Abstract
Stepped spillways have higher energy dissipation than smoother hydraulic structures used to divert flood discharges. The inception point related to air entrainment is, however, located further upstream causing an undesired bulking of the flow depth. For large discharge rates and for straight stepped spillways, the skimming flow regime may be assumed two dimensional; this is an attractive feature for the application of nonintrusive flow visualization techniques because these methods measure the flow characteristics in the vicinity of the sidewalls which are likely to correlate with the flow at the centre of the flume. This paper tests the hypothesis that such techniques can be used to measure the flow inside the flume. The hypothesis is tested against measurements taken with an intrusive probe. Void fraction contour lines and velocity fields are obtained in 12 different stepped spillway configurations using the image processing procedure and the bubble image velocimetry, respectively. The void fraction and velocity results are overall consistent with the probe measurements. The velocity fields show a persistent underestimation of the probe measurements which can at least be partially explained by sidewall effects and possible probe’s overestimation.
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Notes
For BIV replace: Ptr2, smfUL and smfLL, by overlap (OV), SNR threshold (SNR) and of peak height filter (Peak).
\({\text{For BIV replace}}\left\{ {\begin{array}{*{20}c} {Ptr2 \mathop \to \limits_{dx = 20} \left[ {160:240} \right]} \\ {\begin{array}{*{20}c} {smfUl\mathop \to \limits_{dx = 20} \left[ {180:220} \right]} \\ {\begin{array}{*{20}c} {smfLL\mathop \to \limits_{dx = 20} \left[ {80:140} \right]} \\ \end{array} } \\ \end{array} } \\ \end{array} } \right.\) \({\text{by}}\left\{ {\begin{array}{*{20}c} {OL \mathop \to \limits_{dx = 0.25} \left[ {0.25:0.75} \right]} \\ {\begin{array}{*{20}c} {SNR\mathop \to \limits_{dx = 0.1} \left[ {1.1:1.5} \right]} \\ {\begin{array}{*{20}c} {Peak\mathop \to \limits_{dx = 0.1} \left[ {0.2:0.5} \right]} \\ \end{array} } \\ \end{array} } \\ \end{array} } \right..\)
Normalization is only done at the end with the maximum value obtained from all matrices. The normalization enables an easier crosscomparison between matrices.
For BIV replace: nf = (100, 400, 800, 1,200) and gr = (2, 4, 8, 16, 32) by nf = (50, 100, 200, 400, 800, 1,200) and interrogation window size iws = (12, 16, 24, 32, 40).
Abbreviations
 Dx:

Calibration step discretization
 C, Cp, Co:

Void fraction defined as the volume of air per unit volume (air concentration), void fraction measured using the IPP and the dualtip conductivity probes
 Fr*:

Froude number related to stepinduced macroroughness
 g:

Acceleration due to gravity
 gr:

IPP grid resolution
 h_{90} :

Water depth for void fraction = 90 %
 i, j:

Matrix indexes
 iws:

BIV interrogation window size
 \(I_{Tn}^{{}}\) :

IPP nth threshold function
 lim S:

IPP water surface upper limit
 lim St:

IPP water surface lower limit
 lmf :

IPP fuzzy logic linear function
 np :

Number of points measured along the void fraction profile
 nf :

Number of frames (images)
 OL:

BIV overlap parameter
 Peak:

BIV peak height filter parameter
 px:

Pixel units
 \(PI_{i,j} ,\) \(PI_{{_{i,j} }}^{1 \ldots 4}\) :

IPP matrixes of pixel intensity
 \(PI_{i,j}^{f}\) :

IPP transformed matrix
 \(medPI_{i}\) :

IPP average pixel intensity per row of the \(PI_{i,j}\)
 \(vectPI_{i}\) :

IPP vector of the differences between every two \(medPI_{i}\) values distancing k rows apart
 Ptr1, Ptr2, Ptr3:

IPP threshold values
 Q:

Specific discharge
 SNR:

BIV threshold parameter for signaltonoise ratio filter
 Smf :

IPP fuzzy logic S function
 S:

Step height
 S(c.c):

Calibration score
 t_{air} :

Total duration time of air
 u, u_{p}, u_{o} :

Flow velocity in chute direction, flow velocity measured using the BIV and the dualtip conductivity probes,
 x, z:

Horizontal and vertical distances (related to the pseudobottom)
 x′, z′:

Horizontal and vertical distances (related to the step surfaces)
 ϕ:

Chute angle
 Δt_{e} :

Travelling time of detected air bubbles
 Δx_{e} :

Distance in flow direction of the two electrodes
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Acknowledgments
The first and third authors acknowledge the support of the Foundation for Science and Technology, the Operacional Temático Factores de Competitividade (COMPETE) program and the Fundo Europeu de Desenvolvimento Regional (FEDER) through project PTDC/AACAMB/101197/2008.
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Leandro, J., Bung, D.B. & Carvalho, R. Measuring void fraction and velocity fields of a stepped spillway for skimming flow using nonintrusive methods. Exp Fluids 55, 1732 (2014). https://doi.org/10.1007/s0034801417326
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DOI: https://doi.org/10.1007/s0034801417326