Non-prismatic Channel Research Articles

Large-eddy simulation of free-surface turbulent flow in a non-prismatic channel

Abstract Hydraulic engineering applications require a good knowledge of turbulent behaviour in non-prismatic channels. This paper aims to predict turbulent behaviour using large-eddy simulation (LES). The model channel has a warped transition. We perform two-phase LES of free-surface flow and validate the results using experimental data and benchmark solution. We discuss rigorous strategies for model set-up, parameter selection and parametric value assignment, including parameters in spectrum synthesiser (SS) and vortex method (VM) for inlet turbulence. The predicted flow displays complex structures due to eddy motions translated from upstream and locally generated by asymmetrical separation in the transition. The history of the flow dynamics may affect the flow development. The predicted velocity, energy spectrum, root-mean-square error, hit-rate and factor-of-two compare well with measurements and benchmark solution. Mapping mean-velocity distribution from experimental data, combined with SS, gives satisfactory inlet condition; alternatively, a 1/7th power-law for the mean-velocity, combined with VM, is acceptable. This paper uses the Okubo–Weiss parameter to delineate instantaneous coherent structures. The LES methods are reliable, efficient and cost-effective. As compared to the simulation of prismatic channels, the flow dynamics in non-prismatic channels exhibit flow separation and turbulence interactions, which increase the flow-complexity, while offering results with crucial practical applications.

Hydraulics of the subcritical Ventury channels

The purpose of the research is to develop and verify the method of hydraulic calculation of the Venturi channel in the flooded outflow mode. The criterion that separates the flooded and free flow regimes is the ratio of the flow depth in the throat of the Venturi channel hm to the critical depth hc exceeding one (hm/hc > 1). The article theoretically and experimentally substantiates a method for determining the flow rate in a flooded Venturi canal using two control cross-sections, one of which is in the upper basin of the canal, the other in its throat. The differential equation for an uneven flow in a non-prismatic channel was obtained in the form (13). The analysis showed that in a flooded Venturi channel with a subcritical flow at Froude numbers less than one (Fr <1), the denominator of equation (13) is always greater than zero; therefore, at the entrance to the channel in the region of constriction, when db/dl < 0, the depth is downstream decreases (dh/dl < 0), and in the lower diffuser, where db/dl > 0, the flow depth increases (dh/dl > 0). Thus, the curve of the flow surface has a dip in the throat of the flooded Venturi channel. Integration of differential equation (13) made it possible to obtain the function of changing the Froude numbers in the flow along the length of the flooded Venturi channel (16), and then, using relations (17), to determine the depths and flow velocities. The verification showed that the calculated data are in good agreement with the experimental ones. The deviations between calculation and experiment do not exceed ±3%. This makes it possible to recommend the outlined methods for application in engineering practice.

Investigation of Flood Routing Using Variable Parameter Kinematic Wave Model (VPKWM) for Non-Prismatic Natural Channel in an Ungauged Basin

Abstract This research concerns about the development and application of Variable Parameter Kinematic Wave Numerical model (VPKWM) based on 1-D Saint-Venant equation, to study the behaviour of the propagation of a flood wave in Non-prismatic natural waterways in an ungauged basin. The channel slope and wetted perimeter are considered as variable because of the irregularity of the boundary of the channel and the change in magnitude of discharge. The scarcity of reliable inflow data at upstream is a serious problem for the flood routing process in an ungauged basin. In this study the inflow hydrograph and lateral inflow hydrographs are obtained using SCS-CN method as rainfall runoff model. The performance of the model assessed considering four parameters such as root mean square error (RMSE), peak discharge, peak time and total volume. The results indicated that the VPKWM for non-prismatic channel provided reasonable output compared with the observed data.

A lattice Boltzmann model for the open channel flows described by the Saint-Venant equations.

A new lattice Boltzmann method to simulate open channel flows with complex geometry described by a conservative form of Saint-Venant equations is developed. The Saint-Venant equations include an original treatment of the momentum equation source term. Concrete hydrostatic pressure thrust expressions are provided for rectangular, trapezoidal and irregular cross-section shapes. A D1Q3 lattice arrangement is adopted. External forces, such as bed friction and the static term, are discretized with a centred scheme. Bounce back and imposed boundary conditions are considered. To verify the proposed model, four cases are carried out: tidal flow over a regular bed in a rectangular cross-section, steady flow in a channel with horizontal and vertical contractions, steady flow over a bump in a trapezoidal channel and steady flow in a non-prismatic channel with friction. Results indicate that the proposed scheme is simple and can provide accurate predictions for open channel flows.

One-dimensional model of turbulent flow of non-Newtonian drilling mud in non-prismatic channels

One-dimensional model of non-Newtonian turbulent flow in a non-prismatic channel is challenging due to the difficulty of accurately accounting for flow properties in the 1-D model. In this study, we model the 1-D Saint–Venant system of shallow water equations for water-based drilling mud (non-Newtonian) in open Venturi channels for steady and transient conditions. Numerically, the friction force acting on a fluid in a control volume can be subdivided, in the 1-D drilling mud modelling and shallow water equations, into two terms: external friction and internal friction. External friction is due to the wall boundary effect. Internal friction is due to the non-Newtonian viscous effect. The internal friction term can be modelled using pure non-Newtonian viscosity models, and the external friction term using Newtonian wall friction models. Experiments were carried out using a water-based drilling fluid in an open Venturi channel. Density, viscosity, flow depth, and flow rate were experimentally measured. The developed approach used to solve the 1-D non-Newtonian turbulence model in this study can be used for flow estimation in oil well return flow.

Application of BRAHMA hydrodynamic model for flood forecasting

Flood forecasting models are of paramount importance to predict the flood and thereby warning the community living near the floodplains or the vulnerable areas. In the quest for understanding the complex processes of a river, scientist and researchers have given importance to river modeling both analytically and physically by conducting experiments in the laboratory. The numerical model which is basically a mathematical model has gained popularity in the last few decades. BRAHMA (Braided River Aid: Hydro-Morphological Analyzer) is a hydrodynamic model for simulating the spatial variation in water depth, flows, and velocities in the unsteady free surface flow. It is developed by IIT Guwahati in collaboration with Brahmaputra Board, Govt. of India. The BRAHMA 1-D model is capable of simulating both prismatic as well as non-prismatic channel reach. It is also capable of simulating channels with varying width and varying slope. In this paper, an attempt has been made to use the BRAHMA 1-D model for determining the water surface elevation at certain flood-prone areas of Ranganadi River which covers Assam and parts of Arunachal Pradesh, North-East India. The Ranganadi hydroelectric dam is situated in Arunachal Pradesh, India. In this study, the length of the river reach considered is 77.09 km from the Ranganadi Hydroelectric power project. The cross-sectional width of the river in different sections is extracted from Google Earth and depth was obtained by approximate field measurement. The peak release from the dam, the downstream water level and initial water levels are given as input to the model. The water levels at the particular sections of interest are computed as output from the model. From the generated output data set, it is possible to assess the vulnerable areas by the water levels which will be generated from the model.

An Experimental Test for Application of Analytical Model of Surge Flow under Drought and Wet Conditions in a Semi-Arid Region

In this paper, an analytical solution is investigated in the zero-inertia problem for surge flow phenomena in non-prismatic channels considering the impact of infiltration (introduced by Technische Univ. Dresden) in dry-channels under drought and wet conditions in a semi-arid climate in Iran. The hydrodynamic analytical model introduced by Dresden University is free of numerical troubles, easy to run, computationally efficient, and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model can be compared favorably with a full hydrodynamic numerical model (HEC-RAS) in a permeable non-prismatic channel. In the next step, a sensitivity and error analysis was conducted and found that the Manning-Strickler coefficient, hydraulic radius, and inflow hydrograph have important effects on the velocity of the surge, suggesting the importance of an adequate description of the topography. The new approach is finally applied to simulate and compare 10 scenarios to manage artificial groundwater recharge in three channels in the downstream of Garin Dam under wet (more than 25%) and drought (less than 5%) conditions in the west of Iran. Based on tested scenarios, infiltration rate of bad and suitable scenarios varies from 3 to 85% and 1 to 76% of the total volume of released water in Garin in wet and drought phases, respectively.

Unsteady flow simulation using the curvilinear multiple-relaxation-time lattice Boltzmann method: Danube River case study

In order to introduce the lattice Boltzmann method as a competitive approach compared to traditionally based mathematical models when river and coastal hydraulics are considered, the innovative curvilinear multi-relaxation-time lattice Boltzmann method for solving 2D flow equations transformed in curvilinear coordinate system is utilized. The curvilinear approach implemented in the multi-relaxation-time lattice Boltzmann method is tested on a geometrically simple non-prismatic channel and on a section of the Danube River. Steady flow tangential velocity measurements are used in case of the channel model verification, while in case of the Danube unsteady flow is examined. Corresponding velocity and water level measurements acquired during a period of five days are used for calibration and verification of the Danube model, while an alternative mathematical model based on the traditional fractional-step approach has been exploited for comparison. The presented results confirm the aptness of the proposed model to simulate flow in natural water bodies effectively and accurately, therefore it is fully competitive with the classic computational fluid dynamics models.

Urban River Design: A River Restoration Case Study

Human excessive requirements on functions of aquatic ecosystems cause that surface waters often suffer from significant morphological and hydrological alterations. Human induced hydromorphological changes of rivers belong among the most common ecological problems of the water bodies and they appear in all scales of river habitat. These changes have an impact in their ecological status and need to be solved in the near future. Successful sustainable river rehabilitation depends on the identification and understanding of key processes and anthropogenic stressors. These factors enable to estimate a proper longitudinal and lateral riverine system structure including stream habitat improvements at different scales. The article summarizes the basic principles of urban river restoration, that enables to approach to the state of dynamic stability and to increase the „absorbing capacity” of freshwater ecosystem. The authors also provide the background facts and principles of the restoration design of canalized reach of the River Trnavka, which flows through an urbanised part of the city Trnava. The Trnavka River has regulated flow regime affected by operation of Boleraz reservoir located 14 km in upstream direction. The river channel capacity equals to 50 m3.s−1 with return period 100 years and ecological flow is Q=0,150 l.s−1. The heavily modified nonprismatic channel has stone and concrete stream banks. The authors have proposed increasing sinuosity of low flow channel and decreasing capacity of the oversized channel by using gravel matraces with planting different types of macrophytes. The main goal of the proposed river restoration measures was to increase aesthetic value of complex restoration design of close public space (the Rose Park) and to implement technical and biotechnical measures that may improve ecological conditions and management operation of the Trnavka River.

Prediction of discharge in converging and diverging compound channel by gene expression programming

ABSTRACT Discharge estimation in rivers is the most important parameter in flood management. Predicting discharge in the converging and diverging compound open channel by analytical approach leads to solving a system of complex nonlinear equations. In this study, the gene expression programming (GEP) is used for modeling and predicting of flow discharge in the non-prismatic compound open channel. Existing approaches on discharge estimation are surveyed in order to carry out a comparison among them and the proposed GEP model. Comparison of results showed that the divided channel method with vertical division lines with the coefficient of determination (0.74) and root-mean-square error (0.0093) is accurate among the analytical approaches. The non-dimensional parameters like friction factor ratio, area ratio, hydraulic radius ratio, bed slope, width ratio, relative flow depth, angle of converging or diverging, relative longitudinal distance, and flow aspect ratio have been taken as input parameters for predicting discharge. Gamma test has been performed and provided the best combination of input parameters as friction factor ratio, hydraulic radius ratio, relative flow depth, and bed slope which influence the discharge significantly. Results demonstrate that the conveyance capacity computed by the GEP model gives far better outcomes than the customary models. The GEP model with a coefficient of determination greater than 0.80 and mean absolute percentage error less than 15% for the testing stage has a suitable performance for predicting the discharge in the non-prismatic compound open channel.

Non-uniform grid based LBM for the Saint-Venant equations

A novel form of the lattice Boltzmann method for the Saint-Venant equations (LABSVE) is formulated and implemented. To eliminate equidistant property of the lattice structure being the major drawback of the LBM, and thus establish the LB model as tool for practical application (natural water bodies) fully competitive compared to the presently available computational models, new form of equilibrium distribution function (EDF) based on geometrically transformed Saint-Venant equations (SVE) is derived. Introducing the metric relation function between the physical and computational system, the non-uniform spatial discretization is managed by solving the transformed SVE rather than altering the symmetrical properties of lattice structure. Since the geometrical correlation between the two corresponding systems is introduced into the transformed SVE, the very basic structure of the LBM in terms of simplicity in implementing the boundary conditions and computational efficiency (owing to the parallel structure) is maintained and further improved by removing the limitations imposed by the equidistant lattice condition. Furthermore, the discharge-water level definition of the SVE as more applicable form when natural watercourses are considered, is applied. In this way the bed slope term is completely eliminated from the equations, establishing therefore a model more suitable for natural systems characterized by arbitrary cross sectional geometry. In order to test the proposed non-equidistant LABSVE model, steady flow in prismatic channel, unsteady flow in non-prismatic channel of simple cross section geometry, and unsteady flow along a Danube section is modelled. Additional simulations by using the HEC-RAS modelling tool are conducted in order to produce comparison basis for both unsteady simulations, while in case of the Danube River section actual water level and discharge measurements are additionally used for calibration and verification of the model. Very good agreement between compared results is obtained showing that the proposed non-equidistant form of the LABSVE is capable of solving complex environmental problems, maintaining the order of accuracy, simplicity and efficiency of the basic LBM.

Flow Prediction of Boundary Shear Stress and Depth Average Velocity of a Compound Channel with Narrowing Floodplain

Prediction of boundary shear force distributions in open channel flow is crucial in many critical engineering problems such as channel design, calculation of losses and sedimentation. During floods, part of the discharge of a river is carried by the simple main channel and the rest is carried by the floodplains. For such compound channels, the flow structure becomes complicated due to the transfer of momentum between the deep main channel and the adjoining floodplains. The complexity further increases when dealing with a compound channel with non-prismatic floodplains. Knowledge of momentum transfer at the different interfaces originating from the junction between the main channel and floodplain can be acquired from the distribution of boundary shear in the subsections. The calculation of boundary shear and depth average velocity in non-prismatic compound channel flow is more complex and simple conventional approaches cannot predict the boundary shear and depth average velocity with sufficient accuracy. Hence, in this area, an easily implementable technique, the Artificial Neural Network can be used for predicting the boundary shear and depth average velocity at different sections of a converging compound channel for different geometry and flow conditions. The model’s performance has lead satisfactory results. Statistical error analysis is also carried out to know the degree of accuracy of the model.

Comparative Study of One Dimensional and Two Dimensional Steady Surface Flow Analysis

&lt;p&gt;Determination of actual water surface is required for design of hydraulic structures, reservoirs, flood plain management, and flood forecasting. Classical approach of analyzing the river flow using one dimensional flow analysis cannot provide the accurate information of water surface for different return period floods. So, both 1D and 2D steady surface flow analysis in prismatic channel and non-prismatic channel were done using models like HEC-RAS, FESWMS-2DH, GIS, and HECGEORAS to compare the results and recommended to select the best among these two flow analyses. Analysis of result showed that in prismatic channel, the water surface elevations obtained from 1D and 2D steady flow analysis for discharge Q=10cft/s were almost similar with maximum variation of 0.33ft. But in case of non-prismatic channel, the results of water surface elevations from 1D and 2D steady flow analysis for discharge Q = 5000cft/s and 9430cft/s were not similar and the maximum variation of 1.36ft and 1.75ft were found for two discharges respectively. 1D steady flow analysis is acceptable for prismatic channel except at bend which may require 2D analysis. But flow in non-prismatic channel requires 2D steady flow analysis for precise water surface elevation.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Journal of Advanced College of Engineering and Management,&lt;/strong&gt; Vol. 2, 2016, Page: 15-30 &lt;/p&gt;

MRT lattice Boltzmann method for 2D flows in curvilinear coordinates

Objective: The objective of the presented paper is establishing the multi-relaxation-time lattice Boltzmann method (MRT-LBM) for solving 2D flow equations transformed in a curvilinear coordinate system.Method: Using the complete transformation approach – which includes transformation of both dependent and independent variables between the physical and computational domain – corresponding forms of the equilibrium function and of the force term for the 2D Navier–Stokes equations and the shallow water equations have been derived. The physical flow domain of arbitrary geometry in the horizontal plane, is covered with adequate curvilinear mesh, while the calculation procedure is carried out in the D2Q9 square lattice, applying the basic form of the boundary condition method on water-solid and open boundaries as well.Test cases: The method is tested using four different examples: Couette flow in a straight inclined channel, Taylor–Couette flow between two cylinders, a non-prismatic channel in a 180° bend, and a segment of irrigation channel with a parabolic cross section in a 90° bend. In the cases of the bent channels, previously available velocity measurements have been used for validation of the model. In addition, the procedure employs a mathematical model based on traditional CFD procedures.Results: The remarkable agreement between the results obtained by the proposed model and the corresponding analytical values and measurements shows that the presented curvilinear form of the LBM is capable of solving very complex environmental problems, maintaining the order of accuracy, simplicity and efficiency of the basic LBM.

SPH Modeling of One-Dimensional Nonrectangular and Nonprismatic Channel Flows with Open Boundaries

In this study, the authors solve the shallow water equations (SWE) with smoothed particle hydrodynamics (SPH) for one-dimensional (1D) nonrectangular and nonprismatic channel flows with open boundaries. To date, 1D SPH-SWE has been only developed to simulate rectangular prismatic channel flows with closed and open boundaries. However, for practical hydraulic problems, channel cross sections are not always rectangular and prismatic. A general approach is proposed in this study to extend the engineering application range of 1D SPH-SWE to nonrectangular and nonprismatic channels with open boundaries by introducing the wetted cross-sectional area and the water discharge in SWE and combining the method of specified time interval with the inflow/outflow algorithm. Three benchmark study cases, aiming at testing various steady flow regimes in nonrectangular and nonprismatic channels, are adopted to validate the newly proposed approach. Through the investigation of the convergence analysis and numerical accuracy test of the study cases, the results show that the present SPH-SWE approach is capable to model 1D nonrectangular and nonprismatic channel flows with open boundaries.

Flood routing by kinematic wave model

In this study the kinematic wave equation has been solved numerically using the modified Lax explicit finite difference scheme (MLEFDS) and used for flood routing in a wide prismatic channel and a nonprismatic channel. Two flood waves, one sinusoidal wave and one exponential wave, have been imposed at the upstream boundary of the channel in which the flow is initially uniform. Six different schemes have been introduced and used to compute the routing parameter, the wave celerity c. Two of these schemes are based on constant depth and use constant celerity throughout the computation process. The rest of the schemes are based on local depths and give celerity dependent on time and space. The effects of the routing parameter c on the travel time of flood wave, the subsidence of the flood peak and the conservation flood flow volume have been studied. The results seem to indicate that there is a minimal loss/gain of flow volume whatever the scheme is. While it is confirmed that neither of the schemes is 100% volume conservative, it is found that the scheme Kinematic Wave Model-2 (KWM-II) gives the most accurate result giving only 0.1% error in perspective of volume conservation. The results obtained in this study are in good qualitative agreement with those obtained in other similar studies.

Reverse flow routing in open channels: A Bayesian Geostatistical Approach

Summary Reverse flow routing in open channels is a procedure of practical interest: it allows to obtain hydrographs in upstream ungauged stations by means of information available at downstream monitored sites. In this paper a Bayesian Geostatistical Approach for reverse flow routing in open channels is presented. The capabilities of the methodology are shown by means of synthetic test cases. Input hydrographs of different shape were routed downstream using a numerical flow model that solves the one dimensional De Saint Venant equations; the resulting outflow hydrographs were, in almost all the cases, corrupted with random errors and then used for the inversion. Both prismatic and non-prismatic irregular channels, under subcritical flow conditions, were analyzed as well. The considered non-prismatic channel with irregular cross sections and variable friction coefficients represents a very practical situation that can be encountered in the field. The results show that the proposed methodology is able to properly reproduce the input inflows even in presence of errors affecting the downstream discharges up to 10%.

Numerical simulation of shallow-water dam break flows in open channels using smoothed particle hydrodynamics

► We model dam-break flows by SPH technique. ► Numerical sensitivity is performed to study the appropriate particle number. ► Extensive validation by comparison with experimental data is adopted for benchmarks. A meshless numerical model is proposed to investigate shallow-water dam break flows in 1D open channels. The numerical model is to solve the shallow water equations (SWE) based on smoothed particle hydrodynamics (SPH). The concept of slice water particles (SWP) is adopted in the SPH-SWE formulation. The numerical sensitivity analysis is first performed to study the appropriate SWP number and variable smoothing length through dam break flows in an idealized 1D channel with dry/wet beds. Extensive validation by comparison with laboratory and field data is next conducted for four benchmark problems, including dam break flows through a rough flat channel, a rough bumpy channel with various downstream boundary conditions, a nonprismatic channel, and a realistic scale model of the Toce river in Italy. The simulated results indicate that accurate performance is reached in the presence of shock discontinuities, shock front motion, hydraulic jumps, dry/wet bed flow, supercritical/subcritical/transcritical flow, reverse flow, contraction flow, overtopping flow, partial reflections and multiple wave interaction without special numerical treatment. All of the simulations are carried out by PC within 10 min. Thus, the proposed numerical model has proved its efficiency and reliability for dam break flow computations in open channels.

Mathematical simulation of one-dimensional dam-collapse flow over wetted bed

A mathematical model is described and applied to simulate sudden total one-dimensional dam-break flow over wetted bed. The dam collapse takes place in a rough sloping non-prismatic channel of various cross-sections. The water parameters to be instantaneously calculated are the height h , the discharge Q , the mean velocity u and the pressure force P . The mentioned flow is governed by the Saint-Venant shallow water equations and the computation process, on the basis of rectangular grid of points, consists of two complementary solutions: (a) at the first instant after the collapse, an analytical procedure is considered. The calculated parameters are taken as initial values in the water stream embraced by the flood wave. Outside this zone, initial conditions are those which preexist before the rupture. (b) Beyond this time, a numerical computation is carried out by using an iterative explicit method of characteristics. (c) Every time stage of calculation starts by determining the discontinuity (wave front) parameters namely its abscissa x δ , height h δ , celerity c δ and alert delay t δ . The former is the discontinuity arrival time at considered station. Typical results are obtained and compared with similar ones already published by others in the literature.

HIGHER ORDER NUMERICAL METHODS EVALUATION FOR THE COMPUTATION OF ONE DIMENSIONAL FREE SURFACE SHALLOW WATER FLOWS

International Journal of Computational Engineering ScienceVol. 03, No. 01, pp. 13-55 (2002) No AccessHIGHER ORDER NUMERICAL METHODS EVALUATION FOR THE COMPUTATION OF ONE DIMENSIONAL FREE SURFACE SHALLOW WATER FLOWSA. I. DELISA. I. DELISDepartment of Applied Mathematics, University of Crete, 71409 Heraklion, Crete, Greece Search for more papers by this author https://doi.org/10.1142/S1465876302000538Cited by:3 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractSeveral explicit high resolution TVD methods and their detailed application to steady and unsteady one-dimensional free surface channel flow problems are presented. Some of these methods are widely presented in the literature. Their evaluation is based on computations performed for steady state benchmark problems with analytical solutions and for a wide range of cases, which include friction, nonuniform bed slopes, hydraulic jumps and non-prismatic channel cross sections. Results for the classical benchmark problem of an idealised dam-break are also presented. The results obtained by the various TVD methods are compared with each other and the exact solutions, providing insight into the limitations of the methods along with their relative performances in robustness and accuracy. Some subtle points of the methods and the effects of selecting different options for certain methods are emphasized.Keywords:Finite DifferencesShallow WaterTVDComputational Hydraulics Engineering FiguresReferencesRelatedDetailsCited By 3A finite volume method parallelization for the simulation of free surface shallow water flowsA.I. Delis and E.N. Mathioudakis1 Jul 2009 | Mathematics and Computers in Simulation, Vol. 79, No. 11Application of the HLL Approximate Riemann Solver to One-Dimensional Open Channel Flows with Irregular GeometryXinya Ying and Sam S. Y. Wang26 April 2012Improved implementation of the HLL approximate Riemann solver for one-dimensional open channel flowsXinya Ying and Sam S.Y. Wang26 April 2010 | Journal of Hydraulic Research, Vol. 46, No. 1 Recommended Vol. 03, No. 01 Metrics History KeywordsFinite DifferencesShallow WaterTVDComputational Hydraulics EngineeringPDF download