Showing papers on "Pipe flow published in 1970"

Heat Transfer and Friction in Turbulent Pipe Flow with Variable Physical Properties

Abstract: Publisher Summary This chapter discusses heat transfer and skin friction in turbulent pipe flow with variable physical properties. The constant properties solution has been considered only so far as is necessary for the flow and heat transfer analysis with variable physical properties. The chapter highlights analytical methods to describe heat transfer mechanisms for constant liquid properties quite satisfactorily and to take into account the influence of the variation of physical properties with temperature versus heat transfer and skin friction in a number of important cases. Disagreement between theoretical and experimental results observed in other cases, in particular, with a considerable change in physical properties over the flow cross section, may be attributed to imperfect methods of estimating the effect of the variation of physical properties on turbulent diffusivity. Important experimental material has been accumulated on heat transfer and skin friction for variable physical properties. However, certain portions of this material possess relatively low accuracy that prevents its successful use. For a number of important cases, there has been no systematic data collection or that which is available is scanty and contradictory. Therefore, the need for further experimental investigations, with a high degree of accuracy, into the fluid mechanics and heat transfer for variable physical properties is quite urgent.

Dynamics of Dusty Gases

Abstract: This review deals with a certain restricted portion of the mechanics of heterogeneous media. The volume fraction of the solid-particle or droplet cloud is considered to be so small that the interaction between individual particles may be neglected or highly simplified. This limitation applies to the individual flow fields about the particles as well as to collisions, and to heat and mass transfer as well as to momentum exchange between phases. Under this circumstance, the problem of detailed transport processes between particles and gas may be treated independently of the complete dynamical problem, and this aspect, being a study of its own, will be suppressed to a considerable extent here. There are problems, such as the impact of particles on walls, the concentration separation in boundary layers or pipe flow, in which the distortion of the particle flow field due to a solid wall or another particle is the central physical issue. These problems therefore lie outside the scope of the review. On the other hand, the structure of shock waves, sound attenuation, and many flow-field problems can be treated within our present restrictions. The basic equations and exchange processes will be introduced first, together with the physical parameters that indicate the relative importance of the particle cloud and the limitations of the dusty-gas concept. Then several different problems will be discussed that lead to some of the significant results in the field and illustrate analytical techniques that have proven useful.

An eddy cell model of mass transfer into the surface of a turbulent liquid

Abstract: Experimental gas absorption studies for bubbles transported in turbulent pipe flow of water strongly indicate that liquid phase controlled mass transfer is due to surface renewal by turbulent eddies. Predictions of transport behavior from the conditions of turbulent flow cannot be made in support of this mechanism because no satisfactory theory of turbulent transport near a gas-liquid interface is available. This work considers a model of the hydrodynamic behavior near the surface which provides a link between the observed mass transfer behavior and the state of the turbulent field. In this model, the very small scales of turbulent motion are considered to be controlling. These motions are idealized, and their flow and mass transfer behavior are solved analytically. The overall result for eddies of various sizes is related to the turbulent energy spectrum by using only the easily accessible parameter ϵ, the energy dissipation rate. This model gives quantitative agreement to within a factor of 2 for three widely different experimental situations including gas-liquid and liquid-solid interfaces. However, the predicted Reynolds number dependence is somewhat higher than the experimental result. The model attempts to clearly define the basic physical process at the interface. Therefore, it indicates the direction for further experimentation needed to clarify the basic relationship between the mass transfer rates in the liquid phase and the hydrodynamic behavior of the turbulent liquid.

Deposition of Particles in Turbulent Flow on Channel or Pipe Walls

Abstract: This paper describes a method for predicting the deposition of particles entrained in turbulent flow. The method predicts the deposition of particles ranging from molecular size to ∼100µ in diamete...

Phonoangiography: A New Noninvasive Diagnostic Method for Studying Arterial Disease

Abstract: Phonoangiography, the quantitative analysis of sounds produced by blood flow, has been used to investigate local fluid motion in arteries narrowed by atherosclerosis. The sound spectra measured in vivo were found to be identical to those obtained in laboratory investigations of turbulent pipe flow. A theoretical model is proposed which: (a) quantitatively relates the in vivo and in vitro data, and (b) allows estimation of the clinically important parameters of arterial diameter, flow velocity, local turbulence intensity, and wall pressure fluctuations. The results of calculations using data from human subjects agree with known arterial diameters and blood flow velocities.

Bounds for turbulent shear flow

Abstract: Bounds on the transport of momentum in turbulent shear flow are derived by variational methods. In particular, variational problems for the turbulent regimes of plane Couette flow, channel flow, and pipe flow are considered. The Euler equations resemble the basic Navier–Stokes equations of motion in many respects and may serve as model equations for turbulence. Moreover, the comparison of the upper bound with the experimental values of turbulent momentum transport shows a rather close similarity. The same fact holds with respect to other properties when the observed turbulent flow is compared with the structure of the extremalizing solution of the variational problem. It is suggested that the instability of the sublayer adjacent to the walls is responsible for the tendency of the physically realized turbulent flow to approach the properties of the extremalizing vector field.

Turbulent flow drag reduction and degradation with dilute polymer solutions

Abstract: Experimental studies of drag reduction and polymer degradation in turbulent pipe flow with dilute water solutions of unfractionated polyethylene oxide are described. Drag reduction results indicate that the magnitude of the reduction cannot be correlated on the basis of weight average molecular weight, rather the phenomenon depends strongly on the concentration of the highest molecular weight species present in the molecular weight distribution. Polymer degradation in turbulent flow is found to be severe for high molecular weight polymers causing appreciable changes in drag reduction and molecular weight with the duration of flow. Data indicates that drag reduction exists in the limit of infinite dilution suggesting that the phenomenon is due to the interaction of individual polymer molecules with the surrounding solvent and that the extent of reduction is relatively independent of pipe diameter when a comparison is carried out at equal solvent wall shear stresses. Consideration of the high viscosity obtained with solutions in an irrotational laminar flow field suggests this is due to polymer molecule deformation and that this phenomenon is central to the mechanism of turbulent flow drag reduction.

Drop‐size distributions produced by turbulen pipe flow of immiscible liquids

Abstract: Drop-size distributions in turbulently flowing dispersion of immiscible liquids were investigated. The observed drop-size distributions were actually a composite of two superimposed distributions. One is the distribution produced by the injection nozzle and the other is that produced by breakup in the turbulent flow field. A mathematical model was developed which predicted both the shape of the observed distributions and kinetics of the droplet breakup process for the distribution produced by the turbulent flow field. The flowing dispersion composed of water and insoluble organic phase was photographed at 27, 209, 421, and 576 pipe diameters below the mixing jet and at distances of 0.05, 0.1, and 0.4 diam. from the wall. Average flow rates varied from 14 to 20 ft./sec. in the 0.750-in. I.D. tube. Three organic phases were studied at concentrations ranging from 0.6 to 10% by volume. Dispersed phase viscosity and interfacial tension varied from 1 to 18 cp. and 13 to 40 dynes/cm. No distribution law with any theoretical basis could be found which correlated experimental distributions. The stochastic model describing the breakup process postulates that each breakup event leads to two daughter drops with uniformly distributed volume ratios and a very small satellite droplet. An empirical correlation exists to predict only one of the three parameters of the model.

The flow created by a sphere moving along the axis of a rotating, slightly-viscous fluid

Abstract: The title flow has been studied by measuring the drag force on, and by observing the flow field around, a sphere rising through a large, rotating tank of water. Long, almost stagnant, regions are formed up- and downstream within the shadow of the sphere and are surrounded by a thin annular region within which the velocity is larger than the mean velocity of the approach flow. Several regions are found within which vortex-jump phenomena occur and it is concluded that such features exert a controlling influence over the dynamics of the observed flow field.

A hydrodynamic curiosity: The salt oscillator

Abstract: If a vertically oriented hypodermic syringe with the plunger removed is filled with salt water and partially submerged in a beaker of fresh water, then under the proper conditions, the system develops finite amplitude oscillations. These oscillations appear as a downward jet of salt water, followed by an upward jet of fresh water, and so on for many cycles. The geometry of the syringe determines the period of the oscillations: a long, small diameter needle yields a slow, viscous flow; a short, large diameter needle yields fast inviscid pumping. Theoretically, a time‐dependent Hagen‐Poiseuille pipe flow model describes the oscillations; furthermore, the oscillations can be divided into two modes, depending on whether viscous or non‐linear damping predominates. When viscous damping predominates, the geometry of the syringe determines the period of the oscillations, which are independent of the density difference ?ρ except as the viscosity varies with density. When non‐linear damping predominates, t...

Sound Radiation from Rigid Flow Spoilers Correlated with Fluctuating Forces

Abstract: This paper presents the results of a theoretical and experimental study of the correlation of fluctuating forces on rigid flow spoilers with the resulting sound radiation. A system of force transducers was developed to measure simultaneously, yet independently, the drag and lift components of the fluctuating forces on flow spoilers confined within a jet‐pipe system. A direct correlation of fluctuating forces with the radiated sound was found. A theory that considered the effect of the enclosure upon the sources and the effect of pipe‐end reflection was developed to predict the sound power radiated to the free field from pipe‐immersed flow spoilers. Both monopole and dipole sources were treated. An increase of the dipole sound‐power output by a factor of 3 for frequencies below the pipe cutoff frequency was predicted and experimentally confirmed.

Free Surface, Velocity Gradient Flow Past Hemisphere

Abstract: The drag on a hemisphere in a finite-flow field with free surface effects is evaluated by successively studying six flow fields, which allows the study of one new variable at a time. These flow fields are: the semi-infinite uniform and nonuniform flow fields, the finite uniform and nonuniform flow fields without free surface effects, and the finite uniform and nonuniform flow fields with free surface effects. Three regimes of flow are defined for the hemisphere which are: (1) A regime of pronounced free surface effects, (2) a regime of moderate free surface effects, and (3) a regime of negligible free surface effects. The effect of these variables and range of conditions under which they are effective is considered.

Pattern of Potential Flow in a Free Overfall

Abstract: A theory is presented to describe the two-dimensional flow of liquid in an open channel which terminates abruptly at a sharp drop A dimensionless diagram expressing constancy of total head on the upper free surface and similar to the conventional specific-head versus depth and discharge versus depth diagrams is used to trace the course of the flow in the overfall Together with the fact that the ratio of free-surface-velocity magnitude to average horizontal component of velocity in the cross-section is a decreasing function of distance in the direction of flow, an observation drawn from a subsequent, detailed examination of the flow, the diagram is used to show that the limiting case of the free overfall is at a Froude number of approach of unity A detailed description of the flow is given by an integral equation derived from conformal mapping and singularity distributions Comparisons are made between the computed profiles and theoretical and experimental results of other investigators

Turbulence parameters in a stirred tank

Abstract: tirred tanks are widely used in the chemical indusS try for effecting mixing, but their design has so far been empirical. A theoretical treatment of the flow within a stirred tank is rendered intractable by the inherent randomness and three-dimensionality of the flow and non-linearity of the governing equations of motion. Experimental studies of the large- and small-scale turbulence characteristics in stirred vessels may be expected to lead to formulation of realistic models of the flow. These models can then be used to predict such quantities of engineering interest as the mixing efficiency, pumping capacity, power requirements, etc. It was the objective of this work to measure the turbulence characteristics of the high speed stream issuing from a turbine type impeller in a fully baffled tank. Turbulence parameters were measured using a constant-temperature hot-wire anemometer with air as the fluid within the tank. The hot-wire technique was chosen because of the ease of operation and extremely good frequency response. Use of mr as working fluid Cooper‘” recently showed that the temporal mean velocity distribution in the impeller stream is the same with air and water as the fluid in the tank. We have assumed that the small-scale turbulence characteristics would also be similar at equal Reynolds numbers irrespective of the fluid in the tank. There exists sufficient confirmation in the literature for air and water flows in circular pipes and circular jets, and also grid-generated turbulent flows in wind and water tunnels. Chuang and Cermak“’ have compared their measurements of turbulent intensities, shear stress and energy spectra in the pipe flow of distilled water for a Reynolds number of 5 x lo4 with those of Sandborn‘J) and Laufer“) who studied the flow of air in a pipe at the same Reynolds number. The agreement between the air and water data is remarkable

Incompressible Laminar Flow in the Entrance Region of a Rectangular Duct

Abstract: Incompressible laminar flow in entrance region of rectangular duct allowing direct computation of eigenvalues

Oscillatory Flow Measurements with a Directionally Sensitive Laser Velocimeter

Abstract: The concept, design, and construction of a directionally sensitive laser velocimeter for unsteady flow measurements are presented. Oscillatory flow measurements are compared with theoretical predictions.

Slip Point of Beds in Solid-Liquid Pipeline Flow

Abstract: In view of the relatively low mean velocities which give optimum efficiency for pipelines transporting granular solids, it is important to study the conditions for which stationary deposits occur in pipes. The limit of deposition is the slip point, at which the force driving the bed exceeds the coefficient of friction times the total normal force exerted by the bed grains against the pipe wall. Although the state of intergranular stress in the deposit is generally indeterminate, it is shown that near the slip point it is a reasonable assumption that the granular pressure at the periphery of the bed follows a hydrostatic distribution. Experimental verification of this assumption was obtained from two types of tests, one involving flow conditions in a recirculating system and the other the slipping of deposits in a tilting pipe. The relationship derived for the hydrostatic distribution of granular pressure shows that the pressure gradient at the slip point is directly proportional to the underwater weight per unit volume of bed, and increases with the angle subtended by the deposit.

Controlling pressure in fluid transfer conduits

Abstract: The pressure at a downstream point in a conduit through which a fluid is flowing is controlled so as to maintain the pressure at an upstream point in the conduit substantially constant. Said control is effected by measuring the pressure and flow rate at said downstream point, and adjusting said pressure in accordance with the measured pressure and measured flow rate.

Determination of the Pressure Drop Optimum Pipe Size for a Two-Phase Slug Flow in an Inclined Pipe

Abstract: H. D. Beggs. This paper is a welcome addition to the limited work in the area of two phase flow in inclined pipes. Some question arises, however, as to the adquaey of the experimental apparatus used in the study. Griffith and Wallis [1] have shown that entrance effects can persist for lengths as much as 300 pipe diameters in two phase flow. Since the pipe length used by Singh and Griffith was only 20 ft, most of their data were taken in a region where the flow could still be developing. McDonald and Baker [2] indicate that the developing region may be as much as 500 pipe diameters in inclined pipes. The void fractions were determined using two quick closing valves to trap a portion of the flow stream. A description of the method used to measure the trapped liquid would be of interest. Assumptions 3 and 4 imply that there is no pressure drop in the gas filled portion of the pipe. These assumptions are valid if the bubble length is small, but for long bubbles they oversimplify the problem. If the flow pattern developed into the annular region, there would be no pressure drop at all under these assumptions. I t is also assumed that the acceleration pressure drop is negligible. This is a reasonable assumption for low velocities, but Hoogendorn [3] showed that the acceleration pressure drop could be as much as 15 percent of the total pressure drop under certain conditions. Street [4], in a study of vertical slug flow, concluded that the effects of liquid acceleration around the gas bubble cannot be ignored. The authors state that in some cases negative friction pressure drops were obtained. Was this concluded in cases where the calculated gravity pressure drop exceeded the observed total pressure drop? Hagedorn [5] also observed this for the vertical case, but after correcting his values for void fraction and consequently calculated gravity pressure drop, the negative friction condition was eliminated. In equation (4) for bubble velocity, the second term

Hot-Film Turbulence Measurements in Water Flow

Abstract: Turbulence measurements in water have been carried out using hot-film anemometers in a circular conduit. A circulating water loop was specially designed for such measurements. The calibration of the anemometers and measurements of turbulence intensities and energy spectra were made in this water-loop. Two special types of hot-film probes were tried: (1) wedge-shaped probes must take into account a drift of the characteristics which can be corrected experimentally; and (2) conically shaped probes which do not present the disadvantage of drift seem to be of great use for measuring longitudinal velocity components. A study of the heat transfer between such a probe and the water led to the establishment of a non-dimensional relationship. Measurements of relative intensities and energy spectra were carried out and compared with those of previous authors in air and for dynamically similar flows. This comparison proves that hot-film anemometry methods can be used, under controlled conditions, for turbulence measurements in water with the same degree of accuracy as that found for measurements in air.

Inception and Entrainment in Self-Aerated Flows

Abstract: Inception and entrainment of air in self-aerated open channel flows are studied. For inception to occur surface eddies should leave the free surface and the whole fluid should be turbulent. A criterion for the surface eddy to leave the free surface is formulated using the energy concept. A method to locate the zone of boundary layer emergence to the free surface which causes the whole fluid to be turbulent in the case of flow over free overfall spillways is developed. Using the concept of entrainment, the basic equations for aerated flow down prismatic channels are formulated. Using these equations, several flow characteristics of the uniform aerated flow are studied. The investigations help in computing uniform aerated flow characteristics knowing the non-aerated flow data.