The continuous adjoint method as a guide for the design of flow control systems based on jets

Abstract

PurposeThe purpose of this paper is to propose the use of the continuous adjoint method as a tool to identify the appropriate location and “type” (suction or blowing) of steady jets used in active flow control systems.Design/methodology/approachThe method is based on continuous adjoint and covers both internal and external aerodynamics. The adjoint equations, including the adjoint to the SpalartAllmaras turbulence model and their boundary conditions are formulated. At the cost of solving the flow and adjoint equations just once, the sensitivity derivatives of the objective function with respect to hypothetical (normal) jet velocities at all wall nodes are computed. Comparisons of the computed sensitivities with finite differences and parametric studies to assess the present method are included.FindingsThough the sensitivities are computed for zero jet velocities, they adequately support decision making on: the recommended location of jet(s), at boundary nodes with high absolute valued sensitivities; and the selection between suction or blowing jets, based on the sign of the computed sensitivities. Regarding adjoint methods, two important findings of this work are: the role of the adjoint pressure which proves to be an excellent sensor in flow control problems; and the prediction accuracy of the proposed adjoint method compared to the commonly made assumption of “frozen turbulence”.Originality/valueFirst use of the continuous adjoint method using full differentiation of the turbulence model, in flow control optimization. A low‐cost design tool for recommending some of the most important jet characteristics.