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The design of complex hydraulic structures requires its testing through hydraulic models (i.e., reduced scale physical representations). The main practical limitation of hydraulic models are the so called ‘scale effects’, i.e., the fact that only the primary physical mechanisms can be correctly represented, while the secondary ones are distorted. In particular, for free surface flows the gravitational driving forces – primary mechanism – must be correctly scaled in relation to inertia (Froude scaling), leading to an incorrect representation of viscous forces (no Reynolds scaling) – usually the leading secondary mechanism – as the fluid in the hydraulic model is the same as in the prototype (water). Though for most applications Reynolds number effects introduce only small quantitative deviations, which can be readily absorbed within the margin of safety assumed for design, this is not always the case. In fact, they can for example accumulate, in such a way that the effects compete with those arising from the primary mechanism. In those cases, being the Reynolds effects distorted in the hydraulic model, the observed response deviates from the one corresponding to the prototype, thus needing some empirical correction. Numerical modeling is the appropriate tool to help solving in a rigorous way this type of difficulty. A sound numerical model should be able to correctly represent both the primary and secondary mechanisms, i.e., it is not subject to ‘scale effects’. Its main limitations might arise from insufficient resolution, or from inaccurate representation of turbulence effects. The first limitation could be overcome by reducing the spatial step of the numerical grid; the second one, by resorting to more elaborated theoretical approaches. Based on these observations, the following strategy is proposed: (i) the flow in the hydraulic model is numerically simulated, i.e., the dimensions of the hydraulic model are used (thus accounting for the ‘spurious’ scale effects); this constitutes a way of validating the theoretical model; eventually, adjustments in the representation (higher resolution, more elaborated theoretical approaches) are introduced in order to improve the comparison; (ii) the flow in the prototype is numerically simulated, by introducing the dimensions of the prototype in the validated numerical model (i.e., distortion of secondary mechanisms is now avoided); this constitutes the adequate way of extrapolating the results to the prototype dimensions. Two problems (with quite different levels of complexity) are presented as case studies in order to illustrate the proposed approach, both of them associated to the design of the Third Set of Locks of the Panama Canal (communicating the Atlantic and Pacific Oceans), for which the present authors were responsible: (a) the determination of the time for water level |
