Waves In Open Channel Research Articles

Performance of OWC device under Stokes second-order waves

The present work simulates the flow behavior in the system having oscillating water column (OWC) device for wave energy conversion using numerical modelling. To achieve this, the OWC device is structured inside the 2-dimensional numerical wave tank (NWT). Using the ANSYS Fluent software and the multiphase-based CFD technique, the issue is resolved. Unsteady, transient, and pressure-based solvers are included in this work. In this numerical model, the governing equations are based on Reynolds Averaged Navier-Stokes (RANS) equations with the Shear Stress Transport (SST) model, to capture the turbulence effect and the interface of 2-phases are implicitly captured by using volume of fluid (VOF) method. Using an open-channel wave generator, this study generates nonlinear “second-order Stokes waves”. In addition, the impact of nonlinearity on the “free surface description” at specific locations, the vertex average of total pressure near the air-duct, and the vertex average of y-velocity through the air-duct per unit width of the OWC device are investigated in detail. The outcomes indicate that the OWC device will consistently extract energy over an extended period of time.

Critical analysis of turbulence models for simulating positive surge waves in open channels in a RANS-VOF setup

Critical analysis of turbulence models for simulating positive surge waves in open channels in a RANS-VOF setup

Numerical Examples of Non-Dissipative Discontinuous Kinematic Waves in Open Channels

The kinematic wave model under the assumption of balanced gravity and friction forces has been applied in open channel hydraulics and surface hydrology. There persists a severe misunderstanding that a discontinuity of a kinematic wave occurs due to a discontinuity of input and then dissipates. This study clarifies that a discontinuity can develop without dissipation under the smoothness of all input. The theory of first-order quasilinear partial differential equations shows that Cauchy problems for the kinematic wave model have unique measurable and bounded solutions, which are possibly discontinuous. Numerical examples are presented to visualize the fundamental properties of discontinuous kinematic waves.

Numerical investigation on aerodynamic performance of a ducted fan under interferences from the ground, static water and dynamic waves

Ducted fans have been widely applied in various VTOL (vertical takeoff and landing) vehicles due to their high efficiency and low noise. By using the sliding mesh technique to simulate propeller rotation, a ducted fan system is chosen and the effects of the ground, static water and dynamic waves on its aerodynamic performance are evaluated, thereby exploring the adaptability of the system to complicated environments. The ground is set to slip wall moving with the same speed as the free stream and the static water surface is identified by using the VOF model. To generate dynamic waves, the open channel wave boundary is investigated to simulate a Stokes wave combined with the VOF model. A series of calculation cases consisting of free space, the ground effect, the static water effect and the wave effect are observed and analyzed in detail. The results indicate that ground, water surface and wave can strongly affect the aerodynamic performance of the ducted fan, as they interrupt the jet flow from the outlet of the duct and further pull the rebounded flow into the system. A decrease in the height between the system and the surface leads to a greater influence on the ducted fan. The strong effect obtained by the rigid ground benefits the lift of the propeller the most but also greatly weakens the lift of the duct; ultimately, the total lift of the system is lost. The torque changes by a law similar to that of the lift. The soft water surface is impacted to form a “drainage area”, which can be considered to increase the distance between the system and the water. Therefore, the water effect is not as strong as the ground effect. However, the change rules of the lift and the torque are nearly the same as those for the ground effect. The dynamic wave has the most complicated effect on the system. The periodic wave causes unpredictable periodic changes on the lift and the torque of the duct and the propeller, which may be related to numerical wave attenuation and the real-time changes in the soft wave surface. A larger wave height and a shorter distance between the wave and the system lead to a greater influence on the ducted fan. Moreover, the dynamic wave can induce “dynamic uplift” and hysteresis phenomena on the aerodynamic performance of the system.

IMPROVING SUPERVISORY CONTROL WATER DISTRIBUTION OF IRRIGATION CANALS RECLAMATION SYSTEMS

Background: Examine issues of dispatching management of water distribution systems in the reclamation channels using a systematic approach. Materials and methods: Integrated automated control systems are actively developed implemented to manage water distribution in irrigation canals. It needs to take into account the dynamic processes of water flow while the automation of water distribution in open channel irrigation network system must. Imitating mathematical modeling of water distribution during transient driving mode is the process of studying the dynamic properties of these automated control systems on the basis of analytic solutions of differential equations in partial derivatives. Results: Algorithms and mathematical models in the form of a software package, which describes the behavior of object of control, while it’s depending on its condition, control actions and possible disturbances. The elements functional water distribution mathematical model constructed on the basis of control algorithms taking into account the work of the majority of water consumers “on demand”. Conclusion: Based on the simulation and field research there were presented recommendations on the calculation of the propagation time of the disturbance waves in open channels, regarding the selection and appointment of the optimum parameters of channels and structures on them, the lengths of the calculated areas, slope of the bottom of the distribution channels, pressures and quantities shutter opens on structures, the choice of cross-sections sections of the channels for the installation of control equipment at unsteady flow regime.

Roll waves in channels with an active gas phase

A mathematical model of the flow of a thin layer of heavy liquid under an elastic shell filled with gas is constructed. By means of mass exchange with the environment, the gas phase is active and maintains self-organized wave motion in the liquid layer. The conditions under which small perturbations are transformed into quasiperiodic wave packets of finite amplitude which move in the same direction are found. It is shown that the structure of the waves is similar to that of roll waves in open channels.

Multiple-grid finite element solution of the shallow water equations: Water hammer phenomenon

A hybrid Multiple-grid finite element approach is detailed for solving the shallow water equation with shock waves in open channels. This approach addressed as Multiple-grid finite element method (MG-FEM), aims at accelerating the solution to the non-oscillatory desired transient state. For numerical stability, the time step was a function of discharge and flow area to avoid restriction due to the wave celerity variation in the computational analysis when using the method of characteristics. Results of numerical tests were solved with the MG-FEM. The first test involves routing a discharge hydrograph down a rectangular channel. The second consists on routing a dam break problem. The third includes transient flows with shock waves, namely water hammer, due to abrupt closure of the flood gate at the downstream end. The validity of numerical models is obvious compared with experimental and analytical data. Comparison of the developed solution and those obtained from the literature show that the proposed method is consistent, accurate and highly stable in capturing shocks in free surface flows. Moreover, results indicate that the computation effort is competitive compared with the existent shock capturing methods.

Unsteady turbulent properties in negative waves in open channels

In an open channel, a sudden drop in free-surface elevation is associated with the development of a negative wave. While some simple analytical solution is widely described in textbooks, little research was conducted to date on the unsteady turbulence properties beneath negative waves. A series of new physical experiments were conducted in a rectangular channel. The unsteady free-surface profile and turbulence characteristics were measured in a negative wave propagating upstream against an initially steady flow using non-intrusive acoustic displacement meters, video imagery and acoustic Doppler velocimetry (ADV). For one set of flow conditions, the experiments were repeated 25 times at two longitudinal locations and four vertical elevations to yield ensemble-averaged data. The wave leading edge propagated upstream with a speed which was a function of time and space. The velocity data showed that the upstream propagation of the negative wave was linked with a gentle drop in water elevation associated with an acceleration of the flow, while some increased turbulence occurred beneath the wave associated with large velocity fluctuations and large Reynolds stress components. The velocity fluctuations and turbulent stresses were significantly larger than in the initially steady flow and in the final flow motion.

Positive surge in trapezoidal and circular channels

A series of algorithms is proposed for calculating the flow depth ratio and surge wave velocity for positive surge waves in open channels of rectangular and trapezoidal sections and for circular sections running part full. These algorithms make use of the standard formulations for the solution of problems of this kind and propose some iterative protocols (Newton–Raphson, numerical interpolation) for finding the desired result. The algorithms may be incorporated into a spreadsheet or a similar software package for use by hydraulic design engineers. Some results for a few selected cases are presented and show a dependence of depth ratio and surge wave velocity on flow ratio and on Froude number prior to the arrival of the surge wave. There is also a dependence on flow and channel scale in all cases, except that for rectangular flows; the depth ratio is independent of scale for the conditions investigated. There is also evidence of a minimum surge wave velocity for surge waves moving downstream at a specific Froude number for rectangular and circular sections, although not for trapezoidal sections. The algorithms generally give good agreement with the literature, although it is noted that in real situations an undular wave front is generally observed, and that most of the experiments cited have hitherto only been carried out in rectangular channels. Given the effect of friction on moderating the passage of the surge wave, the idealised assumption of a frictionless channel is clearly of importance.

Lagrangian Modeling of Weakly Nonlinear Nonhydrostatic Shallow Water Waves in Open Channels

A Lagrangian, nonhydrostatic, Boussinesq model for weakly nonlinear and weakly dispersive flow is presented. The model is an extension of the hydrostatic model—dynamic river model. The model uses a second-order, staggered grid, predictor-corrector scheme with a fractional step method for the computation of the nonhydrostatic pressure. Numerical results for solitary waves and undular bores are compared with Korteweg-de Vries analytical solutions and published numerical, laboratory, and theoretical results. The model reproduced well known features of solitary waves, such as wave speed, wave height, balance between nonlinear steepening and wave dispersion, nonlinear interactions, and phase shifting when waves interact. It is shown that the Lagrangian moving grid is dynamically adaptive in that it ensures a compression of the grid size under the wave to provide higher resolution in this region. Also the model successfully reproduced a train of undular waves (short waves) from a long wave such that the predict...

TVD scheme for computing open channel wave flows

For the shallow water equations in the first approximation (Saint-Venant equations), a TVD scheme is developed for shock-capturing computations of open channel flows with discontinuous waves. The scheme is based on a special nondivergence approximation of the total momentum equation that does not involve integrals related to the cross-section pressure force and the channel wall reaction. In standard divergence difference schemes, most of the CPU time is spent on the computation of these integrals. Test computations demonstrate that the discontinuity relations reproduced by the scheme are accurate enough for actual discontinuous wave propagation to be numerically simulated. All the qualitatively distinct solutions for a dam collapsing in a trapezoidal channel with a contraction in the tailwater area are constructed as an example.

Solution of the propagation of the waves in open channels by the transfer matrix method

Many problems in mechanics can be solved by the use of the transfer matrix method. The use of this method in hydraulics engineering is not widespread and only limited studies are available. In this study, linearized St. Venant equations were used and the use of transfer matrix in ocean engineering was investigated for long waves in open channels, and numerical application was carried out. The results obtained through the transfer matrix method, which is quite easy to use, program and comprehend, showed similar results obtained from the characteristics method and finite differences method.

Undular bores (favre-waves) in open channels - Experimental studies

New, detailed investigations of the formation of surge waves in open channels are presented in this paper. These supplement the experiments of Favre and also include measurements in a trapezoidal c...

Coupled continuum perturbative Feshbach approach to calculate total and partial widths: 1,3Se(3lnl) resonant states of He, C4+, N5+, and O6+

We apply a perturbative method, which takes into account the interaction between different open channels, to calculate total and partial widths of atomic resonances in the framework of the Feshbach formalism. The method requires the calculation of elastic, e.g., noncoupled open-channel wave functions, as in the case in which only one channel is open, thus avoiding the solution of complicated systems of coupled differential equations. As an illustration we have calculated energy positions, total and partial widths of $^{1}$,3${\mathrm{S}}^{\mathrm{e}}$(3lnl) resonant states of He, ${\mathrm{C}}^{4+}$, ${\mathrm{N}}^{5+}$, and ${\mathrm{O}}^{6+}$. Our results show that the accuracy reached with this simple approach is comparable to other different non-Feshbach methods and that neglect of the coupling between different open channels can be considered as a reasonable approximation to obtain total and partial widths.

Internal waves in an elliptical channel

Abstract Internal waves in open channels of various depths are studied, in this paper, and a wetted cross section with an elliptical bottom is considered. The frequencies of the first three sloshing modes of internal waves in two superposed fluids contained in an elliptical channel are calculated for various ratios of the depths of the two layers. Numerical solutions converge to analytical solutions based on the shallow water theory as the depth of the thin lower layer approaches zero. Also, solutions for the frequencies of the longitudinal modes of progressive internal waves in two superposed fluid layers contained in an elliptical channel are calculated for various ratios of the depths of the two layers and for two different wave numbers k.

Waves in Open Channels

Gravity waves in trapezoidal channels and channels with curved bottoms, including sloshing, longitudinal, and combined modes, are treated. Analytical‐numerical solutions are given for the wave frequency and the velocity potential for waves in trapezoidal channels, and analytical solutions based on the shallow‐water theory are obtained for waves in curved channels.

A new non-linear conceptual model of flood waves

This paper reports the successful simulation of St. Vénant's nonlinear distributed model of flood waves in open channels using a much simpler nonlinear lumped conceptual model. The simpler model is composed of a cascade of equal nonlinear storage elements preceded by an element of pure delay. The simpler model depends on four parameters only. The first two terms of the Taylor expansion of the state trajectory are shown to be equivalent to the first two terms of a Volterra convolution series. The accuracy of this quadratic approximation is shown by an example.

Waves in open channels : Shi, Jinsung and Chia-Shun Yih, 1984. J. Engng Mech., Am. Soc. civ. Engrs, 110(6):847–870

Waves in open channels : Shi, Jinsung and Chia-Shun Yih, 1984. J. Engng Mech., Am. Soc. civ. Engrs, 110(6):847–870

Graphical determination of the height of surge waves

This study deals with the propagation of surge waves in open channels. The governing equations are derived for an arbitrary cross-section and specific solutions are given for rectangular, parabolic, and trapezoidal cross-sections. The method can be applied in each case, where the relation between the level and the area is known in advance. The hypotheses are the same as in classical treatises of surge waves, but the derived equations in dimensionless parameters show the possibility of plotting graphs for the given profile, which allows the finding of the solution in each case without a trial-and-error procedure, as with the classical method. The same equations show that (a) in the case of positive waves generated at the upstream side of a channel, two of the three defined parameters can have any prescribed value and the third can readily be found; (b) in the case of positive waves generated at the downstream end, an inequality must hold in order that the third parameter has a physical interpretation.

Theoretical Estimation of Flood Routing Parameters

Many hydraulic engineering problems involve the computation of the propagation of flood waves in open channels. The complexity inherent in the calculations based on the solution of the full equations has led to the development of approximate methods, which have become especially popular among hydrologists. From the point of view of the application, much interest is focused on their calibration, i.e. on the determination of the model parameters. The scope of this note is to communicate the writer.s experience with this problem, especially with respect to the design of open channels.