Geometric Uncertainty Analysis of Aerodynamic Shapes Using Multifidelity Monte Carlo Estimation

Triston Andrew Kosloske, Purdue University

Abstract

Uncertainty analysis is of great use both for calculating outputs that are more akin to real flight, and for optimization to more robust shapes. However, implementation of uncertainty has been a longstanding challenge in the field of aerodynamics due to the computational cost of simulations. Geometric uncertainty in particular is often left unexplored in favor of uncertainties in freestream parameters, turbulence models, or computational error. Therefore, this work proposes a method of geometric uncertainty analysis for aerodynamic shapes that mitigates the barriers to its feasible computation. The process takes a two- or three-dimensional shape and utilizes a combination of multifidelity meshes and Gaussian process regression (GPR) surrogates in a multifidelity Monte Carlo (MFMC) algorithm. Multifidelity meshes allow for finer sampling with a given budget, making the surrogates more accurate. GPR surrogates are made practical to use by parameterizing major factors in geometric uncertainty with only four variables in 2-D and five in 3-D. In both cases, two parameters control the heights of steps that occur on the top and bottom of airfoils where leading and trailing edge devices are attached. Two more parameters control the height and length of waves that can occur in an ideally smooth shape during manufacturing. A fifth parameter controls the depth of span-wise skin buckling waves along a 3-D wing. Parameters are defined to be uniformly distributed with a maximum size of 0.4 mm and 0.15 mm for steps and waves to remain within common manufacturing tolerances. The analysis chain is demonstrated with two test cases. The first, the RAE2822 airfoil, uses transonic freestream parameters set by the ADODG Benchmark Case 2. The results show a mean drag of nearly 10 counts above the deterministic case with fixed lift, and a 2 count increase for a fixed angle of attack version of the case. Each case also has small variations in lift and angle of attack of about 0.5 counts and 0.08◦ , respectively. Variances for each of the three tracked outputs show that more variability is possible, and even likely. The ONERA M6 transonic wing, popular due to the extensive experimental data available for computational validation, is the second test case. Variation is found to be less substantial here, with a mean drag increase of 0.5 counts, and a mean lift increase of 0.1 counts. Furthermore, the MFMC algorithm enables accurate results with only a few hours of wall time in addition to GPR training.

Degree

M.Sc.

Advisors

Crossley, Purdue University.

Subject Area

Aerospace engineering|Artificial intelligence|Design|Fluid mechanics|Industrial engineering|Mechanics

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