Journal of Hydraulic Engineering

Characteristic solution methods, namely the method of characteristics (MOC) and wave characteristics method (WCM), are widely used for simulating transient pipe network flows. Because the MOC computes solutions at interior nodes, it features higher spatial resolution, whereas the WCM makes simplifications that yield more efficient computations. Practical analyses require numerical methods that are both accurate and computationally efficient. To benefit from the advantages of the two approaches, a generalized characteristic method (GCM) is developed in this paper by combining a flexible friction approximation with a variable reach scheme. Significantly, computational savings are realized by selectively providing greater accuracy and higher resolution solutions only where needed via more interior reaches and higher order solutions; further, the new method reduces to either of the MOC and WCM, thereby showing their intrinsic similarities. Multiple examples compare and contrast the numerical methods. From these, unsteady friction effects and, more importantly, spatial resolution are shown to be directly affected by the interior reach treatment, thus exposing a limitation for solution methods with too few interior reaches. Overall, the key contribution of this work is a methodology featuring a similar degree of accuracy to the MOC, but with a computational cost better than that of the WCM.

This paper studies bubble-entrained plume (BEP) behaviors in a crossflow and proposes a theoretical approach for predicting BEP trajectories and the separation points from the bubble swarm. When rising in a crossflow, the BEP is separated from the bubble swarm and becomes a negatively buoyant fountain. By treating the BEP trajectory as two distinct parts based on the separation point from the bubble swarm, a new BEP trajectory can be expressed as a piecewise equation. Laboratory experiments conducted in different conditions study the effects of air flow rate and crossflow velocity on the BEP behaviors. Experimental results show that the larger the crossflow velocity is, the narrower the width and the smaller the spreading rate of air-bubble plume becomes. The theoretical approach developed in this study is also used to calculate the minimum air injection volume flow rate for artificial upwelling, which has a direct application for estimating the upwelling of nutrient-rich water into the euphotic layer as a way to enhance primary production in nutrient-depleted surface waters.

An analytical solution of the standard $k\text{-}ϵ$ model is proposed to study the turbulent characteristics of nonuniform flow. Initially, the most suitable functional forms are assumed for turbulent kinetic energy, $k$, turbulence dissipation rate, $ϵ$, and streamwise velocity, $u$, and the coefficients of the power series of all three variables are determined by solving Reynolds equation and the standard $k\text{-}ϵ$ equation for nonuniform flow. Additionally, to investigate the effect of the damping function on velocity and length scale, an analytical solution is further formulated by incorporating the damping function into the basic equations. The appropriateness of the analytical solution is verified with experimental data for the most accelerated flow and the most decelerated flow. The profile of turbulent energy dissipation increased near the free surface when the damping function was included in the analytical solution. Moreover, depending on the nature of the nonuniform flow, the turbulent energy is dissipated more for accelerated flow than for decelerated flow. The eddy viscosity reduced near the free surface due to the pronounced effect of the damping function. Turbulent mixing is also damped in the accelerated flow and amplified in the decelerated flow. Finally, the effective distributions of $k$, $ϵ$, $u$, and eddy viscosity for nonuniform flow ensured the desirability of the functional form presumed for turbulent kinetic energy, turbulence dissipation rate, and velocity.

Although we do not understand the complex behavior of leaks in thick-walled plastic pipes, the ability to model them is essential to the assessment and mitigation of the real losses from drinking water–distribution systems. A methodology was followed whereby numerical and physical experimental data were used to develop a generalized model that quantified both the structural and leak dynamics of longitudinal slits in thick-walled viscoelastic pipes. The dimensionally homogeneous time- and pressure-dependent leakage model was validated using experimental data independent from the physical observations used for the viscoelastic calibration. This was shown to be an effective tool to predict the distinct short- and long-term responses. Such accurate models, which describe the characteristic response of complex leaks, are crucial in improving the understanding of leakage behavior and management.

By using particle image velocimetry techniques, this paper presents new insights on the turbulence structure and time-averaged flows in a rectangular cavity with large aspect ratios. The three cavity aspect ratios ($L/D$, where $L$ = cavity length, $D$ = cavity depth) used in this study are 9.9, 13.0, and 18.9. The time-averaged velocity fields and Reynolds shear stress distributions within the cavity show that the flow pattern and turbulence structures are strongly affected by the cavity aspect ratio. The quadrant dynamic analysis of velocity fluctuations on the cavity shear layers and cavity downstream edge for the three cavities is conducted. Considering all of the bursting events with hole size parameter, $\mathrm{H}=0$ in the measured planes, sweeps are found to have the highest probability of occurrence within the zone of the shear layer, and ejections dominate almost all of the areas within the cavity and a certain depth of flow immediately above the shear layer. For the high-magnitude events ($\mathrm{H}=1$), quadrant dominances are almost inverted for all of the measured planes. The quadrant shear stress distributions show that the opposing events are approximately balanced for these regions on the cavity shear layers and along the cavity downstream edge.

New information regarding the influence of a stepped chute on the hydraulic performance of the United States Bureau of Reclamation (Reclamation) Type III hydraulic jump stilling basin is presented for design (steady) and adverse (decreasing tailwater) conditions. Using published experimental data and computational fluid dynamics (CFD) models, this paper presents a detailed comparison between smooth-chute and stepped-chute configurations for chute slopes of 0.8H:1V and 4H:1V and Froude numbers ($\mathsf{F}$) ranging from 3.1 to 9.5 for a Type III basin designed for $\mathsf{F}$ = 8. For both stepped and smooth chutes, the relative role of each basin element was quantified, up to the most hydraulic extreme case of jump sweep-out. It was found that, relative to a smooth chute, the turbulence generated by a stepped chute causes a higher maximum velocity decay within the stilling basin, which represents an enhancement of the Type III basin’s performance but also a change in the relative role of the basin elements. Results provide insight into the ability of the CFD models [unsteady Reynolds-averaged Navier-Stokes (RANS) equations with renormalization group (RNG) $k\text{-}ϵ$ turbulence model and volume-of-fluid (VOF) for free surface tracking] to predict the transient basin flow structure and velocity profiles. Type III basins can perform adequately with a stepped chute despite the effects steps have on the relative role of each basin element. It is concluded that the classic Type III basin design, based upon methodology by reclamation specific to smooth chutes, can be hydraulically improved for the case of stepped chutes for design and adverse flow conditions using the information presented herein.

A new methodology is proposed to spatially filter acoustic Doppler velocimetry data from a Vectrino profiler based on the differential mean velocity equation. Lower and upper bounds are formulated in terms of physically based flow constraints. Practical implementation is discussed, and its application is tested against data gathered from an open-channel flow over a stepped macroroughness surface. The method has proven to detect outliers occurring all over the distance range sampled by the Vectrino profiler and has shown to remain applicable out of the region of validity of the velocity gradient equation. Finally, a statistical analysis suggests that physically obtained bounds are asymptotically representative.

The performance of seven sediment transport equations for bedload transport is compared using almost 2,600 of more than 8,000 measurements from a recent compilation. Named equations tested include the Meyer-Peter Muller, Barry, Pagosa good condition, Wilcock, Parker (both calibrated and uncalibrated), Recking, and that of Elhakeem and Imran. The purpose of the tests was to evaluate the performance of several empirical and semiempirical formulae using a single calibration point relative to three uncalibrated equations. The seven equations were included because they either have a calibration procedure already developed, are used frequently in practice, are historically foundational in the field, or have recently been proposed. Results are expressed in the root mean square error of the logarithms (RMSEL) and the relative mean error (RME) and show that the Pagosa good and Barry equations best predict bedload sediment transport (RMSEL of 0.02 and 0.02, respectively). The Pagosa good equation requires a data point for bankfull discharge and the corresponding bedload transport. The uncalibrated Recking (2013) equation resulted in lower errors than two of the calibrated formulae (Wilcock 2001 and Parker 1990) and was not far behind the calibrated Elhakeem and Imran (2016) formula. The Meyer-Peter Muller and uncalibrated Parker (1990) equations performed the worst (RMSEL of up to 0.85 and 0.86, respectively). The results herein demonstrate: (1) empirical formulae were more successful at predicting bedload transport than semiempirical alternatives, (2) a single calibration point significantly improves the predictive accuracy of any formula, and (3) calibration cannot compensate for all the shortcomings of a model.

Design and analysis of water distribution networks (WDNs) is laden with uncertainty, both aleatory, i.e., natural randomness, such as variations in reservoir elevation heads, and epistemic, i.e., incomplete knowledge, imprecise data, and linguistic ambiguity such as that associated with the characterization of pipe resistance, nodal demands, and hydraulic responses. To accommodate aleatory uncertainty, stochastic analysis is applied to represent the input uncertainties and to estimate resulting uncertainty in nodal pressures and pipe flows. In the analysis of WDNs facing epistemic uncertainty, in particular, fuzzy set theory has widely been suggested as an alternative to stochastic analysis. This technique can identify the extreme values of unknown variables when uncertain input information ranges between prespecified extremes, and when the probability distribution of the information cannot be obtained. Current approaches for conducting fuzzy analysis of WDNs to support operations and design are computationally demanding, and thus limited in their applicability to large networks. Approximations of the gradients of equations that govern WDN analysis, with respect to nodal demands and pipe resistance, are identified herein and harnessed to accelerate fuzzy analysis of system hydraulics. The resulting WDN nodal pressures are inversely proportional to nodal demands, and depending on flow directions, proportional to pipe resistance. Results of fuzzy analyses for two realistically sized WDNs show that the proposed method performs with an acceptable level of accuracy and greatly reduces computational time, relative to existing fuzzy analysis approaches.

By using the particle image velocimetry (PIV) technique, experimental results of the propeller jet flow field within a developing scour hole around an open quay are presented. The experiments were conducted with four toe clearances (defined as the longitudinal distance between the propeller face and toe of the quay slope), which account for three distinct scour profiles corresponding to the three toe clearance fields, namely, near, intermediate, and far clearance fields. To better understand the underlying scour mechanisms associated with each field, the mean flow fields at selected time intervals ($t=0$, 0.5, 2, 12, and 48 h) are presented in vector and streamline plots. The data provide an improved understanding of the development of the main jet flow and vortex that formed in front of the quay slope. The importance of both the main jet flow and vortex in terms of their contribution in shaping the final scour profile in each field is discussed. Moreover, the turbulence intensities and near-bed Reynolds stress, which are analyzed for the intermediate field, exhibited a declining trend with the development of the scour hole.

Results are presented from a numerical simulation to investigate the vertical buoyant wall jet discharged into a linearly stratified environment. A tracer transport model considering density variation was implemented. The standard $k\text{-}ϵ$ model with the buoyancy effect was used to simulate the evolution of the buoyant jet in a stratified environment. Results show that the maximum jet velocity trend along the vertical direction has two regions: acceleration and deceleration. In the deceleration region, jet velocity is reduced by the mixing taking place between jet fluid and ambient lighter fluid. Jet velocity is further decelerated by the upward buoyant force when ambient fluid density is greater than jet fluid density. The normalized peak value of the cross-sectional maximum jet velocity decreases with $\lambda$ (the ratio between the characteristic momentum length and the buoyancy length). When $\lambda <1$, the dimensionless maximum penetration distance (normalized by the characteristic buoyancy length) does not vary much and has a value between 4.0 and 5.0, whereas it increases with increasing $\lambda$ for $\lambda \ge 1$. General good agreement between the simulations and measurements was obtained, indicating that the model can be successfully applied to investigate the mixing of buoyant jet with ambient linearly stratified fluid.