Showing papers on "Open-channel flow published in 1973"

Flexible roughness in open channels

Abstract: The logarithmic flow formula for open channels is valid for flow over a roughness cover made up of flexible plastic strips. The deflection of such roughness is an important parameter as the deflection directly influences the relative roughness. Dimensionless parameters which relate the amount of bending to the stiffness of the roughness and the boundary shear are defined. Three regimes of boundary behavior are observed for flexible plastic roughness, leading to two resistance functions. The flexible plastic roughness is produced by affixing thin plastic strips of various thickness to the bed of a flume. The flow of water over flexible plastic strips simulates flow over a vegetative channel lining.

A survey of the mean turbulent field closure models.

Abstract: C solutions to the differential boundary-layer equations have for some years now been applied to turbulent boundary layers where relief from the difficulty of solution permits more concern for the physical elements of models which purport to simulate some statistical features of turbulent flowfields. A first step has been accomplished; that is, accurate, quite versatile, and practically/useful computer programs have been combined with rather simple and successful empirical statements" which allow one to estimate the Reynolds shear stress in the equations for the mean velocity field. We call this Mean Velocity Field (MVF) closure since it predicts only the mean velocity field in addition to the mean shear stress. For boundarylayer flows a set of empirical constants must be selected. However, it is then possible to accurately predict flows with wall transpiration, heat transfer, and a variety of other boundary conditions, and, remarkably, with no adjustment in the constants. However, the constants must be adjusted for, say, pipe or channel flow or free shear flows. By moving on to the more complicated Mean Turbulent Field (MTF) closure there is some hope of discovering increasingly universal models and a greater range of predictability. There are two other incentives: First, it is rather comforting actually to compute the turbulent kinetic energy; it is, after all, the premier property that distinguishes turbulent from laminar flow. Second, it appears possible to include body forcelike effects such as curvature, buoyancy, and Coriolis effects with no further empiricism. The latter is a line of thought that is not new,' and it has occupied the present authors' interest for some time. However, in this paper we avoid these topics in order to simplify discussion of an already complicated field. We also assume that the fluid is incompressible. Extension to high Mach number flows does not, however, seem to be a major problem. A basis for MTF calculations began appropriately enough with the semiheuristic models of Kolmogoroff and Prandtl in the early 1940's; they include the turbulent kinetic energy transport equation, a turbulent-energy-related eddy viscosity, and either a prescribed length scale function or a differential equation for a length scale. We wish to call this Mean Turbulent Energy (MTE) closure which together with Mean Reynolds Stress (MRS) closure forms two subsets of MTF closure.* MRS closure implies a closed set of equations which include equations for all nonzero components of the Reynolds stress tensor. Chou' seems to be the first to initiate a study of the full set of equations with an eye towards closure. However, it was Rotta in 1951 who laid the foundation for almost all of the current models. In the Reynolds stress tensor equation (the tensor equation for the single-point, double-velocity correlations, the trace of which is the kinetic energy equation) there appear pressure-velocity gradient correlations, (pdujdxj), which Rotta called the energy redistribution terms and which he argued should be proportional to the deviation from isotropy — dtj(uky/3. On the whole, the assumption seems physically correct, but of further importance is the fact that it provides a unity that was lacking, say, in the 1940's.f Thus, the Reynolds shear stress is now determined as a part of the whole; MTE closure can be obtained as an analytic simplification of MRS closure, and, furthermore, MVF closure (that is, eddy viscosity or mixing length concepts) can be viewed as a further simplification. We shall follow this process of simplification in this paper. Despite the unity of thought provided by Rotta's basic assumption, it is, of course, an approximation to nature and is subject to modification in the hands of investigators eager to achieve agreement with data. Furthermore, there are other terms in the Reynolds stress equations, such as the dissipation and diffusion terms, which are modeled differently by different investigators and represent some impass to a consensus theory such as is the near state of MVF closure. In the present development we have attempted to present the basic ideas and a core model for MRS and MTE closure and

The origin of secondary flow in turbulent flow along a corner

Abstract: The mechanisms which initiate secondary flow in developing turbulent flow along a corner are examined on the basis of both energy and vorticity considerations. This is done by experimentally evaluating the terms of an energy balance and vorticity balance applied to the mean motion along a corner bisector. The results show that a transverse flow is initiated and directed towards the corner as a direct result of turbulent shear stress gradients normal to the bisector. The results further indicate that anisotropy of the turbulent normal stresses does not play a major role in the generation of secondary flow. Possible extensions of the present results to other related flow situations are ahstrated and discussed.

The influence of surface properties on flow and erosion processes on debris covered slopes in an arid area

Abstract: Summary A study aiming to obtain quantitative data on the processes of slope runoff and erosion under arid conditions and relate them to rain and surface properties, was conducted near Elat, in southern Israel. Slope-channel relations, with regard to runoff and sediment transport, were also analysed. Data were obtained by means of three overland flow collectors, two rain recorders and one hydrometric station. The research was conducted over one rain season, during which a single channel flow and five overland flow events occurred. The results lead to the following main conclusions: 1) For a small drainage basin, the threshold values for slopes and channel flow are 3 mm and 5 mm per day, respectively; 2) No clear relation exists between the slope angle and slope runoff and an inverse relation exists between slope angle and slope erosion.

Experimental investigation on secondary currents in the turbulent flow through a straight conduit

Abstract: In continuation to an earlier publication, experiments have been made in the turbulent flow through a conduit of rectangular cross-section with large aspect ratio. One of the long walls has been made rough, except for a strip, located centrally. As shown in the earlier paper, secondary currents will occur in the regions of transition from smooth to rough wall-condition. The main purpose of the investigation was to check the admissibility of the simplifying assumptions made to the mechanical-energy balance equation. The results of the measurements indeed justified the neglect of unimportant terms of this equation, leading to the following rule. When in a localized region the production is much greater (smaller) than the viscous dissipation, there must be a secondary current that transports turbulence-poor fluid into (outwards) this region and turbulence-rich fluid outwards (into) the region.

Parametric analysis of turbulent wall jets in still air.

Abstract: An examination has been made of all the data available on incompressible (nominally) plane wall jets in still air, supplementing these when necessary with some additional measurements. For a wall jet in still air, the chief mean flow qualities of interest are the maximum velocity, the inner length scale, and a total thickness, in addition to the wall stress. On the basis of the analysis, a (nominally) plane wall jet flow can be divided into an initial region, a fully developed flow region, and a confined wall jet flow region.

Compressible fluid flow

Abstract: This book is an introductory text on one dimensional and simple wave flows. The topics dealt with are one dimensional, adiabatic, frictionless flow, Fanno and Rayleigh flows, Prandtl-Meyer flow, normal and oblique shock waves and simple, unsteady wave propagation. For each topic, the basic equations are derived and manipulated to obtain various appropriate expressions, these expressions are then applied to a number of worked examples which are interwoven with the development of new material. A set of examples for the student to attempt is also included. The book is made self-contained by the inclusion of suitable flow tables. The material is well presented but little comment is made on its relationship to real flows and, consequently, the stgdent is unlikely to be left with any clear feeling for either the power or the limitations of these approximate methods. For example, shock-boundary layer interaction is given only the briefest mention despite the fact that numerous diagrams show shock waves produced at or reflecting from duct walls. The main attractions of the book lie in its relatively modest price and in the numerous and varied worked examples. Studying the examples should considerably improve the ability of an undergraduate student to solve examination questions. B. L. HUNT

The turbulent mean-flow, Reynolds-stress, and heat flux equations in mass-averaged dependent variables

Abstract: The time-dependent, turbulent mean-flow, Reynolds stress, and heat flux equations in mass-averaged dependent variables are presented. These equations are given in conservative form for both generalized orthogonal and axisymmetric coordinates. For the case of small viscosity and thermal conductivity fluctuations, these equations are considerably simpler than the general Reynolds system of dependent variables for a compressible fluid and permit a more direct extension of low speed turbulence modeling to computer codes describing high speed turbulence fields.

Shape Effects on Resistance in Flood-Plain Channels

Abstract: For flow computation in flood plain channels, the flow cross section is usually divided into subsections to ensure hydraulic homogeneity. However, the question of whether or not to include the division lines as part of the wetted perimeter still remains unanswered. In this study, efforts have been made to determine division lines having zero shear stress so that they need not be included in the wetted perimeter. Laminar flow cases were solved to gain qualitative insight into the shape effects on resistance and location of division lines. For turbulent flows, division lines were determined from velocity distribution patterns; and resistance coefficients for both laminar and turbulent flows are lower than those in wide rectangular channels having the same boundary materials. New formulas are proposed for computation of discharge in both main-channel and flood-plain portions.

A model of flow separation at a free surface

Abstract: Study of flow separation which can be observed at the leading edge of a spilling breaker of 'white-cap', at the lower edge of a tidal bore or hydraulic jump and upstream of an obstacle abutting a steady free-surface flow. At the point of flow separation there is a discontinuity in the slope of the free surface. The flow upstream of this point is relatively smooth; the flow downstream of the discontinuity is turbulent. A local solution for the flow in the neighborhood of the discontinuity is derived. The turbulence is represented by a constant eddy viscosity, and the tangential stress across the interface between the laminar and turbulent zones is expressed in terms of a drag coefficient.

Unit-Response Method of Open-Channel Flow Routing

Abstract: UNIT-RESPONSE FLOW ROUTING IS A TECHNIQUE OF OPEN- CHANNEL FLOW ROUTING BASE ON THE UNIT HYDROGRAPH PRINCIPLE OF LAGGING AND SUPERPOSITION. THE UNIT RESPONSE IS DEFININED AS THE FLOW HYDROGRAPH AT A DOWNSTREAM LOCATION RESULTING FROM A CONSTANT INFLOW OF 1 CFS DURING A SELECTED DURATION PERIOD, D, AT AN UPSTREAM LOCATION. IT CAN BE DERIVED FROM ACTUAL RECORDS, BUT FOR GENERAL APPLICATION IT IS DERIVED SYNTHETICALLY BY ROUTING A TRANSLATION HYDROGRAPH THROUGH RESERVOIR STORAGE TO OBTAIN AN INSTANTANEOUS UNIT RESPONSE, AND TRANSFORMING THIS RESPONSE TO THE SELECTED D-HOUR UNIT RESPONSE. LAG, OR TRANSLATION TIME, IS USED TO ACCOUNT FOR FLOOD-WAVE TRAVEL TIME IN THE CHANNEL. THIS CAN BE VARIED WITH DEPTH. ROUTING INTERVALS OF FROM 1 HR TO 24 HR AND ROUTING REACHES FROM 10 MILES TO 150 MILES HAVE BEEN USED SUCCESSFULLY.

Flows of thin streams with free boundaries

Abstract: A method is developed for determining any thin steady two-dimensional potential flow with free and/or rigid boundaries in the presence of gravity. The flow is divided into a number of parts and in each part the flow and its free boundaries are represented as asymptotic series in powers of the slenderness ratio of the stream. There are three basic flows, having two, one and no free boundaries and called jet flow, wall flow and channel flow, respectively. First the three expansions for these flows are found, extending results of Keller & Weitz (1952). They are called outer expansions to distinguish them from the inner expansions which apply near the ends of the stream or at the junction of two different types of flow. The inner and outer expansions must be matched at a junction to find how the emerging flow is related to the entering flow. This process can be continued to build up any complex flow involving thin streams. The method is illustrated in the case of a wall flow that leaves the wall to become a jet, which includes the case of a waterfall treated by Clarke (1965) in a similar way. In part 2 (to be published) other inner expansions are found and matched to outer expansions, providing the ingredients for the construction of the solutions of many flow problems.

Computer Programming for Flow over Side Weirs

Abstract: A procedure is presented for computing water surface profiles and discharge in an open channel with flow over side weirs. There is little restriction about the channel shape, variation of invert slope, convergence of the channel along the length of weir, etc. A criterion for determining whether flow will be subcritical or supercritical on a mild slope is also developed. The procedure is illustrated by some examples. Some deficiencies in available knowledge are noted.