Journal of Hydraulic Engineering

This paper presents the investigation of gravity currents by both laboratory experiments and a mathematical model. Eleven lock-exchange experiments, in which lock position, the initial current height, and density varied, were carried out to test the model validity and to compare laboratory results with previous expressions found in the literature. A two-layer shallow-water model was used to simulate all the runs. This model is new if compared with previous shallow-water models used to simulate gravity currents, because it accounts for both the entrainment and the free surface. A modified Turner’s formula is used to model the entrainment between the two fluids. The developed shallow-water models with and without entrainment are also compared, showing a better agreement when mixing is accounted for. Also, the effect of the free surface is shown by comparing the developed two-layer shallow-water model with a free surface and two different single-layer models with a rigid-lid approximation. Laboratory experiments and model simulations, accounting for both the entrainment and the free surface, are in good agreement. Front velocities, measured during the slumping phase, were compared with both predicted ones and previous expressions found in the literature, showing in most of the cases better result when the developed model is used.

This paper presents a new method, the water stage prediction-correction (WSPC) method, based on the theory of characteristics to couple numerical models in the boundary-connected way for shallow-water flows. From the WSPC method, a one-dimensional (1D)–two-dimensional (2D) coupled numerical model is established, which incorporates the artificial porosity method and is thus capable of treating wetting and drying. Details of the 1D submodel and the 2D submodel are given, with special emphasis put on the coupling between the submodels. With the help of the WSPC method, the physically coupled submodels are executed separately and then coupled by means of prediction-correction of the water stages at the coupling units (i.e., where the submodels are linked) so that it is possible to make use of existing submodels with minimum modifications. The convergence of the WSPC method is proved, and the parameter identification is discussed, taking a flat-bottom channel with rectangular cross section as an example. The one-dimensional 1D–2D coupled model is applied to both a hypothetic case and a real-life case in central China, and the results show its validity, stability, and practical reliability.

We study the evolution of two-dimensional high-Reynolds-number density currents propagating over horizontal porous substrates initially saturated with a lighter fluid when an impermeable surface under the bed is used and a Darcy flow through the medium takes place. Laboratory experiments were performed varying the initial characteristic parameters such as the volume released, the height-to-width ratio of the dense fluid, the relative density difference between the current and ambient fluids, and the bed depth. The dynamic changes of the gravity-driven flow and the influence of the thickness of the porous substrate are described by means of an empirical analysis that considers two lower boundary conditions of the bed, that is, when it is bounded from below by an impermeable or a permeable layer. Thus, the new experimental results are integrated to previous findings in a unified theoretical treatment. In the present case, the dense fluid penetrates into the porous layer pushing the lighter one through the upper boundary located ahead of the current, as shown by the vorticity distribution, and modifying the interaction between the flows over and inside the bed. This flow in the neighborhood of the front, although important, is smaller than the one that would pass through the lower boundary if this were permeable.

The possibility of leak detection in a viscoelastic pipe system is studied. The frequency response function method (FRFM) is used for leak detection, and the analytical expression for the FRFM originally developed for an elastic pipeline is extended to the viscoelastic situation in this study. The extended FRFM is validated from numerical experiments with one-dimensional viscoelastic transient models. The analysis shows that the pipe-wall viscoelasticity effect has significant impact on the amplitude damping and phase shift of the pressure wave, but little influence on the leak-induced patterns of pressure head peaks in transient system frequency responses. The results indicate that the extended FRFM is applicable to the viscoelastic situation. The impact of viscoelastic parameters and incident wave bandwidth on the applicability of the extended FRFM i also investigated in this paper, and the results imply that transient input signals with rapid changes in time are preferable for leak location in viscoelastic pipelines.

This paper investigates the importance of pipe system scale—specifically pipe length and diameter—on unsteady friction in pipe transients. A dimensionless analysis is conducted for the one-dimensional (1D) water-hammer model in this study and the analytical expression for the relative importance of unsteady friction damping to the total friction damping is obtained in the frequency domain. In addition, a two-dimensional (2D) waterhammer model coupled with a 2D $\kappa \mathrm{\text{-}}\epsilon$ turbulence model is applied to a reservoir-pipe-valve system. A parametric study covering a number of pipe diameters, pipe lengths, and initial Reynolds numbers is conducted. The investigation spans a range of water-hammer travel time and turbulent radial diffusion timescales. In each case, the transient is generated by a sudden and complete valve closure. The analytical solution for the importance of unsteady friction is verified by the numerical simulations and the results show that unsteady friction damping has less effect on the damping rate of the transient envelope as (1) the ratio of the wave travel timescale to the radial diffusion timescale increases and (2) the product of the initial friction factor and Reynolds number increases. Furthermore, the findings of this study are validated by both laboratory and field experiments from literature. The implication of the findings is that the role of unsteady friction on the damping rate of the transient envelope diminishes with the scale ratio of pipe length and pipe diameter and that laboratory experiments, which are usually limited to relatively small scale ratios of pipe lengths and diameters, have lead researchers to overestimate the importance of unsteady friction on the damping of the transient envelope in real large pipe-scale systems.

To promote grade-control, bank stability, and fish habitat enhancement, three-dimensional structures installed within river channels are becoming increasingly popular choices for rehabilitation. A-, U-, and W-shaped rock weirs are commonly used in streams, yet three-dimensional scour holes develop downstream of the weir crest and often undermine the weir foundation. Current approaches for the prediction of scour depth and geometry are generally extrapolated from the case of two-dimensional flow. Furthermore, data from the literature regarding structures inciting significant lateral flow components are sparse. A series of laboratory experiments were conducted in which data from A-, U-, and W-shaped weirs were collected and evaluated using scour-prediction methodologies, focusing on their applicability to predict maximum scour depths. New dimensionless expressions were developed for the prediction of scour depth downstream of A-, U-, and W-shaped weirs on the basis of laboratory data that incorporate specific parameters accounting for weir geometry. The dimensionless expressions were compared with the most accurate relationship found within the literature, as applied to the compiled database, and mean error was reduced from 37.12 to 10.45%.

The results of an experimental study on clear-water scour at pile groups under steady flows at threshold velocity are presented. A wide range of pile group arrangements, spacing, and submergence ratios are studied. Uniform bed material in a 46-m long, 1.52-m wide, and 1.9-m deep flume was used to obtain comprehensive data. Empirical relations to demonstrate the effects of the studied variables are presented. On the basis of the findings of this study, a new method to predict the effect of pile group arrangements, pile spacing, and submergence ratio on local scour depth is proposed. The experimental data obtained in this study and data available from the literature are used to evaluate predictions of existing methods and the accuracy of the proposed method. The proposed method gives reasonable scour depth predictions.

Failures of bridges that span a waterway often result from scour and channel instability near the bridge foundations. The Houfeng Bridge, which crosses the Da-Chia River in central Taiwan, collapsed in the 2008 typhoon flood event. On the basis of the historical records and survey of related data just after the collapse of the bridge, a methodology for the assessment of scour depth, including long-term general scour caused by earthquake and impinging jet scour generated by a concrete encased pipeline, is illustrated in the present study. The proposed method provides reasonable estimates for various scour components, which implies that before constructing a new or rebuilding an old bridge, one should use proper methodology and formulas to evaluate the scour potential and improve the bridge design, especially for bridges that are founded around the Houfeng Bridge. This case study also highlights the important effect of long-term general scour on bridge stability. In addition, a lesson is learned from this case study regarding the importance of bridge operation.

In recent years, spillway rehabilitation has increased in importance and become the subject of many projects worldwide. One solution for this problem is the implementation of a new type of labyrinth spillway, called Piano Key Weir (PK-Weir ). This is an excellent alternative for increasing the overflow capacity of existing dams. Similarly to traditional labyrinth weirs, the hydraulic capacity of a PK-Weir is a function of its geometrical characteristics. Currently, there is a lack of systematic experiments, and the existing data does not allow the proposition of a universal design procedure. This paper reviews the previous studies on the efficiency of planned and built PK-Weirs. The results are evaluated by comparing an actual PK-Weir’s discharge to that theoretically obtained for a sharp-crested spillway with crest length equal to the width of the PK-Weir for a given hydraulic head. On the basis of this evaluation, a preliminary design procedure is proposed.

Fixed-cone valves (FCVs) are practical devices used to regulate flow at dams having medium to high heads. These valves are designed to safely reduce the flow energy by redirecting the pipe flow into a free-discharging conical jet and, under certain circumstances, through a hood or another containment structure to control the conical jet. However, the hood concentrates the jet and, consequently, the remaining energy. A relatively new hood design using baffle blocks has been successful in reducing the area required to contain and dissipate the jet energy. Although baffle blocks have previously been used in cylindrical FCV hoods, there is no established design standard for the placement and sizing of the blocks. This paper considers a design not previously documented in the literature for an FCV with a conventional hood that implements baffle blocks. The design analysis uses both computational fluid dynamics and physical modeling and compares the results.

This study presents a simple model to predict the liquid volume flux induced by round bubbly jets. The model is based on the classical integral equations for bubble plumes, but also accounts for the momentum at the source by including new conditions for the initial liquid jet velocity and radius. Moreover, an exponential functional relationship is used to relate the entrainment coefficient to a densimetric Froude number. The model predicts well the experimental results available in the literature for bubbly jets. Model simulations plotted together with experimental data for both bubbly jets and bubble plumes also reveals a clear jet/plume transition, resulting in entrainment rates in the bubbly jet zone larger than those in the bubble plume zone. Finally, potential applications of the model in aeration/mixing systems are presented.

Finite volume (FV) slope limiting is essential to stabilize discontinuous Galerkin (DG) solutions despite a number of side effects such as local loss of accuracy and increased run-time cost. These side effects have been experienced with DG solutions to the homogeneous system of conservation laws and are usually accepted as long as they do not affect the reliability of the numerical predictions and provide a better stability property. They have also led to the concept of localizing the slope-limiting process. When a model is applied to simulate the flow problems that necessitate the solution of the inhomogeneous shallow water equations (SWEs) with/without flooding and drying, the slope-limiting routine can have extra adverse effects on the local DG framework. These effects, causes, and implications on DG solutions to the SWEs have not yet received adequate attention, and a full investigation is therefore needed. With the aim of improving a second-order Runge-Kutta discontinuous Galerkin (RKDG2) SWE solver, the effects of FV slope limiting on the RKDG2 flow solutions were analyzed. Three versions of the RKDG2 scheme were configured: the first and second versions were respectively associated with the local limiting (LL) and global limiting (GL) processes, which both use limiter-free linear front tracking (LFT) to trace a wet/dry front, and the third was implemented with the local limiting process but with constant front-tracking (CFT) of the wet/dry front. Selected hypothetical and practical hydraulic tests were investigated to demonstrate the effects of different limiting processes and front-tracking techniques.