Despite considerable research on aerodynamic shape optimization, there is no standard benchmark problem allowing researchers to compare results. This work addresses this issue by solving a series of aerodynamic shape optimization problems based on the Common Research Model wing benchmark case defined by the Aerodynamic Design Optimization Discussion Group. The aerodynamic model solves the Reynolds-averaged Navier–Stokes equations with a Spalart–Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with an adjoint method that computes the required derivatives. The drag coefficient is minimized subject to lift, pitching moment, and geometric constraints. A multilevel technique is used to reduce the computational cost of the optimization. A single-point optimization is solved with 720 shape variables using a 28.8-million-cell mesh, reducing the drag by 8.5%. A more realistic design is achieved through a multipoint optimization. Multiple local minima are found when starting...

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Aerodynamic Shape Optimization Investigations of the Common Research Model Wing Benchmark

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and state a central limit theorem for each. We show that one of these estimators has an optimal asymptotic variance. We also generalize our results to the case where the true output is not observable, and is replaced by a noisy version.

Asymptotic normality and efficiency of two Sobol index estimators

The invention relates to a convertible aircraft comprising a fuselage (F), a pair of wings (A1, A2) arranged one on each side of the fuselage (F), at least one ducted rotor (1) installed in a horizontal position at one of the ends of the fuselage (F) and a first and a second nacelle (N1, N2) arranged respectively at the tip of each wing (A1, A2) and each comprising a ducted rotor (R1, R2) and being pivotably mounted relative to the fuselage (F). The nacelles comprise at least a first and a second movable flap (V1, V2), which flaps are arranged respectively at the outlet of the ducted rotor (R1) of the first nacelle (N1) and at the outlet of the ducted rotor (R2) of the second nacelle (N2). The aircraft according to the invention thus represents an advantageous solution to any applications involving helicopters and airplanes, particularly emergency preparedness missions, rescue missions, and public or private transport.

Convertible aircraft provided with two ducted rotors at the wing tips and with a horizontal fan in the fuselage

Probabilistic and non-probabilistic methods have been proposed to deal with design problems under uncertainties. Reliability-based design and robust design are probabilistic strategies traditionall...

Reliability-based robust multi-objective optimization applied to engineering system design

An airplane, including a fuselage having an elongate shape along a longitudinal axis of the airplane, and at least one wing attached to the fuselage between front and back ends of the fuselage and a substantially cylindrical central portion and a rear scaleable portion on which a vertical tail assembly and a rear propulsion assembly are attached. Between a section for connecting the rear portion to the central portion of the fuselage and the back end: the maximum width of each fuselage section is constant or increases towards the rear up to a maximum fuselage width L; the height of each fuselage section decreases towards the rear, such that the back end of the fuselage forms a thin trailing edge substantially horizontal in the indicating line of the airplane and substantially rectilinear; a reactor for the propulsion assembly is provided in a so-called semi-buried configuration in the fuselage.

Airplane with a tailcoat tail assembly and rear engine

An aircraft having an elongated fuselage and a lifting surface fastened to the fuselage. The aircraft has a device for controlling the torque around the yaw axis GZ of the aircraft in which aerodynamic forms that have devices to generate aerodynamic drag are fastened to each end of the lifting surface at non-zero distances from each side of a vertical plane of symmetry XZ of the aircraft. The drag-generating devices are commanded to produce a different aerodynamic drag at each of the two ends to generate a yaw torque on the aircraft. The aerodynamic forms, for example, have winglets improving the aerodynamics of the lifting surface, and provided with aerodynamic drag generators.

Aircraft with yaw control by differential drag

An aircraft displaying a fuselage, a wing attached to the fuselage in an upper part and in a middle part along the length of the fuselage, a set of airfoils situated behind the wing and propulsion engines mounted on the wing. The wing, the set of airfoils and the propulsion engines are solidly fastened to an air propulsion unit that is affixed to the fuselage by a connection system permitting the controlled modification in flight of the position of the air propulsion unit relative to the fuselage in the three directions X, Y and Z of the reference aircraft and in rotation around the three directions X, Y and Z. The control of the relative movements of the air propulsion unit and fuselage permits an improved behavior in flight of the airplane and has advantages in the fabrication and operation of the plane.

Aircraft with its fuselage suspended under the wing

The aircraft has a fuselage, a wing integral with the fuselage in a middle section in a longitudinal direction of the fuselage, and a tail assembly integral with the fuselage. The wing has a rigid central chamber at the fuselage determined in front by a front spar, in the rear by a rear spar, and laterally by root ribs of the wing. The wing is mounted to be movable longitudinally in translation relative to the fuselage between an extreme forward position Xav and an extreme rearward position Xar so that the center of gravity of the aircraft can be displaced longitudinally to be positioned precisely at any time relative to the point of application of the resultant of the aerodynamic lift forces. The wing is mounted to be movable relative to the fuselage through the intermediary of at least two parallel beams, parallel to the longitudinal axis of the fuselage and integral with the fuselage at the rear/forward bulkhead of the fuselage located on each side of the rigid central chamber.

Aircraft with a wing movable along the longitudinal axis of the fuselage

Aero-structural approach coupled with direct operative cost optimization for new aircraft concept in preliminary design

Swiveling engines 5 a , 5 b attached to the fuselage 2 by struts 4 a , 4 b, for example to the rear part of the fuselage are used to control the pitch and yaw movements of an aircraft 1. The swivel axes 41 a , 41 b of the engines are oriented to form a V so that swiveling one engine creates a variation of the vertical and lateral components of the engine thrust. Controlled swiveling of the two swiveling engines makes it possible to generate a component of the resultant thrust in a vertical plane that can be controlled in direction and intensity to generate pitch and yaw torques. The swiveling engines also include pods provided with jet deflection flaps for the engine considered, and the struts are profiled and provided with a trailing edge control surface using ruddervator architecture.

Thierry Druot

Papers

Aircraft with yaw control by differential drag

Aircraft with its fuselage suspended under the wing

Aircraft with a wing movable along the longitudinal axis of the fuselage

Aero-structural approach coupled with direct operative cost optimization for new aircraft concept in preliminary design

Airplane with pitch and yaw command by propulsion system