Open Channel Flow Model Research Articles

Semi-analytical modeling of sediment-laden open-channel flows with the effects of stratification, hindered settling, and eddy viscosities.

This study proposes semi-analytical models for simultaneous distribution of fluid velocity and suspended sediment concentration in an open-channel turbulent flow using three kinds of eddy viscosities. Apart from the classical parabolic eddy viscosity which is based on a log-law velocity profile, we consider two recently proposed eddy viscosities based on the concept of velocity and length scales. To deal with the flows with high sediment concentration, several turbulent features such as the hindered settling mechanism and the stratification effect are incorporated in the model. The governing system of highly nonlinear differential equations is solved using the homotopy analysis method (HAM), which produces solutions in the form of convergent series. Numerical and theoretical convergence analyses are provided for all three types of eddy viscosities. The effects of parameters on the derived models are discussed physically. Experimental data on both dilute and non-dilute flows are considered to verify the HAM-based solutions. The effects of the stratification correction factor (β) and the turbulent Schmidt number (α) reveal that they should be determined optimally for applicability of the proposed models in terms of accurate prediction with data. This optimal procedure required further investigation of these parameters, and, thus, an analysis of β and α is carried out, which linked them with the particle diameter through particle settling velocity, reference fluid velocity, and reference sediment concentration by proposing regression equations. Furthermore, using the optimal values of the parameters, the proposed models corresponding to the eddy viscosities based on the exponentially decreasing turbulent kinetic energy function and von Karman's similarity hypothesis are seen to be superior to the model corresponding to a parabolic eddy viscosity. Finally, a comment on the HAM is made where it is observed that the method can remove the numerical singularity of the governing equations at the water surface, which arises because of the consideration of vanishing eddy viscosity thereat.

Expanding and Enhancing Streamflow Prediction Capability of the National Water Model Using Real-Time Low-Cost Stage Measurements

Abstract This study demonstrates an approach to expand and improve the current prediction capability of the National Water Model (NWM). The primary objective is to examine the potential benefit of real-time local stage measurements in streamflow prediction, particularly for local communities that do not benefit from the improved streamflow forecasts due to the current data assimilation (DA) scheme. The proposed approach incorporates real-time local stage measurements into the NWM streamflow DA procedure by using synthetic rating curves (SRC) developed based on an established open-channel flow model. For streamflow DA and its evaluation, we used 6-yr (2016–21) data collected from 140 U.S. Geological Survey (USGS) stations, where quality-assured rating curves are consistently maintained (verification stations), and 310 stage-only stations operated by the Iowa Flood Center and the USGS in Iowa. The evaluation result from NWM’s current DA configuration based on the USGS verification stations indicated that DA improves streamflow prediction skills significantly downstream from the station locations. This improvement tends to increase as the drainage scale becomes larger. The result from the new DA configuration including all stage-only sensors showed an expanded domain of improved predictions, compared to those from the open-loop simulation. This reveals that the real-time low-cost stage sensors are beneficial for streamflow prediction, particularly at small basins, while their utility appears to be limited at large drainage areas because of the inherent limitations of lidar-based channel geometry used for the SRC development. The framework presented in this study can be readily applied to include numerous stage-only stream gauges nationwide in the NWM modeling and forecasting procedures.

A distributed domain model coupling open channel flow and groundwater flow to quantify the impact of lateral hydrologic exchange on hydrograph

• A distributed-domain coupling model is developed to evaluate the interaction between hydrologic exchange flows and river hydrodynamics. • The buffering effect of lateral HEFs can dominate flood wave patterns. • The falling limb (with a power-law rate) of hydrographs is linked to spatially heterogeneous hydraulic properties. Hydrologic exchange flows (HEFs) of river-aquifer systems are known to affect water flow, but the quantitative influences of lateral HEFs and the riparian zone’s hydraulic conductivity ( K ) distribution on stream fluxes remain obscure under varying hydrologic conditions. To fill this knowledge gap, this study proposed a physical based, distributed domain, coupled (open channel and groundwater) flow model (DDCM) to quantify the effect of lateral HEFs on hydrograph characteristics, including especially the peak discharge and tailing decay which are practically important. Numerical experiments showed that (1) the interaction between the lateral HEFs and river hydrodynamics reduced the peak discharge and flood flow rates, (2) a heterogeneous K field of the riparian zone generated multi-rate HEFs (which then changed flow response) represented by the hydrographs with various declining rates (varying from exponential to power-law), significantly expanding the flow process, and (3) the probability density function of K also affected the tailing and peak of the hydrograph. A preliminary test showed that the DDCM captured the overall pattern of hydrographs observed from a catchment in the Wadi Ahin West, Oman. This study, therefore, provided a model-based quantification of the mechanisms and factors of the lateral HEFs affecting the hydrograph pattern in flood events, and further applications are needed to test the applicability of the DDCM in capturing real-world hydrographs affected by the lateral HEFs.

Rivers in reverse: Upstream-migrating dechannelization and flooding cause avulsions on fluvial fans

AbstractThe process of river avulsion builds floodplains and fills alluvial basins. We report on a new style of river avulsion identified in the Landsat satellite record. We found 69 examples of retrogradational avulsions on rivers of densely forested fluvial fans in the Andean and New Guinean alluvial basins. Retrogradational avulsions are initiated by a channel blockage, e.g., a logjam, that fills the channel with sediment and forces water overbank (dechannelization), which creates a chevron-shaped flooding pattern. Dechannelization waves travel upstream at a median rate of 387 m/yr and last on average for 13 yr; many rivers show multiple dechannelizing events on the same reach. Dechannelization ends and the avulsion is complete when the river finds a new flow path. We simulate upstream-migrating dechannelization with a one-dimensional morphodynamic model for open channel flow. Observations are consistent with model results and show that channel blockages can cause dechannelization on steep (10−2 to 10−3), low-discharge (~101 m3 s−1) rivers. This illustrates a new style of floodplain sedimentation that is unaccounted for in ecologic and stratigraphic models.

Enhancing the understanding of hydrological responses induced by ecological water replenishment using improved machine learning models: A case study in Yongding River

The ecological water replenishment (EWR) of Yongding River has been an important project implemented in response to the Development of an Ecological Civilization policy in China since 2016. A reasonable amount of EWR requires a systematic understanding of the relationship among the surface water, groundwater, ecology and economy. However, studying surface water-groundwater interactions still remains an important issue. Thus, a coupled model integrating a Muskingum method-based open channel flow model and machine learning-based groundwater model is developed to describe the dynamic changes in streamflow and groundwater level in response to the EWR of Yongding River. The model is calibrated using observed streamflow data as well as groundwater level data on a daily scale for the spring EWR in 2020. The simulated results match well with the observed data and suggest that significant groundwater level increases occur only around the main channel of Yongding River. Fifteen scenarios under different EWR schemes are set to obtain reasonable streamflow during EWR, and then the responses of streamflow and groundwater level changes are simulated. Reasonable streamflow at the Guanting Reservoir need to be above 65 m3/s to ensure the streamflow can pass through Beijing and significant groundwater level recoveries of 170 million m3 through EWR. The developed models can improve the understanding of the interaction between surface water and groundwater and provide a quick assessment of the factors influencing the different EWR schemes and thus aid in effective EWR project management.

Flow Structures of the Air-Water Layer in the Free Surface Region of High-Speed Open Channel Flows

In hydraulic engineering, intense free surface breakups have been observed to develop in high-speed open channel flows, resulting in a mixed air-water layer near the free surface that grows with the development of self-aeration. This region is characterized by a substantial number of droplets coexisting with an induced air layer above. Little information about this droplet layer is currently available and no practicable approach has been proposed for predicting the parameters of the induced air layer based on the related flow structures in the droplet layer. In this research, laboratory experiments were accordingly conducted to observe the detailed droplet layer development in terms of layer thickness, droplet size, and frequency distributions under comparative flow conditions. Based on the simplified droplet layer roughness determined using the experimentally measured mean droplet size, the classical power-law of boundary layer theory was applied to provide an analytical solution for the air velocity profile inside the air layer. The relationship of air layer growth to droplet layer thickness, which is a key factor when determining the air velocity distribution, was also established, and the analytical results were proven to be in reasonable agreement with air velocity profiles presented in the literature. By determining the relationship between droplet layer properties and air velocity profiles, the study establishes a basis for the improved modeling of high-speed open channel flows.

Numerical modelling for leak oil flow in tunnel of the cave storage

Abstract Oil storage in cavern tank is one of the important ways of oil storage. More than 80% of the oil tanks in the cave storage have been used for around 30 years in China and leakage accidents are likely to occur. When it occurs, the motor closing facilities preventing leakage spreading should be set up. The leaking oil flow characteristic in tunnel must be known for setting up the motor closing facilities. Based on the open-channel unsteady flow theory, a numerical model of tank leakage coupling the oil flow in tunnel was developed, and the characteristic line method was used to solve the model under the given initial condition and boundary condition. The variation of the depth and flow rate with time of oil flowing in the tunnel can be obtained. In order to verify the accuracy of model, the measurement data of high accuracy experimental system for unsteady open-channel flow were conducted to compare with the calculation. It fully confirms the high precision of the numerical model and reflects the variation characteristics of each hydraulic parameter in the numerical model of unsteady open channel flow truly. And then, the leaking oil flow characteristic in tunnel was obtained. It is that the farther from the leaking tank, the lower depth and flow rate of the oil in the tunnel revealed. Furthermore, the effect of the size of oil tank crack on the depth and flow rate was investigated. The greater size of crack makes the oil flow rate higher and the oil deeper in the tunnel and flow faster.

Sediment transport and bed evolution model for complex river systems.

This work presents the theoretical background, development, and preliminary evaluation of a one-dimensional unsteady sediment transport and bed evolution model for a looped river network. The sediment transport and bed evolution model employs a concept that differentiates sediment particles moving in the form of suspended sediment, and near bed, and bed sediment. Applying the active layer concept, the developed model utilizes the appropriate exchange mechanisms between the suspended sediment and active layer material, which are presented in great detail. The governing transport equations were solved using the split operator approach that resulted in two successive steps. The advection equations were solved using the characteristics method, whereas the diffusion equations were discretized using the Crank-Nicholson scheme. The obtained system was complemented with additional auxiliary equations in order to allow sediment transport and bed evolution simulation at nodes, thus enabling the same in a looped river network. The derived equations were applied to develop an open-channel flow, sediment transport, and bed evolution model that was subjected to a series of preliminary numerical tests.

A comparative study of rigid-lid and level-set methods for LES of open-channel flows: morphodynamics

Computational modeling of open-channel flows is usually carried out using the rigid-lid (RL) assumption to prescribe the water surface. Such an approach deems more appropriate for sub-critical flow regimes with Froude number ≪ 1. When the Froude number is locally high, e.g. flows around hydraulic structures, the free-surface fluctuations affect the induced hydrodynamics. Indeed, prior investigations on the effect of the RL assumption on large-eddy simulation (LES) of open-channel flows around bridge abutments revealed that such an assumption may influence both the first and second order turbulence statistics. In this work, we investigate the effect of the RL assumption on bed-morphodynamics calculations. The fully coupled flow and bed morphodynamics virtual flow simulator (VFS-Geophysics) model is herein employed to numerically investigate the sediment transport around a laboratory-scale model of abutment. Numerical simulations using a mass-conserving level-set (LS) method and a RL assumption are performed to evaluate the influence of free-surface elevation on the computed bed-morphodynamics at a Reynolds number of 7.9 × 104. We also conducted an experimental study to observe the scour development around the abutment model. The instantaneous scour patterns and bed profiles computed with the LS and RL are compared with the measurements. The mean absolute errors of bed-profile predictions at or near quasi-equilibrium of bed evolution, for the LS and RL computed results, are about 4.1% and 4.7%, respectively. Despite the differences in flow field computations of the two methods, the computed bed morphology appeared relatively insensitive to the two numerical approaches. However, the computational cost of the coupled LES-LS-morphodynamics is at least one order of magnitude greater than that of the LES-RL-morphodynamics.

Non-linear shallow water flow modelling over topography with depth-averaged potential equations

Hunter Rouse was the father of the Fluid Mechanics of Open Channel Flow. In this review article the fundamental advances on the non-hydrostatic modeling of shallow open channel flow over topography, since the publication of his 1938 book, are discussed. Flows over uneven topography, like at open channel controls, occurs in a short length, thus rendering ideal fluid flow theory an adequate mathematical tool. This paper emphasis is on depth-averaged modeling of these flows using Boussinesq equations, given the significant advances basically since the 80’s. The one-dimensional steady flow model from Picard iteration is reviewed in detail, including energy and momentum formulations, flow at a weir crest, and on a slope. A new numerical scheme is developed for the solution of transcritical steady weir flow, showing excellent match with experiments. A new derivation for the two-dimensional depth-averaged unsteady ideal fluid model is presented based on a continuum mechanics formulation. The result is the Serre–Green–Naghdi equations (SGNE). It is demonstrated that the extended Bernoulli equation derived from Picard iteration is an integral form of the SGNE for 1D steady flow. A robust MUSCL-Hancock finite volume model is developed to solve the unsteady 1D SGNE, showing excellent agreement with the steady transcritical flow solutions previously constructed. The accuracy of the MUSCL-Hancock solver is critically assessed using a higher-order solver for the SGNE.

Development of the Stage Flow Relations for a Tropical Watershed

The effluent discharge from wastewater treatment plants can permeate through the ground and become a major source of contaminant to ecosystems and water bodies. These toxic contaminants can transport and find a way to the ocean via underground streams harming the aquatic life and promoting algal blooms. This paper presents meteorological and hydrological data collection and analysis to better understand the characteristics of the effluent discharge from the wastewater treatment plant and receiving water in Toguan watershed on the Island of Guam so as to support future regulatory discussions regarding modification of permit conditions and/or water quality standards to achieve compliance. Hydrological data such as rainfall, turbidity and stream level were collected over a period of two years. Crossflow measurements for two stations, one downstream, the other upstream of the effluent discharge point were collected bi-weekly, except at times of very low flow or dangerously high storm runoff in the stream. To better understand the behavior of the Toguan River sub-watersheds, aerial photos were taken from a single-engine Cessna aircraft. By analyzing the collected hydrological data, the relationships among the stream level, volume discharge and rainfall, were developed. The manually collected crossflow data allowed for the calculation of a rating curve for the Toguan River. This effort was somewhat hampered by prolonged drought conditions during roughly half of the period of data collection that severely limited the amount of crossflow measurements taken at high stage heights. The continuous measurement of stream level and rainfall allowed for a more comprehensive analysis of the relationship between the stage height and rainfall. Finally, a complimentary stream stage height short-term prediction scheme was developed using a routing model, and refinements to the stream flow discharge curve using a simple model for open channel flow is also presented. A further benefit of the study was the establishment of a baseline for the hydrologic conditions of the Toguan watershed which can be used to assess changes related to any future improvements to the wastewater treatment plant operations or other significant developments within this watershed.

Comparative Hydrodynamic Study of Rigid-Lid and Level-Set Methods for LES of Open-Channel Flow

AbstractComputational modeling of open-channel flows at low Froude (F) numbers is often carried out using the rigid-lid assumption to prescribe the water surface location. However, the presence of ...

Modeling of interconnected flat open-channel flow: application to inland navigation canals

Inland navigation networks are composed of several artificial canals, usually characterized by no slope. These canals are large-scale systems that can be accurately described by means of the nonlinear Saint-Venant partial differential equations. However, the lack of an analytical solution for these equations is one of the reasons why simplified models have been developed. In this work, the Integrator-Delay-Zero model is used as the input-output model to link the water depths to the discharges. A modeling extension for a canal with inflows and outflows along the water stream is proposed: an overlapping problem is discussed and a criterion choice is defined in order to obtain the general model. With regard to this criterion, a calibration step is needed, both to overcome the natural limitations of the simplified model and to ensure the correct computation of the general model. The application of this modeling approach to a part of the inland navigation network in the north of France serves as the case study for this work.

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development

Abstract. The Saint-Venant equations are commonly used as the governing equations to solve for modeling the spatially varied unsteady flow in open channels. The presence of uncertainties in the channel or flow parameters renders these equations stochastic, thus requiring their solution in a stochastic framework in order to quantify the ensemble behavior and the variability of the process. While the Monte Carlo approach can be used for such a solution, its computational expense and its large number of simulations act to its disadvantage. This study proposes, explains, and derives a new methodology for solving the stochastic Saint-Venant equations in only one shot, without the need for a large number of simulations. The proposed methodology is derived by developing the nonlocal Lagrangian–Eulerian Fokker–Planck equation of the characteristic form of the stochastic Saint-Venant equations for an open-channel flow process, with an uncertain roughness coefficient. A numerical method for its solution is subsequently devised. The application and validation of this methodology are provided in a companion paper, in which the statistical results computed by the proposed methodology are compared against the results obtained by the Monte Carlo approach.

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 2: numerical application

Abstract. The characteristic form of the Saint-Venant equations is solved in a stochastic setting by using a newly proposed Fokker–Planck Equation (FPE) methodology. This methodology computes the ensemble behavior and variability of the unsteady flow in open channels by directly solving for the flow variables' time–space evolutionary probability distribution. The new methodology is tested on a stochastic unsteady open-channel flow problem, with an uncertainty arising from the channel's roughness coefficient. The computed statistical descriptions of the flow variables are compared to the results obtained through Monte Carlo (MC) simulations in order to evaluate the performance of the FPE methodology. The comparisons show that the proposed methodology can adequately predict the results of the considered stochastic flow problem, including the ensemble averages, variances, and probability density functions in time and space. Unlike the large number of simulations performed by the MC approach, only one simulation is required by the FPE methodology. Moreover, the total computational time of the FPE methodology is smaller than that of the MC approach, which could prove to be a particularly crucial advantage in systems with a large number of uncertain parameters. As such, the results obtained in this study indicate that the proposed FPE methodology is a powerful and time-efficient approach for predicting the ensemble average and variance behavior, in both space and time, for an open-channel flow process under an uncertain roughness coefficient.

Impact of initial conditions on the prediction of the spread of thermal pollution in rivers

The influence of initial conditions on the prediction of the increase of river temperature below the point of release of heated water for a designed power plant has been analysed in this study. The results for different assumed values of river flow and different temperatures of the discharged heated water have been presented. The results have been analysed taking into account existing legal frames. The two-dimensional inhouse RivMix model has been used to simulate the temperature distribution whereas the two-dimensional depth-averaged turbulent open channel flow model CCHE2D has been used to simulate the velocity fields and the water depths for the selected flows of the river.

Wappapello Dam Spillway Overtopping Event of 2011

Abstract The one-dimensional HEC-RAS multi-purpose open channel flow modeling software was successfully used, with ArcMap and HEC-GeoRAS, to simulate flow over the Wappapello Dam limited-use Ogee spillway (Wappapello, Missouri). Initial computational hydraulic modeling results predicted a lake elevation of 132.9 m (405.0 ft) [NAVD 1988] would be required for the resulting floodwaters overtopping the spillway to reach the nearby Wappapello Lake Management Office. An intense rainfall event during 2011 led to the spillway being overtopped for the first time since 1945. Spillway performance during the 2011 event was analyzed afterwards. Results indicated that the spillway crest was not submerged by backwater. A technique was employed which successfully estimated the design energy head of 7.160 m (23.49 ft) for the spillway. Hydraulic modeling developed after the 2011 event incorporated this estimated design energy head, allowing the spillway discharge coefficient to vary with discharge in the course of an unsteady modeling run. Results indicated that, while the spillway did perform as designed, the performance is limited by the shallow approach depth.

The influence of sandy clay bed material to local scour behaviour

Abstract As a type of gate that is used to control the water level upstream, sluice gate is the gate with simple shape and outstanding ability to flush the sediment. The operation of the gate is considered an important process. The up and down movement of the gate would affect the velocity and cause local scour as the result of fluctuating rate. This research aims to assess the effects of discharge and gate-opening height variations, as well as the type of bedchannel material, on the change of depth of scour (ds). The research was conducted of open channel flow model with a sluice gate able to up and down movement. The discharges used in the research were 9 types ranging from 1.0 to 5.0 dm3·s−1. There were 5 variations in the height of gate-opening ranging from 0.5 to 2.5 cm at intervals of 0.5 and types of channel-bed material. The results of the research showed that the depth of scour can be analysed as a function of discharge, height of gate-opening, height of water level upstream and downstream, and the type of bed material used. The scour depth equation on is $d_s = 1.7822\left( {{Q \over a}} \right)^{1.1347} a$ . Calculated coefficient of determination of the relationship between two types of channel-bed material and the depth of scour was R2 = 0.946. Consequently, it can be concluded that the equation can be applied on both types of bed-channel material.

Numerical modeling of open channel flow with suspended canopy

Suspended canopies are common in aquatic environments. The mean flow velocity and Reynolds stress in the open channels with the suspended canopies were studied through laboratory experiments and numerical simulations. Numerical modeling was conducted with a modified version of the Delft3D-Flow model using a k–ε turbulence closure scheme. The resistance effects of the suspended canopy were modeled by adding a resistance term in the momentum equations of fluid flow, along with an addition production and dissipation term in the k and ε equations respectively. The numerical results for mean flow velocity and Reynolds stress agreed well with the experimental data of this study and the previously published data by Plew (2010). The spatial evolution of the mixing layer near the bottom of the suspended canopy can be broadly separated into the diverging flow, developing, and fully developed zones. The thickness and density of the suspended canopy significantly influenced the flow characteristics.

Development of a river-groundwater interaction model and its application to a catchment in Northwestern China

The river-groundwater interaction is an important component of the hydrological cycle. This study develops an integrated river-GW model that uses a one-dimensional open channel flow model and a three-dimensional saturated GW flow model to describe the dynamic river-GW relationship at the basin scale, as well as groundwater flow and streamflow in arid regions. The model is tested with three cases, and the good agreement between the simulated and observed results demonstrates that the model can be used to simulate river-GW interactions. The integrated river-GW model is applied to the middle reaches of the Heihe River Basin and is calibrated using multi-source field data, including hydraulic heads from observation wells, streamflow, and spring flow. The case studies in the Heihe River Basin find that the following: (1) the river-GW relationships vary seasonally and spatially and depend on many factors, such as the river flow and GW uses; (2) in the middle reaches, the annual mean river–groundwater flux exchange from Yinluoxia to the Heihe Bridge is approximately 17% of the mean streamflow and increases to more than 49% from the Heihe Bridge to Zhengyixia; and (3) after the implementation of the water reallocation plan in 2000, the river-GW relationship in some reaches changed from a gaining stream to a losing stream due to the increase of GW abstraction. These findings suggest that GW pumpage should be controlled rationally and demonstrate that the integrated river-GW model can be used to analyse the temporal-spatial trends of river-groundwater interaction in arid regions.