Abstract
The results are presented from an experimental study to investigate three-dimensional turbulence structure profiles, including turbulence intensity and Reynolds stress, of different non-uniform open channel flows over smooth bed in subcritical flow regime. In the analysis, the uniform flow profiles have been used to compare with those of the non-uniform flows to investigate their time-averaged spatial flow turbulence structure characteristics. The measured non-uniform velocity profiles are used to verify the von Karman constant κ and to estimate sets of log-law integration constant Br and wake parameter П, where their findings are also compared with values from previous studies. From κ, Br and П findings, it has been found that the log-wake law can sufficiently represent the non-uniform flow in its non-modified form, and all κ, Br and П follow universal rules for different bed roughness conditions. The non-uniform flow experiments also show that both the turbulence intensity and Reynolds stress are governed well by exponential pressure gradient parameter β equations. Their exponential constants are described by quadratic functions in the investigated β range. Through this experimental study, it has been observed that the decelerating flow shows higher empirical constants, in both the turbulence intensity and Reynolds stress compared to the accelerating flow. The decelerating flow also has stronger dominance to determine the flow non-uniformity, because it presents higher Reynolds stress profile than uniform flow, whereas the accelerating flow does not.
Highlights
The analysis of flow turbulence is commonly performed on the time-averaged velocity, turbulence intensity and Reynolds stress in two-dimensional (2D) flow domain [19]
The results are presented from an experimental study to investigate three-dimensional turbulence structure profiles, including turbulence intensity and Reynolds stress, of different non-uniform open channel flows over smooth bed in subcritical flow regime
Two points can be observed from Eqs. (13)–(14): (a) all D1, D2 and D3 have consistent tendency to decrease from higher values at decelerating flow region to lower values at accelerating flow region in the investigated b range; and (b) it is presented in Eq (14) that k1 [ k2 [ k3. These findings suggest that the decelerating flow has higher 3D turbulence intensity profiles than the accelerating flow; and the turbulence intensity characteristics are more dominantly dictated by the streamwise flow
Summary
The analysis of flow turbulence is commonly performed on the time-averaged velocity, turbulence intensity and Reynolds stress in two-dimensional (2D) flow domain [19]. Studying 3D flow characteristics can provide more descriptive flow information about its turbulence structure, which is useful for various hydraulic engineering applications. The time-averaged flow velocity is often reproduced by logarithmic profile that is normalised by the wall shear velocity. To systematically represent flow velocity, the Prandtl van Karman type velocity distribution’s logarithmic-wall law was utilised by Keulegan [10] in his investigation on rectangular open channel flow. To improve Keulegan’s study, Coles [6] proposed the log-wake law with a wake correction to more precisely represent velocity distribution at the outer flow region where the ratio of flow vertical location to full flow depth (z/h) is bigger than 0.2. Coles’ method has been proven to give better accuracy compared to the log-wall law, as concluded by Song and Graf [29] and Dey and Raikar [7]; as well as in the modified log-wake law study by Yang [32]
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