Measuring void fraction and velocity fields of a stepped spillway for skimming flow using non-intrusive methods

Stepped spillways have higher energy dissipation than smoother hydraulic structures used to divert flood discharges. The inception point related to air entrainment is, however, located further upstream causing an undesired bulking of the flow depth. For large discharge rates and for straight stepped spillways, the skimming flow regime may be assumed two dimensional; this is an attractive feature for the application of non-intrusive flow visualization techniques because these methods measure the flow characteristics in the vicinity of the sidewalls which are likely to correlate with the flow at the centre of the flume. This paper tests the hypothesis that such techniques can be used to measure the flow inside the flume. The hypothesis is tested against measurements taken with an intrusive probe. Void fraction contour lines and velocity fields are obtained in 12 different stepped spillway configurations using the image processing procedure and the bubble image velocimetry, respectively. The void fraction and velocity results are overall consistent with the probe measurements. The velocity fields show a persistent underestimation of the probe measurements which can at least be partially explained by sidewall effects and possible probe’s overestimation.     

台阶式溢洪道掺气特性的试验研究

通过试验研究了台阶式溢洪道上的掺气现象以及掺气区域的划分，试验表明，台阶式溢洪道沿程掺气可以分为非掺气区、掺气发展区和掺气充分发展区等三个区域；断面掺气分为台阶影响的含气区、楔形清水区、水中气泡区和空中水滴区。试验还测量了台阶式溢洪道上的断面掺气浓度及其沿程分布，计算了断面含水率，提出了初始掺气点的计算方法。与光滑溢洪道相比较，台阶式溢洪道具有初始掺气点前移，掺气发生早，发展快，掺气浓度大等特点。     

Turbulence manipulation in air–water flows on a stepped chute: An experimental study

In a stepped channel operating with large flow rates, the flow skims over the pseudo-bottom formed by the step edges as a coherent stream. Intense three-dimensional recirculation is maintained by shear stress transmission from the mainstream to the step cavities, while significant free-surface aeration takes place. The interactions between free-surface aeration and cavity recirculation are investigated herein with seven step cavity configurations. The experiments were conducted in a large stepped channel operating at large Reynolds numbers. For some experiments, triangular vanes, or longitudinal ribs, were placed across the step cavities to manipulate the flow turbulence to enhance the interactions between the mainstream flow and the cavity recirculation region. The results showed a strong influence of the vanes on the air–water flow properties in both free-stream and cavity flows. The findings demonstrate some passive turbulence manipulation in highly turbulent air–water flows.     

Air transport in chute flows

The air bubble rise velocity in still water depends mainly on the bubble size and is basically influenced by buoyancy, viscosity and surface tension. In high-speed flows the number of forces acting on air bubbles increases with turbulence, non-hydrostatic pressure gradient, shear forces, bubble clouds and free-surface entrainment. Air bubbles in these flows are used for cavitation protection of hydraulic structures such as chutes, spillways and bottom outlets. Here, air is normally added by means of aerators upstream of regions where the cavitation number falls below a critical value mainly to reduce the sonic velocity of the fluid and cushion the cavitation bubble collapse process. The distance between successive aerators depends basically on the bubble rise velocity. Until today, the bubble rise velocity in high-speed flows was not thoroughly investigated because of limited laboratory instrumentation. The present project focused on the streamwise development of air concentrations in high-speed flows along a 14 m long model chute. The bubble rise velocity was indirectly derived from the air detrainment gradient of the air concentration contour lines downstream of an aeration device. It accounts for the main hydraulic parameters chute slope, Froude number and air concentration. It is demonstrated that the bubble rise velocity in high-speed flow and stagnant water differ significantly due to fracturing processes, turbulence, and the ambient air concentration.     

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.     

Transient two‐layer thin‐film flow

The transient two‐layer thin‐film planar flow is investigated theoretically in this study. The interplay among inertia, viscous and surface/interfacial tension is emphasized. It is found that the film and interface profiles, as well as the flow field, are strongly influenced by the viscosity ratio, velocity and film thickness ratios at inception, and the surface‐to‐interfacial tension ratio. The nonlinear stability of the steady state reveals the formation of a solitary wave after flow inception, which propagates in the form of a convective instability, with the steady state recovered only in the tail (upstream) region of the wave. In the presence of surface/interfacial tension, surface modulation appears, which grows in wavelength and amplitude with position. The flow is found to be particularly stable for higher viscosity of the lower film layer. Copyright © 2010 John Wiley & Sons, Ltd.     

Development of the interfacial air layer in the non-aerated region of high-velocity spillway flows. Instabilities growth,entrapped air and influence on the self-aeration onset

Self-aeration is traditionally explained by the water turbulent boundary layer outer edge intersection with the free surface. This paper presents a discussion on the commonly accepted hypothesis behind the computation of the critical point of self-aeration in spillway flows and a new formulation is proposed based on the existence of a developing air flow over the free surface. Upstream of the inception point of self-aeration, some surface roughening has been often reported in previous studies which consequently implies some entrapped air transport and air–water flows coupling. Such air flow is proven in this study by presenting measured air velocities and computing the air boundary layer thickness for a 1V:2H smooth chute flow. Additionally, the growth rate of free surface waves has been analysed by means of Ultrasonic Sensors measurements, obtaining also the entrapped air concentration. High-speed camera imaging has been used for qualitative study of the flow perturbations.     

An experimental investigation on the effects of surface gravity waves on the water evaporation rate in different air flow regimes

Estimating rate of evaporation from undisturbed water surfaces to moving and quiet air has been the topic a vast number of research activities. The obvious presence of various shapes of gravity waves on the water body surfaces was the motivation of this experimental investigation. In this investigation experimental measurements have been done to quantify evaporation rate from wavy water surfaces in free, mixed and forced convection regimes. The effects of a wide range of surface gravity waves from low steepness, round shaped crest with slow celerity, to steep and very slight spilling crest waves, on the water evaporation rate have been investigated. A wide range of ${\text{Gr}}/{\text{Re}}^{2} (0.01 \le {\text{Gr}}/{\text{Re}}^{2} \le 100)$ was achieved by applying different air flow velocities on a large heated wave flume equipped with a wind tunnel. Results reveal that wave motion on the water surface increase the rate of evaporation for all air flow regimes. For free convection, due to the effect of wave motion for pumping rotational airflows at the wave troughs and the dominant effect of natural convection for the air flow advection, the maximum evaporation increment percentage from wavy water surface is about 70 %. For mixed and forced convection, water evaporation rate increment is more sensitive to the air flow velocity for the appearance of very slight spilling on the steep wave crests and the leeward air flow structures.     

Comparative analyses of phase-detective intrusive probes in high-velocity air–water flows

A comparative analysis of a wide range of air–water flow properties was conducted for two types of phase-detection intrusive probes including fiber-optical and conductivity probes. Experiments were conducted on a stepped spillway model for a skimming flow discharge q = 0.478 m²/s and for Re = 4.7 10⁵ in a flow region just downstream of the inception point of free-surface aeration and in the fully developed flow region. The comparison of a large number of key air–water flow properties showed a very close agreement for the two sensor types including void fraction, interfacial velocity and equivalent clear water flow depth enabling a direct comparison of past and future data collected with either phase-detection probe type. Minor differences were observed in terms of chord sizes, clustered properties and interparticle arrival times linked with the slightly smaller sensor size of the fiber-optical probe. The in-line positioning of the leading and trailing tips of the fiber-optical probe affected the trailing tip properties resulting in elevated turbulence intensities. An optimum dual-tip phase-detection probe design should consist of small probe tips positioned side-by-side.     

Flow regime transitions due to cavitation in the flow through an orifice

This paper presents both experimental and theoretical aspects of the flow regime transitions caused by cavitation when water is passing through an orifice. Cavitation inception marks the transition from single-phase to two-phase bubbly flow; choked cavitation marks the transition from two-phase bubbly flow to two-phase annular jet flow.

It has been found that the inception of cavitation does not necessarily require that the minimum static pressure at the vena contracta downstream of the orifice, be equal to the vapour pressure liquid. In fact, it is well above the vapour pressure at the point of inception. The cavitation number [σ = (P₃ − P_v)/(0.5 pV²); here P₃ is the downstream pressure, P_v is the vapour pressure of the liquid, ρ is the density of the liquid and V is the average liquid velocity at the orifice] at inception is independent of the liquid velocity but strongly dependent on the size of the geometry. Choked cavitation occurs when this minimum pressure approaches the vapour pressure. The cavitation number at the choked condition is a function of the ratio of the orifice diameter (d) to the pipe diameter (D) only. When super cavitation occurs, the dimensionless jet length [L/(D - d); where L is the dimensional length of the jet] can be correlated by using the cavitation number. The vaporization rate of the surface of the liquid jet in super cavitation has been evaluated based on the experiments.

Experiments have also been conducted in which air was deliberately introduced at the vena contracta to simulate the flow regime transition at choked cavitation. Correlations have been obtained to calculate the critical air flow rate required to cause the flow regime transition. By drawing an analogy with choked cavitation, where the air flow rate required to cause the transition is zero, the vapour and released gas flow rate can be predicted.     

Convective transport of air bubbles in strong hydraulic jumps

A hydraulic jump is a flow singularity characterised by a significant amount of air entrainment in the shear zone. The air is entrapped at the jump toe that is a discontinuity between the impinging flow and the roller. The impingement point is a source of air bubbles, as well as a source of vorticity. Herein the convective transport of air bubbles in the jump roller is re-visited. Some analytical extension is presented and the theoretical results are compared with some laboratory experiments conducted in a large-size facility operating at large Froude numbers. The turbulent air bubble mixing coefficient was found to increase linearly with increasing distance and be independent of the Froude and Reynolds numbers. Overall the study highlighted some seminal features of the air–water shear layer in hydraulic jumps with large Froude numbers (5.1 < Fr₁ < 11.2). The air bubble entrainment in the mixing zone was a convective transport process, although there was some rapid flow de-aeration for all Froude numbers.     

Frost formation in vertical channels under natural convection

Processes involving heat transfer from a humid air stream to a cold plate, with simultaneous deposition of frost, are of great importance in a variety of refrigeration equipment. In this paper, frost growth on a cold, vertical plate in free convection has been experimentally investigated. The cold plate (0.095 m high, 0.282 m wide) was placed in vertical channels open at the top and bottom in order to permit the natural circulation of ambient air. The channels, rectangular in shape, were 2.395 m high and 0.36 m wide, with the depth set equal either to 20 mm, or 10 mm, or 6 mm in order to infer the influence of channel flow area on the natural convection and frost formation. The cold plate temperature and the air relative humidity were varied in the −40 to −4 °C and 31–85% range, respectively, with the air temperature held fixed at 27 °C (±1 °C). Several quantities (thickness, temperature and mass of frost, heat flux at the cold plate), were measured during the time-evolution of the process (7.5 h from the frost growth inception), and are presented as functions of the input parameters (relative humidity and cold plate temperature); in particular, the role exerted by the plate confinement on the frost growth is discussed. Data are recast in order to identify compact parameters able to correlate frost mass, thickness and density data.     

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.     

Effect of drag reducing polymers on oil–water flow in a horizontal pipe

Measurements of drag-reduction are presented for oil–water flowing in a horizontal 0.0254 m pipe. Different oil–water configurations were observed. The injection of water soluble polymer solution (PDRA) in some cases produced drag reduction of about 65% with concentration of only 10–15 ppm. The results showed a significant reduction in pressure gradient due to PDRA especially at high mixture velocity which was accompanied by a clear change in the flow pattern. Phase inversion point in dispersed flow regime occurred at a water fraction range of (0.33–0.35) indicated by its pressure drop peak which was disappeared by injecting only 5 ppm (weight basis) of PDRA. Effect of PDRA concentration and molecular weight on flow patterns and pressure drops are presented in this study. Influence of salt content in the water phase on the performance of PDRA is also examined in this paper.     

Air–water flow properties in step cavity down a stepped chute

For the last three decades, the research into skimming flows down stepped chutes was driven by needs for better design guidelines. The skimming flow is characterised by some momentum transfer from the main stream to the recirculation zones in the shear layer developing downstream of each step edge. In the present study some physical modelling was conducted in a relatively large facility and detailed air–water flow measurements were conducted at several locations along a triangular cavity. The data implied some self-similarity of the main flow properties in the upper flow region, at step edges as well as at all locations along the step cavity. In the developing shear layer and cavity region (i.e. y/h < 0.3), the air–water flow properties presented some specific features highlighting the development of the mixing layer downstream of the step edge and the strong interactions between cavity recirculation and mainstream skimming flows. Both void fraction and bubble count rate data showed a local maximum in the developing shear layer, although the local maximum void fraction was always located below the local maximum bubble count rate. The velocity profiles had the same shape as the classical mono-phase flow data. The air–water flow properties highlighted some intense turbulence in the mixing layer that would be associated with large shear stresses and bubble–turbulence interactions.     

Gas displacement of viscoplastic liquids in capillary tubes

The displacement of viscoplastic liquids in capillary tubes by gas injection is examined. The viscoplasticity alters the flow kinematics and changes dramatically the amount of mass left attached at the tube wall as compared to the Newtonian case, studied experimentally by G.I. Taylor in 1961 [G.I. Taylor, Deposition of a viscous fluid on the wall of a tube, J. Fluid Mech. 10 (1961) 161–165]. Experiments with Carbopol aqueous solutions were performed for different flow rates. A recently proposed viscosity function for viscoplastic liquids was fitted to the rheological data of the Carbopol solutions. A new dimensionless rheological property – the jump number – arises in the dimensionless version of this viscosity function. The results show the effect of the viscoplastic character of the liquid on the free surface shape and on the thickness of the film of liquid left attached to the wall. This thickness decreases with the jump number and increases with the flow rate. It is also observed that there is a critical dimensionless flow rate below which the displacement is apparently perfect, i.e. there is no observable liquid left attached to the wall. This behavior is shown to be directly related to the fully developed flow far ahead the air–liquid interface.     

Seed bubbles stabilize flow and heat transfer in parallel microchannels

Seed bubbles are generated on microheaters located at the microchannel upstream and driven by a pulse voltage signal, to improve flow and heat transfer performance in microchannels. The present study investigates how seed bubbles stabilize flow and heat transfer in micro-boiling systems. For the forced convection flow, when heat flux at the wall surface is continuously increased, flow instability is self-sustained in microchannels with large oscillation amplitudes and long periods. Introduction of seed bubbles in time sequence improves flow and heat transfer performance significantly. Low frequency (∼10 Hz) seed bubbles not only decrease oscillation amplitudes of pressure drops, fluid inlet and outlet temperatures and heating surface temperatures, but also shorten oscillation cycle periods. High frequency (∼100 Hz or high) seed bubbles completely suppress the flow instability and the heat transfer system displays stable parameters of pressure drops, fluid inlet and outlet temperatures and heating surface temperatures. Flow visualizations show that a quasi-stable boundary interface from spheric bubble to elongated bubble is maintained in a very narrow distance range at any time. The seed bubble technique almost does not increase the pressure drop across microsystems, which is thoroughly different from those reported in the literature. The higher the seed bubble frequency, the more decreased heating surface temperatures are. A saturation seed bubble frequency of 1000–2000 Hz can be reached, at which heat transfer enhancement attains the maximum degree, inferring a complete thermal equilibrium of vapor and liquid phases in microchannels. Benefits of the seed bubble technique are the stabilization of flow and heat transfer, decreasing heating surface temperatures and improving temperature uniformity of the heating surface.     

Multiphase drag reduction: Effect of eliminating slugs

Two-phase pressure drop measurements were taken for air/water mixtures in a 0.052-m diameter horizontal pipe with special focus on the superficial liquid velocity range of 0.03–1.2 m/s at superficial gas velocities of 3.8, 5.2, and 6.6 m/s. It was found that the addition of 400 ppm of sodium dodecyl sulfate (SDS) to the water reduced the pressure drop by 25–40% when compared to equal flow rates without SDS. The pressure drop reduction occurred where the SDS eliminated the occurrence of the intermittent flow present with water. It was also found that the same concentration of SDS had virtually no effect on single phase liquid pressure drop. The pressure drop reduction appears to be due solely to the suppression of intermittent flow patterns.     

The impingement of sonic and sub-sonic jets onto a flat plate at inclined angles

The flow field associated with a jet impinging onto a surface at an inclined angle is investigated using particle image velocimetry (PIV). The results indicate that as a free jet impinges on a flat surface at an inclined angle the jet is turned by and spread laterally onto the impingement surface. The impingement angle of the jet is the dominant parameter in determining the rate of turning/spreading for the jet. The stagnation point is located using the PIV data and is found upstream of the geometric impingement point and upstream of the location of maximum pressure. The location of the stagnation point is a strong function of impingement angle and a weak function of impingement distance and pressure ratio. The location of the stagnation point is compared with the location of maximum pressure and compared to a curve fit for the location of maximum pressure based an exact solution of the Navier–Stokes equations for a non-orthogonal stagnation flow.     

Falling film flow along steep two-dimensional topography: The effect of inertia

Steady film flow along a vertical wall with isolated step changes is studied numerically for Reynolds numbers Re ∼ O(10⁻³–10²) and capillary numbers Ca ∼ O(10⁻²–10¹). The lengthscale of free surface capillary features upstream of a step-in or step-out decreases uniformly with Re and switches from a −1/3 to a −1/2 power-law dependence on Ca. The height of the capillary features first grows with Re, but eventually diminishes when inertia forces overpower capillary forces. Simultaneously, the key dynamics move from upstream to downstream of the step, and switch from capillary arrest to inertial re-directioning of the falling liquid. The latter mechanism involves a low-pressure region originating from the edge of the step. At a step-out, a new free surface feature appears with increasing Re, which is caused by liquid overshoot in the horizontal direction and is restrained initially by capillary and subsequently by inertial forces. Simple scaling arguments are shown to predict many of the above characteristics.