Variational approach to the problem of optimal propeller design

The aim of this paper is to evaluate the theoretical efficiency of propellers with non-planar blade, optimally shaped. It is well known that non-planar wing configurations can significantly re- duce the induced drag [5], hence this can be of interest also for propeller design. Furthermore the adoption of a curvilinear blade system can be justi- fied not only for an efficiency improvement, but also for reason that concerns the structure and the noise reduction [12], [1]. A solution to the optimum rotor problem, in the context of propeller vortex theory, was given by Goldstein [7]. He considered straight blade pro- pellers and expressed the optimum circulation function via a trigonometrical series of Bessel functions. However, such were the difficulties of computa- tion, even after the solution was found, that Theodorsen resorted to the use of rheoelectrical analogy to evaluate the circulation function, unfortunately without great success [14]. Accurate tabulated values of the Goldstein func- tion covering a wide range of parameters became available with an extensive mathematical effort by Tibery and Wrench [15]. Although this work is based on a completely different approach, Goldstein results are fundamental to validate the procedure for the case of straight blade. In this dissertation, a variational formulation1 of the optimum rotor prob- lem is proposed in order to support the optimization of more complex blade configurations, such as the non-planar ones. The first step of the formulation consists into finding a class of functions (representing the circulation distri- bution along the blade) for which the thrust and the aerodynamic resisting moment functionals are well defined. Then, in this class, the functional to be minimized is proved to be strictly convex; taking into account this result, it is proved that the global minimum exists and is unique. Some of the configurations analysed are: - Classical straight blade - Parabolic blade - Elliptical blade - Superelliptic blade Configurations with the same value of maximum dimensions and perfor- mances required are compared in the case of single and multiple blade pro- pellers. This formulation can be seen as the extension of the one proposed in [11]. The main difficulty in the functionals’ evaluation, is the fact that an an- alytical expression of the velocity induced by a semi-infinite helical vortex filament do not exist2. For this reason the Euler-Lagrange equation asso- ciated with the variational problem is not obtained and a direct method is used. In particular the Ritz Method is adopted. Another task to deal with, is the evaluation of the singular integral rep- resenting the induced velocity. A two-dimensional quadrature rule, based on Legendre polynomials, is used [9]. This procedure is implemented in a MATLAB program that, given the parametric expression of the curve representing the blade, allows the eval- uation of the momentum in the required condition and plots the optimal circulation along the curve

Aeroelastic Design of the oLAF Reference Aircraft Configuration

One of the main aims of the EU Flightpath 2050 is to significantly reducet he fuel consumption of upcoming designs for transport aircraft. To achieve this challenging goal, new technologies have to be investigated. In this context, the development of the 'optimally load adaptive aircraft' (oLAF) for a conventional design is one of the main goals of the DLR project oLAF. Since the lift-to-drag ration, the structural mass and the thrust specific fuel consumption are the main drivers of the aircraft's fuel consumption, an improvement in all three topics seems to be a promising approach to fulfill the intended aims of the European Union. That's why the design of the new oLAF configuration is equipped with a next generation three shaft geared turbofan engine with an ultra-high bypass-ration and an optimized aerodynamic performance combined with aggressive loadalleviation (LA) techniques to lighten the load-carrying structure of the aircraft significantly compared to a conventional state-of-the-art aircraft. Multiple design cycles with different degree of fidelity and LA approaches are planned to be performed within oLAF. At the current state of the project, three different designs are available. On the one hand, there is the more basic configuration of the overall aircraft design (OAD) further called 'oLAF_SLv1'. On the other hand, there are configurations with more mature aerodynamic characteristics further called the oLAF_ASv0 configuration as start design for a multidisciplinary-design-optimization (MDO) process and the 'oLAF_ASv1' as the optimized result of the MDO. All configurations have been analyzed and evaluated using the aeroelastic structural design tool cpacs-MONA. The optimized 'oLAF_ASv1' configuration has furthermore been checked on aeroelastic stability. Conclusively, the stiffness of the structural pylon model has been adapted to shift a hump-mode of the new generation engine to higher airspeeds, so that the instability occurs outside of the flight envelope

Streamlining Cross-Organizational Aircraft Development: Results from the AGILE Project

The research and innovation AGILE project developed the next generation of aircraft Multidisciplinary Design and Optimization processes, which target significant reductions in aircraft development costs and time to market, leading to more cost-effective and greener aircraft solutions. The high level objective is the reduction of the lead time of 40% with respect to the current state-of-the-art. 19 industry, research and academia partners from Europe, Canada and Russia developed solutions to cope with the challenges of collaborative design and optimization of complex products. In order to accelerate the deployment of large-scale, collaborative multidisciplinary design and optimization (MDO), a novel methodology, the so-called AGILE Paradigm, has been developed. Furthermore, the AGILE project has developed and released a set of open technologies enabling the implementation of the AGILE Paradigm approach. The collection of all the technologies constitutes AGILE Framework, which has been deployed for the design and the optimization of multiple aircraft configurations. This paper focuses on the application of the AGILE Paradigm on seven novel aircraft configurations, proving the achievement of the project’s objectives

Multifidelity Sensitivity Study of Subsonic Wing Flutter for Hybrid Approaches in Aircraft Multidisciplinary Design and Optimisation

A comparative sensitivity study for the flutter instability of aircraft wings in subsonic flow is presented, using analytical models and numerical tools with different multidisciplinary approaches. The analyses build on previous elegant works and encompass parametric variations of aero-structural properties, quantifying their effect on the aeroelastic stability boundary. Differences in the multifidelity results are critically assessed from both theoretical and computational perspectives, in view of possible practical applications within airplane preliminary design and optimisation. A robust hybrid strategy is then recommended, wherein the flutter boundary is obtained using a higher-fidelity approach while the flutter sensitivity is computed adopting a lower-fidelity approach

Towards surrogate-based aero-structural design optimization of an Unmanned Aerial Vehicle

In order to be able to assess also unconventional aircraft configurations, aircraft designers need to take into account physics-based analyses even during the early design stages. This highly multidisciplinary task requires the contributions and expertise of several different disciplinary specialists. This also applies to unmanned aerial vehicles, where improvements in performance yield a tactical advantage. In this paper, a partitioned design optimization process is presented, for the OptiMALE UAV configuration, originally introduced during the AeroStruct project and was further investigated during the AGILE project. The optimization will couple panel method aerodynamics and structural sizing to find the design with the maximum range. The process is set up in a modular fashion, using common data models as interfaces. The initial design is provided in the Common Parametric Aircraft Configuration Schema (CPACS), and serves as common input for the disciplinary model generators. The multidisciplinary analysis (MDA) process itself is implemented in Python as a Gauss-Seidel fixed point iteration, using comprehensive interfaces to the disciplinary analysis tools. The structural analysis and sizing is performed on a beam and shell model. For the aerodynamic analysis, a 3D potential method for subsonic flow applying the Green’s function method to the small perturbation potential flow equation after Morino has been implemented. The loads resulting from the converged MDA are used as inputs for a sizing optimization of the wing structural components using Lagrange. Finally, a mission simulation is performed using the updated massed to yield the range of the design. The optimization will be implemented in two steps. First, a design of experiments is performed on the wing design variables. Kriging is used to construct a metamodel from the DOE results, which provides gradients for a subsequent gradient-based optimization

Variational Analysis and Euler Equations of the Optimum Propeller Problem

The problem of the optimum propeller with straight blades was first solved by Goldstein; in this paper, a variational formulation is proposed in order to extend the solution to non-planar blades. First, we find a class of functions (the circulation along the blade axis) for which the thrust and the aerodynamic drag moment are well defined. In this class, the objective functional is proved to be strictly convex and then the global minimum exists and is unique. Then we determine the Euler equation in the case of a general blade and show that the numerical results are consistent with the Goldstein’s solution. Finally, some numerical results with the Ritz method are presented for optimum propeller blade