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Modelling of Uncertainties in the Airfoil Geometry
We model uncertainties in the geometry of RAE-2822 airfoil via random boundary perturbations:
д&£(ю) = {x + £k(x, w)n(x) : x Є dG}, (5)
where n(x) is the normal vector in a point x, k(x, со) a random field, G the computational geometry and є 1. We assume that the covariance function is of Gaussian type
COk(Ki, K2) = cr2-exp(-d2), d = yjxi – x2|2//2+|Zi-Z2|2//22,
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Table 1 Statistics obtained for uncertainties in the airfoil geometry. We used the Gaussian covariance function, PCE of order P = 1 with M = 3 random variables and the sparse Gauss – Hermite grid with nq = 25 points.
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where к1 = k((x1,0,zi), ю), k2 = ((x2,0,z2),ffl) are two random variables in points (xi,0,z1) and (x2,0,z2). For numerical simulations we take the covariance lengths l1 = | maxi(xi) – min;(xj)|/10and l2 = | max^(zi) – mini(zi)|/10, standard deviation а = 10-3, m = 3 the number of KLE terms (see Eq. 6), the stochastic dimension M = 3 and the number of sparse Gauss-Hermite points (in 3D) for computing PCE coefficients in (Eq. 8) nq = 25. In [13] one can see 21 random realisations of RAE – 2822 airfoil.
Table 1 demonstrates the surprisingly small uncertainties (the last column) in the lift and in the drag — 0.58% and 0.65% correspondingly. A possible explanation can be small uncertain perturbations in the airfoil geometry.
