Showing papers on "Open-channel flow published in 1972"

The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments

Abstract: The dynamical equations governing small amplitude wave disturbances in turbulent shear flows are derived. These equations require additional equations or assumptions about the wave-induced fluctuations in the turbulence Reynolds stresses before a closed system can be obtained. Some simple closure models are proposed, and the results of calculations using these models are presented. When the predictions are compared with our data for channel flow, we find it essential that these oscillations in the Reynolds stresses be included in the model. A simple eddy-viscosity representation serves surprisingly well in this respect.

The wall region in turbulent shear flow

Abstract: Hot-film measurements in a fully developed channel flow have been made in an attempt to gain more insight into the process of Reynolds stress production. The background for this effort is the observation of a certain sequence of events (deceleration, ejection and sweep) in the wall region of turbulent flows by Corino (1965) and Corino & Brodkey (1969). The instantaneous product signal uv was classified according to the sign of its components u and v, and these classified portions were then averaged to obtain their contributions to the Reynolds stress . The signal was classified into four categories; the two main ones were that with u negative and v positive, which can be associated with the ejection-type motion of Corino & Brodkey (1969), and that with u positive and v negative, associated with the sweep-type motion. It was found that over the wall region investigated, 3·5 [les ] y [les ] 100, these two types of motion give rise to a stress considerably greater than the total Reynolds stress. Two other types of motion, (i) u negative, v negative, corresponding to low-speed fluid deflected towards the wall, and (ii) u positive, v positive, corresponding to high-speed fluid reflected outwards from the wall, were found to account for the ‘excess’ stress produced by the first two categories, which give contributions of opposite sign.The autocorrelations of the classified portions of uv were obtained to determine the relative time scales of these four types of motion. The positive stress producing motions (u 0 and u > 0, v 0, v > 0). It was further surmised that turbulent energy dissipation is associated with the Reynolds stress producing motions, since these result in localized shear regions in which the dissipation is several orders of magnitude greater than the average dissipation at the wall.

Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow.

Abstract: Experiments on fully developed turbulent flow in a channel which is rotating at a steady rate about a spanwise axis are described. The Coriolis force components in the region of two-dimensional mean flow affect both local and global stability. Three stability-related phenomena were observed or inferred: (1) the reduction (increase) of the rate of wall-layer streak bursting in locally stabilized (destabilized) wall layers; (2) the total suppression of transition to turbulence in a stabilized layer; (3) the development of large-scale roll cells on the destabilized side of the channel by growth of a Taylor-Gortler vortex instability. Local effects of rotational stabilization, such as reduction of the turbulent stress in wall layers, can be related to the local Richardson number in a simple way. This paper not only investigates this effect, but also, by methods of flow visualization, exposes some of the underlying structure changes caused by rotation.-

Role of subsurface flow in generating surface runoff: 2. Upstream source areas

Abstract: Runoff simulation for rainfall events on hypothetical upstream source areas, carried out with a deterministic mathematical model that couples channel flow and saturated-unsaturated subsurface flow, provides theoretical support for the runoff-generating mechanisms observed in the field by Ragan and Dunne. The simulations show that there are stringent limitations on the occurrence of subsurface storm flow as a quantitatively significant runoff component. Only on convex hillslopes that feed deeply incised channels, and then only when saturated soil conductivities are very large, is subsurface storm flow a feasible mechanism. On concave slopes with lower permeabilities, and on all convex slopes, hydrographs are dominated by direct runoff through very short overland flow paths from precipitation on transient near-channel wetlands. On these wetlands surface saturation occurs from below because of rising water tables that are fed by vertical infiltration rather than by lateral subsurface flow. These conclusions, when coupled with field observations that show classic Hortonian overland flow to be a rare occurrence in vegetated humid environments, have implications in the planning of field instrumentation networks, and in the designing of hydrologic response models.

Role of subsurface flow in generating surface runoff: 1. Base flow contributions to channel flow

Abstract: The importance of the subsurface response of watersheds has been vastly underrated in most studies of watershed behavior, both in a quantitative sense and in a generic sense. The mechanism of base flow generation and the nature of watershed response in base flow dominant streams are examined with a deterministic mathematical model that couples three-dimensional, transient, saturated-unsaturated subsurface flow and one-dimensional, gradually varied, unsteady channel flow. The channel flow model uses the single step Lax-Wendroff explicit technique to solve numerically the full shallow water equations. The subsurface flow model uses the line successive overrelaxation technique to solve numerically the Jacob-Richards diffusion equation. The results of the simulations on a hypothetical basin suggest a wide variability in watershed response under the influence of variations in rainfall properties, antecedent moisture conditions, and saturated and unsaturated subsurface hydrogeologic properties. This evidence for a wide range of watershed response functions leads to the development of a healthy skepticism toward black box rainfall-runoff correlations, the concept of basin linearity, and the rationality of hydrograph separation.

Spatially Varied Flow over Side-Weirs

Abstract: An experimental investigation of the flow over sharp edged side-weirs in rectangular channels is reported. The experiments cover subcritical and supercritical flow regimes with weirs of zero as well as finite height. The subcritical flow experimental data agree well with the derived analytical expression for the variation of the De Marchi coefficient with the Froude number of the main channel flow. The De Marchi coefficient for the side weirs of finite height has been found to be essentially the same as for the corresponding side-weir of zero height.

Flow patterns in breaking bubbles

Abstract: Fluid flow during bubble collapse is driven by high pressure gradients associated with high surface curvature. Experiments suggest that the driving force is at a maximum at the surface and preferentially accelerates the surface in boundary-layer shear flow down the cavity wall. An irrotational solitary capillary ripple precedes the main toroidal rim, transporting mass along the surface at about 90% of its phase velocity. The convergence of this flow creates opposed axial jets. About 20% of the boundary-layer thickness flows into the upward jet. The material in the top jet drop was originally spread over the interior bubble surface at an average thickness of some 0.05% of the bubble diameter.

Reaeration in open-channel flow

Abstract: ................................................................................

Applied Fluid Mechanics

Abstract: (NOTE: Most chapters begins with The Big Picture and Objectives and concludes with References, Internet Sites, Practice Problems, and Computer Programming Assignments sections) 1 The Nature of Fluids and the Study of Fluid Mechanics Basic Introductory Concepts The International System of Units (SI) The US Customary System Weight and Mass Temperature Consistent Units in an Equation The Definition of Pressure Compressibility Density, Specific Weight, and Specific Gravity Surface Tension 2 Viscosity of Fluids Dynamic Viscosity Kinematic Viscosity Newtonian Fluids and Nonnewtonian Fluids Variation of Viscosity with Temperature Viscosity Measurement SAE Viscosity Grades ISO Viscosity Grades Hydraulic Fluids for Fluid Power Systems 3 Pressure Measurement Absolute and Gage Pressure Relationship Between Pressure and Elevation Development of the Pressure-Elevation Relation Pascal's Paradox Manometers Barometers Pressure Expressed as the Height of a Column of Liquid Pressure Gages and Transducers 4 Forces Due to Static Fluids Gases Under Pressure Horizontal Flat Surfaces Under Liquids Rectangular Walls Submerged Plane Areas-General Development of the General Procedure for Forces on Submerged Plane Areas Piezometric Head Distribution of Force on a Submerged Curved Surface Effect of a Pressure Above the Fluid Surface Forces on a Curved Surface with Fluid Below It Forces on Curved Surfaces with Fluid Above and Below 5 Buoyancy and Stability Buoyancy Buoyancy Materials Stability of Completely Submerged Bodies Stability of Floating Bodies Degree of Stability 6 Flow of Fluids and Bernoulli's Equation Fluid Flow Rate and the Continuity Equation Commercially Available Pipe and Tubing Recommended Velocity of Flow in Pipe and Tubing Conservation of Energy-Bernoulli's Equation Interpretation of Bernoulli's Equation Restrictions on Bernoulli's Equation Applications of Bernoulli's Equation Torricelli's Theorem Flow Due to a Falling Head 7 General Energy Equation Energy Losses and Additions Nomenclature of Energy Losses sand Additions General Energy Equation Power Required by Pumps Power Delivered to Fluid Motors 8 Reynolds Number, Laminar Flow, Turbulent Flow, and Energy Losses Due to Friction Reynolds Number Critical Reynolds Numbers Darcy's Equation Friction Lass in Laminar Flow Friction Loss in Turbulent Flow Equations for Friction Factor Hazen-Williams Formula for Water Flow Other Forms of the Hazen-Williams Formula Nomograph for Solving Hazen-Williams Formula 9 Velocity Profiles for Circular Sections and Flow in Noncircular Sections Velocity Profiles Velocity Profile for Laminar Flow Velocity Profile for Turbulent Flow Flow in Noncircular Sections 10 Minor Losses Resistance Coefficient Sudden Enlargement Exit Loss Gradual Enlargement Sudden Contraction Gradual Contraction Entrance Loss Resistance Coefficients for Valves and Fittings Application of Standard Valves Pipe Bends Pressure Drop in Fluid Power Valves Flow Coefficients for Valves Using Cv Plastic Valves 11 Series Pipe Line Systems Class I Systems Spreadsheet Aid for Class I Problems Class II Systems Class III Systems Pipeline Design for Structural Integrity 12 Parallel Pipe Line Systems Systems with Two Branches Systems with Three or More Branches-Networks 13 Pump Selection and Application Parameters Involved in Pump Selection Types of Pumps Positive Displacement Pumps Kinetic Pumps Performance Data for Centrifugal Pumps Affinity Laws for Centrifugal Pumps Manufacturer's Data for Centrifugal Pumps The Operating Point of a Pump and Pump Selection Net Positive Suction Head Suction Line Details Discharge Line Details Piping System Design and Pump Selection Procedure Alternate System Operating Modes Pump Selection and Specific Speed Life Cycle Costs for Pumped Fluid System Software for Piping System Design and Pump Selection 14 Open Channel Flow Classification of Open Channel Flow Hydraulic Radius and Reynolds Number in Open Channel Flow Kinds of Open Channel Flow Uniform Steady Flow in Open Channels The Geometry of Typical Open Channels The Most Efficient Shapes for Open Channels Critical Flow and Specific Energy Hydraulic Jump Open Channel Flow Measurement 15 Flow Measurement Flowmeter Selection Factors Variable Head Meters Variable Area Meters Turbine Flowmeter Vortex Flowmeter Magnetic Flowmeter Ultrasonic Flowmeters Positive Displacement Meters Mass Flow Measurement Velocity Probes Level Measurement Computer-Based Data Acquisition and Processing 16 Forces Due to Fluids in Motion Force Equation Impulse-Momentum Equation Problem-Solving Method Using the Force Equations Forces on Stationary Objects Forces on Bends in Pipe Lines Forces on Moving Objects 17 Drag and Lift Drag Force Equation Pressure Drag Drag Coefficient Friction Drag on Spheres in Laminar Flow Vehicle Drag Compressibility Effects and Cavitation Lift and Drag on Airfoils 18 Fans, Blowers, Compressors, And The Flow Of Gases Gas Flow Rates and Pressures Classification of Fans, Blowers, and Compressors Flow of Compressed Air and Other Gases in Pipes Flow of Air and Other Gases through Nozzles 19 Flow Of Air In Ducts Energy Losses in Ducts Duct Design Energy Efficiency and Practical Consideration in Duct Design Appendixes Properties of Water Properties of Common Liquids Typical Properties of Petroleum Lubricating Oils Variation of Viscosity with Temperature Properties of Air Dimensions of Steel Pipe Dimensions of Steel Tubing Dimensions of Type K Copper Tubing Dimensions of Ductile Iron Pipe Areas of Circles Conversion Factors Properties of Areas Properties of Solids Gas Constant, Adiabatic Exponent, and Critical Pressure Ratio for Selected Gases Answers to Selected Problems Index

Shallow Water Waves on a Viscous Fluid—The Undular Bore

Abstract: A theory is presented for the surface profile above a fully developed Poiseuille channel flow. Small disturbances to this flow are examined, and it is shown that if the (channel depth)/(wavelength) ratio is small (shallow waves), and the Reynolds number large enough, these disturbances initially travel at the classical dynamic (Burns) wave speeds. However, by introducing appropriate far‐field coordinates it follows that the disturbance eventually travels at a different wave speed—the kinematic wave speed. To confirm this, the dynamic waves are shown to decay by using standard boundary layer techniques. This general result (of decay) agrees with previous one‐dimensional theories. The profile close to the kinematic wave front is examined and shown to satisfy an equation of the form ηT + ηηX + ηXXX = ΔηXX, where η(X, T) is the surface profile. This equation is called the Korteweg‐de Vries‐Burgers equation. The form of the steady solution of this equation exhibits all the characteristics of the undular bore. A bound on Δ agrees with stability requirements found by other authors using different methods.

Identification of parameters in unsteady open channel flows

Abstract: This paper introduces the influence coefficient algorithm, a simple, easily implemented, and rapidly convergent computational procedure for the solution of the parameter identification problem in unsteady open channel flow from field observations on stage hydrograph and velocity distribution at one or more points along the channel. (Identification is a mathematical process whereby the parameters embedded in a differential equation defining a system are determined from observations of system input and output.) The parameters specifically chosen for identification are the two ‘friction slope’ characteristics: the channel roughness coefficient and the exponent of the hydraulic radius in the empirical friction slope relation, a number usually assumed to be 4/3. These parameters are not physically measurable and have to be determined from the solutions of the mathematical model using concurrent input and output measurements. This new procedure is related to both quasilinearization and gradient methods. Additionally, an effective formulation of the algorithm is shown to depend on certain stability and convergence features related to the finite difference solutions of the governing flow equations but often ignored or glossed over.

Flow visualization of the near-wall region in a drag-reducing channel flow

Abstract: Study to determine whether the addition of drag-reducing macromolecules alters the structure of the viscous sublayer and thereby modifies the production of kinetic energy in turbulent wall flows. This was accomplished by visualizing the near-wall region of a fully developed two-dimensional channel flow. Motion pictures were taken of dye injected into the near-wall region. Both water and a dilute drag-reducing polyethylene oxide--FRA solution were used as working fluids. The data show that the time between bursts for an individual streak in a drag-reducing flow has the value for a water flow at the reduced wall shear. Evidence strongly suggests that the dilute polymer solution decreases the production of turbulent kinetic energy by inhibiting the formation of low-speed streaks.

Laminar Flow in Tubes with Constriction

Abstract: To understand the abnormal flow conditions caused by the presence of stenoses in arteries, an analytical solution is obtained for the steady laminar flow of an incompressible Newtonian fluid in an axisymmetric conduit with irregular surface where the spread of the surface roughness is large compared with the mean radius of the conduit. Numerical results are presented for the streamlines, the distributions of velocity, vorticity, and pressure, the energy dissipation, and the separation and reattachment points for conduits with sinusoidal wall variations. The analysis is also applicable to a locally constricted conduit, provided the separation zone does not extend into the straight wall portion of the conduit.

Transient Flow in Free-Surface, Pressurized Systems

Abstract: Transients may arise in a hydraulic system such that flow conditions may alternate between free surface and submerged or pressurized behavior. Analytical considerations begin with the open-channel surge equations, and the resulting method-of-characteristics solution. The surge wave in the tunnel is described after Meyer-Peter and Favre. At the free-surface, pressurized interface, a method of solution similar to the movement of a hydraulic bore is arrived at. An experimental study is presented which describes the phenomena and gives verification to the numerical mode. As an application the Wettingen system is analyzed and shown to agree favorably with earlier results.

Velocity measurements made with a laser dopplermeter on the turbulent pipe flow of a dilute polymer solution

Abstract: This paper presents some new measurements which have been made on a drag-reducing polymer solution in pipe flow. A novel type of laser dopplermeter, which has been developed by the author, is briefly described and the measurements which have been obtained are given. These results and their implications are then discussed in terms of conventional models for turbulent flow in a pipe. These suggest that the polymer has very little effect upon the turbulent core of the flow, but thickens and stabilizes the viscous sublayer. The turbulent intensity inside the sublayer is unchanged but, owing to its thickening, the velocity fluctuations just outside are greater. There is not a general suppression of turbulence within the sublayer although well inside the sublayer the spanwise velocity component is found to be reduced.

Asymptotic analysis of turbulent channel and boundary-layer flow

Abstract: : Asymptotic expansion techniques are used in the limit of large Reynolds number, to study the structure of fully turbulent shear layers. Two cases examined are channel (or pipe) flow and two-dimensional boundary layer flow with an applied pressure gradient, upstream of any separation. Attention, for these two cases, is confined to the flow of incompressible constant-property fluids. Closure is effected through the introduction of an eddy viscosity model formulated with sufficient generality so that most existing models are special cases.

Laminar Flow Past a Circle in a Shear Flow

Abstract: A numerical solution of the equations governing time‐dependent, viscous, incompressible fluid flow past a circle is presented for Reynolds number 400. The free‐stream velocity profile corresponds to the time‐averaged flow of a turbulent jet. The location and strength of the jet are adjusted so that the free stream approximates a linear shear flow in the vicinity of the circle. The asymmetry of the free stream causes a shift of the upstream stagnation streamline (the Pitot‐tube displacement effect) and small biases in the lift and torque exerted upon the circle. This lift bias is suggested as a contributing factor in the observed stability of raindrops in vertical wind tunnels. Contour plots of the vorticity and stream function are compared with histories of the pressure distribution, drag, lift, torque, and separation angles. These comparisons show how the asymmetry of the free stream manifests itself in terms of fine details within the flow pattern around the circle.

Closed Streamlines Associated with Channel Flow over a Cavity

Abstract: The viscous Stokes flow induced in a rectangular cavity by a parallel shear flow is calculated by a direct finite difference method. The separating streamline and the intensity of the circulation of the closed streamline flow within the cavity are shown as a function of cavity shape, relative channel size to cavity size, and the parallel velocity profile within the channel. Application of the results to viscous flow observations are indicated.

Air–water annular flow in a horizontal tube

Abstract: From international symposium on two-phase systems; Haifa, Israel (29 Aug 1971). See CONF-710836-. Experiments were conducted on low-pressure, air- water, annular flow in a 31.8-mm II) horizontal tube. For two flow conditions and for two distances downstream of liquid injection, the film characteristics were measured as a function of circumferential position, and liquid entrainment measurements were made in the gas core. Large variations in these measurements with circumferential position were found but the variation with length was small. The total entrainmnent flow rates were estimated from the sampling studies and the film flow rates estimated from the film thickness measurements by using the Hewitt model. In evaluating the Hewitt model, it was assumed that the wall shear was constant around the perimeter of the tube. The sum of the calculated film flow rate and entrainment flow rates was found to be in good agreement with the input liquid flow despite the fuct that the assumption of constant shear was of doubtful validity. The measurements were examined for compatibility with the various mechanisms which have been proposed for maintaining the film at the top of the tube. It was found that the results were compatible with the secondary- flow'' and wave-spreading''more » mechanisms, but were incompatible with the entrainment-deposition'' mechanism. It was shown that surface tension can never be an important force (on its own) for maintaining annular flow, except perhaps in extremely small tubes. (auth)« less

Stability of Plane Poiseuille Flow with Heat Transfer

Abstract: The influence of heat transfer on the stability of a plane Poiseuille flow in a channel is under investigation. The liquid flow is affected by the heat transfer through the variation in viscosity with temperature. Additional viscosity gradient terms are included in a modified Orr‐Sommerfeld equation, and it is the presence of these terms which leads to a prediction of more unstable flows, for without the inclusion of these extra terms, the flow is stabilized. The results show that a temperature difference between the walls is always destabilizing and, in particular, a temperature difference between the walls of 100°F leads to a reduction in the critical Reynolds number from 7800 to 4600.

Free-Vortex Theory Applied to Free Overfalls

Abstract: When the flow from an open channel is discharged freely into the air, the depth at the brink can be often closely correlated with the flow rate. Free-vortex velocity distribution and curvature are used to simulate the flow at the brink of smooth horizontal channels of various cross sections. A summary of the analysis is given herein for exponential channels of rectangular, triangular, and parabolic cross sections. The final theoretical values are also given for trapezoidal and circular cross sections. The final relationships for the case of jetted shooting flow just upstream of the end section of a rectangular channel are also given.