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Computational Aerodynamics Methods

  • P. G. Tucker
Chapter
  • 3.6k Downloads
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 104)

Abstract

An overview of the various unsteady modelling hierarchies in aerospace is given ranging from linear harmonic to direct numerical simulation. Unsteady reduced order modelling encompassing deterministic stresses and body forces are discussed. Hierarchies are presented for different modelling lineages and fidelity levels. Mixed fidelity methods are proposed, where low and high fidelity treatments are combined. For example, URANS being combined with body forces to provide appropriate system boundary conditions. This concept is extended further in later chapters. For URANS, the occurrence of a spectral gap in many turbomachinery zones is found to be uncertain. The wide range of other aspects needed to model aeronautical flows and their limitations is discussed.

Keywords

Deterministic stresses Body forces Harmonic balance Non-linear harmonic Phase lagged boundary conditions Sliding planes 

References

  1. J.J. Adamczyk, Model equation for simulating flows in multistage turbomachinery, in ASME, 30th International Gas Turbine Conference and Exhibit, Houston, Texas (1985). ASME Paper No. 85-GT-226 Google Scholar
  2. F. Bardoux, F. Leboeuf, Impact of deterministic correlations on the steady flow field. Proc. Inst. Mech. Eng. A, J. Power Energy 215(6), 687–698 (2001) CrossRefGoogle Scholar
  3. F. Bardoux, F. Leboeuf, C. Dano, C. Toussaint, Characterization of deterministic correlations for turbine stage. Part 1: time average flow analysis, in ASME (1999). ASME Paper No. 99–GT–100 Google Scholar
  4. R.M. Benning, T.M. Becker, A. Delgado, Initial studies of predicting flow fields with an ANN hybrid. Adv. Eng. Softw. 32(12), pp. 895–901 (2001) zbMATHCrossRefGoogle Scholar
  5. T. Biesinger, C. Cornelius, C. Rube, A. Braune, R. Campregher, P.G. Godin, G. Schmid, L. Zori, Unsteady CFD methods in a commercial solver for turbomachinery applications, in ASME Conference Proceedings (2010), 2441–2452. ASME Paper No. GT2010-22762 Google Scholar
  6. R. Blumenthal, B. Hutchinson, L. Zori, Investigation of transient CFD methods applied to a transonic compressor stage, in Proceedings of the ASME Turbo Expo. 2011: Power for Land, Sea and Air, GT2011, Vancouver, BC, Canada, 6–11 June 2011. ASME Paper No. GT2011–46635 Google Scholar
  7. J. Busby, D. Sondak, B. Staubach, R. Davis, Deterministic stress modeling of hot gas segregation in a turbine. J. Turbomach. 122(1), 62–67 (2000) CrossRefGoogle Scholar
  8. M.S. Campobasso, M.H. Baba-Ahmadi, Analysis of unsteady flows past horizontal axis wind turbine airfoils based on harmonic balance compressible Navier-Stokes equations with low-speed preconditioning (2011). ASME Paper No. GT2011-45303 Google Scholar
  9. D. Charbonnier, F. Leboeuf, Development of a model for the deterministic stresses in a transonic turbine stage, in 5th European Conference on Turbomachinery, Prague (2003) Google Scholar
  10. D. Charbonnier, F. Leboeuf, Steady flow simulation of rotor-stator interactions with an unsteady deterministic model, in Proceedings of the 6th European Conference on Turbomachinery, Lille (2005). Paper No. 033–05/151 Google Scholar
  11. D. Coles, A.J. Wadcock, Flying-hot-wire study of flow past an NACA 4412 airfoil at maximum lift. AIAA J. 17, 321–329 (1979) CrossRefGoogle Scholar
  12. Y. Colin, B. Aupoix, J. Boussuge, P. Chanez, Numerical simulation of the distortion generated by crosswind inlet flows, in Proceedings of the 18th ISABE Conference, Beijing, China (2007). Paper No. ISABE-2007-1210 Google Scholar
  13. S. Connell, M. Braaten, L. Zori, R. Steed, B. Hutchinson, G. Cox, A comparison of advanced numerical techniques to model transient flow in turbomachinery blade rows, in Proceedings of the ASME Turbo Expo 2011: Power for Land, Sea and Air, GT2011, Vancouver, BC, Canada, 6–11 June 2011. ASME Paper No. GT2011-45820 Google Scholar
  14. R. Corral, J. Crespo, Development of an edge-based harmonic balance method for turbomachinery flows, in Proceedings of the ASME Turbo Expo 2011: Power for Land, Sea and Air, GT2011, Vancouver, BC, Canada, 6–11 June 2011. ASME Paper No. GT2011–41570 Google Scholar
  15. J.D. Coull, Wake induced transition in low pressure turbines. PhD thesis, Department of Engineering, The University of Cambridge (2009) Google Scholar
  16. C.H. Custer, J.M. Weiss, V. Subramanian, W.S. Clark, K.C. Hall, Unsteady simulation of a 1.5 stage turbine using an implicitly coupled nonlinear harmonic balance method, in Proceedings of ASME Turbo Expo 2012 GT2012, Copenhagen, Denmark, 11–15 June 2012. ASME Paper No. GT2012–69690 Google Scholar
  17. S. Deck, P. Spalart, P. Sagaut, J. Forsythe, K.D. Squires, Numerical simulation of transonic buffet over a supercritical airfoil. AIAA J. 43(7), 1556–1566 (2005) CrossRefGoogle Scholar
  18. J.J. Defoe, Z.S. Spakovszky, Effects of boundary layer ingestion on the aero-acoustics of transonic fan rotors, in Proceedings of ASME Turbo Expo 2012 GT2012, Copenhagen, Denmark, 11–15 June 2012. ASME Paper No. GT2012–68503 Google Scholar
  19. J. Defoe, A. Narkaj, Z.S. Spakovszky, A novel MPT noise prediction methodology for highly-integrated propulsion systems with inlet flow distortion, in 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), Miami, Florida, 11–13 May 2009. Paper No. AIAA 2009–3366 Google Scholar
  20. J.D. Denton, The calculation of three-dimensional viscous flow through multistage turbomachines. J. Turbomach. 114(1), 18–26 (1992) CrossRefGoogle Scholar
  21. K. Dullenkopf, R.E. Mayle, An account of free-stream-turbulence length scale on laminar heat transfer. J. Turbomach. 117(3), 401–406 (1995) CrossRefGoogle Scholar
  22. J.I. Erdos, E. Alzner, W. Mcnally, Numerical solution of periodic transonic flow through a fan stage, in American Institute of Aeronautics and Astronautics, 9th Fluid and Plasma Dynamics Conference, San Diego, California (1976). AIAA Paper No. AIAA 76-369 Google Scholar
  23. G. Fritsch, M. Giles, Second-order effects of unsteadiness on the performance of turbomachines, in 37th International Gas Turbine and Aeroengine Congress and Exposition (1992). ASME Paper No. 92–GT–389 Google Scholar
  24. P.F. Galpin, R.B. Broberg, B.R. Hutchinson, Three-dimensional Navier-Stokes predictions of steady state rotor/stator interaction with pitch change, in Proceedings of 3rd Annual Conference of the CFD Society of Canada (1995) Google Scholar
  25. A. Gangwar, B. Lukovic, P. Orkwis, B. Sekar, Modeling unsteadiness in steady cavity simulations, Part I: parametric solutions, in 39th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada (2001). Paper No. AIAA–2001–0153 Google Scholar
  26. E. Garnier, S. Deck, Large-eddy simulation of transonic buffet over a supercritical airfoil, in Direct and Large Eddy Simulation VII ERCOFTAC Series 12, ed. by V. Aemenio et al. (2008). doi: 10.1007/978-90-481-3652-0-81 Google Scholar
  27. G.A. Gerolymos, G.J. Michon, J. Neubauer, Analysis and application of chorochronic periodicity in turbomachinery rotor/stator interaction computations. J. Propuls. Power 18(6), 1139–1152 (2002) CrossRefGoogle Scholar
  28. M.B. Giles, Calculation of unsteady wake/rotor interaction. J. Propuls. Power 4(4), 356–362 (1988) CrossRefGoogle Scholar
  29. M. Giles, UNSFLO: A numerical method for the calculation of unsteady flow in turbomachinery. Gas Turbine Laboratory, Massachusetts Institute of Technology (1991) Google Scholar
  30. M.B. Giles, An approach for multi-stage calculations incorporating unsteadiness. ASME Paper No. 92-GT-282 (1992) Google Scholar
  31. Y. Gong, A computational model for rotating stall and inlet distortions in multistage compressors. PhD thesis, Massachusetts Institute of Technology (1999) Google Scholar
  32. A. Gopinath, E. Van Der Weide, J.J. Alonso, A. Jameson, K. Ekici, K.C. Hall, Three-dimensional unsteady multi-stage turbomachinery simulations using the harmonic balance technique. AIAA Pap. 892, 2007 (2007) Google Scholar
  33. N. Gourdain, S. Burguburu, F. Leboeuf, H. Miton, Numerical simulation of rotating stall in a subsonic compressor. Aerosp. Sci. Technol. 10(1), 9–18 (2006) CrossRefGoogle Scholar
  34. N. Gourdain, S. Burguburu, F. Leboeuf, G.J. Michon, Simulation of rotating stall in a whole stage of an axial compressor. Comput. Fluids 39(9), 1644–1655 (2010) zbMATHCrossRefGoogle Scholar
  35. E.J. Hall, Aerodynamic modelling of multistage compressor flow fields. Part 2: modelling deterministic stresses. J. Aerosp. Eng. 212(2), 91–107 (1998) Google Scholar
  36. K.C. Hall, J.P. Thomas, W.S. Clark, Computation of unsteady nonlinear flows in cascades using a harmonic balance technique. AIAA J. 40(5), 879–886 (2002) CrossRefGoogle Scholar
  37. L. He, Harmonic solution of unsteady flow around blades with separation. AIAA J. 46(6), 1299–1307 (2008) CrossRefGoogle Scholar
  38. L. He, Fourier methods for turbomachinery applications. Prog. Aerosp. Sci. 46(8), 329–341 (2010) CrossRefGoogle Scholar
  39. L. He, Efficient computational model for nonaxisymmetric flow and heat transfer in rotating cavity. J Turbomach. 133(2) (2011) Google Scholar
  40. L. He, W. Ning, Efficient approach for analysis of unsteady viscous flows in turbomachines. AIAA J. 36(11), 2005–2012 (1998) CrossRefGoogle Scholar
  41. L. He, D.X. Wang, Concurrent blade aerodynamic-aero-elastic design optimization using adjoint method. J. Turbomach. 133(1) (2011) Google Scholar
  42. C.M. Ho, P. Huerre, Perturbed free shear layers. Annu. Rev. Fluid Mech. 16(1), 365–422 (1984) CrossRefGoogle Scholar
  43. A.R. Howell, The present basis of axial flow compressor design: Part I—cascade theory and performance. Aeronautical Research Council R and M 2095 (1942) Google Scholar
  44. J.C.R. Hunt, A theory of turbulent flow round two-dimensional bluff bodies. J. Fluid Mech. 61(4), 625–706 (1973) MathSciNetzbMATHCrossRefGoogle Scholar
  45. R.J. Jefferson-Loveday, P.G. Tucker, V. Nagabhushana Rao, J.D. Northall, Differential equation specification of integral turbulence length scales, in Proceedings of ASME Turbo Expo 2012 GT2012, Copenhagen, Denmark, 11–15 June 2012. ASME Paper No. GT2012–68091 Google Scholar
  46. P. Kulisa, F. Leboeuf, G. Perrin, Computation of a wall boundary layer with discrete jet injections. J. Turbomach. 114, 756–764 (1992) CrossRefGoogle Scholar
  47. E. Labourasse, P. Sagaut, Reconstruction of turbulent fluctuations using a hybrid RANS/LES approach. J. Comput. Phys. 182(1), 301–336 (2002) zbMATHCrossRefGoogle Scholar
  48. L. Lapworth, HYDRA CFD: a framework for collaborative CFD development, in International Conference on Scientific and Engineering Computation (IC-SEC), Singapore (2004) Google Scholar
  49. S. Lardeau, M.A. Leschziner, Unsteady RANS modelling of wake–blade interaction: computational requirements and limitations. Comput. Fluids 34(1), 3–21 (2005) zbMATHCrossRefGoogle Scholar
  50. B.H.K. Lee, Transonic buffet on a supercritical airfoil. Aeronaut. J. 94(935), 143–152 (1990) Google Scholar
  51. M.G. List, S.E. Gorrell, M.G. Turner, Investigation of loss generation in an embedded transonic fan at several gaps using high-fidelity, time accurate CFD, in Proceedings of the ASME Turbo Expo Power for Land, Sea and Air (2008). ASME Paper No. GT-2008–51220 Google Scholar
  52. K. Lodefier, E. Dick, Modelling of unsteady transition in low-pressure turbine blade flows with two dynamic intermittency equations. Flow Turbul. Combust. 76(2), 103–132 (2006) zbMATHCrossRefGoogle Scholar
  53. S. Loiodice, P.G. Tucker, J. Watson, Coupled open rotor engine intake simulations, in Proceedings of the 48th AIAA Aerospace Sciences Meeting and Exhibit, Orlando, Florida (2010). Paper No. AIAA-2010-840 Google Scholar
  54. J.P. Longley, Calculating the flowfield behaviour of high-speed multi-stage compressors, in International Gas Turbine and Aeroengine Congress and Exhibition, (1997). ASME Paper No. 97–GT–468 Google Scholar
  55. B. Lukovic, Modeling unsteadiness in steady simulations with neural network generated lumped deterministic source terms. PhD thesis, Department of Aerospace Engineering, University of Cincinnati (2002) Google Scholar
  56. B. Lukovic, A. Gangwar, P. Orkwis, B. Sekar, Modeling unsteadiness in steady cavity simulations, Part II: neural network modeling, in 39th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada (2001). Paper No. AIAA–2001–0154 Google Scholar
  57. B. Lukovic, P. Orkwis, M. Turner, Modeling unsteady cavity flows with translating walls, in 32nd AIAA Fluid Dynamics Conference and Exhibit, Missouri (2002a). Paper No. AIAA 2002–3288 Google Scholar
  58. B. Lukovic, P. Orkwis, M. Turner, B. Sekar, Effect of cavity L/D variations on neural network-based deterministic unsteadiness source terms, in AIAA Aerospace Sciences Meeting & Exhibit, 40th, Reno, NV (2002b). AIAA Paper No. AIAA 2002–0857 Google Scholar
  59. V.P. Maslov, B.I. Mineev, K.N. Pichkov, A.N. Secundov, A.N. Vorobiev, M.K. Strelets, A.K. Travin, Turbulence intensity, length scale, and heat transfer around stagnation line of cylinder and model blade, in ASME, International Gas Turbine and Aeroengine Congress and Exhibition, Indianapolis (1999). ASME Paper No. 99-GT-423 Google Scholar
  60. M. McMullen, A. Jameson, J. Alonso, Demonstration of nonlinear frequency domain methods. AIAA J. 44(7), 1428–1435 (2006) CrossRefGoogle Scholar
  61. C. Meneveau, J. Katz, A deterministic stress model for rotor-stator interactions in simulations of average-passage flow. J. Fluids Eng. Trans. ASME 124(2), 550–554 (2002) CrossRefGoogle Scholar
  62. V. Michelassi, J.G. Wissink, J. Fröhlich, W. Rodi, Large-eddy simulation of flow around low-pressure turbine blade with incoming wakes. AIAA J. 41(11), 2143–2156 (2003a) CrossRefGoogle Scholar
  63. V. Michelassi, J.G. Wissink, W. Rodi, Direct numerical simulation, large eddy simulation and unsteady Reynolds-averaged Navier-Stokes simulations of periodic unsteady flow in a low-pressure turbine cascade: a comparison. Proc. Inst. Mech. Eng. A, J. Power Energy 217(4), 403–411 (2003b) CrossRefGoogle Scholar
  64. R. Mittal, S. Venkatasubramanian, F.M. Najjar, Large-eddy simulation of flow through a low-pressure turbine cascade. AIAA Pap. 2001–2560 (2001) Google Scholar
  65. F. Montomoli, H.P. Hodson, L. Lapworth, RANS–URANS in axial compressor, a design methodology. Proc. Inst. Mech. Eng. A, J. Power Energy 225(3), 363–374 (2011) CrossRefGoogle Scholar
  66. A. Mosahebi, S.K. Nadarajah, An implicit adaptive non-linear frequency domain method (pNLFD) for viscous periodic steady state flows on deformable grids, in 49th Aerospace Sciences Meeting, Orlando, Florida, January 2011. Paper No. AIAA 2011-0775 Google Scholar
  67. V.W. Nee, L.S.G. Kovasznay, Simple phenomenological theory of turbulent shear flows. Phys. Fluids 12, 473 (1969) zbMATHCrossRefGoogle Scholar
  68. W.E.I. Ning, L. He, Some modeling issues on trailing-edge vortex shedding. AIAA J. 39(5), 787–793 (2001) CrossRefGoogle Scholar
  69. D. Nürnberger, H. Greza, Numerical investigation of unsteady transitional flows in turbomachinery components based on a RANS approach. Flow Turbul. Combust. 69(3), 331–353 (2002) zbMATHCrossRefGoogle Scholar
  70. M. Olausson, Turbomachinery Aeroacoustic Calculations using Nonlinear Methods. PhD thesis, Chalmers University of Technology (2011) Google Scholar
  71. T.S.D. O’Mahoney, Large-eddy simulation of turbine rim seals. PhD thesis, University of Surrey (2011) Google Scholar
  72. P.D. Orkwis, M.G. Turner, J.W. Barter, Linear deterministic source terms for hot streak simulations. J. Propuls. Power 18(2), 383–389 (2002) CrossRefGoogle Scholar
  73. A. Pinelli, I.Z. Naqavi, U. Piomelli, J. Favier, Immersed-boundary methods for general finite-difference and finite-volume Navier-Stokes solvers. J. Comput. Phys. 229(24), 9073–9091 (2010) MathSciNetzbMATHCrossRefGoogle Scholar
  74. B. Raverdy, I. Mary, P. Sagaut, N. Liamis, High-resolution large-eddy simulation of flow around low-pressure turbine blade. AIAA J. 41(3), 390–397 (2003) CrossRefGoogle Scholar
  75. C.M. Rhie, A.J. Gleixner, D.A. Spear, C.J. Fischberg, R.M. Zacharias, Development and application of a multistage Navier-Stokes solver: Part I-multistage modeling using bodyforces and deterministic stresses. J. Turbomach. 120(2), 205–214 (1998) CrossRefGoogle Scholar
  76. M.J. Shaw, P. Hield, P.G. Tucker, The effect of inlet guide vanes on inlet flow distortion transfer and transonic fan stability, in Proceedings of the ASME Turbo Expo 2013 (2013). ASME Paper No. GT2013–94998 Google Scholar
  77. C.H. Sieverding, D. Ottolia, C. Bagnera, A. Comadoro, J.F. Brouckaert, J.M. Desse, Unsteady turbine blade wake characteristics. J. Turbomach. 126(4), 551–559 (2004) CrossRefGoogle Scholar
  78. D.L. Sondak, D.J. Dorney, R.L. Davis, Modeling turbomachinery unsteadiness with lumped deterministic stresses, in 32nd AIAA, ASME, SAE, and ASEE, Joint Propulsion Conference and Exhibit Lake Buena Vista, FL (1996) Google Scholar
  79. S. Stollenwerk, E. Kugeler, Unsteady flow modelling using deterministic flux terms, in ETC 2011, 9th European Turbomachinery Conference, vol. 161, Istanbul, Turkey, 21–25 March 2011 Google Scholar
  80. Y.B. Suzen, P.G. Huang, Numerical simulation of unsteady wake/blade interactions in low-pressure turbine flows using an intermittency transport equation. J. Turbomach. 127(3), 431–444 (2005) CrossRefGoogle Scholar
  81. C.K.W. Tam, Excitation of instability waves in a two-dimensional shear layer by sound. J. Fluid Mech. 89(2), 357–371 (1978) MathSciNetzbMATHCrossRefGoogle Scholar
  82. P.G. Tucker, Computation of Unsteady Internal Flows: Fundamental Methods with Case Studies (Kluwer Academic, Dordrecht, 2001) CrossRefGoogle Scholar
  83. P.G. Tucker, Computation of unsteady turbomachinery flows: Part 1—progress and challenges. Prog. Aerosp. Sci. 47(7), 522–545 (2011) CrossRefGoogle Scholar
  84. D. Van Zante, J. Chen, M. Hathaway, R. Chriss, The influence of compressor blade row interaction modeling on performance estimates from time-accurate, multistage, Navier-Stokes simulations. J. Turbomach. 130(1), 11009 (2008) CrossRefGoogle Scholar
  85. H.P. Wang, R.J. Goldstein, S.J. Olson, Effect of high free-stream turbulence with large length scale on blade heat/mass transfer. J. Turbomach. 121(2), 217–224 (1999) CrossRefGoogle Scholar
  86. J.M. Weiss, V. Subramanian, K.C. Hall, Simulation of unsteady turbomachinery flows using an implicitly coupled nonlinear harmonic balance method, in Proceedings of the ASME Turbo Expo 2011: Power for Land, Sea and Air, GT2011, Vancouver, BC, Canada, 1–11 June 2011. ASME Paper No. GT2011-46367 Google Scholar
  87. L. Xu, Assessing viscous body forces for unsteady calculations. J. Turbomach. 125(3), 425–432 (2003) CrossRefGoogle Scholar
  88. L. Xu, T.P. Hynes, J.D. Denton, Towards long length scale unsteady modelling in turbomachines. Proc. Inst. Mech. Eng. A, J. Power Energy 217(1), 75–82 (2003) CrossRefGoogle Scholar
  89. H. Yang, T. Roeber, D. Kozulovic, Hybrid-grid simulation of unsteady wake-boundary layer interaction on a high lift low pressure turbine airfoil, in Proceedings of GT2007 ASME Turbo Expo Power for Land, Sea and Air, Montreal, Canada, 14–17 May 2007. ASME Paper No. GT2007–28111 Google Scholar
  90. J. Yao, S.E. Gorrell, A.R. Wadia, High-fidelity numerical analysis of per-rev-type inlet distortion transfer in multistage fans: Part I—simulations with selected blade rows, in ASME Turbo Expo 2008: Power for Land, Sea, and Air (GT2008), Berlin, Germany, 9–13 June 2008. ASME No. GT2008-50812 Google Scholar
  91. A. Zachariadis, C.A. Hall, Application of a Navier-Stokes solver to the study of open rotor aerodynamics. J. Turbomach. 133(3) (2011) Google Scholar

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Authors and Affiliations

  • P. G. Tucker
    • 1
  1. 1.Department of Engineering, Whittle LaboratoryUniversity of CambridgeCambridgeUK

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