Showing papers on "Pipe flow published in 1978"

Vortex formation at vertical pipe intakes

Abstract: With the object of determining the similarity criterion, experimental studies on vortex formation at pipe intakes were carried out using two geometrically similar circular vortex tanks, circulation in approach flow was generated by means of adjustable guide vanes Transparent pipe intakes of different sizes and liquids of different viscosities and surface tensions were used in a recirculating system Based on the analysis of data, a method has been proposed according to which a geometrically similar model is operated at the same Froude number as in the prototype and the observed critical submergence is corrected for distortion due to change in the model Reynolds number A criterion to determine the type of vortex for known geometric and kinematic conditions has also been proposed

Extended Stokes series: laminar flow through a loosely coiled pipe

Abstract: Dean's series for steady fully developed laminar flow through a toroidal pipe of small curvature ratio has been extended by computer to 24 terms Analysis suggests that convergence is limited by a square-root singularity on the negative axis of the square of the Dean number An Euler transformation and extraction of the leading and secondary singularities at infinity render the series accurate for all Dean numbers For curvature ratios no greater than , experimental measurements of the laminar friction factor agree with the theory over a wide range of Dean numbers In particular, they confirm our conclusion that the friction in a loosely coiled pipe grows asymptotically as the one-quarter power of the Dean number based on mean flow speed This contradicts a number of incomplete boundary-layer analyses in the literature, which predict a square-root variation

Droplet size spectra generated in turbulent pipe flow of dilute liquid/liquid dispersions

Abstract: Experiments were carried out with water dispersed in hydrocarbons at various flow rates. The measured size spectra can be well represented by either an upper limit log-probability function or a Rosin-Rammler type of equation with constant parameters and only one variable, the maximum drop diameter dmax or d95. The latter can be predicted satisfactorily by a correlation based on the Hinze/Kolmogorov model of droplet breakup.

Structural similarity in radial correlations and spectra of longitudinal velocity fluctuations in pipe flow

Abstract: The paper describes correlation measurements in both broad and narrow frequency bands of the longitudinal velocity fluctuations in fully developed pipe flow at four positions for a reference probe whilst a second probe was traversed radially from deep in the sublayer to a position near the axis with both longitudinal and transverse separations zero (Δx = Δz = 0). Such measurements require that both the Covariant (Co) and Quadrature (Quad) correlations be determined for each of the 15 frequencies used to constrain the wave component λx.The new data demonstrate that low frequency, large scale turbulence fluctuations extend over the majority of the radial region and that these components are highly correlated. By using a similarity variable kxy, along with a normalized wall distance y/y REF, both correlation functions, i.e. the Co and the Quad components, are shown to collapse. The physical significance of this is discussed.The broad-band data do not collapse because of the large range of wave sizes. However, the present experiment does show that strong radial correlations exist even when one probe is at y+ = 1. This conflicts with the earlier data of Favre, but agrees with the more recent work of Comte-Bellot. There is a significant amount of turbulent energy in frequencies less than 16 Hz (ω+ = 0·008) for turbulent flows of about 105 Reynolds number.The spectral function ωΦ(ω) is also presented for a range of y+ values. Using this form for the power spectral density, along with the stochastic wave modelling and similarity arguments of this paper, it is shown how a consistent explanation for the behaviour of these spectra is obtained. In addition some preliminary results from cross-spectral analyses are presented and suggestions made as to their physical significance.

Measurements and prediction of fully developed turbulent flow in an equilateral triangular duct

Abstract: Fully developed air-flows through an equilateral triangular duct of 12·7 cm sides were investigated over a Reynolds number range of 53 000 to 107 000. Based on equivalent hydraulic diameter, friction factors were found to be about 6% lower than for pipe flow. Mean axial velocity distributions near the wall were describable by the inner law of the wall (when based on local wall shear stress) but the constants differ slightly from those for pipe flow. As expected, the secondary flow pattern was found to consist of six counter-rotating cells bounded by the corner bisectors. Maximum secondary velocities of about 1 ½% of the bulk velocity were observed. The effects of secondary currents were evident in the cross-sectional distributions of mean axial velocity, wall shear stress and Reynolds stresses, and very prominent in the turbulent kinetic energy distribution. For the flow prediction, the vorticity production terms were expressed by modelling the Reynolds stresses in the plane of the cross-section in terms of gradients in the mean axial velocity and a geometrically calculated turbulence length scale. The experimental and predicted characteristics of the flow are shown to be in good agreement.

Plane entry flows and energy estimates for the navier-stokes equations

Abstract: One of the classic problems of laminar flow theory is the development of velocity profiles in the inlet regions of channels or pipes. Such entry flow problems have been investigated extensively, usually by approximate techniques. In a recent paper [4], Horgan & Wheeler have provided an alternative approach, based on an energy method for the stationary Navier-Stokes equations. In [4], concerned with laminar flow in a cylindrical pipe of arbitrary cross-section, an analogy is drawn between the end effect issue of concern here, called the “end effect”, and the celebrated “Saint-Venant's Principle” of the theory of elasticity.

Flow in heated curved pipes

Abstract: The fully developed laminar flow in a heated curved pipe under the influence of both centrifugal and buoyancy forces is studied analytically. The pipe is assumed to be heated so as to maintain a constant axial temperature gradient. Both horizontal and vertical pipes are considered. Solutions for these two cases are obtained by regular perturbations in the Dean number and the product of the Reynolds and Rayleigh numbers; the solutions are therefore limited to small values of these parameters. Predictions of the axial and secondary flow velocities, streamlines, shear stress, temperature distribution and heat transfer are given for a representative case.

Flow control device for fluids flowing in a closed conduit

Abstract: A flow control device incorporates a flow sensor and a flow control circuit responsive to the output signal of the flow sensor. The flow control circuit operates, via a servo, a flow control valve. The flow sensor incorporates a self-heated thermistor located in the divergent discharge throat of a nozzle in the flow stream. Two unheated thermistors are also located in the fluid, at arbitrary points distant from the nozzle, and incorporated in the control circuit for temperature compensation. The valve controls the flow of fluids therethrough by the distention of an integral seal tube into a cavity formed in an anvil inset into the seal tube. The cavity is conical in shape and the elastomeric seal tube is pressed thereinto by means of a ball. Two orifices issue into the cavity and terminate in the flow channel at the upstream and downstream ends of the valve. With the ball at the inmost limit of its travel, the seal tube blocks the exits of both orifices into the cavity and prevents flow in the channel.

Secondary Flow in Noncircular Conduits

Abstract: A requirement for calculating an accurate velocity distribution in noncircular conduits is a knowledge of the secondary flow distribution in these conduits. The cause of these secondary flows is considered in this paper and a simple momentum transfer model for Reynolds stresses is used to effect a solution for the secondary flow in a square duct. The calculated secondary flows are similar in magnitude and direction to measurements reported in the literature.

On Itoh's finite amplitude stability theory for pipe flow

Abstract: In two recent papers Itoh has developed a finite amplitude stability theory which indicates that nonlinearity increases the damping rate of a small but finite amplitude disturbance to flow in a circular pipe when the disturbance is concentrated near the axis of the pipe. For such a centre mode, which is the only mode considered by Itoh, Davey & Nguyen found, in an earlier paper, the opposite result that nonlinearity decreases the damping rate. We examine the reasons for this discrepancy and we explain the subtle difference between Itoh's method and the method of Reynolds & Potter, which was used by Davey & Nguyen. We suggest that for the centre mode of pipe flow neither Itoh's result nor Davey & Nguyen's result is a reliable guide to the true situation. However, for the wall mode of pipe flow, and especially for plane Couette flow, both methods give very similar results and we suggest that this similarity indicates that in these cases the damping rate is decreased by nonlinearity. For a particular problem we believe that it is only when the results of the two methods are very similar that either method is likely to be useful.

Differential Equations and Boundary Conditions

Abstract: Publisher Summary This chapter presents differential equations and boundary conditions. Flow is laminar when the velocities are free of macroscopic fluctuations at any point in the flow field. For steady-state laminar flow, all velocities at a stationary point in the flow field remain constant with respect to time, but velocities may be different at different points. Laminar flow, also referred to as viscous or streamline flow, is characteristic of a viscous fluid flow at low Reynolds number. Laminar flow in a two-dimensional stationary straight duct is designated as hydrodynamically fully developed when the fluid velocity distribution at a cross section is of an invariant form. The fluid particles move in definite paths called streamlines, and there are no components of fluid velocity normal to the duct axis. In a fully developed laminar flow, the fluid appears to move by sliding laminar of infinitesimal thickness relative to adjacent layers. Depending upon the smoothness of the tube inlet and tube inside wall, fully developed laminar flow persists up to Re ≤ 2300 for a duct length L greater than the hydrodynamic entry length Lhy.

Three-Dimensional Open Channel Flow

Abstract: An open channel flow is usually three-dimensional consisting of the primary and secondary flows. The primary flow is defined herein as the flow component in the longitudinal direction of the channel, while the secondary flow includes the remaining flow components in the vertical and transverse directions of the channel. In an alluvial channel the channel cross sections and, thus, the three-dimensional flow structure vary irregularly or randomly along the flow. A technique has been developed and presented herein that can be used to compute secondary currents and, thus, the irregular three-dimensional structure of open channel flow. The technique uses analytical, hydrodynamic equations along with measured data of channel geometry and primary flow velocity distribution. Illustrative examples are presented with results of practical applications of the technique, describing the variability of the direction and magnitude of secondary currents with time, space, and discharge rate.

Measurement of acoustic reflection from an obstruction in a pipe with flow

Abstract: An alternative to the impedance tube method is proposed for measurement of acoustic reflection coefficients. The new method has the advantage that it may be used to measure the reflection and transmission coefficients for plane sound waves incident on an obstruction (orifice, nozzle, valve, elbow, etc.) in a long, straight, hard‐walled duct in the presence of flow through the duct. It employs the time‐delayed cross correlation between an acoustic signal source and the output signals from microphones located ahead of, and behind, the obstruction. The method is demonstrated for several situations, including the case of flow through square‐edged orifices where Mach number in the jet downstream of one orifice was as high as 0.73.

Transition to turbulence in starting pipe flows.

Abstract: An experimental investigation was performed to study the transition to turbulence in pipe flow started impulsively with a supercritical Reynolds number. The results show that a turbulentnon-turbulent interface propagates downstream by consuming the non-turbulent region where laminar boundary-layer flow is developing with time. For the startup of a completely quieted fluid, the propagation velocity is equal to the maximum velocity of the steady-state turbulent flow. For restarting the fluid flow after a brief shutoff, however, the propagation velocity is larger than the maximum velocity, and the difference increases with shorter quieting times. In the process of interface propagation, a wave of very low frequency appears ahead of the interface centring around the radial position where the smallest change in velocity is observed at the instant of propagation. A study of the mechanism of interface propagation shows that the final break of the abovementioned wave continuously triggers downstream propagation of the turbulent-flow region. In addition, random jumping of the interface in turbulence-decaying flow is concluded to be the main cause for the increase in propagation velocity for short quieting times.

Initiation and propagation of normal zones in a force-cooled tubular superconductor

Abstract: A numerical analysis has been performed on the time-dependent equations of heat balance, gas convection, pressure drop, and mass-flow rate for supercritical helium gas flowing through a tubular superconductor. Three dimensional graphs of wall temperature, gas temperature, and mass-flow rate as functions of position and time are used to show the evolution of normal zones. In contrast to other methods of studying stability in superconductors by a quasi-steady-state analysis of critical-sized normal zones (minimum propagating zone), our analysis shows that stability is influenced by both the magnitude and the time dependence of the disturbance. As the current is increased in a system subjected to certain types of thermal disturbances, propagating normal zones may originate at positions well downstream from the site of the disturbance. At higher currents, propagating zones may originate both downstream and at the disturbed site, coalescing into a large propagating normal zone. With certain types of disturbances (such as an extraneous heat source over a short length of conductor), higher critical currents may be reached by fast current ramping, while with other types of disturbances (such as self heating in a degraded section of conductor), slow current ramping leads to higher critical currents.

An observation of the effect of integral scale on drag reduction

Abstract: Drag reduction pipe flow experiments using random coiling polymers have been dominated by the small scales of turbulence. An experiment is reported using polyelectrolytes DNA and collagen, which have extended conformations in solution that shows a relationship between the large scales and drag reduction. Turbulent or molecular interactions can explain the observed increase in drag reduction with an increase in pipe diameter.

Modal content of noise generated by a coaxial jet in a pipe

Abstract: Noise generated by air flow through a coaxial obstruction in a long, straight pipe was investigated with concentration on the modal characteristics of the noise field inside the pipe and downstream of the restriction. Two measurement techniques were developed for separation of the noise into the acoustic duct modes. The instantaneous mode separation technique uses four microphones, equally spaced in the circumferential direction, at the same axial location. The time-averaged mode separation technique uses three microphones mounted at the same axial location. A matrix operation on time-averaged data produces the modal pressure levels. This technique requires the restrictive assumption that the acoustic modes are uncorrelated with each other. The measured modal pressure spectra were converted to modal power spectra and integrated over the frequency range 200-6000 Hz. The acoustic efficiency levels (acoustic power normalized by jet kinetic energy flow), when plotted vs. jet Mach number, showed a strong dependence on the ratio of restriction diameter to pipe diameter. The acoustic energy flow analyses based on the thermodynamic energy equation and on the results of Mohring both resulted in orthogonality properties for the eigenfunctions of the radial mode shape equation. These orthogonality relationships involve the eigenvalues and derivatives of the radial mode shape functions.

In-line flow control valve

Abstract: In-line flow regulator for use in hydraulic flow systems is presented using a fixed size orifice which may be manually adjustable by blocking off a part of the orifice to provide an exact rate of flow in the regulated flow direction and which otherwise provides a free flow in the reverse direction.

Flow Development of a Train of Particles in Capillaries

Abstract: The fluid flow and particle motion in a tube are solved numerically by coupling the Navier-Stokes equations with the dynamic equation of a particle. The particulate flow is simulated from rest under a prescribed pressure drop. The symptotic steady state solution is in good agreement with the analytical solution of creeping flow and with the experimental data reported in the literature. The present computational analysis explores the Reynolds numbers effects on the flow processes and gives some insight into qualitative similarities of the kinematics and dynamics of particulate flows. The resistant coefficient, the apparent viscosity, the tube hemotocrit, and the distribution of viscous stresses and pressure on the particle and on the capillary wall are considered along with the curvilinear flow patterns.