CHANSON, H. (2013). "Hydraulics of Aerated Flows: Qui Pro Quo?" Journal of Hydraulic Research, IAHR, Invited Vision paper, Vol. 51, No. 3, pp. 223-243 (DOI: 10.1080/00221686.2013.795917) (ISSN 0022-1686). Hydraulics of Aerated Flows: Qui Pro Quo? Hubert CHANSON (IAHR Member), School of Civil Engineering, The University of Queensland, Brisbane, Australia Email: [email protected] (Corresponding Author) Full correspondence details: The University of Queensland, School of Civil Engineering, Brisbane QLD 4072, Australia Tel.: (61 7) 3365 3516 - Fax: (61 7) 3365 45 99, Email: [email protected] ABSTRACT In turbulent free-surface flows, the deformation of the surface leads to air bubble entrainment and droplet projections when the turbulent shear stress is greater than the surface tension stress that resists to the interfacial breakup. These complex processes at the water-air interface have been the focus of extensive experimental, numerical and theoretical studies over last two decades and this paper reviews the key advancements. It is highlighted that recent progress in metrology enables the detailed measurements of a range of air-water flow properties under controlled flow conditions, representing the sine qua non requirement for the development of improved physical understanding and for validating phenomenological and numerical models. The author believes that the future research into aerated flow hydraulics should focus on field measurements of high quality, development of new measurement approaches and data analyses tools, CFD modelling of aerated flows, and the mechanics of aerated flows in conduits. Keywords: air-water flows, air entrainment, dynamic similarity, hydraulic modelling, metrology, multiphase flows. 1 Introduction In high velocity free-surface flows, large quantities of air are exchanged at the free-surfaces and the air-water flow becomes a compressible fluid with density (1-C)+C  (1-C), where  is the water density,  is w a w w a the air density and C is the void fraction. Such flows are encountered in a wide range of applications in chemical, civil, environmental, mechanical, mining and nuclear engineering. In hydraulic engineering, the flow aeration may induce some flow bulking (Falvey 1980, Wood 1985,1991, Brocchini and Peregrine 2001b) and turbulence modulation which might lead to some drag reduction or enhanced turbulent kinetic energy dissipation depending on the flow characteristics. Drag reduction in aerated flows was documented for chute spillways (Jevdjevich and Levin 1953, Wood 1983, Chanson 1994,2004a) as well as for high-speed submerged bodies with micro-bubble injection (Bogdevich et al. 1977, Madavan et al. 1984, Marié 1987). The aeration of the flow may enhance the rate of energy dissipation in plunging breaking waves (Führboter 1970, Chanson and Lee 1997, Hoque and Aoki 2005a), and reduce the breakup length of water jets discharging into atmosphere (Héraud 1966, Ervine and Falvey 1987, Augier 1996). The air entrainment may also prevent or lessen the damage caused by cavitation (Peterka 1953, Russell and Sheehan 1974, Falvey 1990). In relation to environmental processes, it does substantially contribute to the air-water mass transfer of atmospheric gases (Wilhelms and Gulliver 1989, Gulliver 1990, Toombes and Chanson 2005). Altogether it is acknowledged that design engineers must take into account the effects of flow aeration: "Consideration of the effects of entrained air upon water flow may be essential to provide for the safe operation of a hydraulic structure" (Wood 1991); "(Self-)aeration is by far the most important feature of supercritical flow" (Novak et al. 2001). Since the first successful experiments by Ehrenberger (1926), some major contributions included Straub and Anderson (1958) for supercritical flows, Rajaratnam (1962) and Resch and Leutheusser (1972) for hydraulic jumps, Hoyt and Taylor (1977) for high-speed water jets, Ervine et al. (1980) for plunging jets. Although there have been several experimental studies over the recent decades (see reviews in Wood 1991, Chanson 1997a), there have been only a fe detailed field measurements. Among these are milestone studies CHANSON, H. (2013). "Hydraulics of Aerated Flows: Qui Pro Quo?" Journal of Hydraulic Research, IAHR, Invited Vision paper, Vol. 51, No. 3, pp. 223-243 (DOI: 10.1080/00221686.2013.795917) (ISSN 0022-1686). at Aviemore dam spillway (Keller 1972, Cain 1978, Cain and Wood 1981a,b) and near-full-scale laboratory experiments of Arreguin and Echavez (1986), Xi (1988) and Chanson (2007a). Importantly, all the experimental investigations highlighted the strong interactions between entrained bubbles and turbulence (Brocchini and Peregrine 2001a,b, Hanratty et al. 2003, Balachandar and Eaton 2010). Despite a number of significant advances (Rao and Kobus 1971, Wood 1991, Chanson 1997a, Brocchini and Peregrine 2001b), there are some fundamental issues related to the modelling of aerated flows, turbulence modulation by air bubbles and extrapolation of laboratory and numerical results to full-scale prototype structures (Ervine 1998). There are significant needs for detailed field measurements. In this paper, a brief review of aerated flows is presented first. Then the basic equations and latest advances in the modelling of aerated flows are identified, and the metrology of air-water flows in hydraulic engineering is discussed. The findings emphasise the complexity of the aeration process and address some misunderstandings (qui pro quo). A vision for future research developments concludes the paper. 1.1. Aerated flows in hydraulic engineering Aerated flows are often observed in low-, medium- and high-head structures, including storm waterways, culverts, dropshafts, spillway chutes, water jets taking off from flip bucket and stilling basins. Figures 1 and 2 illustrate some typical hydraulic engineering applications. Aerated flows are observed in small-scale as well as large-scale flows: from a water jet in a fountain (Q ~ 10-3 m3/s, d ~ 5 mm) to a large spillway during w a major flood (Q > 50,000 m3/s, d > 10 m) where Q is the water discharge and d is the flow thickness. In w w all cases, the interactions between the entrained air and the flow turbulence are very significant. In Fig. 1a, 1b and 1c, the maximum discharge capacity of the three dam spillways is about 65,000 m3/s, 12,000 m3/s and 93,000 m3/s respectively. Most hydraulic engineering applications involve turbulent flows characterised by quasi-random unpredictable behaviour, strong mixing properties and a broad spectrum of velocity fluctuations (Bradshaw 1971, Tennekes and Lumley 1972). Aerated flows in hydraulic engineering are extremely complicated with a broad range of relevant length and time scales. The time scales range from less than 1 ms for the turbulence dissipation in a white-water stream to about 24 h and 50 min for the tidal cycle in coastal processes and to more than 50 years for the deep-sea oceanic currents controlling the balances between oxygen and carbon dioxide (Chanson 2004b, Bombardelli and Chanson 2009). At the free-surface, the exchange of air and water is driven by the turbulence next to the air-water interface. The free-surface breakup and air entrainment occur when the turbulent shear stress is greater than the surface tension force per unit area resisting the interfacial breakup (Ervine and Falvey 1987, Chanson 2009). Once some air is entrained within the bulk of the flow, the break-up of air pockets occurs when the tangential shear stress is greater than the capillary force per unit area (Hinze 1955, Chanson 2009). As bubbles and droplets are advected by the flow, particle collisions may lead to their coalescence. The entire process is extremely complicated and experimental observations showed a broad range of air and water particle sizes in aerated flows (Halbronn et al. 1953, Thandaveswara 1974, Volkart 1980, Cummings and Chanson 1997b). The entrainment of air may be either localised at some flow discontinuity or continuous along the free-surface: i.e., defined respectively as singular or interfacial aeration (Chanson 1997a). Figure 3 illustrates some seminal interfacial and singular aeration processes, i.e., a self-aerated chute flow downstream of a gate outlet, a vertical plunging jet and a water jet discharging into atmosphere (from top to bottom). Figure 1b shows an example of interfacial aeration above the Wivenhoe dam spillway. Examples of singular aeration are shown in hydraulic jumps at spillway toe and in rivers in flood (Figs. 1d, 2a, 2e & 2f). In some applications, the free-surface aeration is maximised (e.g., for re-oxygenation in aeration cascades, drag reduction in naval applications). In others cases, aeration must be minimised or prevented: e.g., industrial jet cutting, fire-fighting. In most hydraulic engineering applications, the aeration is un-controlled (Figs. 1 and 2), but the amount of entrained air and its mixing within the flow must be accurately predicted to optimise the system performance and to ensure a safe operation: "For many hydraulic structures, safe operation can only be achieved if not only the characteristics of the water flow are considered, but due attention is also given to the simultaneous movement of air in the system" (Wood 1991). Over the last two decades, an increasing number of scientific contributions were published on aerated flow hydraulics. They reflect (a) a broader range of experimental configurations at laboratory scales, (b) availability of advanced off-the-shelf- instrumentation, and (c) advancements in signal processing. The development of commercial instrumentation, with manufacturers in America, Asia and Europe, reflects the CHANSON, H. (2013). "Hydraulics of Aerated Flows: Qui Pro Quo?" Journal of Hydraulic Research, IAHR, Invited Vision paper, Vol. 51, No. 3, pp. 223-243 (DOI: 10.1080/00221686.2013.795917) (ISSN 0022-1686). increased demand from the chemical and nuclear engineering industries, enhancing capabilities of hydraulic laboratories. This trend has been complemented by some developments in basic signal processing (Chanson 2002, Chang et al. 2003, Chanson and Carosi 2007a). These advances provide a greater range of measured parameters (see below), thus improving capabilities for novel experiments and validation of numerical models. 2 Theoretical framework of aerated flows When there is a sharp interface between immiscible fluids, i.e. air and water herein, the equations governing the multiphase gas-liquid flows at the micro-scale may be derived for each phase, and combined with some interface tracking (Tryggvason et al. 2011). Within a minimum set of restrictions, the equations of fluid motion in conservative form are:  ( v ) w   w wi 0 Water (1a) t x ix,y,z i  ( v ) a   a ai 0 Air (1b) t x ix,y,z i (wvwi)   (wvwivwj) pw  g   wij Water (2a) w i t x x x jx,y,z j i jx,y,z j (avai)   (avaivaj) pa  g   aij Air (2b) a i t x x x jx,y,z j i jx,y,z j where the subscripts a and w refer to the air and water properties respectively, v is the instantaneous velocity component, p is the instantaneous pressure, g is the gravity acceleration in the direction i = x,y,z, and  i ij denotes a instantaneous shear stress tensor component. Equations (1a) and (2a) for the water, and Eqs. (1b) and (2b) for the air phase, must be complemented by a mathematical representation of the moving interface and the associated conditions to couple the equations across the air-water interfaces. This formulation may be used for very detailed direct numerical simulations (DNS), although the application is very complicated (Tryggvason et al. 2011). An alternative approach is based upon ensemble-averaged equations (Drew and Passman 1999). Averaging Equations (1) and (2), the equations of conservations of mass and momentum give for the water and air: ((1C) ) ((1C) V ) w   w wi 0 Water (3a) t x ix,y,z i (C ) (C V ) a   a ai 0 Air (3b) t x ix,y,z i ((1C) V ) ((1C) V V ) w wi   w wi wj  t x jx,y,z j ((1C)( EA)) (1C) P (1C) g   wij wij M Water (4a) x w i x wi i jx,y,z j (CaVai)  (CaVaiVaj)  C P C g   (C(aij aEijA))M t x x a i x ai jx,y,z j i jx,y,z j Air (4b) where C is the averaged void fraction with the instantaneous void fraction c being 0 (water) or 1 (air), V and CHANSON, H. (2013). "Hydraulics of Aerated Flows: Qui Pro Quo?" Journal of Hydraulic Research, IAHR, Invited Vision paper, Vol. 51, No. 3, pp. 223-243 (DOI: 10.1080/00221686.2013.795917) (ISSN 0022-1686). P are the mean velocity and pressure respectively, EA is a shear stress term deriving from the averaging ij procedure and M is the resultant force of the interactions of the phases (Bombardelli 2012). Any mass i transfer between the two phases was ignored in Eqs. (3) and (4). Equation (4) is called the two-phase Navier- Stokes equations, i.e. two fluid model (TFM). Although the averaging of the conservation equations for each phase appears to give simpler expressions, a comparison between Eqs. (2) and (4) shows that the ensemble-averaging process adds two new terms in the right handside of Eq. (4). It becomes necessary to derive a number of closure relationships, also called constitutive relationships, which have some significant consequences on the mathematical structure of the problem (Drew and Passman 1999, Bombardelli 2012). 3 Modelling of aerated flows The analytical and numerical studies of aerated flows in hydraulic engineering are difficult considering the large number of relevant equations and parameters. Numerical simulations, which are typically based upon the two-phase Navier-Stokes equations (i.e. two fluid model TFM), are very demanding in terms of CPU time and computing facilities, not to mention the DNS. Any solution of the (full) N-S equations in a free- surface air-water flow configuration is a real challenge because of the strong interface deformations and air entrainment (Lubin and Caltagirone 2009, Prosperetti and Tryggvason 2009). A recent workshop concluded: "For most engineering applications, solving these equations will be impractical for the foreseeable future" (Hanratty et al. 2003). Current knowledge into aerated flows relies heavily upon laboratory investigations under controlled flow conditions (Wood 1991, Chanson 1997a). This is particularly important for on-going developments of numerical models and their validation (Lubin et al. 2009, Sousa et al. 2009, Ma et al. 2010, Bombardelli et al. 2011). The validation of a numerical model must be based upon some data sets independent of those used for calibration. A number of studies discussed the intricacy of the validation process (Mehta 1998, Roache 1998, Rizzi and Vos 1998). In a complex situation typical of aerated flows, the model outputs must be compared with a range of detailed gas-liquid flow properties including the distributions of void fraction, velocity, turbulence intensity and bubble sizes (Chanson and Lubin 2010). "Unequivocally [...] experimental data are the sine qua non of validation"; "no experimental data means no validation" (Roache 2009). The validation process must be physically sound as recommended by the American Institute of Aeronautics and Astronautics (AIAA 1998, Rizzi and Vos 1998, Roache 1998). Too many numerical studies lack credibility because they did not describe an accurate representation of the flow physics (Mehta 1998, Chanson and Lubin 2010). A key challenge is the uncertainty present in all physical systems. For example, in aerated flows, the data might be affected by the intrusive nature of the probes. More generally, the experimental data are subject to some intrinsic uncertainty, caused by a combination of technological limitations and accuracy of post-processing tools. The same applies to the numerical data, subjected to modelling, numerical and round-off errors, and whose optimal values of various parameters of interest may be biased (Sagaut et al. 2008). An uncertainty analysis must be carried out for both physical and numerical data, and the quality of the validation process is closely linked to both. Many CFD analyses to date fail to address the problem. Possibly because only a few mathematical techniques are presently mastered by the scientific community to analyse the results of the sensitivity analysis and to enhance the numerical solution accordingly (Roache 1998,2009, Chanson and Lubin 2010). Experimental investigations of air-water flows are not trivial (Rao and Kobus 1971), but some advances in metrology (e.g. phase-detection needle probes) combined with advanced post-processing techniques enable a detailed characterisation of high-velocity aerated flows under controlled conditions (Cain and Wood 1981a,b, Wood 1983,1985). A fundamental issue is the extrapolation of laboratory data to full-scale applications, associated with the selection of dynamic similarity, the usage of self-similarity and the development of theoretical relationships. The implications are broad because of the reliance of analytical and numerical modelling upon physical modelling for validation, especially in absence of prototype data. 3.1 Dimensional analysis and physical modelling of aerated flows Any fundamental analysis of aerated flows in hydraulic engineering is based upon a large number of relevant equations to describe the two-phase turbulent flow motion. Physical modelling may provide some insights into the flow motion if a suitable dynamic similarity is selected (Novak and Cabelka 1981, Liggett 1994). For some singular aeration, the relevant dimensional parameters include the air and water physical properties CHANSON, H. (2013). "Hydraulics of Aerated Flows: Qui Pro Quo?" Journal of Hydraulic Research, IAHR, Invited Vision paper, Vol. 51, No. 3, pp. 223-243 (DOI: 10.1080/00221686.2013.795917) (ISSN 0022-1686). and constants, the channel characteristics, the inflow conditions, and the local two phase flow properties at a location (x, y, z) (Kobus 1984, Wood 1991, Chanson 1997a,2009). Considering a vertical circular plunging jet with inflow thickness d and velocity V (Fig. 3, middle), a simplified dimensional analysis yields as a o o first approximation: F d V v' d N d T L C, o , , , ab , c o , int , int ...= V g d V d V d /g d o o o o o o o  x y z V V d g 2 L v '  F  , , , o , o o , w , , o ,... (5) 1d d d g d w   4 d V   o o o o w w o o  where C is the void fraction, V is the interfacial velocity, v' is a characteristic turbulent velocity, F is the bubble count rate defined as the number of bubbles detected per second in a small control volume, d is a ab characteristic bubble size, N is the number of bubble clusters per second, T and L are some turbulent c int int integral time and length scales respectively, x is the longitudinal coordinate, y is the radial coordinate and z is the ortho-radial coordinate both measured from the jet centreline,  is the water dynamic viscosity,  is the w surface tension between air and water, d is the jet diameter, V is the nozzle velocity, L is the free-jet length, o o v ' is a characteristic turbulent velocity at the inflow. o For an interfacial flow such as gated spillway flow in a rectangular chute (Fig. 3, top), a simplified dimensional analysis gives: F d V v' d N d T L C, c , , , ab , c c , int , int ...= V g d V d V d /g d c c c c c c c F  x , y , z ,dc , g dc3 , gw4 ,do ,Vo ,vo',W ,,... (6) 2d d d k w   3 d V V d   c c c s w w c c c c  where k is an equivalent roughness height, d is the gate opening, V is the gate velocity, W is the chute s o o width,  is the chute slope, d is the critical flow depth defined as: c Q 2 d 3 w (7) c gW2 and V is the critical flow velocity: c gQ V 3 w (8) c W In Equation (6), the critical flow depth and velocity, d and V respectively, were selected as the c c relevant length and velocity scales, thus assuming implicitly a Froude similitude since the dimensionless ratio d /k is proportional to a roughness Froude number. c s Equations (5) and (6) express the turbulent aerated flow properties at a position (x,y,z) within the two-phase gas-liquid flow as functions of a number of dimensionless parameters, including the Froude number Fr (4th term in right-hanside term of Eq. (2)), the Reynolds number Re (5th term) and the Morton number Mo (6th term) which is a combination of the Froude, Reynolds and Weber numbers: g 2 We3 Mo w  (9)  4 Fr2 Re4 w Since the -Buckingham theorem states that any dimensionless number can be replaced by a combination of itself and other dimensionless numbers, Equations (5) and (6) are expressed in terms of the Morton number, thus the Weber number should not be considered. The Morton number is a constant in most hydraulic modelling studies because both laboratory and full-scale prototype flows use the same fluids air and water. Note that the effects of surfactants and biochemicals on the air entrainment process and two-phase flow properties were neglected in the above developments. Reif (1978) and Chanson et al. (2006) tested respectively the effects of surfactants in hydraulic jumps and biochemicals in vertical circular plunging jets. CHANSON, H. (2013). "Hydraulics of Aerated Flows: Qui Pro Quo?" Journal of Hydraulic Research, IAHR, Invited Vision paper, Vol. 51, No. 3, pp. 223-243 (DOI: 10.1080/00221686.2013.795917) (ISSN 0022-1686). Their results demonstrated some substantial modulation of the air-water flow properties which were implicitly ignored in Equations (5) and (6). Further the effects of intrusive probes onto the flow were neglected. For phase-detection needle probes, this was recently considered (Chanson and Toombes 2002, Gonzalez 2005, Carosi and Chanson 2006) and the limited findings indicated some non-negligible impact of the sensor size on the detection of small bubbles, especially sub-millimetric ones. Traditionally the free-surface flows including plunging jets and self-aerated chute flows are studied based upon a Froude similarity (Henderson 1966, Liggett 1994, Chanson 2004b, Viollet et al. 2002). In the particular case of a hydraulic jump, basic momentum considerations demonstrate the significance of the inflow Froude number (Bélanger 1841, Lighthill 1978) and the selection of the Froude similitude follows implicitly from basic theoretical considerations (Liggett 1994, Chanson 2012). However the turbulent shear flows are dominated by viscous effects, while the mechanisms of bubble breakup and coalescence are dominated by surface tension forces. A true dynamic similarity of aerated flow does require achieving identical Froude, Reynolds and Morton numbers in both the prototype and its model. This is impossible using geometrically similar models unless working at full-scale. Practically the Froude and Morton dynamic similarities are simultaneously used when the same fluids (air and water) are used in prototype and model. But the Reynolds number is grossly underestimated in laboratory conditions, thus leading to viscous scale effects in small size models typical of hydraulic engineering applications (Kobus 1984, Wood 1991, Chanson 2009). Figure 4 illustrates two examples: a water jet discharging into atmosphere (Fig. 4a) and a dropshaft flow (Fig. 4b). In each case, a drastic reduction in flow aeration is observed in the smaller model operating at smaller Reynolds numbers for identical Froude and Morton numbers. A small number of studies systematically investigated the aerated flow properties, at the local sub- millimetric scale, in geometrically similar models under controlled flow conditions to assess the associated scale effects. These investigations were based upon the Froude and Morton similitudes with undistorted models, encompassing vertical plunging jets (Chanson et al. 2004), hydraulic jumps (Chanson and Gualtieri 2008, Murzyn and Chanson 2008, Chanson and Chachereau 2013), dropshafts (Chanson 2004d), spillway aeration devices (Pfister and Hager 2010) and stepped spillways (Boes and Hager 2003, Chanson and Gonzalez 2005, Felder and Chanson 2009). Despite the limited scope, the results of experimental investigations demonstrated unequivocally the limitations of dynamic similarity and physical modelling of aerated flows. They emphasised further that the selection of the criteria to assess scale affects is critical: e.g., the void fraction distributions, turbulence intensity distributions, distributions of bubble chords. That is, any mention of scale effects must be associated with the list of tested parameters (Chanson 2009, Chanson and Chachereau 2013), including in monophase flows (Schulz and Flack 2013). The experimental results show that some parameters, such as bubble sizes and turbulent scales, are likely to be affected by scale effects, even in 2:1 to 3:1 scale models (Chanson 2004b,2009). No scale effect is observed at full scale only, using the same fluids in prototype and model: i.e., in prototype flow conditions. 3.2 Self-similarity in aerated flows If spatial distributions of flow properties at various times (or/and spatial locations) can be obtained from one another by a similarity transformation, then it is said that a process posses a self-similarity property (Barenblatt 1996). Self-similarity is a powerful tool in turbulent flow research involving a wide spectrum of spatial and temporal scales, and hydraulic engineering applications encompass turbulent flows with a broad range of length and time scales. The non-linear interactions among turbulent vortices and particles at different scales lead to a complicated flow structure, and relationships among flow properties at different scales are of crucial importance (Wang 1998, Barenblatt 1996). These play also a major role in comparing analytical, experimental and numerical results if these results relate to different scales. In some recent studies, self-similarity was tested systematically in terms of the distributions of air-water flow properties in skimming flows on stepped spillways (Chanson and Carosi 2007b, Felder and Chanson 2009). Several self- similar relationships were observed at both macroscopic and sub-millimetric scales. Self-similarity is closely linked to dynamic and kinematic similarities, and the existence of self- similar relationships may have major implications on the measurement strategy in experimental and physical modelling studies (Foss et al. 2007). Although it is nearly impossible to achieve a true dynamic similarity in aerated flows because of the number of relevant dimensionless parameters (see previous section), these experimental findings showed a number of self-similar relationships that remain invariant under changes of scale. Namely, they have scaling symmetry which led in turn to remarkable applications at prototype scales. These results may provide a picture general enough to be used, as a first approximation, to characterise the CHANSON, H. (2013). "Hydraulics of Aerated Flows: Qui Pro Quo?" Journal of Hydraulic Research, IAHR, Invited Vision paper, Vol. 51, No. 3, pp. 223-243 (DOI: 10.1080/00221686.2013.795917) (ISSN 0022-1686). aerated flow field in similar hydraulic structures irrespective of the physical scale (Felder and Chanson 2009). 3.3 Discussion The modelling of aerated flows is presently restricted by the complexity of theoretical equations, some limitations of numerical techniques, a lack of full-scale prototype data, and very-limited detailed experimental data sets suitable for sound CFD model validation. The implications are far reaching including in terms of numerical modelling: can we trust numerical modelling whose validation is based upon small- size scale-affected laboratory data? The findings of systematic experimental studies demonstrated that (a) the notion of scale effects must be defined in terms of some specific set of gas-liquid characteristics, and (b) some aerated flow properties are more affected by scale effects than others, even in large-size facilities. Interestingly, distorted physical modelling of aerated flows has not been considered to date, although the scale distortion may enable to achieve some similitude in terms of bubble rise velocity on chute spillways and inclined plunging jets. There are some basic differences between dynamic similarity and self-similarity, and Fig. 5 provides some illustration. Figure 5a presents some dimensionless distributions of void fractions in chute spillways, with a selection of the dimensionless terms based upon an undistorted Froude similitude. The results show a close agreement between prototype and model data, although the model Reynolds numbers were an order of magnitude smaller than prototype Reynolds numbers (Fig. 5a). In this instance, the findings implied that the laboratory data may be extrapolated to full-scale based upon a Froude similitude with negligible scale effect. Figure 5b shows some self-similar relationship in terms of interfacial velocity distributions in self-aerated smooth chute flows. The results highlighted a sound self-similarity expressed in the form of a power law for y/Y < 1 and an uniform profile above: 90 1/N V  y    y/Y < 1 (10)   90 V Y 90  90  V 1 y/Y > 1 (11) 90 V 90 with Y the characteristic distance from invert where C = 0.90 and V the characteristic velocity at y = Y . 90 90 90 Despite a close agreement between prototype and model data (Fig. 5b), the laboratory results should not be extrapolated to full-scale, unless the scaling relationships in terms of the characteristic distance Y and 90 velocity V are known. If one or the other cannot be extrapolated based upon similarity considerations, the 90 self-similarity may not assist with the engineering design. In addition to dynamic similarity and self-similarity, a further modelling approach may be based upon some theoretical developments leading to theoretically-based equations. An illustration is shown in Figure 5a, in which the void fraction distributions are compared with an analytical solution of the advection diffusion equation for air bubbles. Following Rouse (1937) for suspended sediment flows and Wood (1985) for self-aerated chute flows, a number of theoretical void fraction distributions were derived analytically for self-aerated chute flows, water jets discharging into air, plunging jets and hydraulic jumps (Chanson 1997a,2008). Recent developments included Chanson and Toombes (2002) in self-aerated skimming flows on stepped spillways, and Chanson (2010) in hydraulic jumps. The existence of theoretical relationships may have some implications regarding the laboratory study approach and measurement methods. For example, in self-aerated chute flows (Fig. 5a), the analytical solution of the advection diffusion equation implies that the void fraction distribution is given by C = f(y/Y , C ), where C is the depth-averaged void fraction 90 mean mean defined in terms of the characteristic distance Y ; the analytical solution implies that no additional 90 measurements are needed in regions of identical mean void fraction C for a identical discharge per unit mean width. The fact that an analytical solution exists may allow a drastic reduction of the volume of measurements. CHANSON, H. (2013). "Hydraulics of Aerated Flows: Qui Pro Quo?" Journal of Hydraulic Research, IAHR, Invited Vision paper, Vol. 51, No. 3, pp. 223-243 (DOI: 10.1080/00221686.2013.795917) (ISSN 0022-1686). 4 Metrology of air-water flows 4.1 Instrumentation In a free-surface flow, the void fraction ranges typically from 0 to 100%, and the mass and momentum fluxes are encompassed within the flow region with void fractions less than 95% (Cain 1978, Wood 1985). In this zone (C < 0.95), a number of field and laboratory data sets demonstrated that the high-velocity gas-liquid flows behave as a quasi-homogenous mixture and the two phases travel with a nearly identical velocity, the slip velocity being negligible (Rao and Kobus 1971, Cain and Wood 1981b, Chanson 1997a). Any detailed characterisation of the entire gas-liquid flow must rely upon a metrology, applicable and accurate for a wide range of the void fraction levels (0 < C < 0.95). In a two-phase air-water flow, a description of the turbulent flow field requires a number of parameters significantly larger than for a monophase flow. The additional parameters include the void fraction, the bubble count rate, the bubble and drop size distributions, the clustering properties. Further a number of parameters (e.g. instantaneous velocity) cannot be measured with some traditional instrument (Pitot tube, ADV, LDA) because the presence of bubbles and air-water interfaces affects adversely their operation. With void fractions less than 3% (or even less), some measurement techniques may be used, although with some empirical corrections: e.g., photography, Pitot tube, acoustic Doppler velocimetry (ADV), laser Doppler velocimetry (LDA) (Sheng and Irons 1991, Liu et al. 2004). However the corrections of such type of measurements are highly empirical and rely upon the intrinsic performances of the measurement device. This 'correction' approach should never be used for void fractions larger than 3 to 5%, and it is inappropriate for many free-surface flows in which the local void fractions range between 0 and 100%. Recent developments in particle image velocimetry (PIV) provided detailed data in dilute disperse flows (Balachandar and Eaton 2010), but for flow conditions corresponding to void/liquid fractions less than about 5%. Some specialised instrumentation was developed during the last 50 years, including back-flushing Pitot tubes, needle phase-detection probes, conical hot-film probes and fibre phase Doppler anemometry (FPDA). The needle probe and conical hot-film systems are the two oldest techniques. The conical hot-film probes have been used for 40 years with a range of flow conditions, including hydraulic jumps (Resch and Leutheusser 1972, Babb and Aus 1981), vertical plunging jets (Chanson and Brattberg 1998) and bubble- induced turbulence (Lance and Bataille 1991, Rensen et al. 2005). A major constraint of the hot-film instrumentation is the calibration of the sensor, as well as the rapid probe contamination requiring systematic re-calibrations (e.g. every three minutes if Brisbane tap water is used) (Chanson and Brattberg 1998). The use of demineralised water may significantly reduce the probe sensor contamination rate, although this restricts drastically the test facility size, hence the Reynolds number. Some pertinent reviews of air-water flow probes and their issues include Jones and Delhaye (1976), Cartellier and Achard (1991), Chanson (2002). For the past 40 years, the largest number of and most successful experiments have been conducted with phase-detection needle probes, including some milestone prototype measurements on Aviemore dam spillway in New Zealand (Cain and Wood 1981a,b). The needle-shaped phase detection probe is designed to pierce the bubbles and droplets (Fig. 6). It is particularly well-suited to track interfaces, such data being a requirement for DNS modelling (section 2). Since its introduction in experimental practice by Neal and Bankoff (1963,1965), the designs of the needle probe have been refined. Although the first designs were based upon resistivity probes, both optical fibre and resistivity probes are currently used (Cartellier 1992, Chanson 2002). In practice the signal output quality of phase-detection intrusive probes is closely linked to the sensor size, the sampling rate F and sampling duration T . The size of the sensor is basically the sampl sampl needle diameter Ø , which is the diameter of the optical fibre or inner electrode. Current measurement tip systems use sensor sizes less than 0.1 mm in low flow velocities (V < 1 to 2 m/s), while the studies of high velocity flows (1 < V < 20 m/s and more) require more sturdy probes with diameters typically between 0.1 and 0.5 mm. As an example, the author used 0.025 mm needle probes at flow velocities up to 9 m/s, but the risks of probe damage were high with velocities larger than 3 m/s (Cummings and Chanson 1997b, Brattberg and Chanson 1998, Chanson and Brattberg 2000); he also used needle probes with inner electrodes between 0.1 and 0.35 mm in highly turbulent flows with velocities up to 18.5 m/s without any trouble (Chanson 1989,2002). With a needle probe, the selection of the sampling frequency is linked to the smallest detectable bubble size, which is of the order of magnitude of the needle diameter  . This yields a minimum sampling tip frequency to prevent aliasing: CHANSON, H. (2013). "Hydraulics of Aerated Flows: Qui Pro Quo?" Journal of Hydraulic Research, IAHR, Invited Vision paper, Vol. 51, No. 3, pp. 223-243 (DOI: 10.1080/00221686.2013.795917) (ISSN 0022-1686). V F  2 (12) sampl Ø tip where V is the longitudinal velocity. Some in-depth sensitivity analyses were conducted in terms of the sampling frequency and duration in hydraulic jumps and stepped chutes (Chanson 2007c, Chanson and Felder 2010). The results showed that the sampling rate had to be greater than 10 kHz, and the sampling duration greater than 20 s to have negligible effects on the void fraction, bubble count rate and air-water velocity measurements, while more advanced correlation analyses including the estimate of the turbulence intensity require a sampling duration of 45 s or larger. A dual-tip probe provides further information on the interfacial velocity and turbulence level. With such a dual-tip probe, two key probe characteristics are the longitudinal x and transverse z separation distances of the sensors. Figure 6a shows a dual-tip probe designed at the University of Queensland to minimise the effect of the leading tip onto the bubble piercing by the trailing tip. The wake effects of the leading tip on the trailing tip were discussed by Sene (1984) and Chanson (1988). Cummings (1996) tested the effects of the transverse separation distance on the data outputs, and he obtained optimum results with z/x = 0.08 to 0.10. Some experimental experience is presented in Figure 7 in terms of the longitudinal distance between probes and of sensor size. The data tended to imply that an optimum longitudinal separation distance was linked with the interfacial velocity and sensor size: (x) optimum 33.5V0.27 (13) Ø tip the result being obtained for 0.4 < V < 18.5 m/s and 1.5 < x < 102 mm. The experience indicated that the longitudinal separation distance x impacted only mildly on the data quality, as hinted by Figure 7. While the single-tip and dual-tip needle probe designs are most common, other probe designs were also successfully tested. These include some 3 or 4 sensor needle probes (Kim et al. 2000), a cylindrical probe for cross flow turbine measurements (Borges et al. 2010), single-tip probe arrays (Coakley et al. 2001, Chanson 2004c,2007b), and other electrical probes (Lamb and Killen 1950, Straub and Lamb 1958). 4.2 Signal processing Figure 6c illustrates some typical signal output from an array of two single-tip needle probes similar to the one shown in Fig. 6b. In Fig. 6c, each steep drop of the signal corresponds to an air bubble interface pierced by the probe tip and the graph shows a group of five bubbles detected by the probes. Although the probe response to bubble piercing should be ideally rectangular, the signal output is not exactly that because of the finite size of the tip, the wetting/drying time of the interface covering the tip and the response time of the probe and electronics. The measure raw signal is typically transformed into a binary time-series of instantaneous void fraction (c = 0 in water and 1 in air). Although there are several phase discrimination techniques, the most robust technique in free-surface flows is the single-threshold technique, with a threshold set at 40% to 60% of the air-water range (Toombes 2002, Chanson and Felder 2010, Felder 2013). In a steady stationary flow, the time-averaged void fraction C is the arithmetic mean of the instantaneous void fraction. The bubble count rate F is the number of bubbles (i.e water-to-air interfaces) detected by the probe sensor per second. With a dual-tip probe (Fig. 6a), the time-averaged velocity is deduced from the cross-correlation function between the probe signals: x V  (14) T where T is the average interfacial travel time between the sensors corresponding to the time lag of the maximum cross-correlation function (R ) (Fig. 8). The shape of the auto- and cross-correlation functions xy max provides further information on the turbulent field, including the auto- and cross-correlation time scales, T xx and T respectively (Fig. 8), and the turbulence intensity (Chanson and Carosi 2007a, Felder and Chanson xy 2012): 2 v' 2  T  Tu     xy  T 2 (15) V T (R )  xx  xy max  CHANSON, H. (2013). "Hydraulics of Aerated Flows: Qui Pro Quo?" Journal of Hydraulic Research, IAHR, Invited Vision paper, Vol. 51, No. 3, pp. 223-243 (DOI: 10.1080/00221686.2013.795917) (ISSN 0022-1686). Assuming that the cross-correlation function is a Gaussian distribution and defining  the time scale for  which: R (T+ )=R (T)/2 and T is the characteristic time for which the normalised autocorrelation xy 0.5 xy 0.5 function equals 0.5 (Fig. 8), Equation (15) may be simplified into (Chanson and Toombes 2002): v'  2 T 2 0.5 0.5 0.851 (16) V T Equations (15) and (16) are based upon the assumption that both auto- and cross-correlation functions have a Gaussian shape, and laboratory observations showed that the approximation is reasonable for small to moderate time lags . When an array of two sensors are mounted side by side separated by a transverse distance z (Fig. 6b) and the measurements are performed for a range of separation distances, the turbulent integral length and time scales, L and T respectively, may be calculated as: int int z((R ) 0) xz max L  (R ) dz (17) int xz max z0 z((R ) 0) 1 xz max T  (R ) T dz (18) int xz max xz L int z0 where (R ) and T are the maximum cross-correlation coefficient and cross-correlation integral time xz max xz scales (Chanson 2007b, Chanson and Carosi 2007b). L and T are characteristics of the large vortical int int structures advecting the air bubbles and interacting with the air-water interfaces. Detailed experimental data were obtained in hydraulic jumps (Chanson 2007b, Zhang et al. 2013) and stepped chute flows (Chanson and Carosi 2007b, Felder and Chanson 2009). The results highlighted the importance of the intermediate air- water flow region, where 0.3 < C < 0.7, in which the turbulence intensity, turbulent integral time and length scales were maximum. This is illustrated in Figure 9 for a skimming flow on a stepped spillway: Tu, T and int L are shown as functions of the time-averaged void fraction C. The above method may also be applied in int the longitudinal direction by varying the separation distance x. Experiments in skimming flow above a stepped chute yielded close results in terms of turbulent integral scales between the longitudinal and transverse separation distances (Chanson and Carosi 2007b). The signal processing of needle probes may further characterise the microscopic structure of the gas- liquid flow. Microscopic properties include the distributions of air and water chords at each sampling location, as well as the sequential arrangement of air and water chords (Fig. 6). The latter may allow the characterisation of bubble and droplet clustering, including the cluster properties. The study of particle clustering is relevant in industrial applications to infer whether the formation frequency responds to some particular frequencies of the flow. The level of clustering may give a measure of the magnitude of bubble- turbulence interactions and associated turbulent dissipation. In the bubbly flow region (C < 0.3), clustering is linked with both turbulent particle clustering and the effects of inertial forces leading to bubble trapping and clustering in large scale turbulent structures. It may result from self-excitation of fluctuations of bubble concentration (Elperin et al. 1996) and particle-particle interactions (i.e. near-wake effect). When a bubble is trapped in a vortical structure, the centrifugal pressure gradient moves the bubble inside the coherent structure core where bubble-bubble interactions may further take place (Tooby et al. 1977, Sene et al. 1994). Note that particle clustering analyses are typically restricted to the bubbly and spray region, C < 0.3 and C > 0.7 respectively. There are two main types of signal analyses to investigate particle clustering. One method is based upon the analysis of the water chord between two adjacent air bubbles. If two particles are closer than a characteristic length scale, they may form a bubble cluster. This characteristic length scale may be related to the water chord statistics or to the lead bubble size itself, since bubbles within that distance are in the near- wake of and influenced by the leading particle. A number of early studies were conducted in hydraulic jumps, dropshaft flows and stepped spillway flows (Chanson and Toombes 2002, Chanson et al. 2006, Gualtieri and Chanson 2007,2010), These studies were restricted to the streamwise distribution of bubbles and did not take into account particles travelling side by side or a group of spatially distributed particles (Fig. 6b). A recent numerical study using an Eurlerian-Lagrangian approach showed that the longitudinal signal analysis may be representative of the three-dimensional flow (Calzavarini et al. 2008), while an experimental study of bubbles/droplets using two probes located side by side in skimming flow above a stepped spillway