Journal of Hydraulic Engineering

The computation of three-dimensional unsteady non-hydrostatic flows over large domains and/or for long simulation times is frequently conducted in research and practice using approximate methods to avoid the cost of a fully 3D solution. Among these methods are the shallow-water perturbation theories of St. Venant and Boussinesq, and the theory of directed fluid sheets by Green and Naghdi. The latter theory is not limited to shallow-water flows, and it is essentially a weighted-average residual method of Galerkin type, further developed by Shields and Webster for maritime hydraulics. The method is in essence equivalent to the vertically-averaged and moment (VAM) equations developed by Steffler and Jin for open channel flows, although this has not been recognized in the literature. A general framework for constructing VAM models of high-order, by linking maritime and open channel flow developments, is not available in the literature. In this work, a generalized framework for designing weighted-average residual equations for free-surface flow is presented based on the Kantorovich and Krylov method. The development of physically sound expansions for the hydrodynamic variables, and the construction of general systems of VAM equations to determine the unknowns in the expansions by selecting suitable weighting functions, is discussed in detail. The approach produces high-order models, thereby generalizing Steffler and Jin’s development. A hierarchy of high-order VAM models is demonstrated to progressively converge to the exact dispersion relation of periodic waves by increasing the vertical resolution. These models are not limited by any shallowness assumption and exhibit more accurate wave dispersion properties compared to the Serre-Green-Naghdi equations. Computational results show that the VAM equations produce an accurate prediction of dam-break waves and dispersive wave effects over submerged bars.

Scour by hydraulic plucking is a fundamental process in landscape evolution in which large, competent rock blocks are eroded from a fractured rock mass by flowing water. This process also affects engineered structures interacting with water, such as dams and bridges, and often leads to operational and safety concerns because erosion of large volumes of material can compromise structure foundations and serviceability. To assess potential scour at a site, present methods either are empirically derived, assume a specific failure mode, or significantly simplify the geometry of potentially eroding rock particles. This limits the broader applicability of these methods and their ability to offer actionable insight into scour risk. Therefore, the discrete-element method coupled with the lattice Boltzmann method was applied to assess hydraulic plucking of fractured rock. In this approach, the three-dimensional shape of rock particles was considered explicitly, including how each particle interacts dynamically with fluid. Additionally, the highly turbulent flow conditions at which plucking often occurs were modeled using large-eddy simulation. The results show that this modeling methodology was able to capture the correct kinematic failure mode in block removal in two example scenarios without restricting the potential failure mechanism, and naturally captures the governing response. This capability makes this scour assessment technique broadly applicable since site-specific characteristics can be input directly into scour risk assessments to understand the influence of local features on the plucking process.

Pressure flow due to vertical contraction occurs under a bridge when the river water level rises above the bottom chord of the bridge. The flow accelerates inside the contraction and diverges downstream of it, resulting in increased bed shear stress in the vicinity of the contraction. The present study investigates the effect of vertical contraction on the flow field and bed shear stress inside and downstream of the contraction by conducting laboratory experiments in a smooth, rigid-bed channel. The velocity field is measured using particle image velocimetry (PIV). The effect of independent variables, namely, streamwise length of contraction, amount of contraction, and approach velocity on the velocity and turbulence fields, is studied. Bed shear stress is estimated from the measured velocity field. It is observed that the viscous stresses are amplified inside the contraction. Downstream of the contraction, increased turbulent stresses are observed close to the bed. The local bed shear stress exhibits a dual peak, one inside the contraction and the other downstream of the contraction, suggesting the possibility of two different locations for scour inception. The stochastic nature of the bed shear stress is studied and its implications on scouring are discussed.

Abstract

Siphon frequently is employed in pump stations as a pump outlet with a convenient flow cutoff mode for pump shutdown, and it usually works with axial-flow pumps with a large discharge and low head. After the pump starts, the initial air pocket in the siphon should be removed quickly from the siphon to generate a primed siphon flow, a process called priming. In this study, experiments were conducted to investigate the characteristics of air pocket removal during priming, in which two stages can be defined: air-compression and air-entrainment stages. During the air-compression stage, the air is compressed by the pumped water, and the increased air pressure can break the downstream water seal and expel some air out of the siphon. During the air-entrainment stage, the air is removed mainly in the form of bubbly flow. The air-entrainment stage can be divided further into two states: at a small water discharge, the priming process stays in State 1, in which the air pocket always remained in the siphon hump; and at a large discharge, the residual air pocket can be entirely swept out of the siphon in State 2, finally generating the primed siphon flow. The air-compression stage accounts for less than 5% of the priming time but discharges 20%–60% of the initial air. For the bubbly flow during the air-entrainment stage, the bubble diameters follow a log-normal distribution with the median of about 2.3 mm. The critical flow rate for generating primed siphon flow was predicted based on the bubble clearing velocity and force and on the motion analysis of the bubble, which can be a rough value for the calculation of the critical flow rate. The prediction indicates that the critical flow rate should increase with the descending angle and cross-section area of siphon.

Practical Applications

Siphons are inverted U-shaped pipes that commonly are used as pump outlets. We experimentally studied the air–water interactions during siphon priming in a laboratory-scale siphon model to elucidate the hydraulic removal of the air in the siphon. Because air-entrainment is the typical feature of siphon priming, high-speed photography was used to capture the bubble characteristics during siphon priming. Based on the in-depth observations of siphon priming at the bubble-scale, the priming time and the critical conditions for generating the primed siphon flow are discussed. The study shows that as the flow rate decreases, the priming time increases significantly and even the primed siphon flow cannot be generated; the priming time also increases with the increasing cross-sectional area and descending angle of the siphon. The empirical equation of the priming time was established, and the corresponding coefficients should be decided based on the siphon geometries. The prediction of the critical condition for generating the primed siphon flow was analyzed from the perspective of bubble motion. This study improves the understanding of air–water flow patterns during siphon priming and their influence on the siphon characteristics, which can be a reference for structural design and operational optimization in practical siphons.

Reach-scale experiments simulating the physical characteristics of natural woody plants are required for the improved modeling of flow resistance in channels with instream and floodplain vegetation. The first aim of this study was to investigate the flow resistance caused by patches of foliated woody vegetation at low volumetric blockage factors (4% to 10%) under emergent conditions, as most studies on the effect of patchiness are limited to submerged aquatic plants. Experiments with nature-like willow patches were performed in a reach-scale outdoor flume, where the density and layout of the patches were altered. The bulk friction factors were based on the friction slopes, calculated using the water surface slopes and velocity heads measured by a set of high-accuracy pressure sensors under several flow conditions. Compared to unvegetated conditions, the patches increased the bulk friction factor by 1.7–5.5 times, depending on the patch density and blockage factor. The second aim of this study was to evaluate the performance of four momentum-based models in estimating the bulk friction factors in flows with such flexible patches. For this process, a methodological approach suited for patchy woody vegetation at reach scale was developed to determine the input parameters required in each model. Estimation results using the newly modified and parameterized formulas compared favorably to the experimental data, demonstrating more reliable performance for models explicitly addressing the reconfiguration of vegetation. Overall, this study provides a practical methodology for estimating flow resistance caused by complex distributions of woody riverine vegetation.

Employing a set of well-chosen and maintained air valves is a widely recommended strategy for air management in pressurized pipelines. However, precisely characterizing, modeling, and sizing air valves for the various functions they serve can be a demanding task. This paper considers the key challenges of air valve characterization in light of several potential complications. The paper summarizes and gives context to location criteria for air valves and discusses some of the common pitfalls in selecting such devices. Moreover, the effectiveness of four air flow models in representing data from characterization tests is evaluated. Not surprisingly, the most complex model with an adjustable polytropic exponent is found to have the best curve fitting capability, although the simpler isentropic model fits experimental data reasonably well. However, employing a fixed polytropic exponent of 1.20 tends to underestimate air flows for relatively intense differential pressures, while the incompressible model poorly represents air inflow. The paper also shows how representative air flow curves may be constructed even if only scant characterization data are available.

Impulse waves feature tsunami-like characteristics and are generated by very rapid mass wasting, including landslides and avalanches, into water bodies. In engineered reservoirs, these waves may run up and overtop the dam, thereby exerting hydrostatic and dynamic forces on its structure. For this work, solitary waves were applied as a proxy for impulse waves and the forces acting on vertical structures during wave run-up and overtopping were investigated with hydraulic laboratory experiments. The solitary waves were generated in a wave channel with a piston-type wave generator and the horizontal pressure forces at a vertical wall as well as a vertical dam-like structure were measured with multiple pressure sensors. The discrete pressure data were used to interpolate pressure distributions and the resulting horizontal forces. Empirical equations were derived, approximating the measured maximum forces and their respective centers of pressure within $\pm 7\%$ for both cases with and without wave overtopping. For small freeboards, already small relative wave amplitudes may exert forces similar to those induced by an earthquake as estimated with a pseudo-static approach.

A variational approach was used to derive a set of Serre equations for fully nonlinear, dispersive waves in channels of arbitrary cross section. A family of travelling waves was found, as well as the relation between amplitude and celerity of solitary waves. An upper bound is proposed for the solitary wave amplitude as a function of the Froude number in trapezoidal cross-sectional canals, and it showed good agreement with existing theory. For waves of moderate amplitude, cnoidal waves result with a soliton limit; these waves and their properties (celerity and wave number) are written as functions of the channel bank slope and channel bank curvature. The theoretical findings are in agreement with well-established results in the literature, in particular with more-recent Boussinesq-type theories. A validation is proposed against existing experimental data.

To accurately model a two-dimensional solute transport in drinking water pipes and determine the effective dispersion coefficients for one-dimensional water quality models of water distribution systems, a random walk particle tracking approach was developed to analyze the advection and dispersion processes in circular pipes. The approach considers a solute particle’s two-dimensional random movement caused by molecular or turbulent diffusion and associated velocity profile, and can simulate any mixing time and accurately model the longitudinal distribution of the solute concentration. For long mixing times, the simulation results agreed with a previous analytically derived solution. For turbulent flow conditions, simulations showed that the longitudinal dispersion of the solute is very sensitive to the utilized cross-sectional velocity profiles. This approach is easy to implement programmatically and unconditionally stable. It can predict the mixing characteristics of a pipe under various initial and boundary conditions.

Recent studies have shown that bed load can be monitored with passive acoustic techniques, which consist of measuring the noise generated by the particles impacting the riverbed and converting this measured noise into a sediment flux. The technique still faces the difficulty that each environment has its own acoustic properties and that calibration is needed when operating from a river bank. However, recent work with an extensive field campaign in a large variety of rivers has shown that when measuring as close as possible to the noise sources by attaching a hydrophone to a floating board, the relation between acoustic power and local bed load flux can be described by a unique intersite power function. In this paper, we present the measurement protocol and validation based on a new field campaign comprising 17 measurements on eight rivers. The validation results show that the acoustic method successfully predicts bed load flux within a factor of 3 for more than 70% of the measurements.