Integral analysis of ducted two-stream mixing with recirculation

The integral boundary-layer equations are used to develop an analysis of ducted turbulent mixing of coaxial streams. Non-recirculating flows, as well as flows with a recirculation region along the duct wall, are considered in the formulation. The flow geometry considered is either axisymmetric or planar, and a provision is made to calculate flows with a centerbody. Chemical reactions in the mixing process, if they occur, are assumed to be in equilibrium. A simple eddy viscosity model is used to describe the turbulent transport processes. Comparison of the analytical results with experiments indicates that the location and extent of recirculation are well predicted, at least for flows with moderate density gradients. However, because of the neglect of streamwise turbulent transport processes in the analysis, the predicted concentration field in recirculating flow is in only fair agreement with the experiment. An extended integral analysis, in which the streamwise turbulent transport of momentum and species is included in an approximate manner, is formulated.