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An Improved Proper Orthogonal Decomposition Technique for the Solution of a 2-D Rotor Blade Inverse Design Problem Using the Entropy Generation Rate as the Objective Function

[+] Author Affiliations
G. Panzini, E. Sciubba, A. Zoli-Porroni

University of Roma 1 “La Sapienza”, Roma, Italy

Paper No. IMECE2007-43461, pp. 729-741; 13 pages
doi:10.1115/IMECE2007-43461
From:
  • ASME 2007 International Mechanical Engineering Congress and Exposition
  • Volume 8: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A and B
  • Seattle, Washington, USA, November 11–15, 2007
  • Conference Sponsors: ASME
  • ISBN: 0-7918-4302-5 | eISBN: 0-7918-3812-9
  • Copyright © 2007 by ASME

abstract

This paper discusses the optimization of a 2D rotor profile attained via a novel inverse-design approach that uses the entropy generation rate as the objective function. A fundamental methodological novelty of the proposed procedure is that it does not require the generation of the fluid-dynamic fields at each iteration step of the optimisation, because the objective function is computed by a functional extrapolation based on the Proper Orthogonal Decomposition (POD) method. With this new method, the (often excessively taxing) computational cost for repeated numerical CFD simulations of incrementally different geometries is substantially decreased by reducing much of it to easy-to-perform matrix-multiplications: CFD simulations are used only to calculate the basis of the POD interpolation and to validate (i.e., extend) the results. As the accuracy of a POD expansion critically depends on the allowable number of CFD simulations, our methodology is still rather computationally intensive: but, as successfully demonstrated in the paper for an airfoil profile design problem, the idea that, given a certain number of necessary initial CFD simulations, additional full simulations are performed only in the “right direction” indicated by the gradient of the objective function in the solution space leads to a successful strategy, and substantially decreases the computational intensity of the solution. This “economy” with respect to other classical “optimization” methods is basically due to the reduction of the complete CFD simulations needed for the generation of the fluid-dynamic fields on which the objective function is calculated.

Copyright © 2007 by ASME

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