Uncertainty Quantification and Management in the Context of Loads and Aerodynamic Design

Kurzfassung

In this talk we present a robust design optimization framework for aircraft design and show results for robust aerodynamic design. As a first step, we focus on quantifying uncertainties in the drag coefficient and formulate and investigate two measures of robustness, a worst-case scenario and a formulation based on expectation measure and mean-risk. To reduce the computational effort required to compute the output uncertainties we make use of a Sobol sequence-based quasi Monte Carlo method (QMC) and a gradient-enhanced Kriging (GEK) surrogate model. A small number of samples is computed with the full-order CFD code TAU and its adjoint version to construct the GEK model. The statistics are computed by interrogating the surrogate model with a QMC method using a sufficiently large number of samples. In terms of the input uncertainties, we are interested both in operational and geometrical uncertainties. Our strategy to model the inherently large number of geometrical uncertainties is by using a truncated Karhunen-Loève expansion (tKLE), which introduces some elements of model uncertainty. The test case used here to demonstrate the framework is a transonic RAE2822 airfoil. We confirm that the robust design measures are accurately evaluated to within one drag count and that adaptive sampling techniques are required especially in the worst case scenario. Then, a Subplex algorithm is used to optimize the robustness measure. The robustly optimized airfoil features the best stochastic values in terms of the robustness measure compared with the initial airfoil and a deterministically optimized airfoil. Current work is aiming to extend our framework for uncertainty quantification and management (UQ&M) based on high-fidelity CFD to the loads process, especially at extremes of the flight envelope. There are two issues arising that we are concerned with: One is about efficient nonintrusive UQ&M methods for high-dimensional output uncertainties, in particular reduced order models (ROMs) for loads are sought after. Also, methods for identifying dominant (input) uncertainties and dimension reduction, in particular management and reduction of the critical design load cases are required. The other one is model uncertainty. Model uncertainties arising as part the CFD computations, which are reducible, can have a larger influence on the accuracy of the output uncertainties than the realistic (irreducible) ones, for instance, at high Mach numbers and high angles of attack. Efficient non-intrusive UQ&M methods considering the above two issues are then to be incorporated in the context of multidisciplinary design optimization (MDO) in the future.