Optimal control of diffuser shapes for confined turbulent shear flows

A model for the development of turbulent shear flows, created by non-uniform parallel flows in a confining channel, is used to identify the diffuser shape that maximises pressure recovery when the inflow is non-uniform. Wide diffuser angles tend to accentuate the non- uniform flow, causing poor pressure recovery. On the other hand, shallow diffuser angles create longer regions with large wall drag, which is also detrimental to pressure recovery. Thus, optimal diffuser shapes strike a balance between the two effects. We use a simple model which describes the evolution of an approximate flow profile and pressure in the diffuser. The model equations form the dynamics of an optimal control problem where the control is the diffuser channel shape. A numerical optimisation approach is used to solve the optimal control problem and we use analytical results to interpret the numerics in some limiting cases. The results of the optimisation are compared to calculations from computational fluid dynamics.