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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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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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  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).



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


Froude number related to step-induced macro-roughness


Acceleration due to gravity


IPP grid resolution

h90 :

Water depth for void fraction = 90 %

i, j:

Matrix indexes


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)


BIV overlap parameter


BIV peak height filter parameter


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


Specific discharge


BIV threshold parameter for signal-to-noise ratio filter

Smf :

IPP fuzzy logic S function


Step height


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)


Chute angle

Δte :

Travelling time of detected air bubbles

Δxe :

Distance in flow direction of the two electrodes


  • Amador A, Puertas J (2004) Characterization of the flow field in a stepped spillway by PIV. 12th International symposium on applications of laser techniques (1) 1–10

  • Bazaraa MS, Sherali HD, Shetty CM (1993) Nonlinear programming, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Boes RM (2000) Zweiphasenströmung und Energieumsetzung an Großkaskaden. PhD thesis, ETH Zürich

  • Bung DB (2011a) Developing flow in skimming flow regime on embankment stepped spillways. J Hydraul Res 49(5):639–648

    Article  Google Scholar 

  • Bung DB (2011b) Non-intrusive measuring of air–water flow properties in self-aerated stepped spillway flow. Proceedings of the 34th world congress of the international association for hydro- environment research and engineering: 33rd Hydrology and water resources symposium and 10th conference on hydraulics in water engineering

  • Bung DB (2013) Non-intrusive detection of air–water surface roughness in self-aerated chute flows. J Hydraul Res 51(3):332–329. doi:10.1080/00221686.2013.777373

  • Carvalho RF, Amador AT (2008) Flow field over a stepped spillway: physical and numerical approach. In: IAHR – symposium on hydraulic structures (IAHR), international symposium on hydraulic structures (IAHR), 20–24 Oct 2008, China

  • Chanson H (1993) Stepped spillway flows and air entrainment. Can J Civil Eng 20(3):422–435

  • Chanson H (2007) Bubbly flow structure in hydraulic jump. Eur J Mech - B/Fluids, 26(3):367–384

  • Chanson H, Felder S (2010) Turbulence measurements in air–water self-aerated flows: basic analysis and results. In: Curtis JS, Balachandar S (eds) 7th International conference on multiphase flow ICMF 2010. Tampa FL, USA, pp 1–11

  • Chanson H, Toombes L (2004) Hydraulics of stepped chutes: the transition flow L’ hydraulique des chutes en marches d’ escalier : l’ écoulement de transition. J Hydraul Eng 42(1):43–54

    Article  Google Scholar 

  • Felder S, Guenther P, Chanson H (2012) Air–water flow properties and energy dissipation on stepped spillways: a physical study of several pooled. The University of Queensland School of Civil Engineering, Queensland

    Google Scholar 

  • Gonzalez CA (2005) An experimental study of free-surface aeration on embankment stepped chutes. PhD thesis, The University of Queensland, Queensland

    Google Scholar 

  • Kimmoun O, Branger H (2007) A particle image velocimetry investigation on laboratory surf-zone breaking waves over a sloping beach. J Fluid Mec 588:353–397

  • Kramer K (2004) Mitteilungen development of aerated chute flow. PhD thesis ETH Zurich, Switzerland

    Google Scholar 

  • Kucukali S, Chanson H (2008) Turbulence measurements in the bubbly flow region of hydraulic jumps. Exp Therm Fluid Sci 33(1):41–53

  • Leandro J, Carvalho R, Chachereau Y, Chanson H (2012) Estimating void fraction in a hydraulic jump by measurements of pixel intensity. Exp Fluids 52(5):1307–1318. doi:10.1007/s00348-011-1257-1

  • Lennon JM, Hill DF (2006) Particle image velocity measurements of undular and hydraulic jumps. J Hydraul Eng 132(12):1283–1294

  • Lin C, Hsieh S-C, Kuo K-J, Chang K-A (2008) Periodic oscillation caused by a flow over a vertical drop pool. J Hydraul Eng 134(7):948–960

  • Mossa M, Tolve U (1998) Flow visualization in bubbly two-phase hydraulic jump. J Fluid Eng 120:160–165

    Article  Google Scholar 

  • Murillo RE (2006) Experimental study of the development flow region on stepped chutes. PhD, University of Manitoba, Canada

    Google Scholar 

  • Pfister M, Hager WH (2011) Self-entrainment of air on stepped spillways. Int J Multiph Flow 37(2):99–107

  • Rajaratnam N (1962) An experimental study of air entrainment characteristics of the hydraulic jump. J Inst Eng India 42:247–273

    Google Scholar 

  • Resch F, Leutheusser H, Alemum S (1974) Bubbly two-phase flow in hydraulic jump. J Hydraul Div ASCE 100:137–149

    Google Scholar 

  • Ryu Y, Chang K-A, Lim H-J (2005) Use of bubble image velocimetry for measurement of plunging wave impinging on structure and associated green water. Meas Sci Technol 16(10):1945–1953

  • Sveen JK (2004) An introduction to MatPIV v. 1.6.1. Center for Mathematical Sciences, Department of Applied Mathematics and Theoretical Physics, University of Cambridge

  • Thorwarth J (2008) Hydraulisches verhalten von treppengerinnen mit eingetieften stufen - selbstinduzierte abflussinstationaritäten und energiedissipation (Hydraulics of pooled stepped chutes: self induced unsteady flow and energy dissipation), in German. PhD, RWTH Aachen, Germany

    Google Scholar 

  • Toombes L, Chanson H (2008) Flow patterns in nappe flow regime down low gradient stepped chutes Configurations des écoulements en nappe le long des déversoirs en gradins à pente faible. J Hydraul Res 46(1):4–14

    Article  Google Scholar 

  • Yasuda Y, Ohtsu I (1999) Flow resistance of skimming flow in stepped channels. Proceeding 28th IAHR congress, Graz, Austria, Session B14 (CD-ROM)

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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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Correspondence to J. Leandro.

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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).

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