Dimensional Open Channel Research Articles

Stability analysis and numerical simulations of a one dimensional open channel hydraulic system

This paper is dedicated to the qualitative analysis as well as numerical simulations of a one dimensional open channel hydraulics system which is commonly used in hydraulic engineering to model the unsteady flow dynamics in a river. First, an output feedback control is proposed. Next, the closed-loop system is proved to possess a unique solution in a functional space. Furthermore, the spectrum and resolvent sets of the system operator are characterized. Then, stability results are stated and proved according to a smallness assumption on the feedback gain. The proof invokes Lyapunov direct method. Last but not least, we adopt the Chebychev collocation method, that uses backward Euler method and the Gauss-Lobatto points, to provide numerical simulations in order to ascertain the correctness of the theoretical outcomes.

Iber: herramienta de simulación numérica del flujo en ríos

The recent requirements of Spanish regulations and directives, on their turn based on European directives, have led to the development of a new two dimensional open channel flow modelling tool. The tool, named Iber, combines a hydrodynamic module, a turbulence module and a sediment transport module, and is based in the finite volume method to solve the involved equations. The simulation code has been integrated in a pre-process and post-process interface based on GiD software, developed by CIMNE. The result is a flow and sediment modelling system for rivers and estuaries that uses advanced numerical schemes, robust and stable, which are especially suitable for discontinuous flows taking place in torrential and hydrologically irregular rivers.

Approach to some Properties of Parallel to Wall Shear Flow and its Application

Some properties of two dimensional open channel flow were studied. Energy distribution was calculated to show energy exchanging relationship between the mean flow and the fluctuating flow. Viscous dissipative energy of mean flow, the energy of fluctuating flow and the energy of fluctuating flow taking from the mean flow were calculated. The energy spectrum was explored. The mechanism of two dimensional parallel to wall shear flow were probed to show that not only the energy transfer relates different structures corresponding to different levels of turbulent exciting but also the energy dissipating and diffusing closely connect with resonant vibration and frequency-locking. On the basis of flowing structures, the results applying to waterway regulating was discussed.

Numerical modeling of open channel flows using a multiple grid ENO scheme

In this work, the performance details of a multiple grid ENO scheme for modeling transient one dimensional open channel flows is investigated. The formulation in a multiple grid formulation differs from the conventional algorithm in that, at a constant time period, the equations are solved across different grid levels, so as to facilitate faster propagation of the boundary condition. This results in a faster convergence of the solution to the desired time level. Focus in this paper is split across both testing the accuracy of the end solution and in quantifying the resultant computational savings. Tests conducted for flows with shocks indicate that the solution from current formulation is inline with the theoretical predictions.

A moving domain formulation for modeling two dimensional open channel transient flows

Numerically solving the two dimensional open channel flow equations over large spatial domains coupled with long time periods using an explicit finite difference scheme is constrained by the required computational time. To overcome this limitation, in this paper the effect of using a moving boundary algorithm on both the accuracy of the transient solution and on the associated computational savings is investigated. While all the reported studies that relate to solving the two dimensional shallow water open channel flows have used fixed domain boundaries, this work differs from them in that the location of the domain boundaries is a function of the time period. The theory underlying the Eulerian school of thought is used for identifying the coordinates of the domain boundaries. The results indicate that for simulations in which the transient solution is required, the present approach can accelerate the solution with out affecting its accuracy.

Robust continuous-time and discrete-time flow control of a dam–river system. (I) Modelling

A distributed parameter linear model is derived from simplified physical equations of one dimensional open channel hydraulics. This linear model relating downstream to upstream flow rates is then identified analytically to a second order transfer function with delay, that can be used for controller synthesis. Analytical formulas for exact sampling with zero and first order holds are also given for the discrete-time case. The modelling error made when considering linear models around different reference discharges in a given set can be evaluated with a bound on multiplicative and on additive uncertainties. These bounds are useful for controller robustness analysis and synthesis.

Energy and momentum in one dimensional open channel flow

The equations of continuity, momentum and energy are derived, incorporating depth-dependent correction factors for velocity distributions over compound cross sections. It is shown that the friction slope and the energy slope are equivalent in steady uniform flow but not in unsteady flow. The difference between the two forms is explained and reasons are given for the preferential use of the momentum equation. Comparisons of backwater profiles are presented.

Numerical Computation of Open Channel Flow with Shock Wave using FDS method

Numerical calculation of flow including shock wave is one of the important tools in the practical river engineering works. Flux Difference Splitting, FDS, scheme is one of the numerical method to simulate the flow with shock wave. In this method, the theory of nonlinear characteristic wave and the concept of numerical flux are taken in account and it is very easy to be applied to various condition of open channel flow. In this paper, a numerical model using FDS scheme for two dimensional open channel flow is developed and was applied to several different hydraulic conditions. The calculated results are compared with the theoretical and experimental results and good agreement is obtained.

Calculation of three dimensional open channel flow in continuous bends

Calculation of three dimensional open channel flow in continuous bends

BORE FRONT MODELING IN TERMS OF BURGERS EQUATION AND ITS NUMERICAL CALCULATION METHOD

Bore front hydraulics are investigated in terms of Burgers equation to clarify the dynamics of a moving discontinuity in water flow. Burgers equation has been derived from the one dimensional open channel equation with the horizontal turbulent diffusion term. The derived equation system consists of Burgers with respect to dynamic characteristic and hyperbolic equation with respect to water surface elevation, which satisfys Jeffery-Vedernikov condition FT - 2 through discontinuity. It has been verified from the experiments that the condition FT = 2 is a good approximation of bore front dynamics. The numercal calulation method of Burgers equation employing Cole-Hopf transformation and QUICKEST algorithm was also proposed and confirmed its efficiency.

Turbulent dispersion of a steady discharge of positively or negatively buoyant particles in two dimensions

The eigenfunction solution to the problem of dispersion of neutrally buoyant material presented in Nokes et al. (1984) is extended to encompass the dispersion of particles with a rise or fall velocity in two dimensional open channel flow. Steady state conditions are modelled as this allows the turbulent diffusion equation to be separated and hence reduces it to a Sturm-Liouville eigenvalue problem. A general solution in the form of an eigenfunction expansion can be found for arbitrary velocity and diffusivity distributions but attention in this paper is centred on a comparison between a uniform velocity and diffusivity and the more realistic power law velocity and parabolic diffusivity. The power series technique of solution to ordinary differential equations is used to generate the eigenfunctions and eigenvalues for these two cases. It is demonstrated that the eigenfunction solution uses computing resources efficiently and is readily applied to the problems of sedimentation engineering and spillway aerat...