Proper orthogonal decomposition for reduced-order thermal solution in hypersonic aerothermoelastic simulations

The ability to perform full-order aerothermoelastic simulations of hypersonic vehicles is hindered by the strong coupling exhibited between the aerodynamics, heat transfer, and structural dynamic response in the hypersonic ight regime. As a result of these interactions, alternative techniques are necessary to obtain computationally tractable systems of governing equations and their solutions. This work addresses the use of proper orthogonal decomposition for reduced-order solution of the heat transfer problem within a hypersonic modeling framework. The specic challenge of handling time-dependent boundary conditions due to transient aerodynamic heating is discussed. An overview of the proper orthogonal decomposition is given and two methods for solution of the reduced system of ordinary dierential equations are outlined. The methodology is applied to a representative hypersonic vehicle control surface model for two cases in which the time-history of the thermal load vector is known a priori: one in which the boundary conditions are time-independent and another in which they are time-varying. Results demonstrate the ability of the reduced-order solution to approximate the full-order solution with reasonable accuracy. Finally, a time-marching hypersonic aerothermoelastic framework is described in which proper orthogonal decomposition is used for the transient thermal solution.

[1]  Philipp Birken,et al.  Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.

[2]  Marc P. Mignolet,et al.  STEADY AND UNSTEADY NONLINEAR THERMOELASTODYNAMIC RESPONSE OF PANELS BY REDUCED ORDER MODELS , 2010 .

[3]  Carlos E. S. Cesnik,et al.  Thermoelastic Formulation of a Hypersonic Vehicle Control Surface for Control-Oriented Simulation , 2009 .

[4]  Robert D. Blevins,et al.  Thermo-Vibro-Acoustic Loads and Fatigue of Hypersonic Flight Vehicle Structure , 2009 .

[5]  Ricardo Perez,et al.  NONLINEAR REDUCED ORDER MODELS FOR THERMOELASTODYNAMIC RESPONSE OF ISOTROPIC AND FGM PANELS , 2009 .

[6]  Carlos E. S. Cesnik,et al.  A Reduced-Order Modeling Framework for Integrated Thermo-Elastic Analysis of Hypersonic Vehicles , 2009 .

[7]  Roger Ohayon,et al.  Hybrid proper orthogonal decomposition formulation for linear structural dynamics , 2008 .

[8]  Stefano Zucca,et al.  Reduced-Order Models for the Calculation of Thermal Transients of Heat Conduction/Convection FE Models , 2007 .

[9]  David B. Doman,et al.  Nonlinear Longitudinal Dynamical Model of an Air-Breathing Hypersonic Vehicle , 2007 .

[10]  David B. Doman,et al.  A Flexible Hypersonic Vehicle Model Developed With Piston Theory (Preprint) , 2006 .

[11]  Peretz P. Friedmann,et al.  Aeroelastic and Aerothermoelastic Analysis of Hypersonic Vehicles: Current Status and Future Trends , 2006 .

[12]  David B. Doman,et al.  A Hypersonic Vehicle Model Developed With Piston Theory (Preprint) , 2006 .

[13]  Adam Fic,et al.  Solving Transient Nonlinear Heat Conduction Problems by Proper Orthogonal Decomposition and the Finite-Element Method , 2005 .

[14]  Max D. Gunzburger,et al.  Reduced-Order Modeling of Complex Systems with Multiple System Parameters , 2005, LSSC.

[15]  Alain J. Kassab,et al.  Estimation of constant thermal conductivity by use of Proper Orthogonal Decomposition , 2005 .

[16]  Adam Fic,et al.  Proper orthogonal decomposition and modal analysis for acceleration of transient FEM thermal analysis , 2005 .

[17]  C. Leyens,et al.  Titanium and titanium alloys : fundamentals and applications , 2005 .

[18]  Daniel Petit,et al.  Identification methods in nonlinear heat conduction. Part II: inverse problem using a reduced model , 2005 .

[19]  Daniel Petit,et al.  Identification methods in nonlinear heat conduction. Part I: Model reduction , 2005 .

[20]  Jack J. McNamara,et al.  Aeroelastic and aerothermoelastic behavior of two and three dimensional lifting surfaces in hypersonic flow. , 2005 .

[21]  Adam Fic,et al.  Reduction of the Dimensionality of Transient FEM Solutions Using Proper Orthogonal Decomposition , 2003 .

[22]  Hitay Ozbay,et al.  Proper orthogonal decomposition for reduced order modeling: 2D heat flow , 2003, Proceedings of 2003 IEEE Conference on Control Applications, 2003. CCA 2003..

[23]  Stefano Zucca,et al.  A methodology for on-line calculation of temperature and thermal stress under non-linear boundary conditions , 2003 .

[24]  H. P. Lee,et al.  PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS—PART I: THEORY , 2002 .

[25]  Muzio Gola,et al.  A Method for On-Line Temperature Calculation of Aircraft Engine Turbine Discs , 2002 .

[26]  Stefano Zucca,et al.  Component modes synthesis applied to a thermal transient analysis of a turbine disc , 2002 .

[27]  Peretz P. Friedmann,et al.  Modeling approaches to hypersonic aeroelasticity , 2002 .

[28]  J. Marsden,et al.  Dimensional model reduction in non‐linear finite element dynamics of solids and structures , 2001 .

[29]  Daniel Petit,et al.  Model reduction for the resolution of multidimensional inverse heat conduction problems , 2001 .

[30]  H. Park,et al.  The Karhunen-Loève Galerkin method for the inverse natural convection problems , 2001 .

[31]  Belinda B. King,et al.  Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations , 2001 .

[32]  Jeffrey P. Thomas,et al.  Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows , 2000 .

[33]  A. Chatterjee.  An introduction to the proper orthogonal decomposition , 2000 .

[34]  Chuh Mei,et al.  Review of Nonlinear Panel Flutter at Supersonic and Hypersonic Speeds , 1999 .

[35]  Gene Hou,et al.  Nonlinear Transient Thermal Analysis by the Force-Derivative Method , 1999 .

[36]  H. Park,et al.  On the solution of inverse heat transfer problem using the Karhunen–Loève Galerkin method , 1999 .

[37]  Lee F. Scuderi,et al.  A Hypersonic Cruiser Concept for the 21st Century , 1998 .

[38]  David E. Myers,et al.  Parametric Weight Comparison of Advanced Metallic, Ceramic Tile, and Ceramic Blanket Thermal Protect , 2000 .

[39]  D. Veyret,et al.  A Modal Identification Method To Reduce A High-Order Model: Application To Heat Conduction Modelling , 1997 .

[40]  L. Trefethen,et al.  Numerical linear algebra , 1997 .

[41]  Michael T. Heath,et al.  Scientific Computing: An Introductory Survey , 1996 .

[42]  Edmund Pendleton,et al.  Transonic aeroelastic models of highly swept hypersonic lifting surfaces , 1995 .

[43]  E. Collings,et al.  Materials Properties Handbook: Titanium Alloys , 1994 .

[44]  David K. Schmidt,et al.  Analytical aeropropulsive-aeroelastic hypersonic-vehicle model with dynamic analysis , 1994 .

[45]  Ed Pendleton,et al.  Transonic aeroelastic models of hypersonic highly swept lifting surfaces - Design, analyses, and test , 1994 .

[46]  Thomas A. Zeiler,et al.  A flutter investigation of all-moveable NASP-like wings at hypersonic speeds , 1993 .

[47]  Jack D. Leatherwood,et al.  Acoustic Testing of High-Temperature Panels , 1992 .

[48]  Charles J. Camarda.  Development of advanced modal methods for calculating transient thermal and structural response , 1991 .

[49]  Pramote Dechaumphai,et al.  Application of integrated fluid-thermal-structural analysis methods , 1991 .

[50]  Raphael T. Haftka,et al.  Development of higher-order modal methods for transient thermal and structural analysis , 1989 .

[51]  Alvaro L. G. A. Coutinho,et al.  Modal solution of transient heat conduction utilizing Lanczos algorithm , 1989 .

[52]  J. Prunty,et al.  Thermostructural concepts for hypervelocity vehicles , 1988 .

[53]  C. Hirsch.  Numerical computation of internal and external flows , 1988 .

[54]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[55]  William L. Ko,et al.  Thermal stress analysis of space shuttle orbiter subjected to reentry aerodynamic heating , 1987 .

[56]  Raphael T. Haftka,et al.  An evaluation of higher-order modal methods for calculating transient structural response , 1987 .

[57]  Bahram Nour-Omid,et al.  Lanczos method for heat conduction analysis , 1987 .

[58]  Alberto Cardona,et al.  Solution of non‐linear thermal transient problems by a reduction method , 1986 .

[59]  C. P. Shore.  Reduction method for thermal analysis of complex aerospace structures , 1985 .

[60]  J. Anderson,et al.  Modern Compressible Flow: With Historical Perspective , 1982 .

[61]  L. Pagel,et al.  Design and Fabrication of a Radiative Actively Cooled Honeycomb Sandwich Structural Panel for a Hypersonic Aircraft. , 1978 .

[62]  Thomas J. R. Hughes,et al.  Unconditionally stable algorithms for nonlinear heat conduction , 1977 .

[63]  Roland W. Lewis,et al.  A comparison of time marching schemes for the transient heat conduction equation , 1975 .

[64]  K. Huebner.  The finite element method for engineers , 1975 .

[65]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[66]  R. Guyan.  Reduction of stiffness and mass matrices , 1965 .

[67]  J. M. Coulson,et al.  Heat Transfer , 2018, A Concise Manual of Engineering Thermodynamics.

[68]  V. A. Krasil’nikov,et al.  Atmospheric turbulence and radio-wave propagation , 1962 .

[69]  E. Eckert,et al.  SURVEY ON HEAT TRANSFER AT HIGH SPEEDS , 1961 .

[70]  Holt Ashley,et al.  Piston Theory-A New Aerodynamic Tool for the Aeroelastician , 1956 .

[71]  M. J. Lighthill,et al.  Oscillating Airfoils at High Mach Number , 1953 .