Nonlinear and entropic velocity distribution in open channel
TL;DR: In this article, an entropy-based nonlinear velocity profile model has been also suggested to describe the velocity field in open channels, which has been validated by means of controlled laboratory tests, executed in flume under steady flow conditions and at hydraulically smooth surface.
Abstract: The present study describes the nonlinear vertical velocity distribution in an open channel (with and without hydraulic structure). Conventionally, velocity distribution is based on shear velocity normalization. In this study, maximum velocity has been applied for normalization. Von-Karman logarithmic distribution (based on Karman constant), its proposed analogous models, and entropy-based nonlinear velocity distribution have been compared for both the cases (with and without hydraulic structure). An entropy-based nonlinear velocity profile model has been also suggested to describe the velocity field in open channels. The suggested approach has been validated by means of controlled laboratory tests, executed in flume under steady flow conditions and at hydraulically smooth surface. The higher equivalence between the estimated velocity profiles using entropy and the observed ones. Entropy model has found best replicating model with respect to other four models (based on analogous of Prandtl–von Kar...
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TL;DR: In this paper, a pair of mean and maximum shear stresses are used to evaluate the shear stress distribution on the entire channel cross-section, and then the prediction uncertainty of the sher stress obtained from the Tsallis entropy in a circular open channel is calculated.
Abstract: Accurate prediction of the shear stress distribution is essential for the successful design of stable erodible-bed channels and for the sediment transport studies. Considerable attention in recent years has been given to the estimation of velocity distribution using entropy concept in open channels. Despite the importance of knowledge about shear stress distribution, there are very few studies on the application of the entropy methods for prediction of the shear stress distribution in open channels. The Tsallis entropy has been employed in this study for estimating the shear stress in open channels. In this approach, a pair of mean and maximum shear stresses are used to evaluate the shear stress distribution on the entire channel cross-section. We then calculated the prediction uncertainty of the shear stress obtained from the Tsallis entropy in a circular open channel. Moreover, the distribution of prediction error for the Tsallis approach is examined in two cases, both before and after data normalization. The quantitative results from this uncertainty analysis showed satisfactory results for the Tsallis entropy model for estimating shear stress in the entire section. The 95% Confidence Bounds (CB) are obtained for the shear stress distribution predicted by the model closely match the observed values.
21 citations
TL;DR: In this paper, a more precise and comprehensive model for stream-wise velocities in turbulent smooth-wall open channel flows is presented, where velocity profiles are obtained from the resolution of torsion coefficients.
Abstract: This study attempts to provide a more precise and comprehensive model for stream-wise velocities in turbulent smooth-wall open channel flows. Velocity profiles are obtained from the resolution of t...
5 citations
Cites methods from "Nonlinear and entropic velocity dis..."
...In addition, effort has been employed to derive one and two dimensional equations from probability-based approaches (Barbe et al. 1991; Luo and Singh 2011a, 2011b; Singh et al. 2013; Cui and Singh 2013, 2014; Tiwari and Sharma 2016)....
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...dimensional equations from probability-based approaches (Barbe et al. 1991; Luo and Singh 2011a, 2011b; Singh et al. 2013; Cui and Singh 2013, 2014; Tiwari and Sharma 2016)....
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01 Jan 2017
TL;DR: In this paper, the empirical relationship between the head and discharge over the Piano Key Weir was investigated. And the weir coefficient values of the PKWeir were evaluated through HEC-RAS modeling.
Abstract: Increasing demand of energy and limited conventional energy sources (coal, petroleum, natural gas, etc.) initiated the alternative thinking of hydropower projects. Due to easy and high head availability in mountainous regions, India has immense potential of hydropower. Spillways are the one of the important elements of hydropower projects. Spillways are generally used in the hydropower to spill the excess amount of water. Piano Key Weir is the ungated spillway structure generally used to get high discharge intensity under limited width. This study formulates the empirical relationship between the head and discharge over Piano Key Weir. This study also evaluates the weir coefficient values of Piano Key Weir through HEC-RAS modeling.
4 citations
TL;DR: In this paper, a fully coupled numerical model by integrating the two-dimensional shallow water equations with entropy theory was developed, and the TVD Mac-Cormack predictor-corrector finite difference finite difference (TVD-FDFFDF) was used.
Abstract: This work aims at developing a fully coupled numerical model by integrating the two-dimensional shallow water equations with entropy theory. TVD Mac-Cormack predictor-corrector finite difference sc...
3 citations
Cites background from "Nonlinear and entropic velocity dis..."
...Magnitude and distribution of the velocity components in open channels extremely affected by the degree of complexity in bed topography, bed roughness parameters, flow obstructions and diversion structures, channel geometry and turbulence in the flow (Tiwari and Sharma 2016)....
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References
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TL;DR: A new method for detecting spikes in acoustic Doppler velocimeter data sequences is suggested and it is shown to have superior performance to various other methods and it has the added advantage that it requires no parameters.
Abstract: A new method for detecting spikes in acoustic Doppler velocimeter data sequences is suggested. The method combines three concepts: (1) that differentiation enhances the high frequency portion of a signal, (2) that the expected maximum of a random series is given by the Universal threshold, and (3) that good data cluster in a dense cloud in phase space or Poincare maps. These concepts are used to construct an ellipsoid in three-dimensional phase space, then points lying outside the ellipsoid are designated as spikes. The new method is shown to have superior performance to various other methods and it has the added advantage that it requires no parameters. Several methods for replacing sequences of spurious data are presented. A polynomial fitted to good data on either side of the spike event, then interpolated across the event, is preferred by the authors.
1,433 citations
"Nonlinear and entropic velocity dis..." refers methods in this paper
...The method of phase-space threshold was adopted to get rid of suspected spikes (Goring and Nikora 2002) by applying Win-ADV software....
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TL;DR: In this article, it was shown that the log-law can be applied strictly only to the nearwall region and the von K´rm´n constant κ and integral constant A are truly universal, having values of κ=0.412 and A=5.29 irrespective of the Reynolds and Froude number.
Abstract: A powerful two‐color Laser Doppler Anemometer (LDA) system, with direct digital signal processing has been used to measure accurately the longitudinal and vertical velocity components in two‐dimensional, fully‐developed open‐channel flow over smooth beds. The law of the wall and the velocity defect law were re‐examined because the log‐law has been often applied to open channels without detailed verification. It was found that the log‐law can be applied strictly only to the near‐wall region. In this region, the von K´rm´n constant κ and the integral constant A are truly universal, having values of κ=0.412 and A=5.29 irrespective of the Reynolds and Froude number. As the Reynolds number becomes larger, the deviation from the log‐law cannot be neglected in the outer region. This deviation can be expressed well by Coles' wake function which involves a Reynolds‐number dependent parameter Π. The distributions of eddy viscosity and mixing length were evaluated and found to depend on Π. All the data including the...
892 citations
TL;DR: In this paper, the lateral distributions of depth-mean velocity and boundary shear stress for straight open channels with prismatic complex cross-sections are derived theoretically for channels of any shape, provided that the boundary geometry can be discretized into linear elements.
Abstract: The flow of water in straight open channels with prismatic complex cross-sections is considered. Lateral distributions of depth-mean velocity and boundary shear stress are derived theoretically for channels of any shape, provided that the boundary geometry can be discretized into linear elements. The analytical model includes the effects of bed-generated turbulence, lateral shear turbulence and secondary flows. Experimental data from the Science and Engineering Research Council (SERC) Flood Channel Facility are used to illustrate the relative importance of these three effects on internal shear stresses. New experimental evidence concerning the spatial distribution of Reynolds stresses τyx and τzx is presented for the particular case of compound or two-stage channels. In such channels the vertical distributions of τzx are shown to be highly nonlinear in the regions of strongest lateral shear and the depth-averaged values of τyx are shown to be significantly different from the depth mean apparent shear stresses. The importance of secondary flows in the lateral shear layer region is therefore established. The influence of both Reynolds stresses and secondary flows on eddy viscosity values is quantified. A numerical study is undertaken of the lateral distributions of local friction factor and dimensionless eddy viscosity. The results of this study are then used in the analytical model to reproduce lateral distributions of depth-mean velocity and boundary shear stress in a two stage channel. The work will be of interest to engineers engaged in flood channel hydraulics and overbank flow in particular.
591 citations
"Nonlinear and entropic velocity dis..." refers methods in this paper
...In the past, a range of empirical and semi empirical models have been used to characterize the velocity distribution profiles of open channel flow (Coleman 1981; Keylock et al. 2012; Nezu 2005; Nezu and Rodi 1986; Shiono and Knight 1991)....
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TL;DR: In this article, the accuracy of the acoustic Doppler velocimeter (ADV) is evaluated in a 17m flume using an ADV and a laser DOF.
Abstract: Accuracy of the acoustic Doppler velocimeter (ADV) is evaluated in this paper. Simultaneous measurements of open-channel flow were undertaken in a 17-m flume using an ADV and a laser Doppler velocimeter. Flow velocity records obtained by both instruments are used for estimating the true (“ground truth”) flow characteristics and the noise variances encountered during the experimental runs. The measured values are compared with estimates of the true flow characteristics and values of variance (〈u′2〉, 〈w′2〉) and covariance (〈u′w′〉) predicted by semiempirical models for open-channel flow. The analysis showed that the ADV sensor can measure mean velocity and Reynolds stress within 1% of the estimated true value. Mean velocities can be obtained at distances less than 1 cm from the boundary, whereas Reynolds stress values obtained at elevations greater than 3 cm above the bottom exhibit a variation that is in agreement with the predictions of the semiempirical models. Closer to the boundary, the measure...
566 citations
"Nonlinear and entropic velocity dis..." refers methods in this paper
...Data were gathered in the test section at the center line of the flume with and without PKW and then near wall with PKW (Figure 1). volume 0.09 cc being undisturbed by the presence of probe (Sukhodolov et al. 1998; Voulgaris and Trowbridge 1998)....
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...ADV has been widely used across the world for laboratory (Duan et al. 2011; Nikora and Goring 1998; Song and Chiew 2001; Voulgaris and Trowbridge 1998; Wang et al. 2012) as well as field velocity measurements (Chanson et al. 2005; Chanson et al. 2008; García et al. 2007; Sukhodolov et al. 1998)....
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TL;DR: In this paper, the bottom boundary layer of the York River estuary, Virginia, was estimated from three-dimensional near-bottom velocities measured by Acoustic Doppler Velocimeters (ADVs) and also by a profiling array of electromagnetic current meters.
Abstract: Bed stresses in the bottom boundary layer of the York River estuary, Virginia, were estimated from three-dimensional near-bottom velocities measured by Acoustic Doppler Velocimeters (ADVs) and also by a profiling array of electromagnetic current meters. By assuming the measurements were made in a constant stress layer, four methods of stress estimation were evaluated using ADVs: direct covariance (COV) measurement, turbulent kinetic energy, inertial dissipation utilizing the Kolmogorov spectrum, and log profile. The four methods yielded similar estimates of frictional velocity (U*) based on ADV output from both 14 cm and 44 cm above bed. All eight estimates of average U* were consistent with the overall mean of 1.10 cm/s to within the 95% confidence interval for individual burst estimates. The COV method worked slightly better nearer the bed, possibly because of the sensitivity of COV to the upper limit of the constant stress layer. The inertial dissipation method performed marginally well at 14 cm above bed, likely because of sediment induced stratification and insufficient separation of turbulent production and dissipation scales. The log profile method was the most variable and appeared most sensitive to stratification and to the thickness of the constant stress layer. The turbulent kinetic energy method was the most consistent at both heights and appears most promising for further development. Results encourage future use of the ADV in estuarine environments but also favor the simultaneous use of several methods to estimate bottom stress.
401 citations
"Nonlinear and entropic velocity dis..." refers methods in this paper
...Modified turbulent kinetic energy method suggested by Kim et al. (2000) which uses only the vertical velocity fluctuations is also used to work out bed shear stress in this study. where C2 is 0.9....
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