Abstract
Optimal control theory for shape design has been applied in this paper to design a plane diffuser operating under turbulent flow conditions. The design objective is to maximize the diffuser pressure rise for a prescribed inlet width and length. The flow description is provided by the two-dimensional Reynolds-Averaged-Navier-Stokes (RANS) equations with a Baldwin-Lomax (1978) algebraic turbulence model. A set of turbulent “adjoint” equations are obtained from the formulation, the solution to which along with the “direct” RANS equations permits the calculation of a design function. The choice of a design function is not unique and two different forms are evaluated. It is shown that different initial diffuser shapes lead to nearly identical optimum profiles provided the initial diffuser geometry corresponds to a non-separated flow. Computations carried out for initial diffuser shapes that exhibit gross separation were not successful.
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