Approach Flow Froude Number Research Articles

Numerical study for the computation of critical submergence for side circular intake under uniform flow

This paper discusses a numerical model study for the simulation of flow characteristics and critical submergence for a laterally placed horizontal circular bottom intake under uniform flow. The proposed model simulates the free surface using the volume of fluid model to check the vortex formation at critical submergence. A new combined approach using phase volume fraction and swirl strength-based vortex identification mechanism is used to compute the critical submergence. The swirl strength-based vortex identification mechanism can show the vortex tube in approach flow with swirl generated at the free surface due to the axial flow withdrawal through side bottom intake at critical submergence. The computational fluid dynamics (CFD) model results were validated using experimental data, which showed a maximum error of less than ±10% in the prediction of the critical submergence. The effect of significant parameters like intake and approach flow Froude number and sill height of intake on the critical submergence is discussed. The results of this study help practitioners to adopt CFD-based numerical modelling for the design of water intakes instead of entirely relying on physical model studies, which require more finance and time.

Performance and Design of a Stepped Spillway Aerator

Stepped spillways are frequently limited to specific discharges under around 30 m2/s due to concerns about potential cavitation damages. A small air concentration can prevent such damages and the design of bottom aerators is well established for smooth chutes. The purpose of this study is to systematically investigate the performance of a deflector aerator at the beginning of stepped chutes. Six parameters (chute angle, step height, approach flow depth, approach flow Froude number, deflector angle and deflector height) are varied in a physical model. The spatial air concentration distribution downstream of the aerator, the cavity sub-pressure, water discharge and air discharges are measured. The results describe the commonly used air entrainment coefficient, the jet length, as well as the average and bottom air concentration development to design an aerator. The lowest bottom air concentration measured in all tests is higher than the air concentration recommended in literature to protect against cavitation damages. And, unlike smooth chutes, there appears to be no significant air detrainment downstream of the jet impact. One deflector aerator seems therefore sufficient to provide protection of a stepped spillway.

Energy dissipation of slot-type flip buckets

The energy dissipation is a key index in the evaluation of energy dissipation elements. In the present work, a flip bucket with a slot, called the slot-type flip bucket, is theoretically and experimentally investigated by the method of estimating the energy dissipation. The theoretical analysis shows that, in order to have the energy dissipation, it is necessary to determine the sequent flow depth h1 and the flow speed V1 at the corresponding position through the flow depth h2 after the hydraulic jump. The relative flow depth h2 / ho is a function of the approach flow Froude number Fro, the relative slot width b/Bo, and the relative slot angle θ/β. The expression for estimating the energy dissipation is developed, and the maximum error is not larger than 9.21%.

Flume experiments on baffle-posts for retarding open channel flow

ABSTRACTPresented are the results of flume experiments on the flow-retarding performance of baffle-post structures in openwater flow. Such structures consist of one to two parallel rows of unsubmerged posts that retard an approach flow, reducing flow velocity, increasing flow depth, and altering lateral distribution of flow. The results relate headloss and flow depth increase at the structure to lateral and streamwise variations in post spacing, post diameter, and approach flow conditions, and represent average velocities of flow through the structure. For given approach flows, the flow-retarding performance of baffle-post structures is shown to be much more sensitive to lateral spacing of posts and approach flow Froude number, than to streamwise spacing (for double row structures) and approach-flow depth relative to post diameter. Estimates are given for the percentage increase in water depth that baffle posts will produce. This information informs the design of baffle-post structures and evaluation of the backwater effect.

Ski-jump trajectory based on take-off velocity

The theoretical method estimating ski-jump trajectory was paid attention to and modified. The present method is based on the effects of the take-off velocity and the angle in the sensitivity analysis of parameters. The experiments are conducted for a triangular-shaped flip bucket in order to reveal the relationships between the take-off velocity and its influencing factors. The results show that, the take-off velocity has a much larger effect on the impact point than the take-off angle. The take-off velocities of both upper and lower trajectories are all functions of the approach flow Froude number, the deflector height and the deflection angle, especially, the results of the deflection angle of 25° could be directly used when this angle is larger than 25°. Meanwhile, this method is checked and the maximum relative errors of both xUcal and xLcal are 5.1% and 5.6%, respectively.

Flow choking over weir flow slit-type flip buckets

AbstractThe flow choking may occur for weir flow slit-type flip buckets under common operation conditions. An estimation method is developed through introducing a comprehensive coefficient to determine the approach flow Froude number for the flow choking to occur in those flip buckets. The error of the present method relative to the experimental data is less than 5%. The results show that, the Froude number for the flow choking to occur is related to the contraction ratio and the contraction angle of the flip buckets. When the flow choking occurs, the upper jet trajectory decreases and the lower one is almost not affected, and the dynamic pressures on the bottom and the sidewalls increase due to the flow profile rising on the flip buckets.

Scale Modeling of Wooden Debris Accumulation at a Debris Rack

To prevent damages due to transported wooden debris during a flood, the debris is often retained in defined zones upstream of populated areas using a debris rack. Because thorough numerical modeling of the debris accumulation process is still challenging given the randomness of debris accumulation and the interaction between sediment and wooden debris, one main tool to study debris retention structures involves small-scale modeling. The main purpose of this experimental study is to analyze various aspects regarding the modeling of wooden debris and to provide information on reducing the laboratory effort. The focus is on the various factors influencing the accumulation process and the backwater rise and whether or not it is important to model them properly in small scale. The results indicate a significant effect of the approach-flow Froude number on the debris accumulation process, whereas the debris properties have only a minor effect on the resulting backwater rise so that effects of debris mixture are negligible.

Deflector Effect on Chute Flow

Jet deflection and energy dissipation of ski jumps guarantee the safety of hydraulic structures. Deflectors on spillways and bottom outlets are mostly complex constructions. The aim of this study is to find simple-shaped deflectors allowing for jet deflection into the tailwater, thereby characterizing the parameters of the trajectory under different approach flow conditions. The test program included eight right-angled tetrahedrons and two vertical plate deflectors. A systematic variation of the approach flow depth and Froude number, in combination with different deflector alignments, resulted in basic principles for deflector design. To study scale effects caused by viscosity and surface tension, three symmetric deflectors were tested as a model family at different approach flow depths. The results indicate the importance of the approach flow Froude number and the relative deflector height on the jet trajectory. The relevant jet parameters, including the deflection angle, the maximum jet elevation, and the jet impact onto the tailwater channel, are specified.

Supercritical flow profile improvement by means of a convex corner at a bend inlet

A novel method for the reduction of wave height along the outer wall of a bend is introduced by adding a convex corner to the inner bend wall. The negative waves emitted from the convex corner are then superimposed on the positive waves caused by the outer bend wall. The interaction of positive and negative waves transforms the original single-humped wave along the outer wall to a lower double-humped wave. The optimum expansion angle of the convex corner is a function of the offset width to the bend width, the radius of curvature to the bend width, and the approach flow Froude number. Numerical studies indicate that the convex corner may be used in a wide range of safe conditions free from cavitation damage. By using an optimized convex corner, the wave height may be reduced between 10 and 45%.

Flow through sharp-crested rectangular side orifices under free flow condition in open channels

Abstract Side orifices are widely used in irrigation and environmental engineering to spill or divert water from a channel. Flow characteristic of sharp-crested rectangular orifices under free flow condition in open channels is studied in the present paper. Existing discharge equations are checked for their accuracy using the data collected in the present study and available data in the literature and a new discharge equation has been proposed. The coefficient of discharge mainly depends on the approach flow Froude number and ratio of the size of orifice and bed width of the channel. Relationships for the coefficient of discharge, treating the orifice as large and small were developed. The computed discharges using these relationships were within ±5% of the observed ones. Measurement of three-dimensional velocities and visualisation of streamlines in a horizontal plane at the centerline of the orifice indicates that for the flow of low Froude number, almost all the streamlines divert towards the orifice. However, in the case of high Froude number flows, only those streamlines which are close to the side orifice are diverted towards the orifice. The opposite side of the boundary has significant effect on the diverted discharge of low Froude number compared to the flow of high Froude number. Circular orifice has been found to be more efficient compared to the rectangular orifice of the same opening area.

Probability of Drift Blockage at Bridge Decks

Drift seriously increases the destructive power of a flood event. Drift accumulations and blockages at river bridges are a widespread problem, possibly leading to their total destruction. Although drift is a major threat, limited knowledge is currently available on the likelihood of drift blocking. Drift either accumulates at a single pier, or it spans between two or more piers, or it gets blocked at the bridge deck. The main purpose of this experimental study is to analyze the drift-blocking probability at bridge decks depending on: (1) drift dimensions, (2) freeboard, (3) flow characteristics, and (4) bridge characteristics. Systematic model tests include the accumulation of both single logs and rootstocks. The test flow conditions represent a major flood event, where the freeboard tends to zero and the drift is able to touch the bridge deck. The results indicate significant effects of the freeboard, the approach flow Froude number, and the bridge characteristics on drift accumulation. They allow for an estimation of the blocking probability and therefore can be used as a risk assessment tool to identify endangered bridges prior to a flood event. The model tests demonstrate further the randomness of the blocking process, resulting occasionally in a wide scatter of data.

Discharge characteristics of sharp-crested circular side orifices in open channels

A side orifice is a flow diversion structure provided in one or both side walls of a channel to spill/divert water from the main channel. It is widely used in irrigation and environmental engineering. Analytical and experimental studies related to the discharge characteristics of sharp-crested circular side orifices in open channels under free flow conditions have been presented in this paper. Considering the side orifice as large, the discharge equation for the side orifice is derived analytically. Experiments were performed to estimate the coefficient of discharge which depends on the approach flow Froude number and ratio of the diameter of the orifice and bed width of the channel. Relationships for the coefficient of discharge, considering the orifice as large and small were developed. Such relationships were used to compute the discharge through the orifice for data not used for proposing such relationships for the coefficient of discharge. The computed discharges were within ±5% of the observed ones. The average percentage error in computation of discharge through the orifice considering it as large and small are, respectively, 1.59% and 1.66% which are practically the same. Therefore, it is recommended that the discharge through the side orifice can be computed considering it as a small orifice within the range of data used in the present study.

Chute Aerators. II: Hydraulic Design

Chute aerators are applied if cavitation damage on spillways is expected or observed. The aerator efficiency is usually described with the ratio of the air discharge entrained through the air supply ducts and the water discharge, which does however not account for the resulting air concentration distribution within the flow or for air detrainment. The present study investigates the streamwise development of the air transport along the flow downstream of chute aerators. Based on an extensive test program in which six governing parameters were systematically varied, the development of the average and the bottom air concentrations is provided up to the self-aeration point. Based on this information, an optimization of aerators in terms of increased air entrainment and reduced detrainment rates is possible, by assuming minimum required air concentrations. The main parameters influencing the air transport downstream of aerators are the approach flow Froude number, the deflector angle and the chute bottom angle.

Grade control for urban flood channel design

Grade control by drop structure is a common practice to design a steep channel. For a given design discharge, the drop height is determined by the pre-selected permissible flow Froude number or flow velocity. Design parameters for the energy dissipation over a drop include channel lining roughness, approach flow Froude number, drop number, and downstream jump in the stilling basin. All these design parameters shall be collectively optimized to provide a safe and functional structure. This paper reviews the current design procedure and then presents a methodology to determine the drop height by maximizing the energy dissipation. Design parameters include the limiting Froude number and channel roughness. The sensitivity test conducted in this study suggests that the limiting Froude number for drop structure designs be between 0.6 and 0.8. The optimal dissipation rate can be 80–85% of the specific energy associated with the approach flow.

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.

Aeration Characteristics of Ski Jump Jets

Scour downstream of ski jumps may be avoided by jet deflection to an area where the energy dissipation is accomplished. The main purpose of this experimental study was the analysis of the jet air entrainment downstream of a ski jump, both for pure water and preaerated approach flow conditions. A systematic variation of the Froude number and the flow depth in the approach flow channel resulted in a range of discharge characteristics, whereas the geometry of the ski jump was maintained for all tests. The air concentration profile was measured at different locations downstream from the ski jump to evaluate the: (1) jet air concentration distribution; (2) location of minimum air concentration along the mixture flow jet and development of the minimum and the cross-sectional average air concentrations; (3) jet trajectories; and (4) process of air entrainment characteristics and jet disintegration. The results demonstrate the significant effect of the approach flow Froude number, the approach flow depth, and of preaeration on jet disintegration.

Composite reliability model for local scour around cylindrical bridge piers

Bridge scour is an extremely complex phenomenon because of the random characteristics of sediment laden flow in close proximity to piers and abutments. This occurrence leads to high uncertainties and unavoidable risk in bridge pier and abutment design. In this study, a composite reliability model is developed for the reliability assessment of bridge pier scour using static resistance – loading interference. Based on the physical interpretation of the phenomenon and a statistical analysis of the available information, the relative maximum scour depth (corresponding to the minimum required relative pier footing elevation) and the linear combination of the relative approach flow depth and flow Froude number are defined as the system resistance and external loading, respectively. By examining a set of laboratory and field data, a two-parameter bivariate lognormal distribution is found to represent the joint probability density function of resistance and loading. Reliability expressions are developed in terms of resistance. Use of the model is illustrated in a practical application in which a relationship is obtained between the reliability and safety factors under various return periods. This information is of importance in decision making.Key words: reliability, bridge pier, scour, resistance, loading, safety factor, return period.

Dispersion in an open-cut coal mine in stably stratified flow

Discharges from combustion within a coal pit which occur during night-time inversion conditions may result in stagnant accumulation of smoke and dangerous gases which could inhibit mining operations. A wind-tunnel model study was performed to identify the range of flow and mixing conditions which could exist when stably stratified atmospheric surface flows pass over a large open pit. Flow penetration into the pit depended upon approach-flow stability (Froude number) and the strength of the thermal inversion within the coal pit. Measurements of wind speed and temperature were made upwind, within and downwind of the pit. Concentration measurements were made within the pit, of surface sources released along pit walls. Pollutant levels were found to be strong functions of the approach-flow pit Froude number, source location, and release time.

Initiation of ice jams — a laboratory study

Ice jam initiation by a simple partial surface obstruction in a channel was studied experimentally in laboratory flumes using polyethylene, paraffin, as well as real ice parallelepipeds, as model ice floes. The important dependent parameter under study was the critical surface concentration of floes at the gap in the surface obstruction at which floes would form a stable arch across the gap and an ice jam would be initiated. This critical floe concentration Cg* was found to be independent of the ratio of gap width to flume width and to be a decreasing power function of the ratio of floe size to gap width. In addition Cg* was found to be independent of the approach flow Froude number for flow velocity less than the critical submergence velocity of an ice floe, for artificial model floes, but to increase with increasing Froude number when real ice floes were used. This difference and other quantitatively different results depending on whether natural ice blocks or plastic blocks were used as model ice floes were tentatively attributed to differences in floe material characteristics, mainly interparticle friction force and surface tension property, the latter affecting significantly the critical submergence velocity of thin plastic blocks as compared to that of natural ice floes of the same size and density.