Hydraulic Relations for Clinging Flow of Sharp-Crested Weir

Available discharge coefficient formulas for sharp-crested weirs are only applicable to the free-flow regime. To extend the range of discharge measurement by a rectangular sharp-crested weir, critical heads of the transition flow regime, the head-discharge relation for clinging and free flow, and the discharge coefficient for clinging flow were investigated experimentally based on more than 300 experimental points with head ranging from 0.0048 to 0.0455 m. The results indicate that the transitions from clinging to free flow and vice versa do not occur at the same head. Upper and lower critical heads, Hu,crit and Hl,crit, can be identified at which these transitions occur. For the condition studied, the head relation between clinging and free flow is found to be linearly correlated at the same discharge. Expressions for the discharge coefficient for clinging flow are developed.     

Numerical Simulation of Shallow-Water Flow Using a Modified Cartesian Cut-Cell Approach

The Cartesian cut-cell method can be used to represent irregular and complex computational domains with less computational efforts by cutting the grid cells on the boundary surfaces in a background uniform Cartesian mesh. In this study, a modified Cartesian cut-cell grid technique is proposed to better represent complex physical geometries. A point shifting treatment was employed to determine the start and end points of a line segment in cut-cell grids. This led to an improved representation of sharply-shaped corners in surface polygons. Numerical simulation to solve a set of shallow-water equations was performed by incorporating a finite volume approach into the Cartesian cut-cell mesh. The advective fluxes at intercells were first estimated by a Harten, Lax and van Leer for contact wave approximate Riemann solver. In order to improve the model accuracy to the second order, a total variation diminishing-weighted average flux method was applied to work adaptively with the cut-cell mesh. The numerical model was then employed to simulate dam-break flow propagation in a small channel with a rectangular obstacle or a 45° bend. The numerical results show good agreement with available laboratory measurements.     

Effect of Jet Air Content on Plunge Pool Scour

The effect of air discharge on plunge pool scour was investigated by using a simplified experimental configuration. Instead of considering the complete arrangement involving chute and deflector resulting in an air-water jet impinging on a sediment surface, the mixture flow was produced with a circular pipe for which the air concentration and the jet diameter close to impact on the free water surface are known. The results of this study were primarily directed to the definition of a three-phase Froude number that accounts for the combined effects of an air-water mixture jet on scour. The analysis of data allows simple estimates of the scour geometry including a generalized scour profile, the width of scour, and the temporal advance of the extreme scour depths. It was pointed out that for a certain water velocity and selected grain characteristics, the addition of air to the jet results in an increase of scour depth. However, if the reference would be the air-water mixture velocity, scour depth decreases significantly by the addition of air to the jet.     

Energy Dissipation and Air Entrainment in Stepped Storm Waterway: Experimental Study

For the last three decades, research focused on steep stepped chutes. Few studies considered flat-slope stepped geometries such as stepped storm waterways or culverts. In this study, experiments were conducted in a large, flat stepped chute (θ=3.4°) based upon a Froude similitude. Three basic flow regimes were observed: nappe flow without hydraulic jump, transition flow, and skimming flow. Detailed air–water flow measurements were conducted. The results allow a complete characterization of the air concentration and bubble count rate distributions, as well as an accurate estimate of the rate of energy dissipation. The flow resistance, expressed in terms of a modified friction slope, was found to be about 2.5 times greater than in smooth-chute flow. A comparison between smooth- and stepped-invert flows shows that greater aeration and larger residence times take place in the latter geometry. The result confirms the air–water mass transfer potential of stepped cascades, even for flat slopes (θ<5°).     

Improved Pressurized Pipe Network Hydraulic Solver for Applications in Irrigation Systems

GESTAR is an advanced computational hydraulic software tool specially adapted for the design, planning, and management of pressurized irrigation networks. A summary is given of the most significant characteristics of GESTAR. The hydraulic solver for quasi-steady scenarios uses specific strategies and incorporates several new features that improve the algorithms for pipe network computation, overcoming some of the problems that arise when attempting to apply drinking water software, using the gradient method, to irrigation systems. It is shown that the gradient method is a nodal method variant, where flow rates are relaxed using head loss formula exponents. Although relaxation produces a damping effect on instabilities, it is still unable to solve some of the numerical problems common to the nodal methods. In this contribution the results of the research on computational strategies capable of dealing with low resistance elements, hydrant modelling, multiple regulation valves, numerous emitters, and pumps with complex curves are presented, obtaining accurate results even in conditions where other software fails to converge. GESTAR incorporates all these computational techniques, achieving a high convergence rate and robustness. Furthermore, GESTAR’s solver algorithm was easily adapted to incorporate inverse analysis options for optimum network control and parameter calibration. Illustrative examples are provided, documenting the improved numerical techniques and examples of GESTAR’s performance in comparison with EPANET2, a widely used gradient method-based hydraulic solver.     

Flow over Gabion Weirs

A conventional weir typically consists of an impermeable body constructed of concrete, since its primary functions are to heading up water and efficiently regulate flow. However, an impermeable body prevents the longitudinal movement of aquatic life and transportation of physical and chemical substances in water, eventually having a negative impact on the water environment. One of the advantages of gabions as a building material is that the motion of individual stones comprising the gabion is not of much concern. The wire mesh of the gabion basket serves to restrain any significant movement. Also, gabion weirs offer an alternative design that could be adopted for flash flood mitigation. In this study, a series of laboratory experiments was performed in order to investigate the flow over gabion weirs. For this purpose, two different gabion weir models were tested in two horizontal laboratory flumes of 10-m and 17-m length, 0.3-m width, and 0.3- and 0.5-m depth, respectively, for a wide range of discharge, upstream water depth, downstream water depth, weir height, weir length, and gabion filling gravel material size. The results of the gabion weir were compared with those of experiments carried out on solid weirs having the same dimension and it was found that there is a large deviation when the solid weirs equation is applied to gabion weirs (permeable weirs). So, using one of the existing solid weir flow formulas would lead to an erroneous calculated value. Multiple regression equations based on the dimensional analysis theory were developed for computing the discharge over gabion weirs for both free and submerged flow regimes. Also, equations were introduced for computing the discharge coefficient to be applied with the traditional solid weir equation.     

Transient Flow Caused by Air Expulsion through an Orifice

A pressurized water system may be subjected to high pressure surges because of the expulsion of a trapped air pocket through an orifice at the downstream end of the pipe. Results are presented of laboratory experiments, in which pressure histories were recorded for different upstream heads, air pocket volumes, and orifice sizes. The resulting pressure oscillation pattern was divided into two distinct stages: a first phase of low-frequency pressure oscillation during the air release, followed by a sudden pressure increase with water hammer characteristics when the water column reaches the orifice. The experimental results show that the duration of the first phase decreases substantially with increasing upstream head and orifice size, and increases with air pocket volume. A simple relationship was deduced, which agrees well with experimental data. The maximum pressure peaks, always observed in the water hammer phase, increased with upstream head and orifice size, whereas the volume of the air pocket appeared to be a less significant factor in the range investigated. A simple predictive equation was deduced based on Allievi–Joukowski results.     

Hydraulic Performance of Step Aerator

The step aerator for stepped chutes was recently introduced. Its purpose is to preaerate the zone between the spillway crest and the point of incipient bottom aeration to counter cavitation damage for relatively large unit discharges. The shape of the step aerator is optimized herein by hydraulic modeling to design the air supply and to indicate the aerator blockage characteristics. The shape and the performance of the improved step aerator are described in terms of air supply and the development of air-water flow on the stepped chute. Further, step insets are considered to reduce the spray formation on stepped chutes for small unit discharges, in combination with the step aerator. The performance of the step insets was investigated and their effect on the spray formation analyzed. The step aerator generally increases the maximum spray height at smallest discharges as compared to the standard stepped chute without step aerator. Insets over the first five steps significantly reduce spray relative to standard stepped chutes.     

Transition Effects in Flow Over Side Weirs

The effect of water surface slope in the lateral direction on flow over side weirs was studied. Water surface elevation on the weir plane was expressed by a parameter ψ based upon the hydraulic profile on the channel axis. Two different relationships of ψ as a function of the Froude number were used to calculate side weir discharges. Results were compared with the experimental data. It was shown that better results are obtained when transition conditions of ψ = 1 at the ends of the side weirs with no lateral surface slope are taken into account. However the effect of water surface slope in lateral direction is of secondary importance as compared to the angle of the deflected water jet along the side weir.     

Observations of Air–Water Interaction in a Rapidly Filling Horizontal Pipe

This paper presents the results of an observational study related to the behavior of drainage sewers under conditions of hydraulic overloading. Specifically, the investigation focuses on the interaction of water and trapped air in surcharging drainage and pressurized pipeline systems, by studying the air–water flow behavior in a rapidly filling horizontal pipe. Air–water interface patterns, air entrainment, and air release through an orifice at the pipe end are documented photographically. Synchronously recorded pressure traces are also presented to illustrate the relation between the air–water phase evolution and the pressure oscillation patterns. Depending on the air release rate of the orifice, there are three types of pressure oscillation behavior, each corresponding to a particular behavior of the air–water interface in the rapidly filling horizontal pipe.     

Hydraulic Elements Chart for Pipe Flow Using New Definition of Hydraulic Radius

The Manning formula is used routinely to calculate the mean velocity of uniform flow. Although this empirical formula is effective when applied to uniform flow in simple rectangular or trapezoidal cross sections, the roughness coefficient of the formula is variable when examining flow in a pipe that is partially full. Thus, the coefficient must be altered depending on the relative depth of fluid in the pipe. As this seems to be due to the definition of the hydraulic radius, a new definition of hydraulic radius is proposed here that was used to calculate a hydraulic elements chart for flow in pipes with a constant roughness coefficient. The results of the calculations showed very good agreement with Camp’s chart. Furthermore, with adjustment of the “free-surface weight factor,” this method was also capable of expressing other hydraulic elements charts reported previously. This new definition of hydraulic radius can also be applied to flow in simple cross sections and may be developed further for use with compound channel flows in future studies.     

Practical Formulas for the Dimensioning of Air Valves

On the basis of theoretical considerations, the technical note presents two practical formulas for the dimensioning of air valves when filling a pipe with water. One is to be used for designing air valves on the basis of the maximum allowed water hammer overpressures; the other when the maximum in pipe water velocity is set. The reliability of these formulas was tested with a numerical model based on the same hypothesis, which was in turn verified with experimental tests.     

Unstructured Grid Finite-Volume Algorithm for Shallow-Water Flow and Scalar Transport with Wetting and Drying

A high-resolution, unstructured grid, finite-volume algorithm is developed for unsteady, two-dimensional, shallow-water flow and scalar transport over arbitrary topography with wetting and drying. The algorithm uses a grid of triangular cells to facilitate grid generation and localized refinement when modeling natural waterways. The algorithm uses Roe’s approximate Riemann solver to compute fluxes, a multidimensional limiter for second-order spatial accuracy, and predictor–corrector time stepping for second-order temporal accuracy. The novel aspect of the algorithm is a robust and efficient procedure to consistently track fluid volume and the free surface elevation in partially submerged cells. This leads to perfect conservation of both fluid and dissolved mass, preservation of stationarity, and near elimination of artificial concentration and dilution of scalars at stationary or moving wet/dry interfaces. Multi-dimensional slope limiters, variable reconstruction, and flux evaluation schemes are optimized in the algorithm on the basis of accuracy per computational effort.     

流水线镁电解槽电解质沸腾的探讨

以文献资料为依据,结合生产经验和实验室研究,对流水线镁电解槽的沸腾进行了深入探讨,提出了行之有效的解决措施,从而避免了电解质的沸腾。     

Velocity Profile and Flow Resistance Models for Developing Chute Flow

A developing boundary layer starts at the spillway crest until it reaches the free surface at the so-called inception point, where the natural air entrainment is initiated. A detailed reanalysis of the turbulent velocity profiles on steep chutes is made herein, including mean values for the parameters of the complete turbulent velocity profile in the turbulent rough flow regime, given by the log-wake law. Accounting both for the laws of the wall and the wake, a new rational approach is proposed for a power-law velocity profile within the boundary layer of turbulent rough chute flow. This novel approach directly includes the power-law parameters and does not require for a profile matching, as is currently required. The results obtained for the turbulent velocity profiles were applied to analytically determine the resistance characteristics for chute flows. The results apply to the developing flow zone upstream of air inception in chute spillways.     

Role of Dynamic Flow in Relationships between Suction Head and Degree of Saturation

This paper presents results of the relationship between the degree of saturation and the matric suction head at static equilibrium and during dynamic flow of water using a Buchner funnel and a fully instrumented two-dimensional tank, respectively. The major influences of the dynamic flow on the relationships between the suction head and the degree of saturation are highlighted and discussed. The experimental results show that dynamic flow of water strongly affects the volume of entrapped air. The results also reveal that any scanning curve can be described as two parts, namely, transition and coinciding. The transition curve starts from the recent reversal degree of saturation and continues up to the previous reversal degree of saturation. The shape of the transition curve and the amount of hysteresis are not only a function of the reversal degree of saturation but are also a function of the saturation path history. The experimental results are used to examine the validity of the proposed analytical model by Parker and Lenhard in 1987 for describing the relationships between the degree of saturation and the matric suction head. It was found that Parker and Lenhard’s model provides a good prediction of the relations provided that care should be taken for the value of the reversal degree of saturation at zero suction head.     

Efficient Quasi-Two-Dimensional Model for Water Hammer Problems

Quasi-two-dimensional models for turbulent flows in water hammer are necessary for advancing the understanding of flow behavior in pipe transient; conducting detailed investigation of the fate of transient-induced contamination; and validating one-dimensional water hammer models. An existing quasi-two dimensional numerical model for turbulent water hammer flows has the attributes of being robust, consistent with the physics of wave motion and turbulent diffusion, and free from the inconsistency associated with the enforcement of the no slip condition while neglecting the radial velocity at boundary elements, such as valves and reservoirs. However, this scheme is computationally intensive making it unsuitable for practical pipe systems or for conducting numerical experiments. This paper addresses the efficiency and stability of this existing scheme. In particular, algebraic manipulations show that the original scheme can be decoupled into two tridiagonal systems, one for piezometric head and radial flux and another for axial velocity. This decoupling is the reason for the high efficiency of the modified scheme. The original and proposed schemes are applied to a pipe–reservoir–valve system. It is found that, for the same spatial and temporal discretization, both schemes are of equal accuracy. However, significant saving in computer execution time is achieved by using the modified scheme. Application of the modified scheme to pipes of realistic dimensions and wavespeeds (length 35.2 km, diameter 200 mm, and wave speed 1000 m/s) takes only a few minutes to execute. This small execution time requirement makes the current quasi-two-dimensional model suitable for application to practical water hammer problems. The stability domain of the proposed scheme is established using the Von Neumann method.     

Air/Water Oxygen Transfer in a Biological Aerated Filter

The oxygen-transfer characteristics of an upflow biological aerated filter filled with angular clay media were determined over a wide range of gas and liquid flow rates. Liquid-side, oxygen-transfer coefficients (KLa) were measured using a nitrogen gas stripping method under abiotic conditions and were found to increase as both gas and liquid superficial velocity increases, with values ranging from 12 to 110?h?1 based on empty bed volume. The effect of gas and liquid velocity, wastewater to clean water ratio, and temperature dependence was correlated to within ±20% of the experimental KLa value. Stagnant gas holdup is roughly double in wastewater compared to clean water, but the dynamic gas holdup is the same. The oxygen-transfer coefficient is directly proportional to the dynamic gas holdup. Stagnant gas holdup does not influence the rate of oxygen transfer. The results suggest that dynamic gas holdup largely determines the specific interfacial area (a), whereas the interstitial liquid velocity largely controls the oxygen-transfer coefficient (KL).     

循环冷却水处理系统中旁流处理量的确定

对循环冷却水处理系统中旁流水量问题提出了看法，并提供了一种具体的计算方法。     

Hydraulic Resistance in Grass Swales Designed for Small Flow Conveyance

Grass swales, originally used for erosion control in agricultural settings, are now widely employed in urban environments as an effective best management practice for controlling pollutants in stormwater runoff. In particular, vegetated swales are quite successful in removing heavy metal concentrations when the depth of flow is small relative to grass height. However, guidance materials currently available for design of vegetated channels focus on larger depths of flow (large flow conveyance/erosion control), and for such conditions the hydraulic resistance exerted by the vegetation can be significantly different than that observed when the depth of flow is small (remediation). Utilizing a series of laboratory channels, small-flow retardance curves have been developed in the present work for Bluegrass, Centipede, and Zoysia grass species. These “small-flow” curves extend the well-known Stillwater n versus VR diagram by approximately 1 order of magnitude, to smaller values of VR. Experimental results should provide valuable design guidance to those faced with the need to hydraulically design a swale intended for shallow depths of flow.