Unsteady Open Channel Flow Research Articles

Control of Canal Flow by Adjoint Sensitivity Method

A new method for control of unsteady flow in open channels is presented. Control is achieved using an iterative approach, the Broyden, Fletcher, Goldfarb, and Shanno quasi-Newton method that utilizes an adjoint sensitivity method to efficiently compute gradient information. The adjoint equations are derived from the differential form of the full shallow-water equations in one dimension and the resulting sensitivies allow a wide class of flows to be controlled. In addition, the adjoint sensitivity method permits both scheduled and adaptive flow control to be achieved. Application of the method to scheduled flow control is presented.

Time of Opening of Irrigation Canal Gates

A criterion for the time of opening of irrigation canal gates is developed based on hydrodynamic principles. An analytical model of unsteady open-channel flow is used to calculate the attenuation of small-amplitude surface transients. Wave attenuation is expressed in terms of a dimensionless parameter containing both steady and unsteady components. The developed criterion is shown to be in agreement with actual field practice in the Imperial Valley, Calif.

EFFECTS OF UNSTEADINESS ON INNER-LAYER CHARACTERISTICS IN SMOOTH OPEN-CHANNEL FLOWS

The inner layer and outer layer of unsteady smooth open channel flows were measured by making use of a twocomponent laser Doppler anemometer (LDA) under the condition that the unsteadiness parameter is very high. In such a situation the von Karman constant decreases in the rising stage and decreases in the falling stage. The friction velocity evaluated from the log law does not coincide with that evaluated from the linear formula in the viscous sublayer with an increase of the unsteadiness. In contrast, the characteristics of normalized turbulence are not affected by the unsteadiness so much; the van Driest's damping factor of the turbulence intensity of the streamwize is almost constant against the normalized time. The third-order moments of the turbulence agree well with those of the steady uniform flow.

Burgers' Equation Model for Unsteady Flow in Open Channels

To simulate slow transients in wide rectangular open channels of finite length, the St. Venant equations are approximated by a single Burgers' equation for flow depth. Flow velocity is expressed as a function of flow depth and its gradient to satisfy the continuity of flow. The Burgers' equation model has three constants uniquely determined with the Froude number of initial uniform flow to satisfy approximately the conservation of momentum for small perturbations of flow depth about an initial constant. For a given set of fixed boundary depths, depth profile and channel storage of final steady nonuniform flow are readily obtained in analytical form. This is a useful feature of the Burgers' equation model. Comparison of the Burgers' equation model with the St. Venant equations is made based on numerical results.

3-D Computation of Unsteady Flows in Compound Open Channels with Horizontal Vortices and Secondary Currents

The non-linear k-ε model is applied to 3-D computation of unsteady flows in compound open channels with horizontal vortices generated by the shear instability and the secondary currents of 2nd kind. Model performance is investigated through the examination of the calculated results. It is pointed out that the typical flow features such as the horizontal vortices and the secondary currents can be simulated numerically by the non-linear k-ε model considering the effect of the strain parameter on the eddy viscosity, though further model refinement is needed to reproduce the 3-D flow structure precisely.

Variational Problem of Water-Level Stabilization in Open Channels

A method is resented for minimization of water-level fluctuations in an open channel controlled by pumping stations at both ends. The situation is posed as a variational problem to determine the optimum upstream flow control, given constraints at the opposite end. the method of indefinite Lagrangian multipliers is used. A global measure—integrated in space and time —of the water level deviation away from some desired water level is defined. The problem involves minimizing this deviation while still satisfying the governing equations and the initial and boundary conditions for the flow. The solution is obtained numerically. The equations governing gradually varied, unsteady open-channel flow are assumed to be valid. A horizontal, frictionless channel of constant trapezoidal crosssection is assumed, although the method could readily be extended to more general conditions. The problem has many applications related to hydropower and water supply canals. An example is resented to illustrate the utility and effectiveness of the method.

Turbulent Structure in Unsteady Depth-Varying Open-Channel Flows

Turbulence measurements over a smooth wall in unsteady depth-varying open-channel flows were conducted by the simultaneous use of a two-component laser Doppler anemometer (LDA) and a water-wave gauge. In the present study, velocity measurements in the viscous sublayer of highly unsteady flow have been first conducted to evaluate the friction velocity independently of the log-law. The von Kármán constant κ was calculated using this friction velocity. It was proven then that the value of κ was really a constant of 0.41 even in unsteady open-channel flows. Next, statistical structures of mean velocity and turbulence characteristics were investigated across the whole flow from the near-wall region up to the free surface. In particular, turbulence measurements near the depth-varying water-surface zone of flood flow were conducted successfully for the first time with the LDA; such measurements have been impossible with conventional velocity instruments such as hot-film anemometers. Mean velocity profiles and turbulence characteristics were revealed in both the rising and the falling stages of the flood period.

Comparison of Numerical Procedures for Gate Stroking

A study was conducted to compare three existing solution methods for the inverse problem of unsteady open-channel flow (i.e., gate stroking). Both the accuracy of the results and the robustness of the methods were examined. Similar solutions were computed with a method-of-characteristics and an implicit finite-difference model, except under extreme transients, in which case the method-of-characteristics model performed better. However, the characteristic model was unable to find a solution for some proposed examples. An explicit finite-difference model was also examined and, although it produced satisfactory results for some examples, it is inherently unstable. A nonlinear, implicit finite-difference gate-stroking method was developed, which was sufficiently accurate and more robust than the existing methods.

Hydraulic Analysis of Undular Bore in Open Channels with Circular Cross Section

Rapidly varied unsteady flow in open channels with the circular cross section is investigated to predict the hydraulic transients in the underground floodways, which have been constructed to mitigate the flood disaster in the metropolitan area for the last decade. The momentum equation for open channel flows with the circular cross section including the effect of the vertical acceleration is derived in this study. The basic equations are applied to the laboratory test on the undular bore, and are verified through the comparison of the calculated results to the experimental ones.

Visualization of Coherent Vortices Generated behind Dune in Unsteady Open-Channel Flows

Coherent vortices such as separated vortex and kolk-boils often occur especially in flood flows. The hydrodynamic behavior of the flood structures is quite different between the rising and falling stages of the flood period. In the rising stage, the concentration of suspended sediment increases due to the kolk-boil vortex because the rising stage corresponds to the growing period of dunes and because separated vortex from the dune collides intermittently at the next dune and washes out bed materials around there. Therefore, the structure of turbulence and the associated coherent vortices over dunes in rivers and estuaries is one of the most important topics in hydraulic engineering. In the present study, flow visualizations by means of dyeinjection and hydrogen-bubble techniques are adopted in order to discuss the elemental structures and unsteadiness effects on separated and kolk-boil vortices from the dune crest.

Velocity and Turbulence Distribution in Unsteady Open-Channel Flows

Unsteady flow properties are experimentally studied in an open channel with a rough bed. A recently developed acoustic Doppler velocity profiler (ADVP) is used to obtain instantaneously the flow profiles. From these measurements, using the Fourier components method, the mean velocities, the turbulence intensities and the Reynolds-stress profile, are obtained. Thirty-three different hydrographs are experimentally investigated. The experimental results show several things. First, unsteady flow can be characterized by the overall unsteadiness parameter, Γ\DHG\N, and by the longitudinal pressure-gradient parameter, β\Du\N. Second, the hydrographs investigated are complete dynamic waves, where the time sequence of \IU\N, \IQ\N, and \ID\N is respected, resulting in the looping rating curves. Third, the distribution of the horizontal velocities, \Iū(y)\N is given by the log law with \IB\N\Dr\N ≅ 8.5 ± 15% in the inner region, being almost independent of the unsteadiness, and by the Coles’ law in the entire region where the wake-strength parameter, Π, depends (inconclusively) on the β\Du\N-value. Fourth, the distribution of the vertical velocities, v¯(\Iy\N), being almost always negative, could be explained with a theoretical relation. Fifth, during the passage of a hydrograph, the turbulence intensities (root-mean-square values) and the Reynolds stress in the rising branch are larger than in the falling branch. Finally, using the equation of Reynolds, a theoretical expression for the Reynolds-stress distribution could be obtained, which compares reasonably well with the measured data.

Friction-Term Response to Boundary-Condition Type in Flow Models

The friction-slope term in the unsteady open-channel flow equations is examined using two numerical models based on different formulations of the governing equations and employing different solution methods. The purposes of the study are to analyze, evaluate, and demonstrate the behavior of the term in a set of controlled numerical experiments using varied types and combinations of boundary conditions. Results of numerical experiments illustrate that a given model can respond inconsistently for the identical resistance-coefficient value under different types and combinations of boundary conditions. Findings also demonstrate that two models employing different dependent variables and solution methods can respond similarly for the identical resistance-coefficient value under similar types and combinations of boundary conditions. Discussion of qualitative considerations and quantitative experimental results provides insight into the proper treatment, evaluation, and significance of the friction-slope term, thereby offering practical guidelines for model implementation and calibration.

Numerical Analysis of Channel Processes with Bank Erosion by Means of Moving Boundary Fitted Co-ordinate System

Channel processes with bank erosion in unsteady open channel flows are investigated in this paper by numerical analysis. As bank erosion and deposition occur with the lapse of time, the area of the numerical object changes with moving the boundaries. Therefore a moving boundary fitted coordinate system is used to analyze the channel process. The model is applied to experiments for the channel processes with bank erosion of straight and meandering channels. The model is verified for the widening process of straight channel, and modified for the meandering channel process by introducing equations of secondary flow component.

Knowledge Acquisition and Representation for Unsteady Open Channel Flow

Knowledge Acquisition and Representation for Unsteady Open Channel Flow

Bed-shear stress in non-uniform and unsteady open-channel flows

(1995). Bed-shear stress in non-uniform and unsteady open-channel flows. Journal of Hydraulic Research: Vol. 33, No. 5, pp. 699-704.

Interaction of surface waves with turbulence: direct numerical simulations of turbulent open-channel flow

We report direct numerical simulations of incompressible unsteady open-channel flow. Two mechanisms of turbulence production are considered: shear at the bottom and externally imposed stress at the free surface. We concentrate upon the effects of mutual interaction of small-amplitude gravity waves with in-depth turbulence and statistical properties of the near-free-surface region. Extensions of our approach can be used to study turbulent mixing in the upper ocean and wind–sea interaction, and to provide diagnostics of bulk turbulence.

Turbulence measurements i n unsteady free-surface flows

Turbulence measurements over a smooth wall in unsteady open-channel flows were conducted accurately by the simultaneous use of a two-component LDA system and water-wave gauges. The ‘general’ log-law distributions, in which the von Karman constant is the universal one of κ = 0.41 but the integration constant A is a function of the main-flow conditions, were satisfied well in the wall region for both the rising and falling stages of flood. On the other hand, the log-wake law was reasonably applied to the outer region including the depth-varying zone. The Coles' wake parameter II increased for the rising stage, whereas it decreased for the falling one. The turbulence is stronger for the rising stage than for the falling one, except for very near the free surface. These unsteady characteristics in open-channel flows with varying water surface are quite different from those in closed duct flows. Of particular significance is the finding of an anticlockwise loop of the velocity and turbulence against varying depth in unsteady open-channel flows.

Unsteadiness Effects on Viscous Sublayer and Wall Region in Open-channel Flows

Near-wall region which consists of viscous sublayer and buffer layer in unsteadyopen-channel flows was measured accurately by making use of a two-component threebeam LDA system; the effects of pressure gradient produced by the time-variation of water surface and discharge were revealed experimentally. Friction velocities evaluated from linear formula and log-law formula coincided well with each other. However, the van Driest damping factor B which indicates the thickness of sublayer varied in the decelerating flows, whereas it showed an opposite manner in the accelerating flows.The von Karman constant K is nearly universal one even in strong unsteady flows. The normalized turbulence intensity was affected by the pressure gradient. The Reynolds stress and other statistical quantities were also changed from their universal distribution of zero pressure-gradient flows.

Structuring and evaluation of VP-Expert based knowledge bases

The effective structuring of knowledge bases is most important for knowledge-based expert-system design, whilst the reliable evaluation of these knowledge bases is the key point for the acceptance of artificial intelligence technology. This paper describes the structuring and evaluation of the knowledge bases for unsteady open channel flow in a river network employing the VP-Expert shell. A tree structure and its parameter hierarchy are designed and implemented in the VP-Expert environment. The architecture of the system is described and some proofs of its satisfactory performance are given. Moreover, the manuscript discusses the experience gained through this implementation process. White-box and black-box testing strategies are used to evaluate the knowledge bases. Some typical rule errors and debugging techniques are also summarized.

EXPERIMENTAL STUDY ON TURBULENT STRUCTURES IN UNSTEADY OPEN-CHANNEL FLOWS

洪水時の河川にはコルクボイル渦に代表されるように様々な組織構造が存在する. これらの実河川にみられる現象は, 洪水の増水期と減水期とではまったく異なる特性を示すことが知られている. 本研究では, 実河川に発生する各種の組織乱流を解明する第一段階として, 非定常開水路流れにおける平均流速分布の特性, 乱れ特性およびせん断応力特性, さらに2次流の影響について実験的検討を行った.