Skip to main content
SpringerLink
Log in

Computational Aerodynamics Methods

  • Chapter
Unsteady Computational Fluid Dynamics in Aeronautics

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 104))

  • 4130 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • 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 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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)

    Article  MATH  Google Scholar 

  • 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 

  • 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 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • J.D. Coull, Wake induced transition in low pressure turbines. PhD thesis, Department of Engineering, The University of Cambridge (2009)

    Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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 

  • J.D. Denton, The calculation of three-dimensional viscous flow through multistage turbomachines. J. Turbomach. 114(1), 18–26 (1992)

    Article  Google Scholar 

  • K. Dullenkopf, R.E. Mayle, An account of free-stream-turbulence length scale on laminar heat transfer. J. Turbomach. 117(3), 401–406 (1995)

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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)

    Article  Google Scholar 

  • M.B. Giles, Calculation of unsteady wake/rotor interaction. J. Propuls. Power 4(4), 356–362 (1988)

    Article  Google Scholar 

  • M. Giles, UNSFLO: A numerical method for the calculation of unsteady flow in turbomachinery. Gas Turbine Laboratory, Massachusetts Institute of Technology (1991)

    Google Scholar 

  • M.B. Giles, An approach for multi-stage calculations incorporating unsteadiness. ASME Paper No. 92-GT-282 (1992)

    Google Scholar 

  • Y. Gong, A computational model for rotating stall and inlet distortions in multistage compressors. PhD thesis, Massachusetts Institute of Technology (1999)

    Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • L. He, Harmonic solution of unsteady flow around blades with separation. AIAA J. 46(6), 1299–1307 (2008)

    Article  Google Scholar 

  • L. He, Fourier methods for turbomachinery applications. Prog. Aerosp. Sci. 46(8), 329–341 (2010)

    Article  Google Scholar 

  • L. He, Efficient computational model for nonaxisymmetric flow and heat transfer in rotating cavity. J Turbomach. 133(2) (2011)

    Google Scholar 

  • L. He, W. Ning, Efficient approach for analysis of unsteady viscous flows in turbomachines. AIAA J. 36(11), 2005–2012 (1998)

    Article  Google Scholar 

  • L. He, D.X. Wang, Concurrent blade aerodynamic-aero-elastic design optimization using adjoint method. J. Turbomach. 133(1) (2011)

    Google Scholar 

  • C.M. Ho, P. Huerre, Perturbed free shear layers. Annu. Rev. Fluid Mech. 16(1), 365–422 (1984)

    Article  Google Scholar 

  • 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 

  • J.C.R. Hunt, A theory of turbulent flow round two-dimensional bluff bodies. J. Fluid Mech. 61(4), 625–706 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

  • P. Kulisa, F. Leboeuf, G. Perrin, Computation of a wall boundary layer with discrete jet injections. J. Turbomach. 114, 756–764 (1992)

    Article  Google Scholar 

  • E. Labourasse, P. Sagaut, Reconstruction of turbulent fluctuations using a hybrid RANS/LES approach. J. Comput. Phys. 182(1), 301–336 (2002)

    Article  MATH  Google Scholar 

  • L. Lapworth, HYDRA CFD: a framework for collaborative CFD development, in International Conference on Scientific and Engineering Computation (IC-SEC), Singapore (2004)

    Google Scholar 

  • S. Lardeau, M.A. Leschziner, Unsteady RANS modelling of wake–blade interaction: computational requirements and limitations. Comput. Fluids 34(1), 3–21 (2005)

    Article  MATH  Google Scholar 

  • B.H.K. Lee, Transonic buffet on a supercritical airfoil. Aeronaut. J. 94(935), 143–152 (1990)

    Google Scholar 

  • 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 

  • 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)

    Article  MATH  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • M. McMullen, A. Jameson, J. Alonso, Demonstration of nonlinear frequency domain methods. AIAA J. 44(7), 1428–1435 (2006)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • 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 

  • V.W. Nee, L.S.G. Kovasznay, Simple phenomenological theory of turbulent shear flows. Phys. Fluids 12, 473 (1969)

    Article  MATH  Google Scholar 

  • W.E.I. Ning, L. He, Some modeling issues on trailing-edge vortex shedding. AIAA J. 39(5), 787–793 (2001)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • M. Olausson, Turbomachinery Aeroacoustic Calculations using Nonlinear Methods. PhD thesis, Chalmers University of Technology (2011)

    Google Scholar 

  • T.S.D. O’Mahoney, Large-eddy simulation of turbine rim seals. PhD thesis, University of Surrey (2011)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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 

  • 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)

    Article  Google Scholar 

  • C.K.W. Tam, Excitation of instability waves in a two-dimensional shear layer by sound. J. Fluid Mech. 89(2), 357–371 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  • P.G. Tucker, Computation of Unsteady Internal Flows: Fundamental Methods with Case Studies (Kluwer Academic, Dordrecht, 2001)

    Book  Google Scholar 

  • P.G. Tucker, Computation of unsteady turbomachinery flows: Part 1—progress and challenges. Prog. Aerosp. Sci. 47(7), 522–545 (2011)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

  • L. Xu, Assessing viscous body forces for unsteady calculations. J. Turbomach. 125(3), 425–432 (2003)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering, Whittle Laboratory, University of Cambridge, Cambridge, UK

    P. G. Tucker

Authors
  1. P. G. Tucker
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Tucker, P.G. (2014). Computational Aerodynamics Methods. In: Unsteady Computational Fluid Dynamics in Aeronautics. Fluid Mechanics and Its Applications, vol 104. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7049-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-7049-2_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-7048-5

  • Online ISBN: 978-94-007-7049-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation