OPEN ACCESS
Cavitation is a heavy threat for spillways with concrete chutes. Besides a proper design and execution, aeration is an effective means to avoid severe damages. A detailed study on bottom aerators of spillway chutes is presented here. Data from laboratory experiments were used to calibrate the coefficients of a physically based equation, which considers the effects of aerator geometry and different roughnesses of the surface of the aerator. After adjustment of scale factors, results computed by this equation showed a good agreement with observed data of different prototypes found in the literature. The main physical concepts of the developed equation are presented. The quantification of the air flow into the water jet was performed by separately considering the gas and liquid phases and using the subpressure under the jet of the aerator as a liaison between the two formulations. Consequently, this subpressure does not appear explicitly in the final formulation and does not need to be known for the quantification of the gas flow. The results show that the approach is suitable for the given problem.
aeration of channel flows, bottom aerators, designs of spillways
[1] Pinto, N.L.S., Neidert, S.H. & Ota, J.J., Aeration at high velocity fl ows. Water Power and Dam Construction, 34(2), pp. 34–38; 34(3), pp. 42–44, 1982.
[2] Pinto, N.L.S. & Neidert, S.H., Evaluation of entrained air fl ow through aerators. Water Power and Dam Construction, Aug., pp. 40–44, 1983.
[3] Rutschmann, P. & Volkart, P., Spillway chute aeration. Water Power and Dam Construction, Jan., pp. 10–15, 1988.
[4] Rutschmann, P. & Hager, W.H., Air entrainment by spillway aerators. Journal of Hydraulic Engineering, 116(6), pp. 765–782, 1990. doi: http://dx.doi.org/10.1061/(ASCE)0733-9429(1990)116:6(765)
[5] Pinto, N.L.S., Prototype aerator measurements. IAHR Hydraulic Structures Design Manual 4, Air Entrainment in Free-Surface Flow, ed. Wood, Balkema: Rotterdam, pp. 115–130, 1991.
[6] Kökpinar, M.A. & Gögüs, M., High-speed jet fl ows over spillway aerators. Journal of Civil Engineering, 29, pp. 885–898, 2002.
[7] Pfi ster, M. & Hager, W.H., Chute aerators II: hydraulic design. Journal of Hydraulic Engineering, 136(6), pp. 507–518, 2010. doi: http://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0000201
[8] Falvey, H.T., Discussion of “air uptake along the lower nappe of a spillway aerator”. Journal of Hydraulic Research, 47(5), pp. 683–684, 2009.
[9] Carvalho, P.D., Aeration of High-speed Flows in Chutes with Large Slopes (Aeração de Escoamentos de Alta velocidade em Canais de Forte Declividade – in Portuguese). Doctor thesis. School of Engineering at São Carlos, University of São Paulo, Brazil, 1997.
[10] Lima, A.C.M., Determination of turbulent structures of aerated fl ows in chutes using PIV (Caracterização da estrutura turbulenta em escoamentos aerados em canal de forte declividade com auxílio de técnicas de velocimetria a laser – in Portuguese). Doctor thesis. School of Engineering at São Carlos, University of São Paulo, Brazil, 2004.
[11] Lima, A.C.M., Schulz, H.E. & Gulliver, J.S., Air uptake along the lower nappe of a spillway aerator. Journal of Hydraulic Research, 46(6), pp. 839–843, 2008.
[12] Lima, A.C.M., Schulz, H.E. & Gulliver, J.S., Discussion of “air uptake along the lower nappe of a spillway aerator”. Journal of Hydraulic Research, 47(5), pp. 683–684, 2009.
[13] Arantes, E.J., Stepped Spillways’ Flow Characterization using CFD Tools (Caracterização do Escoamento sobre Vertedores em Degraus via CFD – in Portuguese). Doctor thesis. School of Engineering at São Carlos, University of São Paulo, Brazil, 2007.
[14] Arantes, E.J., Porto, R.M., Gulliver, J.S., Lima, A.C.M. & Schulz, H.E., Lower nappe aeration in smooth channels: experimental data and numerical simulation. Anais da Academia Brasileira de Ciências 82(2), pp. 521–537, 2010. doi: http://dx.doi.org/10.1590/S0001-37652010000200027
[15] Schulz, H.E., Brito, R.J.R., Simões, A.L.A., Puche, A.A.S. & Lobosco, R.J., Theoretical models for analyses of bed aerators using physical principles (Modelos Teóricos para Análise de Aeração em Aeradores de Fundo Utilizando Princípios Físicos – in Portuguese), Memorias del XXIV Congreso Latinoamericano de Hidráulica. IAHR: Punta del Este, Uruguay, 13 pp, 2010.
[16] Brito, R.J.R., Simões, A.L.A., Puche, A.A.S., Schulz, H.E. & Porto, R.M., Air uptake in high-velocity aerators in spillways: analyses of data and models (Incorporação de Arpor Aeradores de Escoamentos de Alta Velocidade em Vertedores: Análise de Dados e Modelos – in Portuguese). Memorias del XXIV Congreso Latinoamericano de Hidráulica, IAHR: Punta del Este, Uruguay, 11 pp, 2010.
[17] Brito, R.J.R., Analysis of aeration through bed aerators in high speed fl ows on weirs (Análise da aeração em escoamento de alta velocidade em calhas de vertedores – in Portuguese). MSc dissertation. School of Engineering at São Carlos, University of São Paulo, Brazil, 2011.
[18] Schulz, H.E. & Brito, R.J.R., Predicting aeration in spillways through bed aerators based on physical principles (Previsão da Aeração em Vertedores com o Uso de Aeradores de Fundo Fundamentada em Princípios Físicos – in Portuguese). Proceedings, CLME´2011/III CEM, Ed INEGI, Maputo, Moçambique, 15 pp., 2011.
[19] Brito, R.J.R. & Schulz, H.E., Equations with physical bases for bed-aerator: analyses of data and models (Equações com Bases Físicas para Aerador de Fundo: Análise de Dados e Modelos – in Portuguese). Proceedings, CLME´2011/III CEM, Ed INEGI, Maputo, Moçambique, 15 pp, 2011.
[20] Fuhrhop, H., Spillway chute aeration – calibration of a physically based approach by using measured data. Bachelor Thesis. Leuphana University Lüneburg, Germany, 2011.
[21] Fuhrhop, H., Schulz, H.E. & Wittenberg, H., Solving bottom aerators in spillways (Solução para Aeradores de Fundo em Vertedores – in Portuguese), Memorias del XXV Congreso Latinoamericano de Hidráulica, IAHR, San José, Costa Rica, 10 pp, 2012.
[22] Schlurmann, T., Skriptum Wasserbauliches Versuchswesen. Bergische Universität Wuppertal, Obering, p. 22, 2002.
[23] Chanson, H. & Murzyn, F., Froude similitude and scaling effects affecting air entrainment in hydraulic jumps. World Environmental and Water Resources Congress, Ahupua’a, Hawaii, 10 pp, 2008.
[24] Fox, R.W. & McDonald, A.T., Introduction to Fluid Mechanics (in Portuguese), ed. Guanabara Dois, Rio de Janeiro, 1981.
[25] Chow, V.T., Open-Channel Hydraulics, McGraw Hill Book Company, New York, 1959.
[26] Simões, A.L.A., Schulz, H.E. & Porto, R.M., Stepped and smooth spillways: resistance effects on stilling basin lengths. Journal of Hydraulic Research, 48(3), pp. 329–337, 2010. doi: http://dx.doi.org/10.1080/00221686.2010.481853
[27] Schwarz, I. & Nutt, L.P., Projected Nappes subjected to transverse pressure. Journal of Hydraulic Engineering ASCE, 89(HY7), pp. 97–104, 1963.