Two-Dimensional Velocity Distribution in Open Channels Using the Tsallis Entropy

Cui, Huijuan; Singh, Vijay P.

doi:10.1061/(asce)he.1943-5584.0000610

Cited by 58 publications

(39 citation statements)

References 20 publications

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“…Figure 8. Verification of the proposed model (Equation (13)) with runs K11, K12, K13, K21, K22 and K23 of [31] and comparison with the models of Greimann et al (GM), Cheng (CM) and DM, given by Equations (19), (18) and (20).…”

Section: Comparison With Experimental Data and Other Modelsmentioning

confidence: 99%

“…For the past 25 years, entropy theory has been advantageously applied in fluvial hydraulics. Using this theory, several models of velocity (Chiu [18], Cui and Singh [19,20], Kumbhakar and Ghoshal [21,22]), sediment concentration (Chiu et al [23], Cui and Singh [24]), debris flow (Singh and Cui [25]), etc., have been developed. The objective of this study therefore is to model velocity lag using the entropy theory, verify the model using a wide range of twenty-two experimental datasets obtained from the literature and compare the proposed model with the existing velocity lag models.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Entropy-Based Modeling of Velocity Lag in Sediment-Laden Open Channel Turbulent Flow

Kumbhakar

Kundu

Ghoshal

et al. 2016

Entropy

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Abstract:In the last few decades, a wide variety of instruments with laser-based techniques have been developed that enable experimentally measuring particle velocity and fluid velocity separately in particle-laden flow. Experiments have revealed that stream-wise particle velocity is different from fluid velocity, and this velocity difference is commonly known as "velocity lag" in the literature. A number of experimental, as well as theoretical investigations have been carried out to formulate deterministic mathematical models of velocity lag, based on several turbulent features. However, a probabilistic study of velocity lag does not seem to have been reported, to the best of our knowledge. The present study therefore focuses on the modeling of velocity lag in open channel turbulent flow laden with sediment using the entropy theory along with a hypothesis on the cumulative distribution function. This function contains a parameter η, which is shown to be a function of specific gravity, particle diameter and shear velocity. The velocity lag model is tested using a wide range of twenty-two experimental runs collected from the literature and is also compared with other models of velocity lag. Then, an error analysis is performed to further evaluate the prediction accuracy of the proposed model, especially in comparison to other models. The model is also able to explain the physical characteristics of velocity lag caused by the interaction between the particles and the fluid.

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Section: Comparison With Experimental Data and Other Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Entropy-Based Modeling of Velocity Lag in Sediment-Laden Open Channel Turbulent Flow

Kumbhakar

Kundu

Ghoshal

et al. 2016

Entropy

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show abstract

“…The velocity profiles obtained from the power law velocity distribution [Equation (17)] and the logarithmic velocity distribution [Equation (18)] were almost the same (negligible differences), as shown in Figure 1. Figure 1.…”

Section: D Velocity Distribution and Maximum Velocity On The Water Lmentioning

confidence: 75%

“…Following Chiu [3], it is plausible to consider time-averaged velocity as a probabilistic variable, derive the probability distribution of velocity and then derive the velocity distribution. Chiu [3] proposed the entropy theory for deriving the velocity distribution which has since been employed by Chiu and his associates [3][4][5][6][7][8][9][10], as well others [11][12][13][14][15][16][17]. Some of these investigations dealt with 1D and some with 2D velocity distributions.…”

Section: Introductionmentioning

confidence: 99%

Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory

Singh

Marini

Fontana

2013

Entropy

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Abstract:The one-dimensional (1D) power law velocity distribution, commonly used for computing velocities in open channel flow, has been derived empirically. However, a multitude of problems, such as scour around bridge piers, cutoffs and diversions, pollutant dispersion, and so on, require the velocity distribution in two dimensions. This paper employs the Shannon entropy theory for deriving the power law velocity distribution in two-dimensions (2D). The development encompasses the rectangular domain, but can be extended to any arbitrary domain, including a trapezoidal domain. The derived methodology requires only a few parameters and the good agreement is confirmed by comparing the velocity values calculated using the proposed methodology with values derived from both the 1D power law model and a logarithmic velocity distribution available in the literature.

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“…Recently, one and two dimensional velocity distribution in open channels is derived by maximizing the Tsallis entropy showing an advantage in capturing low velocities near the channel bed for heavy sediment flows with high entropy value Singh 2013, Cui andSingh 2014b). Later Singh et al (2014) derived a function for modelling the flow duration curve.…”

Section: Average Velocity (U*avg)mentioning

confidence: 99%

The Hysteresis and Shear Velocity in Unsteady Flows

Bombar

2016

JAFM

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The shear velocity is an important parameter in characterizing the shear at the boundary in open channels and there exist methods to estimate the shear velocity in steady flows, but the application and comparison of these methods to non-uniform unsteady flows is limited. In this study, three artificial triangular-shaped hydrographs were generated where the base flow is non-uniform with fine sand bed and the shear velocity was obtained by the methods, u*SV by using the Saint-Venant equations, u*L by using the procedure given by Clauser Method, u*P by using the parabolic law, u*UN by using the momentum equation assuming the slope of energy grade line is equal to bed slope and u*avg by using the average velocity equation are used in this study. The stream-wise components of velocity time series and the velocity profiles were obtained by means of an acoustic Doppler velocity meter. The variation of the shear velocity and the constant for the parabolic law with time is discussed. It is concluded that the shear velocities found by the parabolic law and the average velocity equation can be used interchangeably. Furthermore a hysteresis intensity parameter is proposed in order to examine the depth variation of hysteretic behavior of depth variation both with point velocity and average velocity. It is revealed that the more the unsteady the hydrograph the more the hysteresis both in terms of point velocity and cross-sectional mean velocity.

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Two-Dimensional Velocity Distribution in Open Channels Using the Tsallis Entropy

Cited by 58 publications

References 20 publications

Entropy-Based Modeling of Velocity Lag in Sediment-Laden Open Channel Turbulent Flow

Entropy-Based Modeling of Velocity Lag in Sediment-Laden Open Channel Turbulent Flow

Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory

The Hysteresis and Shear Velocity in Unsteady Flows

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