Developing Flow Region and Pressure Fluctuations on Steeply Sloping Stepped Spillways

The hydrodynamic pressure field is important for the design and safety of steeply sloping stepped spillways, which are typically designed for considerably lower maximum specific discharges than smooth spillways. The hydraulic performance of stepped spillways at high velocities may compromise its use due to major concern with safety against cavitation damage. Hydraulic model investigations were conducted in different large-size stepped chutes to characterize the nonaerated flow region which is potentially prone to cavitation damage and the pressure field acting on the step faces. The clear water depths and energy dissipation in the developing flow region are described in terms of integral measures of the turbulent boundary layer. Expressions for the location of and the flow depth at the inception point of air entrainment are derived. Pressure distributions on the horizontal and vertical faces of the step along the spillway are presented. Measurements indicated a different behavior of the pressure field in the aerated and nonaerated flow region. The mean and fluctuating pressure coefficients along the spillway are approximated by a regression function. The vertical face near the outer step edge close to the inception point of air entrainment is identified as a critical region for predicting cavitation inception in flow over stepped spillways. From the analysis of the pressure fluctuations in that region a maximum velocity of 15 m/s is proposed as a criterion to avoid extreme negative pressures in typical prototype steeply sloping stepped spillways, eventually leading to the occurrence of cavitation in the nonaerated flow.     

Dissolved Oxygen Demand at the Sediment-Water Interface of a Stream: Near-Bed Turbulence and Pore Water Flow Effects

A microbial dissolved oxygen (DO) uptake model was developed for a stream bed, including the effect of turbulence in the flow over the bed and pore water flow in the porous bed. The fine-grained sediment bed has hydraulic conductivities 0.01 ≤ k ≤ 1??cm/s, i.e., sediment particle diameter 0.006 ≤ ds ≤ 0.06??cm. The pore water flow is driven by pressure fluctuations at the sediment-water interface, mostly attributable to near-bed coherent motions in the turbulent boundary layer above the sediment bed. An effective mass transfer coefficient (De) coupled to a pore water flow model was used in the DO transport and DO uptake model. DO flux across the sediment-water interface and into the sediment, i.e., sedimentary oxygen demand (SOD), was related to hydraulic conductivity and microbial oxygen uptake rate in the sediment and shear velocity at the sediment-water interface. Simulated SOD values were validated against experimental data. For hydraulic conductivities of the sediment bed up to k ≈ 0.01??cm/s, the pore water flow effect on SOD was found negligible. Above this threshold, the effective mass (DO) transfer coefficient in the sediment bed (De) becomes larger as the hydraulic conductivity (k) becomes larger as the interstitial flow velocities increase; consequently, DO penetration depth increases with larger hydraulic conductivity of the sediment bed (k), and SOD increases as well. The enhancement of vertical DO transport into the sediment bed is strongest near the sediment-water interface, and rapidly diminishes with depth into the sediment layer. An increase in shear velocity at the sediment-water interface also enhances DO transfer. Shear velocity increases at the sediment-water interface will raise SOD regardless of the maximum oxidation rate if the hydraulic conductivity is above the threshold of k ≈ 1??cm/s. The relationship is nearly linear when U*<0.8??cm/s. At shear velocity U* = 1.6??cm/s, SOD for oxidation rates μ = 1000 and 2000??mg?l-1?d-1 are almost five times larger than those with no pore water flow. When pore water transport of DO is not limiting, SOD is a linear function of oxygen demand rate μ in the sediment when 0 ≤ μ ≤ 200??mg?l-1?d-1.     

Performances of Hydraulics and Bedload Sediment Flushing in Rigid Channel Using Surge Flows

This paper presents an investigation of the performance of the hydraulic and sediment removal of a flushing system in a detention basin. A hydraulic criterion for the design of the flushing system is proposed. An equation for the maximum height of the flushing wave front as a function of the distance from the gate, the initial water depth in the chamber, and the chamber length is proposed. The Lauber and Hager equation for the maximum velocity of a flushing wave is also verified. Effective removal of sediment particles on the bed is a direct function of the bed shear stress generated by the flushing flow. This study reveals that the bed shear stress on the channel bed induced by the flushing flow can be attributed to the hydrostatic pressure, the flow acceleration, and the convection-induced momentum. The shear stress associated with fluid distortion and the turbulent viscosity may be neglected. Significant error would occur if the hydrostatic pressure component were used as an estimate of the bed shear stress on a mild slope channel. The energy slope method may provide an overestimate of the bed shear stress. Finally, an appropriate equation to evaluate the maximum bed shear stress is proposed.     

Structure of Flow Upstream of Vertical Angled Screens in Open Channels

This paper presents the results of a laboratory study of the structure of flow in a diversion structure with a vertical angled wedge-wire fish screen. This screen had a 10×25?mm mesh and was tested at three angles of 10.4, 17.5, and 26.8°, to the direction of the approaching flow, for two mean velocities of 0.5 and 0.8?m/s, with a depth of flow of about 0.75?m. In this water and fish diversion (channel or) structure, it was found that the depth of flow at any section is approximately constant with a drop at the screen on the side of the canal and decreased towards the bypass located at the downstream end. The distribution of the velocity component u in the direction of the approaching flow as well as the perpendicular component w and the resultant velocity V was uniform in the vertical direction. The depth averaged mean velocity for different verticals at any section in the diversion structure increased with the longitudinal distance x and was correlated with the relative width, bs/b (in the diversion structure) for all five experiments. Correlations have been found for the depth averaged transport velocity and the impinging velocity on the screen in terms of the approach velocity U. A general relation has also been developed for the attack angle of the flow on the screen. The downstream part of the screen carried more flow into the canal compared to the upstream part as a result of the uniform mesh size used in this study. The results of this hydraulic study should be useful, particularly for freshwater adult fish, in designing screens in irrigation canals and for micro-hydro sites that use diversion canals.     

Turbulent Velocity Profiles and Boundary Shear in Gravel Bed Rivers

Vertical profiles of turbulent streamwise velocities in gravel bed rivers are investigated. Field measurements made at high and low flows with electronic pitot tubes show logarithmic velocity profiles to extend over much of the flow depth. For the gravel bed rivers studied the velocity at 0.6 of the total depth was generally a good indicator of depth-averaged flow velocity. An unambiguous definition of flow depth is adopted to deal with situations where the bed is uneven or moving. When hydraulic roughness Z0 is defined as a fitted parameter of a logarithmic velocity profile, the river data indicate that the profile origin displacement below the tops of roughness elements scales with Z0. No direct relation between Z0 and bed material size is evident under mobile bed conditions. For these conditions a relation between hydraulic roughness and U*2 is identified (with U* also derived as a log profile parameter). A flow resistance equation using this relation is verified by comparison with mobile bed laboratory measurements in which U* is not fitted from velocity profiles.     

Case Study: Dam Safety during Construction, Lessons of the Overtopping Diversion Works at Aguamilpa Dam

A study on risk analysis by overtopping of the diversion works of Aguamilpa Dam in Mexico was carried out to examine the overtopping event of January, 1992. Specifically, this study focuses on the upstream water surface elevation during the flood considering the tunnel discharge actual width and roughness. During this maximum flow event, the upstream cofferdam was overtopped and the discharge tunnels exceeded their maximum hydraulic capacity. The risk analysis was made considering the original hydrologic data (until 1992), the final constructed conditions, to establish a performance function that compares the risk of original deterministic analysis with a probabilistic analysis made in 1992. The study also focuses on practical improvements in the construction stage of tunnels; like lining the floor with hydraulic concrete and shotcrete in vaults and walls, that improves the safety of dams during construction and increases the real return period. The work here is presented as a case study because of the unique large-scale flow conditions that are registered in diversion works of dams.     

钢包卷渣临界底吹流量规律的水力学模拟研究

用水模拟钢水、油模拟钢渣,通过水力模型研究了底吹钢包中的临界卷渣流量.结果表明,临界卷渣流量随渣层厚度的增加而减小,随粘度的增加而增大,通过分析渣-钢界面的速度分布和能量平衡,对以临界流量作为卷渣发生的判定条件的准确性进行了检验.采用因次分析得到了底吹钢包临界卷渣流量的无因次表达式Qcr∝(Δρσ/ρ2s)0.35(μs/μm)0.3(Hs/Hm)-0.42,利用该表达式计算了实际钢包卷渣的临界流量,分析了影响因素,建议110 t钢包进行钢水弱搅拌净化操作时最大底吹流量为QN＝240 L/min.     

Application of Several Depth-Averaged Turbulence Models to Simulate Flow in Vertical Slot Fishways

Vertical slot fishways are hydraulic structures which allow the upstream migration of fish through obstructions in rivers. The velocity, water depth, and turbulence fields are of great importance in order to allow the fish swimming through the fishway, and therefore must be considered for design purposes. The aim of this paper is to assess the possibility of using a two-dimensional shallow water model coupled with a suitable turbulence model to compute the flow pattern and turbulence field in vertical slot fishways. Three depth-averaged turbulence models of different complexity are used in the numerical simulations: a mixing length model, a k?ε model, and an algebraic stress model. The numerical results for the velocity, water depth, turbulent kinetic energy, and Reynolds stresses are compared with comprehensive experimental data for three different discharges covering the usual working conditions of vertical slot fishways. The agreement between experimental and numerical data is very satisfactory. The results show the importance of the turbulence model in the numerical simulations, and can be considered as a useful complementary tool for practical design purposes.     

Remarks on Camp’s Criterion for Self-Cleansing Storm Sewers

This study brings to the attention the difficulty imposed by the design on the development of a self cleansing storm sewer based on a general rule of minimum water velocity of 0.75 m/s under pipe full capacity and suggests the Camp’s criterion as an alternative. The key finding is the determination of the lower limit of flow strengths above which the Camp’s criterion can be applied to warrant the development of a more efficient storm sewer system. The lower limit is adjusted for storm sewers with loose or rigid boundary serving two transport conditions: to sustain equal sediment mobility on pipe invert instead of selective transport, and to avoid progressive deposition of finer grains due to low and reducing water flows.     

Scale Independent Linear Behavior of Alluvial Channel Flow

For flow in a rigid open channel with no bed sediment, the achievement of the special state of stationary equilibrium yields a linear characteristic. To examine the existence of a linear characteristic in alluvial channel flow, this study presents a direct formulation of the special equilibrium state following a variational approach. It finds that a linear relationship between shear stress and width/depth ratio of alluvial channels emerges under the commonly identified flow resistance and sediment transport conditions. Most importantly, this linear relationship yields not only the theoretical equilibrium channel geometry that is very close to a widely identified empirical counterpart but also a nondimensional number H, defined as the ratio of the relative increment of shear stress to the increment of width/depth ratio. This study suggests that H needs to be adopted as a criterion of hydraulic similitude for modeling sediment (bed-load) transport in alluvial channels.     

Numerical Simulation of Street Canyon Flows with Simple Building Geometries

The velocity and pressure fields of the flow over street canyons formed by groups of buildings are studied numerically. The flow fields are computed by solving the time-dependent incompressible Navier–Stokes equations using the fractional step method. The numerical model is validated by simulating flows over a square cylinder at different Reynolds numbers. The Strouhal numbers, which reflect the dynamic flow characteristics, agree well with published experimental data over a wide range of Reynolds numbers. The wind field model is then applied to two street canyon configurations. First, flows inside street canyons formed by four identical buildings are simulated. The incidental flow is raised by the most upstream building and becomes parallel to the ground at the rooftop level of the fourth building downstream, resulting in a clockwise rotating vortex in downstream street canyons with an inflow from left to right. Second, flows inside street canyons formed by two identical buildings are simulated. In this case, a primary eddy that is counterclockwise rotating may be formed due to flow separation at the front corner of the upstream building. A clockwise rotating primary eddy is formed in the wake area of the separate zone above the street canyon, which drives the counterclockwise rotating eddy in the street canyon. The result indicates that rooftop level flows cannot be assumed parallel to the ground as some modelers have done in their studies. Studies also show that flow regimes in the street canyon will remain unchanged while the inflow velocity is greatly increased from 0.1 to 6.0?m/s. In addition, the wind velocities in the street canyon have a linear response to the inflow velocity.     

Process Modeling of Storm-Water Flow in a Bioretention Cell

A two-dimensional variable saturated flow model was developed to simulate subsurface flow in bioretention facilities employing the Richards’ equation. Variable hydrologic performances of bioretention are evaluated using the underdrain outflow hydrographs, outflow volumes for 10 storms with various duration and depth, and flow duration curves for 25 different storms. The effects of some important design parameters and elements are tested, including media type, surrounding soils, initial water content, ratio of drainage area to bioretention surface area, and ratio of cell length to width. Model results indicate that the outflow volume via underdrain is less than the inflow; the flow peak is significantly reduced and delayed. Underdrain outflow volume from loamy sand media (with larger Ks) is larger than that from sandy clay loam media. The saturated hydraulic conductivity, storage capacity, and exfiltration into surrounding soils contribute to the hydrologic performance of a bioretention cell. Initial media storage capacity is affected by the hydraulic properties of media soils, initial water content, and bioretention surface area. The exfiltration volume is determined by the surrounding soil type and exfiltration area, dominated by flow through the bottom of the media.     

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.     

Relatively Rough Flow Resistance Equations

The definitions of depth and hydraulic radius become ambiguous when bed roughness is large relative to flow depth. Various statistics are currently used to describe bed roughness and many different flow resistance formulas have been developed. The volumetric hydraulic radius Rv and the standard deviation of bed surface elevations dz are rational and unambiguous measures suitable for large relative roughness conditions. Their influence on flow resistance is investigated using conceptual models and digital elevation models of natural alluvial beds. The results show that head-losses for large-scale relative roughness beds can be related to (Rv/dz); the (Rv/dz) exponent of power-law flow resistance equations increases from 1/6 to more than 1/2 as relative roughness increases, and flow velocity can be determined from boundary topography measures, water level and slope, without any calibrated coefficients. An overlooked form of the log law, using standard deviation dz, performs as well as power laws for predicting flow resistance with high relative roughness and it reverts to the conventional log law when relative roughness is low. A field technique for determining Rv and dz is described.     

Deflecting Velocity Rod for Flow Measurements in Small Channels

A hinged rod, when immersed in flowing water, deflects against its weight due to the hydrodynamic force of water. A relationship was derived to calculate the average flow velocity in small channels from the deflection of the rod, length and thickness of the rod, density of the rod's material, flow depth, and an experimentally determined rod's velocity coefficient. The rod's velocity coefficient was found to be invariant with flow velocity (V) and Reynolds number (R) for the range investigated in this study (V ? 60 cm∕s and 25,000 ? R ? 60,000). The calculated velocity compared very well with the measured velocity, with an average error of only 0.7%. Analysis suggested that a rectangular rod made of seasoned wood (density ? 0.7) with length = 100 cm, width = 2 to 4 cm, and thickness = 3 to 5 cm will provide a simple but acceptable technique for determination of average flow velocity in small prismatic channels having a flow velocity ?1 m∕s and flow depth ?45 cm with less than 5% error.     

Scour Vulnerability of River Bridge Piers

A simple procedure is proposed to assess the vulnerability of bridge piers in rivers, taking into account the phenomena governing fluvial dynamics during flood events. The procedure requires an estimation of the maximum scour depth of the soil surrounding both the pier and the foundation as well as an analysis of the bearing capacity of the pier–foundation–soil geotechnical system. The scour depth is determined in terms of the physical and mechanical properties of the streambed soil, the shape of the pier foundation and the destabilizing effects induced by hydrodynamic forces. The coupling of both the hydraulic and geotechnical analyses enables to identify the most significant factors characterizing scour depth and affecting pier vulnerability. Two levels (low, medium) of allowable vulnerability, bounded by an extreme condition of high vulnerability, are defined and analytically determined in function of the maximum scour depth and the foundation depth. Specific diagrams corresponding to each category of foreseen actions allow a quick evaluation of the vulnerability of a bridge pier.     

Numerical Study on Flow over Buildings in Street Canyon

A 2D numerical investigation of the relationships between building height, gap distance, and wind velocity for flow in a street canyon is conducted using the computational fluid dynamics technique. The numerical scheme is first applied to a backward-facing step flow over a wide range of Reynolds numbers. Good agreement with experimental data from literature is found. It is then applied to study the flow around two rectangular buildings with various building heights, gap distances, and approaching wind velocities. Simulations show that the wind profile upstream of buildings is similar under different inflow wind velocities for a fixed building height. The maximum wind velocity in the street canyon largely depends on the configuration of the buildings. It increases dramatically when the gap-to-height ratio (G∕H) of the buildings is increased from 0.75 to 1.0 but increases only mildly for G∕H rising from 1.0 to 1.5. No significant increase in velocity can be found for a further increase in G∕H. The flow pattern in the street canyon becomes more complex with an increasing height-to-gap ratio (H∕G), particularly at low inflow velocity. Two or more stable recirculation vortices, which stack vertically in the street canyon, are found for H∕G ≥ 3. For those simulations with nonidentical buildings, natural ventilation tends to be better in the case of the higher building located upstream.     

Discontinuous Galerkin Finite-Element Method for Simulation of Flood in Crossroads

A numerical solution of the two-dimensional Saint Venant equations is presented for the study of the propagation of the floods through the crossroads of the city. The numerical scheme is a Runge-Kutta discontinuous Galerkin method (RKDG) with a slope limiter. The work studies the robustness and the stability of the method. The study is organized around three aspects: the prediction of the water depths, the location of the right and oblique hydraulic jumps in the crossing, and especially the distribution of the flow discharges in the downstream branches. The objective of this paper was to use the RKDG method in order to simulate supercritical flow in crossroads and to compare these simulations with experimental results and to show the advantage of this RKDG method compared to a second-order finite-volume method. A good agreement between the proposed method and the experimental data was found. The method is then able to simulate the flow patterns observed experimentally and to predict accurately the water depths, the location of the hydraulic jumps, and the discharge distribution in the downstream branches.     

Total Load Transport Formula for Flow in Alluvial Channels

A user-friendly total bed-material load transport formula for flow in alluvial channels under equilibrium transport conditions has been developed based on dimensional analysis. The main advantages of this formula are its ease of computation, accuracy in prediction, and the wide range of application. The total sediment discharge gt is computed directly and is linearly related to the new total load transport parameter, TT. The latter involves variables that can be easily measured in field conditions, i.e., flow depth, mean flow velocity, energy slope, median sediment size and density, and water temperature. The factor of proportionality k in the formula has been checked for a wide range of hydraulic conditions and it remains a constant equal to 12.5. Comparisons between the computed and measured total sediment discharge indicate that the predictions are good.