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Air–water flows
(2024)
High Froude-number open-channel flows can entrain significant volumes of air, a phenomenon that occurs continuously in spillways, in free-falling jets and in hydraulic jumps, or as localized events, notably at the toe of hydraulic jumps or in plunging jets. Within these flows, turbulence generates millions of bubbles and droplets as well as highly distorted wavy air–water interfaces. This phenomenon is crucial from a design perspective, as it influences the behaviour of high-velocity flows, potentially impairing the safety of dam operations. This review examines recent scientific and engineering progress, highlighting foundational studies and emerging developments. Notable advances have been achieved in the past decades through improved sampling of flows and the development of physics-based models. Current challenges are also identified for instrumentation, numerical modelling and (up)scaling that hinder the formulation of fundamental theories, which are instrumental for improving predictive models, able to offer robust support for the design of large hydraulic structures at prototype scale.
This paper presents a novel method for airfoil drag estimation at Reynolds numbers between 4×10⁵ and 4×10⁶. The novel method is based on a systematic study of 40 airfoils applying over 600 numerical simulations and considering natural transition. The influence of the airfoil thickness-to-chord ratio, camber, and freestream Reynolds number on both friction and pressure drag is analyzed in detail. Natural transition significantly affects drag characteristics and leads to distinct drag minima for different Reynolds numbers and thickness-to-chord ratios. The results of the systematic study are used to develop empirical correlations that can accurately predict an airfoil drag at low-lift conditions. The new approach estimates a transition location based on airfoil thickness-to-chord ratio, camber, and Reynolds number. It uses the transition location in a mixed laminar–turbulent skin-friction calculation, and corrects the skin-friction coefficient for separation effects. Pressure drag is estimated separately based on correlations of thickness-to-chord ratio, camber, and Reynolds number. The novel method shows excellent accuracy when compared with wind-tunnel measurements of multiple airfoils. It is easily integrable into existing aircraft design environments and is highly beneficial in the conceptual design stage.