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Total pressure fluctuations and two-phase flow turbulence in hydraulic jumps

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Abstract

The large-scale turbulence and high air content in a hydraulic jump restrict the application of many traditional flow measurement techniques. This paper presents a physical modelling of hydraulic jump, where the total pressure and air–water flow properties were measured simultaneously with intrusive probes, namely a miniature pressure transducer and a dual-tip phase-detection probe, in the jump roller. The total pressure data were compared to theoretical values calculated based upon void fraction, water depth and flow velocity measured by the phase-detection probe. The successful comparison showed valid pressure measurement results in the turbulent shear region with constant flow direction. The roller region was characterised by hydrostatic pressure distributions, taking into account the void fraction distributions. The total pressure fluctuations were related to both velocity fluctuations in the air–water flow and free-surface dynamics above the roller, though the time scales of these motions differed substantially.

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Abbreviations

C :

Time-averaged void fraction

C max :

Local maximum time-averaged void fraction in the shear flow region

D # :

Dimensionless diffusivity in the turbulent shear region

D*:

Dimensionless diffusivity in the free-surface region

d 1 :

Inflow water depth immediately upstream of the jump toe (m)

F :

Bubble count rate (Hz)

F clu :

Longitudinal bubble cluster count rate (Hz)

(F clu)max :

Maximum cluster count rate in the shear flow region (Hz)

F fs :

Characteristic free-surface fluctuation frequency (Hz)

F max :

Maximum bubble count rate in the shear flow region (Hz)

F (H)p :

Upper total pressure fluctuation frequency (Hz)

F (L)p :

Lower total pressure fluctuation frequency (Hz)

Fr 1 :

Inflow Froude number, \(Fr_{1} = {{V_{1} } \mathord{\left/ {\vphantom {{V_{1} } {\sqrt {g \times d_{1} } }}} \right. \kern-0pt} {\sqrt {g \times d_{1} } }}\)

g :

Gravity acceleration (m/s2)

h :

Upstream gate opening (m)

L r :

Length of jump roller (m)

P :

Time-averaged total pressure (Pa)

P k :

Kinetic pressure (Pa)

P max :

Maximum mean total pressure in the shear flow region (Pa)

P o :

Piezometric pressure (Pa)

p′:

Standard deviation of total pressure (Pa)

p′max :

Maximum total pressure fluctuation (Pa)

Q :

Flow rate (m3/s)

Re :

Reynolds number, \(Re \, = {{\rho \times V_{1} \times d_{1} } \mathord{\left/ {\vphantom {{\rho \times V_{1} \times d_{1} } \mu }} \right. \kern-0pt} \mu }\)

T :

Time lag for maximum cross-correlation coefficient (s)

T 0.5 :

Time lag for auto-correlation coefficient being 0.5 (s)

Tu:

Turbulence intensity

Tu″:

Decomposed turbulence intensity of high-frequency signal component

U :

Free-stream velocity in upstream supercritical flow (m/s)

V :

Average air–water interfacial velocity (m/s)

V max :

Maximum interfacial velocity in the shear flow region (m/s)

V recirc :

Average recirculation velocity in the free-surface region (m/s)

V 1 :

Average inflow velocity (m/s)

v′:

Standard deviation of interfacial velocity (m/s)

W :

Channel width (m)

x :

Longitudinal distance from the upstream gate (m)

x 1 :

Longitudinal position of jump toe (m)

Y Cmax :

Characteristic elevation of local maximum void fraction in the shear region (m)

Y Fmax :

Characteristic elevation of maximum bubble count rate in the shear region (m)

Y Pmax :

Characteristic elevation of maximum mean total pressure in the shear region (m)

Y p′max :

Characteristic elevation of maximum total pressure fluctuation in the shear region (m)

Y Vmax :

Characteristic elevation of maximum interfacial velocity in the shear region (m)

Y 0.5 :

Characteristic elevation of half maximum interfacial velocity (m)

Y 50 :

Characteristic elevation where C = 0.5 (m)

Y 90 :

Characteristic elevation where C = 0.9 (m)

y :

Vertical distance from the channel bed (m)

y*:

Characteristic elevation of local minimum void fraction (m)

z :

Transverse distance from the channel centreline (m)

Δx :

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

δ :

Inflow boundary-layer thickness at channel bed (m)

μ :

Water dynamic viscosity (Pa × s)

ρ :

Water density (kg/m3)

τ :

Time lag (s)

τ 0.5 :

Time lag between maximum and half maximum cross-correlation coefficients (s)

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Acknowledgments

The financial supports of the Australian Research Council (Grant DP120100481) and ESTACA (France) are acknowledged.

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Authors and Affiliations

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

    Hang Wang & Hubert Chanson

  2. ESTACA Campus Ouest, Parc Universitaire de Laval Changé, BP 53061, Laval Cedex 9, France

    Frédéric Murzyn

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  1. Hang Wang
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Correspondence to Hang Wang.

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Wang, H., Murzyn, F. & Chanson, H. Total pressure fluctuations and two-phase flow turbulence in hydraulic jumps. Exp Fluids 55, 1847 (2014). https://doi.org/10.1007/s00348-014-1847-9

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