Airfoil design optimization using reduced order models based on proper orthogonal decomposition

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Abstract

This paper present s a met od for inviscid airfoil analysis and design opt imizatz(t hat uses reduced order modelst o reducet he cost of comput at ion.St rong emphasis is placed on obt aining reasonably accurat e solut ionst ot he Euler equat ions wit h comput at ional cost s which are far lowert hant hose required byt it al Comput at al Fluid Dynamics (CFD)t echniques. The design procedure present ed here begins by comput ing a series of flow solut ions (snapshots) in whicht he design variables of int erest are pert urbed using a Design of Experiment approach. Proper Ort ogonal Decomposit POD) is t hen usedt o producet he opt imal linear represent at ion oft hese snapshots using a finit e series of basis funct ions or modes. These basis modes aret hen usedt o const ruct arbit rary solut( st ot he Euler equat s about modified airfoil geomet( s wit very small comput at ional expense. The flow solut ion problem is reduced int his wayt o a non-linear least squares fit problem wit h a small number of variablest hat can be solved e#cient ly. For design purposes, a gradient -based opt imizat ion procedure is used wit ht he informat ion supplied byt he reduced order model. Result s for bot h direct airfoil analysis and for an inverse design opt imizatz( problem are present ed. Observat s regarding t e useabilit y oft hist echnique in a design environment are also discussed. Nomenclature a j generic coe#cientof the j-th POD mode E total energy (internal plus kinetic) f , g Euler flux vectors H total enthalpy M number of modes used in approximation p static pressure R(x,x # ) autocorrelationf unction R autocorrelation tensor,finite-volume residual R autocorrelation matrixf or method of snapshots u -componentof velocity vy-componentof velocity u arbitraryf unction...

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