Abstract
The influence of the air entrained by water jets on the dynamic pressures applied on the bottom of a plunge pool and inside underlying fissures was analyzed with systematic experiments. The large experimental facility reproduced aerated high-velocity jets up to 22.1 m/s impinging on a pool and impacting on an instrumented cubic block embedded on the bottom. Plunging and submerged jets are compared, as well as jet impingement on the center or on the side of the block. A relationship is proposed to describe the time-averaged pressures at stagnation as a function of the relative pool depth, considering pressure measurements in this position as well as recent experimental evidence on the jet centerline velocity decay. Air bubbles influence the dynamic pressures on the rock bottom by reducing jet momentum, but also by reducing the jet dissipation rates in the water pool. These two processes are opposed. The reduction of momentum, consequence of a jet with a lower apparent density, results in lower pressures, while lower jet dissipation in the pool results in higher kinetic energy of the jet impacting the bottom and higher pressures. Finally, the spectral contents show that the resonance frequencies of aerated jets are shifted as a consequence of wave celerity reduction caused by lower mean densities inside the fissures, which is an evidence of the presence of air bubbles.
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References
Bellin A, Fiorotto V (1995) Direct dynamic force measurement on slabs in spillway stilling basins. J Hydraul Eng (ASCE) 121(10):686–693. doi:10.1061/(ASCE)0733-9429(1995)121:10(686)
Beltaos S, Rajaratnam N (1974) Impinging circular turbulent jets. J Hydraul Eng Div (ASCE) 100(NHY10):1313–1328
Beltaos S, Rajaratnam N (1977) Impingement of axisymmetric developing jets. J Hydraul Res 15(4):311–326. doi:10.1080/00221687709499637
Bin AK (1993) Gas entrainment by plunging liquid jets. Chem Eng Sci 48(21):3585–3630. doi:10.1016/0009-2509(93)81019-r
Blevins RD (1984) Applied fluid dynamics handbook. Van Nostrand Reinhold Company, Inc., New York
Bollaert E (2002) Transient water pressures in joints and formation of rock scour due to high-velocity jet impact. In: Schleiss AJ (ed) Communication 13. Laboratory of Hydraulic Constructions (LCH), Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne
Bollaert E, Schleiss A (2003a) Scour of rock due to the impact of plunging high velocity jets. Part I: a state-of-the-art review. J Hydraul Res 41(5):451–464. doi:10.1080/00221680309499991
Bollaert E, Schleiss A (2003b) Scour of rock due to the impact of plunging high velocity jets. Part II: experimental results of dynamic pressures at pool bottoms and in one- and two-dimensional closed end rock joints. J Hydraul Res 41(5):465–480. doi:10.1080/00221680309499992
Bollaert E, Schleiss A (2005) Physically based model for evaluation of rock scour due to high-velocity jet impact. J Hydraul Eng (ASCE) 131(no 3):153–165. doi:10.1061/(ASCE)0733-9429(2005)131:3(153)
Chanson H (1997) Air bubble entrainment in free-surface turbulent shear flows. Academic Press, London
Chanson H (2009) Turbulent air–water flows in hydraulic structures: dynamic similarity and scale effects. Environ Fluid Mech 9(2):125–142
Chanson H, Aoki S, Hoque A (2004) Physical modelling and similitude of air bubble entrainment at vertical circular plunging jets. Chem Eng Sci 59(4):747–758. doi:10.1016/j.ces.2003.11.016
Duarte R (2013) Air concentrations in plunge pools due to aerated plunging high-velocity jets and dynamic pressures in underlying fissures. In: Proceedings of 35th IAHR world congress, Chengdu, China, 8–13 September
Duarte R, Schleiss A, Pinheiro A (2013) Dynamic pressure distribution around a fixed confined block impacted by plunging and aerated water jets. In: Proceedings of 35th IAHR world congress, Chengdu, China, 8–13 September
Duarte R, Schleiss AJ, Pinheiro A (2014) Discussion on CFD analysis of the effect of nozzle stand-off distance on turbulent impinging jets. Can J Civ Eng 1–2. doi:10.1139/cjce-2013-0540
Ervine DA (1998) Air entrainment in hydraulic structures: a review. Proc Inst Civ Eng Water Manag 130(3):12. doi:10.1680/iwtme.1998.30973
Ervine DA, Falvey HT (1987) Behavior of turbulent jets in the atmosphere and in plunge pools. Proc Inst Civ Eng 2 83:295–314
Ervine DA, Falvey HT, Withers W (1997) Pressure fluctuations on plunge pool floors. J Hydraul Res 35(2):257–279
Federspiel MPEA (2011) Response of an embedded block impacted by high-velocity jets. In: Schleiss AJ (ed) Communication 47. Laboratory of Hydraulic Constructions (LCH), Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne. doi:10.5075/epfl-thesis-5160
Fiorotto V, Rinaldo A (1992) Turbulent pressure fluctuations under hydraulic jumps. J Hydraul Res 30(4):499–520. doi:10.1080/00221689209498897
Hachem FE, Schleiss AJ (2011) A review of wave celerity in frictionless and axisymmetrical steel-lined pressure tunnels. J Fluid Struct 27(2):311–328. doi:10.1016/j.jfluidstructs.2010.11.009
Heller V (2011) Scale effects in physical hydraulic engineering models. J Hydraul Res 49(3):293–306. doi:10.1080/00221686.2011.578914
Kolmogoroff A (1941) The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C R Acad Sci URSS 30:301–305
Manso PFA (2006) The influence of pool geometry and induced flow patterns in rock scour by high-velocity plunging jets. In: Schleiss AJ (ed) Communication 25. Laboratory of Hydraulic Constructions (LCH), Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne
Manso PFA, Bollaert EFR, Schleiss AJ (2008) Evaluation of high-velocity plunging jet-issuing characteristics as a basis for plunge pool analysis. J Hydraul Res 46(2):147–157. doi:10.1080/00221686.2008.9521852
Melo JF, Pinheiro AN, Ramos CM (2006) Forces on plunge pool slabs: influence of joints location and width. J Hydraul Eng (ASCE) 132(1):49–60. doi:10.1061/(asce)0733-9429(2006)132:1(49)
Müller G, Hull P, Allsop W, Bruce T, Cooker M, Franco L (2002) Wave effects on blockwork structures: model tests. J Hydraul Res 40(2):117–124. doi:10.1080/00221680209499854
Pinheiro AN, Melo JF (2008) Effect of jet aeration on hydrodynamic forces on plunge pool floors. Can J Civ Eng 35(5):521–530. doi:10.1139/l07-138
Acknowledgments
This research project is funded by the Fundação para a Ciência e a Tecnologia (FCT, Portugal, Grant No. SFPH/BD/51074/2010) and LCH-EPFL.
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Duarte, R., Schleiss, A.J. & Pinheiro, A. Influence of jet aeration on pressures around a block embedded in a plunge pool bottom. Environ Fluid Mech 15, 673–693 (2015). https://doi.org/10.1007/s10652-014-9392-x
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DOI: https://doi.org/10.1007/s10652-014-9392-x