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.     

Hydraulics of Circular Drop Manholes

Circular drop manholes are widely employed in steep urban drainage systems. Drop manholes may lead to poor hydraulic conditions if their energy dissipation is inadequate. The dominant hydraulic features of drop manholes depend on the flow regimes, characterized in terms of the dimensionless impact parameter. Depending on the latter parameter, the energy dissipation can vary within large limits, affecting thereby the downstream flow features. Also, the water pool depth inside the manhole and the air entrainment have been studied in terms of both the hydraulic and geometric parameters. Moreover, the conditions for which a drop manhole generates flow choking at its inlet or outlet have been investigated. Empirical equations for practical manhole design are provided. The importance of suitable manhole aeration is highlighted.     

Hydraulics of Rectangular Dropshafts

A dropshaft is an energy dissipator connecting two channels with a drop in invert elevation. The hydraulics of vertical rectangular shafts was systematically investigated in seven configurations. A particular emphasis was on the effects of shaft pool, outflow direction, and drop height, while geometrically similar shafts (scale 3.1:1) were studied using a Froude similitude. The results demonstrate that rectangular dropshafts with 90° outflow are the most efficient energy dissipators. The shaft pool and drop height have little effect on the rate of energy dissipation. Recirculation time results exhibited marked differences between flow regimes and the longest dimensionless residence times were observed at low flow rates. Although basic flow characteristics were similar between model and prototype, observations of dimensionless bubble penetration depths and recirculation times showed some discrepancy, highlighting limitations of the Froude similitude for studies of air entrainment and residence times in dropshafts.     

Sequent Depth Ratio of a B-Jump

A B-jump is defined as the jump having the toe section located on a positively sloping upstream channel and the roller end on a downstream horizontal channel. This jump often occurs in the stilling basins with a horizontal bottom and located downstream of a steep channel. For a B-jump, a completely theoretical approach is not sufficient to solve the momentum equation and to establish the sequent depth ratio. In this paper, by using the laboratory measurements carried out in this investigation, some available empirical relationships useful for estimating the sequent depth ratio are tested. Then, by using the Π theorem of the dimensional analysis and the incomplete self-similarity theory, a generalized functional relationship for estimating the sequent depth ratio for different types of jumps is deduced. The estimate of the coefficient appearing in this relationship is dependent on the particular type of jump. In conclusion, the analysis established that the sequent depth ratio for a B-jump depends on a parameter E accounting for the toe section position, the upstream Froude number F1, and the channel slope.     

Turbulence Structure of Hydraulic Jumps of Low Froude Numbers

Turbulence characteristics of hydraulic jumps with Froude numbers of 2.0, 2.5, and 3.32 are presented. A Micro Acoustic Doppler velocimeter was used to obtain measurements of the velocities, turbulence intensities, Reynolds stresses, and power spectra. The maximum turbulence intensities and Reynolds stress at any section were found to decrease rapidly from the toe of the jump towards downstream within the jump and then gradually level off in the transition region from the end of the jump to the friction dominated open channel flow downstream. The maximum turbulence kinetic energy at each section decreases linearly with the longitudinal distance within the jump and gradually levels off in the transition region. The Reynolds stress and turbulence intensities within the jump show some degree of similarity. The dissipative eddy size was estimated to vary from 0.04 mm within the jump to 0.15 mm at the end of the transition region. The dominant frequency is in the range from 0 to 4 Hz for both horizontal and vertical velocity components.     

Velocity Distribution and Energy Dissipation along Stepped Chutes Lined with Wedge-Shaped Concrete Blocks

Stepped channels lined with wedge-shaped concrete blocks may constitute a low-cost alternative to provide overtopping protection of embankment dams if the discharge capacity of existing spillways is not adequate or even to be used as the main spillway of newly built embankment dams. This paper addresses the velocity distribution and the energy dissipation, downstream of the inception point, on stepped chutes lined with wedge-shaped concrete blocks. An experimental setup was developed with two flumes designed with a relative scale of 1∶2.5. Air concentration was measured with an optical probe in several cross sections of both flumes. The velocity profiles along chutes lined with wedge-shaped blocks with the upper face sloping downstream were analyzed. The measurements’ accuracy was checked by comparing discharges indicated by a facility flowmeter and obtained by the integration of velocity and air concentration profiles. The effect of the steps-slope in the energy dissipation is studied. Values of the Darcy-Weissbach friction factor are proposed for this type of chute lining, for transition flows, and for skimming flows.     

Minimum Specific Energy and Critical Flow Conditions in Open Channels

In open channels, the relationship between the specific energy and the flow depth exhibits a minimum, and the corresponding flow conditions are called critical flow conditions. Herein they are reanalyzed on the basis of the depth-averaged Bernoulli equation. At critical flow, there is only one possible flow depth, and a new analytical expression of that characteristic depth is developed for ideal-fluid flow situations with nonhydrostatic pressure distribution and nonuniform velocity distribution. The results are applied to relevant critical flow conditions: e.g., at the crest of a spillway. The finding may be applied to predict more accurately the discharge on weir and spillway crests.     

Hydraulics of 3D Plunge Pool Scour

The main flow features of three-dimensional plunge pool scour are explored in this experimental research for steady flow conditions. These include the maximum depth of the scour hole, its streamwise geometry, and the maximum width, the maximum height of the ridge, its shape in plan view, and its profile. Expressions for all these parameters are presented in terms of the basic scour variables, including the approach flow densimetric Froude number, the jet impact angle, the jet diameter, and the tailwater elevation above the originally horizontal sediment bed. This research is based on a previous work relating to two-dimensional plunge pool scour. Differences between the two phenomena are outlined, and the results are discussed in terms of engineering applications. The results of the two works allow for the prediction of the most salient features of plunge pool scour for both the dynamic and the static scour holes.     

Inception Point and Air Concentration in Flows on Stepped Chutes Lined with Wedge-Shaped Concrete Blocks

Stepped channels lined with wedge-shaped concrete blocks are a promising solution to provide overtopping protection for embankment dams if the discharge capacity of existing spillways is not adequate. The paper addresses the characteristics of the two-phase transition and skimming flows in stepped channels lined with this type of block. An experimental setup was developed with two flumes designed with a relative scale of 1:2.5. Air concentration was measured with an optical probe in several cross sections of both flumes. The scale effects are analyzed. An expression for the location of the inception point is proposed. The vertical air concentration profiles and their longitudinal variation are studied, considering data and models proposed by other researchers. The establishment of the uniform flow regime is analyzed.     

Hydraulics of Stacked Drop Manholes

This paper presents the results of an experimental investigation on flows inside stacked drop manholes (SDM). An SDM consists of two identical rectangular or square manhole chambers stacked together at an elevation difference. SDMs for different conditions were assessed on their ability to dissipate the energy of the approaching flow and their suitability to perform adequately under different flow conditions. Flow regimes were classified based on the inflow conditions and geometry of the structure in the first chamber and downstream outflows in the second chamber. An analysis based on the integral momentum equation was developed to estimate pool depths and energy losses under critical flow conditions. A fully surcharged stage with inflow and outflow pipes running full was also tested and velocity profiles were measured at a horizontal center plane to the opening connecting both shafts. Additionally, air flow rates were measured to assess the air demand into a large-height SDM.     

Energy Model to Predict Suspended Load Deposition Induced by Woody Debris: Case Study

Large woody debris (LWD) has been used repeatedly to create aquatic habitats. This study attempts to quantify and predict geomorphological changes induced by LWD. Six cylindrical bundles of LWD were anchored in a stream in central Ohio, and bed elevations were monitored for up to seven months. A model was developed to predict deposition downstream of the LWD. Sediments accumulated immediately downstream of the LWD structures. The average accumulation depth 0.25 m downstream of the LWD was 0.10 m. At 1.25 m downstream, accumulation depth averaged 0.07 m. The model to predict the sediment deposition had R2 values of 0.87–0.77, respectively, at the two downstream locations. The most important terms in the model were the Froude number and bankfull depth. An advantage of this model was the use of easily measurable variables including average bankfull velocities, depth, and cross-sectional area. This fact will facilitate the use of the model in field settings. Suggestions for future improvements to the model include calibration/validation in different streams, inclusion of a temporal variable, and sediment characterization.     

Experimental Approach to the Hydraulics of Vertical Slot Fishways

The performance of two particular designs of vertical slot fishways for two different slopes was studied in a wide range of discharges. Water depths were measured in almost the whole surface of pools. A linear relation between dimensionless discharge and depth of flow, and the same flow patterns for each design were found. With an acoustic Doppler velocimeter, three-dimensional velocities were measured at several levels in the entire pool to detect the structure of the flow and quantify velocity distribution. Two different regions in flow patterns were found: a direct flow region characterized by maximum velocities; and a recirculation region, defined by low velocities and horizontal eddies. For a given slope, the velocity at any point of the pool (particularly at the slot) may be considered independent of the discharge and constant with the depth. Some suggestions on kinetic turbulent energy are also made.     

Hydraulic Design of Stepped Spillways

An experimental study on a large model flume using fiber-optical instrumentation indicated that the onset of skimming flow is a function of critical depth, chute angle, and step height. Uniform mixture depths that determine the height of chute sidewalls and uniform equivalent clear water depths are described in terms of a roughness Froude number containing unit discharge, chute angle and step height. The spillway length needed to attain uniform flow is expressed as a function of critical depth and chute angle. The flow resistance of stepped spillways is significantly larger than for smooth chutes due to the macro roughness of the steps. The friction factor for uniform aerated flow is of the order of 0.1 for typical gravity dam and embankment dam slopes, whereas the effect of relative roughness is rather small. The energy dissipation characteristics of stepped spillways and the design of training walls are also discussed. The paper aims to focus on significant findings of a research program and develops design guidance to lessen the need for individual physical model studies. A design example is further presented.     

Hydraulics of Plane Plunge Pool Scour

Plunge pool scour involves a significant risk with trajectory spillways because of structural undermining at a dam foot or destabilization of adjacent valley slopes. An experimental program towards the understanding of plane plunge pool scour of a completely disintegrated rock surface was conducted, in which the following items received attention: jet shape, jet velocity, jet air content, tailwater elevation, granulometry, upstream flow to the scour hole, and the end scour profile in terms of the basic scour features. These effects were experimentally investigated based on a systematic variation of the governing scour parameters. The results of this paper allow answering questions that have so far not been addressed. Design equations were proposed to sketch the main tendency of the data sets. The significant effect of the densimetric particle Froude number was substantiated. This research may be used to estimate the prominent scour features for nearly two-dimensional jet arrangements involving a pre-aerated high-speed flow.     

Resistance Characteristics of Surface Aerators

The resistance characteristics in terms of power consumption, interpreted in terms of Power number (P0), of unbaffled surface aeration systems consisting of flat bladed impellers, were studied in two shapes of surface aerations tanks: square and circular. Experiments were conducted in three different sizes in each of the geometrically similar unbaffled square and circular surface aerators. Results have shown that the P0 cannot be simulated singularly either with Reynolds number R or with Froude number as there are scale effects; hence there appears to be a need for incorporating the effects of both R and F. It is found that P0 is uniquely related to a parameter X ( = F4/3R1/3), which is defined as a parameter governing the theoretical power per unit volume for both shapes of aeration tanks; however, such relationships are different for both shapes of aerators. Interestingly P0 values are always higher in square surface aerators than in circular surface aerators, which suggests that the circular surface aerators require less power input than the square surface aerators. The usefulness of such correlations was demonstrated in estimating the power requirement while achieving a required oxygen transfer coefficient in surface aerators.     

Supercritical Flow over a Dentated Sill

Experimental analysis concerning supercritical flow over a dentated sill in nonsubmerged conditions and the local scour downstream of this sill is presented. In this case, the energy dissipation is incomplete so that a scour control downstream of the hydraulic structure could be required. The use of this type of dissipation device could be needed in cases where the maximum flow depth upstream of the sill must be limited to satisfy physical or structural conditions. This could happen, for instance, in the restoration of stilling basin in gravity dams and at the outlet of diversion systems. Experimental and theoretical results, useful in the design of this type of stilling basin and scour control, are presented in the paper, with an application to the case of the Molato Dam in Italy.     

Direct Equations for Hydraulic Jump Elements in Rectangular Horizontal Channel

Many problems in the design of stilling basins require a knowledge of various elements of a hydraulic jump with known values such as discharge intensity and the energy loss in the jump. Even for a simple case of a rectangular horizontal channel the solutions of equations involve tedious methods of trial and error. In this paper, direct explicit empirical equations for prejump and postjump depths and specific energies in a rectangular horizontal channel have been developed. These present forms of equations for hydraulic jump elements having very high accuracy and are applicable for a very wide range of values of discharge intensity and head loss without any limitations in comparison to other methods attempted so far.     

Turbulence Dissipation in Stirred Jars

A two-compartment analytical model was developed to estimate the turbulent dissipation rates in a standard jar stirred by a radial impeller. A simple numerical simulation was also performed to support the analytical arguments. Results of the numerical model showed that away from the impeller, the turbulent dissipation rate rapidly decays proportionally with z?2, where z is the axial distance. The turbulent velocity away from the impeller region showed a decay proportional to z?0.5. Although the dissipation rates at the wall boundary layer were higher compared to those in the tank interior, the total energy dissipated in the boundary layer is smaller compared to that expended in the impeller zone.     

Design of a Scroll Vortex Inlet for Supercritical Approach Flow

Vortex drop shafts are used in urban drainage systems to connect two sewers located at considerably different elevations. After their introduction in 1947, these were studied with particular reference to subcritical approach flow. Vortex shafts for supercritical approach flow can also be used, but the intake structure may have relatively high cost due to the complex geometry. The present study includes experimental results of a specific investigation on the changes to be made in the supercritical approach channel if a subcritical vortex intake is used. The experimental investigation analyzes the effect of a hydraulic jump on the performance of vortex intake structure to define appropriate technical solutions, essentially consisting in a negative step to be located along the supercritical approach channel. Design criteria are finally presented for the evaluation of the step height and its distance from the vortex intake structure.     

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.