# Computing Stability Derivatives and Their Gradients for Aerodynamic Shape Optimization

 Title Computing Stability Derivatives and Their Gradients for Aerodynamic Shape Optimization Publication Type Journal Articles Year of Publication 2014 Authors Mader, CA, Martins, JRRA Journal AIAA Journal Volume 52 Start Page 2533 Issue 11 Pagination 2533-2546 Abstract Aerodynamic shape optimization of aircraft configurations often ignores stability considerations. To address this, a method for the computation of static, dynamic, and transient aircraft stability derivatives and their sensitivities for use in gradient-based optimization is introduced and evaluated. Computational fluid dynamics in the form of a three-dimensional, structured-grid, multi-block flow solver with both Euler and Reynolds-averaged Navier--Stokes equations is used. To compute the stability derivatives, a time-spectral formulation is used to compute an oscillating solution for the configuration of interest. From this oscillating solution, a series of linear regressions is performed to calculate the various stability derivatives. Because the solution is time-dependent, it contains the information required to compute the transient---or dot''---derivatives for the configuration. An adjoint method is used to compute the gradients of the stability derivatives of interest, enabling gradient-based stability-constrained aerodynamic shape optimization with respect to a large number of design variables. The computed stability derivatives are verified for an airfoil, and validated for the Stability and Control Configuration unmanned aerial vehicle. The stability-constrained optimization of a wing demonstrates the viability and usefulness of the method for aircraft design optimization. DOI 10.2514/1.J052922 Citation Key mader2014computing
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