Efficient computation of the POD manifold containing the information required to generate a multi-parameter aerodynamic database

Abstract A method is presented to calculate efficiently the proper orthogonal decomposition (POD) manifold (spanned by POD modes) that contains the information needed to generate a multi-parameter aerodynamic database. This work is motivated by the need, driven by market competition, to improve the efficiency of both aerodynamic design and analysis processes in the aeronautic sector. Current aerodynamic database generation is carried out in industry performing CFD computations at the nodes of a dense Cartesian grid in the parameter space. This approach does not account for the redundancies that are necessarily involved and, therefore, it is not the most efficient from the points of view of computational cost and time needed to generate the database. Such redundancies are an advantage when generating the database by means of the (already described in the literature) reduced order models based on projection of the governing equations on a POD manifold, which must be previously calculated from a set of CFD computed snapshots. The method proposed in this paper provides such POD manifold with a small number of snapshots, comparable to the dimension of the POD manifold itself, which is a crucial step for the computational efficiency of the proposed database generation method. The method is tested considering the aerodynamic flow around a horizontal tail plane (HTP) in the parameter range 0.4 ⩽ Mach number ⩽ 0.8 and − 3 ° ⩽ angle of attack ⩽ 3 ° , obtaining the POD manifold with a good precision using 20, conveniently selected snapshots.

[1]  A. Velazquez,et al.  Reduced-Order Model for Viscous Aerodynamic Flow Past an Airfoil , 2010 .

[2]  R. DeLoach.  Improved Quality in Aerospace Testing Through the Modern Design of Experiments , 2000 .

[3]  K. Willcox,et al.  Aerodynamic Data Reconstruction and Inverse Design Using Proper Orthogonal Decomposition , 2004 .

[4]  Steven A. Orszag,et al.  CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS , 1978 .

[5]  D. Gottlieb,et al.  Numerical analysis of spectral methods : theory and applications , 1977 .

[6]  Raymond S. Castner.  Design of Experiments for Both Experimental and Analytical Study of Exhaust Plume Effects on Sonic Boom , 2009 .

[7]  A. Velazquez,et al.  Generation of Aerodynamics Databases Using High-Order Singular Value Decomposition , 2008 .

[8]  A. Velazquez,et al.  A method to generate computationally efficient reduced order models , 2009 .

[9]  M. Fathi Jegarkandi,et al.  Aeroelastic stability consideration of supersonic flight vehicle using nonlinear aerodynamic response surfaces , 2009 .

[10]  P. Holmes,et al.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 1996 .

[11]  Juan J. Alonso,et al.  Investigation of non-linear projection for POD based reduced order models for Aerodynamics , 2001 .

[12]  P. Sagaut,et al.  Towards an adaptive POD/SVD surrogate model for aeronautic design , 2011 .

[13]  Jeffrey S. Robinson,et al.  Developing Conceptual Hypersonic Airbreathing Engines Using Design of Experiments Methods , 2000 .

[14]  J. Edwards,et al.  Comparison of eddy viscosity-transport turbulence models for three-dimensional, shock-separated flowfields , 1996 .

[15]  L. E. Chávez-Valencia,et al.  Modelling of the performance of asphalt pavement using response surface methodology , 2005 .

[16]  Farrokh Mistree,et al.  Kriging Models for Global Approximation in Simulation-Based Multidisciplinary Design Optimization , 2001 .

[17]  L. Cambier,et al.  elsA - An efficient object-oriented solution to CFD complexity , 2002 .

[18]  Siep Weiland,et al.  Missing Point Estimation in Models Described by Proper Orthogonal Decomposition , 2004, IEEE Transactions on Automatic Control.

[19]  A. Velazquez,et al.  Robust reduced order modeling of heat transfer in a back step flow , 2009 .

[20]  P. Sagaut,et al.  Building Efficient Response Surfaces of Aerodynamic Functions with Kriging and Cokriging , 2008 .

[21]  J. Pereira,et al.  Surrogate models based on function and derivative values for aerodynamic global optimization , 2010 .

[22]  Edward Ng,et al.  Response surface models for CFD predictions of air diffusion performance index in a displacement ventilated office , 2008 .

[23]  N. Galanis,et al.  Sensitivity Analysis of Entrance Design Parameters of a Backward-Inclined Centrifugal Fan Using DOE Method and CFD Calculations , 2006 .

[24]  J. Vega,et al.  Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows , 2012 .

[25]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[26]  Shelly M. Ferlemann,et al.  The Role of Formal Experiment Design in Hypersonic Flight System Technology Development , 2002 .

[27]  A. Velazquez,et al.  Compression of aerodynamic databases using high-order singular value decomposition , 2010 .

[28]  R. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer. By D. A ANDERSON, J. C. TANNEHILL and R. H. PLETCHER. Hemisphere, 1984. 599 pp. $39.95. , 1986, Journal of Fluid Mechanics.