Author(s): Francisco Nicolas Cantero-Chinchilla; Rafael J. Bergillos; Oscar Castro-Orgaz; Luis Cea; Willi H. Hager

Linked Author(s): Rafael J. Bergillos, Oscar Castro-Orgaz

Keywords: Depth-Averaged Modeling; Non-hydrostatic Flow; Open-Channel Flow; Transcritical Flow; Unsteady Flow

Abstract:

Transcritical flows, i.e. flows evolving from sub- to supercritical conditions or vice versa, are typical during the operation of hydraulic structures or in the river environment. The operation of dams and weirs, sudden water releases and gate closures in canals or simulation of dam break waves are relevant examples. A comprehensive understanding of these flows is required for accurate channel design and environmental risk evaluations. The transition across the critical depth occurs with significant streamline curvature effects both in steady and unsteady flow conditions. The operation of gates in open channels produces unsteady flows with moving critical points and bores along the domain, with steady control sections and hydraulic jumps as particular equilibrium conditions. Flows along a sequence of obstacles and slope breaks in a river stream is another significant example. At the critical point, the flow acceleration produces significant non-hydrostatic effects, whereas a bore may be undular or broken, depending on the local flow conditions. A simulation of these flows in practice is accomplished resorting to the de Saint Venant (dSV) equations, given their benefits in terms of computational cost and relative accuracy in a wide range of flow conditions. However, critical points and undular bores are hardly determined by the dSV equations with accuracy, and, thus, a more advanced modeling approach is desirable. Unsteady flow modeling of transcritical open channel flow is a challenging task given that it is necessary to reproduce the moving critical points and bores while the flow evolves in time, and then produce the converged steady state of the system, including the possibility of having sections with minimum specific energy and hydraulic jumps. Suitable modeling tools for these situations are the Boussinesq-type equations; however, breaking sub-models are required to produce broken waves, complicating model implementation. An interesting but almost unexplored tool in this field are the so-called Vertically-Averaged and Moment (VAM) equations. This model accounts for an extra vertical resolution of the flow by adding perturbation parameters to deviate the field variables from those considered in the dSV equations. The mathematical technique consists in producing additional transport equations by a proper weighting under the umbrella of Galerkin methods, thereby resulting moment equations for mathematical closure. The ensuing system of equations has been found capable to model unsteady transcritical open channel flows. This work explores the capabilities of the VAM model for these problems applying it to (i) steady flows over an embankment weir, (ii) unsteady flows over a bottom sill, and (iii) dam break flows with different up- to downstream water depth ratios. The VAM model results are compared with those obtained by the dSV and Boussinesq-type equations, thereby highlighting the accuracy of the VAM model to simulate transcritical flows in the river environment.

DOI: https://doi.org/10.3850/IAHR-39WC25217119202277

Year: 2022