Journal of Hydraulic Engineering

An optimal control methodology is developed to evaluate reservoir management policies that minimize sediment scour and deposition in multiple-reservoir river networks. Consideration is given to adverse effects occurring in both reservoirs and rivers of a hydraulic network. The sedimentation problem is formulated as a discrete-time optimal control problem in which a successive approximation linear quadratic regulator optimization scheme is coupled with the U.S. Army Corps of Engineers HEC-6 sediment transport simulation model. Operational constraints imposed on reservoir storage levels and releases are accommodated using either a bracket or hyperbolic penalty function method. The resulting model also allows the user to evaluate policies that alternatively maximize sedimentation or consider adverse effects only at specified locations. Comparisons of the computational efficiencies between the successive approximation linear quadratic regulator and differential dynamic programming methodology and between different penalty functions are performed. Capabilities of the model are demonstrated through applications to a hypothetical three-reservoir network and the Yazoo Basin river-reservoir network in Mississippi.

This paper presents a numerical analysis of river channel processes with bank erosion. The model can be used for investigating both bed-deformation and bankline shifting in 2D plan form. The basic equations are used in a moving boundary fitted-coordinate system, and a new formulation of nonequilibrium sediment transport is introduced to reproduce the channel processes. The model was applied to examine the morphological behavior of experimental channels. Temporal changes in the plan form in a meandering channel can be classified into two patterns: meander developing and meander straightening. Comparison of the observed and calculated results indicates that the model is applicable to both channel changes under various hydraulic conditions. On the basis of the numerical findings, the paper clarifies the influence of hydraulic variables on the location of bank erosion and bed scouring. The model also was used to investigate the effect of alternate bars on bank erosion and to investigate the development of channel meandering from an initially straight channel.

A second-order hybrid type of total variation diminishing (TVD) finite-difference scheme is investigated for solving dam-break problems. The scheme is based upon the first-order upwind scheme and the second-order Lax-Wendroff scheme, together with the one-parameter limiter or two-parameter limiter. A comparative study of the scheme with different limiters applied to the Saint Venant equations for 1D dam-break waves in wet bed and dry bed cases shows some differences in numerical performance. An optimum-selected limiter is obtained. The present scheme is extended to the 2D shallow water equations by using an operator-splitting technique, which is validated by comparing the present results with the published results, and good agreement is achieved in the case of a partial dam-break simulation. Predictions of complex dam-break bores, including the reflection and interactions for 1D problems and the diffraction with a rectangular cylinder barrier for a 2D problem, are further implemented. The effects of bed slope, bottom friction, and depth ratio of tailwater/reservoir are discussed simultaneously.

The distribution of boundary shear stress in circular conduits flowing partially full, with and without a smooth flat bed simulating deposited sediments, has been examined experimentally ranging from 0.375 < F < 1.96 and 6.5 × 10⁴ < R < 3.42 × 10⁵, using the Preston tube technique The invert level of the flat bed and the water depth have been varied to simulate a wide range of possible flow conditions that may occur in culverts, sewers, and hydropower tunnels. The distribution of boundary shear stress around the wetted perimeter is shown to be highly sensitive to changes in cross-sectional shape. The results have been analyzed in terms of the variation of local/global shear stress versus perimetric distance, and the percentage of the total shear force acting on the wall or bed of the conduit. The %SF_w results have been shown to agree well with Knight's empirical formula for prismatic channels. The influence of secondary flows on the distribution of boundary shear stress and the implications of this for sediment transport have also been examined.

Extended irreversible thermodynamics (EIT) provides a framework for deriving extensions to phenomenological equations (e.g., Newton's law of viscosity, Fick's law of mass transport, and Darcy's law for porous media flow) for problems involving high frequencies (i.e., rapid transients). In this paper, a phenomenological equation is derived for energy loss in 1D unsteady pipe flow using an EIT formalism. The resulting wall shear stress is equal to the sum of (1) the steady-state shear stress; (2) a term that is proportional to the local (i.e., temporal) acceleration; and (3) a term that is proportional to the product of the velocity and the convective (i.e., spatial) acceleration. The form of this EIT-based wall shear stress formula shows that EIT provides a physical basis for instantaneous acceleration based unsteady friction formulas. It also illustrates the limitations and underlying assumptions of these models. For example, instantaneous acceleration based unsteady friction formulas are limited to fast transients (i.e., transients in which the water hammer timescale is significantly smaller than the diffusion timescale). A characteristics solution for unsteady pipe flow is proposed in which the phenomenological equation is used to model energy dissipation. Comparison of numerical test results with measured data from upstream and downstream valve closure laboratory experiments shows excellent agreement.

In this study, the effects of intake-pipe blockage and location of impervious boundaries on critical submergence of an intake pipe are presented. Experiments were conducted on a horizontal intake pipe sited in a dead-end canal flow. Theoretical results and available experimental data are compared. It is shown that, as the distance between the intake-pipe entrance and the dead end gets smaller than the critical submergence depth, the deviation between theoretical and experimental results increases. A potential flow solution still gives acceptable results when this distance is smaller than the critical submergence, but it overpredicts by about 80% when the distance between the intake-pipe entrance becomes much smaller than the critical submergence depth.

The inverse problem of estimating the open-channel flow roughness is solved using an embedded optimization model. Measurement data for flow depths and discharges at several locations and times are used as inputs to the optimization model. The nonlinear optimization model embeds the finite-difference approximations of the governing equations for unsteady flow in an open channel as equality constraints. The Sequential Quadratic Programming Algorithm is used to solve the optimization model. The performance of the proposed parameter estimation model is evaluated for different scenarios of data availability and noise in flow measurement data. Solution results for illustrative problems indicate the potential applicability of the proposed model.

A valve closure algorithm is presented for inclusion within a slow transient (rigid water column) pipe network model. The algorithm is specifically formulated for (but not limited to) node-based, graph-theoretical models and is both direct and accurate. It is distinguished from conventional approaches by its direct assignment of the final discharge at closure to zero and subsequent use of the head loss at the closing valve to compute the flow rate in pipes incident to the closing valve. As a result, redistribution of residual flow prior to closure to these incident pipes is not required, leading to a less computationally demanding and more robust algorithm than previously published valve closure procedures. Application of the valve closure algorithm is illustrated in a pipe network, which also nicely demonstrates again the relation between rigid water column and water hammer models.

Laboratory experiments have shown that screens or porous baffles with a porosity of about 40% could be used as effective energy dissipators below small hydraulic structures, either in a single wall or a double wall mode. The experiments were carried out for a range of supercritical Froude numbers F₁ from about 4 to 13, and the relative energy dissipation was appreciably larger than that produced by the corresponding classical hydraulic jumps. These screens or porous baffles produced free hydraulic jumps, forced hydraulic jumps, and in some cases submerged jumps. The flow leaving these screens was found to be supercritical with a Froude number approximately equal to 1.65 and a tailwater depth equal to 0.28 times the subcritical sequent depth ${\mathit{y}}_{\mathit{2}\mathit{*}}$ of the classical hydraulic jump with the same F₁. To produce a secondary jump downstream of the screens, the tailwater depth needed was found to be about one half of ${\mathit{y}}_{\mathit{2}\mathit{*}}$.