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"Channel flow"
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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.
Journal Article
A Comparative Analysis of Logarithmic Law, Reynolds Stress, and Turbulence Kinetic Energy Methods for Bed Shear Stress Estimation in Complex Open‐Channel Flow
Numerous indirect methods for estimating the bed shear stress using velocity or turbulent stress profiles have been suggested in previous research. Although these methods have proven effective for simple boundary‐layer‐type flows, their efficacy in complex flow scenarios remains largely unexplored. This study aimed to evaluate the predictive capabilities of three popular indirect bed‐shear‐stress estimation methods—the logarithmic law, Reynolds shear stress (RSS), and turbulence kinetic energy (TKE) techniques—in a complex flow environment involving an obstacle in an open channel, producing massive flow separation and unsteady vortex shedding. To circumvent the difficulties of direct bed shear‐stress measurements, the reference bed shear stress was obtained from a high‐resolution wall‐resolving large‐eddy simulation (LES) data set. The key findings of this study are as follows: First, the logarithmic law and TKE methods were effective only in regions where the streamlines were almost parallel to the primary flow direction. Second, the ratio of the bed shear stress to TKE varied significantly in space in complex‐flow regions, rendering TKE methods virtually ineffective in these areas. Third, the RSS methods successfully reproduced the LES‐computed bed shear stress distributions, both qualitatively and quantitatively. Fourth, the accuracy of the RSS methods was influenced by two critical factors: (a) the incorporation of the transverse RSS component in the RSS extrapolation and (b) the selection of extrapolation techniques. Finally, this study recommends the use of RSS methods employing two‐point extrapolation for bed shear‐stress estimation in complex flows. Key Points Indirect methods were tested to estimate bed shear stress in a complex flow setting using high‐resolution large‐eddy simulation data Log‐law and turbulence kinetic energy methods were effective for straight flow regions but unsuitable for regions with complex flows The Reynolds shear stress method using two‐point extrapolation with a lower point close to the bed was the most effective
Journal Article
Performance and wake characteristics of tidal turbines in an infinitely large array
The efficiency of tidal stream turbines in a large array depends on the balance between negative effects of turbine-wake interactions and positive effects of bypass-flow acceleration due to local blockage, both of which are functions of the layout of turbines. In this study we investigate the hydrodynamics of turbines in an infinitely large array with aligned or staggered layouts for a range of streamwise and lateral turbine spacing. First, we present a theoretical analysis based on an extension of the linear momentum actuator disc theory for perfectly aligned and staggered layouts, employing a hybrid inviscid-viscous approach to account for the local blockage effect within each row of turbines and the viscous (turbulent) wake mixing behind each row in a coupled manner. We then perform large-eddy simulation (LES) of open-channel flow for 28 layouts of tidal turbines using an actuator line method with doubly periodic boundary conditions. Both theoretical and LES results show that the efficiency of turbines (or the power of turbines for a given bulk velocity) in an aligned array decreases as we reduce the streamwise turbine spacing, whereas that in a staggered array remains high and may even increase due to the positive local blockage effect (causing the local flow velocity upstream of each turbine to exceed the bulk velocity) if the lateral turbine spacing is sufficiently small. The LES results further reveal that the amplitude of wake meandering tends to decrease as we reduce the lateral turbine spacing, which leads to a lower wake recovery rate in the near-wake region. These results will help to understand and improve the efficiency of tidal turbines in future large arrays, even though the performance of real tidal arrays may depend not only on turbine-to-turbine interactions within the array but also on macro-scale interactions between the array and natural tidal currents, the latter of which are outside the scope of this study.
Journal Article
Compound open-channel flows: effects of transverse currents on the flow structure
The structure of free-surface flows in a straight compound channel was investigated in a laboratory flume, consisting of a central smooth-bed main channel (MC) and two adjacent rough-surface floodplains (FPs). The experiments covered both uniform and non-uniform flow conditions, with the latter generated by imposing an imbalance in the discharge distribution between MC and FPs at the flume entrance. The non-uniform cases involved transverse currents directed from MC to FPs and vice versa . The focus of the study was on assessing the effects of transverse currents on: (i) transverse shear layer and horizontal Kelvin–Helmholtz-type coherent structures (KHCSs) forming at the interfaces between MC and FPs; (ii) helical secondary currents (SCs) developing across the channel due to topography-induced flow heterogeneity; and (iii) turbulent large- and very-large-scale motions (VLSMs). Transverse currents can entirely displace the shear layer over FP or in MC, but they do not alter the KHCSs to the same degree, resulting in a mismatch between shear layer extent and KHCS length scales. KHCSs emerge once dimensionless velocity shear exceeds a critical value above which KHCS length scales increase with the shear. Three well-established SC cells, which are induced by turbulence anisotropy, are observed in uniform flow and non-uniform flow with transverse currents towards FP. They are replaced by a single cell in the presence of a transverse mean flow towards MC. The spectral signatures of VLSMs are visible at the upstream section of the flume but they quickly disappear along the flow, being suppressed by simultaneous development of KHCSs and SCs.
Journal Article
Friction factor decomposition for rough-wall flows: theoretical background and application to open-channel flows
A theoretically based relationship for the Darcy–Weisbach friction factor$f$for rough-bed open-channel flows is derived and discussed. The derivation procedure is based on the double averaging (in time and space) of the Navier–Stokes equation followed by repeated integration across the flow. The obtained relationship explicitly shows that the friction factor can be split into at least five additive components, due to: (i) viscous stress; (ii) turbulent stress; (iii) dispersive stress (which in turn can be subdivided into two parts, due to bed roughness and secondary currents); (iv) flow unsteadiness and non-uniformity; and (v) spatial heterogeneity of fluid stresses in a bed-parallel plane. These constitutive components account for the roughness geometry effect and highlight the significance of the turbulent and dispersive stresses in the near-bed region where their values are largest. To explore the potential of the proposed relationship, an extensive data set has been assembled by employing specially designed large-eddy simulations and laboratory experiments for a wide range of Reynolds numbers. Flows over self-affine rough boundaries, which are representative of natural and man-made surfaces, are considered. The data analysis focuses on the effects of roughness geometry (i.e. spectral slope in the bed elevation spectra), relative submergence of roughness elements and flow and roughness Reynolds numbers, all of which are found to be substantial. It is revealed that at sufficiently high Reynolds numbers the roughness-induced and secondary-currents-induced dispersive stresses may play significant roles in generating bed friction, complementing the dominant turbulent stress contribution.
Journal Article
On the role of turbulent large-scale streaks in generating sediment ridges
The role of turbulent large-scale streaks or large-scale motions in forming subaqueous sediment ridges on an initially flat sediment bed is investigated with the aid of particle resolved direct numerical simulations of open channel flow at bulk Reynolds numbers up to 9500. The regular arrangement of quasi-streamwise ridges and troughs at a characteristic spanwise spacing between 1 and 1.5 times the mean fluid height is found to be a consequence of the spanwise organisation of turbulence in large-scale streamwise velocity streaks. Ridges predominantly appear in regions of weaker erosion below large-scale low-speed streaks and vice versa for troughs. The interaction between the dynamics of the large-scale streaks in the bulk flow and the evolution of sediment ridges on the sediment bed is best described as ‘top-down’ process, as the arrangement of the sediment bedforms is seen to adapt to changes in the outer flow with a time delay of several bulk time units. The observed ‘top-down’ interaction between the outer flow and the bed agrees fairly well with the conceptual model on causality in canonical channel flows proposed by Jiménez (J. Fluid Mech., vol. 842, 2018, P1, § 5.6). Mean secondary currents of Prandtl's second kind of comparable intensity and lateral spacing are found over developed sediment ridges and in single-phase smooth-wall channels alike in averages over ${O}(10)$ bulk time units. This indicates that the secondary flow commonly observed together with sediment ridges is the statistical footprint of the regularly organised large-scale streaks.
Journal Article
Secondary currents and very-large-scale motions in open-channel flow over streamwise ridges
It is widely acknowledged that streamwise ridges on the bed of open-channel flows generate secondary currents (SCs). A recent discovery of meandering long streamwise counter-rotating vortices in open-channel flows, known as very-large-scale motions (VLSMs), raises a question regarding the interrelations between VLSMs and SCs in flows over ridge-covered fully rough beds. To address it, we conducted long-duration experiments using stereoscopic particle image velocimetry, covering a range of ridge spacings ($s$) from${\\approx}0.4$to${\\approx}4$flow depths ($H$). For a benchmark no-ridge case, the flow is quasi-two-dimensional in the central part of the channel, exhibiting a strong spectral signature of VLSMs, as expected. With ridges on the bed at$s\\lessapprox 2H$, two SC cells are formed between neighbouring ridges and VLSMs are entirely suppressed, suggesting that ridge-induced SCs prevent the formation of VLSMs by absorbing their energy or overpowering their formation. At the same time, velocity auto- and cross-spectra reveal a new feature that can be explained by low-amplitude meandering of the alternating low- and high-momentum flow regions associated with instantaneous manifestations of SCs. Two-point velocity correlations and smooth velocity field reconstructions using proper orthogonal decomposition further support the validity of this effect. Its origin is probably due to the instability related to the presence of inflection points in the spanwise distribution of the streamwise velocity within the SC cells. These results have implications for bed friction in open channels, where the friction factor may increase if depth-scale SCs are present, or decrease under conditions of sub-depth-scale SCs and suppressed VLSMs.
Journal Article
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.
Journal Article