European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006 P. Wesseling, E. Oñate, J. Périaux (Eds) © TU Delft, The Netherlands, 2006
Title of the STS presentation :Application of sonic boom
optimization to supersonic aircraft design
Names L.Daumas,Q.V.Dinh,S.Kleinveld,G.Rogé Affiliations Dassault Aviation Countries France e-mails gilbert.roge@dassault-aviation.fr steven.kleinveld@dassault-aviation.fr
Keywords: adjoint, CAD modeller, optimization, sonic boom, supersonic aircraft design
Objectives :
In this talk preliminary results will be discussed on sonic boom optimization applied to supersonic aircraft design. The cost functional considered will aim at reducing sonic boom overpressure. The tools used to achieve this goal and their interaction, which defines the setup of the optimization loop, are shown in figure 1.
The process is gradient based and includes an adjoint solver for the Euler CFD code Eugenie. An interior point algorithm is used as optimizer in the loop.
The geometric CAD modeller used for the parameterization of the aircraft gives access to local as well as global design variables. Local design variables allow geometry modifications in position, tangency and curvature at the nodes defining the patches whereas global design variables or features enable changes in characteristics of geometrical entities. As global design variables of the wing for instance we can name its thickness, camber, twist and dihedral distribution.
Applications :
Application of the optimization loop to minimize the sonic boom overpressure will be outlined and results will be described. The geometry considered consists of a double swept wing mounted on a generic fuselage and is illustrated in figure 2.
S.Kleinveld, G.Rogé, L.Daumas, Q.V.Dinh
keeping the reference length of the fuselage to a constant value of 30 m. The available passenger cabin volume has also been kept constant during the optimization process.
The figure of merit consists of an evaluation of the pressure distortion in a box taken around the aircraft as a measure for the sonic boom overpressure. More precisely the objective function computes the L2 norm of the overpressure dp/p∞ at a distance R/L=0.5 beneath the aircraft in its symmetry plane i.e.Θ=0°.
The gradient of the cost functional was validated with respect to the mesh coordinates, the state variables and the angle of attack and showed the typical V-shaped curves when compared to a first or second order finite difference evaluation while decreasing the step size. The curve obtained for the derivative of the functional with respect to the mesh coordinates is given in figure 3.
Concerning the design variables control was chosen for the fuselage entity over 18 sections in scale, thickness and camber angle and for the wing entity over 9 sections in twist, camber angle and chord position.
Results:
The near and far field pressure distributions at several stages of the optimization process are shown in figure 4. The propagation code using the near field results to predict the overpressure at ground level shows that the most important overpressure reduction is obtained at an intermediate iteration and not at the final iteration. It shows care has to be taken when evaluating the best solution through an optimization process based on near field criteria. The final geometry obtained for the generic shape is shown in figure 5.
Future: As future enhancements we can name:
• use of wing/fuselage dihedral as design parameter
• cost function modelling: functional based on far field data, functional based on near field data extracted at several azimuthal angles
• additional constraint on the pitching moment
• adjoint based mesh adaptation in optimization process • multipoint/robustness studies
• cost - constraint exchange rates
Acknowledgement:
S.Kleinveld, G.Rogé, L.Daumas, Q.V.Dinh
Figure 1 : optimization loop
Figure 2 : Generic supersonic wing-fuselage geometry Reference
Geometry
S.Kleinveld, G.Rogé, L.Daumas, Q.V.Dinh
Figure 3 :Validation gradient cost functional with respect to coordinates
Figure 4:Near field (left) and far field (right) pressure distribution Initial Iteration 7
Iteration 10
