Some Insights on Flow over Sharp-Crested Weirs Using Computational Fluid Dynamics: Implications for Enhanced Flow Measurement

Sinclair, Joseph M.; Venayagamoorthy, Subhas K.; Gates, Timothy K.

doi:10.1061/(asce)ir.1943-4774.0001652

J. Irrig. Drain Eng.

2022

DOI: 10.1061/(asce)ir.1943-4774.0001652

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Some Insights on Flow over Sharp-Crested Weirs Using Computational Fluid Dynamics: Implications for Enhanced Flow Measurement

Joseph M. Sinclair

Subhas K. Venayagamoorthy

Timothy K. Gates

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Cited by 3 publications

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On the turbulent viscosity parameter C_μ in the k–ϵ model

Mishra,

Venayagamoorthy

2024

Flow

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The Reynolds-averaged Navier–Stokes (RANS) models depend on empirical constants to close the Reynolds stress terms. The empirical constants were obtained using experiments conducted at low Reynolds numbers several decades ago. In this paper, we revisit the turbulent viscosity parameter $C_\mu$ , based on the stress–intensity ratio $c^2 = {|\overline {uw}|}/{k}$ . Here, $\overline {|uw|}$ and $k$ are the absolute values of the Reynolds stress and turbulent kinetic energy, respectively. Through a priori comparisons, we find that the currently accepted value of $C_\mu = 0.09$ does not agree with the latest direct numerical simulation (DNS) and experimental datasets of wall-bounded turbulent planar flows. Therefore, a new value is suggested by averaging $c^2$ in the equilibrium region, where the production ( $\mathcal {P}$ ) of $k$ is within 10 % of the dissipation rate ( $\epsilon$ ), and consequently, $c^4 \approx C_\mu$ . We evaluate flows up to friction Reynolds number $Re_\tau \approx 10\,000$ and find that with increasing $Re_\tau$ , $C_\mu$ approaches a value of 0.06, which is almost 50 % lower than the prevalent value of 0.09. Finally, we perform an a priori test with the new (proposed) value of $C_\mu = 0.06$ to show that the estimated turbulent viscosity $\nu _T$ for wall-bounded flows is in much closer agreement with the exact (DNS) values than when $\nu _T$ is estimated using $C_\mu = 0.09$ .

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On the turbulent viscosity parameter C_μ in the k–ϵ model

Mishra,

Venayagamoorthy

2024

Flow

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A Novel and Enhanced Calibration of the Tilting Weir as a Flow Measurement Structure

Pugh,

Venayagamoorthy,

Gates

et al. 2024

J. Hydraul. Eng.

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Theoretical Correction of Viscosity Coefficient Measurement by Falling Ball Method

Wang

Cui

et al. 2022

International Transactions on Electrical Energy Systems

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The measurement of viscosity coefficient of liquids is vital in plentiful fields. There are numerous ways to measure the viscosity coefficient such as capillary and rotary rheometry in which falling ball method is mostly widely used. The uncertainty of the terminal velocity and the limit of the viscosity coefficient scale are the principled disadvantages of the method. In our work, the relationship between the displacement and time is obtained by integral calculation. What’s more, we considered the radius of the ball, the radius of the graduated cylinder, and the height of the graduated cylinder by theoretical correction of the stokes expression. The new correction expression broadens the measured viscosity coefficient scale and also improves the precision dramatically. Experimental verification is also well processed which fits well with our theory. The deviation between the viscosity coefficient of castor oil measured by the new correction method and the standard value is only 0.045. The relationship between displacement and time is consistent with the theoretical prediction, and the room mean square error of the two is 0.065. Based on them, this method can be widely used in scientific researches and teaching practices.

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Some Insights on Flow over Sharp-Crested Weirs Using Computational Fluid Dynamics: Implications for Enhanced Flow Measurement

Cited by 3 publications

References 21 publications

On the turbulent viscosity parameter C_μ in the k–ϵ model

On the turbulent viscosity parameter C_μ in the k–ϵ model

A Novel and Enhanced Calibration of the Tilting Weir as a Flow Measurement Structure

Theoretical Correction of Viscosity Coefficient Measurement by Falling Ball Method

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Some Insights on Flow over Sharp-Crested Weirs Using Computational Fluid Dynamics: Implications for Enhanced Flow Measurement

Cited by 3 publications

References 21 publications

On the turbulent viscosity parameter C μ in the k–ϵ model

On the turbulent viscosity parameter C μ in the k–ϵ model

A Novel and Enhanced Calibration of the Tilting Weir as a Flow Measurement Structure

Theoretical Correction of Viscosity Coefficient Measurement by Falling Ball Method

Contact Info

Product

Resources

About

On the turbulent viscosity parameter C_μ in the k–ϵ model

On the turbulent viscosity parameter C_μ in the k–ϵ model