Overview
Proposed work aimed at developing efficient optimisation tools for NLF design where the cost function is the total drag (pressure and friction). The tool utilises efficient and accurate computation of gradients of objective functions as well as robust parametrisation of the geometry. Our approach uses Computational Fluid Dynamics followed by accurate boundary-layer stability analysis in order to find, by optimisation, geometries that damp growth of boundary-layer disturbances in order to delay the laminar-turbulence transition. Gradient-based optimisation and adjoint solvers are used in order to obtain the best numerical efficiency. The gradients are obtained through a chain of computations including adjoints of the flow equations and of the parabolized stability equations.
Our method was initially developed for airfoils and recently extended to 3D wing design. Here, the tool was improved by replacing the Euler equations of fluid dynamics by the Reynolds-Averaged Navier-Stokes (RANS) equations. This allowed us to account for the viscous-inviscid interactions and therefore obtain a more accurate evaluation of the aerodynamic performances such as the total drag, lift and pitching moment. In order to ensure high accuracy of the gradients, the adjoint of the RANS solver included an adjoint of the turbulence model. A mesh-less method based on Radial Basis Functions was used for deforming the RANS meshes. This approach was proven to be much faster than elliptic smoothers on meshes that are suitable for RANS computations. Here, two shape parametrisation methods suitable for industrial design were implemented and compared. Further, an automatic and efficient procedure for nonlocal stability analysis was implemented in order to facilitate the use of this approach in industrial projects.
Funding
Results
Executive Summary:
The objective was to develop or improve algorithms for aerodynamic shape optimization for Natural Laminar Flow design (NLF). In our approach of NLF Computational Fluid Dynamics (CFD) was coupled to boundary-layer stability analysis in order to find, by gradient-based optimization, geometries that damp boundary-layer disturbances. Delaying the growth of certain disturbances in the boundary layer was assumed to delay laminar-turbulence transition, which is an efficient way to reduce the viscous drag. The gradients were obtained through the adjoints of the flow and the parabolized stability equations (PSE). In HIPERLAM we replaced the Euler equations of fluid dynamics by the Reynolds-Averaged Navier-Stokes (RANS) equations, which required, when using gradient based optimisation, solving the adjoint of the RANS equations. The prospect here was to include the viscous-inviscid interaction in order to achieve better designs. In addition to the development of the adjoint RANS equations, key algorithms involved in the optimisation were analyzed or improved: methods to initialise the analysis of the boundary layer instabilities, algorithms used to deform unstructured CFD meshes for RANS computations, and methods to parameterise wing deformations in the context of optimal shape design.
The results obtained during the project was a progression towards our objectives: adjoint equations for the Spalart-Almaras have been derived and implemented in the CFD program Edge, an adjoint of the Menter SST k-omega turbulence models was integrated as well in Edge, and progress were made on the convergence speed of the adjoint Navier-Stokes equations solver. The numerical solution procedure of the adjoint RANS equations needs now to be improved in order to achieve satisfying results. Regarding the influence of the quality of the flow solution obtained by CFD, which was used for carrying boundary layer simulations and stability analysis, it was shown that alternative boundary conditions schemes would not improve the oscillations in computed pressures, which are typical for unstructured flow solvers like Edge. A database was generated in order to improve the robustness of stability analysis, which will facilitate the use of NLF in aircraft design. During the project algorithms for the deformation of the geometry (FFD) and of the CFD mesh (RBF), were further developed and compared demonstrating the possibility to obtain large improvements in aerodynamic shape optimization applications by carefully selecting those methods.