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

Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

Volumn , Issue , 2010, Pages

  Falkiewicz, Nathan J ^a   Cesnik, Carlos E S ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CONTROL SURFACES; CONTROL SYSTEM SYNTHESIS; FLIGHT SIMULATORS; HEAT TRANSFER; HYPERSONIC AERODYNAMICS; ORDINARY DIFFERENTIAL EQUATIONS; PRINCIPAL COMPONENT ANALYSIS; STRUCTURAL DYNAMICS;

GOVERNING EQUATIONS; HEAT TRANSFER PROBLEMS; HYPERSONIC FLIGHT REGIME; MODEL FRAMEWORK; PROPER ORTHOGONAL DECOMPOSITIONS; REASONABLE ACCURACY; THERMAL SOLUTION; TIME INDEPENDENTS;

HYPERSONIC VEHICLES;

EID: 84855635326     PISSN: 02734508     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2010-2798     Document Type: Conference Paper

References (76)

1. Bolender, M. A. and Doman, D. B., "Nonlinear Longitudinal Dynamical Model of an Air-Breathing Hypersonic Vehicle," Journal of Spacecraft and Rockets, Vol. 44, No. 2, March-April 2007, pp. 374-387.
2. Chavez, F. R. and Schmidt, D. K., "Analytical Aeropropulsive/ Aeroelastic Hypersonic-Vehicle Model with Dynamic Analysis," Journal of Guidance, Control, and Dynamics, Vol. 17, No. 6, March-April 2007, pp. 1308-1319.
3. Anderson, Jr., J. D., Hypersonic and High-Temperature Gas Dynamics, McGraw-Hill, 1989.
4. Bertin, J. J., Hypersonic Aerothermodynamics, American Institute of Aeronautics and Astronautics, Reston, Virgina, 1994.
5. Minkowycz, W. J. and Sparrow, E. M., editors, Advances in Numerical Heat Transfer, Vol. II, Taylor & Francis, New York, 2000.
6. Guyan, R. J., "Reduction of Stiffness and Mass Matrices," AIAA Journal, Vol. 3, No. 2, 1965, pp. 380.
7. Craig, Jr., R. R. and Bampton, M. C. C., "Coupling of Substructures for Dynamic Analysis," AIAA Journal, Vol. 6, No. 7, July 1968, pp. 1313-1319.
8. Botto, D., Gola, S., Troncarelli, M. M., and Pasquero, G., "Component Modes Synthesis Applied to a Thermal Transient Analysis of a Turbine Disc," Worldwide Aerospace Conference and Technology Showcase, Toulouse, 2002.
9. Botto, D., Zucca, S., Gola, M. M., and Salvano, S., "A Method for on Line Temperature Calculation of Aircraft Engine Turbine Discs," ASME Turbo Expo, Amsterdam, 2002.
10. Botto, D., Zucca, S., and Gola, M. M., "A Methodology for On-Line Calculation of Temperature and Thermal Stress Under Non-Linear Boundary Conditions," Int. J. Press. Vess. Pip., Vol. 80, No. 1, 2003, pp. 21-29.
11. Botto, D., Zucca, S., and Gola, M. M., "Reduced-Order Models for the Calculation of Thermal Transients of Heat Conduction/Convection FE Models," Journal of Thermal Stresses, Vol. 30, No. 8, August 2007, pp. 819-839.
12. Petit, D., Hachette, R., and Veyret, D., "A Modal Identification Method to Reduce a High-Order Model: Application to Heat Conduction Modelling," International Journal of Modelling & Simulation, Vol. 17, No. 3, 1997, pp. 242-250.
13. Videcoq, E. and Petit, D., "Model Reduction for the Resolution of Multidimensional Inverse Heat Conduction Problems," Int. J. Heat Mass Transfer, Vol. 44, No. 10, 2001, pp. 1899-1911.
14. Girault, M. and Petit, D., "Identification methods in nonlinear heat conduction. Part I: model reduction," Int. Journal of Heat Mass Transfer, Vol. 48, No. 1, 2005, pp. 105-118.
15. Girault, M. and Petit, D., "Identification methods in nonlinear heat conduction. Part II: Inverse Problem Using a Reduced Model," Int. Journal of Heat Mass Transfer, Vol. 48, No. 1, 2005, pp. 119-133.
16. Shore, C. P., "Reduction Method for Thermal Analysis of Complex Aerospace Structure," Technical Paper NASA-TP- 2373, Langley Research Center, Jan. 1985.
17. Balakrishnan, N. V., Nonlinear Transient Thermal Analysis by the Force-Derivative Method, Ph.D. thesis, Old Dominion University, Norfolk, Virginia, 1995.
18. Camarda, C. J. and Haftka, R. T., "Development of Higher-Order Modal Methods for Transient Thermal and Structural Analysis," Tech. Rep. NASA TM-101548, NASA Langley Research Center, February 1989.
19. Camarda, C. J., "Development of Advanced Modal Methods for Calculating Transient Thermal and Structural Response," Tech. Rep. NASA TM-104102, NASA Langley Research Center, December 1991.
20. Coutinho, A. L. G. A., Landau, L., Wrobel, L. C., and Ebecken, N. F. F., "Modal Solution of Transient Heat Conduction Utilizing Lanczos Algorithm," International Journal for Numerical Methods in Engineering, Vol. 28, No. 1, 1989, pp. 13-25.
21. Cardona, A. and Idelsohn, S., "Solution of Non-Linear Thermal Transient Problems by a Reduction Method," International Journal for Numerical Methods in Engineering, Vol. 23, No. 6, 1986, pp. 1023-1042.
22. Nour-Omid, B., "Lanczos Method for Heat Conduction Analysis," International Journal for Numerical Methods in Engineering, Vol. 24, No. 1, 1987, pp. 251-262.
23. Camarda, C. J., Haftka, R. T., and Riley, M. F., "An Evaluation of Higher-Order Modal Methods for Calculating Transient Structural Response," Computers & Structures, Vol. 27, No. 1, 1987, pp. 89-101.
24. Holmes, P., Lumley, J., and Berkooz, G., Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, 1996.
25. Liang, Y. C., Lee, H. P., Lim, S. P., Lin, W. Z., Lee, K. H., and Wu, C. G., "Proper Orthogonal Decomposition and its Applications-Part I: Theory," Journal of Sound and Vibration, Vol. 252, No. 3, 2002, pp. 527-544.
26. Lumley, J. L., "The Structure of Inhomogeneous Turbulent Flows," Atmospheric Turbulence and Radio Wave Propagation, edited by A. Yaglon and V. Tatarsky, Nauka, Moscow, 1967, pp. 166-178.
27. Krysl, P., Lall, S., and Marsden, J. E., "Dimensional Model Reduction in Non-Linear Finite Element Dynamics of Solids and Structures," International Journal for Numerical Methods in Engineering, Vol. 51, 2001, pp. 479-504.
28. Placzek, A., Tran, D., and Ohayon, R., "Hybrid proper orthogonal decomposition formulation for linear structural dynamics," Journal of Sound and Vibration, Vol. 318, No. 4-5, December 2008, pp. 943-964.
29. Hall, K. C., Thomas, J. P., and Dowell, E. H., "Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows," AIAA Journal, Vol. 38, No. 10, October 2000, pp. 1853-1862.
30. Atwell, J. A. and King, B. B., "Proper Orthogonal Decomposition for Reduced Basis Feedback Controllers for Parabolic Equations," Mathematical and Computer Modelling, Vol. 33, 2001, pp. 1-19.
31. Bialecki, R. A., Kassab, A. J., and Fic, A., "Proper Orthogonal Decomposition and Modal Analysis for Acceleration of Transient FEM Thermal Analysis," International Journal for Numerical Methods in Engineering, Vol. 62, No. 6, 14 Feb. 2005, pp. 774-797.
32. Bialecki, R. A., Kassab, A. J., and Fic, A., "Reduction of the Dimensionality of Transient FEM Solutions Using Proper Orthogonal Decomposition," Proceedings of the 36th AIAA Thermophysics Conference, Orlando, Florida, AIAA 2003-4207.
33. Fic, A., Bialecki, R. A., and Kassab, A. J., "Solving Transient Nonlinear Heat Conduction Problems by Proper Orthogonal Decomposition and the Finite-Element Method," Numerical Heat Transfer, Part B: Fundamentals, Vol. 48, No. 2, Aug. 2005, pp. 103-124.
34. Önder Efe, M. and Özbay, H., "Proper Orthogonal Decomposition for Reduced Order Modeling: 2D Heat Flow," Proceedings of the 2003 IEEE Conference on Control Applications, Istanbul, Turkey, 2003.
35. Park, H. M., Chung, O. Y., and Lee, J. H., "On the solution of inverse heat transfer problem using the Karhunen-Loève Galerkin Method," Int. J. Heat Mass Transfer, Vol. 42, No. 1, 1999, pp. 127-142.
36. Park, H. M. and Jung, W. S., "The Karhunen-Loève Galerkin Method for the Inverse Natural Convection Problems," Int. J. Heat Mass Transfer, Vol. 44, No. 1, 2001, pp. 155-167.
37. Ostrowski, Z., Bialecki, R. A., and Kassab, A. J., "Estimation of Constant Thermal Conductivity by Use of Proper Orthogonal Decomposition," Computational Mechanics, Vol. 37, No. 1, Dec. 2005, pp. 52-59.
38. Falkiewicz, N. J. and Cesnik, C. E. S., "A Reduced-Order Modeling Framework for Integrated Thermo-Elastic Analysis of Hypersonic Vehicles," Proceedings of the 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Springs, California, AIAA 2009-2308.
39. Sirovich, L., "Turbulence and Dynamics of Coherent Structures, Part I: Coherent Structures," Quarterly of Applied Mathematics, Vol. XLV, 1987, pp. 561-571.
40. Gunzburger, M. and Peterson, J., "Reduced-Order Modeling of Complex Systems with Multiple System Parameters," Large-Scale Scientific Computing, 5th International Conference, Sozopol, Bulgaria, edited by I. Lirkov, S. Margenov, and J. Wasniewski, Vol. LNCS 3743, Springer Verlag, 2006, pp. 15-27.
41. Trefethen, L. N. and Bau, III, D., Numerical Linear Algebra, Society for Industrial and Applied Mathematics, 1997.
42. Heath, M. T., Scientific Computing: An Introductory Survey, McGraw-Hill, 2nd ed., 2002.
43. Chatterjee, A., "An introduction to the proper orthogonal decomposition," Current Science, Vol. 78, No. 7, April 2000, pp. 808-817.
44. Huebner, K., Dewhirst, D., Smith, D., and Byrom, T., The Finite Element Method for Engineers, John Wiley & Sons, Inc., 4th ed., 2001.
45. Wood, W. L. and Lewis, R. W., "A Comparison of Time Marching Schemes for the Transient Heat Conduction Equation," Int. J. Numer. Methods Eng., Vol. 9, No. 3, 1975, pp. 679-689.
46. Hirsch, C., Numerical Computation of Internal & External Flows, Butterworth-Heinemann, 2nd ed., 2007.
47. Hughes, T. J. R., "Unconditionally Stable Algorithms for Nonlinear Heat Conduction," Computer Methods in Applied Mechanics and Engineering, Vol. 10, 1977, pp. 135-139.
48. Oppenheimer, M. W. and Doman, D. B., "A Hypersonic Vehicle Model Developed with Piston Theory," Proceedings of the 2006 AIAA Atmospheric Flight Mechanics Conference, Keystone, Colorado, AIAA 2006-6637.
49. Pendleton, E., Moster, G., and Farmer, M., "Transonic Aeroelastic Models of Hypersonic Highly Swept Lifting Surfaces: Design, Analyses, and Test," Proceedings of the 35th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Hilton Head, South Carolina, AIAA 1994-1489-574.
50. Pendleton, E., Moster, G., and Keller, D., "Transonic Aeroelastic Models of Highly Swept Hypersonic Lifting Surfaces," Journal of Aircraft, Vol. 32, No. 6, Nov. - Dec. 1995, pp. 1169-1176.
51. Spain, C. V., Zeiler, T. A., Bullok, E. P., and Hodge, J. S., "A Flutter Investigation of All-Moveable NASP-Like Wings at Hypersonic Speeds," Proceedings of the 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, La Jolla, California, AIAA-93-1315.
52. McNamara, J. J., Aeroelastic and Aerothermoelastic Behavior of Two and Three Dimensional Lifting Surfaces in Hypersonic Flow, Ph.D. thesis, University of Michigan, Ann Arbor, Michigan, 2005.
53. Shih, P., Prunty, J., and Mueller, R., "Thermostructural Concepts for Hypervelocity Vehicles," Journal of Aircraft, Vol. 28, No. 5, May 1991, pp. 337-345.
54. Myers, D., Martin, C., and Blosser, M., "Parametric Weight Comparison of Advanced Metallic, Ceramic Tile, and Ceramic Blanket Thermal Protection Systems," Tech. Rep. NASA TM-210289, Langley Research Center, June 2000.
55. Orton, G. and Scuderi, L., "A Hypersonic Cruiser Concept for the 21st Century," Proceedings of the 1998 World Aviation Conference, Anaheim, California, AIAA 1998-5525.
56. Wieting, A., Dechaumphai, P., Bey, K., Thornton, E., and Morgan, K., "Application of Integrated Fluid-Thermal-Structural Analysis Methods," Thin-Walled Structures, Vol. 11, No. 1-2, 1991, pp. 1-23.
57. Leatherwood, J., Clevenson, S., Powell, A., and Daniels, E., "Acoustic Testing of High-Temperature Panels," Journal of Aircraft, Vol. 29, No. 6, Nov. - Dec. 1992, pp. 1130-1136.
58. Blevins, R., Bofilios, D., Holehouse, I., Hwa, V., Tratt, M., Laganelli, A., Pozefsky, P., and Pierucii, M., "Thermo-Vibro-Acoustic Loads and Fatigue of Hypersonic Flight Vehicle Structure," Tech. Rep. AFRL-RB-WP-TR-2009-3139, Air Force Research Laboratory, June 2009.
59. Ellis, D., Pagel, L., and Schaeffer, D., "Design and Fabrication of a Radiative Actively Cooled Honeycomb Sandwich Structural Panel for a Hypersonic Aircraft," Tech. Rep. NASA-CR-2957, NASA, March 1978.
60. Ko, W. and Fields, R., "Thermal Stress Analysis of Space Shuttle Orbiter Subjected to Reentry Aerodynamic Heating," Tech. Rep. NASA-TM-88286, NASA, Oct. 1987.
61. Leyens, C. and Peters, M., Titanium and Titanium Alloys, Wiley-VHC, 2003.
62. Noor, A. K., editor, Structures Technology: Historical Perspective and Evolution, American Institute of Aeronautics and Astronautics, 1998.
63. Department of Defense, Military Handbook - MIL-HDBK-5H: Metallic Materials and Elements for Aerospace Vehicle Structures, December 1998.
64. Welsch, G., Boyer, R., and Collings, E. W., Materials Properties Handbook: Titanium Alloys, ASM International, 1994.
65. "Titanium IMI 834," http://http://www.matweb.com/search/ DataSheet.aspx?MatGUID=a74096c99aa6486382a9c9e1be0883c4&ckck=1, Last Accessed 9/3/2009.
66. Craig, R. R. and Kurdila, A. J., Fundamentals of Structural Dynamics, John Wiley & Sons, Inc., 2nd ed., 2006.
67. Falkiewicz, N. J., Cesnik, C. E. S., Bolender, M. A., and Doman, D. B., "Thermoelastic Formulation of a Hypersonic Vehicle Control Surface for Control-Oriented Simulation," Proceedings of the 2009 AIAA Guidance, Navigation, and Control Conference, Chicago, Illinois, AIAA 2009-6284.
68. Holman, J. P., Heat Transfer, McGraw-Hill, Inc., 8th ed., 1997.
69. Eckert, E. R. G., "Survey on Heat Transfer at High Speeds," Technical Report ARL 189, Aeronautical Research Laboratory, University of Minnesota, Minneapolis, MN, December 1961.
70. Lighthill, M., "Oscillating Airfoils at High Mach Number," Journal of the Aeronautical Sciences, Vol. 20, No. 6, June 1953, pp. 402-406.
71. Ashley, H. and Zartarian, G., "Piston Theory - A New Aerodynamic Tool for the Aeroelastician," Journal of the Aeronautical Sciences, Vol. 23, No. 12, 1956, pp. 1109-1118.
72. Oppenheimer, M. W., Skujins, T., Bolender, M. A., and Doman, D. B., "A Flexible Hypersonic Vehicle Model Developed with Piston Theory," Proceedings of the 2007 AIAA Atmospheric Flight Mechanics Conference, Hilton Head, South Carolina, AIAA 2007-6396.
73. Mei, C., Motagaly, K. A., and Chen, R., "Review of Nonlinear Panel Flutter at Supersonic and Hypersonic Speeds," Applied Mechanics Review, Vol. 52, No. 10, October 1999, pp. 321-332.
74. McNamara, J. J. and Friedmann, P. P., "Aeroelastic and Aerothermoelastic Analysis of Hypersonic Vehicles: Current STatus and Future Trends," Proceedings of the 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, Hawaii, AIAA 2007-2013.
75. Anderson, J. D., Modern Compressible Flow: With Historical Perspective, McGraw-Hill, Boston, 3rd ed., 2003.
76. Thuruthimattam, B. J., Friedmann, P. P., McNamara, J. J., and Powell, K. G., "Modeling Approaches to Hypersonic Aeroelasticity," 2002 ASME International Mechanical Engineering Congress and Exposition, New Orleans, Louisiana, November IMECE/2002-32943.