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Experimental investigation of air concentration profiles in a dam bottom outlet by using gray scale images with high resolution

Abstract

Most dams include bottom outlets consisting of tunnels or pipes to control water discharge by using valves or slide gates to regulate water level in reservoirs for service operation or during an emergency. When the gates are partially open, subatmospheric pressure can develop on the downstream side of the gates, leading to possible damage by cavitation and vibration. In order to avoid the latter, an aeration system is usually installed downstream of the gates to keep the local pressure above the vapor pressure for preventing cavitation. The present study aims to estimate the air concentration profiles for a series of hydraulic jumps that occur on the downstream side of a partially open gate of a bottom outlet using a flow visualization technique, known as Image Processing Procedure (IPP), which consists of the Image Editing and the Pixel Intensity Matrix algorithms. This technique uses a high-speed camera and is based on the hypothesis that air concentration profiles can be estimated from the pixel intensity of each photograph, and also offers the possibility to obtain such profiles in any point along the hydraulic jump without disturbing the flow. The results obtained after applying the IPP to the photographs of the experimental study have very good agreement with the profiles obtained with a conductivity probe, indicating that the IPP can be a powerful tool to complement intrusive probe measurements. In addition, to evaluate the capability of the proposed IPP the experimental data were compared with a two-dimensional diffusion equation. Comparisons between predicted and measured results show good correlation demonstrating the potential of the proposed methodology.

Graphical abstract

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Abbreviations

COP:

Cross-over point

IE:

Image editing

IPP:

Image processing procedure

PIM:

Pixel intensity matrix

a, b :

Parameters of the fuzzy logic S function

A :

Area of flow (m2)

AvPI:

Averaged pixel intensity matrix (pi)

AvPIt:

Time average matrix (pi)

C :

Air concentration or void fraction defined as the volume of air per unit volume of air and water

D :

Inner diameter of the pipe (m)

Fr:

Froude number

g :

Acceleration due to gravity (g = 9.81 m2/s)

h :

Distance normal to the bottom of the pipe or water depth (m)

i, j :

Matrix indexes

I Tn :

nTh thresholding function used for editing calibration

K′:

Constant parameter deduced from the mean air concentration

limS :

Water surface upper limit

limSt:

Water surface lower limit

lmf:

Fuzzy logic linear function

n, m :

Matrix dimensions

P:

Wetted perimeter (m)

p, q :

Factors of m and n

pi:

Pixel intensity defined as a single point in a gray scale image

PIi , j :

Pixel intensity matrix

PIf i , j :

Transformed matrix

Ptr, Ptr2:

Threshold values (pi)

Q water :

Flow rate (l/s)

r :

Correlation coefficient

R 2 :

Determination coefficients

RPI:

Resized pixel intensity matrix (pi)

Smf:

Fuzzy logic S function

tanh:

Hyperbolic tangent function

T :

Top width (m)

x, y :

Horizontal and vertical coordinates (m)

y1, y2:

Parameters of the Fuzzy logic linear function

Xi :

Data points in data set X

Yi :

Data points in data set Y

\({\overline{\text{X}}}\) :

Mean of data set X

\({\overline{\text{Y}}}\) :

Mean of data set Y

Y 90 :

Depth where the local air concentration is 90% (m)

ε :

Constant parameter deduced from the mean air concentration

θ :

Angle subtended by the wetted perimeter

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Acknowledgements

The authors are grateful for the financial support from the Dirección General de Asuntos del Personal Académico (DGAPA-UNAM) (Proyecto PAPIIT IN101618).

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Correspondence to Oscar Pozos-Estrada.

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Pozos-Estrada, O., Rojas-Flores, M.E., Avalos-Saucedo, F.V. et al. Experimental investigation of air concentration profiles in a dam bottom outlet by using gray scale images with high resolution. J Vis (2022). https://doi.org/10.1007/s12650-022-00853-8

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  • DOI: https://doi.org/10.1007/s12650-022-00853-8

Keywords

  • Bottom outlet
  • Hydraulic jump
  • Visualization technique
  • Air concentration
  • Pixel intensity