Abstract

Knowledge of extreme pressures and fluctuations within the stilling basins is of the utmost importance, which may cause potential severe damages. It is complicated to measure the fluctuating pressures of hydraulic jumps in the real-scale structures. Therefore, little information is available on pressure fluctuations in the literature. In this paper, minimal and maximal pressures are analyzed on the flat bed of a stilling basin downstream of an Ogee spillway. Attention has been focused on dimensionless pressures related to the low and high cumulative probabilities of occurrence (P*0.1 and P*99.9%), respectively. The results are presented based on laboratory-scale experiments. These parameters for the relatively high Froude numbers have not been investigated. The total standard uncertainty for the dimensionless mean pressures (P*m) is obtained around 1.87%. Spectral density analysis showed that the dominant frequency in the classical hydraulic jumps is about 4 HZ. Low-frequency of pressure fluctuations indicates the existence of large-scale vortices. In the zone near the spillway toe, P*0.1% reached to negative values around – 0.3. The maximum values of pressure coefficients, namely |CP0.1%|max and CP99.9%max, were achieved around 0.19 and 0.24, respectively. New original expressions were proposed for P*0.1 and P*99.9%, which are useful for estimating extreme pressures.

HIGHLIGHTS

  • Analysis of the minimal and maximal values of pressures (P*0.1% and P*99.9%). It should be noted that most of researchers in the literature usually used the parameters of P*1% and P*99%, or P*min and P*max. In addition, for the first time, analysis of the P*0.1 and P*99.9% values for different incident Froude numbers (Fr1) with relatively high values (7.12 to 9.46) along the free hydraulic jumps. These parameters for the relatively high Froude numbers have not been investigated in the literature.

  • Investigation of the longitudinal distribution of dimensionless pressure coefficients along the hydraulic jumps (CP0.1%, CP99.9% and C'P). It should be noted that most of researchers in the literature usually used the coefficients of CP+ [(Pmax–Pm)/V12/2 g] and CP– [(Pmin–Pm)/V12/2 g]. The results of Alves (2008) showed that the CP+ and CP– values have the wide dispersion, due to the difficulty in measuring absolute extreme values (CP+ and CP–) in reduced models. On the other hand, the longitudinal distribution of the CP99.9% and CP0.1% coefficients has a much smaller dispersion. As stated by Toso & Bowers (1988), the fluctuations related to 1% of cumulative probability of occurrence do not offer conservative pressure values.

  • Evaluation of the power spectral density analysis to determine the dominant frequency of fluctuating pressures in the classical hydraulic jumps. Also, assessment of the probability density functions (PDF) for the fluctuating pressures at different pressure taps.

  • For the first time, calculation of the total standard uncertainty for the multiple variables (P*0.1%, P*99.9%, P*m, CP0.1% and CP99.9%) along the stilling basin and present error bars in the relevant Figures.

  • Propose new original best-fit relationships to estimate the dimensionless extreme pressure data (P*0.1 and P*99.9%) as a function of the dimensionless position along the stilling basin.

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