<p>Uncertainty analysis is of great use both for calculating outputs that are more akin to real<br>
flight, and for optimization to more robust shapes. However, implementation of uncertainty<br>
has been a longstanding challenge in the field of aerodynamics due to the computational cost<br>
of simulations. Geometric uncertainty in particular is often left unexplored in favor of uncer-<br>
tainties in freestream parameters, turbulence models, or computational error. Therefore, this<br>
work proposes a method of geometric uncertainty analysis for aerodynamic shapes that miti-<br>
gates the barriers to its feasible computation. The process takes a two- or three-dimensional<br>
shape and utilizes a combination of multifidelity meshes and Gaussian process regression<br>
(GPR) surrogates in a multifidelity Monte Carlo (MFMC) algorithm. Multifidelity meshes<br>
allow for finer sampling with a given budget, making the surrogates more accurate. GPR<br>
surrogates are made practical to use by parameterizing major factors in geometric uncer-<br>
tainty with only four variables in 2-D and five in 3-D. In both cases, two parameters control<br>
the heights of steps that occur on the top and bottom of airfoils where leading and trailing<br>
edge devices are attached. Two more parameters control the height and length of waves<br>
that can occur in an ideally smooth shape during manufacturing. A fifth parameter controls<br>
the depth of span-wise skin buckling waves along a 3-D wing. Parameters are defined to<br>
be uniformly distributed with a maximum size of 0.4 mm and 0.15 mm for steps and waves<br>
to remain within common manufacturing tolerances. The analysis chain is demonstrated<br>
with two test cases. The first, the RAE2822 airfoil, uses transonic freestream parameters<br>
set by the ADODG Benchmark Case 2. The results show a mean drag of nearly 10 counts<br>
above the deterministic case with fixed lift, and a 2 count increase for a fixed angle of attack<br>
version of the case. Each case also has small variations in lift and angle of attack of about<br>
0.5 counts and 0.08◦, respectively. Variances for each of the three tracked outputs show that<br>
more variability is possible, and even likely. The ONERA M6 transonic wing, popular due<br>
to the extensive experimental data available for computational validation, is the second test<br>
case. Variation is found to be less substantial here, with a mean drag increase of 0.5 counts,<br>
and a mean lift increase of 0.1 counts. Furthermore, the MFMC algorithm enables accurate<br>
results with only a few hours of wall time in addition to GPR training. </p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/22693450 |
| Date | 27 April 2023 |
| Creators | Triston Andrew Kosloske (15353533) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Geometric_Uncertainty_Analysis_of_Aerodynamic_Shapes_Using_Multifidelity_Monte_Carlo_Estimation/22693450 |
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