Robust Aerodynamic Optimization through Conjugate Gradient Method with Taguchi's Theory

Robust Aerodynamic Optimization through Conjugate Gradient Method with Taguchi's Theory

He, D.

Dwight, R.P. (mentor)

Aerospace Engineering

Flight Performance and Propulsion

2015-11-10

The main objective of this thesis project is to establish an optimization framework that can carry out robust aerodynamic design tasks. The work is based on the single-point optimization module of the SU2 code, which contains the partial differential equation solver for flow evaluation and gradient calculation based on the adjoint method. The research work can be divided into two parts: the first one is the establishment of the optimization structure and the corresponding implementation. And the second part is the aerodynamic design examples. During creating the framework of the robust optimization process, the conjugate gradient (CG) algorithm is used to establish the main structure (outer loop). With the conjugate search directions provided by the CG method, line searches are implemented with the application of the strong Wolfe condition (inner loop). In order to carry out robust optimizations within the uncertain operating conditions, the format of the objective function should be defined properly. The Taguchi’s robust design theory is used to create the objective function that takes both the performance expectation and the variance into account simultaneously. As the CG algorithm cannot directly deal with constraints, they should be converted to the penalty terms in the objective function. To check the validity of the established robust optimization process, two examples are tested concerning the wave drag reduction of the NACA0012 airfoil under subsonic condition, with lift and thickness constraints. The first problem is to reduce the drag under the uncertain Mach number and angle of attack which obey certain kind of normal distributions separately. The continuous probabilities of the two uncertainties are firstly discretized into 9 operating conditions and the joint probability is calculated. After that optimizations are carried out under these sampled conditions. The results show that the process can indeed provide robust drag reduction. Compared to the results of the two single-point optimizations under different conditions, the drag value is effectively reduced especially under higher Mach numbers and larger angles of attack. The change of the weight factor distribution for the drag expectation and the variance has noticeable influence on the drag value under the most critical condition. The second problem is to reduce the drag within a certain range of the Mach number while keep a constant lift. The Mach number is the only uncertainty source and it is discretized at 3 sampled points. The results show that the shock wave can be eliminated under all 3 conditions. As a result, both the drag expectation and the variance are significantly reduced. The robust optimizations with different weight factor distribution have similar results except for the one that only focuses on the drag variance reduction. The latter optimization provides a result with nearly no drag variance at the cost of higher drag values throughout the whole tested domain. And the drag increases more quickly than other robust optimization results with the increment of Mach number. Actually, for this problem, a single-point optimization under the highest Mach number could also provide robust drag reduction performance. The test examples preliminarily proved the validity of the established robust optimization process. However, it is recommended that the effectiveness should be further tested with more complicated problems in the future.

robust
conjugate gradient
Taguchi's theory

http://resolver.tudelft.nl/uuid:6c384e64-9fad-4289-93e8-5a3a863cfed8

Student theses

master thesis

(c) 2015 He, D.