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Measuring void fraction and velocity fields of a stepped spillway for skimming flow using non-intrusive methods

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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 non-intrusive 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

  1. For BIV replace: Ptr2, smfUL and smfLL, by overlap (OV), SNR threshold (SNR) and of peak height filter (Peak).

  2. \({\text{For BIV replace}}\left\{ {\begin{array}{*{20}c} {Ptr2 \mathop \to \limits_{dx = 20} \left[ {160:240} \right]} \\ {\begin{array}{*{20}c} {smfUl\mathop \to \limits_{dx = 20} \left[ {180:220} \right]} \\ {\begin{array}{*{20}c} {smfLL\mathop \to \limits_{dx = 20} \left[ {80:140} \right]} \\ \end{array} } \\ \end{array} } \\ \end{array} } \right.\) \({\text{by}}\left\{ {\begin{array}{*{20}c} {OL \mathop \to \limits_{dx = 0.25} \left[ {0.25:0.75} \right]} \\ {\begin{array}{*{20}c} {SNR\mathop \to \limits_{dx = 0.1} \left[ {1.1:1.5} \right]} \\ {\begin{array}{*{20}c} {Peak\mathop \to \limits_{dx = 0.1} \left[ {0.2:0.5} \right]} \\ \end{array} } \\ \end{array} } \\ \end{array} } \right..\)

  3. Normalization is only done at the end with the maximum value obtained from all matrices. The normalization enables an easier cross-comparison between matrices.

  4. 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 dual-tip conductivity probes

Fr*:

Froude number related to step-induced macro-roughness

g:

Acceleration due to gravity

gr:

IPP grid resolution

h90 :

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 signal-to-noise ratio filter

Smf :

IPP fuzzy logic S function

S:

Step height

S(c.c):

Calibration score

tair :

Total duration time of air

u, up, uo :

Flow velocity in chute direction, flow velocity measured using the BIV and the dual-tip conductivity probes,

x, z:

Horizontal and vertical distances (related to the pseudo-bottom)

x′, z′:

Horizontal and vertical distances (related to the step surfaces)

ϕ:

Chute angle

Δte :

Travelling time of detected air bubbles

Δxe :

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/AAC-AMB/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 non-intrusive methods. Exp Fluids 55, 1732 (2014). https://doi.org/10.1007/s00348-014-1732-6

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  • DOI: https://doi.org/10.1007/s00348-014-1732-6

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