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Unsteady shallow meandering flows in rectangular reservoirs: a modal analysis of URANS modelling
(2022)
Shallow flows are common in natural and human-made environments. Even for simple rectangular shallow reservoirs, recent laboratory experiments show that the developing flow fields are particularly complex, involving large-scale turbulent structures. For specific combinations of reservoir size and hydraulic conditions, a meandering jet can be observed. While some aspects of this pseudo-2D flow pattern can be reproduced using a 2D numerical model, new 3D simulations, based on the unsteady Reynolds-Averaged Navier-Stokes equations, show consistent advantages as presented herein. A Proper Orthogonal Decomposition was used to characterize the four most energetic modes of the meandering jet at the free surface level, allowing comparison against experimental data and 2D (depth-averaged) numerical results. Three different isotropic eddy viscosity models (RNG k-ε, k-ε, k-ω) were tested. The 3D models accurately predicted the frequency of the modes, whereas the amplitudes of the modes and associated energy were damped for the friction-dominant cases and augmented for non-frictional ones. The performance of the three turbulence models remained essentially similar, with slightly better predictions by RNG k-ε model in the case with the highest Reynolds number. Finally, the Q-criterion was used to identify vortices and study their dynamics, assisting on the identification of the differences between: i) the three-dimensional phenomenon (here reproduced), ii) its two-dimensional footprint in the free surface (experimental observations) and iii) the depth-averaged case (represented by 2D models).
Robust estimators for free surface turbulence characterization: A stepped spillway application
(2020)
Robust estimators are parameters insensitive to the presence of outliers. However, they presume the shape of the variables’ probability density function. This study exemplifies the sensitivity of turbulent quantities to the use of classic and robust estimators and the presence of outliers in turbulent flow depth time series. A wide range of turbulence quantities was analysed based upon a stepped spillway case study, using flow depths sampled with Acoustic Displacement Meters as the flow variable of interest. The studied parameters include: the expected free surface level, the expected fluctuation intensity, the depth skewness, the autocorrelation timescales, the vertical velocity fluctuation intensity, the perturbations celerity and the one-dimensional free surface turbulence spectrum. Three levels of filtering were utilised prior to applying classic and robust estimators, showing that comparable robustness can be obtained either using classic estimators together with an intermediate filtering technique or using robust estimators instead, without any filtering technique.
A new formulation for the prediction of free surface dynamics related to the turbulence occurring nearby is proposed. This formulation, altogether with a breakup criterion, can be used to compute the inception of self-aeration in high velocity flows like those occurring in hydraulic structures. Assuming a simple perturbation geometry, a kinematic and a non-linear momentum-based dynamic equation are formulated and forces acting on a control volume are approximated. Limiting steepness is proposed as an adequate breakup criterion. Role of the velocity fluctuations normal to the free surface is shown to be the main turbulence quantity related to self-aeration and the role of the scales contained in the turbulence spectrum are depicted. Surface tension force is integrated accounting for large displacements by using differential geometry for the curvature estimation. Gravity and pressure effects are also contemplated in the proposed formulation. The obtained equations can be numerically integrated for each wavelength, hence resulting in different growth rates and allowing computation of the free surface roughness wavelength distribution. Application to a prototype scale spillway (at the Aviemore dam) revealed that most unstable wavelength was close to the Taylor lengthscale. Amplitude distributions have been also obtained observing different scaling for perturbations stabilized by gravity or surface tension. The proposed theoretical framework represents a new conceptualization of self-aeration which explains the characteristic rough surface at the non-aerated region as well as other previous experimental observations which remained unresolved for several decades.
Vectrino profiler spatial filtering for shear flows based on the mean velocity gradient equation
(2018)
A new methodology is proposed to spatially filter acoustic Doppler velocimetry data from a Vectrino profiler based on the differential mean velocity equation. Lower and upper bounds are formulated in terms of physically based flow constraints. Practical implementation is discussed, and its application is tested against data gathered from an open-channel flow over a stepped macroroughness surface. The method has proven to detect outliers occurring all over the distance range sampled by the Vectrino profiler and has shown to remain applicable out of the region of validity of the velocity gradient equation. Finally, a statistical analysis suggests that physically obtained bounds are asymptotically representative.