Journal of Hydraulic Engineering

The main focus of this study is on the near-field flow and mixing characteristics of the thermal and saline wall jets. A numerical study of the buoyant wall jets discharged from submerged outfalls (e.g., from desalination plants) has been conducted. The performance of different Reynolds-averaged Navier-Stokes (RANS) turbulence models has been investigated and various $k\text{-}\epsilon$, $k\text{-}\omega$, and other turbulence models have been studied. The results of cling length, plume trajectory, temperature dilutions, and temperature and velocity profiles are compared to both available experimental and numerical data. It was found that two models perform best among the seven models chosen in this paper. According to the results from different simulations, the paper proposes corresponding relationships and comparative graphs that are helpful for a better understanding of buoyant wall jets.

A new and efficient variant of the method of characteristics for solving the quasi-two-dimensional water hammer model is proposed. The method requires the fully implicit discretization scheme for radial velocity, to eliminate this velocity from the equations for axial velocity and piezometric head. As the radial velocity is typically outside the scope of interest, the computation time is reduced by omitting its calculation. The proposed method is compared with an existing method by means of two water hammer benchmark tests. The results of the two methods practically match, but the proposed method requires approximately 50% less CPU time for the laminar flow test, and 30% for the turbulent one. In addition, the numerical accuracy of four implicit interpolation schemes is compared for the case of laminar flow. The obtained results suggest that the required fully implicit discretization is not a significant limitation of the proposed method. The new method offers high numerical efficiency, while retaining all merits of the existing method.

A laboratory flume experiment was performed to investigate the time development of scour around a vertical cylinder acting as a scaled model of an offshore wind turbine monopile in tidal currents. The tidal current was simulated by resolving each half-cycle into three time steps, between which flow velocity and depth were varied. Flow direction was reversed between half-cycles, which were otherwise identical. Between them, the three time steps exhibited clear water, transitional, and live-bed conditions. The experiment was run over two full-simulated tidal cycles. The scour hole formed tended to a symmetrical shape after two half-cycles and was both shallower and slower developing than the scour hole in a unidirectional current test carried out in the same flume. This was due mainly to the variable rates of scour caused by the variable flow conditions within each half-cycle, and to a lesser extent to the infilling of the scour hole when the current direction reversed. The lower scour depth recorded in tidal conditions implies that the amount of scour protection required may be less than previous studies suggest.

A formula is derived for the prediction of the average velocity of a solitary coarse grain moving over a rigid flat channel bed. To verify the theoretical consideration, data collected in the present study and reported in the literature (811 sets in total) are analyzed for typical bed roughness configurations. The results show significant improvements in the prediction of solitary grain velocity for both smooth- and rough-bed conditions in comparison with other formulas available in the literature. From the proposed formula, it follows that for rough-bed conditions, the dimensionless grain velocity depends on the Shields number and also the ratio of bed-roughness height to the grain diameter. The present study is limited to motion of solitary grains, but the result obtained implies that bed-load transport rate could be also affected by the equivalent bed-roughness height even under mobile bed conditions and such effects may become pronounced for nonuniform sediments.

To investigate hydraulic features of the flooding flow on a staircase with a rest platform, experiments were conducted on a 1:2-scale physical model of a staircase with a middle rest platform between two stair segments. The transition or skimming flow occurring on the first segment is similar to that on a stepped chute. However, a jet flow forms immediately downstream of the rest platform, followed by a redeveloping transition flow on the second segment. The measured profiles of air concentrations in those flow regions agree well with that in the skimming and transition flow known from stepped spillways. The amount of air entrained into the free-falling jet increases dramatically because of a higher air concentration in the approaching flow. Rapid rises of the air-water mixture depth and the flow velocity in part of the jet and the transition flow downstream were observed. These features could affect human maneuverability on a flooding staircase with rest platform(s) and make it more difficult for people to safely evacuate from underground spaces.

Pump station scheduling is a major issue in optimal water system operation. Pump operation may be of an on/off form or of a fluctuating form using a variable-frequency drive (VFD). This research proposes an iterative linear discrete pump-scheduling algorithm using linear programming (LP). The examined problem includes nonlinear convex headloss, leakage, and varying total-head pump energy consumption constraints. A discrete pump operation index is proposed to select time steps on which to enforce a discrete pump operation constraint. After each iteration step, the index is recalculated based on the previous iteration steps’ results and the discrete operation constraint is added or removed from the time steps accordingly. The iterative process stops when all time steps have been discretely evaluated. The algorithm is first demonstrated on a small illustrative example application and compared to the global minimal results found by enumeration. Next, the algorithm is demonstrated on two complex example applications using several test cases. The resulting optimization model may be used to provide applicable operational schemes, including hydraulic water head constraints, leakage, varying pump energy consumption, and sequential discrete pump operation, minimizing operational cost. As linear programming is used, the proposed algorithm has short solution times with assurances of solution convergence to the global minimum. Different from commonly used approaches, including mixed integer programming (MIP), or evolutionary methods, a new approach is presented for discrete pump scheduling using linear programming, applicable to general discrete decision problems.

Classical theories developed for investigating bedload sediment transport are applicable largely for channel beds of a gentle slope. Examples are the well-known Shields diagram for the evaluation of the critical condition for initial sediment motion and the classical bedload transport formulas derived with deterministic or probabilistic approaches. How to apply the existing bedload formulas for steep channels remains challenging. In this study, a simple procedure is proposed for correcting slope effects so that the existing bedload formulas can be extended for steep channels. To verify the proposed correction factor, two representative bedload formulas are modified and checked against published data of sediment transport rates that were significantly affected by steep slopes.

The features of an axial-symmetric two-dimensional (2D) model in a transient cavitating pipe flow are investigated. A distributed vaporous cavitation model is proposed, based on the mass and momentum balance equations for a liquid-vapor mixture. A conservation form of the continuity equation allows a simple numerical solution. Both one-dimensional (1D) and 2D models are considered to quantify the effect of friction in the simulation of experimental data. The axial-symmetric 2D model allows the evaluation of the velocity profile and a more accurate estimate of the wall shear stress. The comparison between the results of numerical runs and experimental data of pressure head oscillations in transient cavitating pipe flows shows that the errors on maximum head oscillations of 2D model are generally greatly reduced with respect to those of the 1D model. As expected, the quasi-steady 1D model does not adequately represent the experimental data, with exception of the first maximum oscillations, whereas the 2D model allows for a better evaluation of the observed energy dissipation. In some cases, the 2D model does not estimate properly the experimental phase. This is probably due to the simplifying hypotheses, namely the neglecting of the convective terms, and it is influenced also by the release of dissolved gas, which can be important when the duration of presence of vapor increases. The 2D model also reproduces the observed experimental spikes better than the 1D model.

The simulation of hydraulic transients within fluid line networks is important for many applications (for example, water hammer analysis within distribution networks). However, in many instances, modeling efforts are impeded by the fact that the pipeline parameters are either unknown or can vary significantly from their assumed design values. Consequently, research efforts have focused on the development of parameter identification techniques, mapping from measured transient data to pipeline parameter estimates. A limitation of previous works has been the need for systems to have all boundary conditions either measured or known (e.g., transient pressure measurements or reservoir boundary conditions). This paper aims to relax this requirement and presents a parameter identification method for fluid line networks based on transient-state measurements of the hydraulic state variables of pressure and flow, in the presence of unmeasured and unknown boundary conditions. Utilizing a Laplace-domain admittance matrix representation of the system, the contribution to the hydraulic system dynamics from the measured and unmeasured state variables (i.e., boundary conditions) is made explicit. This model is then used as the basis for the development of a parameter estimation methodology based on the expectation-maximization (EM) algorithm. The importance of the EM approach is that it provides a framework for parameter estimation in the presence of unmeasured state variables by effectively integrating out the influence of the unmeasured variables. Numerical examples demonstrate the utility of this method for a network with a range of pipeline models.

Water diversions along alluvial rivers cause water and sediment loss, and thereby affect morphological development. Assuming spatially continuous diversions along a constant-width channel, previous studies suggest a longitudinally convex bed at the equilibrium state. However, the validity of a convex bed profile for practically discrete diversions in natural channels of longitudinally varying width remains to be justified. Moreover, such equilibrium analysis does not reveal the morphological time scale (MTS) associated with water diversions. To solve these issues, a general theoretical framework is proposed for predicting the equilibrium state of the fluvial system, which is applicable to both continuous and discrete water diversions in a longitudinally width-varying channel. Numerical experiments complement the MTS studies for water diversions. The effects of diversion intensity, diversion placement (discrete and continuous), and diversion scheme (pure water and water-sediment mixture) are also systematically studied. The present work confirms the previous findings that water diversions lead to a decrease of the equilibrium depth with respect to natural conditions and a convex bed in a constant-width channel. Moreover, it reveals that in a widening channel a convex bed also develops under water diversions, whereas convex, concave, or quasi-linear beds may occur in a narrowing channel. Nonmonotonic beds may develop in a strongly narrowing channel, depending on the diversion schemes. On large spatial scales, diversion placement is less important for the equilibrium development. The MTS for water diversions and natural development are very similar and large, indicating considerable influences of water diversions on river morphology. The present work advances the understanding of the long-term effect of water diversions on river evolution.

Dunes are common bed forms in sand bed rivers and are of central interest in water management purposes. Due to flow separation and associated energy dissipation, dunes form the main source of hydraulic roughness. A large number of dune dimension data sets was compiled and analyzed in this study—414 experiments from flumes and the field—showing a significantly different evolution of dune height and length in flows with low Froude numbers (negligible free surface effects) and flows with high Froude numbers (large free surface effects). For high Froude numbers ($0.32–0.84$), relative dune heights are observed to grow only in the bed load dominant transport regime and start to decay for $u_{*}/w_s$ (suspension number) exceeding 1. Dunes in this case are not observed for suspension numbers greater than 2.5. For low Froude numbers (0.05–0.32), relative dune heights continue to grow from the bed load to suspended load dominant transport regime. Dunes in this case are not observed for suspension numbers greater than 5. It was concluded that for reliable predictions of dune morphology and their evolution to upper stage plane beds, it is essential to address both free surface effects and sediment transport mode.