Flow Conditions of Undular Hydraulic Jumps in Horizontal Rectangular Channels

The flow conditions of undular jumps for fully developed inflow condition have been investigated systematically. If the inflow Froude number is larger than 1.2, an undular jump has lateral shock waves near the toe of the jump. For a narrow channel, the shock waves cross upstream of the first wave crest, and the flow conditions of undular jumps depend on the aspect ratio and the inflow Froude number. In contrast, for a wide channel the shock waves do not cross upstream of the first wave crest, and the flow conditions of undular jumps are independent of the aspect ratio. The flow conditions of undular jumps are classified by considering the cross position of the lateral shock waves and the inflow Froude number. Also, the hydraulic conditions for the formation of nonbreaking and breaking undular jumps are determined. The effect of the Reynolds number on undular-jump formations is discussed, and changes of the flow conditions with the Reynolds number are described.     

Ski Jump Hydraulics

Ski jumps are a major element of each dam spillway because these are the only structures able to accomplish satisfactory energy dissipation for takeoff velocities in excess of some 20?m/s. This research aims to add to several hydraulic problems with ski jumps that have not yet been systematically solved so far. Based on an experimental campaign, the following problems were addressed: (1) pressure head maximum and pressure distribution along a circular-shaped flip bucket; (2) takeoff characteristics for a certain bucket deflection and a relative bucket curvature including the jet trajectories of both the lower and the upper nappes; (3) impact characteristics in a prismatic tailwater channel with details of shock wave formation and height of recirculation depth; (4) energy dissipation across the ski jump, from the upstream channel to downstream of jet impact; and (5) choking flow conditions by the flip bucket. These results demonstrated the significant effect of the approach Froude number, the relative bucket curvature and the bucket angle. The results allow immediate application to the design of ski jumps in hydraulic engineering.     

Particle Image Velocity Measurements of Undular and Hydraulic Jumps

Measurements of the mean and turbulent flow fields in undular and hydraulic jumps have been acquired with single-camera particle image velocimetry (PIV). Three Froude numbers, ranging from 1.4 to 3.0, were studied, and in each case data were collected at numerous streamwise locations. The data from these streamwise locations were subsequently compiled into spatially dense ( ～ 80,000 grid points) “mosaic” images encompassing both the supercritical and subcritical portions of the flow. The measured mean and turbulent velocity fields provide more detailed views inside undular and hydraulic jumps than were previously available from studies using pointwise measurement techniques. The two-dimensional spatial density of the measurements provides for the determination of gradient-based quantities such as vorticity. The potential for determining boundary shear stress from the velocity data is evaluated with several methodologies. The results are found to be consistent with recent measurements made using Preston tubes. Discussion of the technical aspects of and difficulties involved with applying PIV to hydraulic jumps is provided. These challenges included the identification and tracking of the free surface through image analysis and the scattering of laser light by entrained air bubbles in the roller region.     

Hydraulic Jumps in Sloping Channels: Sequent Depth Ratio

A large variety of hydraulic jumps on horizontal and sloping inverts at the end of an ogee standard weir is investigated. An ogee standard weir was used to create supercritical flow and slopes of 0.0, ?0.025, ?0.05, ?0.075, and ?0.10 were built downstream of the weir. Based on the momentum equation in the horizontal direction, a method to predict the sequent depth ratio is presented. The theory agrees well with the results of the writers and previous investigators. A correlation was developed to predict the minimum Froude number needed to establish jumps on negative slopes. Observations showed that in those cases where the gravity force component in the jump was opposite to the flow direction, the water surface of the surface roller became undular and unstable. The hydraulic jump on an entirely adverse slope was almost impossible to control. The analysis of experimental data showed that the negative slope of the basin reduces the sequent depth ratio, while a positive slope increases the sequent depth ratio.     

Deflector Ski Jump Hydraulics

Ski jumps are a standard element of dam spillways for an efficient energy dissipation if takeoff velocities are large, and stilling basins cannot be applied. This laboratory study investigates the hydraulic performance of a triangular-shaped, rather than the conventional circular-shaped, bucket placed at the takeoff of ski jumps. The following items were addressed: (1) pressure head maximum and pressure distribution along the triangular-shaped bucket; (2) takeoff characteristics as a function of the bucket deflector angle and the relative bucket height including the lower and the upper jet trajectories; (3) jet impact characteristics in a prismatic tailwater channel including the shock wave formation and the height of recirculation depth below the jet cavity; (4) energy dissipation across the ski jump, from the approach flow channel to downstream of jet impact; and (5) choking flow conditions of the flip bucket. A significant effect of the approach flow Froude number, the relative bucket height, and the deflector angle is found. A comparison with previous results for the circular-shaped bucket geometry indicates a favorable behavior of the novel bucket design.     

Comparison of FISH PRINS, and conventional and fluorescent PCR for single-cell sexing: suitability for preimplantation genetic diagnosis

Valved homograft conduits play an important role in the right ventricular outflow tract (RVOT) reconstruction for the surgical treatment of complex congenital heart disease. An excellent immediate rather than long-term outcome could be obtained. The hemodynamics for late failure, however, remained unclear. In vitro pulsatile flow visualization was not conducted before. A simplified right heart duplicator system was set up and driven under physiologic conditions. Polystyrene of 0.18 mm in diameter was applied as the tracing particle. Flow characteristics of models of normal pulmonary circulation as well as pulmonary artery atresia with the RVOT reconstructed utilizing valved and non-valved extracardiac conduits were observed. Flow patterns in the normal pulmonary circulatory model were mainly of axial flow associated with small scope of flow disturbances. A single vortex in the right ventricle was noted in diastole. In the pulmonary artery atresia model, a couple of vortexes were found in the right ventricle, a secondary flow in the main pulmonary artery, and a stronger secondary flow than in the normal pulmonary circulatory model in the two branches in both systole and diastole. A secondary flow was found in the proximal, an axial flow was observed in the distal portion of the extracardiac conduit with normal bioprosthetic valves and a secondary flow was observed in the entire conduit with stenotic bioprosthetic valves. The secondary flow intensity became stronger with the development of the stenosis. Severe insufficiency occurred in the bileaflet ceramic tilting-disc prosthesis during the entire cardiac circle, i.e., the prosthesis was in a maximum open position. Severe reverse flow could be found in the extracardiac conduit in the deceleration phase. Concavity of the crank shaft was found by examination to be filled with tracing particles and the prosthesis became stuck. Model of RVOT reconstruction with non-valved conduit yielded reverse flow inside the extracardiac conduit as well. Secondary flow may occur in normal or diseased extracardiac conduit for RVOT reconstruction. If micro-thrombus of over 0.18 mm in diameter attached in the concave of the crank shaft of a bileaflet tilting-disc prosthesis under a condition of resistance as occurred in the present study, the prosthesis may become stuck. Model of RVOT reconstruction with non-valved extracardiac conduit yielded reverse flow inside the conduit, of which the flow pattern was of greater energy consumption. Thus, a non-valved conduit should be avoided in clinical practice as far as possible.     

Lagrangian Modeling of Weakly Nonlinear Nonhydrostatic Shallow Water Waves in Open Channels

A Lagrangian, nonhydrostatic, Boussinesq model for weakly nonlinear and weakly dispersive flow is presented. The model is an extension of the hydrostatic model—dynamic river model. The model uses a second-order, staggered grid, predictor-corrector scheme with a fractional step method for the computation of the nonhydrostatic pressure. Numerical results for solitary waves and undular bores are compared with Korteweg-de Vries analytical solutions and published numerical, laboratory, and theoretical results. The model reproduced well known features of solitary waves, such as wave speed, wave height, balance between nonlinear steepening and wave dispersion, nonlinear interactions, and phase shifting when waves interact. It is shown that the Lagrangian moving grid is dynamically adaptive in that it ensures a compression of the grid size under the wave to provide higher resolution in this region. Also the model successfully reproduced a train of undular waves (short waves) from a long wave such that the predicted amplitude of the leading wave in the train agreed well with published numerical and experimental results. For prismatic channels, the method has no numerical diffusion and it is demonstrated that a simple second-order scheme suffices to provide an efficient and economical solution for predicting nonhydrostatic shallow water flows.     

Design of Circular Urban Storm Sewer Systems Using Multilinear Muskingum Flow Routing Method

In this study, a multilinear Muskingum method is presented for hydrologic routing through circular conduits. In order to increase accuracy, the reference discharge is assumed to be a nonlinear function of conduit diameter, Manning coefficient, bed slope, and peak discharge of the inflow hydrograph. The reference discharge function has been determined using a nonlinear regression technique. Flow depths are computed at every time step by solving the continuity equation using an implicit finite difference scheme. Many storm hydrographs were routed through circular conduits of various sizes by the proposed model. The calculated routed hydrographs and water surface profiles indicate close agreement with those obtained by solving Saint Venant equations. Using this method, a branched urban sewer system was designed. This indicates that the method can be easily implemented for design purposes because of its simplicity, accuracy, and computational efficiency.     

Flow Establishment in Elastic Pipes

The paper addresses the problem of unsteady flow in an elastic pipe, starting from rest and tending towards a turbulent steady state. Careful experiments, involving uncommonly long, smooth-walled conduits, indicate that the hydraulic performance of an elastic pipe is controlled by its finite speed of response to a change in boundary conditions. The actually occurring, pulsatile flow is well described by a water-hammer analysis of the establishment process, but disagrees significantly with theoretical predictions based on assumed conduit rigidity. Flow accelerations, both temporal and convective, are shown to cause a significant increase in the values of the lower-critical Reynolds number of laminar-to-turbulent transition.     

Hydraulics of Broad-Crested Weirs with Varying Side Slopes

The flow of water over a trapezoidal, broad-crested, or embankment weir with varying upstream and downstream slopes has been investigated. Data are presented comparing the effect of slopes of 2H:1V, 1H:1V and vertical in various combinations on the upstream and downstream faces of the weir. Pressure and surface profiles were self-similar for all cases tested. Increasing the upstream slope to the vertical decreased the height of the surface profile and, hence, the static pressure of the crest. It also reduced the discharge coefficient. The variation in downstream static pressures was negligible though. Varying the downstream slope had a negligible effect on the surface and pressure profiles over the weir. Changes in flow were constrained to the region downstream of the crest. Cavitation could occur at the downstream corner of the weir if the upstream head was sufficiently high and a sloped face was used. This paper presents data that will be of use in the design of hydraulic structures for flow control and measurement.     

Undular Tidal Bores: Basic Theory and Free-Surface Characteristics

The present study examines the free-surface properties of undular tidal bores observed for 1相似文献   

Discharge Rating Equation and Hydraulic Characteristics of Standard Denil Fishways

This paper introduces a new equation to predict discharge capacity in the commonly used Denil fishway using water surface elevation in the upstream reservoir and fishway width and slope as the independent variables. A dimensionless discharge coefficient based only on the physical slope of the fishway is introduced. The discharge equation is based on flow physics, dimensional analysis, and experiments with three full-scale fishways of different sizes. Hydraulic characteristics of flow inside these fishways are discussed. Water velocities decreased by more than 50% and remained relatively unchanged in the fully developed flow downstream of the vena contracta region, near the upstream baffle where fish exit the fishway. Engineers and biologists need to be aware of this fact and ensure that fish can negotiate the vena contracta velocities rather than velocities within the developed flow region only. Discharge capacity was directly proportional to the fishway width and slope. The new equation is a design tool for engineers and field biologists, especially when designing a fishway based on flow availability in conjunction with the swimming capabilities of target fish species.     

Modeling Study of Free Overfall in a Rectangular Channel with Strip Roughness

Results from combined laboratory experimental and turbulent numerical modeling studies are presented to investigate the effects of bed roughness (discrete square strips) and slope on the flow over a free overfall in a rectangular channel. A broad range of model parameters such as the bed roughness, channel slope, and incoming upstream Froude number is investigated. The water surface profiles upstream of the brink of the channel, the velocity fields in cavity between two strips, and end depth (water depth at the brink of the channel) are simulated, measured, and discussed for various input conditions. The results show that for a given dimension of bed roughness the relative spacing of roughness (defined as the ratio of the center to center distance to the height of the strip) has a significant effect on the flow. The computational results are in good agreement with the experimental measurements.     

3D Simulation of Combining Flows in 90° Rectangular Closed Conduits

Combining flows are encountered often in environmental engineering and hydraulic engineering. Experimental data are available to assist the engineers who need the various loss coefficients associated with combining flows in closed conduits. For the combining flows in 90° rectangular conduit junctions, the Reynolds averaged Navier–Stokes equations are applied, while using the three-dimensional k-ω model. The energy loss coefficients and the mean flow pattern are obtained and validated by experimental data. The numerical modeling is less time-consuming and less expensive to obtain the various flow parameters needed for engineering design.     

Full-Flowing Collection Conduits with Nonuniform Inflow

Collection conduits flowing full with nonuniform inflow (variable rate of increase in flow with distance along the conduit length) include well screens (vertical and directionally drilled); submerged effluent collectors; and certain types of inboard weir configurations for settling tanks. Certain subsurface drains used in environmental engineering applications and civil engineering more generally may be inadvertently designed for full-flowing conditions. Formulation of the problem for such collection conduits is presented in terms of the applicable differential equation, slope invariance, the frictionless solution for a general cross section, a uniform-inflow solution, and the difference formulation. The importance of checking inflow uniformity is discussed and exemplified. Dimensional analysis is then employed to demonstrate the relationship between variables, leading to a new generalized numerical solution. That solution is presented in a graphical form which provides further useful display of the relationships between variables and quantitative information for design and analysis. The detrimental effects of flowing-full conditions in subsurface drains is demonstrated, and it is noted that existing design methods may unintentionally cause such conditions to occur.     

Modeling Study of the Flow past Irregularities in a Pressure Conduit

Results are presented to investigate the characteristics of turbulent flow in a pressure conduit, such as water supply pipes and flood discharging tunnels. The turbulent flow governing equations, the Reynolds-averaged Navier–Stokes equations, in conjunction with a k–ε turbulent model are numerically solved using SIMPLEC. The study focuses on the modeling and calculation of the flow velocity field, pressure distribution, and the incipient cavitation number of the surface irregularities in the conduit. Different types and sizes of irregularities are simulated for various incoming flow velocities. The computed results are in good agreement with laboratory experimental data.     

Interaction of Nonlinear Progressive Waves with Two Serially Arranged Submerged Obstacles

The purpose of the present study is to develop a numerical model for the investigation of water waves propagating over a pair of impermeable submerged obstacles. The mathematic model is formulated by coupling solutions of the Navier–Stokes equations and transport equations for the surface elevation using the volume of fluid method. Based on a staggered computational mesh, an explicit numerical algorithm is employed with a predictor–corrector procedure of pressure and velocity field. The proposed model provides good agreement with other experimental results and validates its good performance. Regarding the spatial harmonic evolutions of various cases, it is noted that the present fluctuating mode of harmonic amplitudes exists upstream and at the gap between obstacles. The results show that the nonlinearity of propagating waves becomes stronger than the initial wave in such areas, and reveals much steeper wave profiles compared to the initial ones. The fluctuating harmonic amplitudes vary with the gap width and form two hydrodynamic cycles. The vortices play an important role in the wave reflection as they form a water column wall to reflect the incoming waves. The reflection ratio depends on the extent of vortex development near the upstream obstacle. The maximum wave reflection occurs in cases with dimensionless gap width S/L equal to 3/8 and 7/8 in this study.     

Choked Flows through Short Contractions

This paper presents a study on choked flows through short, lateral contractions in subcritical open channels. A new discharge equation is developed based on the conservation of energy and experimental data with a wide range of opening ratios (ratio of contracted width-to-total width). The theoretical derivation accounts for the critical flow conditions that take place in the contraction under choking conditions. The effects of opening ratio σ, encroachment structure shape, inlet angle α, and relative contraction length L* on discharge coefficients are considered. The coefficients of the newly developed discharge equation are determined using a total of 186 sets of choking experiments conducted by various researchers. The analysis shows that the discharge coefficient is mainly affected by σ and may vary between 0.29 and 0.54 for the range of σ values used in the study (0.12–0.88). It is shown that the discharge coefficient (correspondingly the discharge) can vary up to 16% for encroachment-structure shape changing from sharp corner to rounded corner conditions—up to 11% for α going from 30° to 90° and up to 6% for L* ranging from 0 to 1.33. This study extends the traditional choking analysis to severe contractions. The proposed equation fits previous experimental data well and can be used to predict either the water discharge through a contraction for a given upstream depth or the water depth upstream from a contraction corresponding to a given discharge under choking conditions.     

Subcritical 90° Equal-Width Open-Channel Dividing Flow

Based on experimental observations, for a subcritical, right-angled, equal-width, open-channel dividing flow over a horizontal bed, the contraction coefficient at the maximum width-contracted section in the recirculation region is almost inversely related to the main channel upstream-to-downstream discharge ratio. The energy heads upstream and downstream of the division in the main channel are found to be almost equal. Under the assumption that the velocities are nearly uniformly distributed at the considered boundaries, the depth-discharge relationship follows the commonly used energy equation. The predicted results correlate fairly with the experimental data from this and other studies. The energy-loss coefficient of a division is expressed in terms of discharge ratio, upstream Froude number, and depth ratio. An expression for practical engineering applications is to determine the maximum possible branch-channel discharge at a given upstream discharge with a prescribed downstream Froude number or the maximum possible downstream Froude number if both branch- and main-channel discharges are prescribed.