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Aerodynamic Shape Optimization in Aeronautics: A Fast and Effective Multi-Objective Approach

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Abstract

The present work aims at introducing a fast and effective CFD-based automatic loop for optimization of rotorcraft components. The automatic loop presented here was strictly designed around an innovative Multi Objective Evolutionary Algorithm, developed at University of Padua, namely the GeDEA-II. Recent papers showed its excellent performance when tested on state-of-the-art problems. In order to test the performance of this algorithm two test cases are presented, each having its peculiar characteristics. The first problem regards the single-objective, multi-constraints aerodynamic optimization of the ERICA tilt-rotor cockpit region. The second one is a multi-point multi-constraint optimization of the left intake of the AgustaWestland AW101 helicopter. Results demonstrate the effectiveness of this automatic optimization loop in tackling real-word engineering problems.

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Notes

  1. Please visit the web site http://www.cleansky.eu for more elucidations.

  2. A computer cluster is a group of linked computers, working together closely so that in many respects they form a single computer. The components of a cluster are commonly, but not always, connected to each other through fast local area networks. Clusters are usually deployed to improve performance and/or availability over that of a single computer, while typically being much more cost-effective than single computers of comparable speed or availability.

  3. Vilfredo Pareto (1848–1923): Italian engineer, economist and sociologist.

  4. Let us consider three vectors in \({\mathbb {R}}^3\) design space, namely a = (1,0,0), b = (0,1,0), and c = (0,0,1). There can be found three couples of linearly independent vectors, that is [a,b], [a,c] and [b,c] but only a triplet of mutually and simultaneously independent vectors, that is the triplet [a,b,c]. This simple demonstration remains valid when extended to the \({\mathbb {R}}^n\) space.

  5. Individual mutation probability (probability that a certain individual undergoes mutation); individual recombination probability (probability that a certain pair of individuals undergoes recombination); variable mutation probability (probability that a certain variable in a given individual is mutated); variable swap probability (probability that a certain pair of variables is swapped during recombination); variable recombination probability (probability that the SBX recombination operator is used for a given pair of variables; this decision is independent from variable swap probability); \(\eta _{mutation}\) (distribution index for mutation operator); \(\eta _{recombination }\)(distribution index for recombination operator).

  6. This software is available for public use at PISA website http://www.tik.ee.ethz.ch/pisa/.

  7. The Hypervolume is a Pareto compliant indicator as stated in [22].

  8. The contribution of the outliers is negligible from a statistical point of view.

  9. Sponsons are projections from the sides of an aircraft or helicopter, for protection, stability, or the mounting of equipment such as armaments or lifeboats, etc. They are often used in larger helicopters where the internal space of the sponson can be used for fuel or to house landing gear without reducing cargo or passenger space in the fuselage.

  10. The aspect ratio is defined as the ratio of the prism base length to the prism layer height.

  11. Tcl (Tool Command Language), commonly pronounced “tickle”, is a scripting language like Perl, JavaScript, Born, and Korn. It can be used coupled with HyperMesh, by calling HyperMesh commands directly from a Tcl script.

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Acknowledgments

The present research has been funded in the framework of the Joint Technology Initiatives: Clean Sky under grant agreement number 270609 “CODE-Tilt, Contribution to design optimization of tiltrotor components for drag reduction.” Authors acknowledge Antonio Saporiti and the Aerodynamic Office of AgustaWestland for the invaluable support they have given to this work.

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Authors and Affiliations

  1. HIT09 S.r.l., Galleria Storione 8, 35131 , Padova, Italy

    Claudio Comis Da Ronco & Rita Ponza

  2. Department of Industrial Engineering, University of Padova, Via Venezia, 1, 35131 , Padova, Italy

    Ernesto Benini

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  1. Claudio Comis Da Ronco
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  3. Ernesto Benini
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Correspondence to Claudio Comis Da Ronco.

Appendix A: Methodology for Assessing the Compliance with the Visibility Requirements

Appendix A: Methodology for Assessing the Compliance with the Visibility Requirements

Visibility requirements are to be satisfied during certification campaign. For this reason, it is vital to establish if a particular aircraft configuration meets these requirements. In order to establish whether a particular parameterized configuration provides adequate external vision from within the aircrew station or not, a rectilinear graph showing the total vision plot must be built up. The vision requirements set forth in this paragraph are applicable to the ERICA configuration introduced in the results section present within the Sect. 7.7.1 and are given relative to the longitudinal fuselage reference line. Total vision envelope of the baseline ERICA configuration is depicted in Fig. 123 and compared to the envelope suggested in [3] for a transport side-by-side pilot aircraft. As apparent, while the Down Angles of the baseline ERICA cockpit are nearly coincident with the values given by certification rules, the Up Angles envelope largely overcomes the certification ones.

Figure 123 shows the total vision envelope (\(\pm 110^{\circ }\) in azimuth and \(\pm 90^{\circ }\) in elevation), referred to the baseline configuration of the ERICA.

Fig. 123
figure 123

Total vision envelope for ERICA nose baseline configuration

Full size image

The plots shall reflect the unobstructed vision area, which is defined as that area of transparent material through which vision is unobstructed by structure, edge bonding material, or any other material, which prohibits clear vision. Convention for azimuth angles is shown in Fig. 124. The reference plane, from which the vision angles are specified, shall be the pilot’s horizontal vision plane (or line) with respect to the specific aircraft longitudinal fuselage reference line (see Fig. 124). The zero reference in azimuth shall be straight ahead of the design eye position.

Fig. 124
figure 124

Assumed azimuth angles convention

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A subroutine written in Tcl Footnote 11 script language was created in order to find, for each azimuth coordinate, the intersection between the iso-azimuth lines and the windscreen edges. Based on these values, the Up and Down angles were then calculated via a Matlab script. Definition of Up angles and Down angles is clearly visible in Fig. 125.

Fig. 125
figure 125

Assumed elevation angles convention

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Up angle is defined as the angle ranging from the horizontal vision plane to the intersection with the upper windscreen edge (at that particular azimuth angle). Down angle is defined as the angle ranging from the horizontal vision plane to the intersection with the lower windscreen edge (once again, at that particular azimuth angle).

It follows that for each azimuth angle, two elevation angles can be defined, that is the Up and the Down angles. The envelope of these angles constitute the total vision plot of the investigated aircraft configuration, and it has been already presented in Fig. 123.

The zero reference in azimuth is coincident with the pilot eye (as suggested in [3]). As far as the ERICA nose opti-mization problem is concerned, it is located at x = 2,976 mm, y = 525 mm and z = 1,358 mm.

During the optimization run, the calculated Up and Down angles related to the deformed configurations were compared to those reported in Table 33.

Table 33 Up and down angles as a function of azimuth angles for the ERICA baseline configuration
Full size table

In the case the calculated angles were lower or equal than the baseline ones, the parameterized configuration was automatically replaced by a new one. This replacement was performed until the visibility requirements were met. Hard constraints were set for every azimuth angles, exception given for the low azimuth angles, for which only soft constraints were fixed. This choice was made in order not to penalize excessively the design space exploration.

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Comis Da Ronco, C., Ponza, R. & Benini, E. Aerodynamic Shape Optimization in Aeronautics: A Fast and Effective Multi-Objective Approach. Arch Computat Methods Eng 21, 189–271 (2014). https://doi.org/10.1007/s11831-014-9123-y

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