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DISCUSSION / DISCUSSION
Discussion of ‘‘Verification and validation of a computational fluid dynamics (CFD) model for air entrainment at spillway aerators’’ by M.C. Aydin and M. Ozturk1 Michael Pfister
The Authors present a remarkable contribution combining and comparing two basic engineering tools, namely physical and numerical modeling. The Discusser would like to draw the attention to a statement of the Authors on physical aerator modeling. The Authors conclude their paper with the statement that physical model studies ‘‘include considerable scale effects’’. This statement is based on the comparison of their numerical CFD simulation in prototype dimensions with a single physical model study of Demiro¨z (1985, 1986) and Ko¨kpinar and Go¨g˘u¨s¸ (2002). The Discusser suggests that this generalization to arbitrary model tests on chute aerators is inappropriate. Limitations defined in literature include minimum values of the Weber number We = V/(s/r Lref)0.5 and the Reynolds number Re = (V Lref)/y, where Lref is reference length, V is approach flow velocity, s is fluid surface tension, r is fluid density, and y is kinematic fluid viscosity (Table 1), as well as some restrictions concerning the maximum scale factor. The Lref value is typically defined either as h, approach flow depth or as L, air cavity length. If these limitations are respected, as thoroughly described in literature, scale effects still exist but are not significant. As a consequence, the Authors basically demonstrate that the equation derived by Ko¨kpinar and Go¨g˘u¨s¸ (2002) may obviously not be considered for the specific case presented in their paper. This, however, does not legitimate the conclusion drawn and cited above, beside the remark that ‘‘model studies are very costly and time consuming’’. The time and cost issues for numerical and physical model studies do not differ fundamentally, based on the Discusser’s experience. Received 27 September 2009. Revision accepted 27 September 2009. Published on the NRC Research Press Web site at cjce.nrc.ca on 22 January 2010. M. Pfister. Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zurich, Switzerland (e-mail:
[email protected]). 1Appears
in the Canadian Journal of Civil Engineering 36(5):
826-838. Can. J. Civ. Eng. 37: 143–144 (2010)
The Authors state that ‘‘scale effects were allowed’’ in the reference model operated by Demiro¨z (1985, 1986) and Ko¨kpinar and Go¨g˘u¨s¸ (2002). A reason for these scale effects is probably the large scale factor of 25, as indicated by the Authors’ literature review. As a consequence, the minimum model value is Re = 1.1 105, where Lref = h, which is close to the limitations mentioned in Table 1, whereas the minimum of We = 82, again with Lref = h, is below the limitations to avoid significant scale effects. Furthermore, Ko¨kpinar and Go¨g˘u¨s¸ (2002) did not measure the cavity subpressures but used the related data from Demiro¨z (1985) to study this effect, which is relevant for the aerator performance. They found that the data ‘‘clearly indicate scale effects’’. The cavity sub-pressure differences between the model tests and the prototype certainly add to the inaccurate prediction of b. Which approach is closer to prototype conditions: physical or numerical modeling? They both include uncertainties or simplifications. This question may only be answered with accurate prototype measurements. The Authors add the example of the first Foz do Areia spillway aerator (Pinto 1991). They intend to prove thereby the inadequacy of model-derived empirical equations. There exist, however, model studies respecting the above mentioned limitations to avoid significant scale effects, resulting in reliable predictions of the prototype air entrainment coefficient b, as shown in Fig. 1. To conclude, it is illegitimate to compare a model study subjected to scale effects with a prototype-CFD model to determine b of a prototype aerator, and then criticize model studies in general for this pretended deficit of the particular cited physical model study. Air entrainment and air transport in physical scale models may be accurately determined if the limitations regarding the effects of viscosity and surface tension are respected. The Discusser has the opinion that both, physical and numerical models are powerful tools to design prototype aerators. They both have advantages and drawbacks, and therefore, should co-exist to improve the quality of each other and, ultimately provide an adequate definition of the prototype aerator performance.
doi:10.1139/L09-167
Published by NRC Research Press
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Can. J. Civ. Eng. Vol. 37, 2010 Table 1. Limitations to avoid significant scale effects in two-phase flows. Reference Kobus (1984) Pan and Shao (1984) Pinto (1984) Koschitzky (1987) Rutschmann (1988) Skripalle (1994) Boes (2000) Pfister (2008) Chanson (2009)
Limitation Re > 1 105 Re > 3.5 106 We > 500 Re > 1 105 We > 110 We > 170 Re > 1 105 Re > 2.2 105 Wo > 140 Re > 5 105
Lref h L L h h h h h
Application range Local air entrainment Aerators, particularly b Aerators, particularly b Aerators, particularly b Aerators, particularly b Aerators, particularly b Two-phase stepped spillway flow Aerators, bottom air concentration development
h
Self-aerated chute flow
Fig. 1. Air entrainment coefficient b from prototype measurements of first Foz do Areia spillway aerator by Pinto (1991), compared with (*) CFD model of Aydin and Ozturk (2009), (*) Pfister and Hager (in press), (~) Pinto (1991), and (!) Ko¨kpinar and Go¨g˘u¨s¸ (2002).
References Aydin, M.C., and Ozturk, M. 2009. Verification and validation of a computational fluid dynamics (CFD) model for air entrainment at spillway aerators. Canadian Journal of Civil Engineering, 36(5): 826–836. doi:10.1139/L09-017. Boes, R.M. 2000. Scale effects in modelling two-phase stepped spillway flow. In Hydraulics of Stepped Spillways. Edited by H.E. Minor and W.H. Hager. A.A. Balkema, Rotterdam. pp. 53–60. Chanson, H. 2009. Turbulent air-water flows in hydraulic structures: dynamic similarity and scale effects. Environmental Fluid Mechanics, 9(2): 125–142. doi:10.1007/s10652-008-9078-3. Demiro¨z, E. 1985. Spillway aerator project criterions used for highspeed chute flows. Engineering Research Group, Project 606.
TUBITAK, The Scientific and Technical Research Council of Turkey, Ankara, Turkey [in Turkish]. Demiro¨z, E. 1986. Determination of project criterions relating to adding aerators to structures for the aeration of spillway chute. HI-751, M-212. State Water Works (DSI), Ankara, Turkey [in Turkish]. Kobus, H. 1984. Local air entrainment and detrainment. In Proceedings of the Symposium on Scale Effects in Modelling Hydraulic Structures. Edited by H. Kobus. Technische Akademie, Esslingen. Paper No. 4.10, pp. 1–10. Koschitzky, H.-P. 1987. Dimensionierungskonzept fu¨r Sohlbelu¨fter in Schussrinnen zur Vermeidung von Kavitationsscha¨den. Mitteilung 65. Institut fu¨r Wasserbau, Stuttgart, Germany [in German]. Ko¨kpinar, M.A., and Go¨g˘u¨s¸, M. 2002. High-speed jet flows over spillway aerators. Canadian Journal of Civil Engineering, 29(6): 885–898. doi:10.1139/l02-088. Pan, S., and Shao, Y. 1984. Scale effects in modeling air demand by a ramp slot. In Scale Effects in Modelling Hydraulic Structures. Edited by H. Kobus. Technische Akademie, Esslingen. Paper No. 4.7, pp. 1–5. Pfister, M. 2008. Schussrinnenbelu¨fter: Lufttransport ausgelo¨st durch interne Abflussstruktur. Mitteilung 203. Edited by H.-E. Minor. Laboratory of Hydraulics, Hydrology and Glaciology (VAW). ETH, Zurich [in German]. Pfister, M., and Hager, W.H. 2009. Chute aerators II: Hydraulic performance. Journal of Hydraulic Engineering, In press. Pinto, N.L. 1984. Model evaluation of aerators in shooting flow. In Scale Effects in Modelling Hydraulic Structures. Edited by H. Kobus. Technische Akademie, Esslingen. Vol. 4.2, pp. 1–6. Pinto, N.L. 1991. Prototype aerator measurements. In Proceedings of the Air Entrainment in Free-surface Flows, IAHR Hydraulic Structures Design Manual 4. Edited by I.R. Wood. A.A Balkema, Rotterdam. pp. 115–130. Rutschmann, P. 1988. Belu¨ftungseinbauten in Schussrinnen. In Mitteilung 97. Edited by D. Vischer. Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH, Zurich [in German]. Skripalle, J. 1994. Zwangsbelu¨ftung von Hochgeschwindigkeitsstro¨mungen an zuru¨ckspringenden Stufen im Wasserbau. In Mitteilung 124. Technische Universita¨t, Berlin [in German].
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