Self-aeration on chute spillways

Self-aeration on chute and stepped spillways
Air entrainment and flow aeration in open channel flows
by Hubert CHANSON (h.chanson@uq.edu.au)
M.E., ENSHM Grenoble, INSTN, PhD (Cant.), DEng (Qld), Eur.Ing., MIEAust., MIAHR, 13th Arthur Ippen awardee
School of Civil Engrg., Univ. of Queensland, Brisbane QLD 4072, Australia

Presentation Detailed photographs References

Footnotes Related links Acknowledgments

Presentation
The process of air entrainment (1) in high-velocity open channel flows was initially studied because of the effects of entrained air on the thickness of flowing water. Further, the presence of air within the boundary layer reduces the shear stress between the flow layers and hence the shear force (2). Also it may prevent or reduce the damage caused by cavitation (3). Self-aeration on chutes is now recognised for its substantial contribution to the air-water transfer of atmospheric gases such as oxygen and nitrogen (4).

In an open channel, free-surface aeration occurs downstream of the inception point. The 'inception point of air entrainment' is defined as the point of apparition of 'white waters' or free-surface aeration (e.g. Photo No. 1 and Photo No. 6). At the channel intake, the flow free-surface is smooth and glassy. Next to the bottom, turbulence is generated and a boundary layer grows. It is generally accepted that the inception point occurs when the outer edge of the turbulent boundary layer reaches the surface (5). Downstream of the point of inception, a layer containing a mixture of both air and water extends gradually through the fluid. The rate of growth of the layer is small and the air concentration distribution varies gradually with distance. Self-aeration is an interfacial aeration process, with an uncontrolled supply of air. Next to the free-surface, the entrained air is advected in region of low shear (10).

In the aerated flow region, the distribution of air concentration (6) may be estimated by the solution of the air bubble diffusion equation :
(1)
where C is the void fraction, y is the distance normal to the invert, Y₉₀ is the characteristic distance where C = 90%, D' is a dimensionless air bubble diffusivity, K' is an integration constant and tanh is the hyperbolic tangent function (7) (8). K' and D' are functions only of the mean air concentration C_mean, where the depth-averaged mean void fraction is defined as :
(2) C_mean = 1 - d/Y₉₀
and d is the equivalent clear water depth (or blackwater depth) (9). Equation (1) was validated successfully with prototype and model data (10) (Photo No. 3). It applies to smooth-invert chute flows and skimming flows down stepped cascades.
More sophisticated models were recently developed assuning a non-constant diffusivity distribution (10, 11). They were successfully applied to self-aerated flow on smooth chutes, skimming and transition flows on stepped chutes, and flow aeration at nappe impact and downstream of nappe impact at drop structures and in nappe flow regime above stepped cascades.

Table 1 - Relationship between C_mean, D' and K' (after CHANSON 1995,1997)

C_mean	D'	K'	f_e/f
(1)	(2)	(3)	(4)
0.0	0.0	+¥	1.0
0.01	0.007312	68.70445	1.0
0.05	0.036562	14.0029	1.0
0.10	0.073124	7.16516	0.9969
0.15	0.109704	4.88517	0.973
0.20	0.146489	3.74068	0.9216
0.30	0.223191	2.567688	0.7824
0.40	0.3111	1.93465	0.6449
0.50	0.423441	1.508251	0.5176
0.60	0.587217	1.178924	0.3893
0.70	0.878462	0.896627	0.2474

Discussion
At uniform equilibirum (i.e. normal flow conditions), the momentum principle states that the boundary friction force equals exactly the gravity force component in the flow direction: i.e., the weight-of-water component acting parallel to the invert. The uniform equilibrium velocity and depth must be calculated in terms of the air-water flow properties, including the air-water friction factor f_e. Recent results showed convincingly that the Darcy friction factor f_e is smaller than the monophase flow friction coefficient because the entrained air induced some drag reduction. In smooth chute, the reduction in skin friction is associated with air entrainment causing a thickening of the momentum sublayer (CHANSON 1994, Photo No. 4). In skimming flow, drag reduction is caused by interactions by entrained air bubbles and the developing mixing layers (CHANSON 2004).

Footnotes

(1) Natural aeration occurring at the free surface of high velocity open channel flows is referred to as free surface aeration, air entrainment, flow aeration, self-aeration or 'white waters'.

(2) For a full explanation, see CHANSON (1994), "Drag Reduction in Open Channel Flow by Aeration and Suspended Load", Journal of Hydraulic Research and CHANSON (2004). "Drag Reduction in Skimming Flow on Stepped Spillways by Aeration", Jl of Hydraulic Research. The above Table 1, column 4, shows the ratio of the air-water friction factor f_e to the clear-water Darcy friction factor f (for identical flow rate and clear-water flow depth) as a function of the mean air concentration for smooth-invert chutes. See also Photo No. 4.

(3) For example, WOOD (1984), CHANSON (1997).

(4) That includes re-oxygenation, supersaturation in dissolved nitrogen. While the re-oxygenation of depleted water is a positive outcome, supersaturation of dissolved nitrogen may increase fish mortality. In the Columbia and Snake rivers (USA), 'gas bubble disease' caused by water supersaturated in nitrogen was a significant cause of fish mortality for salmonids and steelheads.

(5) This statement is widely accepted in steep chutes (smooth invert and stepped cascade), but it is not correct on flat waterways. CHANSON (1997) presents some evidence supercritical open channel flows for flat chutes.

(6) The air concentration or void fraction is defined as the volume of air per unit volume of air and water.

(7) Although this relationship was developed for smooth-invert chutes (CHANSON 1995,1997), model and prototype data show that it is also valid in skimming flow down stepped spillways. A limitation of the model is the assumption of a constant vertical distribution of air bubble diffusivity D'. CHANSON and TOOMBES (2001,2002) presented however more advanced analytical models with non-constant vertical distributions, that compared well with transition flows on stepped chute and the flow immediately downstream of a drop structure.

(8) Next to the spillway invert, model and prototype data depart from Equation (1) (CHANSON 1994). The air concentration tends to zero at the bottom (i.e. y=0) indicating an air concentration boundary layer. The existence of an air concentration boundary layer is consistent with experimental data of fine air bubble injection in turbulent boundary layer flows. This air boundary layer plays a major role in the drag reduction process taking place in self-aerated flows.

(9) For very long spillway chutes, the mean air concentration reaches an equilibrium C_e at the downstream end that is a function of the bed slope q only : C_e = 0.9 * sinq (WOOD 1983, CHANSON 1997).

(10) See CHANSON (1995,1997) and CHANSON and TOOMBES (1997,2001).

(11) See CHANSON and TOOMBES (2001, pp. 59-61; 2002, 2003).

Detailed photographs

Photo No. 1 : Free-surface aeration down Chinchilla weir spillway during a small overflow on 8 Nov. 1997. Chinchilla weir is a minimum energy loss weir design near the township of Chinchilla (QLD, Australia) on the Condamine river. It is 14-m high earthfill structure (410-m long at crest) with a spillway capacity of 850 m3/s. Completed in 1973, the minimum energy loss weir design was selected to pass large floods with minimum energy loss, hence with minimum upstream flooding. The weir was tested shortly after completion with a large overflow (~ 400 m³/s) and it is listed as a large dam by ANCOLD and ICOLD. (More information : CHANSON, Butterworth-Heinemann, 1999, pp. 417-421.)

Photo No. 2 : View from upstream of the Split Rock dam spillway on 6 Sept. 1998 (Courtesy of Mr. Noel BEDFORD). The Split Rock dam is a rockfill embankment (66-m high, 469-m long) completed in 1987 near Tamworth (NSW, Australia). The point of inception of air entrainment is clearly visible with white waters downstream. At the downstream end, the kinetic energy of the flow is dissipated in a 6-m deep plunge pool, before rejoining the natural stream bed.

Photo No. 3 : Air concentration distributions : comparison between Equation (1) and experimental data (STRAUB and ANDERSON 1958)

Photo No. 4 : Drag reduction caused by self-aeration observed in prototype spillways and spillway models (after CHANSON 1994). Figure after CHANSON (1997).

Photo No. 5 : Air entrainment in skimming flow down a 50 degree slope (h = 20 mm). The inception point of air entrainment is clearly visible upstream of the measurement trolley system.

Photo No. 6 : Air entrainment in skimming flow down a 22 degree slope for d_c/h = 1.1 (h = 100 mm).

Related photographs of free-surface aeration at hydraulic structures
Photos No. 11 to 13 : Air entrainment in high-velocity water jets discharging into air, Three Gorges Project and Dam (Yichang, China, 2002-2007). Concrete gravity dam. Length: 2300 m, Height: 181 m. Powerplant: 32 Francis turbines (700 MW each). Photo No. 11: scour outlet discharge below the spillway section on 20 Oct. 2004 (Q = 7000 m3/s, V = 35 m/s). Photo No. 12 : high-velocity flow from an outlet sluice on 20 Oct. 2004 (V = 35 m/s); note the large amount of 'white waters' highlighting strong free-surface aeration. Photo No. 13 : free-surface aeration along the bottom outlet jet flow downstream of the spillway section on 20 Oct. 2004 (V = 35 m/s).
Photos No. 14 to 15 : Air entrainment in a near-full-scale dropshaft. Drop in invert elevation: 1.7 m, pool depth: 1 m, shaft dimensions: 0.75 m by 0.76 m, flow rates: 5 to 70 L/s (CHANSON 2003, IAHR Congress; CHANSON 2004, Jl Irrig. & Drainage Engrg). Photo No. 14 : Regime R1, photograph for Q = 7.6 L/s (July 2002) ; Photo No. 15 : Regime R3, photograph for Q = 67 L/s (Aug. 2002).
Photos No. 16 to 19: Air entrainment in hydraulic jumps. A hydraulic jump is a stationary transition from a rapid (supercritical flow) to a slow flow motion (subcritical flow). It is extremely turbulent and characterised by the development of large-scale turbulence, surface waves and spray, energy dissipation and air entrainment (eg CHANSON and BRATTBERG 2000). The large-scale turbulence region is usually called the 'roller'. Photo No. 16 : air entrainment in a steady jump; Photo No. 17 : air entrainment in a strong hydraulic jump (Fr >10); Photo No. 18 : surfer riding on a hydraulic jump roller in a river (Munich, Germany), flow from right to left and 'white waters' (Courtesy of Dale YOUNG); Photo No. 19: air entrainment and surfer on a hydraulic jump roller, looking downstream (Courtesy of Dale YOUNG).
Photos No. 20 to 28: Air entraiment in plunging jets.
Air entrainment at a vertical supported jet. Photo No. 20 : Individual bubble entrainment at a vertical supported jet [Ref.: CUMMINGS & CHANSON 1999], low-speed air bubble entraiment, elongated air cavity formation & entrainment of bubbles, cavity and scaling located 45-mm towards the camera from the jet centre line; Jet impact flow conditions : V = 1.20 m/s, Tu = 1.08 %, d = 8.0 mm, L_j = 34mm - Video shutter speed : 1.0 ms; Frame interval : 20 ms. Photo No. 21 : Strong air entrainment for V1 = 6.14 m/s, x1 = 0.090 m, probe position : x-x1 = 0.10 m [Ref.: BRATTBERG and CHANSON 1998].
More on Air entrainment in the developing flow region of two-dimensional plunging jets ...
Air bubble entrainment at a circular vertical plunging jet. Photo No. 22 : Experiments at the University of Queensland (CHANSON and MANASSEH 2003), flow from top to bottom (Circular jet, V1 = 3.3 m/s, do = 25 mm) with freshwater. Photo No. 23 : Experiments at Toyohashi University of Technology (CHANSON et al. 2004) with freshwater, air entrainment at a 12.5 mm diameter plunging jet (V1 = 2 m/s). Photo No. 24 : air entrainment at a 6.83 mm diameter jet (V1 = 2.1 m/s). Photo No. 25 : Experiments at Toyohashi University of Technology with seawater, air bubble entrainment at a 12.5 mm diameter plunging jet (x1 = 0.05 m, V1 = 2.5 m/s) (CHANSON et al. 2002). Photo No. 26 : same flow conditions, high shutter speed (1/1,000 s). Photo No. 27 : seawater collection on 25 Oct. 2001. Photo No. 28 : seawater collection and checking on 25 Oct. 2001.
More on Acoustic characteristics of air entrainment at plunging jets ...
Photos No. 29 to 31: Air entrainment on stepped spillway and stilling basin
Paradise dam, Biggeden QLD (Australia) - RCC gravity dam equipped with an uncontrolled stepped spillway. Photo No. 29: General view of the spillway on 5 March 2013. Photo No. 30: Details of the free-surface next to the inception of free-surface aeration on the stepped spillway on 5 March 2013. Photo No. 31: turbulence and air-water flow in the stilling basin on 5 March 2013.

Related links

{http://dataweb.usbr.gov/html/cadams.html}	USBR Californian dams
{http://www.uq.edu.au/~e2hchans/photo.html}	Gallery of photographs
{http://www.nwp.usace.army.mil/im/v/photofil.htm}	US Army Corps of Engineers, Portland district, Photofile
{http://im.edfgdf.fr/der/html/der/environnement/ptiso.en.htm}	Water quality and self-aeration downstream of Petit-Saut dam
{http://www.uq.edu.au/~e2hchans/photo.html#Fountains}	Stepped cascades and fountains
{http://www.uq.edu.au/~e2hchans/dpri/topic_2.html}	Stepped spillway hydraulics
{http://www.uq.edu.au/~e2hchans/photo.html#Step_spillways}	Photographs of stepped chute flows
{http://www.boof.com/photos/showgallery.php?ppuser=2&cat=500}	California Whitewater community
{http://www.brettvalle.com/photos/index.php}	Brett Valle's photographs
{http://www.uq.edu.au/~e2hchans/aer_dev.html}	Spillway aeration devices to prevent cavitation damage on spillways

References

[1] CHANSON, H. (1994) "Drag Reduction in Open Channel Flow by Aeration and Suspended Load." Jl of Hyd. Res., IAHR, Vol. 32, No. 1, pp. 87-101 (ISSN 0022-1686). (download PDF file)
[2] CHANSON, H. (1995). "Air Bubble Diffusion in Supercritical Open Channel Flow." Proc. 12th Australasian Fluid Mechanics Conference AFMC, Sydney, Australia, R.W. BILGER Ed., Vol. 2, pp. 707-710 (ISBN 0 86934 034 4). (Download PDF File)
[3] CHANSON, H. (1997). "Air Bubble Entrainment in Free-Surface Turbulent Shear Flows." Academic Press, London, UK, 401 pages (ISBN 0-12-168110-6).
[4] STRAUB, L.G., and ANDERSON, A.G. (1958). "Experiments on Self-Aerated Flow in Open Channels." Jl of Hyd. Div., Proc. ASCE, Vol. 84, No. HY7, paper 1890, pp. 1890-1 to 1890-35.
[5] WOOD, I.R. (1984). "Air Entrainment in High Speed Flows." Proc. Intl. Symp. on Scale Effects in Modelling Hydraulic Structures, IAHR, Esslingen, Germany, H. KOBUS editor, paper 4.1.
[6] CHANSON, H., and TOOMBES, L. (1997). "Flow Aeration at Stepped cascades." Research Report No. CE155, Dept. of Civil Engineering, University of Queensland, Australia, June, 110 pages (ISBN 0 86776 730 8). (PDF version at EprintsUQ)
[7] CHANSON, H., and TOOMBES, L. (2001). "Experimental Investigations of Air Entrainment in Transition and Skimming Flows down a Stepped Chute. Application to Embankment Overflow Stepped Spillways." Research Report No. CE158, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, July (ISBN 1 864995297). (Download PDF files : Part 1 and Part 2) (Alternate PDF file at EprintsUQ)
[8] CHANSON, H., and TOOMBES, L. (2002). "Air-Water Flows down Stepped chutes : Turbulence and Flow Structure Observations." Intl Jl of Multiphase Flow, Vol. 27, No. 11, pp. 1737-1761 (ISSN 0301-9322). (Download PDF File)
[9] CHANSON, H., and TOOMBES, L. (2003). "Strong Interactions between Free-Surface Aeration and Turbulence in an Open Channel Flow." Experimental Thermal and Fluid Science, Vol. 27, No. 5, pp. 525-535 (ISSN 0894-1777). (Download PDF File)
[10] CHANSON, H. (2004). "Air-Water Flows in Water Engineering and Hydraulic Structures. Basic Processes and Metrology." Proc. Intl Conf. on Hydraulics of Dams and River Structures, Tehran, Iran, Keynote lecture, Balkema Publ., The Netherlands, F. YAZDANDOOST and J. ATTARI Ed., pp. 3-16 (ISBN 90 5809 632 7). (Also CD-ROM, Taylor & Francis, ISBN 90 5809 683 4.) (Download PDF file)
[11] CHANSON, H. (2004). "Drag Reduction in Skimming Flow on Stepped Spillways by Aeration." Jl of Hyd. Research, IAHR, Vol. 42, No. 3 , pp. 316-322 (ISSN 0022-1686). (Download PDF file)
[12] CHANSON, H., and GONZALEZ, C.A. (2005). "Physical Modelling and Scale Effects of Air-Water Flows on Stepped Spillways." Journal of Zhejiang University SCIENCE, Vol. 6A, No. 3, March, pp. 243-250 (ISSN 1009-3095). (Download PDF file)

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Acknowledgments

The writer acknowledges the assistance of Noel BEDFORD to obtain some photographs of interest.

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Hubert CHANSON is a Professor in Civil Engineering, Hydraulic Engineering and Environmental Fluid Mechanics, at the University of Queeensland, Australia. His research interests include design of hydraulic structures, experimental investigations of two-phase flows, applied hydrodynamics, hydraulic engineering, water quality modelling, environmental fluid mechanics, estuarine processes and natural resources. He has been an active consultant for both governmental agencies and private organisations. His publication record includes over 600 international refereed papers and his work was cited over 3,500 times since 1990. Hubert Chanson is the author of several books : "Hydraulic Design of Stepped Cascades, Channels, Weirs and Spillways" (Pergamon, 1995), "Air Bubble Entrainment in Free-Surface Turbulent Shear Flows" (Academic Press, 1997), "The Hydraulics of Open Channel Flow : An Introduction" (Butterworth-Heinemann, 1st edition 1999, 2nd editon 2004), "The Hydraulics of Stepped Chutes and Spillways" (Balkema, 2001), "Environmental Hydraulics of Open Channel Flows" (Butterworth-Heinemann, 2004), "Applied Hydrodynamics: an Introduction of Ideal and Real Fluid Flows" (CRC Press, 2009), and "Tidal Bores, Aegir, Eagre, Mascaret, Pororoca: Theory And Observations" (World Scientific, 2011). He co-authored two further books "Fluid Mechanics for Ecologists" (IPC Press, 2002) and "Fluid Mechanics for Ecologists. Student Edition" (IPC, 2006). His textbook "The Hydraulics of Open Channel Flows : An Introduction" has already been translated into Spanish (McGraw-Hill Interamericana) and Chinese (Hydrology Bureau of Yellow River Conservancy Committee), and the second edition was published in 2004. In 2003, the IAHR presented him with the 13th Arthur Ippen Award for outstanding achievements in hydraulic engineering. The American Society of Civil Engineers, Environmental and Water Resources Institute (ASCE-EWRI) presented him with the 2004 award for the Best Practice paper in the Journal of Irrigation and Drainage Engineering ("Energy Dissipation and Air Entrainment in Stepped Storm Waterway" by Chanson and Toombes 2002). Hubert Chanson edited further several books : "Fluvial, Environmental and Coastal Developments in Hydraulic Engineering" (Mossa, Yasuda & Chanson 2004, Balkema), "Hydraulics. The Next Wave" (Chanson & Macintosh 2004, Engineers Australia), "Hydraulic Structures: a Challenge to Engineers and Researchers" (Matos & Chanson 2006, The University of Queensland), "Experiences and Challenges in Sewers: Measurements and Hydrodynamics" (Larrate & Chanson 2008, The University of Queensland), "Hydraulic Structures: Useful Water Harvesting Systems or Relics?" (Janssen & Chanson 2010, The University of Queensland), "Balance and Uncertainty: Water in a Changing World" (Valentine et al. 2011, Engineers Australia). He chaired the Organisation of the 34th IAHR World Congress held in Brisbane, Australia between 26 June and 1 July 2011.
His Internet home page is http://www.uq.edu.au/~e2hchans. He also developed a gallery of photographs website {http://www.uq.edu.au/~e2hchans/photo.html} that received more than 2,000 hits per month since inception.