Journal of Hydraulic Engineering

Local clear-water and live-bed scour tests were performed for a range of water depths and flow velocities with two different uniform cohesionless sediment diameters (0.27 and $0.84\mathrm{mm}$ ) and a circular pile with a diameter of $0.15\mathrm{m}$ . The tests were performed in a tilting flume ( $1.5\mathrm{m}$ wide, $1.2\mathrm{m}$ deep, and $45\mathrm{m}$ long) located in the Hydraulics Laboratory at the University of Auckland in Auckland, New Zealand. These tests extend local scour data obtained in controlled experiments to velocity ratio $(V∕V_c)$ values as high as 6. This is near the velocity where the peak live-bed scour occurs for the sediment and flow conditions. Scour depth predictions are made with four different local scour equations for the conditions of the tests and the results compared with the measured values.

Turbulent open-channel flow over a two-dimensional dune is studied using an established large-eddy simulation code. The free surface is approximated as a shear free boundary. Turbulence statistics and instantaneous flow structures are examined. Numerical results from two computational grids agree with each other, and are also in good agreement with recently obtained experimental data. The mean velocity profiles show significant changes along the dune and there is no region that conforms to the standard law-of-the-wall. Profiles of the Reynolds stresses show distinct peaks marking the shear layer that originates from flow separation at the dune crest. Secondary peaks found further from the dune are ascribed to the shear layer over the upstream dune. Details of the separated flow and development of the flow after reattachment are well predicted. Quadrant analysis of the Reynolds shear stress shows that turbulent ejections dominate the near-wall motions. Complex water surface flow structures are visualized.

A novel technique is presented for the treatment of the bed slope source terms within the numerical solution of the shallow water equations. The proposed method consists of writing the bed slope source term as the divergence of a proper matrix, related to the static force due to bottom slope. Such a technique is founded on analytical reasoning and is physically based, so that it can be easily applied to a wide range of numerical models, as it is completely independent of any adopted discretization technique, and requires a minimum computational effort. Herein, we show an application to a Godunov-type model, second order accurate both in space and time, based on the finite-volume method. The presented technique leads to a strong improvement in the source terms numerical treatment, especially for steady states, in which flux gradients are exactly balanced by source terms. A surprising degree of simplicity is maintained, with respect to different existing methods. The numerical model has been applied to a set of classical test cases and to a selected laboratory experiment, in order to verify its stability, accuracy, and applicability to practical real-world cases.

The Saint Venant equations are often combined into a single equation for ease of solution. As a result however, this single equation gives rise to several redundant nonlinear terms that may impose significant limitations on model analyses. In order to avoid this, our paper employs a new procedure that separates, in the Laplace frequency domain, the governing equation of water depth from that of flow velocity and thus enables us to consider two independent equations rather than two coupled ones. The so-obtained analytical solutions are valid for prismatic channels of any shape. Solution validity is assured by repeated comparison with the corresponding numerical solutions based on Crump’s algorithm, which accelerates solution convergence. Utilizing this new procedure, this paper will construct a basic wave spectrum for classifying subcritical flow waves in a prismatic channel. The spectrum is basically a contour plot of the normalized specific energy loss for a small water wave moving in the channel for a finite distance of approximately $100\mathrm{m}$ . The distance is chosen so that four distinct regions with different contour patterns that represent kinematic, diffusion, gravity, and dynamic waves in a river are shown in the spectrum. By incorporating the spectrum with Ferrick’s criteria and Manning’s formula, a single contour line is also generated, which serves as the boundary of the four regions. Example computations show that the spectrum predicts a similar trend of wave attenuation for waves propagating in a trapezoidal channel. When the rising speed of a wave is of concern, the full Saint Venant equations are solved numerically to reconstruct a similar spectrum good for supercritical flow as well.

Unsteady depth-varying open-channel flows are really observed in flood rivers. Owing to highly accurate laser Doppler anemometers (LDA), some valuable experimental databases of depth-varying unsteady open-channel flows are now available. However, these LDA measurements are more difficult to conduct in open-channel flows at higher unsteadiness, in comparison with unsteady wall-bounded flows such as oscillatory boundary layers and duct flows. Therefore, in this study, a low-Reynolds-number $k–\epsilon$ model involved with a function of unsteadiness effect was developed and some numerical calculations were conducted using the volume of fluid method as a free-surface condition. The present calculated values were in good agreement with the existing LDA data in the whole flow depth from the wall to the time-dependent free surface. These values were also compared with those of unsteady wall-bounded flows. The present calculations were able to predict the distributions of turbulence generation and its dissipation, and consequently the unsteadiness effect on turbulence structure was discussed on the basis of the outer-variable unsteadiness parameter $\alpha$ , which is correlated with the inner-variable unsteadiness parameter ${\omega }^{+}$ in unsteady wall-bounded flows.

In this paper, basic unsteady flow types and transient event types are categorized, and then unsteady friction models are tested for each type of transient event. One important feature of any unsteady friction model is its ability to correctly model frictional dissipation in unsteady flow conditions under a wide a range of possible transient event types. This is of importance to the simulation of transients in pipe networks or pipelines with various devices in which a complex series of unsteady flow types are common. Two common one-dimensional unsteady friction models are considered, namely, the constant coefficient instantaneous acceleration-based model and the convolution-based model. The modified instantaneous acceleration-based model, although an improvement, is shown to fail for certain transient event types. Additionally, numerical errors arising from the approximate implementation of the instantaneous acceleration-based model are determined, suggesting some previous good fits with experimental data are due to numerical error rather than the unsteady friction model. The convolution-based model is successful for all transient event types. Both approaches are tested against experimental data from a laboratory pipeline.

The accurate simulation of pressure transients in pipelines and pipe networks is becoming increasingly important in water engineering. Applications such as inverse transient analysis for condition assessment, leak detection, and pipe roughness calibration require accurate modeling of transients for longer simulation periods that, in many situations, requires improved modeling of unsteady frictional behavior. In addition, the numerical algorithm used for unsteady friction should be highly efficient, as inverse analysis requires the transient model to be run many times. A popular model of unsteady friction that is applicable to a short-duration transient event type is the weighting function-based type, as first derived by Zielke in 1968. Approximation of the weighting function with a sum of exponential terms allows for a considerable increase in computation speed using recursive algorithms. A neglected topic in the application of such models is evaluation of numerical error. This paper presents a discussion and quantification of the numerical errors that occur when using weighting function-based models for the simulation of unsteady friction in pipe transients. Comparisons of numerical error arising from approximations are made in the Fourier domain where exact solutions can be determined. Additionally, the relative importance of error in unsteady friction modeling and unsteady friction itself in the context of general simulation is discussed.

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 $\mathsf{H}$ , defined as the ratio of the relative increment of shear stress to the increment of width/depth ratio. This study suggests that $\mathsf{H}$ needs to be adopted as a criterion of hydraulic similitude for modeling sediment (bed-load) transport in alluvial channels.

The movement of finite amplitude sediment accumulations is studied using a simple advection-diffusion relation derived from the sediment continuity equation and using some heuristic reasoning. The movement of a finite amplitude sediment accumulation is found to be strongly diffusive with a small advection component due to the increase in transport rate of the sediment accumulation relative to the transport rate of the original bed material. A semianalytical solution to the advection-diffusion equation is found and the equation is applied to two laboratory experiments. The equation is found to predict the general movement of finite amplitude sediment accumulations with a minimal number of parameters.

Large-scale horizontal vortical structures are generic features of shallow flows which are often modeled using the two-dimensional (2D) depth-averaged equations. Such modeling is investigated for the well-defined case of shallow wakes of a conical island of small side slope for which a three-dimensional (3D) boundary-layer (3DBL) model has previously been validated through comparison with experiment. The 3DBL model used a 3D, two-mixing-length, eddy-viscosity turbulence model with a vertical mixing length of classical Prandtl form and a horizontal mixing length some multiple of this. A multiple of six gave good predictions. This mixing length approach is reduced to depth-averaged form, giving a horizontal mixing length of about half the water depth. The shallow wakes may be vortex shedding or steady/stable and are conventionally defined by a stability parameter. The critical value above which a stable wake is formed is considerably overestimated by the depth-averaged model (for a range of mixing lengths) and the length of stable wake bubble is considerably underestimated. It seems likely that this is because the amplification of friction coefficient due to horizontal strain rates is not represented. However, when vortex shedding is prominent the 2D and 3DBL wake structures are quite similar. These results show, for example, the limitations of depth-averaged models for the prediction of solute dispersion.

A three-dimensional (3D) computational fluid dynamics (CFD) model of a contact tank is presented in this paper. The model results are compared against 3D velocities and flow through curve (FTC) data, representing a tracer concentration profile, from a 1:8 scale physical model. The objective is to demonstrate that CFD models can simulate both the FTC and the 3D velocity field quite well. Simultaneous validation of velocities and FTC is important in ascertaining the predictive capabilities of CFD models, as physical model studies indicate that different baffle arrangements can lead to similar FTCs. Therefore, a good prediction of only FTC, as presented in previous 3D CFD model studies, does not necessarily imply a correct simulation of the flow field.