Turbulent Open Channel Flow Research Articles

Predicting the wall-shear stress and wall pressure through convolutional neural networks

The objective of this study is to assess the capability of convolution-based neural networks to predict the wall quantities in a turbulent open channel flow, starting from measurements within the flow. Gradually approaching the wall, the first tests are performed by training a fully-convolutional network (FCN) to predict the two-dimensional velocity-fluctuation fields at the inner-scaled wall-normal location ytarget+, using the sampled velocity fluctuations in wall-parallel planes located farther from the wall, at yinput+. The predictions from the FCN are compared against the predictions from a proposed R-Net architecture as a part of the network investigation study. Since the R-Net model is found to perform better than the FCN model, the former architecture is optimized to predict the two-dimensional streamwise and spanwise wall-shear-stress components and the wall pressure from the sampled velocity-fluctuation fields farther from the wall. The data for training and testing is obtained from direct numerical simulation (DNS) of open channel flow at friction Reynolds numbers Reτ=180 and 550. The turbulent velocity-fluctuation fields are sampled at various inner-scaled wall-normal locations, i.e.y+={15,30,50,100,150}, along with the wall-shear stress and the wall pressure. At Reτ=550, both FCN and R-Net can take advantage of the self-similarity in the logarithmic region of the flow and predict the velocity-fluctuation fields at y+=50 using the velocity-fluctuation fields at y+=100 as input with about 10% error in prediction of streamwise-fluctuations intensity. Further, the network model trained in this work is also able to predict the wall-shear-stress and wall-pressure fields using the velocity-fluctuation fields at y+=50 with around 10% error in the intensity of the corresponding fluctuations at both Reτ=180 and 550. These results are an encouraging starting point to develop neural-network-based approaches for modelling turbulence near the wall in numerical simulations, especially large-eddy simulations (LESs).

Secondary motions and wall-attached structures in a turbulent flow over a random rough surface

Large-eddy simulations (LESs) are performed to explore the effects of roughness on the secondary motions (SMs) and wall-attached structures in a turbulent open-channel flow over a random rough surface at a friction Reynolds number of Reτ≈1000. Turbulent flow over two groups of rough walls – a homogeneous random arrangement and a clustered arrangement – is considered, and the results are compared with the turbulence over a smooth wall. The results show that the two roughness arrangements exhibit minor differences in the variation of mean streamwise velocity. The rough surfaces of a clustered arrangement can generate large-scale SMs, resulting in spanwise-alternating high-momentum pathways (HMPs) and low-momentum pathways (LMPs) in the time-averaged velocity. Because of SMs, the streamwise turbulence intensity is enhanced in the outer region and a larger-scale spectral peak occurs in the turbulence energy spectra. On the other hand, the outer-layer similarity is still satisfied for the homogeneous random arrangement. The wall-attached structures of streamwise velocity fluctuations in the presence of roughness are extracted through a three-dimensional clustering identification approach. The wall-attached structures retain their geometric self-similarity for both rough surfaces, whereas the length and width of these structures decreases and increases, respectively. The population density scales inversely with the height, reflecting the hierarchical nature of the structures. In addition, when the streamwise velocity fluctuations within the wall-attached structures are conditionally averaged, the profile exhibits logarithmic behavior in the logarithmic region for the homogeneous random arrangement; in the case of the clustered arrangement, the reconstructed profile is affected by the SMs. A new identification approach is applied to decompose the secondary flow structures into wall-detached structures, and the logarithmic behavior of the streamwise turbulence intensity is reconstructed on the basis of the new wall-attached structures. The present results provide evidence of the presence of the wall-attached structures in instantaneous flow fields of rough-wall turbulence, for both homogeneous and heterogeneous roughness arrangements.

Fractional entropy-based modeling of suspended concentration distribution of type I and type II and sediment discharge in pipe and open-channel turbulent flows

Fractional entropy-based modeling of suspended concentration distribution of type I and type II and sediment discharge in pipe and open-channel turbulent flows

PIV Measurements of Open-Channel Turbulent Flow under Unconstrained Conditions

Many open-channel turbulent flow studies have been focused on highly constrained conditions. Thus, it is rather conventional to note such flows as being fully developed, fully turbulent, and unaffected by sidewalls and free surface disturbances. However, many real-life flow phenomena in natural water bodies and artificially installed drain channels are not as ideal. This work is aimed at studying some of these unconstrained conditions. This is achieved by using particle image velocimetry measurements of a developing turbulent open-channel flow over a smooth wall. The tested flow effects are low values of the Reynolds number based on the momentum thickness Reθ (ranging from 165 to 930), low aspect ratio AR (ranging from 1.1 to 1.5), and Froude number Fr (ranging from 0.1 to 0.8). The results show that the mean flow has an inner region with a logarithmic layer with a von Kármán constant of 0.40–0.41, and a log law constant ranging from 5.0 to 6.0. The friction velocity and coefficient of skin friction are predictable using the formulations of Fr and Reθ presented in this work. The outer region is also characterized by a dip location, which is predictable using an equation associated with Reθ. The higher-order turbulence statistics, on the other hand, show distinguishing traits, such as correlation coefficients ranging from −0.1 to 0.5. Overall, this work demonstrates that for the unconstrained conditions studied, friction evaluations associated with Reynolds shear stress and some notable turbulence modelling functions used in conventional open-channel flows are inapplicable.

Reconstruction of three-dimensional turbulent flow structures using surface measurements for free-surface flows based on a convolutional neural network

A model based on a convolutional neural network (CNN) is designed to reconstruct the three-dimensional turbulent flows beneath a free surface using surface measurements, including the surface elevation and surface velocity. Trained on datasets obtained from the direct numerical simulation of turbulent open-channel flows with a deformable free surface, the proposed model can accurately reconstruct the near-surface flow field and capture the characteristic large-scale flow structures away from the surface. The reconstruction performance of the model, measured by metrics such as the normalised mean squared reconstruction errors and scale-specific errors, is considerably better than that of the traditional linear stochastic estimation (LSE) method. We further analyse the saliency maps of the CNN model and the kernels of the LSE model and obtain insights into how the two models utilise surface features to reconstruct subsurface flows. The importance of different surface variables is analysed based on the saliency map of the CNN, which reveals knowledge about the surface–subsurface relations. The CNN is also shown to have a good generalisation capability with respect to the Froude number if a model trained for a flow with a high Froude number is applied to predict flows with lower Froude numbers. The results presented in this work indicate that the CNN is effective regarding the detection of subsurface flow structures and by interpreting the surface–subsurface relations underlying the reconstruction model, the CNN can be a promising tool for assisting with the physical understanding of free-surface turbulence.

Direct numerical simulation of the distribution of floating microplastic particles in an open channel flow

AbstractMicroplastic fragments in the aquatic environment constitute a major threat for the health and fitness of organisms. However, our quantitative understanding in the microplastic load in typical natural river systems is severely limited due to the large uncertainties associated with the sources and the pathways of the microplastic contamination. To address this knowledge gap, we performed direct numerical simulations of the dynamics and distribution of microplastic particles in turbulent open channel flow at moderate Reynolds numbers. The particle dynamics is characterised by four nondimensional parameters, namely: Reynolds number of the open channel flow (), nondimensional particle diameter () and Galileo () and Stokes () numbers of the particles of which the latter two include the particle‐fluid density ratio (). To limit our scope to the most relevant configuration, we focused on the distribution of weakly buoyant microplastic particles at , whereas the remaining parameters were adjusted to cover the orders of magnitude that can be found in a typical laboratory facility, as well as a natural river. Our simulation results show that the steady‐state microplastic distribution in the turbulent flow is influenced by the Stokes and the Galileo numbers significantly, which ranges from the complete accumulation on the free surface to the homogeneous distribution, and somewhere in between. Moreover, the Galileo number, alongside the flow Reynolds number, were also shown to influence the temporal scaling of the transient behaviour of the gradual accumulation of the microplastics towards the free surface. Both of our findings highlight the complex nature of the particle–turbulence interactions, and motivate further investigations in this approach.

Modified Second Log-Wake Law for Mean Velocity Distributions Along Vertical and Transverse Directions in Smooth Open-Channel Turbulent Flows With Application to Natural Rivers

Modified Second Log-Wake Law for Mean Velocity Distributions Along Vertical and Transverse Directions in Smooth Open-Channel Turbulent Flows With Application to Natural Rivers

Analytical Eddy Viscosity Model for Turbulent Wave Boundary Layers: Application to Suspended Sediment Concentrations over Wave Ripples

Turbulence related to flow oscillations near the seabed, in the wave bottom boundary layer (WBBL), is the phenomenon responsible for the suspension and transport of sediments. The vertical distribution of turbulent eddy viscosity within the WBBL is a key parameter that determines the vertical distribution of suspended sediments. For practical coastal engineering applications, the most used method to parameterize turbulence consists in specifying the shape of the one-dimensional-vertical (1DV) profile of eddy viscosity. Different empirical models have been proposed for the vertical variation of eddy viscosity in the WBBL. In this study, we consider the exponential-type profile, which was validated and calibrated by direct numerical simulation (DNS) and experimental data for turbulent channel and open-channel flows, respectively. This model is generalized to the WBBL, and the period-averaged eddy viscosity is calibrated by a two-equation baseline (BSL) k-ω model for different conditions. This model, together with a β-function (where β is the inverse of the turbulent Schmidt number), is used in modeling suspended sediment concentration (SSC) profiles over wave ripples, where field and laboratory measurements of SSC show two kinds of concentration profiles depending on grain particles size. Our study shows that the convection–diffusion equation, for SSC in WBBLs over sand ripples with an upward convection term, reverts to the classical advection–diffusion equation (ADE) with an “apparent” sediment diffusivity εs*=α εs related to the sediment diffusivity εs by an additional parameter α associated with the convective sediment entrainment process over sand ripples, which is defined by two equations. In the first, α depends on the relative importance of upward convection related to coherent vortex shedding and downward settling of sediments. When the convective transfer is very small, above low-steepness ripples, α≈1. In the second, α depends on the relative importance of coherent vortex shedding and random turbulence. When random turbulence is more important than coherent vortex shedding, α≈1, and “apparent” sediment diffusivity reverts to the classical sediment diffusivity εs*≈ εs. Comparisons with experimental data show that the proposed method allows a good description of both SSC for fine and coarse sand and “apparent” sediment diffusivity εs*.

Turbulent secondary flows in low aspect ratio open-channels over heterogeneous surfaces: Anisotropy in forces

Studies of turbulent flows over heterogeneous surfaces revealed elevated turbulent kinetic energy and Reynolds shear stress in low-momentum-path regions. These regions induce large-scale multi-cellular secondary flows. The aim of the current study is to analyze the influence of these regions on drag, lift, and lateral forces acting on spherical particles at different exposure levels, thereby addressing the hitherto unknown contribution of the spanwise inhomogeneities. For this reason, numerical simulations of turbulent open-channel flow with varying aspect ratio (AR=1,3,5) over single-sized spherical particles with diameter D were studied. Ensemble-averaged cross-flow velocity vectors showed large-scale secondary flows to penetrate in-between the spherical particles, therefore stretching over the entire flow depth. Their magnitude above 0.8D was observed to range between 12.9%and14.9% of U. Strong tertiary vortices in the vicinity of the lateral walls were identified by analysis of swirl strength. Triple decomposition of streamwise velocity fluctuations showed strong backflow at the trailing edge of the spherical particles in high-momentum-path (HMP) regions. Furthermore, it was found that drag forces are higher in HMPs, which is attributed to the larger streamwise pressure gradient.

Direct numerical simulation of turbulent open channel flows at moderately high Reynolds numbers

Well-resolved direct numerical simulations of turbulent open channel flows (OCFs) are performed for friction Reynolds numbers up to $Re_\tau =2000$ . Various turbulent statistics are documented and compared with the closed channel flows (CCFs). As expected, the mean velocity profiles of the OCFs match well with the CCFs in the near-wall region but diverge notably in the outer region. Interestingly, a logarithmic layer with Kárman constant $\kappa =0.363$ occurs for OCF at $Re_\tau =2000$ , distinctly different from CCF. Except for a very thin layer near the free surface, most of the velocity and vorticity variances match between OCFs and CCFs. The one-dimensional energy spectra reveal that the very-large-scale motions (VLSMs) with streamwise wavelength $\lambda _x>3 h$ or spanwise wavelength $\lambda _z>0.5 h$ contribute the most to turbulence intensity and Reynolds shear stress in the overlap and outer layers (where h is the water depth). Furthermore, the VLSMs in OCFs are stronger than those in CCFs, resulting in a slightly higher streamwise velocity variance in the former. Due to the footprint effect, these structures also have significant contributions to the mean wall shear stress, and the difference between OCF and CCF enlarges with increasing $Re_\tau$ . In summary, the free surface in OCFs plays an essential role in various flow phenomena, including the formation of stronger VLSMs and turbulent kinetic energy redistribution.

The local energy flux surrogate in turbulent open-channel flows

We present a local analysis of turbulence in open-channel flows, using time-series velocity measurements. The method is based on a local form of the Kolmogorov “4/3-law” of homogeneous turbulence for the third-order moment of velocity increments. Following the Duchon and Robert [“Inertial energy dissipation for weak solutions of incompressible Euler and Navier–Stokes equations,” Nonlinearity 13, 249 (2000)] idea, which envisions turbulence dissipation as a lack of smoothness of the Navier–Stokes solutions, we estimate the local energy flux in a laboratory experiment with natural bed flows. Taking advantage of one-dimensional filtering techniques, under reasonable hypothesis, simple expressions of a surrogate of the energy flux are provided. The local energy flux surrogate reveals that, independently of the geometry, turbulence dissipation is highly intermittent. Among a variety of eddies that populate turbulence, dissipative singularities appear in sheet-like, tube, and filament structures, with large amplitude variations and rotations. This simplified technique can be applied to any measurement of hydrodynamic turbulence.

Numerical Investigation of Regime Transition in Canopy Flows

We have carried out highly resolved simulations of turbulent open channel flows. The channel wall is covered with different filamentous layers sharing the same thickness (h=0.1H, where H is the open channel height) and bulk Reynolds number (i.e., Re_b=U_bH/nu , , U_b is the bulk velocity and nu the kinematic fluid viscosity). The layers are composed of rigid, slender cylindrical filaments mounted perpendicular to the bottom wall. We have selected two layer configurations characterised by filament spacing ratios of Delta S/H=pi /24simeq 0.13 and Delta S/H=pi /32simeq 0.098. The geometrical features of the two layers, allow to classify them as transitional canopies (lambda =dh/Delta S^2simeq 0.15, where d is the filament diameter, i.e. dh is the filament frontal area) (Monti et al. 2020), which is defined as the separation between the sparse-dense asymptotic regimes, proposed by Nepf (2012). While the physical characterisation of the two asymptotic regimes is fairly understood, the transitional conditions remain an open question since the physical characteristics unique to the sparse and dense scenarios coexist in the transitional regime. By resolving every single filament with the aid of an immersed boundary technique in the framework of a Large Eddy formulation, we report the physical mechanisms that emerge at the onset of different regimes (chosen values of lambda fall on the verge between a dense and a sparse condition) and verify the criterion associated with the inception of the transition regime.

Longitudinal dispersion of multiple Microcystis patches in a turbulent open-channel flow

Longitudinal dispersion of multiple Microcystis patches in a turbulent open-channel flow

Effects of meander curvature in thermally stratified turbulent open-channel flow

Thermal stratification can lead to the damping of turbulence, which reduces the mixing of solutes in a fluid body. A series of direct numerical simulation (DNS) solutions sweeping through a range of four different meandering channel curvatures, from a sharp to mild curvature range, are obtained to investigate the effect of curvature on stratification in meandering thermally stratified turbulent open channel flow with an internal heat source that models radiative heating from above. Based on the DNS results, the present paper addresses two issues. First, the influence of changing curvature on the complex bi-cellular pattern of the secondary flow is investigated, including the distribution of the temperature field. Second, the effects of changing curvature on the degree of stratification are analyzed. Stratification can be characterized by the friction Richardson number Riτ and the bulk Richardson number Rib. Stratification can also be viewed in terms of the transfer of energy from mean flow kinetic energy to potential energy via buoyancy fluxes. We study the effect of curvature on stratification by investigating its effect on the friction and bulk Richardson numbers. We also study the transfers between the global potential and kinetic energy reservoirs, including the global available Ea, background Eb, and total potential energy Ep, and the domain-averaged mean kinetic and turbulent kinetic energy. It is found that, in meandering channels, with the increase in curvature, Ep increases and Riτ and Rib decrease, indicating that increasing curvature leads to a decrease in the level of stratification. On the other hand, we also find that a low curvature meandering channel has a higher level of stratification than a straight channel.

Numerical investigation of the dynamics of flexible vegetations in turbulent open-channel flows

Numerical investigation of the dynamics of flexible vegetations in turbulent open-channel flows

On the solidity parameter in canopy flows

We have performed high-fidelity simulations of turbulent open-channel flows over submerged rigid canopies made of cylindrical filaments of fixed length $l=0.25H$ ( $H$ being the domain depth) mounted on the wall with angle of inclination $\theta$ . The inclination is the free parameter that sets the density of the canopy by varying its frontal area. The density of the canopy, based on the solidity parameter $\lambda$ , is a widely accepted criterion defining the ongoing canopy flow regime, with low values ( $\lambda \ll 0.1$ ) indicating the sparse regime, and higher values ( $\lambda > 0.1$ ) the dense regime. All the numerical predictions have been obtained considering the same nominal bulk Reynolds number (i.e. $Re_b=U_b H/\nu = 6000$ ). We consider nine configurations of canopies, with $\theta$ varying symmetrically around $0^{\circ }$ in the range $\theta \in [\pm 78.5^{\circ }$ ], where positive angles define canopies inclined in the flow direction (with the grain) and $\theta =0^{\circ }$ corresponds to the wall-normally mounted canopy. The study compares canopies with identical solidity obtained inclining the filaments in opposite angles, and assesses the efficacy of the solidity as a representative parameter. It is found that when the canopy is inclined, the actual flow regime differs substantially from the one of a straight canopy that shares the same solidity, indicating that criteria based solely on this parameter are not robust. Finally, a new phenomenological model describing the interaction between the coherent structures populating the canopy region and the outer flow is given.

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