Showing papers on "Open-channel flow published in 1976"

The mixing layer at high Reynolds number - Large-structure dynamics and entrainment

Abstract: A turbulent mixing layer in a water channel was observed at Reynolds numbers up to 3 × 10^6. Flow visualization with dyes revealed (once more) large coherent structures and showed their role in the entrainment process; observation of the reaction of a base and an acid indicator injected on the two sides of the layer, respectively, gave some indication of where molecular mixing occurs. Autocorrelations of streamwise velocity fluctuations, using a laser-Doppler velocimeter (LDV) revealed a fundamental periodicity associated with the large structures. The surprisingly long correlation times suggest time scales much longer than had been supposed; it is argued that the mixing-layer dynamics at any point are coupled to the large structure further downstream, and some possible consequences regarding the effects of initial conditions and of the influence of apparatus geometry are discussed.

Experiments on transition to turbulence in an oscillatory pipe flow

Abstract: Experiments on transition to turbulence in a purely oscillatory pipe flow were performed for values of the Reynolds number Rδ, defined using the Stokes-layer thickness δ = (2ν/ω)½ and the cross-sectional mean velocity amplitude U, from 19 to 1530 (or for values of the Reynolds number Re, defined using the pipe diameter d and U, from 105 to 5830) and for values of the Stokes parameter λ = ½d(ω/2ν)½ (ν = kinematic viscosity and ω = angular frequency) from 1·35 to 6·19. Three types of turbulent flow regime have been detected: weakly turbulent flow, conditionally turbulent flow and fully turbulent flow. Demarcation of the flow regimes is possible on Rλ, λ or Re, λ diagrams. The critical Reynolds number of the first transition decreases as the Stokes parameter increases. In the conditionally turbulent flow, turbulence is generated suddenly in the decelerating phase and the profile of the velocity distribution changes drastically. In the accelerating phase, the flow recovers to laminar. This type of partially turbulent flow persists even at Reynolds numbers as high as Re = 5830 if the value of the Stokes parameter is high.

The interfacial drag and the height of the wall layer in annular flows

Abstract: A method to predict the height of the wall layer and the interfacial drag in annular flow under conditions that the flow rate of the entrained liquid is known is developed from measurements on air-water flow in circular tubes. Flow conditions are found to be characterized by a generalized Martinelli flow parameter.

Foundations of aerodynamics: bases of aerodynamic design

Abstract: The Fluid Medium. Kinematics of a Flow Field. Dynamics of Flow Fields. Irrotational Incompressible Flow About Two-Dimensional Bodies. Aerodynamic Characteristics of Airfoils. The Finite Wing. Introduction to Compressible Fluids. Energy Relations. Some Applications of One-Dimensional Compressible Flow. Waves. Linearized Compressible Flow. Airfoils in Compressible Flows. Wings and Wing-Body Combinations in Compressible Flow. The Dynamics of Viscous Fluids. Incompressible Laminar Flow in Tubes and Boundary Layers. Laminar Boundary Layers in Compressible Flow. Flow Instabilities and Transition from Laminar to Turbulent Flow. Turbulent Flows. Airfoil Design, Multiple Surfaces, Vortex Lift, Secondary Flows, Viscous Effects. Appendices. Tables. Oblique Shock Chart. References. Index.

Flow and Bed Topography in Curved Open Channels

Abstract: Mean flow characteristics and bed shear distributions in uniformly curved open channels have been studied theoretically, and the results are compared with experiments and field observations. Next, an equation which expresses the variation of transverse bed profile is derived by considering an equilibrium of forces acting on a sand particle. It is shown that the magnitude of the secondary flow and the transverse bed slope determine the direction of sand movement. The numerical solution of the bed variation with time are compared with experiments, and it is concluded that the model employed here describes the bed variation fairly well. The stable profile of the bed is obtained analytically, and from this result the maximum depth of scour which occurs at the outer banks is calculated.

Roll-cell instabilities in rotating laminar and trubulent channel flows

Abstract: The stability of laminar and turbulent channel flow is examined for cases where Coriolis forces are introduced by steady rotation about an axis perpendicular to the plane of mean flow. Linearized equations of motion are derived for small disturbances of the Taylor type. Conditions for marginal stability in laminar Couette and Poiseuille flow correspond, in part, to the analogous solutions of buoyancy-driven convection instabilities in heated fluid layers, and to those of Taylor instabilities in the flow between rotating cylinders. In plane Poiseuille flow with rotation, the critical disturbance mode occurs at a Reynolds number of Rec = 88.53 and rotation number Ro = 0.5. At higher Reynolds numbers, unstable conditions canexist over the range of rotation numbers given by 0 < Ro < 3, provided the undisturbed flow remains laminar. A two-layer model is devised to investigate the onset of longitudinal instabilities in turbulent flow. The linear disturbance equations are solved essentially in their laminar form, whereby the velocity gradient of laminar flow is replaced by a numerically computed profile for the gradient of the turbulent mean velocity. The turbulent stress levels in the stable and unstable flow regions are represented by integrated averages of the eddy viscosity. Onset of instability for Reynolds numbers between 6000 and 35 000 is predicted to occur at Ro = 0.022, a value in remarkable agreement with the experimentally observed appearance of roll instabilities in rotating turbulent channel flow.

Transport processes in boiling and two-phase systems, including near-critical fluids

Abstract: Aspects of pool boiling are considered, taking into account nucleate boiling, the nucleate boiling mechanism, film boiling, and the transition between nucleate and film boiling. The characteristics of two-phase flow are also investigated, giving attention to two-phase flow parameters and equations, the flow pattern in two-phase flow, the pressure drop in two-phase flow, heat transfer in two-phase flow, two-phase flow dynamics, the boiling crisis in two-phase flow, the critical flow rate, the propagation of the pressure pulse and the sonic velocity in two-phase media, instrumentation for two-phase flow, and geometry and field effects on boiling and two-phase flow. Near-critical fluids are also considered.

Minimum Unit Stream Power and Fluvial Hydraulics

Abstract: Fluvial hydraulics is complex because the velocity, slope, depth, and channel roughness are all subject to change. The unit stream power, defined as the rate of potential energy expenditure per unit weight of water, required to transport a given sediment load is sensitive to water depth when the sediment concentration is low. The interdependence between unit stream power and water depth decreases as sediment concentration increases. A computer program is used to generate different combinations of velocity, slope, depth, and unit stream power for a given sediment load. The generated unit stream power in the lower flow regime either has a clear minimum value at a particular depth or approaches a minimum value for a given sediment load. These agreements suggest that an alluvial channel in the lower flow regime adjusts its velocity, slope, depth, and roughness in such a manner that a given sediment load can be transported with the minimum amount of unit stream power.

Experimental Investigation of Flow Over Side Weirs

Abstract: Observations at numerous cross sections in a side weir channel showed that the total energy of flow decreases substantially along the channel, contrary to the assumption that has frequently been made. The decrease in total energy occurs because the longitudinal component of velocity of the spill flow is greater than the longitudinal velocity of the flow remaining in the channel. A satisfactory flow equation is derived from momentum principles and this is further developed into a computer technique for calculating flow profiles and spill discharges for side weirs.

STAN5: A program for numerical computation of two-dimensional internal and external boundary layer flows

Abstract: A large variety of two dimensional flows can be accommodated by the program, including boundary layers on a flat plate, flow inside nozzles and diffusers (for a prescribed potential flow distribution), flow over axisymmetric bodies, and developing and fully developed flow inside circular pipes and flat ducts. The flows may be laminar or turbulent, and provision is made to handle transition.

The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls

Abstract: A numerical investigation is made to establish whether multiple solutions exist for laminar, incompressible, steady flow in a parallel plate porous channel with uniform suction at both walls. For values of the wall suction Reynolds number,R, greater than 12.165 three numerical solutions are observed for eachR, while forR less than 12.165 only one solution for eachR can be found. A method involving the inclusion of exponentially small terms in a perturbation series is used to find two of the solutions analytically, while an appeal to the numerical results gives an indication of how the third solution can be obtained. The series involving the exponentially small terms, as well as predicting dual solutions, gives more accurate analytic results for the skin friction at the channel walls.

Observations on turbulent-drag reduction in a dilute suspension of clay in sea-water

Abstract: Hot-wire anemometer measurements have been made in a dilute sea-water/claymineral suspension. For fully developed turbulent flows in an open channel with a smooth mud (from the North Sea) bottom, mean streamwise velocity profiles were measured for Reynolds numbers between 5400 and 27 800 (i.e. non-eroding and eroding flow rates) and compared with Newtonian flows under the same experimental conditions. For the clay-mineral suspensions, measurements of the kinematic viscosity v, Karman's constant k and the mean streamwise velocity of the logarithmic layer seemed to verify a Newtonian flow structure. Although the distributions of concentration showed no substantial increase towards the wall, it was found that beneath this Newtonian core there existed a viscous sublayer whose thickness was enhanced by a factor of 2–5. The friction velocity u* determined by the gradient method in the viscous sublayer was reduced by as much as 40 %. The mean flow structure exhibited an additional new layer in the region 10 < y+ < 30.The measurements indicate that turbulent-drag reduction occurs for the experimental clay-mineral suspension at non-eroding and also at eroding velocities. Agglomeration of suspended clay-mineral particles is suggested as possible explanation of this phenomenon.

The static electrification of particles in gas-solids pipe flow

Abstract: Electrostatic characteristics in gas-solids flow in a metal pipe are studied both theoretically and experimentally with particular attention to the collision between particles and pipe wall. Effects of gas velocity and particle diameter on the electrification are also examined.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

Abstract: The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

Baroclinic Instability in the Denmark Strait Overflow

Abstract: Current meter records and hydrographic data taken in the Denmark Strait overflow during a one-month experiment in August-September 1973 are analyzed. Mean conditions indicate that a strong, cold overflow current existed throughout the experiment. The most outstanding feature of the velocity and temperature spectra is a strong peak at a period of 1.8 days. These oscillations appear to amplify in the downstream direction and are highly correlated over the entire flow at the southern end of the Strait. Phase estimates indicate that velocity components are in quadrature, while the cross-stream perturbation heat flux acts to reduce the mean potential energy associated with the sloping isotherms. To explain the low-frequency variability, a quasi-geostrophic two-layer model for channel flow with a sloping bottom is developed. Using measured values of shear and other physical parameters, the model is found to be unstable over a limited range of wavelengths and frequencies. The most unstable wave is 80 km...

Flow Resistance in Broad Shallow Grassed Channels

Abstract: Resistance to sheet flows over natural turf surface is investigated experimentally. The formulation of a functional relationship between the resistance coefficient and controlling parameters for shallow flows over various turf surfaces is essential to the mathematical modeling of the rainfall-runoff process and sediment yield from a watershed which may consist of various vegetated surfaces. An analysis of results obtained from laboratory experiments for laminar flow on Kentucky Blue grass and Bermuda grass surfaces reveals that a relationship exists between the Darcy-Weisbach friction coefficient, Reynolds number, and bed slope. A further analysis of previous investigators' experimental results for flow on various smooth and rough surfaces under or no rainfall leads to the qualitative determination of a general trend of the resistance relationship for shallow flows over such dense turf surfaces as affected by bed slope, raindrop impact, and roughness size.

Air-Entrainment in High Head Gated Conduits

Abstract: For the successful operation of high head gated conduits, adequate supply of air is of paramount importance. However, no dependable solution is yet available to determine the required quantity of air for different flow types. Based on systematic experiments backed by theoretical considerations, suitable relationships and diagrams have been developed that predict results compatible with prototype measurements. Conduit roughness has no significant effect on air-entrainment. No linear relationship has been found to exist between the head and the maximum air-entraining capacity of the flow. Measurements of air velocity by means of high speed cinematography indicate that the velocity at the interface is much higher than the mean velocity of water flow and that the air velocity distribution is far removed from being logarithmic.

Theoretical model of river ice jams

Abstract: A mathematical analysis is developed to describe the evolution and characteristics of river ice jams. The principal components of the analytical model are the static force equilibrium of the fragmented ice cover; the unsteady continuity equations for the frozen and liquid water; the nonuniform unsteady momentum relation for the flow; and relations in which compressive and shear strengths of the floating fragmented ice cover vary linearly with local jam thickness. A numerical method is outlined for solving the equations for the case in which the jam has evolved to the point that it propagates upstream with constant velocity (quasi-steady conditions), and a complete set of example results is presented for a specific flow and channel. Estimates are derived for the time required for the jam to evolve to the quasi-steady state and for the velocity of the jam front during the evolutionary stage.

A Theory of Flow Resistance for Vegetated Channels

Abstract: ATHEORY is developed to predict the flow resistance in vegetated open channels. The solution technique is based on an analytical method originally proposed by Roberson for smooth conduits roughened with discrete submerged roughness elements. The theory uses small diameter cylinders to simulate vegetative roughness elements. Flow conditions may either partially or fully submerge the cylinders. Included in the analysis is a method to predict the effect of flexible vegetation on flow resistance. The model also predicts resistance effects of a smooth boundary or one roughened by dense concentrations of small elements such as soil particle aggregates. An initial comparison of flume measurements of resistance for small diameter cylinders is given. The analytical model provides, in addition to resistance factor, other flow parameters involved in analytical solutions of vegetated open channel flow.

A theoretical study of the acoustic impedance of orifices in the presence of a steady grazing flow

Abstract: An analysis of the oscillatory fluid flow in the vicinity of a circular orifice with a steady grazing flow is presented The study is similar to that of Hersh and Rogers but with the addition of the grazing flow Starting from the Navier‐Stokes and continuity equations, a considerably simplified system of partial differential equations is developed with the assumption that the flow can be described by an oscillatory motion superimposed upon the known steady flow The equations are seen to be linear in the region where the grazing flow effects are dominant, and a solution and the resulting orifice impedance are presented for these equations Some preliminary conclusions of the study are that orifice resistance is directly proportional to grazing flow velocity (known previously from experimental data) and that the orifice inductive (mass reactance) end correction is not a function of grazing flow This latter conclusion is contrary to the widely held notion that grazing flow removes the effect of the orifice inductive end correction This conclusion also implies that the experimentally observed total inductance reduction with grazing flow might be in the slug flow within the orifice rather than in the end correction

Turbulent flow past a porous plate

Abstract: The method of Vickery for calculating the drag of plane lattice structures normal to a turbulent stream is extended to cases of increased solidity. The analysis incorporates an extended version of Taylor's theory for the flow through a porous plate, and a simplified version of Hunt's analysis of the distortion of a turbulent flow by the mean flow field of a body. Some comparisons are made with experimental data.

Fluid flow into a curved pipe

Abstract: The influence of curvature on a pipeflow is discussed for a pipe that starts bending uniformly after an initial straight section. The Reynolds number and curvature are assumed large and small respectively, and the motion is examined first for distances from the starting of the bend that are com­parable with the tubewidth. When the Dean number is finite, the coreflow remains practically undisturbed, i. e. unidirectional, until the bend and thereafter streams uniformly towards the outside of the curve, inducing a three dimensional boundary layer. This layer, however, has to react before the bending in order to adjust to the downstream conditions. It does so by means of a novel kind of upstream response. The azimuthal pressure variation generated by the bend is felt upstream and therefore both drives an inwards azimuthal motion in the boundary layer and produces an axial shear maximum at the inside wall. In the curved section the centrifuging then causes the maximum to shift to the outer bend at 1.51 pipe-radii beyond the start of bending. Finally, the theory is extended to longer lengthscales, to large Dean numbers and to general initial profiles.