Shallow Open Channel Flows Research Articles

Modelling of flow pattern in an open channel with sidewall obstruction

To predict flow pattern of shallow obstructed open channel flows, laboratory experiments of flow around a vertical emergent sidewall abutment (lateral constriction) in an open channel flow is simulated numerically and results of water surface and vertical profile of velocity are compared with the numerical results. The turbulence kinetic energy at the separation zone and bed shear stresses are also investigated. A computational fluid dynamic (CFD) numerical tool and volume of fluid (VOF) were used to predict water surface profiles. Results showed a very good agreement between the numerical and the experimental results of the water surface profiles. The numerical findings highlighted an increase in the velocity around the structure of two times the average flow velocity. The maximum pressure was observed in front of the constriction increases with increasing discharges. The vertical velocity profiles upstream the sidewall abutment at the three selected locations showed reasonable results. The maximum turbulence kinetic energy is shown at the zone of separation when the flow passes around the nose with high velocity. In this research, numerically it was found that the estimated bed shear stresses are 2-3 times the mean bed-shear stress of incoming flow. While, previous researchers finding showed a maximum value of bed shear stress near the leading edge 3.63 to 5 times the bed shear stress of the incoming flow. Because of the wide rang variation in calculating bed shear stresses by the previous researchers, so our research aims to calculate it using CFD and compare it with others. Also, dynamics of the flow around the obstacle was considered in this research under uniform flow conditions for an aspect ratio ranged 5 to 10.

Application of the sampling moiré method to shallow open-channel flows with circular roughness elements

This research presents an application of the sampling moiré method, a novel technique originally developed for measuring slight deformation of a static object such as a plate, to fluctuating free water surface in rough open channel flows. The method was used to capture the two-dimensional water surface deformation at a high sampling rate by dyeing the color of water white. The target flow was a very shallow subcritical flow with a depth of 1.5 times the height of the roughness. As a result, a series of instantaneous water surface profiles with non-uniform rough planes were successfully measured at a sampling rate of 100 Hz.It has become clear that the effect of dispersive gravity waves traveling on the water surface is greater than that of non-dispersive waves driven by the turbulence, and that this feature becomes more pronounced as the Froude number increases in such shallow flow conditions. Furthermore, it was experimentally and theoretically verified that the intensity of water surface fluctuation increases with the square of the Froude number. The decomposition of surface fluctuations due to gravity waves and subsurface turbulence using the wavenumber frequency spectrum revealed that the effects of subsurface turbulence are about 20%. This is much less than the contribution from gravity waves in very shallow flows as in this experiment.

Solid-flow interactions of a large aspect ratio cylinder in a shallow open channel

The complex wake created by an emergent slender circular cylinder in a shallow open channel flow is studied at a cylinder Reynolds number (ReD) of 3300 and at a subcritical Froude number of 0.58 in water. Methodical laser Doppler velocimetry measurements were taken in a very fine grid in three horizontal planes at near bed, mid-depth, and near free surface both upstream and downstream of the cylinder. Demarcation of the entire wake region starting from the first point of the onset of disturbed flow upstream to undisturbed flow downstream entirely based on experiments successfully added a novel contribution to the research on wake flow over a single cylinder. The proximity of the bed and free surface has a significant effect on the structure of the wake compared to the mid-depth. The size, shape, and development of the recirculation region behind the cylinder vary in the vertical direction from the bed to free surface. The longest wake closure point was found in the near bed region and the shortest was found near the free surface. The new model developed pertinent to longitudinal velocity deficit can be used as a velocity deficit scale for the entire far wake region for shallow wakes at mid-depth and near free surface. Urms/Us profiles along the transverse direction initially show a double peak behavior for all three levels, and well away from the cylinder downstream, the double peak becomes broader and less distinct, which is attributed to the effect of the separating shear layers. It is also noted that the wake characteristics of slender cylinders are significantly different from those of wakes generated by cylinders with small aspect ratios.

Improvement of Performance of Undershot Cross-Flow Water Turbines Based on Shock Loss Reduction

Undershot cross-flow turbines are applicable to shallow open channel flows and are characterized by a simple structure free of guide vanes or a casing. Since these water turbines operate in a free surface flow field, the optimum inlet blade angle and outlet blade angle are considered to vary with the flow rate in the open channel; however, guidelines for setting these angles are yet to be established. In this study, a method to improve the performance of an undershot cross-flow water turbine based on shock loss reduction was proposed. First, by varying the blade angle of the straight blades of the turbine, the inlet blade angle and outlet blade angle which reduced shock loss in the first-stage inlet region and second-stage inlet region were investigated through free surface flow analysis. From the results, it was shown that by taking the inlet and outlet blade angles which minimize the first-stage and second-stage shock losses for straight blades and applying them to curved blades, shock loss is reduced, thereby improving turbine efficiency and turbine output.

ESTUDO COMPARATIVO ENTRE AS EQUAÇÕES EMPÍRICAS E O MÉTODO DA VELOCIDADE NA ESTIMATIVA DO TEMPO DE CONCENTRAÇÃO

RESUMO: Tão importante para projetos hidrológicos, a estimativa do tempo de concentração (tc) é realizada pela utilização de equações empíricas obtidas em estudos internacionais; desconsiderando-se, muitas vezes, os limites de aplicabilidade a que foram propostas. Não obstante, observa-se a não utilização do método da velocidade do Natural Resources Conservation Service (NRCS), o mais recomendado para a estimativa do referido tempo em bacias urbanas. Deste modo, o presente artigo objetivou analisar qual a estimativa de “tc”, utilizando equações empíricas versus a adoção do método da velocidade, resulta no melhor ajuste de projeto. Para tal, compararam-se os valores obtidos entre os métodos por meio da construção de 168 cenários hipotéticos oriundos da combinação entre parâmetros como a declividade, a extensão do escoamento natural; do escoamento em canais rasos revestidos e do escoamento em canais artificiais. Calculou-se, então, para todos cenários, a vazão de projeto pelo Método Racional. Pela discrepância dos valores obtidos para os tempos de concentração e vazões entre as equações e o método da velocidade, ressalta-se a importância do levantamento em campo da bacia em estudo, bem como do conhecimento das faixas de aplicação de equações empíricas. Verificou-se que a influência das extensões de escoamentos em trechos naturais ou definidos, afetará sobremaneira nas vazões de projeto calculadas; demonstrando a importância da definição do método mais apropriado pelo projetista.

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.

Lateral bed-roughness variation in shallow open-channel flow with very low submergence

Quantifying turbulent fluxes and secondary structures in shallow channel flows is important for predicting momentum and mass transfer in rivers as well as channel capacity and associated water levels. Here, we focus on the flow over a lateral bed-roughness variation with very low relative submergence of the roughness elements, h/k = {3, 2, 1.5}, where h is the flow depth and k is the roughness height. Measurements were performed in a 1.1 m wide and 26 m long glass flume whose bed was fitted with cubes arranged in two regular side-by-side patterns with frontal densities lambda _f = 0.2 and 0.4 to create a rough-to-rougher variation. Measurements were performed using stereoscopic PIV in two orthogonal planes, in a vertical transverse plane spanning the two roughness types, and in a longitudinal one at the interface between the roughness types. The results show that the bulk velocity difference between the two sides of the channel increases with decreasing h/k. Also, contrary to what is observed at high relative submergence with smooth-to-rough transitions, higher bulk velocities occur on the side with higher roughness. This difference is increasing as the flow becomes shallower and is shown to be due to increasing effective depths ratios, leading to increasingly lower friction factor ratios with lower friction factors on the high-velocity but rougher side. Although increasing streamwise momentum transfer at the interface is needed as h/k decreases, the turbulent and secondary circulation transfer of momentum is increasingly inhibited. A globally-driven secondary-circulation at h/k=3 ceases for lower h/k and roughness-scale circulation becomes dominant. Also, even the increased global shear does not lead to large-scale Kelvin Helmholtz instabilities structures. However, the relative importance of the roughness difference on the flow is augmented as the flow becomes shallower and momentum transfer due to lateral dispersive stresses increases.

Cost effective measuring technique to simultaneously quantify 2D velocity fields and depth-averaged solute concentrations in shallow water flows

This paper presents a cost-effective methodology to simultaneously measure mixing processes and surface velocity fields in shallow flows using multiple, synchronized low cost cameras and lighting. Velocity fields and depth averaged concentration of a soluble fluorescent tracer are obtained over a 4.8 × 1.22 m2 measurement area using the new techniques and the results verified against traditional point probe measurements in a laboratory flume. An example of simultaneous velocity/concentration measurement is presented for an instantaneous release of tracer into flow around an obstruction. The method will help to improve the understanding of mixing processes in shallow open channel flows. It is anticipated that the technique will be useful in physical modelling studies where the mixing and hydraulic length scales under investigation are in the order of 1–10 m, for example in compound channels and partially vegetated streams.

Characteristics of flow past a slender, emergent cylinder in shallow open channels

The complex wake created by an emergent cylinder with a large aspect ratio in a shallow open channel flow is studied experimentally using particle image velocimetry. The unique characteristics of the bed-mounted slender cylinder wake are analysed. Velocity fields, turbulence parameters, and wake development in shallow open channel flow are studied at two different Reynolds numbers and subcritical Froude numbers by carrying out measurements in different horizontal and vertical planes. In the mid-depth plane, velocity and turbulence statistics are independent of Reynolds number, while higher turbulence intensities and Reynolds shear stresses were observed in the near-bed plane for the low Reynolds number case. The narrower wake is observed in the near-bed plane due to the effect of the bed. Combined with stronger vertical velocity and turbulence intensities noted near the bed in the vertical midplane, this suggests increased activity of the vortex structures in the low Reynolds number case. Under shallow conditions, stronger disturbances of the free surface are observed for the case of high Reynolds and Froude numbers. The study also revisits the definition of the wake stability parameter and proposes a new definition which incorporates not only the bed friction but also the drag experienced by the cylinder.

Reconsideration of the overlap region in smooth shallow open channel flows

In this paper, data sets for mean velocity distributions in smooth shallow open channel flow are reconsidered to evaluate the characteristics of the overlap region and estimate the friction velocity (u∗). Both new and existing velocity measurements are used in the analysis. The velocity profiles are obtained using laser Doppler velocimetry and particle image velocimetry at typical Reynolds numbers (20 000–60 000) achieved in laboratory flumes. Validation of the estimated u∗ values using different forms of power law is established by comparing these values with the ones available in literature. Also, the Reynolds shear stress distribution based on two-dimensional measurements validate the estimated u∗. The availability of new data sets allows one to verify the usefulness of the log-law and evaluate the log-law constants. Different fitting methods; least squares, derivative, and scattered methods are used to evaluate the value of von Kármán coefficient. It is found that the value of κ obtained from the least squares method varies between 0.35 and 0.51 and depends on the Reynolds number. This refutes the conventional constant value assumption for the von Kármán coefficient (κ = 0.41). By considering the Prandtl’s mixing-length theory, the present values of the von Kármán coefficient are used to evaluate the mixing length distributions. The mixing length distributions in smooth open channel flow are found to depend on Reθ.

Application of continuous wavelet transform to the study of large-scale coherent structures

It is generally recognized that large-scale turbulent coherent structures play an important role in the transport of sediment and contaminants in rivers. They are also believed to be related to the origin and development of a variety of fluvial bed and plan forms. While intensive laboratory and field research has been devoted in recent years to the study of large-scale vertical coherent structures, no such efforts have yet been directed to the study of large-scale horizontal coherent structures. This paper is intended as a contribution to address the existing lack of information on the latter structures. Its objective is to report an application of continuous wavelet transform (CWT) to the detection and establishment of the length and time scales of the largest coherent structures existing in a shallow open channel flow (width to depth ratio equal to 25), focusing primarily on the horizontal structures. The analysis is based on measurements of instantaneous flow velocity previously carried out in a 21 m long, 1 m wide flume. These include 306 single point velocity measurements collected throughout the flow field at a constant distance from the bed surface, the duration of each measurement being 120 s; and 20 min long measurements carried out at selected locations. The velocity was measured with the aid of a 2D Micro Acoustic Doppler Velocity meter. Large-scale horizontal coherent structures could be identified in all of the velocity records, and appeared as quasi-cyclic, sustained features in the flow. The intervals of time where such structures could not be detected were invariably short in comparison to the measurement time. CWT was found to be particularly well suited to determine the average time and length scales of the structures, two quantities of special significance in river morphodynamics. The average time scale of the large-scale horizontal structures for the investigated flow was found to be equal to 22.3 s, which implies a length scale of five times the flow width. Individual horizontal coherent structures with characteristic times approximately twice larger than the value of average time scale could be identified in the flow. However, these were infrequent occurrences in the flow.

Weak Imposition of Essential Boundary Conditions in Isogeometric Analysis of Depth Averaged Advection Dispersion Equation

The “depth averaged advection dispersion” equation is the governing equation in two-dimensional (2D) modelling of contaminant transport in shallow open channel flows. Isogeometric analysis (IGA) is a good method used for accurate geometrical modeling and approximation of the solution space. So, the aim of this study is to conduct the IGA of the depth averaged advection dispersion equation. Due to the non-interpolatory nature of NURBS basis functions the properties of Kronecker Delta are not satisfied, thus imposition of the essential BCs needs special treatment. Therefore, in order to improve the accuracy of the IGA in solution of depth averaged advection dispersion equation, the essential BCs are imposed in three weak forms, including: The Least Square Method (LSM), Lagrange Multiplier Method (LM) and the Penalty Method (PM). For this purpose, the numerical modeling is initially developed and the lateral diffusion problem is solved for a rectangular straight channel and the results of three models are compared with each other. Results indicate that the LSM has the best accuracy while the PM has the poorest. Likewise, despite accurate results, the system of the equation suffers from dimensional enlargement in LM which requires more calculation time. Moreover, in the case of skew advection, adapting the LM produces lower RMSE value and thus more accurate results in contrast to the strong enforced essential BCs in classical FEA and IGA solutions.

Experimental and large eddy simulation study of the flow developed by a sequence of lateral obstacles

In this paper we provide a description of the three-dimensional flow induced by a sequence of lateral obstacles in a straight shallow open-channel flow with flat bathymetry. The obstacles are modelled as rectangular blocks and are located at one channel wall, perpendicular to the main stream direction. Two aspect ratios of the resulting dead zones are analysed. The flow structure is experimentally characterised by particle image velocimetry measurements in a laboratory flume and simulated using three-dimensional Large Eddy Simulations. Good agreement between experimental measurements and numerical results is obtained. The results show that the effect of the obstacles in the main channel is observed up to one obstacle length in the spanwise direction. The spacing between obstacles does not seem to have a large influence in the outer flow. The mean flow within the dead zone is characterised by a large recirculation region and several additional vortex systems. They are discussed in the paper, as well as the mean and root-mean-square wall shear-stresses.

Numerical and experimental turbulence studies on shallow open channel flows

The standard shallow water equations (SWEs) model has been proven to be insufficient to consider the flow turbulence due to its simplified Reynolds-averaged form. In this study, the k-ε model was used to improve the ability of the SWEs model to capture the flow turbulence. In terms of the numerical source terms modelling, the combined SWEs k-ε model was improved by a recently proposed surface gradient upwind method (SGUM) to facilitate the extra turbulent kinetic energy (TKE) source terms in the simulation. The laboratory experiments on both the smooth and rough bed flows were also conducted under the uniform and non-uniform flow conditions for the validation of the proposed numerical model. The numerical simulations were compared with the measured data in the flow velocity, TKE and power spectrum. In the power spectrum comparisons, a well-studied Kolmogorov's rule was also employed to complement both the numerical and experimental results and to demonstrate that the energy cascade trend was well-held in the investigated flows.

Near Wake Structure of Wall-Mounted Finite Cylinders in Shallow Open Channel Flow

Near Wake Structure of Wall-Mounted Finite Cylinders in Shallow Open Channel Flow

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.

Instability of shallow open channel flow with lateral velocity gradients

The turbulent flow in a wide rectangular open channel partially covered with vegetation is studied using linear stability analysis. In the base state normal flow condition, the water depth is constant and the transverse velocity vanishes, while there is a lateral gradient in the streamwise velocity with an inflexion point at the boundary between the vegetated zone and the main channel. The Reynolds stress is expressed by introducing the eddy viscosity, which is obtained from assuming a logarithmic distribution of the velocity near the bed. Perturbation expansions are introduced to the streamwise and transverse velocities, as well as to the water depth. The system of governing equations was solved in order to determine the maximum growth rate of the perturbations as a function of parameters which describe physical characteristics of the channel and the flow.

Coherent structure statistics in the wake of a sharp-edged bluff body placed vertically in a shallow channel

Proper orthogonal decomposition and closed-streamline-based vortex identification algorithm has been applied to extract information on coherent structures downstream of a sharp-edged bluff body, placed vertically in a shallow open channel flow. The friction effect of the bed was found to reduce the size and strength of the coherent structures close to the bed. The free surface weakly decreases the size and strength of the prevalent coherent structures. The population trends of coherent structure statistics with downstream distance indicate the phenomenon of merging and spatial growth of coherent structures with time and space. But the rates of merging and growth were found to be different at different vertical locations over the flow depth. The distribution functions of the location, size and strength in the transverse direction were examined to shed light on the dynamics of these structures.

Reynolds Stress Anisotropy in Open-Channel Flow

This paper reports the results of an experimental study characterizing turbulence and turbulence anisotropy in smooth and rough shallow open-channel flows. The rough bed consists of a train of two-dimensional transverse square ribs with a ratio of the roughness height (k) to the total depth of flow (d) equal to 0.10. Three rib separations (p/k) of 4.5, 9, and 18 were examined. Here, p is the pitch between consecutive roughness elements and was varied to reproduce the classical condition of d- and k-type roughness. For each case, two-component velocity measurements were obtained using a laser Doppler velocimetry system at two locations for p/k=4.5 and 9: on the top of the rib and above the cavity, and an additional location for p/k=18. The measurements allow examination of the local variations of the higher-order turbulent moments, stress ratios as well as turbulence anisotropy. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and turbulence production are found for y1<3k. In this region, the flow is more directly influenced by the shear layers from the preceding ribs. The higher-order moments appear to be similar for all rough surfaces beyond y1≈7k. In the outer layer (y1>3k), all higher-order turbulent moments for the k-type roughness show a substantial increase due to the complex interactions between the roughness and the remnants overlying shear layers shed from succeeding ribs. Analysis of the components of the Reynolds stress anisotropy tensor shows that at p/k=18, the flow at y1<5k tends to be more isotropic which implies that for this particular case, the effect of the roughness density could also be important. On the smooth bed, at the shallower depths, the correlation coefficient near the free surface increases and turbulence tends to become less anisotropic.

URANS Computations of Shallow Grid Turbulence

This paper describes the unsteady Reynolds-averaged Navier–Stokes (URANS) computations of a quasi-two-dimensional (2D) grid turbulence in shallow open-channel flows, generated downstream of multiple piers aligned at regular intervals over the channel width. In shallow open-channel flows, the vertical confinement of the flow generally suppresses the three dimensionality and attains two-dimensional features with up-cascading of turbulent kinetic energy from small-scale toward large-scale structures. In this study, 2D depth averaged and 3D Reynolds-averaged equations with linear and nonlinear URANS turbulence models are applied to a shallow open-channel flow downstream of multiple piers and numerical results are discussed through a comparison with the experimental results performed by Uijttewaal and Jirka in 2003. We employed 0-equation models and k-e models for the 2D and 3D computations, respectively. In 2D computations, vortices downstream of the grid occurred synchronously in the computation with both th...