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Numerical modeling of free and submerged labyrinth weir flow for a large sidewall angle

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Abstract

In recent decades, the advancement of knowledge on the hydraulics of labyrinth weirs has resulted mainly from physical modeling. In this study, numerical simulations of free-flow and submerged labyrinth weirs were conducted for a large sidewall angle, using commercially available computational fluid dynamics software, for three different turbulence models. These simulations were compared with experimental data gathered in a fairly large-scale facility. In general, very good agreement was found on the discharge capacity, in free-flow and submerged conditions, regardless of the turbulence model tested. A dimensionless approaching free surface profile, which was virtually independent of the relative upstream head, was obtained. Downstream of the weir, under subcritical flow conditions, the numerical flow depths agreed reasonably well with the corresponding experimental data.

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Abbreviations

a :

Half width of the labyrinth weir apex

C L :

Dimensionless discharge coefficient related to the centerline length of the weir crest L

F s :

Safety factor

g :

Gravitational acceleration

H d :

Total downstream head over the weir crestin a submerged condition

H t :

Total upstream head over the weir crestin a free-flow condition

H * :

Total upstream head over the weir crestin a submerged condition

h :

Free surface elevation over the weir crest

h 0 :

Depth of flow over the weir crestin a free-flow condition

L :

Total centerline length of the labyrinth weir crest

n :

Number of labyrinth weir cycles

P :

Labyrinth weir height

p :

Pressure

Q :

Labyrinth weir discharge

S M :

Momentum source

t :

Time

t w :

Vertical thickness of labyrinth weir wall

U :

Velocity vector

U 0 :

Mean velocity upstream of the labyrinth weir

\( u_{i}^{{\prime }} \) :

Turbulent velocity in each direction (i: 1–3 for x, y, z directions, respectively)

W :

Channel width

w :

Cycle width of the labyrinth weir

x :

Horizontal distance

y 10 :

Characteristic depth where the local air concentration is 10%

y 90 :

Characteristic depth where the local air concentration is 90%

α :

Labyrinth weir sidewall angle

δ :

Kronecker delta function

ε :

Dissipation rate of turbulent kinetic energy

\( k = \left( {1/2} \right)\overline{{u_{i}^{{\prime }} u_{i}^{{\prime }} }} \) :

Turbulent kinetic energy

µ t :

Eddy dynamic viscosity

ρ :

Density

\( -\uprho\overline{{u_{\text{i}}^{{\prime }} u_{\text{j}}^{{\prime }} }} \) :

Reynolds stress (i = 1–3 for x, y, z directions, respectively)

σ :

Standard deviation of the relative error of CL

τ :

Stress tensor

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Acknowledgements

This study was carried out in the framework of a research stay by the first author at the Instituto Superior Técnico, University of Lisbon, funded by the PMPDI-UPCT-2018 Program of the Universidad Politécnica de Cartagena. The support given in the framework of the Ph.D. thesis of the third author by the Fundação para a Ciência e Tecnologia (FCT), Portugal, Project PTDC/ECM/108128/2008, and by the National Laboratory of Civil Engineering (LNEC), in particular by Dr. J. Falcão de Melo, is acknowledged. The authors also thank the support given by the Fundación Séneca, Project 20879/PI/18, to the numerical modeling simulations.

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Authors and Affiliations

  1. Civil Engineering Department, Universidad Politécnica de Cartagena, Cartagena, Spain

    José M. Carrillo

  2. CERIS, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    Jorge Matos

  3. Hidra, Hidráulica e Ambiente, Lda., Lisbon, Portugal

    Ruth Lopes

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  1. José M. Carrillo
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  2. Jorge Matos
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Correspondence to José M. Carrillo.

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Carrillo, J.M., Matos, J. & Lopes, R. Numerical modeling of free and submerged labyrinth weir flow for a large sidewall angle. Environ Fluid Mech 20, 357–374 (2020). https://doi.org/10.1007/s10652-019-09701-0

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