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Experimental investigation of bubbly flow and turbulence in hydraulic jumps

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Abstract

Many environmental problems are linked to multiphase flows encompassing ecological issues, chemical processes and mixing or diffusion, with applications in different engineering fields. The transition from a supercritical flow to a subcritical motion constitutes a hydraulic jump. This flow regime is characterised by strong interactions between turbulence, free surface and air–water mixing. Although a hydraulic jump contributes to some dissipation of the flow kinetic energy, it is also associated with increases of turbulent shear stresses and the development of turbulent eddies with implications in terms of scour, erosion and sediment transport. Despite a number of experimental, theoretical and numerical studies, there is a lack of knowledge concerning the physical mechanisms involved in the diffusion and air–water mixing processes within hydraulic jumps, as well as on the interaction between the free-surface and turbulence. New experimental investigations were undertaken in hydraulic jumps with Froude numbers up to Fr = 8.3. Two-phase flow measurements were performed with phase-detection conductivity probes. Basic results related to the distributions of void fraction, bubble frequency and mean bubble chord length are presented. New developments are discussed for the interfacial bubble velocities and their fluctuations, characterizing the turbulence level and integral time scales of turbulence representing a “lifetime” of the longitudinal bubbly flow structures. The analyses show good agreement with previous studies in terms of the vertical profiles of void fraction, bubble frequency and mean bubble chord length. The dimensionless distributions of interfacial velocities compared favourably with wall-jet equations. Measurements showed high turbulence levels. Turbulence time scales were found to be dependent on the distance downstream of the toe as well as on the distance to the bottom showing the importance of the lower (channel bed) and upper (free surface) boundary conditions on the turbulence structure.

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Abbreviations

C:

Void fraction defined as the volume of air per unit volume of mixture

Cmax :

Maximum void fraction in the air bubble diffusion layer

Dt :

Turbulent diffusivity (m2/s) of air bubbles in air–water flow

D* :

Dimensionless turbulent diffusivity: D* = Dt/(U1d1)

dmbcl :

Mean bubble chord size (m)

d1 :

Upstream flow depth (m)

F:

Bubble count rate (Hz) or bubble frequency

Fmax :

Maximum bubble count rate (Hz) at a given cross-section

Fr:

Upstream Froude number

g:

Acceleration of gravity: g = 9.80 m/s2 in Brisbane (Australia)

hc :

Channel height (m)

Lc :

Channel length (m)

lc :

Channel width (m)

Nab :

Number of air bubbles per record

Q:

Water discharge (m3/s)

Re:

Reynolds number (Re = ρU1d1/μ)

Rxx :

Normalised auto-correlation function (reference probe)

Rxz :

Normalised cross-correlation function between two probes output signals

(Rxz)max :

Maximum cross-correlation coefficient between two probes output signals

Tu:

Measure of the turbulence level in the air–water flow

Txx :

Auto-correlation integral time scale (s)

T0.5 :

Characteristic time lag for which Rxx = 0.5 (s)

U1 :

Depth-averaged flow velocity upstream of the hydraulic jump

V:

Interfacial velocity (m/s)

Vmax :

Maximum velocity measured in a cross-section (m/s)

x:

Longitudinal distance from the upstream gate (m)

x1 :

Longitudinal distance from the gate to the jump toe (m)

y:

Distance measured normal to the bed channel (m)

y*:

Distance measured normal to the channel bed corresponding to the boundary between the turbulent shear layer and the mixing layer

yCmax :

Distance normal to the jet support where C = Cmax

yFmax :

Distance normal to the jet support where F = Fmax

z:

Transverse distance from the channel centreline

δ :

Boundary layer thickness (m)

μ :

Dynamic viscosity of water (Pa s)

ρ :

Density of water (kg/m3)

Δx :

Longitudinal distance between probe sensors (m)

τ 0.5 :

Characteristic time lag for which Rxz = 0.5(Rxz)max

1:

Upstream flow conditions

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Authors and Affiliations

  1. ESTACA Campus Ouest, Parc Universitaire de Laval – Changé, RueGeorges Charpak, BP 53061, Laval Cedex 9, France

    Frédéric Murzyn

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

    Hubert Chanson

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  1. Frédéric Murzyn
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  2. Hubert Chanson
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Correspondence to Frédéric Murzyn.

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Murzyn, F., Chanson, H. Experimental investigation of bubbly flow and turbulence in hydraulic jumps. Environ Fluid Mech 9, 143–159 (2009). https://doi.org/10.1007/s10652-008-9077-4

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