suspensions through a circular tube, particles migrate into a concentric annular region with the radius about 0.6 of the tube radius. This phenomenon is well-known as the tubular pinch effect. To clarify the mechanism, the influences of relative particle-fluid velocity, Reynolds number and particle diameter on radial particle displacement (lateral migration) were investigated by measuring the motion of a suspended spherical particle in laminar flow through a circular tube. Consequently, it was found that the motions of particles could be classified by the particle Reynolds number. And, especially, the relation between the particle Reynolds number and the equilibrium radial position of particles and the existence of critical particle Reynolds number for shifting from unilateral migration to bilateral migration were clarified.

Parabolic Procedure for Flows in Ducts with Arbitrary Cross Sections

Abstract: A computer program has been developed to predict three-dimensional compressible viscous flows in ducts with arbitrary cross-sectional shapes. A curvilinear boundary-fitted coordinate system is used to simplify boundary conditions. The parabolized Navier-Stokes equations are transformed, and the solution is marched down the duct using an iterative ADI procedure. Computed results are compared with test data for laminar test cases in square and round ducts. A two-equation turbulence model is demonstrated for a developing turbulent pipe flow. A comparison between predicted results and test data is presented for a turbulent diffuser flow with a rectanguiar-to-round transition in cross-sectional geometry.

Pulsating Viscoelastic Pipe Flow - Water-Hammer

Abstract: This theoretical study of the effect of viscoelastic material properties of a pipe conveying one-dimensional, non-stationary flow shows that, in addition to exponential attenuation of wave fronts, the disturbance is transformed into a diffusion front whose thickness increases as √t, and which propagates at a velocity corresponding to the retarded elasticity of the pipe material [E(∞)] The behaviour of pressure disturbances in the special case of water-hammer resulting from sudden closure of a valve is illustrated by a numerical application based on the characteristics method For a pipe of finite length L fed from a constant-level tank, a damped oscillation of period 2L/ā is observed, corresponding to a pseudo-velocity of propagation ā which is calculated on the assumption that deformations associated with relaxation times smaller than 2L/a 0 are instantaneous, where a 0is the true elastic wave celerity (a 0>ā)

Development of local turbulent drag reduction due to nonuniform polymer concentration

Abstract: Turbulent drag reduction produced by injection of polymer at the centerline of a pipe flow was found to increase with streamwise distance from the injection point. This was due to radial dispersion of the injected polymer. A tentative relationship between the two is proposed.

The interaction of sound with low Mach number wall turbulence, with application to sound propagation in turbulent pipe flow

Abstract: This paper discusses the influence of turbulence convection on the formation of acoustic momentum and thermal boundary layers over a rigid surface in the presence of a low Mach number wall-turbulence shear flow. Equations which determine the modified boundary-layer profiles are obtained from a consideration of the relaxation of coherent perturbations in the Reynolds stress. These equations can be solved analytically for a wide range of conditions which are investigated in detail. The theory is applied to the problem of sound propagation in fully-developed turbulent pipe flow, and at low Mach numbers good agreement is obtained between predicted acoustic attenuation rates and experimental results available in the literature.

Measurements of Mean Velocity and Reynolds Stresses in Some Regions of Recirculating Flow

Abstract: The paper describes measurements of mean velocities and Reynolds stresses in recirculating flows associated with the flow past a number of simple bluff bodies. The principal instrument used was the pulsed-wire anemometer.

Further observations on transition in a pipe.

Abstract: : Fully developed Poiseuille flow in a pipe was artificially disturbed at x/D = 400 and 17RE4000. Puffs and slugs generated by the disturbance were identical to the structures observed when the flow in the inlet region had undergone transition (Wygnanski and Champagne 1973). Since the disturbance was sufficiently strong to cause transition even at low Reynolds numbers the appearance of either puffs or slugs depended on the Reynolds number only. Velocity measurements in the pipe were taken with rakes of hot wires using digital acquisition methods and in this way each realization could be observed in its entirety. The coherence of the large structures was studied in radial and azimuthal directions. Puffs and slugs generated by the disturbance were mapped and found to be identical to the structures observed at the inlet region of the pipe. It was established that a slug which has all the attibutes of a fully developed turbulent pipe flow is generated by a coalescence of puffs. The puff, which seems to contain a small number of toroidal eddies appears to be a fundamental coherent structure in a fully developed turbulent pipe flow. Previous observations, which were based on a single-point measurement and ensemble-averaged data did not reveal the full structure of the puff in the same detail as the present techniques. Single realizations were analysed showing instantaneous velocity profiles, vorticity perturbation contours, as well as streamlines moving with the structure. Artificially generated successions of puffs which were allowed to interact, closely resembled a slug. The evolution of a slug from puffs was thus established. (Author)

Process and apparatus for carrying out (bio)chemical reactions and unit operations in fluid systems

Abstract: To carry out (bio)chemical reactions and unit operations in homogeneous and heterogeneous fluid systems, the fluid systems are guided in such a way that during the reaction they are subject to various flow characteristics. First the fluid systems are guided in a loop (8) whose pipe characteristic is adjustable between an idealised stirred tank characteristic and a real pipe characteristic. On leaving the loop the fluid systems are guided through a spatially and temporally up- and/or downstream pipe (9) having pipe flow characteristics.