Turbulent Open Channel Flow Research Articles

Generalized non-equilibrium suspended sediment transport model with hindered settling effect for open channel flows

The present paper formulates a generalized model for non-equilibrium suspended sediment transport through an open channel turbulent flow that contains all the existing models in literature as special cases. The two-dimensional (2D) unsteady model for suspended concentration distribution contains the effect of hindered settling and the bottom boundary condition considers deposition velocity together with equilibrium bottom concentration. OpenFOAM, an open-source Finite Volume (FV) method based framework, has been used for the numerical approximation of the model. The proposed model addresses the non-linearity in the governing equation as well as the non-linearity in boundary conditions. Picard iteration approach has been utilized to ensure the convergence of the numerical solution. With different physical parameters and conditions, concentration profiles of suspended sediment particles have been analysed theoretically and graphically. It greatly extends the domain of the numerical solutions for determining sediment distribution in suspension through an open channel turbulent flow in a non-equilibrium state.

Large Eddy Simulation of a sediment particle under entrainment conditions

A Large Eddy Simulation of a fully developed turbulent open-channel flow with a Reynolds number of was performed to study dynamics of coherent structures in the vicinity of a stationary sediment particle. The sediment particle was positioned at the bottom on a smooth channel bed. The impulse concept was employed by computing three-dimensional hydrodynamic forces acting on the sediment particle in order to predict the onset of particle motion. Results of quadrant analyses at high impulse events yielded mostly outward and sweep events. Auto- and cross-correlation of the hydrodynamic forces and the flow field were studied and discussed. An identification of coherent structures at high impulse events showed that large-scale, long-lived hairpin-like vortices whose bed-normal lengths are larger than viscous units were resulting in an increase of lift and drag forces simultaneously, facilitating initiation of particle motion.

Secondary Currents at Very Low and High Aspect Ratios of Open Channels

The present numerical study is an attempt to better understand the effect of the aspect ratio (AR) on the velocity field characteristics of the fully-developed turbulent flow in a straight open channel by contrasting a very low and very high aspect ratio cases (AR = 1 and 12). The AR is defined as the ratio of the width of the channel in a plane normal to the flow direction, to the flow depth. The bulk velocity and water depth considered in this study are 0.75 m/s and 30 mm, respectively, which yield a Reynolds number of ReH = 22,500. The transient three-dimensional Navier-Stokes equations were numerically solved using a finite-volume approach with improved-delayed detached-eddy simulation (IDDES) turbulence model. The results revealed that the normalized components of the normal stresses by the turbulent kinetic energy k are constant over most of the velocity field, although k varies in magnitude throughout the velocity field in both AR cases. In addition, the results also revealed a strong anisotropic flow which justifies the formation of secondary currents as a means for transporting the kinetic energy. The results also reveal that both vertical and transverse components of the normal stresses are correlated to the side-recirculation zone (SRZ) and bottom-recirculation zone (BRZ), respectively, which highlights the role of the mean recirculation zones (BRZ & SRZ) in the re-distribution of the turbulent kinetic energy k in the velocity field.

Application of the fractional entropy for one-dimensional velocity distribution with dip-phenomenon in open-channel turbulent flows

Application of the fractional entropy for one-dimensional velocity distribution with dip-phenomenon in open-channel turbulent flows

Turbulence structure in a very sharp thermally stratified open-channel meander

Direct numerical simulation (DNS) results for turbulent open-channel flow through an idealized sine-generated meander with and without an internal heat source that models radiative heating from above are used to analyze the effect of a very sharp meander configuration and thermal stratification on the turbulence structure in the channel with friction Reynolds number Reτ=200. Spatial distributions of temperature, mean velocities, vorticity, mean-flow kinetic energy, and turbulent kinetic energy (TKE) are presented. In both cases, the cross-sectional motion is characterized by three circulation cells: a center-region cell and two weaker outer bank and inner bank cells. However, there is also a small cell observed near the corner of the channel bed inner bank at the channel outlet and the channel bed outer bank at the channel inlet. The tri-cellular cross-stream motions control the distributions of temperature and kinetic energy. In the stratified case, two separated shear layers (SSLs) are found: the first one is formed before the bend apex, and the second one is observed in the wake after the bend apex. In the neutral case, only the first SSL is observed. Turbulent amplification can be seen in both cases; however, in the stratified case, the second SSL stretches out to the channel outlet and is introduced back to the channel inlet by an anti-symmetric periodic boundary condition and then follows the outer bank line. The two SSLs converge in the region before the bend apex and amplify the turbulence more strongly there than in the neutral case. The turbulence kinetic energy budget terms for the stratified case are analyzed to determine the characteristics of production, dissipation and transport of TKE in thermally stratified meandering flow.

Analytical models of mean secondary velocities and stream functions under different bed-roughness configurations in wide open-channel turbulent flows

Analytical models of mean secondary velocities and stream functions under different bed-roughness configurations in wide open-channel turbulent flows

Analysis and validation of mathematical models of secondary velocities along vertical and transverse directions in wide open-channel turbulent flows

Cellular secondary flows are inevitably present in turbulent flows through ducts, natural or artificial channels, and compound channels. Secondary currents significantly modify the characteristics of turbulent quantities, the pattern of primary flow velocity by causing dip-phenomenon. To understand the detailed mechanism and hidden cause, modelling of secondary flow velocities is crucial. In this study, proper mathematical models of secondary flow velocities along vertical and transverse directions are proposed for steady and uniform turbulent flow through wide open channels with equal smooth and rough bed strips. Starting from the continuity and the Reynolds averaged Navier–Stokes equations, governing equation for secondary velocity is derived first and then using appropriate boundary conditions (no-slip boundary conditions at channel bottom and free surface, and maximum vertical velocity in magnitude at the interface of two cellular secondary cells and at mid-depth of the channel. All these conditions are consistent with several experimental observations). A new model of the streamwise Reynolds shear stress is proposed for the entire cross-sectional plane and using it, the analytical solutions are obtained. Proposed models include the effects of viscosity of the fluid and the eddy viscosity model of turbulence. All suggested models are validated with existing experimental data in rectangular open-channel flows, compound open channel flows, and duct flows, and satisfactory results are obtained. Furthermore, models are also compared with existing empirical models from literature to show the effectiveness and superiority of proposed models. Apart from these, the obtained results from this study are used to investigate the effects of vertical and transverse secondary flow velocities on the settling velocity vector in a cross-sectional plane. Effective alternative models for the settling velocity vector are suggested. The model of settling velocity vector is also compared with the existing model. Finally, all results are justified from physical viewpoints.

Parameterization of mixing in stratified open channel flow

The dynamics and parameterization of mixing in temporally evolving turbulent open-channel flow is investigated through direct numerical simulations as the flow transitions from an initially neutral state to stable stratification. We observe three distinctly different mixing regimes separated by transitional values of turbulent Froude number $Fr$ : a weakly stratified regime for $Fr >1$ ; an intermediate regime for $0.3< Fr<1$ ; and a saturated regime for $Fr<0.3$ . The mixing coefficient $\varGamma =B/\epsilon _K$ , (where $B$ is the buoyancy flux and $\epsilon _K$ is the dissipation rate of kinetic energy), is well predicted by the parameterization schemes of Maffioli et al. (J. Fluid Mech., vol. 794, 2016) and Garanaik & Venayagamoorthy (J. Fluid Mech., vol. 867, 2019, pp. 323–333) across all three regimes through instantaneous measurements of $Fr$ and the ratio $L_E/L_O$ , where $L_E$ and $L_O$ are the Ellison and Ozmidov length scales, respectively. The flux Richardson number $R_f = B/(B+\epsilon _K)$ shows linear dependence on the gradient Richardson number $Ri_g$ up to a transitional value of $Ri_g =0.25$ , past which it saturates again to a constant value independent of $Fr$ or $Ri_g$ . By examining the flow as a balance of inertial, shear and buoyancy forces, we derive physically based scaling relationships to demonstrate that $Ri_g \sim Fr^{-2}$ and $Ri_g \sim Fr^{-1}$ in the weakly and moderately stratified regimes and that $Ri_g$ becomes independent of $Fr$ in the saturated regime. Our results suggest that the $L_E/L_O \sim Fr^{-1}$ scaling of Garanaik & Venayagamoorthy (J. Fluid Mech., vol. 867, 2019, pp. 323–333) in the intermediate regime manifests due to the influence of mean shear. The differences in the relationships between $Fr$ and $L_E/L_O$ for non-sheared flows within this regime are discussed.

Study on flow characteristics and diversity index of diamond-type boulder cluster with different spacing ratios.

The placement of boulder or boulder cluster in rivers can increase or repair the complexity of river structure and the diversity of hydraulic conditions, which is very important for the habitat of many aquatic organisms. In this study, the diamond-type boulder cluster was modeled as four hemispheres exposed to a fully developed turbulent open channel flow. Numerical simulation was conducted to investigate the time-averaged flow characteristics, three-dimensional coherent structures, turbulence characteristics, and flow diversity index at different spacing ratios L/D (the ratio of the distance L to the diameter D, 1.0 ≤ L/D ≤ 3.5, where L is the center-to-center distance between two adjacent hemispheres and D is the diameter of the hemisphere). The results show that with the increase of the spacing ratio, the shear layer on the side of the gap flow gradually strengthens, and the single Karman vortex street in the wake region of the hemisphere array is suppressed. The time-averaged peak velocity in the gap flow gradually decreases with the increase of the spacing ratio, and the single of the recirculation zone behind the hemisphere array transforms into the recirculation zone behind each hemisphere, and the length of the each recirculation zone increases to the same. The turbulence intensity of the array first increases with the increase of the spacing ratio and then gradually decreases to a constant, reaching the peak intensity at L/D = 2. Based on the Shannon entropy concept, the flow diversity index in the zone of influence (ZOI) is calculated by considering the velocity and turbulence kinetic energy. The flow diversity index is the largest in the ZOI at the spacing ratio of 1.5.

Direct numerical simulation of turbulent mass transfer at the surface of an open channel flow

We present direct numerical simulation results of turbulent open channel flow at bulk Reynolds numbers up to 12 000, coupled with (passive) scalar transport at Schmidt numbers up to 200. Care is taken to capture the very large-scale motions which appear already for relatively modest Reynolds numbers. The transfer velocity at the flat, free surface is found to scale with the Schmidt number to the power ‘$-1/2$’, in accordance with previous studies and theoretical predictions for uncontaminated surfaces. The scaling of the transfer velocity with Reynolds number is found to vary, depending on the Reynolds number definition used. To compare the present results with those obtained in other systems, we define a turbulent Reynolds number at the edge of the surface-influenced layer. This allows us to probe the two-regime model of Theofanouset al.(Intl J. Heat Mass Transfer, vol. 19, 1976, pp. 613–624), which is found to correctly predict that small-scale vortices significantly affect the mass transfer for turbulent Reynolds numbers larger than 500. It is further established that the root mean square of the surface divergence is, on average, proportional to the mean transfer velocity. However, the spatial correlation between instantaneous surface divergence and transfer velocity tends to decrease with increasing Schmidt number and increase with increasing Reynolds number. The latter is shown to be caused by an enhancement of the correlation in high-speed regions, which in turn is linked to the spatial distribution of surface-parallel vortices.

Entrainment and adaptation processes in the evolution of collisional bedload layers

We performed laboratory experiments which describe the evolution, from triggering until full formation, of a bedload layer. The phenomenon is driven by a turbulent open-channel flow at about constant discharge since the very initiation of the process. The flow stays uniform and the slope constant during the transient phase, during which we measured the instantaneous velocity and concentration profiles of the solid phase within the bedload layer. The timing of the process is governed by inertia and resistance forces. The bedload layer progressively thickens, fed by sediments entrained from the bed, which is progressively eroded, until the final steady uniform condition (i.e., equilibrium) is reached. We then applied a recent numerical model, able to cope with collisional suspensions using extended kinetic theories, to replicate the experimental results. The model results are used to further analyze and discuss the physical processes within the flow.

Time fractional advection-dispersion model to study transportation of particles with time-memory for unsteady nonequilibrium suspension in open-channel turbulent flows

In this study, the effects of time-memory on the mixing and nonequilibrium transportation of particles in an unsteady turbulent flow are investigated. The memory effect of particles is captured through a time-fractional advection-dispersion equation rather than a traditional advection-dispersion equation. The time-fractional derivative is considered in Caputo sense which includes a power-law memory kernel that captures the power-law jumps of particles. The time-fractional model is solved using the Chebyshev collocation method. To make the solution procedure more robust three different kinds of Chebyshev polynomials are considered. The time-fractional derivative is approximated using the finite difference method at small time intervals and numerical solutions are obtained in terms of Chebyshev polynomials. The model solutions are compared with existing experimental data of traditional conditions and satisfactory results are obtained. Apart from this, the effects of time-memory are analyzed for bottom concentration and transient concentration distribution of particles. The results show that for uniform initial conditions, bottom concentration increases with time as the order of fractional derivative decreases. In the case of transient concentration, the value of concentration initially decreases when T < 1 and thereafter increases throughout the flow depth. The effects of time-memory are also analyzed under steady flow conditions. Results show that under steady conditions, transient concentration is more sensitive for linear, parabolic, and parabolic-constant models of sediment diffusivity rather than the constant model.

Solute dispersion in an open channel turbulent flow: Solution by a generalized model

In this work, the classic problem in environmental hydraulics of solute dispersion in an open channel turbulent flow is analytically investigated by Gill’s generalized dispersion model to account for all the basic characteristics as dispersivity, skewness and kurtosis of the mean concentration evolution. A complete solution is presented for the whole process and three typical time-scales are determined: after a convection-dominated initial stage, a transient stage with essential transverse diffusion effect begins at a dimensionless time-scale of t∼0.1 and gives way to an asymptotic stage of normal distribution of mean concentration from t∼1, slowly approaching to a final stage with relative uniformity in transverse concentration distribution at t∼10. Two-dimensional concentration distribution shows that there is a high concentration zone near the free water surface at a small time due to the small velocity gradient, indicating that it is not enough to characterize the dispersion process by the mean concentration, especially for the transient stage. The obtained analytical solutions of concentration distribution consist well with numerical simulation results by the random displacement method (RDM).

Entropy-Based Shear Stress Distribution in Open Channel for All Types of Flow Using Experimental Data.

Korean river design standards set general design standards for rivers and river-related projects in Korea, which systematize the technologies and methods involved in river-related projects. This includes measurement methods for parts necessary for river design, but does not include information on shear stress. Shear stress is one of the factors necessary for river design and operation. Shear stress is one of the most important hydraulic factors used in the fields of water, especially for artificial channel design. Shear stress is calculated from the frictional force caused by viscosity and fluctuating fluid velocity. Current methods are based on past calculations, but factors such as boundary shear stress or energy gradient are difficult to actually measure or estimate. The point velocity throughout the entire cross-section is needed to calculate the velocity gradient. In other words, the current Korean river design standards use tractive force and critical tractive force instead of shear stress because it is more difficult to calculate the shear stress in the current method. However, it is difficult to calculate the exact value due to the limitations of the formula to obtain the river factor called the tractive force. In addition, tractive force has limitations that use an empirically identified base value for use in practice. This paper focuses on the modeling of shear-stress distribution in open channel turbulent flow using entropy theory. In addition, this study suggests a shear stress distribution formula, which can easily be used in practice after calculating the river-specific factor T. The tractive force and critical tractive force in the Korean river design standards should be modified by the shear stress obtained by the proposed shear stress distribution method. The present study therefore focuses on the modeling of shear stress distribution in an open channel turbulent flow using entropy theory. The shear stress distribution model is tested using a wide range of forty-two experimental runs collected from the literature. Then, an error analysis is performed to further evaluate the accuracy of the proposed model. The results reveal a correlation coefficient of approximately 0.95–0.99, indicating that the proposed method can estimate shear-stress distribution accurately. Based on this, the results of the distribution of shear stress after calculating the river-specific factors show a correlation coefficient of about 0.86 to 0.98, which suggests that the equation can be applied in practice.

Differences of turbulence modulation by heavy particles on solid wall and erodible bed surface

In this paper, wall-resolved large-eddy simulation of turbulence, Lagrangian point-force model of particle tracking, and two-way coupling approach are used to simulate the particle-laden flow over a rigid wall. The flow is a turbulent open channel flow with the particle-free friction Reynolds number of Reτ=4200. Together with the simulated results over an erodible bed from Zheng et al. [J. Fluid Mech. 918, 1–27 (2021)], the influence of the lower boundary condition of particle motion with the wall-normal gravity on turbulence modulation is thoroughly compared. It is found that high-inertia (St+=244.5) particles studied in this work moving over a rigid wall increase the mean fluid velocity and the scales of turbulence structures away from the wall, suppress turbulence fluctuations and Reynolds stress, and reduce the scales of turbulence structures near the wall as compared with the particle-free flow. Gravitational settling of particles accounts for most of the changes, and the crossing trajectory caused by particles bouncing near the rigid wall is responsible for the reduction of the scales of the near-wall turbulence structures. On the contrary, the splashing process of particles over the erodible bed leads to the decrease in the mean fluid velocity, the anisotropic variation of turbulent kinetic energy, the shrink of the outer turbulence structure, and the enlargement of the near-wall streaks. The results reveal the significance of the near-wall particle motion (rebound or splashing) on turbulence modulation.

Convolutional-network models to predict wall-bounded turbulence from wall quantities

Two models based on convolutional neural networks are trained to predict the two-dimensional instantaneous velocity-fluctuation fields at different wall-normal locations in a turbulent open-channel flow, using the wall-shear-stress components and the wall pressure as inputs. The first model is a fully convolutional neural network (FCN) which directly predicts the fluctuations, while the second one reconstructs the flow fields using a linear combination of orthonormal basis functions, obtained through proper orthogonal decomposition (POD), and is hence named FCN-POD. Both models are trained using data from direct numerical simulations at friction Reynolds numbers $Re_{\tau } = 180$ and 550. Being able to predict the nonlinear interactions in the flow, both models show better predictions than the extended proper orthogonal decomposition (EPOD), which establishes a linear relation between the input and output fields. The performance of the models is compared based on predictions of the instantaneous fluctuation fields, turbulence statistics and power-spectral densities. FCN exhibits the best predictions closer to the wall, whereas FCN-POD provides better predictions at larger wall-normal distances. We also assessed the feasibility of transfer learning for the FCN model, using the model parameters learned from the $Re_{\tau }=180$ dataset to initialize those of the model that is trained on the $Re_{\tau }=550$ dataset. After training the initialized model at the new $Re_{\tau }$ , our results indicate the possibility of matching the reference-model performance up to $y^{+}=50$ , with $50\,\%$ and $25\,\%$ of the original training data. We expect that these non-intrusive sensing models will play an important role in applications related to closed-loop control of wall-bounded turbulence.

Stability analysis of open-channel flows with secondary currents

This paper presents some results coming from a linear stability analysis of turbulent depth-averaged open-channel flows (OCFs) with secondary currents. The aim was to identify plausible mechanisms underpinning the formation of large-scale turbulence structures, which are commonly referred to as large-scale motions (LSMs) and very-large-scale motions (VLSMs). Results indicate that the investigated flows are subjected to a sinuous instability whose longitudinal wavelength compares very well with that pertaining to LSMs. In contrast, no unstable modes at wavelengths comparable to those associated with VLSMs could be found. This suggests that VLSMs in OCFs are triggered by nonlinear mechanisms to which the present analysis is obviously blind. We demonstrate that the existence of the sinuous instability requires two necessary conditions: (i) the circulation of the secondary currents $\omega$ must be greater than a critical value $\omega _c$ ; (ii) the presence of a dynamically responding free surface (i.e. when the free surface is modelled as a frictionless flat surface, no instabilities are detected). The present paper draws some ideas from the work by Cossu, Hwang and co-workers on other wall flows (i.e. turbulent boundary layers, pipe, channel and Couette flows) and somewhat supports their idea that LSMs and VLSMs might be governed by an outer-layer cycle also in OCFs. However, the presence of steady secondary flows makes the procedure adopted herein much simpler than that used by these authors.

Numerical study on the drag characteristics of rigid submerged vegetation patches

Aquatic plants play a crucial role in the hydrodynamic and material transport processes within the aquatic environments due to the additional flow resistance induced by vegetation stems. In this study, high-resolution numerical experiments were performed to investigate the drag characteristics of circular vegetation patches fully immersed in a turbulent open channel flow. The submerged vegetation patch was modeled as a rigid cylinder array with a diameter D composed of N cylinder elements with a diameter d. The effects of vegetation density Φ (0.023 ≤ Φ ≤ 1) and relative diameter d/D (d/D = 0.051 and 0.072) were tested. The simulation results show that Φ and d/D affect the flow resistance exerted by the vegetation patch by modifying the bleeding flow intensity. With the increase in Φ, the drag forces acting on the individual cylinder elements decrease, whereas the total drag forces of the patch increase. The oscillation strength of the drag force of individual cylinders depends on Φ and the fixed positions within the patch. The presence of the free end of submerged cylinder array leads to enhanced wake entrainment with the increase in Φ. The drag coefficient of the submerged patch is smaller than that of the emergent patch when the dimensionless frontal area aD &amp;gt; 3. However, the two patches exhibit comparable drag coefficients for smaller aD values.

A spanwise oscillating plate in a crossflow: Implication for mass transfer and locomotion

AbstractMany aquatic processes (i.e., organism locomotion, macrophyte response to unsteady flow and mass/heat transfer) involve oscillatory or undulatory movements perpendicular to the direction of flow and perpendicular to the plane of oscillation (i.e., spanwise). The reduction of boundary layer (BL) thickness () and increased turbulence have been identified as the mechanisms for faster heat and mass transfer on these moving surfaces. We examined the hydrodynamics of a submerged spanwise‐oscillating plate in a crossflow within turbulent open channel flow at different oscillation frequencies (f) and channel velocity (U). The BL over the plate was characterized using moving particle image velocimetry to understand the effects of f and U on boundary stress, vorticity, and transfer processes. Changes in the velocity gradient at the plate surface depend on the interactions between spanwise vorticities of opposite directions that reversed downstream along the plate. The vorticity structure reduced shear stress at the surface of the plate resulting in &gt; 65% drag reduction near the upstream edge. Whereas was reduced in comparison to a stationary plate, vorticity increased the diffusive sublayer thickness ) over the oscillating plate (≲1.75 thicker than stationary), which would reduce rather than increase mass transfer based on the film model. Conversely, oscillations would enhance the mass transfer by a factor of ≤ 7 due to periodic renewal of water at the DSL. Similar arguments indicate that renewal would lead to increased convective heat transfer along the plate. Results of this work will increase our understanding of the physical and biological processes that occur in environmental boundary layers.

From coarse wall measurements to turbulent velocity fields through deep learning

This work evaluates the applicability of super-resolution generative adversarial networks (SRGANs) as a methodology for the reconstruction of turbulent-flow quantities from coarse wall measurements. The method is applied both for the resolution enhancement of wall fields and the estimation of wall-parallel velocity fields from coarse wall measurements of shear stress and pressure. The analysis has been carried out with a database of a turbulent open-channel flow with a friction Reynolds number Reτ=180 generated through direct numerical simulation. Coarse wall measurements have been generated with three different downsampling factors fd=[4, 8, 16] from the high-resolution fields, and wall-parallel velocity fields have been reconstructed at four inner-scaled wall-normal distances y+=[15, 30, 50, 100]. We first show that SRGAN can be used to enhance the resolution of coarse wall measurements. If compared with the direct reconstruction from the sole coarse wall measurements, SRGAN provides better instantaneous reconstructions, in terms of both mean-squared error and spectral-fractional error. Even though lower resolutions in the input wall data make it more challenging to achieve highly accurate predictions, the proposed SRGAN-based network yields very good reconstruction results. Furthermore, it is shown that even for the most challenging cases, the SRGAN is capable of capturing the large-scale structures that populate the flow. The proposed novel methodology has a great potential for closed-loop control applications relying on non-intrusive sensing.