Characteristics of curvilinear flows over tilting weirs: laboratory, computational, and field investigations

Abstract

The phenomenon of flow over a hydraulic control structure, such as a weir, is a cornerstone of open-channel hydraulics. These structures help regulate water levels in channels and reservoirs, measure discharge, and can even be used as grade control structures to manage channel morphology. The structural configurations that form the basis of centuries of research and application are the vertical sharp-crested weir and the rectangular free overfall. Tilting weirs, which span the range between these classical limits through an adjustable inclination angle, are increasingly being used in engineered systems for stage regulation and more recently, flow measurement. However, current rating methodologies for these structures are limited in scope and overly empirical. Furthermore, a unifying physical framework for the discharge coefficient of weirs that accounts for the constituent aspects influencing discharge characteristics is currently lacking. An investigation of the underlying fluid dynamics, including boundary layer development, flow separation, non-hydrostatic pressure distributions, and local energy loss has thus far seen limited application for weir flows. Motivated by the need for more accurate and physically interpretable discharge predictions and reliable control of water surface elevations, this dissertation seeks to revisit the classical weir discharge problem under the new light of advanced experimental techniques, apply this knowledge to the general case of the tilting weir, and work to close key knowledge gaps in the application of laboratory-derived rating equations to prototype-scale structures operating in the field. This research combines laboratory experimentation, computational fluid dynamics, and field-scale observations to construct a robust and generalizable framework for understanding the hydraulics of tilting weirs. Laboratory flume experiments were conducted using high-resolution velocity measurements from particle-image velocimetry (PIV) and acoustic-Doppler velocimetry (ADV), and were complemented by Reynolds-Averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) simulations to examine flow field dynamics in detail across a generous range of flow cases. These efforts informed a new discharge equation for tilting weirs that accounts for the inclination angle of the structure, and was calibrated based upon more than 400 observations of flow over physical models at two unique laboratories. Practical limitations for flow measurement, concerned with scale effects occurring at low inertial states and the transition from weir to sill flow at high inertial states, were examined and accessible measurement recommendations were set forth to enhance accuracy. PIV results in conjunction with computational simulations helped elucidate the underlying fluid dynamics influencing these discharge characteristics. Finally, the laboratory-derived equation was applied to prototype-scale weirs operating within an irrigation system in Northern Colorado and adapted to reflect field-scale variability, such as approach channel conditions and localized energy losses due to flow separation. The key contributions of this work are as follows. The theoretical framework for the classical weir discharge coefficient (Cd) is revisited and new physical insight is provided by decomposing Cd into its contributing components, which are shown to account for the combined effects of kinetic energy, contraction, and local energy loss and together inform an understanding of Cd as a type of Froude number. Furthermore, a clear delineation of the transition from weir flow to the sill flow which occurs in the limit of the rectangular free overfall, is explained. This transition in regimes of discharge characteristics is analyzed in light of practical constraints for accurate flow measurement, and to inform the rating equation of the tilting weir, which operates within the physical limits of the vertical sharp-crested weir and rectangular free overfall. A generalized rating equation for tilting weirs is established, incorporating kθ as an inclination angle correction factor to the head term. This allows for the accurate prediction of discharge across the full spectrum of inclination angles observed in practice, harmonizing with classical theory at both operational limits. Laboratory results demonstrated consistent accuracy under different experimental configurations. Flow field analysis from experimental PIV and computational simulations revealed that boundary layer separation, turbulent mixing characterized by Reynolds stresses, vertical pressure gradients, and regions of high shear caused by large mean velocity gradients are the major factors influencing the discharge characteristics. Field application of the tilting weir discharge equation framework, with the addition of the field characteristics correction factor, kF, showed strong agreement with measured flows, indicating the robustness of the laboratory-derived approach and charting a path forward for future adaptions of lab-derived discharge relationships to field settings. A discussion of the kF correction factor reveals the viability of physical model experiments of weir flows to accurately capture the governing physics observed in the field, with the need for slight calibration and modification due to site-specific characteristics. Opportunities for future research include further validation of these results with additional physical models and computational simulations, investigating tilting weir blade characteristics such as curvature and surface roughness on the discharge characteristics to enhance functionality, and leveraging the tilting weir towards ecological goals such as a mechanism for sediment transport management and fish passage. This work advances the theoretical and practical understanding of flow measurement in general and tilting weirs specifically, laying the groundwork for further innovation in water resources engineering.