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Analysis of the velocity field in a large rectangular channel with lateral shockwave

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Abstract

In this work the authors describe the main characteristics of the velocity field of hydraulic jumps in a very large channel where lateral shockwaves occur. Experiments were carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). Extensive flow velocity measurements were investigated in order to have a clearer understanding of both hydraulic jump development and lateral shockwave formation in a very large channel. Eight experiments were performed in a 4m wide rectangular channel; the experiments differed in the inlet Froude number F 0 and the jump type. Seven tests were carried out with undular jumps and one with a roller jump. The flow velocity and the flow free surface measurements were taken using a two-dimensional Acoustic Doppler Velocimeter (ADV) and an ultrasonic profiler, respectively. The experimental results can be summarized as follow: (i) the formation of well developed lateral shockwaves similar to those of oblique jumps were observed; (ii) the comparison of the experimental and theoretical data shows that the classic shockwave theory is sufficiently confirmed in the analyzed range of Reynolds number, taking into account the experimental errors and the difference between the theoretical and experimental assumptions; (iii) the transversal flow velocity profiles in the recirculating zone show a good agreement with the numerical simulations presented in literature in the case of a separated turbulent boundary layer over a flat plate. This conclusion enables us to confirm the hypothesis that the lateral shockwaves in the channel are the result of a boundary layer which, as observed, forms on the channel sidewalls.

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Abbreviations

β :

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

θ :

Angle between the horizontal velocity component 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)

δ * :

Displacement thickness of the lateral boundary layer (m)

ψ :

Streamline function (m2 s−1)

AR:

Jump aspect ratio = B/h 0(−)

B :

Channel width (m)

bj :

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

F 0 :

Froude number at the vena contracta (−)

F 1 :

Local Froude number (−)

g :

Gravity acceleration (ms−2)

h g :

Opening of sluice gate (m)

h 0 :

Flow depth at the vena contracta (m)

h1, h2:

Local flow depth (subscript 1 for supercritical flow, 2 for subcritical flow) (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 (m3 s−1)

Re:

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

Re x :

= U c x/ν = local Reynolds number (−)

T:

Water temperature (°C)

U 0 :

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

U c :

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

U x :

Streamwise (longitudinal) velocity (ms−1)

U y :

Wall-normal velocity (ms−1)

Vn1, Vn2:

Horizontal velocity component normal to the shockwave front (subscript 1 for supercritical flow, 2 for subcritical flow) (ms−1)

Vt1, Vt2:

Horizontal velocity component tangential to the shockwave front (subscript 1 for supercritical flow, 2 for subcritical flow) (ms−1)

x :

Longitudinal coordinates from the upstream channel gate (m)

y :

Distance from the wall (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

Authors
  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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Ben Meftah, M., De Serio, F., Mossa, M. et al. Analysis of the velocity field in a large rectangular channel with lateral shockwave. Environ Fluid Mech 7, 519–536 (2007). https://doi.org/10.1007/s10652-007-9034-7

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  • DOI: https://doi.org/10.1007/s10652-007-9034-7

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