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Turbulence structure parameter a 1 = v s ′ v z ′ ¯ 2 + v n ′ v z ′ ¯ 2 ∕ 2 k ; (a) theoretical profile in straight uniform flow; (b) measured distribution in curved flow.
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![(a)–(e) Isolines of normalized mixing coefficients [Eq. (10) ]; (f)...](profile/K-Blanckaert/publication/46014417/figure/fig3/AS:316726756560897@1452524951199/a-e-Isolines-of-normalized-mixing-coefficients-Eq-10-f-width-distribution_Q320.jpg)
In spite of its importance, little is known about the turbulence characteristics in open-channel bends. This paper reports on an experimental investigation of turbulence in one cross section of an open-channel bend. Typical flow features are a bicellular pattern of cross-stream circulation (secondary flow) and a turbulence activity in the outer ben...
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Context 1
... to Schwarz and Bradshaw, 22 3 holds for k. The a 1 profile increases from 0 at the water surface, reaches a maximum of about 0.14 around mid-depth and subsequently decreases to about 0.1 at the bed. The ex- perimental distribution of a 1 for our curved open-channel flow is shown in Fig. 5b. In the center region, values are high, O1, mainly due to very high values of the s-z com- ponent of the Reynolds stress, which are probably associated with the deformation of the downstream velocity profile and the downward directed secondary flow. 24 Moreover, the dis- tribution of k in this area does not exhibit the sharp increase ...Context 2
... di- rection, from O1 to 10 in the center region to O0.1 to 1 in the outer-bank region. nz Fig. 6e behaves similarly, ex- cept that it assumes high values near the center of the outer- bank cell. This outward decrease of the mixing coefficients related to the turbulent shear stresses is in agreement with the outward decrease of the coefficient a 1 Fig. 5b and con- firms the observation that the efficiency of shear stress pro- duction for a given turbulent kinetic energy is reduced in curved flow. Figure 6f shows the lateral distribution in the outer bend of the mixing coefficients jk , being the depth- averaged absolute values evaluated within the measuring grid and excluding the ...Similar publications
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Citations
... Estimation of the TKE budget differs from classical turbulence observations reported in the literature on clear-water, sediment-laden open-channel and wall-bounded boundary layer flows (Wallace, Eckelmann & Brodkey 1972;Brodkey, Wallace & Eckelmann 1974;Nakagawa & Nezu 1977;Raupach 1981;Nezu & Rodi 1986;Lyn 1988;Kironoto & Graf 1994;Graf & Cellino 2002;Hurther & Lemmin 2003;Cellino & Lemmin 2004;Blanckaert & de Vriend 2005). This can mainly be attributed to difficulties in measuring accurately all terms involved in the production, dissipation and transport of mean TKE. ...
New experiments in highly turbulent, steady, subcritical and uniform water open-channel flows have been carried out to measure the mean turbulent kinetic energy (TKE) budget of sediment-laden boundary layer flows with two sizes (d p = 3 mm and 1 mm) of Plexiglas particles (relative density = 1.192). The experiments covered energetic sediment transport conditions (Shields number of 0.35 < θ < 1.2) ranging from non-capacity to full-capacity flows in bedload-to-suspension-dominated transport modes (suspension number of 0.5 < w s /u * < 1.3 where w s is the settling velocity and u * is the friction velocity) and for weakly to highly inertial, finite size turbulence-particle conditions (Stokes number of 0.1 < St < 3.5 and d p /η > 10 where η is the Kolmogorov length scale). It was shown that the effects of sediments on the TKE budget are very pronounced in all large particle experiments for which a bedload layer of several grain diameter thickness is developed above the channel bed. When compared with the corresponding reference clear-water flows, the TKE shear-production rate for the 3 mm particle flows is strongly reduced in the wall region corresponding to the bedload layer. This turbulence damping is seen to increase with sediment load until full capacity for flows with constant Shields value, as well as with Shields number value. Inside this damped TKE shear-production zone, a distinct peak of maximal turbulence production appears to coincide with the upper edge of the bedload layer delimited by a sharp gradient in mean sediment concentration. This vertically upshifted peak of TKE production is accompanied by an enhanced net downward oriented TKE flux when compared with the reference clear-water flows. The downward diffused TKE is found to act in the bedload layer as a local energy source in reasonable balance with the sediment transport term. The mechanism behind this downward TKE transport was further analysed on the basis of coherent flow structure dynamics controlled by ejection-and sweep-type events. The agreement between the height of downward directed mean TKE flux and the height below which sweep-type events dominate the Reynolds shear-stress contribution over ejections, revealed the leading role played by sweeps in mean TKE transport. This agreement holds for all reference clear-water flows supporting the well-known wall-roughness-induced dominance of the sweep contribution in turbulent, rough clear-water boundary layer flows. Furthermore, for all 3 mm particle flows, the two referred to transition levels were significantly and similarly upshifted to the upper edge of the bedload layer. Only for these sediment-laden flows, the bedload layer thickness is seen to exceed the wall-roughness sublayer of the reference clear-water flows. This supports a strong analogy between wall-roughness effects in clear-water flows and bedload layer effects in sediment-laden flows, on the mean TKE budget induced by a similarly modified coherent flow structure dynamics. The bedload layer-controlled wall roughness is finally confirmed by the good prediction of the wall-roughness parameter k s of the logarithmic velocity distribution. An empirical formulation fitting the presented measurements is presented, valid over the range of Shields number values covered herein.
... The quantitative analysis of turbulent flow was based on measurements of fluctuations in velocity at a measuring point within the channel. The dimensionless turbulent kinetic energy (DTKE) was calculated as the sum of the intensities of the velocity fluctuations (Blanckaert and De Vriend, 2005): ...
Turbulence generated within the vegetated confluence system is important for water quality and river management. In this study, we conducted a series of experiments to explore the extent to which emergent rigid vegetation in the confluence channel influences hydrodynamic characteristics and contaminant transport. First, a series of tests with increasing discharge ratios (from 0.35, 0.5, and 1) was conducted to quantify the effects of the discharge ratio on hydrodynamic conditions within the vegetated confluence. Then, tests with different discharge ratios were also set up to explore how contaminants released locations and modes (line and point source) influence the transport and mixing of contaminants. The results showed that increasing the discharge ratio induced larger momentum in the confluence area. The increase in discharge ratio rendered the circulation stronger, and its position came earlier in the non-vegetative area. In addition, the dimensionless turbulent kinetic energy peaked near the interface of the non/vegetated zone. With the increase in the discharge ratio, the dimensionless turbulent kinetic energy was found to be smaller. In the contaminants transport tests, the results revealed larger discharge ratio could speed up contaminants transport and mixing. The applications from this study would be helpful to pollutant transport management in natural confluences.
... The nature and turbulent flow characteristics of a sinuous river differ from those of a straight channel. In fact, the velocity profile of a sinuous river does not completely conform to the logarithmic law [14][15][16][17]. Blanckaert [18] and Taye and Kumar [19] confirmed that helical flows occurred in meandering rivers owing to the distribution of Reynolds shear stress (RSS). ...
... Blanckaert [18] and Taye and Kumar [19] confirmed that helical flows occurred in meandering rivers owing to the distribution of Reynolds shear stress (RSS). Previously, researchers considered rigid banks when conducting experiments in meandering rivers [7,8,16,18]. However, most banks are mobile, which aggravates erosion and further meandering in the channel. ...
Laboratory experiments have been conducted to investigate flow patterns in a sinuous curvilinear channel with flexible banks. Those experiments focused primarily on rectangular or trapezoidal cross-sections with rigid banks, whereas comprehensive experiments pertaining to curved cross-sections with flexible banks in a sinuous/meandering channel have not been performed. Hence, the flow characteristics in a curved sinuous channel with erodible banks are analyzed in this study. The velocity profile does not reflect the typical straight flow logarithmic profile owing to secondary flow. The velocity magnitude at the entry and exit of the bend is greater than that at the apex of the final and next bends, respectively. The magnitude of the depth-averaged velocity in the bend entry region is 40% greater than that in the bend exit section of the sinuous channel. A negative streamwise Reynolds shear stress is observed at some locations of the bend, which confirm the presence of helical flow therein. The turbulent intensities and an analysis of the turbulent kinetic energy (TKE) reveal that the magnitude of the helical flow at the inner bank is greater than that at the outer bend of the apex. The depth-averaged TKE magnitude in the inner band is higher than that at the outer bend in the apex cross-section by more than 50%. This finding is opposite to that pertaining to the velocity magnitude, thus indicating that a region with a greater mean velocity does not imply greater fluctuations. Higher-order correlations show that the flux and diffusion of streamwise and vertical normal stresses are indicated in both positive and negative signs, thus indicating sediment mobility in the channel.
... Turbulent shear stress includes viscous shear stress and turbulent additional shear stress (Shiono and Knight, 1989). The additional shear stress, also known as Reynolds stress, is far greater than the viscous shear stress in fully developed turbulence, and it can be used to measure the shear effect in flows (Barman and Kumar, 2022;Blanckaert and de Vriend, 2005;and Nguyen et al., 2022). Reynolds stress is expressed as the time average product of velocities fluctuating in two directions. ...
Large eddy simulations were conducted to simulate the flow in compound meandering channels whose main channel sinuosity was 1.381. Then, the floodplain vegetation was generalized using the momentum equation coupled with the drag force formula. The mean flow pattern, secondary flow, coherent structure, turbulence characteristics, and lateral mass and momentum transport with and without floodplain vegetation with relative depths (Dr) of 0.3-0.5 were studied. Results showed that the floodplain vegetation enabled the flow of the main channel to be more concentrated. The maximum average velocity in the cross section of the main channel increased by 100% and 30% when the relative depth was 0.3 and 0.5. Under the influence of floodplain vegetation, the secondary flow cell transformed greatly with the change in relative depth. When Dr < 0.3, the vegetation caused the vortex center of the secondary flow to move closer to the concave bank side, and the secondary flow distribution presents a flow pattern not flooding the floodplain. When Dr > 0.3, the spatial change in the secondary flow was not obvious. In addition, the floodplain vegetation did not change the large-scale vortex that was separated from the boundary layer of the convex bank side. Meanwhile, the floodplain vegetation increased the overall turbulence intensity, turbulent kinetic energy, and Reynolds stress of the main channel, and it increased the range of lateral mass exchange of the inbank flow and the mean and turbulent transport flux of each cross section. Published under an exclusive license by AIP Publishing. https://doi.
... Thus, the overall value of the nonvegetative system was larger than that of the vegetative system. TKE can be considered a measure of turbulence intensity (Blanckaert & De Vriend, 2005), as it describes the extent of mixing and water exchange between different layers. The presence of vegetation caused the TKE to be distributed more unevenly. ...
Vegetation greatly affects the flow characteristics and contaminant transport in river confluences. In this study, the flow characteristics and contaminant transport in the non‐vegetated/vegetated Y‐shaped confluence were explored systematically through a series of experiments. A total of 10 scenarios were designed to answer the three main research questions: what is the difference between the flow characteristics and contaminant transport in (1) asymmetrical and Y‐shaped confluences; (2) non‐vegetated/vegetated Y‐shaped confluences; (3) vegetated Y‐shaped confluences with different confluence ratios? The experimental results revealed that vegetation remarkably changes the internal flow structure in Y‐shaped confluences. Briefly, the velocity profile can be divided into three vertical layers within the vegetated system, but it remains nearly constant in the non‐vegetated channel. Vegetation changes the circulation location and reduces the intensity of the secondary current, weakening the strength of contaminant mixing. However, the turbulent kinetic energy within the vegetated system is larger than that in the non‐vegetated case, and it peaks at the top of the vegetation canopy. Under different confluence ratio cases, the overall fluctuation of the longitudinal dispersion coefficients along the cross‐sections in the mainstream was similar but increasing the confluence ratio causes the circulation to appear to advance and enhances its intensity. In addition, the vegetation density (200 item/m2) in this study render the manning roughness coefficient at 0.068, which is larger than that under lower vegetation density cases. The outcomes from this study are helpful for both environmental and river management applications. This article is protected by copyright. All rights reserved.
... The dynamic process of the complex morphology in a sinuous bend can be characterized by linear and nonlinear development of morphologies (Song et al. 2016). Several studies have reported bank erosion due to maximum velocity at the outer bend (Blanckaert and de Vriend 2005;Constantinescu et al. 2013;da Silva and Ebrahimi, 2017). However, this does not hold in all cases. ...
Sinuous channel flows are complex and represent heterogeneity in the flow characteristics. Experiments were conducted in a sinuous channel of a rectangular cross-section to identify the velocity fluctuations and the turbulence present in the flow. Secondary vectors, Reynolds shear stress, turbulent kinetic energy, and the anisotropy turbulence were evaluated in the sinuous bend. The secondary vectors show a large circulation cell at the center of the bend apex. The streamwise-vertical component of RSS was high at the bend apex. The streamwise-transverse and transverse-vertical components of RSS showed high peaks at the bend apex, indicating greater fluctuations in the transverse direction. The turbulent kinetic energy is higher away from the bed and shows decay near the bed. Anisotropy invariant map (AIM) identified the turbulence at bend sections and varying flow depth. Two-dimensional, cigar-shaped, and pancake-shaped turbulence was observed at the bend sections. Near the bed (z/h < 0.2) and away from the bed (z/h > 0.4), pancake-shaped and cigar-shaped turbulence were observed.
... Besides that, the significance of the curve angle of the flow has been studied, such as in 30°, 60°, 120°, and 150°curved open channels. For example, Blanckaert and De Vriend (2005) measured the turbulent stress components of curved currents and analysed the flow turbulence in a sharp 120°bend. Zhang and Shen (2008) presented a 3-D numerical model to determine water depth changes and longitudinal and transverse velocity profiles in curved channels. ...
This paper aims to study the flow characteristics through angled baffle-plates in open channel. The experiments were conducted in a self-circulating hydraulic flume with three designated baffle-plates angles (30°, 60°, and 90°) and three flow conditions (high, medium, and low). Results showed that all the designed angles for the different flow conditions do retard the flow resulting in reduced downstream mean discharge as compared to without the baffle-plates. The baffle-plates installed at 90° showed the greatest percentage of mean discharge reduction for all the flow conditions (ranged between 5.32% to 11.67%) as compared to 60° (ranged between 3.96% to 8.3%) and 30° (ranged between 3.55% to 7.07%). An equation to predict the relative flow depth increase due to the retarding behavior of the angled baffle-plates structure was also developed in this study using multiple linear regression. The proposed equation has a R² value of 0.69, R²adj value of 0.62, Mallow’s Cp value of 2 and mean square error (MSE) value of 0.4548 which is the best among all the possible regression models for this study. The equation can be used by designer in determining the desired angle for baffle-plates structure to prevent overflow at upstream of the structure.
... This is often named turbulence-induced secondary flow, which is generated by the non-homogeneity and anisotropy of turbulence (Einstein and Li 1958;Hinze, 1973;Perkins, 1970;Gessner, 1973). As mentioned in Section 2, the velocity of the centre region cell is about 20-30% of the streamwise velocity, in contrast with the much smaller velocity of the outer-bank cell, which is typically 3% of the streamwise velocity (Blanckaert and de Vriend, 2005). Blanckaert and Graf (2001) also showed that the cross-sectional velocities of the centre region cell are = O (0.03). ...
In sharp open-channel bends, there exists nonlinear interactions between streamwise and cross-stream velocities, which leads to the adjustment of flow energy transport, increases the energy dissipation and eventually influences the development of river bends. However, previous studies have not yet fully understood the mechanisms underlying the transport and dissipation of energy in open-channel bends. In addition, energy dissipation is directly related to the evolution of enstrophy Ω·Ω/2. However, it has not yet received much attention in the study of the resistance in meandering rivers. To gain an insight into these mechanisms, with the aid of detailed experimental data collected in a sharp open-channel bend, this study quantified the impacts of the key terms in the kinetic energy equation and the enstrophy equation. Results show that the term related to the transport of kinetic energy by cross-stream circulation is at least an order of magnitude larger than the other terms in the kinetic energy equation, which contributes significantly to the redistribution of kinetic energy over the cross section. The term related to the production of turbulent kinetic energy in the kinetic energy equation shows the smallest order of magnitude and thus is almost negligible for the time-averaged flow field. Furthermore, over most of the measured area, the term related to the centrifugal force shows values of at least an order of magnitude larger than the other terms in the enstrophy equation, which means that this term exerts the dominant influence on the energy dissipation. The results also revealed that the transformation process is insensitive to the variations in Froude number. These results are expected to improve the understanding of the complete process of energy transformation, especially the resistance caused by secondary flow in meandering rivers.
... In general, turbulent kinetic energy can be considered a measure of turbulence intensity [37]. In this study, the turbulent kinetic energy Ek was calculated using Equation (1), which was proposed by Li [38] and defines Ek as follows in terms of streamwise, lateral, and vertical directions: ...
A laboratory measurement with acoustic Doppler velocimeter (ADV) was used to investigate the flow through a Y-shaped confluence channel partially covered with rigid vegetation on its inner bank. In this study, the flow velocities in cases with and without vegetation were measured by the ADV in a Y-shaped confluence channel. The results clearly showed that the existence of non-submerged rigid plants has changed the internal flow structure. The velocity in the non-vegetated area is greater than in the vegetated area. There is a large exchange of mass and momentum between the vegetated and non-vegetated areas. In addition, due to the presence of vegetation, the high-velocity area moved rapidly to the middle of the non-vegetated area in the vicinity of tributaries, and the secondary flow phenomenon disappeared. The presence of vegetation made the flow in non-vegetated areas more intense. The turbulent kinetic energy of the non-vegetated area was smaller than that of the vegetated area.
... Blanckaert K. [45] and Ma [24] investigated the distribution of TKE in the cross-section of the bend. In this study, the equation of TKE calculation is as follows: ...
Curved channel with trapezoidal cross-section is approximate to the common form in nature fluvial networks and its hydraulic characteristics are considerably complex and variable. Combined with volume of fluid (VOF) method, renormalization group (RNG) k-ε turbulence model was employed to numerically investigate the flow properties in the U-shaped channel with various trapezoidal cross-sections. Analyses were performed from the aspects of the water surface transverse slope in bend apex (WTS-BA), longitudinal velocity, secondary flow, shear stress and turbulent kinetic energy (TKE) under several scenarios, specifically, four types of radius-to-width ratio and seven types of slope coefficient with a constant aspect ratio. The calculated results suggested that the maximums of shear stress and TKE in the bend were observed in the convex bank and the maximal intensities of secondary flow were observed within the range of 60 to 75 degrees for various varieties. As the radius-to-width ratio increased, the maximums of shear stress, TKE and WTS-BA decreased; but increased with increasing slope coefficients. The intensity of secondary flow decreased as slope coefficients increased and the angle of maximum intensity of secondary flow moved to the upstream for the increasing radius-to-width ratios. In addition, a new equation concerning the vertical distribution of longitudinal velocity in trapezoidal cross-sectioned channel was presented.
