Réflexions sur la recherche de similitude hyperdistordue pour l'étude des écoulements à surface libre dans les canaux

Considerations on achieving hyperdistorted similitude in free-surface flow wave flume investigations

¹ Maître de Conférences à la Faculté des Sciences de Toulouse.
² Docteur en Hydrodynamiqne.

Résumé

Unavoidable level and flow measurement errors, the very definite uncertainty as to how loss to head varies with depth of water, and variations in the coefficient of frictional resistance all combine to limit the possibilities of reproducing free-surface flows. It seems to be interest, therefore, to examine the similitude conditions whereby given prototype and model flows could be made to correspond to within a degree of approximation not exceeding the degree of uncertainty attached to the evaluation of the relevant characteristic parameters. The basic idea is thus to define similitude conditions enabling an operating point on the prototype to strictly correspond with on the model, and which is approximately satisfied near these "reference operating points". This is by no means a new assumption, as it has already been used implicitly in backwater curve calculation methods (e.g. Bakhmeteff) or simplified procedures for the investigation of transient regimes. The authors have considered two possible approaches, one of which makes use of the equivalence of flows in prismatic and very broad channels, and the other being based on profile similitary. In the case of steady flow conditions, the authors have attempted to base the definition of similitude criteria on the intuitive idea of conserving both Froude number and the slope J/I of the hydraulic gradient J with respect to the longitudinal canal slope I in the vicinity of two homologous "reference points". By using non-dimensional quantities, non-dimensional groups G (h) and M (h) are obtained; these are considered in the definition of the similitude parameters, being similar, to the non-dimensional critical flow rate and characteristic slope defined by Lazard and Silber. The local conservation of Froude number and the J/I ratio is not sufficient to ensure approximate similitude for transient flow conditions, however, for which a third condition "S/BM = a constant" has to be added. The conjunction of these three assumptions is only possible where the profiles can be transformed by similarity. For the general case, the validity has been examined of a similitude condition based on the constancy of J/I and S/BM. These approximations are comparable to those considered for the basic assumptions made for graphical constructions using the depth of water and discharge functions H and Q; they nearly always give satisfactory results. All things considered, however, the experimental approach still remains the most reliable basis of assessment for the validity of this approximate similitude. The first tests have shown that, allowing for unavoidable measurement error, agreement between flows connected by these similitude rules is satisfactory, especially for structures of moderate length. The "hyperdistorted" similitude discussed above is a transformation which makes flows correspond rather than structures. It only hold good within a limited range of depth variations about a reference depth. Its three possible types of application are the following: 1. Investigation of a flow similar to the basic prototype flow on a scale model differing in profile from the prototype. A laboratory Hume with its sides set at a certain slope can be used to study transient How conditions for a different structural profile. 2. Attempted classification of transient flows into groups. Geometrical similitude__and even more so longitudinally distorted similitude__enable a whole "family" of flows to he associated with flows observed on the model or the prototype. 3. Study of equivalent tangent flows in very broad flames. The "hyperdistorted" similitude notion also facilitates use of the equivalence between basic and tangent flows in very broad flumes. Flows of this sort are of very valuable assistance for graphical constructions.