Session: 39-01 Adjoint-based and adjoint-enhanced design optimization methods and applications

Paper Number: 80806

80806 - Application of Adjoint-Enhanced First Order Second Moment Method for Robust Design Optimization of a High Pressure Compressor Rotor 

The occurrence of geometric and operational uncertainties due to manufacturing and environmental factors are inevitable and should be considered already during the design process to obtain configurations that are less sensitive to these effects. Once the uncertainty of the input space is quantified and described by a stochastic model it can be propagated through the system under investigation. This gives rise to an additional layer of complexity, as the system response is no longer a deterministic but a random variable. Various techniques exist to perform the uncertainty propagation, such as Monte Carlo simulations, response surface methods, stochastic collocation and differential analysis. The result obtained by these techniques is the probabilistic description of the objective function of the robust design optimization (RDO) problem. However, each method has its particular difficulties when dealing with a high-dimensional correlated non-Gaussian input space and a very expensive blackbox simulation in an industrial context, since an accurate propagation of the uncertainty is required in each iteration step of the RDO. The differential analysis based on first-order derivatives is very efficient, but may suffer from low accuracy if the system behaviour exhibits nonlinearities. Higher-order derivatives on the other hand are more accurate, but require many function evaluations. However, the first-order differential analysis is very appealing in an industrial context, as its efficiency essentially depends only on the method to calculate the first-order partial derivatives. This gives rise to the idea to couple this approach with the adjoint method to obtain satisfactory approximations of the statistical moments at a very low cost. Furthermore, the approach allows for a seamless integration into a gradient-based optimization framework, while being independent of the dimensionality of the design space. The simplicity and efficiency of the proposed approach are key features for an application within an industrial workflow.

This paper applies the computationally advantageous combination of differential analysis techniques and the adjoint method in the context of uncertainty quantification to the gradient-based robust design optimization of aerofoils. First, the accuracy and feasibility of the method is evaluated using analytical test functions. Finally, the application of the method to a high pressure compressor rotor aerofoil under geometric uncertainty showed promising results, yielding a substantially more robust configuration after 5 iterations with a total of only 95 flow and adjoint solver evaluations.

Presenting Author: Max Dittmann Technische Universität Dresden

Presenting Author Biography: Max Dittmann studied aerospace engineering at the Technische Universität Dresden from 2014 to 2021, specializing in turbomachinery and flight propulsion. After an initial internship at Rolls-Royce Deutschland Ltd. & Co. KG in Flight Test Management, he first came into contact with the topic of probabilistics as part of his student research project "Statistical Analysis of Geometric Variability of Ex-Service HPC Blades and the Influence on their Aerodynamic Properties". As a result, he had the opportunity to complete another internship at Rolls-Royce Deutschland Ltd. & Co. KG in the Compressor Aerodynamics Group and subsequently to develop his diploma thesis on the topic "Robust Aerodynamic Optimization of a Compressor Blade using the Adjoint Method".

Authors:

Max Dittmann Technische Universität Dresden
Robin Schmidt Rolls-Royce Deutschland Ltd. & Co. KG
Marcus Meyer Rolls-Royce Deutschland Ltd. & Co. KG