Showing papers on "Open-channel flow published in 1978"

Mechanical Characteristics of Debris Flow

Abstract: A mechanism of occurrence of bore-like debris flow due to the appearance of overland flow on the debris accumulation is considered using the applying shear stress and resisting stress relationship in the bed. The criteria for the occurence of the nonstationary bed flow and the partly stationary bed flow are made clear. The partly stationary bed flow approaches a quasi-steady state, whose depth, velocity and concentration are predictive applying the concept of dilatant fluid introduced by Bagnold. Although the front height of the nonstationary bed flow increases versus distance, the translation velocity and concentration are nearly constant and flow characteristics are theoretically predictive by some appropriate assumptions.

Applicability of kinematic and diffusion models.

Abstract: The applicability of the kinematic and diffusion models of open channel flow is assessed by comparing the propagation characteristics of sinusoidal perturbations to the steady uniform flow for the kinematic, diffusion, and dynamic models (the dynamic model is that based on the complete Saint Venant equations). The comparison allows the determination of inequality criteria that need to be satisfied if the kinematic or diffusion models are to simulate the physical phenomena within a prescribed accuracy. It is shown that bed slope and wave period (akin to wave duration in waves of shape other than sinusoidal) are the important physical characteristics in determining the applicability of the approximate models. Larger bed slopes or long wave periods, or both, will satisfy the inequality criteria. In practice, larger bed slopes are those of overland flow, and long wave periods are those corresponding to slow-rising flood waves.

Predictions of Heat and Mass Transfer in Open Channels

Abstract: The paper describes a three-dimensional model for calculating the distribution of velocity, temperature, and pollutant concentration in open channel flows, and a depth-averaged two-dimensional version for situations with insignificant stratification and secondary currents. Both models are restricted to parabolic flows where influences cannot be transmitted upstream. The turbulent stresses and heat/concentration fluxes appearing in these equations are determined from the so-called k-ϵ turbulence model that solves differential transport equations for the turbulence kinetic energy k and the rate of its dissipation ϵ. In the depth-averaged model, the bottom shear stress, surface heat flux and turbulence production due to bottom shear are accounted for by source/sink terms in the relevant equations. The 3D calculations compare favorably with available measurements. The 2D and 3D predictions agree well for high Froude numbers; for a Froude number of 5 they agree only for the rough bed, while for the smooth bed they start to deviate significantly at a Froude number of 10.

Particle motions near the bottom in turbulent flow in an open channel. Part 2

Abstract: This study continues the investigation of particle motions near the bottom in a turbulent open channel flow, reported by Sumer & Oguz (1978; hereafter referred to as part 1). Paths of suspended heavy particles were recorded in three dimensions and in time, employing a stereo-photogrammetric system coupled with a stroboscope. In the case of smooth bottom, the measured kinematical quantities concerning the particle motions were found to be in accord with the available information on the ‘bursting process’. Agreement between the particle motion and the bursting process provided further support for the mechanism of particle suspension near the bottom proposed in part 1. Similar experiments were carried out when the bottom was rough. Comparison between the smooth- and rough-bottom cases could be made on the same basis as the flow Reynolds number as well as the particle properties were kept almost unchanged in both the smooth and rough boundary experiments. The observations showed that particle motions close to the rough bottom are very similar in character to those in the smooth-bottom case. The findings of the present paper suggested that the suspension mechanism given for the smooth-boundary flow could be extended to the rough-boundary case.

Flow Resistance of Large-Scale Roughness

Abstract: A theory of the resistance to flow in rivers with large-scale roughness is developed and a resistance equation is constructed using data from the upper River Tees, England. The theoretical analysis shows that, in channels with large values of relative roughness, resistance to flow depends mainly on the size, shape, spacing, and size distribution of the boundary roughness elements. Channel geometry is important only in its effect on the drag of the elements. This theory is illustrated using data from field sites at which roughness shape and size distribution were similar and roughness spacing could be directly related to relative roughness. In the resistance equation (which is specific to the field sites) the resistance coefficient varies with just relative roughness and a parameter of channel geometry.

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

A depth-averaged mathematical model for the near field of side discharges into open-channel flow

Abstract: A two-dimensional mathematical model is described for the calculation of the depth-averaged velocity and temperature or concentration distribution in open-channel flows, an essential feature of the model being its ability to handle recirculation zones. The model employs the depth-averaged continuity, momentum and temperature/concentration equations, which are solved by an efficient finite-difference procedure. The ‘rigid lid’ approximation is used to treat the free surface. The turbulent stresses and heat or concentration fluxes are determined from a depth-averaged version of the so-called k, e turbulence model which characterizes the local state of turbulence by the turbulence kinetic energy k and the rate of its dissipation e. Differential transport equations are solved for k and e to determine these two quantities. The bottom shear stress and turbulence production are accounted for by source/sink terms in the relevant equations. The model is applied to the problem of a side discharge into open-channel flow, where a recirculation zone develops downstream of the discharge. Predicted size of the recirculation zone, jet trajectories, dilution, and isotherms are compared with experiments for a wide range of discharge to channel velocity ratios; the agreement is generally good. An assessment of the numerical accuracy shows that the predictions are not influenced significantly by numerical diffusion.

Computing Two-Dimensional Dam-Break Flood Waves

Abstract: A mathematical model of two-dimensional unsteady flow through a breached dam is developed. The numerical method of characteristics in three independent variables is used to construct an algorithm correct to second order with respect to time. The solution progresses at specified time intervals. At any time, the flow conditions are obtained by extending characteristic conoids back to a previously computed time plane and allowing information to propagate along the curvilinear rays of these conoids. Both the negative wave propagating into the reservoir and the jet emerging from the breach and eventually inundating the valley downstream of the dam are modeled in detail. Arbitrary dam geometry and channel topography can be taken into account. Propagation of the wave fronts is simulated by a computational grid moving with time. The exact computed results of the model are presented graphically as axonometric projects for the depth, and as plan-view, two-dimensional vector fields for the flow velocities.

Measurements of turbulent flow downstream of a rearward-facing step

Abstract: Measurements have been made in a water channel of the flow in and around the separation region due to a rearward-facing step. Detailed profiles of mean velocities, turbulence intensities and Reynolds shear stress are presented. The turbulence measurements reveal the development of a new shear layer, which splits at reattachment with about one-sixth of the mass flow deflected upstream. The new shear layer is associated with a region of roughly constant values of both the non-dimensional mixing length l/x and the shear correlation coefficient K. The mixing-length ratio is larger than that found in plane mixing layers, whereas the shear coefficient is roughly the same. There is strong evidence that near the wall the length scales increase more rapidly with distance from the wall than in an attached boundary layer, and that a local maximum occurs.

Transverse bed slopes in curved alluvial streams

Abstract: Forty-nine experiments were conducted in three different constant radius, erodible bed, curved flumes using two different sediments to investigate the relationship between channel geometry, flow and sediment properties, and bed topography An analytical model based on moment equilibrium of the flow and force equilibrium of the bed particles is used to develop an equation for the mean radial bed slope in terms of the friction factor, flow depth and velocity, channel radius, and particle densimetric Froude number The relation is found to be in good agreement with reported experimental data and with bed topography measured by Hooke in a sinuous channel

Dynamics of Blocking Highs

Abstract: It is proposed that the nonlinear interaction of forced waves and slowly moving free waves May lead to the development of blocking highs under favorable conditions. This idea is tested numerically for three types of quasi-geostrophic inviscid channel flow with low spectral resolution in the zonal direction where the forcing is provided by orography. First, barotropic channel flow without wave-mean flow interaction and a constant mean velocity u¯ is considered. The forcing induces standing waves, whereas the phase speed c of the free waves is given by the Rossby formula. A booking high develops when u¯ is chosen to make c≈0 for some of those waves which can interact with the forced standing waves. Blocking does not occur without forcing. Next, the model is extended to include wave-mean flow interaction. Blocking highs with realistic lifetimes develop when u¯ is appropriately chosen initially. The meridional profile of u¯ shows a double let when the block is fully developed. As a third step barocli...

A comprehensive experimental investigation of tubular entry flow of viscoelastic fluids: Part I. Vortex characteristics in stable flow

Abstract: The characteristics of a vortex found at the entry of a 2:1 and 4:1 contraction for viscoelastic fluids is investigated. Two distinct flow regimes are identified in the contraction flow field: a vortex growth regime and a divergent flow regime. In the vortex flow regime, rheological forces are found to dominate the flow, with the vortex detachment length being a linear function of the Weissenberg number. In the divergent flow regime, the flow is found to diverge at the center line upstream of the vortex detachment plane, and the vortex size decreases with increasing flow rates. Inertial forces are important in the divergent flow regime. The entry flow characteristics for the 2:1 and 4:1 contraction are quantified in terms of the vortex detachment length as a function of Reynolds and Weissenberg number over the range of 0:2 < N′Re < 200 and 0.10 < NWS < 0.7.

Transient gas-liquid flow in horizontal pipes: Modeling the flow pattern transitions

Abstract: The theory for predicting flow pattern transition under transient flow conditions is developed and compared with experiment. This work represents an extension of the methods presented by Taitel and Dukler (1976) for steady state flows. Under transient conditions, flow pattern transitions can take place at flow rates substantially different than would occur under steady flow conditions. In addition, flow patterns can appear which would not be expected for a slow change in flow rates along that same path. Methods are presented for predicting the flow rates at which flow pattern transitions will take place during flow transients. The method also reveals when spurious flow patterns will appear.

On the Nonunique Solutions of Laminar Flow through a Porous Tube or Channel

Abstract: The equations describing similarity solutions for flow through a uniformly porous tube and channel with equal rates of injection or suction at the walls are analyzed. The number and character of the solutions possible for various values of suction and injection are found. For the channel problem it is shown there is exactly one solution possible for injection and exactly three solutions possible for suction. For the tube problem it is found there are two types of solutions for injection and small suction and at most four possible solutions for large suction under the assumption that the solutions are analytic at zero. It is also shown that for one value of suction no solutions are possible under these assumptions. Numerical integration is then applied to obtain those solutions which have not been completely reported previously.

Large eddy simulation of incompressible turbulent channel flow

Abstract: The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow A partially implicit numerical method was developed An important feature of this scheme is that the equation of continuity is solved directly The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented

The stability of a two-dimensional stagnation flow to three-dimensional disturbances

Abstract: Experiments have shown that the two-dimensional flow near a forward stagnation line may be unstable to three-dimensional disturbances. The growing disturbance takes the form of secondary vortices, i.e. vortices more or less parallel to the original streamlines. The instability is usually confined to the boundary layer and the spacing of the secondary vortices is of the order of the boundary-layer thickness. This situation is analysed theoretically for the case of infinitesimal disturbances of the type first studied by Gortler and Hammerlin. These are disturbances periodic in the direction perpendicular to the plane of the flow, in the limit of infinite Reynolds number. It is shown that the flow is always stable to these disturbances.

Undular Hydraulic Jump

Abstract: When a supercritical flow in a channel is forced to change into a subcritical flow, the transition will normally occur as a hydraulic jump, and the energy loss in the jump will be large. With increasing supercritical depth and decreasing difference between the corresponding depths the energy loss will diminish and the transition will at last occur in an oscillating manner. The character of the transition has a natural explanation that will be considered.

Rimming flow: numerical simulation of steady, viscous, free-surface flow with surface tension

Abstract: Flow in a partly liquid-filled, rotating, horizontal cylinder is analysed by means of finite-element numerical simulation. Of alternative methods for locating the free surface, a boundary collocation scheme with Newton-Raphson iteration converges. This method forces the residual in the normal-stress boundary condition to zero at a finite set of points on the liquid meniscus. Solutions of the steady, two-dimensional, incompressible flow problem show circumferential variation of the liquid-film thickness and corresponding pressure and velocity fields, including recirculation zones. The complications of an unknown meniscus location and a nonlinear normal-stress condition when surface tension is significant are illustrated. The finite-element method proves an effective and convenient tool for such flows, in which inertial, gravitational, pressure, viscous and capillary forces are all important.

Drainage density changes during rainfall

Abstract: Observations of stream behaviour during rainfall indicate that previous notions of a simple expanding and contracting network need review and refinement. In a small rural catchment near Armidale, N.S.W. changes in flowing stream length during rainfall have been depicted on flow length graphs which indicate a varied network response to similar rainfall amounts. Channel flow phenomena include discontinuous flow, the generation of flow points within the channel and movement of water downslope from saturated depression sources. Localized physical controls have a significant effect on stream growth which is a sensitive indicator of the catchment response to rainfall. During rapid changes in stream length total flowing length and discharge are highly correlated. A model of the pattern of network expansion and contraction involves several phases of flow contraction.

Three-parameter model of shear turbulence

Abstract: A model of shear turbulence is proposed in which transport equations are used for three flow chracteristics: the energy E, the friction stress — (u′v′), and the function F, whose dimensionality coincides with that of the quantity EmLn. Well-known equations are used for the first two quantities, while a special analysis is required to construct the third equation. The constants in the equations are determined by analyzing the flow behind a grid with constant shear and the behavior of the solutions in different flow regions in the channel. The results of a numerical solution for a flow in a channel are given, and the results are compared with the known experimental data.

Simulation of flow geometry in a riffle‐pool stream

Abstract: The nature of the flow in most natural streams is gradually varied rather than uniform. This is particularly true of streams with coarse gravel bed material organized into relatively stable riffle and pool features. In spite of this, there are few applications of the gradually varied flow models (e.g. the Bernoulli equation) to such streams. This paper presents some initial results of a simulation of flow patterns in two riffle-pool reaches, using an open channel flow profile computation method based on an equation defining an energy balance between successive cross-sections separated by an incremental distance.

Flow turbulence generating and mixing device

Abstract: A device for generating special turbulence patterns in fluids flowing in pipes, such as for mixing, promoting chemical reactions, or accelerating the transfer of heat to or from the fluid through the pipe wall. Two or more sets of flow dividers are mounted in the pipe, each set including a first and second flow divider with septum panel elements that overlap longitudinally of the pipe. The first flow divider septum elements mutually diverge downstream in a selected longitudinal plane in longitudinally overlapping relationship with septum elements of the second flow divider mutually diverging upstream in a different longitudinal plane so as to divert the fluid in such manner that the flow regions adjoining the pipe wall are caused to exchange positions with flow regions in the vicinity of the pipe axis. By reversing the relative incline angles of the septum elements of corresponding flow dividers of successive sets alternately when a succession of two or more sets are installed in direct series, the desired effects are augmented.

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.