ON THE ENTRAINMENT ASSUMPTION IN SCHATZMANN INTEGRAL PLUME MODEL

The behaviour of stationary, non-passive plumes can be simulated in a reasonably simple and accurate way by integral models. One of the key requirements of these models, but also one of their less well-founded aspects, is the entrainment assumption, which parameterizes turbulent mixing between the plume and the environment. The entrainment assumpti on developed by Schatzmann and adjusted to a set of experimental resul ts requires four constants and an ad hoc hypothesis to eliminate undes irable terms. With this assumption, Schatzmann's model exhibits numeri cal instability for certain cases of plumes with small velocity excess es, due to very fast radius growth. The purpose of this paper is to pr esent an alternative entrainment assumption based on a first-order tur bulence closure, which only requires two adjustable constants and seem s to solve this problem. The asymptotic behaviour of the new formulati on is studied and compared to previous ones. The validation tests pres ented by Schatzmann are repeated and it is found that the new formulat ion not only eliminates numerical instability but also predicts more p lausible growth rates for jets in co-flowing streams.