Open Channel Flow Model Research Articles

3D CFD validation of invert trap efficiency for sewer solid management using VOF model

Earlier investigators have numerically carried out performance analysis of the invert trap fitted in an open channel using the stochastic discrete phase model (DPM) by assuming the open channel flow to be closed conduit flow under pressure and assuming zero shear stress at the top wall. This is known as the fixed lid model. By assuming the top wall to be a shear free wall, they have been able to show that the velocity distribution looks similar to that of an open channel flow with zero velocity at the bottom and maximum velocity at the top, representing the free water surface, but no information has been provided for the pressure at the free water surface. Because of this assumption, the validation of the model in predicting the trap efficiency has performed significantly poorly. In addition, the free water surface subject to zero gauge pressure cannot be modeled using the fixed lid model because there is no provision of extra space in the form of air space for the fluctuating part of the water surface profile. It can, however, be modeled using the volume of fluid (VOF) model because the VOF model is the appropriate model for open channel or free surface flow. Therefore, in the present study, three-dimensional (3D) computational fluid dynamics (CFD) modeling with the VOF model, which considers open channel flow with a free water surface, along with the stochastic DPM, was used to model the trap efficiency of an invert trap fitted in an open rectangular channel. The governing mathematical flow equations of the VOF model were solved using the ANSYS Fluent 14.0 software, reproducing the experimental conditions exactly. The results show that the 3D CFD predictions using the VOF model closely fit the experimental data for glass bead particles.

Potential of remote sensing and open street data for flood mapping in poorly gauged areas: a case study in Gonaives, Haiti

The Hispaniola Island, in the Caribbean tropical zone, is prone to extreme flood events. Floods are caused by tropical springs and hurricanes and may lead to human losses, economical damages, and spreading of waterborne diseases. Flood studies based upon hydrological and hydraulic modelling are hampered by almost complete lack of hydro-meteorological data. Thenceforth, and given the cost and complexity in the organization of field measurement campaigns, the need for exploitation of remote sensing data, and open source data bases. We present here a feasibility study to explore the potential of (i) high-resolution of digital elevation models (DEMs) from remote imagery and (ii) remotely sensed precipitation data, to feed hydrological flow routing and hydraulic flood modelling, applied to the case study of river La Quinte closed to Gonaives (585 km2), Haiti. We studied one recent flood episode, namely hurricane Ike in 2008, when flood maps from remote sensing were available for validation. The atmospheric input given by hourly rainfall was taken from downscaled Tropical Rainfall Measuring Mission (TRMM) daily estimates, and subsequently fed to a semi-distributed DEM-based hydrological model, providing an hourly flood hydrograph. Then, flood modelling using Hydrologic Engineering Center River Analysis System (HEC-RAS 1D, one-dimensional model for unsteady open channel flow) was carried out under different scenarios of available digital elevation models. The DEMs were generated using optical remote sensing satellite WorldView-1 and Shuttle Radar Topography Mission (SRTM), combined with information from an open source database (OpenStreetMap). Observed flood extent and land use have been extracted using Systeme Pour l’Observation de la Terre-4 (SPOT-4) imagery. The hydraulic model was tuned for floodplain friction against the observed flooded area. We compared different scenarios of flood simulation and the predictive power given by model tuning. Our study provides acceptable results in depicting flooded areas, especially considering the tremendous lack of ground data, and shows the potential of hydrological modelling approach fed by remote sensing information in Haiti, and in similarly data-scarce areas. Our approach may be useful to provide depiction of flooded areas for the purpose of (i) flood design for urban planning under a frequency-driven approach and (ii) forecasting of flooded areas for warning procedures, pending availability of weather forecast with proper lead time.

Variational-Based Data Assimilation to Simulate Sediment Concentration in the Lower Yellow River, China

AbstractThe heavy sediment load of the Yellow River makes it difficult to simulate sediment concentration using classic numerical models. In this paper, on the basis of the classic one-dimensional numerical model of open channel flow, a variational-based data assimilation method is introduced to improve the simulation accuracy of sediment concentration and to estimate parameters in sediment carrying capacity. In this method, a cost function is introduced first to determine the difference between the sediment concentration distributions and available field observations. A one-dimensional suspended sediment transport equation, assumed as a constraint, is integrated into the cost function. An adjoint equation of the data assimilation system is used to solve the minimum problem of the cost function. Field data observed from the Yellow River in 2013 are used to test the proposed method. When running the numerical model with the data assimilation method, errors between the calculations and the observations are ...

The rheometry of free surface flows

Classically, open channel design for Newtonian turbulent flow is conducted using the pipe flow paradigm, incorporating the classical concept of the hydraulic radius. Although this approach has merit in turbulent flow, where inertial stresses dominate, it becomes problematic in laminar flow, where the tailings rheology dominates the flow behaviour. Arguably, the pipe flow paradigm for open channel flow has been taken as far as it is useful. The objective of this paper is to develop the fundamentals of sheet flow, and translate these into a sheet flow paradigm. Previous work on the pipe flow paradigm is reviewed, and the limits of its usefulness are exposed. A sheet flow approach is presented, developing a bulk shear rate which can be related directly to the tailings’ rheology. This paradigm is then extended to a generalised laminar flow open channel flow model, incorporating the classical concept of the hydraulic radius. It is shown analytically that bulk shear rate is a unique function of wall shear stress for a given rheology and for all values of flow depth and slope. The significance of this is that in general the bulk shear rate is a unique function of the rheogram and the wall shear stress, and can be used for scale-up and design at any required slope and depth in laminar flow. Conversely, reversing the process provides the link between the pseudo shear diagram and the rheogram. This is validated using experimental results which show that the laminar data are collinear, the turbulent branches are succinct, and different for each slope, reminiscent of the pipe flow diagram. Experimental validation provides convincing evidence that the new sheet flow paradigm model for open channel flow can provide a competent basis for the analysis, flow behaviour prediction and design of open channel flow.

Mean Velocity Modeling of Open-Channel Flow with Submerged Rigid Vegetation

Mean Velocity Modeling of Open-Channel Flow with Submerged Rigid Vegetation

Changes in bedrock channel morphology driven by displacement rate increase during normal fault interaction and linkage

AbstractWe attribute changes in the morphology of relay ramp channels (increased slope and decreased width) to variations in displacement rate on ramp‐adjacent normal faults. We map the faults and fluvial channels associated with four sites in different stages of fault interaction and linkage on the Volcanic Tableland, a Late Pleistocene ash‐flow tuff in east‐central California. Because these channels are inactive today, we estimate downstream changes in channel width and depth using HEC‐RAS, a one‐dimensional open channel flow model. Our results show that channel slope must be greater than about 0.05 before there are substantial decreases in width or substantial increases in depth. Displacement rate increases during interaction between en echelon segments results in the increases in channel slope and decreases in channel width. Moreover, our data show that these changes begin to occur during the very early stages of fault interaction, well before the fault geometry would indicate ongoing or imminent linkage.

Development of Two-layered model for compound open-channel flow

Present study deals with the development of two-dimensional two-layered model for straight compound open-channel flow using Smagorinsky-based subgrid-scale turbulence model, based on large eddy simulation approach. The two-layer depth averaged governing equations are solved using finite volume method based on MacCormack predictor-corrector explicit scheme. Model results for symmetric and asymmetric straight compound channel flows are verified with the available numerical and experimental data. Variations of flow variables in symmetric and asymmetric straight compound channels in terms of shear stress distributions and spanwise and vertical velocities are analyzed at the horizontal interface between the lower layer and the upper layer. Spanwise and vertical velocities at the horizontal interface revealed the existence of horizontal vortices near the junction of the main channel and the floodplain where momentum exchange takes place. Further, the model result, showing the spanwise shear stresses distribution at the interface of symmetric and asymmetric compound channel, revealed the existence of peak shear stress near the channel junction. Sensitivity of the two important model parameters is also undertaken and their roles in longitudinal velocity distribution along the channel width are discussed.

Two-layer model for open channel flow with submerged flexible vegetation

A two-layer model for predicting the vertical distribution of stream-wise velocity in open channel flow with submerged flexible vegetation is proposed. Using the predicted deflection height of the flexible vegetation determined via the large-deflection cantilever beam theory, the flow is vertically separated into a bottom vegetation layer and an upper free water layer, and corresponding momentum equations for each layer are formulated. In the bottom vegetation layer, the resistance caused by the deflected plants is calculated accounting for plant bending rather than adopting the existing resistance formula for erect rigid vegetation. For the upper free water layer, a new type of polynomial velocity distribution is suggested instead of the traditional logarithmic velocity distribution to obtain a zero velocity gradient at the water surface. To validate the proposed model, the published experimental data are employed.

Measurements and modeling of open-channel flows with finite semi-rigid vegetation patches

The hydrodynamics of flows through a finite length semi-rigid vegetation patch (VP) were investigated experimentally and numerically. Detailed measurements have been carried out to determine the spatial variation of velocity and turbulence profiles within the VP. The measurement results show that an intrusion region exists in which the peak Reynolds stress remains near the bed. The velocity profile is invariant within the downstream part of the VP while the Reynolds stress profile requires a longer distance to attain the spatially invariant state. Higher vegetation density leads to a shorter adjustment length of the transition region, and a higher turbulence level within the VP. The vegetation density used in the present study permits the passing through of water and causes the peak Reynolds stress and turbulence kinetic energy each the maximum at the downstream end of the patch. A 3D Reynolds-averaged Navier–Stokes model incorporating the Spalart–Allmaras turbulence closure was employed subsequently to replicate the flow development within the VP. The model reproduced transitional flow characteristics well and the results are in good agreement with the experimental data. Additional numerical experiments show that the adjustment length can be scaled by the water depth, mean velocity and maximum shear stress. Empirical equations of the adjustment lengths for mean velocity and Reynolds stress were derived with coefficients quantified from the numerical simulation results.

Modelling rollers for shallow water flows

AbstractHydraulic jumps, roll waves or bores in open channel flows are often treated as singularities by hydraulicians while slowly varying shallow water flows are described by continuous solutions of the Saint-Venant equations. Richard & Gavrilyuk (J. Fluid Mech., vol. 725, 2013, pp. 492–521) have enriched this model by introducing an equation for roller vorticity in a very elegant manner. This new model matches several experimental results that have resisted theoretical approaches for decades. This is the case of the roller of a stationary hydraulic jump as well as the oscillatory instability that the jump encounters when the Froude number is increased. The universality of their approach as well as its convincing comparisons with experimental results open the way for significant progress in the modelling of open channel flows.

Local sensitivity for uncertainty analysis in one-dimensional open channel flow modelling

Uncertainty analysis may be of high importance in the field of water engineering. Sampling-based techniques, that resort to extensive exploration of the space of possible model inputs are a common approach. When inputs uncertainties can be described statistically by means of probability distribution functions, Monte Carlo simulation yields a statistical description of uncertain model outputs. However, the combination of commonly encountered input space dimensions and model CPU times often makes this approach hardly practicable. We propose to assess the potential of a local sensitivity analysis for uncertainty analysis in the modelling of open channel flows with the one-dimensional shallow water equations, which are generally viewed as being largely non linear. The first-order local sensitivity is simply assessed using the so-called empirical method requiring only two runs of the model (for a single uncertain parameter). The global sampling-based approach consists in running Monte Carlo simulations with the hydrodynamic model, given a statistical distribution of the model input parameters. Monte Carlo results can be analysed through classical statistical estimators, such as mean and standard deviation. It is shown that these characteristics can also be accurately estimated from the local sensitivity and the input distribution. Steady state and highly transient configurations (gate opening and closing) are explored, accounting for uncertainty of the main parameters (bottom slope, friction coefficient, boundary and initial conditions).

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.

Auxiliary Variable-based Balancing (AVB) for source term treatment in open channel simulations

Practical engineering applications of open channel flow modelling involve geometric terms arising from variations in channel shape, bottom slope and friction. This paper presents the family of schemes that satisfy the generalised C-property for which static equilibrium is a particular case, in the framework of one-dimensional open channel flows. This approach, named Auxiliary Variable-based Balancing, consists of using an auxiliary variable in place of the flow variables in the diffusive part of the flux estimate. The auxiliary variable is defined so as to achieve a zero gradient under steady-state conditions, whatever the geometry. Many approaches presented in the literature can be viewed as a particular AVB case. Three auxiliary variables are presented in this paper: water elevation, specific force and hydraulic head. The methodology is applied to three classical Riemann solvers: HLL, Roe and the Q-scheme. The results are compared on five test-cases: three steady-state configurations including friction, singular head losses and variations in bottom elevation, channel width and banks slope and two transient test-case (dam-break problems on rectangular and triangular channel). In each case, the auxiliary variable that best preserves the steady-state configuration is the hydraulic head. Besides, using the head as auxiliary variable allows head loss functions due to singularities to be incorporated directly in the governing equations, without the need for internal boundaries. However, it is generally less accurate when sharp transients are involved.

Effect of Friction on Spurious Oscillations in Open Channel Modeling with Variable Bathymetry or Roughness

AbstractNumerical issues for the friction-dominated steady-state Saint-Venant equations with a shock-capturing upwind finite-element scheme are studied using nonuniform-flow test cases and Fourier analysis. The friction-dominated case is a common phenomenon in open channel flow modeling when the depth becomes small compared with the discretization length. In the nonuniform-flow test cases, abrupt slope changes and abrupt roughness changes are introduced, and in the Fourier analysis, a periodic bed perturbation is used. Nondimensional parameter groups identified are as follows: the upwinding coefficient, the number of elements per wavelength, the average-flow Froude number, and the numerical friction number. The results show that errors in both depth and discharge variables are observed whenever there is any perturbation in the bed topography or bed roughness. These errors increase with increasing Froude number and increasing numerical friction number. A combined friction parameter is introduced for practi...

A Direct Solution Approach to the Inverse Shallow‐Water Problem

The study of open channel flow modelling often requires an accurate representation of the channel bed topography to accurately predict the flow hydrodynamics. Experimental techniques are the most widely used approaches to measure the bed topographic elevation of open channels. However, they are usually cost and time consuming. Free surface measurement is, on the other hand, relatively easy to obtain using airborne photographic techniques. We present in this work an easy to implement and fast to solve numerical technique to identify the underlying bedrock topography from given free surface elevation data in shallow open channel flows. The main underlying idea is to derive explicit partial differential equations which govern this inverse reconstruction problem. The technique described here is a “one‐shot technique” in the sense that the solution of the partial differential equation provides the solution to the inverse problem directly. The idea is tested on a set of artificial data obtained by first solving the forward problem governed by the shallow‐water equations. Numerical results show that the channel bed topographic elevation can be reconstructed with a level of accuracy less than 3%. The method is also shown to be robust when noise is present in the input data.

Exploration on the Widening Value Calculation Method of Continuous Bends in Inland River

The widening value formulas of continuous bends currently in use cannot meet the requirements of the practical engineering because the values of them are far less than the realistic situation needs. Based on the method of combing the generalized open channel flow model of continuous bends with the experiment of small-sized ship model, and in accordance with the experimental data and the precursors’ experience, two of the channel widening value empirical formulas are obtained, which can respectively used in the upper bend and the lower bend of the continuous bends according to the length of the transitional linear segment sufficient or not.

A Multiple Grid Algorithm for One-Dimensional Flood Flow

Numerical modeling of open channel flows with dam-break using explicit finite difference schemes is constrained by the choice of time step, which is limited by the CFL stability criteria. To overcome this limitation, in this work we introduce the application of an algorithm to the field of computational hydraulics. By coupling this algorithm to a second-order accurate MacCormack scheme, we demonstrate that the solution can be accelerated to the desired transient state. The present formulation has been tested to simulate a dam-break flow. The close agreement between the obtained results and the theoretical findings indicates the reliability of the proposed algorithm.

Ensemble Modeling of Hydrologic and Hydraulic Processes at One Shot: Application to Kinematic Open-Channel Flow under Uncertain Channel Properties and Uncertain Lateral Flow Conditions by the Stochastic Method of Characteristics

A stochastic kinematic wave model for open channel flow is developed under uncertain channel properties and uncertain lateral flow conditions. Applying a known methodology, the Fokker-Planck equation (FPE) of the kinematic open-channel flow process under uncertain channel properties and uncertain lateral flow conditions is derived using the method of characteristics. Because every stochastic partial differential equation has a one-to-one relationship with a nonlocal Lagrangian-Eulerian Fokker-Planck equation (LEFPE), the LEFPE for the governing equation of any hydrologic or hydraulic process can be developed as the physically based stochastic model of the particular process. To quantify the ensemble behavior of a process, LEFPE provides a quantitative description of the time-space evolution of the probability density function of the state variables of the process at one shot. The nonlocal LEFPE reduces to the classical local FPE, which is more convenient to solve, under certain assumptions. The developed ...

Ensemble Modeling of Hydrologic and Hydraulic Processes at One Shot: Application to Kinematic Open-Channel Flow under Uncertain Channel Properties by the Stochastic Method of Characteristics

A stochastic kinematic wave model for open-channel flow under uncertain channel properties is developed. The Fokker-Planck equation (FPE) of the kinematic open-channel flow process under uncertain channel properties is developed by using the method of characteristics. Every stochastic partial differential equation has a one-to-one relationship with a nonlocal Lagrangian-Eulerian FPE (LEFPE). As such, one can develop an LEFPE for the governing equation of any hydrologic or hydraulic process as the physically based stochastic model of the particular process. A linear, deterministic, differential equation in Eulerian-Lagrangian form, LEFPE provides a quantitative description of the evolution of the probability density functions of the state variables of the process at one shot to describe the ensemble behavior of the process instead of the commonly used many Monte Carlo simulations to quantify the same ensemble behavior. Under certain assumptions, the nonlocal LEFPE reduces to the classical local FPE, which is more convenient in practical applications. The numerical solutions of the resulting FPE are validated by Monte Carlo simulations under varying channel conditions. The validation results demonstrated that the developed FPE can express the ensemble behavior of the kinematic wave process under uncertain channel properties adequately.

3D Open Channel Flow Modeling by Applying 1D Adjustment

A three-dimensional (3D) finite volume model with a novel adjustment scheme was developed to solve shallow water equations in open channels. An explicit finite volume method was used to discretize the governing equations in a boundary-fitted structured and collocated grid system. Because a simple second-order central scheme was used for spatial discretization and due to the occurrence of high Peclet numbers in open channel flows, some treatments were needed to reduce oscillation. Thus, a special adjustment scheme designed to minimize differences in the averaged free surface elevation and flow discharge in a 3D model and 1D flow data was applied to some cross-sections. The model was applied to simulate shallow water flow in a backwardfacing step, a meandering channel with 90° bends and a 180° bend channel. A comparison of the model results with available experimental and numerical data illustrated that the proposed numerical procedure decreases the numerical oscillations and increases the stability of the 3D numerical model in open channel flow modeling.