Figure 2 -1 - Sketch of the hydraulic jump channel
Related Figures (61)
Fig. 1-1 - Sketch of plunging jet flows (after CHANSON 1995a) Table 2-1 - Summary of the experimental configurations and instrumentation Fig. 2-3 - Sketch of the double-tip conductivity probe developed at the University of Queensland (Design: H. Further probe contamination (in Brisbane tap water) induced some signal shift over time: e.g., the voltage level of water could shift by 100% in less than 10 minutes. The variations of the air-voltage and water-voltage levels Table 3-1 - Experimental flow conditions: two-dimensional water jets Notes: dg, Vo: initial nozzle thickness and flow velocity; a: streamline angle with horizontal at nozzle. bubble is used in a broad sense to define an air volume surrounded continuously or not by liquid interfaces. tip conductivity probe scanned at 10 kHz per channel (see Section 2). Fig. 3-2 - Air-water flow characteristics in the free-falling jet (V, = 3.75 m/s, d, = 0.012 m): distributions of air Figures 3-2 and 3-3 present typical distributions of air concentration C, dimensionless velocity V/V, and dimensionless bubble frequency 9p = Fap*./X*do/Vo, where x is the distance from the nozzle in the flow direction, y is the distance normal to the jet support, V is the mean air-water velocity, V, is the nozzle velocity. d, is the jet thickness at the nozzle and F,p is the air bubble frequency!. fable 3-2 - Air bubble diffusion properties in two-dimensional water jets discharging into ai measured between C = 10% and C = 90%. Fig. 3-7 - Air concentration distributions at the free-surface of a water wall jet (CHANSON 1995a) conclusions regarding momentum and air concentration development of jump-entrained air-water flows. Fig. 4-2 - Typical distributions of air concentration, dimensionless velocity and dimensionless bubble frequency Fig. 4-3 - Definition sketch of the air-water flow properties in hydraulic jump with partially-developed inflow Table 4-1 - Experimental investigations of hydraulic jump flows Table 4-1 - Experimental investigations of hydraulic jump flows Notes: LDV: laser Doppler velocimeter; (8): also NAKAGAWA (1996). Table 4-2 - Air concentration distribution in the turbulent shear region of hydraulic jump flows Notes: V1: mean inflow velocity (V1 = qy//d1); (®) analysis by CHANSON (1997a). conditions: comparison between data (present study and re-analysed data, table 4-1) and equation (4-4) Equation (4-4) is shown in figure 4-4 and compared with new data (Present study) and some re-analysed data Fig. 4-4 - Location of the maximum air content YCy,4x/dy in hydraulic jump with partially developed inflow Table 4-4 - Empirical correlations of hydraulic jump flow velocity distributions velocity (V1 =qy/d 1); Vo: downstream flow velocity. Table 4-4 - Empirical correlations of hydraulic jump flow velocity distributions Table 4-5 - Empirical correlations of wall jet velocity distributions Fig. 4-5 - Dimensionless maximum velocity Vjyax/V1: comparison between data (table 4-1) and equation (4-8) Fig. 4-6 - Dimensionless distance yg 5/d,: comparison between data (table 4-1) and equation (4-9) 4.4 Experimental results: air bubble frequency distribution Fig. 4-7 - Dimensionless distance yy ,,.,/Yg.5: comparison between data (table 4-1) and equation (4-10) Fig. 4-9 - Dimensionless characteristic parameters as functions of the dimensionless distance from the jump toe - Table 5-1 - Experimental investigations of two-dimensional plunging jet flows otes: dy: impact jet thickness; Tuy: turbulence intensity of the impinging jet; U,: free-stream velocity at Table 5-2 - Plunging jet experiments: characteristics of the free-falling impinging jets (Present study) and x is the longitudinal distance from the nozzle. 'The mean air content and dimensionless quantity of entrained air are related as : Crean = Gair/(air+ dw) Table 5-3 - Quantity of entrained air Notes: dj: impact jet thickness; Fry = (U,-Ve)/ | g*d13; air: quantity of entrained air; U,: free-stream velocity t impact; V,: inception velocity of air entrainment; x,: fall height; (#) observed by CUMMINGS and at larger jet velocities (see reviews by WOOD 1991 and CHANSON 1997a). Table 5-4 - Quantity of entrained air at two-dimensional plunging water jets Notes: For a two-dimensional plunging jet (fig. 5-1), the air bubble diffusion process may be modelled by a solution of normal to jet support) where the air content is maximal (i.e. C = C,),x) at a given position x. 5.3 Experimental results: air bubble diffusion equation (5-4A) may be approximated by: Fig. 5-5 - Dimensionless distance from the jet support of the maximum air concentration, of the location where V = Uj/2 and of the maximum bubble frequency The location of the maximum air content was observed to be independent of the jet impact velocity. Overall th with a normalised coefficient of correlation of 0.966. Equation (5-5) is compared with the experimental data in properties of the shear layer are likely to be affected by the air bubble diffusion process. The early study of CUMMINGS (1996) (see also CUMMINGS and CHANSON 1997b) indicated further that Table 5-5 - Characteristics of two-dimensional free-shear layers: location of the streamline {y = y50} Table 5-6 - Air bubble diffusivity, Goertler's constant K and eddy viscosity in the developing shear region of plunging water jets: experimental results Notes: (8): analysis by CHANSON (1997a); (--): data not available. (with a normalised coefficient of correlation of 0.945) while, for monophase flows, the following relationship Fig. 5-7 - Dimensionless air bubble diffusivity D,/(U;*d1) and eddy viscosity v7/(U1*d 1) as a function of the Table 5-7 - Characteristic maximum bubble frequency F,,4x: experimental observations Fig. 5-10 - Longitudinal distribution of the dimensionless maximum air bubble frequency I _V\ hdd red Fig. 5-9 - Air bubble frequency as a function of the local air concentration different air-water flow situations, first suggested by the senior author (CHANSON 1995a, 1997a). developing shear flow may be predicted by analytical solutions of the diffusion equation: For each investigated flow situation (fig. 6-1), the results indicate that the air concentration distributions in the Fig. 6-2 - Dimensionless air bubble diffusivity D;/(U*Y) as a function of the dimensionless number Pw*U-*Y/o where Vinax is the maximum velocity measured at a distance yy,,,, from the bottom and yg 5 is the location Fig. 6-3 - Dimensionless maximum air bubble frequency (Fah) 44x“ Y/U as a function of the dimensionless In free-surface flows, air entrainment may be defined as the entrainment/entrapment of un-dissolved air bubbles
