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Volumn 200, Issue 1-4, 2011, Pages 216-232

Shape optimization of an airfoil in a BZT flow with multiple-source uncertainties

Author keywords

Polynomial chaos; Real gas; Robust optimization; Sparse grid; Thermodynamic model; Uncertainty quantification

Indexed keywords

POLYNOMIAL CHAOS; REAL GAS; ROBUST OPTIMIZATION; SPARSE GRID; THERMODYNAMIC MODEL; UNCERTAINTY QUANTIFICATIONS;

EID: 78649629594     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.08.006     Document Type: Article
Times cited : (57)

References (59)
  • 1
    • 36849107087 scopus 로고
    • A fundamental derivative in gas dynamics
    • Thompson P.A. A fundamental derivative in gas dynamics. Phys. Fluids 1971, 14:1843-1849.
    • (1971) Phys. Fluids , vol.14 , pp. 1843-1849
    • Thompson, P.A.1
  • 2
    • 34347259209 scopus 로고    scopus 로고
    • Airfoil shape optimization for transonic flows of Bethe-Zel'dovich-Thompson fluids
    • Congedo P.M., Corre C., Cinnella P. Airfoil shape optimization for transonic flows of Bethe-Zel'dovich-Thompson fluids. AIAA J. 2007, 45(6).
    • (2007) AIAA J. , vol.45 , Issue.6
    • Congedo, P.M.1    Corre, C.2    Cinnella, P.3
  • 3
    • 0025958410 scopus 로고
    • Steady, isentropic flows of dense gases
    • Cramer M.S., Best L.M. Steady, isentropic flows of dense gases. Phys. Fluids A 1991, 3:219-226.
    • (1991) Phys. Fluids A , vol.3 , pp. 219-226
    • Cramer, M.S.1    Best, L.M.2
  • 4
    • 84971872360 scopus 로고
    • Transonic flows of Bethe-Zel'dovich-Thompson fluids
    • Cramer M.S., Tarkenton G.M. Transonic flows of Bethe-Zel'dovich-Thompson fluids. J. Fluid Mech. 1992, 240:197-228.
    • (1992) J. Fluid Mech. , vol.240 , pp. 197-228
    • Cramer, M.S.1    Tarkenton, G.M.2
  • 5
    • 0030835187 scopus 로고    scopus 로고
    • Supersonic flows of dense gases in cascade configurations
    • Monaco J.F., Cramer M.S., Watson L.T. Supersonic flows of dense gases in cascade configurations. J. Fluid Mech. 1997, 330:31-59.
    • (1997) J. Fluid Mech. , vol.330 , pp. 31-59
    • Monaco, J.F.1    Cramer, M.S.2    Watson, L.T.3
  • 6
    • 0034322917 scopus 로고    scopus 로고
    • Application of Bethe-Zel'dovich-Thompson fluids in organic Rankine cycles
    • Brown B.P., Argrow B.M. Application of Bethe-Zel'dovich-Thompson fluids in organic Rankine cycles. J. Propul. Power 2000, 16:1118-1124.
    • (2000) J. Propul. Power , vol.16 , pp. 1118-1124
    • Brown, B.P.1    Argrow, B.M.2
  • 7
    • 6044265048 scopus 로고    scopus 로고
    • Numerical studies of transonic BZT gas flows around thin airfoils
    • Wang C.W., Rusak Z. Numerical studies of transonic BZT gas flows around thin airfoils. J. Fluid Mech. 1999, 396:109-141.
    • (1999) J. Fluid Mech. , vol.396 , pp. 109-141
    • Wang, C.W.1    Rusak, Z.2
  • 8
    • 0021427871 scopus 로고
    • On the propagation of waves exhibiting both positive and negative nonlinearity
    • Cramer M.S., Kluwick A. On the propagation of waves exhibiting both positive and negative nonlinearity. J. Fluid Mech. 1984, 142:9-37.
    • (1984) J. Fluid Mech. , vol.142 , pp. 9-37
    • Cramer, M.S.1    Kluwick, A.2
  • 9
    • 34548163860 scopus 로고    scopus 로고
    • Inviscid and viscous aerodynamics of dense gases
    • Cinnella P., Congedo P.M. Inviscid and viscous aerodynamics of dense gases. J. Fluid Mech. 2007, 580:179-217.
    • (2007) J. Fluid Mech. , vol.580 , pp. 179-217
    • Cinnella, P.1    Congedo, P.M.2
  • 10
    • 40549125963 scopus 로고    scopus 로고
    • Admissibility region for rarefaction shock waves in dense gases
    • Zamfirescu C., Guardone A., Colonna P. Admissibility region for rarefaction shock waves in dense gases. J. Fluid Mech. 2008, 599:363-381.
    • (2008) J. Fluid Mech. , vol.599 , pp. 363-381
    • Zamfirescu, C.1    Guardone, A.2    Colonna, P.3
  • 11
    • 78649634271 scopus 로고    scopus 로고
    • http://www.turboden.eu/en/rankine.
  • 12
    • 30044445560 scopus 로고    scopus 로고
    • Non classical gasdynamic region of selected fluorocarbons
    • 17
    • Guardone A., Argrow B.M. Non classical gasdynamic region of selected fluorocarbons. Phys. Fluids 2005, 17. pp. 116102-116111, 17.
    • (2005) Phys. Fluids , vol.17 , pp. 116102-116111
    • Guardone, A.1    Argrow, B.M.2
  • 15
    • 54849417796 scopus 로고    scopus 로고
    • Structural optimization under uncertain loads and nodal locations
    • Guest J.K., Igusa T. Structural optimization under uncertain loads and nodal locations. Comput. Methods Appl. Mech. Engrg. 2008, 198:116-124.
    • (2008) Comput. Methods Appl. Mech. Engrg. , vol.198 , pp. 116-124
    • Guest, J.K.1    Igusa, T.2
  • 16
    • 69549126120 scopus 로고    scopus 로고
    • Confidence structural robust design and optimization under stiffness and load uncertainties
    • Guo X., Bai W., Zhang W., Gao X. Confidence structural robust design and optimization under stiffness and load uncertainties. Comput. Methods Appl. Mech. Engrg. 2009, 198:3378-3399.
    • (2009) Comput. Methods Appl. Mech. Engrg. , vol.198 , pp. 3378-3399
    • Guo, X.1    Bai, W.2    Zhang, W.3    Gao, X.4
  • 17
    • 34548800730 scopus 로고    scopus 로고
    • Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval
    • Jiang C., Han X., Liu G.R. Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval. Comput. Methods Appl. Mech. Engrg. 2007, 196:4791-4800.
    • (2007) Comput. Methods Appl. Mech. Engrg. , vol.196 , pp. 4791-4800
    • Jiang, C.1    Han, X.2    Liu, G.R.3
  • 18
    • 52749087968 scopus 로고    scopus 로고
    • A sequential nonlinear interval number programming method for uncertain structures
    • Jiang C., Han X., Liu G.P. A sequential nonlinear interval number programming method for uncertain structures. Comput. Methods Appl. Mech. Engrg. 2008, 197:4250-4265.
    • (2008) Comput. Methods Appl. Mech. Engrg. , vol.197 , pp. 4250-4265
    • Jiang, C.1    Han, X.2    Liu, G.P.3
  • 19
    • 13844314867 scopus 로고    scopus 로고
    • Robust design of non-linear structures using optimization methods
    • Doltsinis I., Kang Z., Cheng G. Robust design of non-linear structures using optimization methods. Comput. Methods Appl. Mech. Engrg. 2005, 194:1779-1795.
    • (2005) Comput. Methods Appl. Mech. Engrg. , vol.194 , pp. 1779-1795
    • Doltsinis, I.1    Kang, Z.2    Cheng, G.3
  • 20
    • 0036715119 scopus 로고    scopus 로고
    • Probabilistic approach to free-form airfoil shape optimization under uncertainty
    • Huyse L., Padula S.L., Michael Lewis R., Li Wu Probabilistic approach to free-form airfoil shape optimization under uncertainty. AIAA J. 2002, 40(9).
    • (2002) AIAA J. , vol.40 , Issue.9
    • Huyse, L.1    Padula, S.L.2    Michael Lewis, R.3    Li, W.4
  • 21
    • 78649634310 scopus 로고    scopus 로고
    • Environmental MDO and Uncertainty Hybrid Approach Applied to a Supersonic Business Jet, AIAA-5832.
    • Y. Deremaux, N. Pietremont, J. Négrier, E. Herbin, M. Ravachol, Environmental MDO and Uncertainty Hybrid Approach Applied to a Supersonic Business Jet, AIAA 2008-5832.
    • (2008)
    • Deremaux, Y.1    Pietremont, N.2    Négrier, J.3    Herbin, E.4    Ravachol, M.5
  • 22
    • 77957764111 scopus 로고    scopus 로고
    • Validation and minimizing CFD uncertainty for commercial aircraft applications, AIAA 2008-6902, in: 26th AIAA Applied Aerodynamics Conference, 18-21 August, Honolulu, Hawaii.
    • E.N. Tinoco, Validation and minimizing CFD uncertainty for commercial aircraft applications, AIAA 2008-6902, in: 26th AIAA Applied Aerodynamics Conference, 18-21 August 2008, Honolulu, Hawaii.
    • (2008)
    • Tinoco, E.N.1
  • 23
    • 36749026640 scopus 로고    scopus 로고
    • Approach to discrete optimization under uncertainty: The population-based sampling genetic algorithm
    • Hassan R., Crossley W. Approach to discrete optimization under uncertainty: The population-based sampling genetic algorithm. AIAA J. 2007, 45(11).
    • (2007) AIAA J. , vol.45 , Issue.11
    • Hassan, R.1    Crossley, W.2
  • 25
    • 63649131723 scopus 로고    scopus 로고
    • Stochastic optimization using a sparse grid collocation scheme
    • Sankaran Sethuraman Stochastic optimization using a sparse grid collocation scheme. Probab. Engrg. Mech. 2009, 24:382-396.
    • (2009) Probab. Engrg. Mech. , vol.24 , pp. 382-396
    • Sankaran, S.1
  • 27
    • 37349126727 scopus 로고    scopus 로고
    • Optimal airfoil shapes for viscous transonic flows of BZT fluids
    • Cinnella P., Congedo P.M. Optimal airfoil shapes for viscous transonic flows of BZT fluids. Comput. Fluids 2008, 37:250-264.
    • (2008) Comput. Fluids , vol.37 , pp. 250-264
    • Cinnella, P.1    Congedo, P.M.2
  • 28
    • 0000876320 scopus 로고
    • On upstream differencing and Godunov-type schemes for hyperbolic conservation laws
    • Harten A., Lax P.D., van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 1983, 25(1):35-61.
    • (1983) SIAM Rev. , vol.25 , Issue.1 , pp. 35-61
    • Harten, A.1    Lax, P.D.2    van Leer, B.3
  • 29
    • 0003122153 scopus 로고
    • Restoration of the contact surface in the HLL Riemann solver
    • Toro E.F., Spruce M., Speares W. Restoration of the contact surface in the HLL Riemann solver. Shock Waves 1994, 4(25):25-34.
    • (1994) Shock Waves , vol.4 , Issue.25 , pp. 25-34
    • Toro, E.F.1    Spruce, M.2    Speares, W.3
  • 30
    • 20444449776 scopus 로고    scopus 로고
    • Extension of Harten-Lax-van Leer scheme for flows at all speeds
    • Luo H., Baum J.D., Löhner R. Extension of Harten-Lax-van Leer scheme for flows at all speeds. AIAA J. 2005, 43(6):1160-1166.
    • (2005) AIAA J. , vol.43 , Issue.6 , pp. 1160-1166
    • Luo, H.1    Baum, J.D.2    Löhner, R.3
  • 32
    • 2442433925 scopus 로고
    • Toward the ultimate conservative difference scheme, 5: A second-order sequel to Godunov's method
    • Van Leer B. Toward the ultimate conservative difference scheme, 5: A second-order sequel to Godunov's method. J. Comput. Phys. 1979, 32(2):101-136.
    • (1979) J. Comput. Phys. , vol.32 , Issue.2 , pp. 101-136
    • Van Leer, B.1
  • 33
    • 78649636528 scopus 로고
    • The Design and Application of Upwind Schemes on Unstructured Meshes, AIAA Paper 89-0366
    • T.J. Barth, D.C. Jespersen, The Design and Application of Upwind Schemes on Unstructured Meshes, AIAA Paper 89-0366, 1989.
    • (1989)
    • Barth, T.J.1    Jespersen, D.C.2
  • 34
    • 0038115255 scopus 로고    scopus 로고
    • An upwind difference scheme for meshless solvers
    • Sridar D., Balakrishnan N. An upwind difference scheme for meshless solvers. J. Comput. Phys. 2003, 189(1):1-29.
    • (2003) J. Comput. Phys. , vol.189 , Issue.1 , pp. 1-29
    • Sridar, D.1    Balakrishnan, N.2
  • 35
    • 65049090410 scopus 로고    scopus 로고
    • A residual-based scheme for computing compressible flows on unstructured grids
    • Corre C., Du X. A residual-based scheme for computing compressible flows on unstructured grids. Comput. Fluids 2009, 38:1338-1347.
    • (2009) Comput. Fluids , vol.38 , pp. 1338-1347
    • Corre, C.1    Du, X.2
  • 36
    • 0040075637 scopus 로고
    • Convergence to steady-state solutions of the Euler equations on unstructured grids with limiters
    • Venkatakrishnan V. Convergence to steady-state solutions of the Euler equations on unstructured grids with limiters. J. Comput. Phys. 1995, 118(1):120-130.
    • (1995) J. Comput. Phys. , vol.118 , Issue.1 , pp. 120-130
    • Venkatakrishnan, V.1
  • 37
    • 0032209239 scopus 로고    scopus 로고
    • A fast matrix-free implicit method for compressible flows on unstructured grids
    • Luo H., Baum J., Löhner R. A fast matrix-free implicit method for compressible flows on unstructured grids. J. Comput. Phys. 1998, 146(2):664-690.
    • (1998) J. Comput. Phys. , vol.146 , Issue.2 , pp. 664-690
    • Luo, H.1    Baum, J.2    Löhner, R.3
  • 38
    • 0000942772 scopus 로고
    • An approximate linearised Riemann solver for the Euler equations for real gases
    • Glaister P. An approximate linearised Riemann solver for the Euler equations for real gases. J. Comput. Phys. 1988, 74:382-408.
    • (1988) J. Comput. Phys. , vol.74 , pp. 382-408
    • Glaister, P.1
  • 40
    • 0035838094 scopus 로고    scopus 로고
    • Direct numerical simulations of supercritical fluid mixing layers applied to heptane-nitrogen
    • Miller R.S., Harstad K.G., Bellan J. Direct numerical simulations of supercritical fluid mixing layers applied to heptane-nitrogen. J. Fluid Mech. 2001, 436:1-39.
    • (2001) J. Fluid Mech. , vol.436 , pp. 1-39
    • Miller, R.S.1    Harstad, K.G.2    Bellan, J.3
  • 41
    • 0036151494 scopus 로고    scopus 로고
    • Roe linearization for the van der Waals gas
    • Guardone A., Vigevano L. Roe linearization for the van der Waals gas. J. Comput. Phys. 2002, 175:50-78.
    • (2002) J. Comput. Phys. , vol.175 , pp. 50-78
    • Guardone, A.1    Vigevano, L.2
  • 42
    • 7644221431 scopus 로고    scopus 로고
    • Real gas effects in turbomachinery flows: A computational fluid dynamics model for fast computations
    • Boncinelli P., Rubechini F., Arnone A., Cecconi M., Cortese C. Real gas effects in turbomachinery flows: A computational fluid dynamics model for fast computations. ASME J. Turbomachinery 2004, 126:268-276.
    • (2004) ASME J. Turbomachinery , vol.126 , pp. 268-276
    • Boncinelli, P.1    Rubechini, F.2    Arnone, A.3    Cecconi, M.4    Cortese, C.5
  • 43
    • 28844442840 scopus 로고    scopus 로고
    • Numerical solver for dense gas flows
    • Cinnella P., Congedo P.M. Numerical solver for dense gas flows. AIAA J. 2005, 43(11):2457-2461.
    • (2005) AIAA J. , vol.43 , Issue.11 , pp. 2457-2461
    • Cinnella, P.1    Congedo, P.M.2
  • 44
    • 33750889613 scopus 로고    scopus 로고
    • The impact of gas modeling in the numerical analysis of a multistage gas turbine, in: Proceedings of ASME Turbo Expo, Barcelona, Spain, 8-11 May, ASME Paper GT2006-90129.
    • F. Rubechini, M. Marconcini, A. Arnone, M. Maritano, S. Cecchi, The impact of gas modeling in the numerical analysis of a multistage gas turbine, in: Proceedings of ASME Turbo Expo 2006, Barcelona, Spain, 8-11 May, ASME Paper GT2006-90129.
    • (2006)
    • Rubechini, F.1    Marconcini, M.2    Arnone, A.3    Maritano, M.4    Cecchi, S.5
  • 46
    • 0022699554 scopus 로고
    • An improved Peng-Robinson equation of state for pure compounds and mixtures
    • Stryjek R., Vera J.H. An improved Peng-Robinson equation of state for pure compounds and mixtures. Can. J. Chem. Engrg. 1986, 64:323-333.
    • (1986) Can. J. Chem. Engrg. , vol.64 , pp. 323-333
    • Stryjek, R.1    Vera, J.H.2
  • 47
    • 37549048679 scopus 로고    scopus 로고
    • Multiparameter equations of state for siloxanes: [(CH3)3-Si-O1/2]2-[O-Si-(CH3)2]i=1,...,3, and [O-Si-(CH3)2]6
    • Colonna P., Nannan N.R., Guardone A. Multiparameter equations of state for siloxanes: [(CH3)3-Si-O1/2]2-[O-Si-(CH3)2]i=1,...,3, and [O-Si-(CH3)2]6. Fluid Phase Equilibr. 2008, 263:115-130.
    • (2008) Fluid Phase Equilibr. , vol.263 , pp. 115-130
    • Colonna, P.1    Nannan, N.R.2    Guardone, A.3
  • 48
    • 70349198889 scopus 로고    scopus 로고
    • On the computation of the fundamental derivative of gas dynamics using equations of state
    • Colonna P., Nannan N.R., Guardone A., van der Stelt T.P. On the computation of the fundamental derivative of gas dynamics using equations of state. Fluid Phase Equilibr. 2009, 286:43-44.
    • (2009) Fluid Phase Equilibr. , vol.286 , pp. 43-44
    • Colonna, P.1    Nannan, N.R.2    Guardone, A.3    van der Stelt, T.P.4
  • 49
    • 0034342158 scopus 로고    scopus 로고
    • Low-drag airfoils for transonic flow of dense gases
    • Rusak Z., Wang C.W. Low-drag airfoils for transonic flow of dense gases. Z. Angew. Math. Phys. (ZAMP) 2000, 51(3):467-480.
    • (2000) Z. Angew. Math. Phys. (ZAMP) , vol.51 , Issue.3 , pp. 467-480
    • Rusak, Z.1    Wang, C.W.2
  • 51
    • 2542489292 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D., Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. J. Sci. Comput. 2002, 26.
    • (2002) J. Sci. Comput. , vol.26
    • Xiu, D.1    Karniadakis, G.E.2
  • 52
    • 0000148817 scopus 로고
    • The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals
    • Cameron R.H., Martin W.T. The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals. Ann. Math. 1947, 48:385.
    • (1947) Ann. Math. , vol.48 , pp. 385
    • Cameron, R.H.1    Martin, W.T.2
  • 54
    • 0242440688 scopus 로고    scopus 로고
    • Numerical Integration using sparse grids
    • Gerstner T., Griebel M. Numerical Integration using sparse grids. Numer. Algorithms 1998, (18):209-223.
    • (1998) Numer. Algorithms , Issue.18 , pp. 209-223
    • Gerstner, T.1    Griebel, M.2
  • 55
    • 78649633419 scopus 로고    scopus 로고
    • http://opus-project.fr.
  • 56
    • 78649634543 scopus 로고    scopus 로고
    • SmolPack - A software for Smolyaks quadrature with Clenshaw Curtis basic sequences
    • K. Petras, SmolPack - A software for Smolyaks quadrature with Clenshaw Curtis basic sequences, http://www.public.tu-bs.de:8000/~petras/software.html.
    • Petras, K.1
  • 58
    • 0000760143 scopus 로고
    • Sensitivity estimates for non linear mathematical models
    • Sobol I.M. Sensitivity estimates for non linear mathematical models. Math. Model. Comput. Exp. 1993, 1(4):407-414.
    • (1993) Math. Model. Comput. Exp. , vol.1 , Issue.4 , pp. 407-414
    • Sobol, I.M.1
  • 59
    • 0000852513 scopus 로고
    • Multiobjective function optimization using nondominated sorting genetic algorithms
    • Srinivas N., Deb K. Multiobjective function optimization using nondominated sorting genetic algorithms. Evol. Comput. 1995, 2(3):221-248.
    • (1995) Evol. Comput. , vol.2 , Issue.3 , pp. 221-248
    • Srinivas, N.1    Deb, K.2


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