Experimental assessment of scale effects affecting two-phase flow properties in hydraulic jumps

A hydraulic jump is the rapid transition from a supercritical to subcritical free-surface flow. It is characterised by strong turbulence and air bubble entrainment. New air–water flow properties were measured in hydraulic jumps with partially developed inflow conditions. The data set together with the earlier data of Chanson (Air bubble entrainment in hydraulic jumps. Similitude and scale effects, 119 p, 2006) yielded similar experiments conducted with identical inflow Froude numbers Fr ₁ = 5 and 8.5, but Reynolds numbers between 24,000 and 98,000. The comparative results showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. The present comparative analysis demonstrated quantitatively that dynamic similarity of two-phase flows in hydraulic jumps cannot be achieved with a Froude similitude. In experimental facilities with Reynolds numbers up to 10⁵, some viscous scale effects were observed in terms of the rate of entrained air and air–water interfacial area.     

Turbulent time and length scale measurements in high-velocity open channel flows

In high-velocity open channel flows, the measurements of air–water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air–water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8E+5 to 7.1E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air–water depth Y ₉₀. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95–0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.     

Current knowledge in hydraulic jumps and related phenomena. A survey of experimental results

The hydraulic jump is the sudden transition from a high-velocity open channel flow regime to a subcritical flow motion. The flow properties may be solved using continuity and momentum considerations. In this review paper, recent advances in turbulent hydraulic jumps are developed: the non-breaking undular hydraulic jump, the positive surge and tidal bore, and the air bubble entrainment in hydraulic jumps with roller. The review paper demonstrates that the hydraulic jump is a fascinating turbulent flow motion and the present knowledge is insufficient, especially at the scales of environmental and geophysical flows.     

A versatile access to unsymmetrical and symmetrical α-diketones via organotin reagents

Unsymmetrical α -diketones have been obtained via cross coupling of acyltins with acyl halides under PdCl₂(PPh₃)₂ catalysis while symmetrical α -diketones have been readily obtained via “in situ” formation of acyltins using hexabutylditin and acyl chlorides under similar experimental conditions.     

Free-surface fluctuations and turbulence in hydraulic jumps

A hydraulic jump is the highly turbulent transition between a high-velocity impinging flow and a turbulent roller. The jump flow is characterised by some substantial air bubble entrainment, spray and splashing. In the present study, the free-surface fluctuations and air-water properties of the hydraulic jump roller were investigated physically for relatively small Froude numbers (2.4 < Fr₁ < 5.1) and relatively large Reynolds numbers (6.6 × 10⁴ < Re < 1.3 × 10⁵). The shape of the mean free surface profile was well defined, and the time-averaged free-surface elevation corresponded to the upper free-surface, with the quantitative values being close to the equivalent clear-water depth. The turbulent fluctuation profiles exhibited a maximum in the first part of the hydraulic jump roller. The free-surface fluctuations presented some characteristic frequencies between 1.4 and 4 Hz. Some simultaneous free-surface measurements at a series of two closely located points yielded the free-surface length and time scales of free-surface fluctuations in terms of both longitudinal and transverse directions. The length scale data seemed to depend upon the inflow Froude number, while the time scale data showed no definite trend. Some simultaneous measurements of instantaneous void fraction and free-surface fluctuations exhibited different features depending upon the phase-detection probe sensor location in the different regions of the roller.