On the physical modelling of large vortex drop structures in municipal sewerage systems

摘要

Classically, dimensional analysis is used to establish the fundamental scaling laws to predict prototype behaviour from observed model results. However, the same dimensional analysis demonstrates that it is not possible to avoid scale effects if the prototype fluid - normally water - is used in the model studies. Flow through hydraulic structures is typically gravity-driven, and equality of Froude Numbers at homologous points in model and prototype leads to the determination of fundamental scaling laws. However, it is well known that, as a consequence, homologous values of other non-dimensional parameters, such as Reynolds Number and Weber Number, are not equivalent and this leads to scale effects due to the imperfect replication in the model of (for example) friction and surface tension effects. In such cases, it is necessary to use process functions to determine the magnitude of the scale effects and to inform the adjustment of measured flow properties in the model to reflect the true value of the flow properties in the prototype. The present paper extends the use of process functions to annular flows, such as those that occur in vortex drop structures and plunge pools. Within the vortex drop, it is shown that the process functions cannot be used to evaluate scale effects directly, but, instead, must be used in conjunction with the model data to develop an analytical model for the prediction of corresponding prototype behaviour. Within the plunge pool, it is hypothesised that the momentum flux at the exit of the vortex pipe must be correctly modelled to ensure the proper replication of flow conditions within the plunge pool. The techniques are developed, and their use illustrated through application to a large physical model study of a vortex drop and plunge pool in a municipal sewerage system. It is shown, further, that ignoring the insight gained from the developed process functions would lead to large errors in the prediction of prototype flow behaviour from measured model results.