Predictive Modeling the Free Hydraulic Jumps Pressure through Advanced Statistical Methods

Abstract

Pressure fluctuations beneath hydraulic jumps potentially endanger the stability of stilling basins. This paper deals with the mathematical modeling of the results of laboratory-scale experiments to estimate the extreme pressures. Experiments were carried out on a smooth stilling basin underneath free hydraulic jumps downstream of an Ogee spillway. From the probability distribution of measured instantaneous pressures, pressures with different probabilities could be determined. It was verified that maximum pressure fluctuations, and the negative pressures, are located at the positions near the spillway toe. Also, minimum pressure fluctuations are located at the downstream of hydraulic jumps. It was possible to assess the cumulative curves of pressure data related to the characteristic points along the basin, and different Froude numbers. To benchmark the results, the dimensionless forms of statistical parameters include mean pressures (P*m), the standard deviations of pressure fluctuations (σ*X), pressures with different non-exceedance probabilities (P*k%), and the statistical coefficient of the probability distribution (Nk%) were assessed. It was found that an existing method can be used to interpret the present data, and pressure distribution in similar conditions, by using a new second-order fractional relationships for σ*X, and Nk%. The values of the Nk% coefficient indicated a single mean value for each probability.

A Novel Comparative Statistical and Experimental Modeling of Pressure Field in Free Jumps along the Apron of USBR Type I and II Dissipation Basins

“…The instantaneous pressures were measured with pressure transducers (Atek BCT 110 series with 100 mbar-A-G1/4 model). The pressure transducers used a 6-channel digital board and have an accuracy of ±0.5% within the range of −1.0 to 1.0 m [24][25][26]. Pressure transducers were calibrated before the experiments using a static pressure gauge in the laboratory.…”

“…Figure 8 presents the distribution of the experimental values of the N K% coefficient obtained from the pressure data along basin II for different probabilities from 0.1% to 99.9% with different flow conditions in free jumps. The distribution of the N K% coefficient along basin I with the free jumps has been previously investigated by Mousavi et al [25].…”

“…For instance, the longitudinal distribution of the experimental and estimated data of the P * K% parameter with different probabilities along basin II is shown in Figure 10. The distribution of the P * K% parameter for different probabilities of occurrence along basin I with the free jumps has been previously investigated by Mousavi et al [25].…”

“…Mousavi et al [24] focused on the minimal and maximal pressures, the pressure coefficients, the power spectral density (PSD), the probability density function (PDF), and the uncertainty analysis of the pressures along a USBR Type I basin (basin I ). Mousavi et al [25] assessed the statistical parameters of free jumps, including mean pressure (P * m ), the standard deviation of pressure fluctuations (σ * X ), the probability distribution coefficient (N K% ), and the pressures with different probabilities (P * K% ) along basin I . Mousavi et al [26] evaluated artificial intelligence models to estimate the C P coefficient for the free and submerged jumps at the bottom of a USBR Type II basin (basin II ).…”

Numerical Study of Fluctuating Pressure on Stilling Basin Slab with Sudden Lateral Enlargement and Bottom Drop

“…Liu et al [2] discussed fluctuating pressure propagation within lining slab joints in stilling basins. Seyed Nasrollah et al [3] advanced and predicted fluctuating pressure and extreme pressure beneath hydraulic jumps with a statistical method.…”