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Turbulent time and length scale measurements in high-velocity open channel flows

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Abstract

In high-velocity open channel flows, the measurements of air–water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air–water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8E+5 to 7.1E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air–water depth Y 90. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95–0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.

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Abbreviations

C :

void fraction defined as the volume of air per unit volume of air and water; it is also called air concentration or local air content

C mean :

depth-average void fraction defined in terms of Y 90:C mean =  1 − d/Y 90

D H :

hydraulic diameter (m) also called equivalent pipe diameter

D o :

dimensionless constant

d :

equivalent clear water flow depth defined as \({d = {\int\nolimits_{C = 0}^{C = 0.90} {(1 - C)\,\hbox{d}y}}}\)

d c :

critical flow depth (m): \({d_{\rm c} = \root 3\of{{\it{Q}_{\it w} ^{2} /(gW^{2})}}}\)

F :

air bubble count rate (Hz) or bubble frequency defined as the number of detected air bubbles per unit time

F max :

maximum bubble count rate (Hz) at a cross-section

g :

gravity constant: g = 9.80 m/s2 in Brisbane, Australia

h :

vertical step height (m)

K′:

dimensionless integration constant

K*:

dimensionless constant

L xx :

air–water advection integral length scale (m): L xx = VT xx

L xy :

transverse/streamwise air–water integral turbulent length scale (m): \({L_{{\rm xy}} = {\int\limits_{Y = 0}^{Y_{{\rm max}}} {(R_{{\rm xy}})_{{\rm max}}\,\hbox{d}Y}}}\)

(L xx)max :

maximum advection air–water length scale (m) in a cross-section

(L xy)max :

maximum air–water integral length scale (m) in a cross-section

l :

horizontal step length (m)

N :

power law exponent

Q w :

water discharge (m3/s)

Re :

Reynolds number defined in terms of the hydraulic diameter

R xx :

normalised auto-correlation function

R xy :

normalised cross-correlation function between two probe output signals

(R xy)max :

maximum cross-correlation between two probe output signals

S o :

bed slope: S o = sin θ

T :

time lag (s) for which R xy = (R xy)max

T :

integral turbulent time scale (s) characterising large eddies advecting the air bubbles

Tu:

turbulence intensity defined as Tu = u′/V

T xx :

auto-correlation time scale (s): \({T_{{\rm xx}} = {\int\nolimits_{\tau = 0}^{\tau = \tau (R_{{\rm xx}} = 0)} {R_{{\rm xx}} (\tau)\,\hbox{d}\tau}}}\)

T xy :

cross-correlation time scale (s): \({T_{{\rm xy}} = {\int\nolimits_{\tau = \tau (R_{{\rm xy}} = (R_{{\rm xy}})_{{\rm max}})}^{\tau = \tau (R_{{\rm xy}} = 0)} {R_{{\rm xy}} (\tau)\,\hbox{d}\tau}}}\)

T 0.5 :

characteristic time lag (s) for which R xx = 0.5

T max :

maximum integral time scale (s) in a cross-section

(T xy):

maximum cross-correlation time scale (s) in a cross-section

U w :

flow velocity (m/s): U w = Q w /(dW)

u′:

root mean square of longitudinal component of turbulent velocity (m/s)

V :

interfacial velocity (m/s)

V c :

critical flow velocity (m/s)

V 90 :

characteristic interfacial velocity (m/s) where C = 0.90

W :

channel width (m)

x :

distance along the channel bottom (m)

Y :

separation distance (m) between two phase-detection probe sensors

Y 90 :

characteristic depth (m) where the void fraction is 90%

y :

distance (m) measured normal to the invert (or channel bed)

y′:

dimensionless distance (m) normal to the invert (or channel bed): y′ = y/Y 90

z :

transverse distance (m) from the channel centreline

Δx :

streamwise separation distance (m) between sensor

Δz :

transverse separation distance (m) between sensor

μ:

dynamic viscosity (Pa s)

μw :

water dynamic viscosity (Pa s)

θ:

angle between the pseudo-bottom formed by the step edges and the horizontal

ρ:

density (kg/m3)

ρw :

water density (kg/m3)

τ :

time lag (s)

τ 0.5 :

characteristic time lag τ for which R xy = 0.5(R xy)max

χ:

dimensionless parameter: χ =  K′ − y′/(2D o) +  (y′ − 1/3)3 /(3D o)

Ø:

diameter (m)

w:

water flow

xx:

auto-correlation of reference probe signal

xy:

cross-correlation

90:

flow conditions where C = 0.90

References

  • Amador A, Sanchez-Juny M, Dolz J, Sanchez-Tembleque F, Puertas J (2004) Velocity and pressure measurements in skimming flow in stepped spillways. In: Proceedings of the international conference on hydraulics of dams and river structures, Tehran, Iran, Balkema Publ., Netherlands, pp 279–285

  • Barenblatt GI (1994) Scaling, phenomena in fluid mechanics. Inaugural lecture delivered before the University of Cambridge on 3 May 1993, Cambridge University Press, UK, 49 pp

    Google Scholar 

  • Barenblatt GI (1996) Scaling, self-similarity, and intermediate asymptotics. Cambridge University Press, UK, 386 pp

    MATH  Google Scholar 

  • Boes RM (2000) Scale effects in modelling two-phase stepped spillway flow. In: Proceedings of the international workshop on hydraulics of stepped spillways, Balkema Publ., Zürich, Switzerland, pp 53–60

  • Cain P, Wood IR (1981a) Instrumentation for aerated flow on spillways. J Hydraul Div 107:1407–1424

    Google Scholar 

  • Cain P, Wood IR (1981b) Measurements of self-aerated flow on a spillway. J Hydraul Div 107:1425–1444

    Google Scholar 

  • Carosi G, Chanson H (2006) Air–water time and length scales in skimming flows on a stepped spillway. Application to the spray characterisation. Report no. CH59/06, Division of Civil Engineering, The University of Queensland, Brisbane, Australia, July, 142 pp

  • Chang KA, Lim HJ, Su CB (2003) Fiber optic reflectometer for velocity and fraction ratio measurements in multiphase flows. Rev Scientific Instrum 74:3559–3565, Discussion: 2004, 75:284–286

    Google Scholar 

  • Chanson H (1997b) Air bubble entrainment in open channels. Flow structure and bubble size distributions. Int J Multiphase Flow 23:193–203

    Article  Google Scholar 

  • Chanson H (1997a) Air bubble entrainment in free-surface turbulent shear flows. Academic, London, UK, 401 pp

    Google Scholar 

  • Chanson H (2001) The hydraulics of stepped chutes and spillways. Balkema, Lisse, The Netherlands, 418 pp

    Google Scholar 

  • Chanson H (2002) Air–water flow measurements with intrusive phase-detection probes. Can we Improve their interpretation? J Hydraul Eng 128:252–255

    Article  Google Scholar 

  • Chanson H, Gonzalez CA (2005) Physical modelling and scale effects of air–water flows on stepped spillways. J Zhejiang Univ Sci 6A:243–250

    Article  Google Scholar 

  • Chanson H, Toombes L (1997) Flow aeration at stepped cascades. Research report no. CE155, Department of Civil Engineering, University of Queensland, Australia, June, 110 pp

  • Chanson H, Toombes L (2002) Air–water flows down stepped chutes: turbulence and flow structure observations. Int J Multiphase Flow 27:1737–1761

    Article  Google Scholar 

  • Crowe C, Sommerfield M, Tsuji Y (1998) Multiphase flows with droplets and particles. CRC Press, Boca Raton, USA, 471 pp

    Google Scholar 

  • Euh DJ, Yun BJ, Song CH (2006) Benchmarking of the five-sensor probe method for a measurement of an interfacial area concentration. Exp Fluids 41:463–478

    Article  Google Scholar 

  • Gonzalez CA (2005) An experimental study of free-surface aeration on embankment stepped chutes. Ph.D. thesis, Department of Civil Engineering, The University of Queensland, Brisbane, Australia, 240 pp

  • Hayes MH (1996) Statistical, digital signal processing and modeling. Wiley, New York, USA

    Google Scholar 

  • Herringe RA, Davis MR (1974) Detection of instantaneous phase changes in gas–liquid mixtures. J Phys E: Sci Inst 7:807–812

    Article  Google Scholar 

  • Hoyt JW, Sellin RHJ (1989) Hydraulic jump as ’mixing layer’. J Hydraul Eng 115:1607–1614

    Article  Google Scholar 

  • Jones OC, Delhaye JM (1976) Transient and statistical measurement techniques for two-phase flows: a critical review. Int J Multiphase Flow 3:89–116

    Article  Google Scholar 

  • Kim S, Fu XY, Wang X, Ishii M (2000) Development of the miniaturized four-sensor conductivity probe and the signal processing scheme. Int J Heat Mass Transf 43:4101–4118

    Article  MATH  Google Scholar 

  • Ohtsu I, Yasuda Y (1997) Characteristics of flow conditions on stepped channels. In: Proceedings of the 27th IAHR Biennial Congress, San Francisco, USA, Theme D, pp 583–588

  • Ruff JF, Frizell KH (1994) Air concentration measurements in highly-turbulent flow on a steeply-sloping chute. In: Proceedings of the hydraulic engineering conference, vol 2. ASCE, Buffalo, USA, pp 999–1003

  • Toombes L (2002) Experimental study of air–water flow properties on low-gradient stepped cascades. Ph.D. thesis, Department of Civil Engineering, The University of Queensland, Brisbane, Australia

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Acknowledgments

The writers acknowledges the technical assistance of Graham ILLIDGE and Clive BOOTH.

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Authors and Affiliations

  1. Division of Civil Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia

    Hubert Chanson & Giovanna Carosi

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  1. Hubert Chanson
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  2. Giovanna Carosi
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Correspondence to Hubert Chanson.

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Chanson, H., Carosi, G. Turbulent time and length scale measurements in high-velocity open channel flows. Exp Fluids 42, 385–401 (2007). https://doi.org/10.1007/s00348-006-0246-2

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