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

AIAA Journal

Volumn 49, Issue 5, 2011, Pages 994-1009

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

^a UNIVERSITY OF MICHIGAN   (United States)

^b Department of Aerospace Engineering ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GOVERNING EQUATIONS; HANDLING TIME; HEAT TRANSFER PROBLEMS; HYPERSONIC FLIGHT REGIME; MODELING FRAMEWORKS; PROPER ORTHOGONAL DECOMPOSITIONS; REDUCED ORDER; REDUCED SYSTEMS; STRONG COUPLING; THERMAL SOLUTION; TIME HISTORY; TIME VARYING;

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

HYPERSONIC VEHICLES;

EID: 79955407467     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.J050701     Document Type: Conference Paper

References (65)

1. Anderson, J. D., Jr., Hypersonic and High-Temperature Gas Dynamics, McGraw-Hill, New York, 1989, pp. 214-215.
2. Bertin, J. J., Hypersonic Aerothermodynamics, AIAA, Reston, VA, 1994, pp. 1-3.
3. Minkowycz, W. J., and Sparrow, E. M. (eds.), Advances in Numerical Heat Transfer, Vol. 2, Taylor and Francis, New York, 2000, pp. 20, 37, 71, 143.
4. Guyan, R. J., "Reduction of Stiffness and Mass Matrices," AIAA Journal, Vol. 3, No. 2, 1965, p. 380. doi:10.2514/3.2874
5. Craig, R. R., Jr., and Bampton, M. C. C., "Coupling of Substructures for Dynamic Analysis," AIAA Journal, Vol. 6, No. 7, July 1968, pp. 1313-1319. doi:10.2514/3.4741
6. 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, France, MSC.Software Corp. Paper 2001-149, Santa Ana, CA, 2002.
7. 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, American Soc. of Mechanical Engineers, Fairfield, NJ, 2002, pp. 49-55.
8. Botto, D., Zucca, S., and Gola, M. M., "A Methodology for On-Line Calculation of Temperature and Thermal Stress Under Non-Linear Boundary Conditions," International Journal of Pressure Vessels and Piping, Vol. 80, No. 1, 2003, pp. 21-29. doi:10.1016/S0308-0161(02)00139-4 (Pubitemid 36370798)
9. 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, Aug. 2007, pp. 819-839. doi:10.1080/01495730701415806 (Pubitemid 47142872)
10. 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 and Simulation, Vol. 17, No. 3, 1997, pp. 242-250.
11. Videcoq, E., and Petit, D., "Model Reduction for the Resolution of Multidimensional Inverse Heat Conduction Problems," International Journal of Heat and Mass Transfer, Vol. 44, No. 10, 2001, pp. 1899-1911. doi:10.1016/S0017-9310(00)00239-8
12. Girault, M., and Petit, D., "Identification Methods in Nonlinear Heat Conduction. Part I: Model Reduction," International Journal of Heat and Mass Transfer, Vol. 48, No. 1, 2005, pp. 105-118. doi:10.1016/j. ijheatmasstransfer.2004.06.032 (Pubitemid 39553926)
13. Girault, M., and Petit, D., "Identification Methods in Nonlinear Heat Conduction. Part II: Inverse Problem Using a Reduced Model," International Journal of Heat and Mass Transfer, Vol. 48, No. 1, 2005, pp. 119-133. doi:10.1016/j.ijheatmasstransfer.2004.06.033 (Pubitemid 39553927)
14. Shore, C. P., "Reduction Method for Thermal Analysis of Complex Aerospace Structures," NASA Langley Research Center, TP NASATP-2373, Jan. 1985.
15. Balakrishnan, N. V., "Nonlinear Transient Thermal Analysis by the Force-Derivative Method," Ph.D. Thesis, Old Dominion Univ., Norfolk, VA, 1995.
16. Camarda, C. J., and Haftka, R. T., "Development of Higher-Order Modal Methods for Transient Thermal and Structural Analysis," Tech. Rep. NASA Langley Research Center TM 101548, Feb. 1989.
17. Camarda, C. J., "Development of Advanced Modal Methods for Calculating Transient Thermal and Structural Response," NASA Langley Research Center, TM 104102, Dec. 1991.
18. 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. doi:10.1002/nme.1620280104
19. 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. doi:10.1002/nme.1620230604 (Pubitemid 17616553)
20. Nour-Omid, B., "Lanczos Method for Heat Conduction Analysis," International Journal for Numerical Methods in Engineering, Vol. 24, No. 1, 1987, pp. 251-262. doi:10.1002/nme.1620240117 (Pubitemid 17510566)
21. Perez, R.,Wang, X. Q., and Mignolet, M. P., "Nonlinear Reduced Order Models for Thermoelastodynamic Response of Isotropic and FGM Panels," 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA AIAA Paper 2009-2309, 2009.
22. Perez, R., Wang, X. Q., and Mignolet, M. P., "Steady and Unsteady Nonlinear Thermoelastodynamic Response of Panels by Reduced Order Models," 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Orlando, FL AIAA Paper 2010-2724, 2010.
23. Camarda, C. J., Haftka, R. T., and Riley, M. F., "An Evaluation of Higher-Order Modal Methods for Calculating Transient Structural Response," Computers and Structures, Vol. 27, No. 1, 1987, pp. 89-101. doi:10.1016/0045- 7949(87)90184-2
24. Holmes, P., Lumley, J., and Berkooz, G., Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge Univ. Press, New York, 1996, p. 86.
25. Liang,Y. C., Lee, H. P., Lim, S. P., Lin,W. Z., Lee, K. H., andWu, C. G., "Proper Orthogonal Decomposition and its Applications-Part I: Theory," Journal of Sound and Vibration, Vol. 252, No. 3, 2002, pp. 527-544. doi:10.1006/jsvi.2001.4041 (Pubitemid 35262887)
26. Lumley, J. L., "The Structure of Inhomogeneous Turbulent Flows," Atmospheric Turbulence and Radio Wave Propagation, edited by A. M. Yaglom, and V. I. Tatarski, 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, No. 4, 2001, pp. 479-504. doi:10.1002/nme.167 (Pubitemid 32411907)
28. Placzek, A., Tran, D., and Ohayon, R., "Hybrid Proper Orthogonal Decomposition Formulation for Linear Structural Dynamics," Journal of Sound and Vibration, Vol. 318, Nos. 4-5, Dec. 2008, pp. 943-964. doi:10.1016/j.jsv. 2008.05.015
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, Oct. 2000, pp. 1853-1862. doi:10.2514/2.867
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, Nos. 1-3, 2001, pp. 1-19. doi:10.1016/S0895- 7177(00)00225-9 (Pubitemid 32062551)
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, Feb. 2005, pp. 774-797. doi:10.1002/nme.1205 (Pubitemid 40195779)
32. Bialecki, R. A., Kassab, A. J., and Fic, A., "Reduction of the Dimensionality of Transient FEM Solutions Using Proper Orthogonal Decomposition," 36th AIAA Thermophysics Conference, Orlando, FL, AIAA Paper 2003-4207, 2003.
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. doi:10.1080/10407790590935920 (Pubitemid 41205139)
34. Efe, M. Ö., and Özbay, H., "Proper Orthogonal Decomposition for Reduced Order Modeling: 2D Heat Flow," Proceedings of the 2003 IEEE Conference on Control Applications, Istanbul, Turkey, IEEE Publ., Piscataway, NJ, 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," International Journal of Heat and Mass Transfer, Vol. 42, No. 1, 1999, pp. 127-142. doi:10.1016/S0017-9310(98)00136-7
36. Park, H. M., and Jung, W. S., "The Karhunen-Loève Galerkin Method for the Inverse Natural Convection Problems," International Journal of Heat and Mass Transfer, Vol. 44, No. 1, 2001, pp. 155-167. doi:10.1016/S0017-9310(00)00092-2
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. doi:10.1007/s00466-005-0697-y (Pubitemid 41521406)
38. Falkiewicz, N. J., and Cesnik, C. E. S., "A Reduced-Order Modeling Framework for Integrated Thermo-Elastic Analysis of Hypersonic Vehicles," 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA, AIAA Paper 2009-2308, 2009.
39. Sirovich, L., "Turbulence and Dynamics of Coherent Structures, Part I: Coherent Structures," Quarterly of Applied Mathematics,Vol. 45, 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, Lecture Notes in Computer Science, Vol. 3743, Springer-Verlag, New York, 2006, pp. 15-27. (Pubitemid 43937301)
41. Trefethen, L. N., and Bau, D. III, Numerical Linear Algebra, Society for Industrial and Applied Mathematics, Philadelphia, 1997, pp. 35-36, 41-46, 48-49.
42. Heath, M. T., Scientific Computing : An Introductory Survey, 2nd ed., McGraw-Hill, New York, 2002, p. 137.
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, 4th ed., Wiley, New York, 2001, pp. 324-325.
45. Wood, W. L., and Lewis, R. W., "A Comparison of Time Marching Schemes for the Transient Heat Conduction Equation," International Journal for Numerical Methods in Engineering, Vol. 9, No. 3, 1975, pp. 679-689. doi:10.1002/nme.1620090314
46. Hirsch, C., Numerical Computation of Internal and External Flows: Fundamentals of Computational Fluid Dynamics, 2nd ed., Elsevier/ Butterworth-Heinemann, Amsterdam, 2007, p. 286.
47. Hughes, T. J. R., "Unconditionally Stable Algorithms for Nonlinear Heat Conduction," Computer Methods in Applied Mechanics and Engineering, Vol. 10, No. 2, 1977, pp. 135-139. doi:10.1016/0045-7825(77)90001-9
48. Oppenheimer, M.W., and Doman, D. B., "AHypersonicVehicle Model Developed with Piston Theory," 2006 AIAA Atmospheric Flight Mechanics Conference, Keystone, CO, AIAA Paper 2006-6637, 2006.
49. Pendleton, E., Moster, G., and Farmer, M., "Transonic Aeroelastic Models of Hypersonic Highly Swept Lifting Surfaces: Design, Analyses, and Test," 35th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Hilton Head, SC, AIAA Paper 1994-1489, 1994.
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. doi:10.2514/3.46860
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," 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, La Jolla, CA, AIAA Paper 1993-1315, 1993.
52. McNamara, J. J., "Aeroelastic and Aerothermoelastic Behavior of Two and Three Dimensional Lifting Surfaces in Hypersonic Flow," Ph.D. thesis, Univ. of Michigan, Ann Arbor, MI, 2005.
53. Shih, P., Prunty, J., and Mueller, R., "Thermostructural Concepts for HypervelocityVehicles," Journal of Aircraft,Vol. 28, No. 5, May 1991, pp. 337-345. doi:10.2514/3.46032
54. Myers, D., Martin, C., and Blosser, M., "Parametric Weight Comparison of Advanced Metallic, Ceramic Tile, and Ceramic Blanket Thermal Protection Systems," NASA Langley Research Center, TM 210289, June 2000.
55. Orton, G., and Scuderi, L., "A Hypersonic Cruiser Concept for the 21st Century," 1998 World Aviation Conference, Anaheim, California, AIAA Paper 1998-5525, 1998.
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, Nos. 1-2, 1991, pp. 1-23. doi:10.1016/0263- 8231(91)90008-7
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. doi:10.2514/3.46295 (Pubitemid 23617382)
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," U.S. Air Force Research Laboratory, TR AFRL-RB-WP-TR-2009-3139, 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," NASA CR 2957, March 1978.
60. Ko, W., and Fields, R., "Thermal Stress Analysis of Space Shuttle Orbiter Subjected to Reentry Aerodynamic Heating," NASA TM 88286, Oct. 1987.
61. Leyens, C., and Peters, M., Titanium and Titanium Alloys: Fundamentals and Applications, Wiley, Hoboken, NJ, 2003, pp. 343.
62. Military Handbook: MIL-HDBK-5H: Metallic Materials and Elements for Aerospace Vehicle Structures, U.S. Department of Defense, Washington, D.C., Dec. 1998, pp. 6-83-6-85, 6-88.
63. Welsch, G., Boyer, R., and Collings, E. W., Materials Properties Handbook: Titanium Alloys, ASM International, Materials Park, OH, 1994, pp. 439-440.
64. Noor, A. K. (ed.), Structures Technology: Historical Perspective and Evolution, AIAA, Reston, VA, 1998, p. 436.
65. Craig, R. R., and Kurdila, A. J., Fundamentals of Structural Dynamics, 2nd ed., Wiley, New York, 2006, p. 228.