Performance evaluation and improvements of CFD-based aerodynamic design optimization
Eyi, Sinan
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Permalink
https://hdl.handle.net/2142/21001
Description
Title
Performance evaluation and improvements of CFD-based aerodynamic design optimization
Author(s)
Eyi, Sinan
Issue Date
1995
Doctoral Committee Chair(s)
Lee, Ki D.
Department of Study
Aerospace Engineering
Discipline
Aerospace Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Aerospace
Engineering, Mechanical
Language
eng
Abstract
A study was performed to evaluate the effects of different flow solvers, optimization methods, and design variables on aerodynamic design optimization. The Euler, Euler/boundary-layer, and compressible and incompressible Navier-Stokes equations were used for the flow analyses. Inverse design optimization used a least-square method to minimize pressure discrepancies between a target and the designed airfoils, and designs were performed for transonic airfoils and turbomachinery blades. Constrained design optimization, based on a modified feasible direction methods was used to improve the aerodynamic performance of single and multi-element airfoils with specified design constraints.
The ease of implementation makes the finite-difference sensitivity derivative evaluation popular in many aerodynamic design optimization applications. The accuracy of finite-difference sensitivity derivatives was examined, and two methods were introduced to improve the accuracy. The first method is a modified finite-difference approach, which improves the accuracy of computed derivatives over the traditional approaches. The second method finds the optimum step size by using an asymptotic error formula to reduce errors in the sensitivity derivative evaluations. These two new methods were implemented for inverse and constrained design optimizations, exhibiting consistently better performances in both the design quality and the convergence of the design cycle, compared to the traditional finite-difference method.
The direct differentiation method to calculate the sensitivity derivatives was also developed. Sensitivity equations were obtained by differentiating the Navier-Stokes equations with respect to design variables. The material derivative concept of continuum mechanics was implemented to obtain shape sensitivities. The sensitivity equations share the same Jacobian matrices with the Navier-Stokes equations and, therefore, the sensitivity analysis uses the same iterative integration scheme as the flow analysis. The analytical sensitivity method consistently gives accurate sensitivity derivatives, compared to the finite-difference sensitivity method. In order to evaluate the effects of the accuracy of sensitivity derivatives on the performance of design process, several inverse designs were performed using both analytical and finite-difference sensitivity derivatives. The results show that the design cycle converges faster, and hence costs less, when analytical sensitivity derivatives are used as opposed to finite-difference sensitivities.
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