The classical numerical approach used for Natural Laminar Flow (NLF) design relies on the experience of the engineers in finding pressure distributions that would improve the extent of laminar flow and could reasonably be approximated in an inverse design phase. Recent initiatives improve this approach, eliminating the “man in the loop”, by including a measure of the laminar flow in the shape optimization problem itself. The numerical solution of such problems with many parameters and constraints is challenging. Our method of optimization for NLF design is an implementation of a gradient-based approach enabling us to efficiently solve problems with many design parameters. The use of CFD, followed by boundary-layer stability analysis, enables to directly find geometries that damp growth of disturbances (which cause transition) in order to delay the laminar-turbulent transition. Moreover, the computation of the gradients is efficiently performed thanks to the work carried out in last years at FOI and KTH on adjoints of the flow and stability equations, making the cost for computing gradients independent of the number of optimization parameters. Our method has been successfully tested for optimization of airfoils and has already come in use in several projects with industrial applications. In the scope of the present project the NLF-optimization toolkit (developed by FOI & KTH) will be extended to three-dimensional geometries. Another important improvement is to include the sensitivities with respect to flow separation because the extension of the laminar boundary layer at cruise can severely penalize the performance of the NLF wing at high angles of attack if laminar separation occurs too early. An attempt will be made to include the Reynolds Averaged Navier-Stokes (RANS) equations as a replacement for the Euler equation in our optimization loop, which involves the use of the adjoint RANS solver already developed by FOI in Edge.
Field of science
- /natural sciences/mathematics/pure mathematics/geometry
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