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Experimental study of recirculating flows generated by lateral shock waves in very large channels

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Abstract

Due to the lack of data on hydraulic-jump dynamics in very large channels, the present paper describes the main characteristics of the velocity field and turbulence in a large rectangular channel with a width of 4 m. Although a hydraulic jump is always treated as a wave that is transversal to the channel wall, in the case of this study it has a trapezoidal front shape, first starting from a point at the sidewalls and then developing downstream in an oblique manner, finally giving rise to a trapezoidal shape. The oblique wave front may be regarded as a lateral shockwave that arises from a perturbation at a certain point of the lateral wall and travels obliquely toward the centreline of the channel. The experimental work was carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). In addition to the hydraulic jump formation, a large recirculating flow zone starts to develop from the separating point of the lateral shock wave and a separate boundary layer occurs. Intensive measurements of the streamwise and spanwise flow velocity components along one-half width of the channel were taken using a bidimensional Acoustic Doppler Velocimeter (ADV). The water surface elevation was obtained by means of an ultrasonic profiler. Velocity vectors, transversal velocity profiles, turbulence intensities and Reynolds shear stresses were all investigated. The experimental results of the separated boundary layer were compared with numerical predictions and related work presented in literature and showed good agreement. The transversal velocity profiles indicated the presence of adverse pressure gradient zones and the law of the wall appears to govern the region around the separated boundary layer.

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Abbreviations

β :

Angle between the lateral shockwave and the channel side wall (°)

λ :

Minimum distance from the upstream gate in order to have flow development (m)

ν :

Water kinematic viscosity (m2 s−1)

ψ :

Streamline function (m2s−1)

κ :

Von Karman’s constant (–)

\({\Phi}\) :

Parameter of the velocity logarithmic law (–)

δ * :

Displacement thickness of the lateral boundary layer (m)

A, B:

Parameters of Eq. 3 (ms−1)

AR:

Jump aspect ratio=B/h0 (–)

B:

Channel width (m)

bj:

Length of the hydraulic jump front normal to the upstream current (m)

F0 :

Froude number at the vena contracta (–)

h0 :

Flow depth at the vena contracta (m)

hg :

Opening of sluice gate (m)

ks :

Representative roughness height (m)

L:

Longitudinal length from the upstream channel gate to the hydraulic jump front normal to the upstream current (m)

l:

Longitudinal distance from the upstream channel gate to the toe of the shockwave (m)

Q:

Flow discharge (m3s−1)

Re:

=Q/(Bν)=Channel flow Reynolds number (–)

Rex :

=Ucx/ν=local Reynolds number (–)

U:

Time-averaged streamwise (longitudinal) velocity (ms−1)

U*:

Friction velocity (ms−1)

u′, v′:

r.m.s of the longitudinal and transversal turbulent velocity components, respectively, i.s. longitudinal and transversal turbulent intensities (ms−1)

\({\overline{u^{\prime}v^{\prime}}}\) :

Crosscorrelation of the turbulent streamwise and wall normal velocity components, i.e. Reynolds shear stress apart from the water density (m2s−2)

U+ :

=U/U*=Dimensionless time-averaged streamwise velocity (–)

U0 :

Channel flow velocity at the vena contracta (ms−1)

Uc :

Channel flow velocity at a distance equal to l/2 from the upstream gate (ms−1)

V:

Time-averaged wall-normal velocity, positive if oriented toward the channel right wall (ms−1)

V :

Time-averaged horizontal velocity vector (ms−1)

x:

Longitudinal coordinates from the upstream channel gate (m)

y:

Distance from the wall (m)

Y:

Distance transversal to the channel, starting from the separated boundary layer ψ = 0, i.e. Y=0 is where ψ = 0 (m)

Y+ :

=YU*/ν=dimensionless Y distance (–)

Y0 :

Distance normal to the channel side wall from the separated boundary layer where ψ = 0 to the channel longitudinal axis where y = 2m (m)

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Authors and Affiliations

  1. Department of Water Engineering and Chemistry, Technical University of Bari, Via E. Orabona 4, Bari, 70125, Italy

    M. Ben Meftah, F. De Serio & A. Pollio

  2. Department of Environmental Engineering and Sustainable Development, Technical University of Bari, Via E. Orabona 4, Bari, 70125, Italy

    M. Mossa

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  1. M. Ben Meftah
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  2. F. De Serio
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  3. M. Mossa
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  4. A. Pollio
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Correspondence to M. Mossa.

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Meftah, M.B., De Serio, F., Mossa, M. et al. Experimental study of recirculating flows generated by lateral shock waves in very large channels. Environ Fluid Mech 8, 215–238 (2008). https://doi.org/10.1007/s10652-008-9057-8

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