ARANTES_et_al_Lower Nappe Aeration in Smooth Channels

8/3/2019 ARANTES_et_al_Lower Nappe Aeration in Smooth Channels

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Anais da Academia Brasileira de Cincias (2010) 82(2): 521-537(Annals o the Brazilian Academy o Sciences)ISSN 0001-3765www.scielo.br/aabc

Lower nappe aeration in smooth channels: experimental data

and numerical simulation

EUDES J. ARANTES1, RODRIGO M. PORTO2, JOHN S. GULLIVER3,

ALBERTO C.M. LIMA4 and HARRY E. SCHULZ2,5

1UTFPR, Campus Campo Mouro, Caixa Postal 271, 87301-005 Campo Mouro, PR, Brasil2Departamento de Hidrulica e Saneamento/EESC/USP,

Av. Trabalhador So-carlense, 400, 13566-590 So Carlos, SP, Brasil3Department o Civil Engineering, University o Minnesota, 2 Third Avenue S.E, 55455 Minneapolis, MN, USA

4Universidade da Amaznia, Av. Alcindo Cancela, 287, Umarizal, 66060-000 Belm, PA, Brasil5Ncleo de Engenharia Trmica e Fluidos/EESC/USP,

Av. Trabalhador So-carlense, 400, 13566-590 So Carlos, SP, Brasil

Manuscript received on September 14, 2008; accepted or publication on September 30, 2009

ABSTRACT

Bed aerators designed to increase air void ratio are used to prevent cavitation and related damages in

spillways. Air entrained in spillway discharges also increases the dissolved oxygen concentration o the

water, which can be important or the downstream shery. This study considers results rom a systematic

series o measurements along the jet ormed by a bed aerator, involving concentration proles, pressure

proles, velocity elds and corresponding air discharges. The experimental results are, then, compared,

with results o computational fuid dynamics (CFD) simulations with the aim o predicting the air discharge

numerically. Comparisons with jet lengths and the air entrainment coecients rom the literature are also

made. It is shown that numerical predictive tools urnish air discharges comparable to measured values.

However, i more detailed predictions are desired, verication experiments are still necessary.

Key words: spillway aerators, air entrainment, air-water fows, multiphase fows.

INTRODUCTION

Bottom aerators are a technique used to prevent cavitation erosion on spillways and to enhance the oxygencontent o the water. Air vented through the bottom aerators is entrained into the fowing water, increasing

the compressibility o the air-water mixture and lowering the velocity o pressure waves. When implosion

o cavitation bubbles occurs, the higher compressibility o the surrounding fuid dampens the impact o the

pressure waves. Additionally, the bubbles increase the contact area between air and water, improving the

oxygen dissolution into the water and the DO content downstream o the spillway.

Correspondence to: Pro. Harry Edmar SchulzE-mails: [email protected]; [email protected]; [email protected]

An Acad Bras Cienc (2010) 82 (2)


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522 EUDES J. ARANTES et al.

Experimental investigations on spillway air entrainment by bottom aerators have resulted in empirical

design equations. Schwarz and Nutt (1963) presented a theoretical equation or the jet length ormed ater

the ramp. Pan et al. (1980) and Pinto et al. (1982) related the air discharge to geometrical parameters o

the jet. Additionally, Tan (1984) and Rutschmann and Hager (1990) explained the dependence o the air

discharge on the jet length. The jet length predictions obtained by Tan (1984) are close to those o Schwarz

and Nutt (1963).

In Brazil, the studies on aerated spillways were intensied during the construction o the hydropower

dams in the 1970 and 1980 decades. The rst relevant conclusions or spillways were presented by Pinto et

al. (1982), while Borsari (1986) and Fuentes (1992) urnished reviews o important studies and procedures.

These aerator studies helped in the establishment o locally adopted procedures. Some early studies,

like Volkart (1980) and Wood (1985), added important conceptual contributions or the understanding o

aerated fows. Practical applications o the research results, however, require more detailed measurements

and the review o existent results. Kkpinar and Ggs (2002) conducted an extensive experimental study

and urnished correlations not only or the jet length, but also or the air entrainment in lower and uppernappes, and a graphical presentation o the eect o ramp heights and bed slopes. The redistribution o

fow velocity in the aeration zone was considered by Toombes and Chanson (2005), while the details o the

geometry o the air-water interace were used to propose the concept o entrapped air by Wilhelms and

Gulliver (2005). A similar entrapped air concept was used by Lima et al. (2008) to explain measurements

o air void ratios in lower nappe aeration.

This paper seeks to compare CFD simulations with a detailed experimental study o the lower nappe

o a jet generated by an aerator in a laboratory chute. Measurements o velocity elds, pressure and air

concentration (void ratio) proles will be compared to CFD results. The CFD simulations o air discharges

were comparable to the measured values. It is also shown that, i a more detailed description is needed,

experiments are still necessary.

EXPERIMENTAL METHODS

The experiments were conduced in a chute built in the Laboratory o Environmental Hydraulics o the

School o Engineering at So Carlos, Brazil. The chute had a slope o 14.5, an useul length o 5.0 m, with

a rectangular cross section 0.20 m wide and 0.50 m high. The bed aerator was composed o a ramp with a

length o 23.0 cm, a nal height tr = 4.0 cm and an angle o 10 relative to the chute. The chamber under

the jet had a depth o 12.0 cm, a length o 18.0 cm and a width o 20.0cm. The air discharge was measured

in the air supply tube, which had a diameter o 71.65mm. Air velocities were obtained rom pressure

measurements, with a micromanometer having one side opened to the atmosphere and the other xed in a

pre-calibrated position in the tube. The concentration measurements in the fow were made with a Cesium

137 probe, as shown in Figure 1. Calibration was made with the channel a) ull with water and b) empty.

The Cesium 137 radiation was projected perpendicularly to the fow in the channel and a counter registered

the remaining radiation ater passing the mixture o air and water and the glass walls. The concentration

measurements thus consider the entire width o the channel. Air concentration proles were obtained by

positioning the probe and radiation counter along the vertical o every studied cross section. Each obtained

concentration is a horizontal mean value transverse to the fow direction.



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BED AERATION IN SMOOTH CHANNELS: EXPERIMENTS AND NUMERICAL SIMULATION 523

Fig. 1 Equipment used or the concentration measurements with Cesium 137 probe.

An electromagnetic fow meter was used to measure the water discharges, which were checked with

a rectangular weir located at the outlet o the channel. The measurement o velocity elds in the jet was

perormed or nine runs, using a mirror inside o the fow. Velocity elds were measured using particle

image velocimetry (PIV). The light source was a copper gas Laser, with a mean power o 20 W and pulses

at 10 kHz. The pulse power ranged rom 60 to 140 kW. Generated wavelengths were 510.6 nm (green)

and 578.2 nm (yellow). A CCD camera with a resolution o 1024 pixels 1024 pixels was used to record

the images. Ater capturing and storing the images in the computer, PIV sotware was applied to each

image to obtain velocity vector elds by using auto-correlation calculations. 234 images were taken or

each run. Figure 2 shows all cross sections used in the present study. Sections 1, 2 and 3 were used to

obtain the approach fow inormation (velocity and water depth). Sections 4 through 8 were used or theconcentration measurements. Additional sections SIX and SX were used or velocity measurements in the

jet core. For velocity measurements in sections 1 and 2, the laser sheet was introduced in the fow rom the

bottom o the channel.

Fig. 2 Measurement sections or the present study. Distances are in centimeters.



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For velocity measurements in the jet core, a mirror was positioned downstream in the jet beore the

upper and lower white water regions came together, as shown in Figure 3, and the laser sheet was intro-

duced into the fow rom the side o the channel. Detailed descriptions o the chute and the measurement

equipment may be ound in Carvalho (1997) and Lima (2004).

Fig. 3 Experimental arrangement or the velocity measurements in the jet core using a mirror.

SIMULATION METHODS

In this study, the inhomogeneous multiphase model was applied with the liquid and the gaseous phases

considered. There is one solution eld or each separate phase, and the fuids interact via interphase transer

terms. For example, the two phases may have separated velocity and temperature elds, but there will be a

tendency or these to come to an equilibrium through interphase drag and heat transer terms (CFX 2004).

The ollowing equations or inhomogeneous multiphase fow were used to simulate the air and waterfows, and air uptake:

Continuity Equations:

t

raa

+

raa a

= SMSa +

Npb=1

ab (1)

Momentum Equations:

t

ra a a

+

ra

a a a=

rapa +

raa a +

a

T+

Npb1

+ab b +ba a

+ SM A + Ma

(2)

where: ra is the volume raction o each phase (phases indicated by a, with a assuming values rom

1 to Np, the total number o phases), a is the density o phase a,Ua is the velocity vector o phase

a, a is the viscosity o phase a, SMSa represents mass sources specied by the user; ab is the mass

fow rate per unit volume rom phase b to phase a. This term only occurs i interphase mass transer

takes place; SMa represents momentum sources due to external body orces, and Ma represents interacial

orces acting on phase a due to the presence o other phases. The term

+abUb

+ba

Ua

represents



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momentum transer induced by interphase mass transer. The volume ractions o the phases sum to unity,

that is:Npa=1

ra = 1 (3)

There are 4NP+ 1 equations to describe the fuid dynamics or the 5NP unknowns ra, Ua||, ||Va, Wa,

(components o the velocity vectorial eldUa), and Pa (the pressure eld o each phase). The additional

NP 1 equations needed to close the system o equations were supplied by assuming that all phases

shared the same pressure eld, P, that is:

Pa = P or all a = 1, . . . , NP (4)

A scalar variable in phase a has the corresponding transport equation:

traaa+ raa a a ra aD()a +

ta

Sctaa = S()a + T()a (5)

where D()a is the Diusivity o a, S()a represents an external source in phase a, and T

()a represents

sources oa due to interphase transers. Details o the multiphase model may be ound in CFX (2004).

To initialize a simulation, a relatively gross mesh was rst used to locate the air-water interace. Then,

the regions o the upper and lower ree suraces were rened, allowing a detailed location o the interace

or the denitive run. The nal mesh o each case presented a higher concentration o cells in the upper

and lower nappes o the jet, as shown in Figure 4. Details are described by Arantes (2007). Table I shows

the main characteristics o the grids and the simulated fuids (air and water). The number o nodes and

elements o the grids are mean values or all simulated conditions.

Fig. 4 Example o rened mesh used or the numerical calculations.

The model allows the adjustment o constants and boundary conditions in order to calibrate the pre-

dictions with measured results. Dierent combinations were tested, but they in general reproduced only



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TABLE I

The Domain, Fluids and Simulation characteristics,

initial and boundary conditions.

Domain (ater adaptation)

Number o Nodes 550000Number o Elements 2750000

Fluid: Water

Temperature 25C

Dynamic Viscosity 8.899*104 kg.m1.s1

Density 998 kg.m3

Surace Tension Coe. 0.0732 N.m1

Fluid: Air

Temperature 25C

Dynamic Viscosity 1.831*105 kg.m1.s1

Density 1.185 kg.m3

Simulation

Time step 0.1 s

Simulation Time 10 s

Processor Processor 3.2 GHz

Characteristics (Opteron 64 bits)

CPU Processing time 1*105 s

a portion o the observed results. The CFX standard constants and conditions, on the other hand, led to

acceptable predictions or the whole set o experiments, being thus used in this study.

The conditions in the inlet were imposed as:

Pressure: hydrostatic pressure,

Turbulence intensity: xed at 5% o the water velocity (standard or CFX),

Turbulence model: SSG Reynolds Stresses using CFX standard parameters. The model allows the

simulation o non-isotropic situations, and the use o the law o the wall.

Roughness or the law o the wall: 1.0 mm.

The calibration was primarily based on the predictions o the jet lengths.

RESULTS AND DISCUSSION

Fourteen runs were conducted in the chute. Table II provides the experimental conditions. The jet length

o run 2 is not available because the jet was longer than the channel. Velocity eld measurements using

PIV were perormed in the nine runs indicated by (*). Results o all ourteen runs were used to check the

reproducibility o the data, while the results o the nine runs with velocity data were used to compare with

CFD predictions.



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TABLE II

Experimental conditions.

Run

OpeningDepth Water Velocity Froude Jet Air fow Air Water

o theat S2 fow rate at S2 Number Length rate Temp. Temp.

foodgate h (cm) Qw (l/s) Vw (m/s) Fr L (m) Qai r (l/s) (C) (C)H (cm)

1*3

3.37 45.77 6.79 11.81 2.08 23.06 27.5 24.2

2* 3.51 63.93 9.11 15.52 NA 27.82 26.0 25.1

3* 5.26 47.65 4.53 6.31 1.08 12.66 24.0 22.0

46

5.50 58.85 5.35 7.28 1.38 18.37 24.7 24.0

5* 5.40 64.37 5.96 8.19 1.48 20.17 25.5 24.1

6* 5.85 92.05 7.87 10.39 2.28 29.49 23.0 24.1

7 6.00 44.44 3.70 4.82 0.78 9.92 29.0 28.0

8*9

7.05 64.38 4.57 5.50 0.98 14.26 28.0 22.5

9* 8.31 98.20 5.91 6.55 1.48 22.92 21.4 21.0

10 8.54 119.86 7.02 7.67 2.08 31.69 29.0 22.011 6.92 46.58 3.37 4.09 0.68 11.28 23.8 21.8

12*11

7.94 64.38 4.05 4.59 0.88 15.52 25.8 23.0

13* 9.10 94.64 5.20 5.50 1.18 20.28 25.8 22.1

14 10.16 128.76 6.34 6.35 1.58 27.45 21.4 21.0

COMPARISON OF MEASUREMENTS WITH LITERATURE

Verifcation o the jet length L

Jet lengths are commonly used to quantiy the air uptake by the water fows. The jet lengths o Table IIwere compared with theoretical predictions o Schwarz and Nutt (1963) and Tan (1984), given respectively

by equations 6 and 7, and plotted in Figure 5. Also shown are the predictions o the empirical correlation

o Kkpinar and Ggs (2002), given by equation 8. The theoretical equations 6 and 7 were obtained with

no restrictions to . Equation 8 was adjusted rom experimental data, being thus restricted by the range o

tested during the experiments. A systematic underestimation o equation 8 is observed, which may be

due to extrapolations o its limits o application. For example, the ramp slope is limited to 0 < < 9.45,

but in this study = 10.

The good agreement between measured and literature results is taken as an indication that the experi-

mental data or jet length can be used to compare with CFD simulations.

L

h=

(1+ tan )

cos Fr2

1+

1+ 2

tr + ts

h

cos

(Fr)2

+

tr+ ts

htan (6)

L

h=

gsin

2ht2 +

(V cos )

ht, t=

V sin

g

cos + Pwgh

1+

1+ 2(tr+ ts )

g

cos + Pwgh

(V sin )2

(7)



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L

h= 0.28(1+ )0.22 Fr1.75

tr+ ts

h

0.44 (1+ tan )

Aa

Aw

0.087(8)

In the above equations, is the ramp slope, is the chute slope, is the take o angle (which is the

angle ollowed by the liquid when it leaves the ramp. is equal to because no inertial eects alteredthe observed direction o the fow ater leaving the ramp), tr is the ramp height, ts is the step height (zero

in the present experiments), t is the time, w is the water density, g is the gravity acceleration, P is the

relative pressure under the jet (taken positive), h, V, Fr and L are dened in Table I, and Aai r/Aw is the

ratio between the air supply pipe entrance area, Aa, and the area o the water fow beore the aerator, Aw.

Fig. 5 Predicted and measured jet lengths.

Verifcation o the air entrainment coefcient as a unction oL/ h

Pinto et al. (1992) proposed that the ratio between Qai r and Qw||, ||Qai r/Qw, is proportional do L/ h,

with a coecient o proportionality between 0.023 and 0.033. Rutschmann and Hager (1990) ound a

coecient o proportionality o 0.030, or the maximum value o (zero relative pressure in the cavity

under the jump). The authors showed that the straight line o vs. L/ h intercepted the L/ h axis around

L/ h = 5 or a rst set o data, so that the equation = 0.030(L/ h 5) was proposed. For a second set o

data, the simple proportionality = 0.030L/ h was ollowed. The authors measured L/ h up to around 45.

Chanson (1991) suggested that and L/ h ollow linear trends with lower slopes or L/ h < 20 and higher

slopes or L/ h > 20. The L/ h values ranged up to around 25. Kkpinar and Ggs (2002) presented the

empirical correlation

= 0.0189(L/ h)0.82

Aa/A2

(1+ tan 0.24

(9)in which the coecient o = (L/ h) depends on the channel slope ( ) and the ratio Aai r/Aw. L/ h

ranged up to 30. Equation 9 shows a nonlinear dependence between and L/ h, and that the coecient

may be lower than 0.0189. The equation is valid or 0 < < 51.3.

Figure 6 shows against L/ h or the data o these experiments. A constant seems to occur orL/ h

between 10 and 15. However, as no measurements were made or L/ h < 10, this apparent constancy may

be only the scatter o the data. Figure 6 also shows the region containing the lower nappe data o Low (1986)

and analyzed by Chanson (1991), obtained or a chute slope = 52.33; and the equations o Rutschmann



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and Hager (1990), or = 51.3 and = 34.4. The dependence o the unction = (L/ h) on

geometrical characteristics, such as the slope o the spillway, is clearly visible. Applying equation 9 or the

conditions o this study ( = 14, 5) led to good predictions o the measured data, with deviations occurring

or the lower range o L/ h. These deviations may be due to the extrapolations o the application limits o

equation 9 or bias in the measurements. As already mentioned, the used ramp slope = 10 extrapolates

the 0 < < 9.45 limits. Also the experimental range o Froude numbers (Fr), 4.08 < Fr < 15.5,

extrapolates the application limits o equation 4, given as 5.56 < Fr < 10.00. However, equation 9 shows

that the data ollowed the general expected behavior or the applied experimental conditions, indicating that

the experimental data or air/water fow ratio can be used to compare with CFD simulations.

Fig. 6 Measured and L / h values, together with data and correlations rom other authors. is the angle o the spillway in each

experiment. The present set o data approximates to the general trend o the correlation o Kkpinar and Ggs (2002).

Verifcation o the air entrainment coefcient as a unction oFrFigure 7 shows the data o the present study (white circles) and those o Kkpinar and Ggs (2002)

(gray circles) against the Froude number. The data o Kkpinar and Ggs were obtained or fows over a

step height ts o 5 cm, while, or the present data, ts = 0. Moreover, theirtr/ h values ranged rom 0.0 to

0.4, while in the present study they ranged rom 0.4 to 1.2. The dierent experimental conditions generated

clouds o points with similar trends, but separated in the graph vs. Fr, as shown in Figure 7.

Fig. 7 Measured against the Froude number.

To consider the dierent parameters in a correlation or , a dimensional analysis leads to

= f

Fr ,

tr

h,

ts

h

(10)



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The combined eect o tr and ts is represented here through the ratio (tr + k ts )/ h, where k is an

adjusted constant. A multiple regression analysis urnished the result

= 0.0278 Fr1.044 tr+ 3ts

h0.460

(11)

Predicted and measured data are presented in Figure 8, showing that the present data and those rom

literature are complementary and orm a single cloud o points. The agreement between present and

literature data (Figs. 5, 6 and 8) allowed the use o the corresponding experimental results o air concen-

tration proles, pressure proles, velocity proles and air discharges to compare to the CFD predictions.

Fig. 8 Calculated obtained using equation 6 against measured .

COMPARISON OF CFD PREDICTIONS WITH EXPERIMENTS

Jet length

Table III shows six predictions o the jet length. As mentioned, the turbulence conditions were adjusted in

the inlet o the numerical domain, but the CFX standard parameters o the turbulence model urnished the

best predictions or the set o jet lengths. These conditions were similar or all runs. The simulated lengths

were in the range o 0.81 to 1.08 times the measured length or the six runs. These runs were used to obtain

numerical air discharges.

TABLE III

Simulated runs, showing predicted and measured

lengths of the jet.

Measured Predicted LpredictedLmeasured

Run Length Length

(m) (m)3 1.08 1.17 1.08

5 1.48 1.18 0.81

8 0.98 1.02 1.04

9 1.48 1.32 0.89

12 0.88 0.88 1.00

13 1.18 1.21 1.03



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Pressure distribution

The pressure distribution along the channel bed was used to measure the jet length, taken as the position o

the pressure peak. Figure 9 presents an example measurement and simulation results or run 13, showing

good agreement between CFD simulations and the experiment.

Fig. 9 Pressure distribution along the channel bed or run 13. The axis x

represents the longitudinal distance with origin taken at the beginning o the jet.

Velocity distribution

The velocity distribution in section S3, measured using the PIV technique, was compared with the predicted

distribution. Figure 10 shows the comparison or runs 3 and 5, taken as examples. The agreement between

measured and predicted proles is considered acceptable, having a maximum dierence o ten percent. The

imposed turbulence intensity in the inlet o the numerical domain, maintained constant or all simulations,

may be a cause o the observed deviations. No numerical bias o the related concentration elds were

observed (see Fig. 11), so that the obtained velocity distributions were considered adequate or this study.

Fig. 10 Velocity distributions or runs 3 and 5.



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Fig. 11 Void ratio proles along the jet upstream o the reattachment section (run 5).

Concentration profles

Lima et al. (2008) presented measured values or the air discharge entering into the cavity under the jet, and

also values obtained calculating the air discharge rom air concentration proles measured at cross sections

along the lower nappe o the jet. The authors applied Equation (12) along sections 4 through 8 (Fig. 2),

corresponding to a distance between 3.9% and 132% o the jet lengths.

Qx = B

Upper boundary

Lower boundary

C(y)Vx (y)d y (12)

where Qx is the air discharge, B is the channel width, C is the air concentration (void ratio), Vx is thevelocity in the x direction and y is the distance normal to the chute ace. The upper and lower boundaries

o the domain were set at two conditions: 1) C values o 95% and 5%, and 2) C values o 90% and 10%.

Lima et al. (2008) showed that the measured air discharges are substantially lower than the air dis-

charges evaluated rom the concentration proles. Previous results o Wilhelms and Gulliver (2005), when

evaluating entrained air rom concentration proles or upper surace aeration, showed that corrections must

be made because the measurements involve air among water parcels o the surace distortions, not absorbed

by the water. Lima et al. (2008) suggested that a similar eect infuenced the measurements along the lower

nappe, with the addition o the eect o the spray that emanates rom the aerator lip as water. Substantial

sprays could account or water measurement throughout the air pocket, aecting the air discharge results.

Numerical predictions o air concentrations are shown in Figure 11. Run 5 is presented becauseit represents the worst agreement between the measured and predicted jet lengths (predicted length =

81% o measured length). Even or this condition, the agreement between measured and predicted

concentration proles is good. The displacement observed between proles, mainly or sections S7

and S8, is due to the lower predicted position o the jet when compared with the measured position.

Measurements and predictions considered the entire thickness o the jet.

All proles o Figure 11 were obtained upstream o jet reattachment with the channel bed. Figure 12a

shows the predicted concentration eld along the jump. Figures 11 and 12 show that the concentration



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Fig. 12 a) Concentration eld along the jet, showing the end o the region o the water core with zero air concentration (arrow).

b) A sketch o a possible path ollowed by a bubble originated in the upper nappe.

proles o the upper and lower nappes interact downstream o the position indicated by the black arrow

in Figure 12a, where the concentration in the water core ceases to be zero (shown in black). Non-zero airconcentrations in the core are related to bubbles originating either at the upper or at the lower suraces.

Figure 12b shows a sketch o an eventual intrusion o air originated in the upper nappe. In this case,

concentration measurements can also be aected by this new air source, and air discharges obtained rom

concentration measurements can eventually be dierent rom those measured in the inlet structure.

The measured and calculated concentration proles or the impact region could also be compared or

one run o the present set o experiments. Figure 13 shows the results obtained or run 12 at section 8, the

only case in which the pressure point that quanties the jet length coincided with a measurement section.

Although the general behavior o both proles is the same, substantial dierences are observed between

the concentration values. The measured prole is, in general, steeper than the calculated prole, and the

concentration dierences are higher or distances to the channel bottom between 0 and 5 cm. Also in

this case, the dierences may result rom the turbulence condition imposed in the inlet o the simulation

domain. For example, higher levels o homogenization (soter proles) are obtained or higher turbulent

diusivities, which are dependent on the turbulent conditions.

Fig. 13 Void ratio prole at the impact section. (Run 12, section 8).



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Air discharges

Predicted air discharges are compared with measurements or the six simulated cases presented in Fig-

ure 14. Although the predicted air discharges have the same magnitude as the measured air discharges, a

relatively high spread is observed. The predicted air discharges were obtained by integrating air concen-tration at the cross section o the inlet tube (Fig. 2). The dierences between experimental and numerical

data are probably associated with the constant parameters o the turbulence model (the CFX standards

were used) or the dierent experimental situations, and the constant turbulence intensity in the inlet o the

numerical domain (5%), as previously mentioned. As shown by Ervine et al. (1995), the air uptake by the

water depends on the turbulence intensity perpendicular to the fow direction.

Fig. 14 Comparison between measured and predicted air dis-

charges, or the six conditions simulated in the present study.

Theresults indicate that, ora rst evaluation o themagnitudeo theairdischarge, numerical procedures

can be used to help in the decision-making process. However, the numerical code must be calibrated, based

on measured characteristics. In the present study, the jet lengths were used to calibrate the model (to adjust

parameters and inlet conditions), and the measured concentration, pressure, and velocity proles were used

to check the numerical results. I more detailed inormation is needed, say or cavitation erosion potential, it

is still necessary to conduct experimental studies and to scale up the results based on empirical procedures.

CONCLUSIONS

Experimental studies on air absorption by fows over a bed aerator were described and compared with

theoretical and empirical predictions ound in the literature and computational results conducted here.

1. Jet lengths were well predicted by the equations o Schwarz and Nutt (1963) and Tan (1984). The air

entrainment coecients , when expressed as a unction o L/ h, were well predicted by the equation

o Kkpinar and Ggs (2002), unless or the lower range o L/ h, that is, or 10 < L/ h


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data here described and those o Kkpinar and Ggs (2002) can be presented together, ollowing

the same trend.

2. Computational predictions o the jet length were taken as control parameter or the numerical sim-

ulations (calibrations). The CFX standard parameters were adopted or the turbulence model. The

turbulence intensity at the inlet was xed at 5% o the mean fow velocity, and the roughness used in

the law o the wall was xed at 1.0 mm, which generated predicted jet lengths between 0.8 and 1.2

times the measured length.

3. It was observed that the pressure distribution alongthe channel bed, the velocity proles at the end o the

ramp, and the concentration proles along the jet could be represented by the calibrated computational

code. Considering the air concentration at the impact point, the measured and predicted proles

presented the same general orm, although concentration dierences were observed.

4. The computational predictions o the air discharges ollowed the magnitude o the measured data.

However, a relatively large scatter was observed. For a rst evaluation o the magnitude o the airdischarge, computational procedures can be used to help in making decisions. However, the numerical

code must be calibrated, based on previous measured characteristics. In the present study, the jet

lengths were used to calibrate the model (to adjust parameters and inlet conditions), and the measured

concentration, pressure, and velocity proles were used to check the numerical results.

NOMENCLATURE TABLE

a a physical phase t time

A amplitude o oscillation tr ramp height

Aa area crossed by air ts step height

Aw area crossed by water T()

a sources oaB channel width

Ua velocity vector o phase a

C air concentration (void ratio) Ua , Va , Wa components oUa

D()a diusivity oa V generic velocity

Fr Froude number Vx velocity in the x direction

g acceleration o gravity x longitudinal axis

h height y distance normal to the chute ace

L jet length ramp slope

Ma interacial orces acting on phase a take o angle

Np total number o physical phases air entrainment coecients ( = Qa /Qw)

Pa pressure eld o phase a ab specic mass fow rate rom phase b to aQa air discharge a conserved specic variable o phase a

Qw water discharge P relative pressure under the jet

ra volume raction o phase a a viscosity o phase a

S()a external source in phase a chute slope

SMa momentum sources a density o phase a

SMSa mass sources w water density



16/17


ACKNOWLEDGMENTS

The authors thank Pros. M.A. Kkpinar and M. Ggs, who urnished the data used in Figures 7 and 8;

Coordenao de Apereioamento de Pessoal de Nvel Superior (CAPES pr. 2201/06-2) and Fundao

de Amparo Pesquisa do Estado de So Paulo (FAPESP), or supporting this research. The authors do nothave any propriety and nancial interest in any product or company cited in this manuscript.

RESUMO

Aeradores de undo projetados para aumentar a concentrao de ar so utilizados para previnir a cavitao e danos

dela derivados em vertedouros. O oxignio contido na gua tambm um parmetro relevante para garantir alta

qualidade das guas a jusante do vertedouro, com refexos na qualidade ambiental. Equaes e critrios de projeto

existentes ainda so considerados aproximados, mostrando a necessidade de mais estudos para elucidar os meca-

nismos que governam o carreamento de ar. Este trabalho apresenta resultados de uma srie sistemtica de medidas

de concentrao de ar ao longo da supercie inerior do jato de um aerador de undo, juntamente com medidas

pertinentes de descargas de ar e campos de velocidade da gua. Foram eitas comparaes com resultados da lite-

ratura, considerando pers de concentrao ao longo do jato do aerador at a regio de jusante. As medies sob

condies controladas orneceram inormaes necessrias para testar resultados numricos de aerao obtidos em

simulaes desses escoamentos, utilizando mecnica dos fuidos computacional (CFD). Mostra-se que erramen-

tas numricas preditivas ornecem vazes de ar comparveis aos valores medidos. Tambm concludo que, se

detalhes so necessrios, experimentos so ainda teis.

Palavras-chave: aeradores de vertedouros, carreamento de ar, escoamento ar-gua, escoamentos multisicos.

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ARANTES_et_al_Lower Nappe Aeration in Smooth Channels