Turbulence, dynamic similarity and scale effects in high-velocity free-surface flows above a stepped chute

In high-velocity free-surface flows, air entrainment is common through the interface, and intense interactions take place between turbulent structures and entrained bubbles. Two-phase flow properties were measured herein in high-velocity open channel flows above a stepped chute. Detailed turbulence measurements were conducted in a large-size facility, and a comparative analysis was applied to test the validity of the Froude and Reynolds similarities. The results showed consistently that the Froude similitude was not satisfied using a 2:1 geometric scaling ratio. Lesser number of entrained bubbles and comparatively greater bubble sizes were observed at the smaller Reynolds numbers, as well as lower turbulence levels and larger turbulent length and time scales. The results implied that small-size models did underestimate the rate of energy dissipation and the aeration efficiency of prototype stepped spillways for similar flow conditions. Similarly a Reynolds similitude was tested. The results showed also some significant scale effects. However a number of self-similar relationships remained invariant under changes of scale and confirmed the analysis of Chanson and Carosi (Exp Fluids 42:385-401, 2007). The finding is significant because self-similarity may provide a picture general enough to be used to characterise the air– water flow field in large prototype channels

Turbulence and aeration in hydraulic jumps: free-surface fluctuation and integral turbulent scale measurements

In an open channel, a change from a supercritical to subcritical flow is a strong dissipative process called a hydraulic jump. Herein some new measurements of free-surface fluctuations of the impingement perimeter and integral turbulent time and length scales in the roller are presented with a focus on turbulence in hydraulic jumps with a marked roller. The observations highlighted the fluctuating nature of the impingement perimeter in terms of both longitudinal and transverse locations. The results showed further the close link between the production and detachment of large eddies in jump shear layer, and the longitudinal fluctuations of the jump toe. They highlighted the importance of the impingement perimeter as the origin of the developing shear layer and a source of vorticity. The air–water flow measurements emphasised the intense flow aeration. The turbulent velocity distributions presented a shape similar to a wall jet solution with a marked shear layer downstream of the impingement point. The integral turbulent length scale distributions exhibited a monotonic increase with increasing vertical elevation within 0.2 < Lz/d1 < 0.8 in the shear layer, where Lz is the integral turbulent length scale and d1 the inflow depth, while the integral turbulent time scales were about two orders of magnitude smaller than the period of impingement position longitudinal oscillations

Characteristics of Proportional Weirs

A theorem termed the Geometrical Continuity Theorem is enunciated and proven. This theorem throws light on the aspects of the continuity of the proportional portion with the base weir portion. These two portions constitute the profile of a proportional weir. A weir of this type with circular bottom is designed. The theorem is used to establish the continuity at the junction of the proportional and the base weir portions of this weir. The coordinates of the weir profile are obtained by numerical methods and are furnished in tabular form for ready use by designers. The discharge passing through the weir is a linear function of the head. The verification of the assumed linear discharge-head relation is furnished for one of the three weirs with which experiments were conducted. The coefficient of discharge for this typical weir is found to be a constant with a value of 0.59

On the definition of a small orifice

An attempt is made to draw a line of demarcation between small orifices and large orifices. It is proposed that an orifice can be considered 'small' if the discharge through it calculated on the small-orifice assumption differs from the exact discharge by less than half of one per cent. Using this criterion, it is shown that a circular or elliptic orifice can be deemed 'small' as long as the ratio of the depth of the orifice to the head causing the flow (measured from the center of the orifice to the liquid surface) is less than 0.8; a rectangular orifice can be deemed 'small' if the ratio is less than 0.7. A correction factor is suggested for the coefficient of discharge to account for the deviation from the exact discharge