Comparaison des résultats des essais d'intumescences effectués sur le modèle réduit et sur le modèle mathématique du canal Oraison-Manosque

Comparison of physical and mathematical model test results on translation waves in the Oraison-Manosque power canal

Ingénieur à la SOGREAH.

Résumé

The first part of the article discusses the difficulties encountered in the development of mathematical models for the study of steep-fronted translation waves in power canals. The assumptions behind St. Venant's equations are briefly reviewed. The non-linear nature of these equations is brought out and also the consequences which this entails, in particular, the fact that after a certain time there can be no continuity in their solution. The steepening of the wave invalidates the flow theory which ignores vertical acceleration. The use of the method of characteristics to compute the moving hydraulic jump is rejected after a discussion of the difficulties involved in its application to practical cases. Finite difference methods can however be used for this type of computation. The section of the Oraison canal represented by the scale and mathematical models contains several transitions, including sills, a lateral spillweir, a flow divider and a syphon. Although it was possible to express the roughness of the running sections of the canal in the mathematical model with the aid of known Strickler coefficients, adjustments had to be made for the individual head losses at the transitions. As the sketches in part III show, a schematic method was devised using a generalised head loss term. Thus, for example, the separate head losses at the flow divider, the canal fork and the syphon, were replaced by a single head loss applied to the syphon. The adjustment consisted in reproducing the natural water surface under steady flow conditions. Table 2 compares the natural flow profiles with those obtained from the computer and scale models under steady flow conditions. The adjustment of the two models can be assessed from these results. With the mathematical model thus adjusted, 4 earlier scale model tests on translation waves were put through the computer. Table 3 gives the test conditions. The results obtained on both models in each test, at various points in the canal, are given in figures 5-8. Lastly, a prototype test, carried out on 15th September 1964 in the first reach of the Oraison canal, was reproduced on each model. Figure 9 compares the computed levels with those recorded on the prototype and the scale model. The comparison is satisfactory on both models, except during a short period just after turbine shutdown at about 10 a.m. This is due to the fact that neither model was designed to allow for the effect of the Oraison power station tailrace tunnel. The conclusion is that the computer model results are quite comparable with those yielded by a distorted scale model. The use of mathematical models in preference to distorted scale models would seem to be technically justified in all cases where it is not overruled by economic or other considerations.