Abstract
Predicting the accurate hydrodynamic pressure at plunge pool bottoms due to the impact of plunging high-velocity jets is essential in assessing the stability of the bed rock blocks and concrete slabs. In this context, the subsequent scour depth evaluation is essential. The regression-derived model of multiple nonlinear regression (MNLR) and two intelligent models of artificial neural network and adaptive neuro-fuzzy inference system are developed to predict the hydrodynamic pressure mean and hydrodynamic pressure fluctuations at flat and scoured plunge pool bottom. By running statistical analysis on a wide range of large-scale experimental data, it is revealed that, in general the intelligent models outperform the regression-derived equations of MNLR. The average values of RMSE and R2 in the prediction of hydrodynamic pressure coefficients are improved to 0.054 and 0.87, respectively. Nevertheless, due to its simplicity the empirical equations based on MNLR model are accurate enough for engineering applications. These equations predict both the dynamic pressure mean and root mean square of pressure fluctuations at flat bottoms and scoured bottoms more accurately than the available equations for this purpose, with 70% and 90% of data within 20% range of discrepancy, respectively. An empirical equation of pressure fluctuation at SB is introduced for the first time in this study.
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Abbreviations
- C p :
-
Mean dynamic coefficient
- C ׳ p :
-
RMS coefficient of pressures
- C + p :
-
Maximum pressure coefficient
- C − p :
-
Minimum pressure coefficient
- C i :
-
Aeration coefficient
- C * p :
-
Mean dynamic pressures of scoured bottom
- C ׳ * p :
-
RMS value of dynamic pressures of scoured bottom
- D 0 :
-
Diameter of jet at issuance
- D c :
-
Diameter of scour hole
- D j :
-
Jet diameter at tail water surface impact
- Frc :
-
Froude number of scoured pool
- g :
-
Acceleration due to gravity
- H :
-
Pressure head
- H ׳ :
-
RMS volume of pressure
- H max :
-
Maximum pressure head
- H min :
-
Minimum pressure head
- \(\overline{H}_{\rm m}\) :
-
Mean value of pressure
- L :
-
Falling height
- L b :
-
Disintegration length
- N :
-
Pressure sample count
- O :
-
Observed values
- \(\overline{O}\) :
-
Mean predicted values
- P :
-
Predicted values
- Q a :
-
Air discharge
- Q w :
-
Water discharge
- Re:
-
Reynolds number
- t :
-
Depth of scour hole
- Tu:
-
Turbulence intensity
- v' :
-
Velocity fluctuation
- V 0 :
-
Jet velocity at issuance
- V j :
-
Impact jet velocity at tail water surface
- Y :
-
Plunge pool water depth
- ρ :
-
Fluid density
- μ :
-
Dynamic viscosity of fluid
- β :
-
Air–water ratio
- η :
-
Turbulence jet coefficient
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Acknowledgements
Appreciations are extended to Dr. Pedro Manso from EPFL, Switzerland for his constructive discussions regarding the range and validity of the experimental data.
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Fatahi-Alkouhi, R., Shanehsazzadeh, A. & Hashemi, M. Empirical Models for Hydrodynamic Pressure at Plunge Pool Bottoms Due to High-Velocity Jet Impact. Iran J Sci Technol Trans Civ Eng 46, 1359–1374 (2022). https://doi.org/10.1007/s40996-021-00608-9
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DOI: https://doi.org/10.1007/s40996-021-00608-9