Title: Optimal control of diffuser shapes for confined turbulent shear flows,
Abstract: 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.