Aleatory Uncertainties in Aerodynamic Design

Aleatory uncertainties arises because of natural, unpredictable variations of the boundary conditions. Additional knowledge cannot reduce aleatory uncertainties, but it may be useful in getting a better characterization of the variability. In order to formulate the robust design optimization problem, we analyze the boundary condi­tions and input parameters identifying the uncertainties which cannot be avoided at all before constructing an aircraft [39].

In the following, we distinguish two types of uncertainties: uncertainties with respect to the flight conditions and geometrical uncertainties.

The main characteristics of the macroscopic flight conditions are angle of incid­ence, the velocity (Mach number) of the plane, the density of air and the Reynolds number. The uncertainty of these parameters mostly results from atmospheric turbu­lences which can occur during a flight. Gusts causes changes of the velocity in the range of ±10™. Measurements of the changes in the angle of attack and the density are not published so far, so they are assumed to be less than 10% of the setpoint. The variations of the Reynolds number will only effect the simulation, if the Reynolds number is in the range of 12 – 15 • 106, that means this uncertain parameter has not to be taken into account in our testcases.

On the other hand, we consider the shape itself as an uncertainty source. The real shape may vary from the planned shape due to manufacturing tolerances, temporary factors like icing e. g. or fatigue of material. Since there are so many factors hav­ing effects on the shape, this uncertainty has to be considered in the optimization problem in order to produce a design which is robust to small perturbations of the shape itself. In the literature, there can be found only a few papers on this topic investigating the influence of variations of the profile (cf. [17], [32]).

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