A critique of predictive and correlative models for turbulent flow and convection

Direct simulations of turbulent now and convection constitute a new and invaluable resource but are as yet limited to only a few geometries and conditions. The accuracy and generality of correlating equations for the turbulent shear stress itself preclude the need for approximate modeling for simple flows such as in round tubes and along flat plates. For asymmetric, one-dimensional flows, such as in a circular annulus, the turbulent shear stress remains well-behaved but the eddy viscosity and the mixing length become unbounded at one point and negative over an adjacent region. The kappa-epsilon model is then invalidated as well; the kappa-epsilon-u'(y)u'(2) model remains valid but is truly predictive only for the turbulent core. All of these elementary models are inadequate for two-dimensional channels owing to the secondary motion. The same considerations apply to convection in turbulent flow.