Optimization of Transonic Wing with Advanced 3D Mesh Morphing

Aerodynamic efficiency is a key aspect in commercial aircraft design as it allows reducing fuel consumption and meeting emission and performance requirements. The main goal of this work is to improve the initial shape of the wing of an innovative three lifting surfaces configuration aircraft in order to minimize drag at transonic cruise condition.


The classic approach to aerodynamic shape optimization requires the definition of a geometrical parameterization of the CAD model. In this case, whenever a parameter is changed, a new mesh must be generated for the new configuration and the CFD model must be updated. Using Shaper™ the parameterization can be defined directly on the CFD model and the new configuration can be immediately obtained morphing the original mesh. The optimization process can then be integrated with any external CFD solver using Nexus™ and the whole procedure can be completely automated. This allows to save time and to drastically reduce design costs.

Three lifting surface aircraft, initial design

Three lifting surface aircraft, initial design

The twist of seven spanwise stations of the main wing is optimized under lift and pitching moment constraints. This approach requires to solve two nested optimization problems. The first is an unconstrained optimization of the twist distribution. The second, to be run every time a proposed twist distribution is computed, search for the trim configuration that guarantees the minimal global drag.

To speed-up the optimization process Surrogate Models based on Kriging response surfaces were employed. To populate the initial Design of Experiment, 120 configurations were created using Shaper™ to morph the main wing and to rigidly rotate the control surfaces to trim the aircraft. The evaluations of the aerodynamics forces were performed using Fluent®.

Once the response surfaces were built, the aerodynamic optimization was solved with Nexus™ using a Genetic Algorithm: each twist distribution analysed by the genetic algorithm was trimmed with an MMA gradient-based method.

3D morphing of the main wing and rigid rotation of the canard and tail with ShaperTM

3D morphing

Advantages in using Shaper and Nexus:

Main advantages of using Shaper and Nexus are:

  • easy definition of the design parameterization directly on FEM and CFD numerical grids;
  • accurate 3D morphing using advanced nonlinear techniques that preserve the original quality of the mesh;
  • easy integration of external FEM and CFD solvers among which Nastran®, Abaqus®, Radioss®, Fluent®, Ansys® and Adams®;
  • parallel and concurrent evaluations to exploit your hardware and software resources in the best possible way. A scalable architecture that you can tune application by application;
  • access to all your results via organised tables and SQL extern databases;
  • advanced Design of Experiment (DoE) and statistical tools to explore and analyse results;
  • state-of-the-art libraries for single- and multi-objective optimisations, Design of Experiments and Response Surfaces modelling.


The aerodynamic efficiency of the initial design, that was already optimized to have a shock free flow and a low induced drag, has been further improved using Shaper™ and Nexus™. The final twist distribution of the main wing identified after 450 iterations guarantees a drag reduction of about 1% for the whole aircraft. Employing Shaper™ and its advanced morphing capabilities, it was possible to explore a big number of designs in a completely automated way allowing significant savings both in costs and time as shown in the summary table on the right.

Optimization history and comparison between initial and final solutions

Optimization history

Case Presented at the 3rd International Conferece of the European Aerospace Societies. E. Fabiano, G. Quaranta, A. Colbertaldo and L. Lanzi “Mesh morphing applied to transonic wing optimization”, Venice 2011.