Total pressure losses minimization in turbomachinery cascades using the exact Hessian

Zervogiannis, T; Papadimitriou, DI; Giannakoglou, KC

dc.contributor.author	Zervogiannis, T	en
dc.contributor.author	Papadimitriou, DI	en
dc.contributor.author	Giannakoglou, KC	en
dc.date.accessioned	2014-03-01T01:34:48Z
dc.date.available	2014-03-01T01:34:48Z
dc.date.issued	2010	en
dc.identifier.issn	0045-7825	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20862
dc.subject	Discrete adjoint	en
dc.subject	Hessian matrix	en
dc.subject	Shape optimization	en
dc.subject	Total pressure losses minimization	en
dc.subject	Turbomachinery	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	Adjoint methods	en
dc.subject.other	Adjoints	en
dc.subject.other	Automatic differentiations	en
dc.subject.other	Blade thickness	en
dc.subject.other	Constrained optimization problems	en
dc.subject.other	Design variables	en
dc.subject.other	Direct differentiation	en
dc.subject.other	First cycle	en
dc.subject.other	First-order sensitivity	en
dc.subject.other	Flow equations	en
dc.subject.other	Flow turning	en
dc.subject.other	Hessian matrices	en
dc.subject.other	Lagrange methods	en
dc.subject.other	Memory requirements	en
dc.subject.other	Objective functions	en
dc.subject.other	Quasi-Newton methods	en
dc.subject.other	Second-order sensitivity	en
dc.subject.other	Total pressure	en
dc.subject.other	Total-pressure loss	en
dc.subject.other	Cascades (fluid mechanics)	en
dc.subject.other	Constrained optimization	en
dc.subject.other	Machine design	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Newton-Raphson method	en
dc.subject.other	Turbomachinery	en
dc.subject.other	Shape optimization	en
dc.title	Total pressure losses minimization in turbomachinery cascades using the exact Hessian	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cma.2010.05.014	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cma.2010.05.014	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	A method for the design of turbomachinery cascades with minimum total pressure losses, subject to constraints on the minimum blade thickness and flow turning, is presented. It is based on the Newton-Lagrange method which requires the computation of first- and second-order sensitivities of the objective function and the constraints, with respect to the design variables. The computation of the exact Hessian of the function which expresses the difference in total pressure between the inlet to and the outlet from the cascade, is new in the literature. To compute the Hessian, the direct differentiation of the viscous flow equations is used for the first-order sensitivities of the functional and the flow-related constraints, followed by the discrete adjoint method. Since the objective function is defined along boundaries other than those controlled by the design variables, it is challenging to investigate the significance of all terms comprising the exact second-order sensitivity expressions. All these terms were temporarily computed using automatic differentiation and those which proved to be significant are hand-differentiated to minimize CPU cost and memory requirements. Insignificant terms are eliminated, giving rise to the so-called "exact" Hessian matrix. An "exactly" initialized quasi-Newton method was also programmed and tested. In the latter, at the first cycle, the exact gradients and Hessians are computed and used; during the subsequent optimization cycles, the discrete adjoint method provides the exact gradient whereas the Hessian is updated as in quasi-Newton methods. The comparison of the efficiency of the aforementioned methods depends on the number of design variables used; the "exactly" initialized quasi-Newton method constantly outperforms its conventional variant in terms of CPU cost, particularly in non-convex and/or constrained optimization problems. (C) 2010 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE SA	en
heal.journalName	Computer Methods in Applied Mechanics and Engineering	en
dc.identifier.doi	10.1016/j.cma.2010.05.014	en
dc.identifier.isi	ISI:000284676500008	en
dc.identifier.volume	199	en
dc.identifier.issue	41-44	en
dc.identifier.spage	2697	en
dc.identifier.epage	2708	en