Modelling free surface flow with curvilinear streamlines by a non-hydrostatic model

Abstract

This study addresses a particular phenomenon in open channel flows for which the basic assumption of hydrostatic pressure distribution is essentially invalid, and expands previous suggestions to flows where streamline curvature is significant. The proposed model incorporates the effects of the vertical curvature of the streamline and steep slope, in making the pressure distribution non-hydrostatic, and overcomes the accuracy problem of the Saint-Venant equations when simulating curvilinear free surface flow problems. Furthermore, the model is demonstrated to be a higher-order one-dimensional model that includes terms accounting for wave-like variations of the free surface on a constant slope channel. Test results of predicted flow surface and pressure profiles for flow in a channel transition from mild to steep slopes, transcritical flow over a short-crested weir and flow with dual free surfaces are compared with experimental data and previous numerical results. A good agreement is attained between the experimental and computed results. The overall simulation results reveal the satisfactory performance of the proposed model in simulating rapidly varied gravity-driven flows with predominant non-hydrostatic pressure distribution effects. This study suggests that a higher-order pressure equation should be used for modelling the pressure distribution of a curvilinear flow in a steeply sloping channel.

Non-Hydrostatic Transitional Open-Channel Flows from a Supercritical to a Subcritical State

“…It is apparent from Eq. (10a) that the main differences between this Boussinesq-type equation and earlier equations presented by Fenton and Zerihun (2007) and Zerihun (2008Zerihun ( , 2016 are all in the non-linear coefficients associated with the spatial derivative terms. In Eq.…”

On Steady Two-dimensional Free-surface Flows with Spatially-varied Discharges

“…It is applicable to flow problems with moderately sloped and curved streamlines. For the case of spatially-varied flows in steep-slope channels, flow models that incorporate the effects of a hydraulically steep slope might be extended and used (e.g., Berger, 1992;Steffler and Jin, 1993;Zerihun, 2016;Darvishi et al, 2017). The numerical solutions of the two equations will be compared with the measurements in order to assess quantitatively the contributions of the non-hydrostatic terms of the governing equation of the present study.…”