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Modified saint-venant equations for flow simulation in tidal rivers

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Water Science and Engineering 2012年第1期5卷 34-45页

作者： Xiao-qin ZHANG Wei-min BAO College of Hydrology and Water Resources Hohai UniversityNanjing 210098P.R.China State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Hohai UniversityNanjing 210098P.R.China

Flow in tidal rivers periodically propagates upstream or downstream under tidal influence. Hydrodynamic models based on the saint-venant equations （the SVN model） are extensively used to model tidal rivers. A force-corrected term expressed as the combination of flow velocity and the change rate of the tidal fevel was developed to represent tidal effects in the SVN model. A momentum equation incorporating with the corrected term was derived based on Newton＇s second law. By combing the modified momentum equation with the continuity equation, an improved SVN model for tidal rivers （the ISVN model） was constructed. The simulation of a tidal reach of the Qiantang River shows that the ISVN model performs better than the SVN model. It indicates that the corrected force derived for tidal effects is reasonable; the ISVN model provides an appropriate enhancement of the SVN model for flow simulation of tidal rivers.

关键词： tidal river, tidal effect, dynamic water pressure saint-venant equations corrected force, flow simulation

Analysis of the Flow of a Molten Slag in an Open Channel Using Transient and Steady-State Solutions of the saint-venant equations

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World Journal of Engineering and Technology 2024年第4期12卷 976-986页

作者： Miguel A. Barron Joan Reyes Aristeo Garrido Departamento de Materiales Universidad Autonoma Metropolitana Azcapotzalco Ciudad de Mexico Mexico

In recent years, metallurgical slags have been increasingly used as materials for the manufacture of cement, pavement and filling material. The transport of the molten slag to the receiving pots is carried out through open channels. The transient and steady-state flow of a molten slag in a rectangular open channel is numerically analyzed here. For the transient flow, the saint-venant equations were numerically solved. For the steady-state flow, the derivatives in time and space in the saint-venant equations were set equal to zero and a polynomial of degree 3 is obtained whose roots are the slag height values. It was assumed that the viscosity of the slag has an Arrhenius-type behavior with temperature. Four values of temperature values, namely 1723.15, 1773.15, 1823.15, 18873.15 ˚K, and five values of the angle of inclination of the channel, namely 1, 2, 3, 4, 5 degrees, are considered. Numerical results show that the steady-state values of the height and velocity of the molten slag depend strongly on the temperature of the slag and the angle of inclination of the channel. As the slag temperature and channel angle increase, the value of the steady-state slag height decreases. The value of the steady-state slag velocity increases as the slag temperature and channel inclination angle increase.

关键词： Molten Slag Open Channel Phase-Portrait saint-venant equations Steady State Transient Solution

Numerical Simulation of saint-venant equations with Thermal Energy Dependency: Applications on Global Warming

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Open Journal of Fluid Dynamics 2023年第4期13卷 191-205页

作者： Raphael de O. Garcia Graciele P. Silveira Department of Actuarial Science Federal University of S&atildeo Paulo Osasco Brazil Department of Physics Chemistry and Mathematics Federal University of S&atildeo Carlos Sorocaba Brazil

Since the Industrial Revolution, humanity has been intensifying the burning of fossil fuels and as a consequence, the average temperature on Earth has been increasing. The 20th century was the warmest and future prospects are not favorable, that is, even higher temperatures are expected. This demonstrates the importance of studies on the subject, mainly to predict possible environmental, social and economic consequences. The objective of this work was to identify the interference of the increase in ambient temperature in the dynamics of fluids, such as ocean waves advancing over the continent. For this, thermal energy was considered in the saint-venant equations and computational implementations were performed via Lax-Friedrichs and Adams-Moulton methods. The results indicated that, in fact, depending on the amount of thermal energy transferred to the fluid, the advance of water towards the continent can occur, even in places where such a phenomenon has never been observed.

关键词： Computational Fluid Dynamics saint-venant equations Numerical Methods Global Warming

Transient flow control for an artificial open channel based on finite difference method

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Science China(Technological Sciences) 2011年第4期54卷 781-792页

作者： SHANG YiZi LIU RongHua LI TieJian ZHANG Cheng WANG GuangQian State Key Laboratory of Hydroscience and Engineering Tsinghua UniversityBeijing 100084China School of Renewable Energy North China Electric Power University Beijing 102206 China

The particular challenges of modeling control systems for the middle route of the south-to-north water transfer project are *** channel dynamics are approximated by well-known saint-venant nonlinear partial differential *** better control purpose,the finite difference method is used to discretize the saint-venant equations to form the state space model of channel *** avoid calculation divergence and improve control stability,balanced model reduction together with poles placement procedure is proposed to develop the control *** entire process to obtain this scheme is described in this paper,important application issue is considered as *** results show the adopted techniques are properly used in the control scheme design,and the system is able to drive the discharge to the demanded set point or maintain it around a reasonable range even if comes across big withdrawals.

关键词： the south-to-north water transfer project control scheme saint-venant equations model reduction pole placement

Lyapunov-based boundary feedback control in multi-reach canals

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Science in China(Series F) 2009年第7期52卷 1157-1164页

作者： CEN LiHui XI YuGeng Department of Automation Shanghai Jiao Tong University Shanghai 200240 China

This paper presents a Lyapunov-based approach to design the boundary feedback control for an open-channel network composed of a cascade of multi-reach canals, each described by a pair of saint-venant equations. The weighted sum of entropies of the multi-reaches is adopted to construct the Lyapunov function. The time derivative of the Lyapunov function is expressed by the water depth variations at the gate boundaries, based on which a class of boundary feedback controllers is presented to guarantee the local asymptotic closed-loop stability. The advantage of this approach is that only the water level depths at the gate boundaries are measured as the feedback.

关键词： saint-venant equations multi-reach canal entropy Lyapunov function asymptotic stability boundary feedback control

Hydraulic model with roughness coefficient updating method based on Kalman filter for channel flood forecast

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Water Science and Engineering 2011年第1期4卷 13-23页

作者： Hong-jun BAO Lin-na ZHAO Public Meteorological Service Center China Meteorological Administration Beijing 100081 P. R. China National Meteorological Center China Meteorological Administration Beijing 100081 P. R. China

A real-time channel flood forecast model was developed to simulate channel flow in plain rivers based on the dynamic wave theory. Taking into consideration channel shape differences along the channel, a roughness updating technique was developed using the Kalman filter method to update Manning＇s roughness coefficient at each time step of the calculation processes. Channel shapes were simplified as rectangles, triangles, and parabolas, and the relationships between hydraulic radius and water depth were developed for plain rivers. Based on the relationship between the Froude number and the inertia terms of the momentum equation in the saint-venant equations, the relationship between Manning＇s roughness coefficient and water depth was obtained. Using the channel of the Huaihe River from Wangjiaba to Lutaizi stations as a case, to test the performance and rationality of the present flood routing model, the original hydraulic model was compared with the developed model. Results show that the stage hydrographs calculated by the developed flood routing model with the updated Manning＇s roughness coefficient have a good agreement with the observed stage hydrographs. This model performs better than the original hydraulic model.

关键词： flood routing," Manning's roughness coefficient updating method," Kalman filter," Froude number saint-venant equations hydraulic model

Modification of Multiple Knot B-Spline Wavelet for Solving (Partially) Dirichlet Boundary Value Problem

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Advances in Applied Mathematics and Mechanics 2012年第6期4卷 799-820页

作者： Fatemeh Pourakbari Ali Tavakoli Department of Mathematics Vali-e-Asr University of RafsanjanIran

A construction of multiple knot B-spline wavelets has been given in[*** and ***,Wavelet on a bounded interval,In:*** and ***,*** methods of approximation ***:Birkhauser Verlag;(1992),pp.57–76].In this work,we first modify these wavelets to solve the elliptic(partially)Dirichlet boundary value problems by Galerkin and Petrov Galerkin *** generalize this construction to two dimensional case by Tensor product *** addition,the solution of the system discretized by Galerkin method with modified multiple knot B-spline wavelets is *** also consider a nonlinear partial differential equation for unsteady flows in an open channel called *** the solving of this problem by some methods such as finite difference and finite element produce unsuitable approximations specially in the ends of channel,it is solved by multiple knot B-spline wavelet method that yields a very well ***,some numerical examples are given to support our theoretical results.

关键词： Galerkin method semi-orthogonal B-spline wavelet multi-resolution analysis tensor product hyperbolic partial differential equation saint-venant equations

Numerical Simulation of the Flow of a Molten Blast Furnace Slag in an Open Channel

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World Journal of Engineering and Technology 2024年第4期12卷 963-975页

作者： Miguel A. Barron Joan Reyes Aristeo Garrido Departamento de Materiales Universidad Autonoma Metropolitana Azcapotzalco Mexico City Mexico

Despite its industrial importance, the flow of molten blast furnace slag in open channels has not been sufficiently studied. In this work, the unsteady non-uniform flow of a molten blast furnace slag in a rectangular open channel is numerically studied by solving the saint-venant equations by means of an explicit backwards finite difference scheme. An Arrhenius-type dependence of the viscosity of the slag on temperature is assumed. To calculate that viscosity, four temperatures are considered, namely 1450˚C, 1500˚C, 1550˚C and 1600˚C. To study the dynamic response of the system, a half-sinusoidal pulse with duration of 5 s is imposed at the channel entrance. According to the numerical simulations, for all the temperatures considered, the slag flow in the channel for an angle of 5 degrees is supercritical in nature. However, for an angle of 1 degree, the flow is transcritical, that is, it presents a transition from subcritical to supercritical.

关键词： Blast Furnace Slag Molten Slag Open Channel Flow saint-venant equations Supercritical Flow Transcritical Flow

Unsteady Non-Uniform Flow of Molten Metals in Rectangular Open Channels

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World Journal of Engineering and Technology 2022年第3期10卷 593-604页

作者： Miguel A. Barron Joan Reyes Dulce Y. Miranda Departamento de Materiales Universidad Autonoma Metropolitana Azcapotzalco Mexico City Mexico

In the metallurgical industries, it is very important to characterize the flow of molten metals in open channels given that they are transported through these devices to different plant sections. However, unlike the flow of water which has been studied since ancient times, the flow of molten metals in open channels has received little attention. The unsteady non-uniform flow of blast furnace molten pig iron in a rectangular open channel is analyzed in this work by numerical solution of the saint-venant equations. The influence of mesh size on the convergence of molten metal height is studied to determine the proper mesh and time step sizes. A sinusoidal inflow pulse is imposed at the entrance of the channel in order to analyze the propagation of the resulting wave. The influence of the angle of inclination of the channel and the roughness coefficient of the walls on the amplitude and the dynamic behavior of the height of the molten metal are analyzed. Phase portraits of the channel state variables are constructed and interpreted. Numerical simulations show that as the angle of inclination of the channel increases, the amplitude of the formed wave decreases. From 10 degrees onwards, the peak of the wave descends even below the initial height. On the other hand, the roughness coefficient affects the molten pig iron height profiles in an inverse way than the angle of inclination. The amplitude of the formed wave increases as the roughness coefficient increases.

关键词： Molten Metals Flow Non-Uniform Flow Open Channels Pig Iron Transport saint-venant equations Sinusoidal Pulse Unsteady Flow