Gilbert Rogé

A relationship between stabilized finite element methods and the Galerkin method with bubble functions

Abstract A relation between stabilized finite element methods and the Galerkin method employing interpolations with bubble functions is established for the advective-diffusive model and for the linearized compressible Navier-Stokes equations. The bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy. In particular, for the advective-diffusive model, the Galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline-upwind/Petrov-Galerkin (SUPG) method in the diffusive limit.

Benchmarking the prediction of dynamic derivatives: Wind tunnel tests, validation, acceleration methods

The dynamic derivatives are widely used in linear aerodynamic models which are considered to determine the flying qualities of an aircraft: the ability to predict them reliably, quickly and sufficiently early in the design process is more and more important, in order to avoid late and costly component redesigns. This paper describes some experimental and computational activities dealing with the determination of dynamic derivatives. The work has been carried out within the FP6 European project SimSAC. Numerical and experimental results are compared for two aircraft configurations: the generic civil transport aircraft, wing-fuselage-tail configuration DLR-F12 and a generic Transonic CRuiser (TCR), which is a canard configuration. Static and dynamic wind tunnel tests have been carried out for both configurations and are briefly described. The data base generated for the DLR-F12 configuration includes force and pressure coefficients obtained during small amplitude pitch, roll and yaw oscillations while the data base for the TCR configuration includes force coefficients for small amplitude oscillations, dedicated to the determination of dynamic derivatives, and large amplitude oscillations, in order to investigate the dynamic effects on nonlinear aerodynamic characteristics. The influence of the canard has been investigated too. Dynamic derivatives have been determined on both configurations with a large panel of tools, from linear aerodynamic (Vortex Lattice Methods) to CFD (unsteady Reynolds-Averaged Navier-Stokes solvers). The study confirms that an increase in fidelity level enables dynamic derivatives to be better calculated. Linear aerodynamics (VLM) tools can give satisfactory results but are very sensitive to the geometry/mesh input data. Although all the quasi-steady CFD approaches give very comparable results (robustness) on steady dynamic derivatives, they do not allow the prediction of unsteady components of the dynamic derivatives (angular derivatives w.r.t. time): this can be done with either a fully unsteady approach (with a time-marching scheme) or with Frequency Domain solvers, both of them giving very comparable results for the DLR-F12 test case. As far as the canard configuration is concerned; strong limitations of linear aerodynamic tools are observed. A specific attention is paid to acceleration techniques in CFD methods, which allow the computational time to be dramatically reduced while keeping a satisfactory accuracy.

European Benchmark on Numerical Prediction of Stability and Control Derivatives

Reliable prediction of flight dynamic criteria is conditioned by a satisfactory prediction of aerodynamic static and dynamic derivatives. A numerical benchmark has been conducted within the framework of the European Project SimSAC “Simulating Aircraft Stability And Control Characteristics for Use in Conceptual Design”. The objective was to establish the ability as well as the productivity of different tools to predict stability and control derivatives. Different levels of fidelity have been included, from quasi-steady VLM to fully unsteady RANS solvers. The numerical data have been compared to experimental ones, on the DLR-F12 generic civil aircraft. It has been wind-tunnel tested during the project, with several forced-motion oscillations; the data base includes unsteady pressures (not analysed in this paper). The study confirms that an increase in fidelity level allows for a better estimation of dynamic derivatives. VLM tools can give very satisfactory results but are very sensitive to the geometry/mesh input data. All the quasi-steady CFD approaches give very comparable results (robustness) on steady dynamic derivatives. However, they do not allow for the prediction of unsteady components of the dynamic derivatives (so called damping derivatives): this can be done with either a fully unsteady approach (with a time-marching scheme) or with Frequency Domain solvers, both of them giving very comparable results.

Differentiated parametric CAD used within the context of automatic aerodynamic design optimization

As environmental concern grows, the need for fuel -ef ficient aircraft becomes more and more stringent in order to meet up with the rapidly evolving standards which are set to reduce noise and emissions. In order to reach that goal relying on an efficient design process defining the detailed shape of aircraft is mandatory . In that respect the use of automatic aerodynamic o ptimization has been proven to be of great benefit over the recent past. It enables significant reduction in development cost and cycle time. After a brief overview of the set -up of the overa ll optimization process , which includes a finite volume Euler flow solver in combination with a discrete adjoint approach, we will focus in the present paper more specifically on the use of a differentiated parametric CAD modeler. Thus far the gradient of the CAD model was obtained through a finite difference approach. When using different types of variables the more the process gets dependent on the choice of the different step sizes which is not straightforward to make. Therefore the CAD definition has be en recently differentiated and its impact on convergence and final result will be described. Validation and application of differentiated CAD were performed through a set of inverse problems by progressively including a growing number of modules in to the o ptimization loop . Eventually the complete loop for automatic aerodynamic optimization was used on a generic business jet in transonic cruise conditions.

Automatic shape optimization using parametric CAD applied to sonic boom reduction

Over the recent past automatic aerodynamic optimization has proven to be of great benefit in the design process defining the detailed shape of aircraft. It has shown to significantly reduce its development cost and cycle time. Besides giving a brief overview of the set-up of the overall optimization process, which includes a finite volume Euler flow solver in combination with a discrete adjoint approach, we will focus in the present paper more specifically on the extension of the parametric CAD modeler to cope with a flexible mean line parameterization enabling to handle local and global dihedral and sweep modifications. Geometric constraints related to a multidisciplinary design context will also be addressed. As an application of these new features we concentrate on sonic boom reduction of a supersonic business jet and its impact on cruise performance. Several test cases based on an inverse problem formulation of the near field pressure signature are considered while also conflicting objectives as maximum lift to drag ratio will be taken into account thereby stressing on the multi-objective and/or multi-constrained aspects of the problem at hand.

Aerodynamic Design Process of a Supersonic Business Jet

A CAD-based optimization process designed on top of an unstructured mesh finite volume Euler flow solver is presented. Two major optimization examples of a supersonic business jet are then described : a wing shape optimization at given supersonic cruise conditions and an engine integration optimization through fuselage area-ruling. Both examples show a substantial reduction of the drag coefficient.

Status and Future Challenges of CFD in a Coupled Simulation Environment for Aircraft Design

The state of the art of Computational Fluid Dynamics and the axis of improvements are described. The issue of flutter prediction is addressed first: the use of linearized Euler solvers for transonic flutter is explained. Recent advances in optimum aerodynamic shape design are presented next, the results demonstrate the applicability of optimization based on the Euler equations and open the way to multidisciplinary optimum design. Finally, the use of Large Eddy Simulation for accurate turbulent flow simulation is illustrated.

Fuselage shape automatic optimization with geometric constraints using a CAD based process

Use of an automated design process in order to define the detailed aerodynamic shape contributes significantly to the reduction of aircraft development cost and cycle time. Our optimization loop combines a gradient -based optimizer, a C AD modeler, mesh deformation (laplacian like operator), a Finite Volume Cell Vertex Euler CFD code and discrete adjoint approach. As an application of the Euler shape optimization loop serving this purpose we will focus on fuselage and wing design for a co mplete aircraft configuration of a Dassault Aviation Supersonic Business Jet project. The automated shape optimization enables further improvement of supersonic aircraft performance compared to traditional methods. The present paper covers two test cases: the first one deals with engine integration drag minimization, while the second one copes with sonic boom reduction. Drag reduction during the cruise phase will lead to an increase in range, thereby leading to an overall decrease in fuel consumption and th us lowering the environmental impact. Previous studies concentrating on the multipoint wing and canard design showed that a substantial gain in pressure drag could be obtained using geometric camber and twist features and encouraged to extend the capacitie s of our automated design loop to other parts of the aircraft and in particular the fuselage, taking into account the wing intersection. Several configurations, including various scaling and shifting of the nacelle, applied on fuselage design will be prese nted. It is noted that these optimization test cases will concern the detailed design and will therefore not affect the planform characteristics of the reference geometry. The second test case focuses on sonic boom reduction. We compare several inverse pro blems based on near field pressure, while maintaining constant lift. These optimizations differ from each other by geometric parameters (such as wing dihedral angle) and aerodynamic constraints (such as pitching moment and wave drag) involved. Analysis of the results of these test cases show the large benefit of the automated shape design process emphasizing on the short response time (several hours) fitting within the industrial context of shape design.

Multimodel design strategies applied to sonic boom reduction

The shape optimization of a supersonic aircraft need a composite model combining a 3D CFD high-fidelity model and a simplified boom propagation model. The management of this complexity is studied in an optimization loop, with exact discrete adjoints of 3D flow and mesh deformation system. The introduction of a mesh adaptation algorithm is also considered.

HOW TO TAKE INTO ACCOUNT DEFORMATION IN A CAD-BASED EULER OPTIMIZATION PROCESS? *

In order to reduce the costs involved in designing new airplanes with increased configuration complexity, a real necessity emerges to develop efficient optimization tools. The present paper discusses the implementation within the Euler optimization loop of a new approach to take into account surface displacements: the mesh deformation.