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Multiple-Frequency Phase-Lagged Unsteady Simulations of Experimental Axial Compressor

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This paper presents an evaluation of the multiple-frequency phase-lagged approach, which enables the performance of unsteady Reynolds-averaged Navier–Stokes simulations on multistage turbomachinery configurations using a time-marching method. The major advantage of this approach is to reduce the computational domain to one single blade passage per row. The first part of the paper presents the method and discusses the associated assumptions and limitations. The method is then evaluated on the axial compressor configuration “Compresseur de Recherche pour l’Etude des effets Aérodynamiques et TEchnologiques” investigated experimentally at Laboratory of Fluid Mechanics and Acoustics. The computational fluid dynamics results are analyzed and compared both with experimental data and with a reference multipassage computation based on a sliding mesh approach. These comparisons enable the highlighting of the interests of this approach but also the underlining of its limits. The multiple-frequency phase-lagged approach enables the simulation of unsteady effects on a multistage turbomachinery and access to unsteady information that would not be available with a mixing-plane approach. However, if the method is capable of capturing unsteady effects linked to the adjacent upstream and downstream blade rows passing frequency, it fails modeling clocking effects, i.e., the relative influence between rows N and N+2.


  • [1] Giles M. B., “Calculation of Unsteady Wake/Rotor Interactions,” 25th Aerospace Sciences Meeting, AIAA Paper  1987-0006, Reno, NV, 1987. LinkGoogle Scholar

  • [2] Parker R., “Relation Between Blade Row Spacing and Potential Flow Interaction Effects in Turbomachines,” Proceedings of the Institution of Mechanical Engineers, AIAA Paper  1967-0068, 1967. Google Scholar

  • [3] Salvadori S., Martelli F., Adami P. and Castillon L., “Aero-Thermal Study of the Unsteady Flow Field in a Transonic Gas Turbine with Inlet Temperature Distortions,” Journal of Turbomachinery, Vol. 133, No. 3, 2011, Paper 031030. doi: JOTUEI 0889-504X CrossrefGoogle Scholar

  • [4] Paniagua G., Yasa T., De la Loma A., Castillon L. and Coton T., “Unsteady Strong Shock Interactions in a Transonic Turbine Experimental and Numerical Analysis,” Journal of Propulsion and Power, Vol. 24, No. 4, 2008, pp. 722–731. doi: JPPOEL 0748-4658 LinkGoogle Scholar

  • [5] Hodson H. P., “Bladerow Interactions in Low Pressure Turbines,” von Kármán Inst. for Fluid Dynamics, Lecture Series, Paper  1998-0002, Rhode-St-Genèse, Belgium, Feb. 1998. Google Scholar

  • [6] Denton J. D. and Singh U. K., “Time Marching Methods for Turbomachinery Flow Calculation: Application of Numerical Methods to Flow Calculations in Turbomachichines,” von Kármán Inst. for Fluid Dynamics, Lecture Series, Paper  1979-0007, Rhode-St-Genèse, Belgium, 1979. Google Scholar

  • [7] Gourdain N., Burguburu S., Michon G. J. and Leboeuf F., “Simulation of Rotating Stall in a Whole Stage of an Axial Compressor,” Computers and Fluids, Vol. 39, No. 9, 2010, pp. 1644–1655. doi: CPFLBI 0045-7930 CrossrefGoogle Scholar

  • [8] Erdos J. I., Alzner E. and McNally W., “Numerical Solution of Periodic Transonic Flow Through a Fan Stage,” AIAA Journal, Vol. 15, No. 11, 1977, pp. 1559–1568. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [9] Gerolymos G. A., Michon G. and Neubauer J., “Analysis and Application of Chorochronic Periodicity in Turbomachinery Rotor/Stator Interaction Computations,” Journal of Propulsion and Power, Vol. 18, No. 6, 2002, pp. 1139–1152.doi: JPPOEL 0748-4658 LinkGoogle Scholar

  • [10] Van Zante D., Chen J., Hathaway M. and Chris R., “The Influence of Compressor Blade Row Interaction Modeling on Performance Estimates from Time-Accurate, Multistage, Navier–Stokes Simulations,” Journal of Turbomachinery, Vol. 130, No. 1, 2008, pp. 011009-1–011009-10. doi: JOTUEI 0889-504X CrossrefGoogle Scholar

  • [11] He L., “Method of Simulating Unsteady Turbomachinery Flows with Multiple Perturbations,” AIAA Journal, Vol. 30, No. 11, Nov. 1992, pp. 2730–2735. AIAJAH 0001-1452 LinkGoogle Scholar

  • [12] Li H. D. and He L., “Single-Passage Analysis of Unsteady Flows Around Vibrating Blades of a Transonic Fan Under Inlet Distortion,” Journal of Turbomachinery, Vol. 124, No. 2, April 2002, pp. 285–292. doi: JOTUEI 0889-504X CrossrefGoogle Scholar

  • [13] Li H. D. and He L., “Toward Intra-Row Gap Optimization for One and Half Stage Transonic Compressor,” Journal of Turbomachinery, Vol. 127, No. 3, July 2005, pp. 589–598. doi: JOTUEI 0889-504X CrossrefGoogle Scholar

  • [14] Li H. D. and He L., “Blade Aerodynamic Damping Variation with Rotor-Stator Gap: A Computational Study Using Single-Passage Approach,” Journal of Turbomachinery, Vol. 127, No. 3, July 2005, pp. 573–579. doi: JOTUEI 0889-504X CrossrefGoogle Scholar

  • [15] Neubauer J., “Aerodynamique 3D Instationnaire des Turbomachines Axiales Multi-Etages,” Ph.D. Thesis, PARIS 6 University, Institut Jean Le Rond d'Alembert, 2004. Google Scholar

  • [16] Gerolymos G. A., “Filtered Chorochronic Interface as a Capability for 3-D Unsteady Throughflow Analysis of Multistage Turbomachinery,” International Journal of Computational Fluid Dynamics, Vol. 27, No. 2, 2013, pp. 100–117. doi: IJCFEC 1061-8562 CrossrefGoogle Scholar

  • [17] Castillon L., Evaluation of a Multiple Frequency Phase Lagged Method for Unsteady Numerical Simulations of Multistage Turbomachinery, International Council of the Aeronautical Science, Brisbane, Australia, Sept. 2012, pp. 1–12. Google Scholar

  • [18] He L., “Fourier Methods for Turbomachinery Applications,” Progress in Aerospace Sciences, Vol. 46, No. 8, June 2010, pp. 329–341, doi: PAESD6 0376-0421 CrossrefGoogle Scholar

  • [19] Sicot F., Guedeney T. and Dufour G., “Time-Domain Harmonic Balance Method for Aerodynamic and Aeroelastic Simulations of Turbomachinery Flows,” International Journal of Computational Fluid Dynamics, Vol. 27, No. 2, 2013, pp. 68–78. doi: IJCFEC 1061-8562 CrossrefGoogle Scholar

  • [20] Gopinath A. K., van der Weide E., Alonso J. J and Jameson A., “Three-Dimensional Unsteady Multi-Stage Turbomachinery Simulations Using the Harmonic Balance Technique,” 45th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper  2007-0892, Jan. 2007. LinkGoogle Scholar

  • [21] Vilmin S., Hirsch C., Lorrain E. and Swoboda M., “Unsteady Flow Modeling Across the Rotor/Stator Interface Using the Non Linear Harmonic Method,” American Soc. of Mechanical Engineers Turbo Expo, ASME Paper  GT2006-90210, May 2006, pp. 1227–1237. doi: Google Scholar

  • [22] Dufour G., Guedeney T. and Sicot F., “Multifrequential Harmonic Balance Computations for a Multistage Compressor,” 20th International Symposium on Air Breathing Engines, AIAA, Reston, VA, Sept. 2011, pp. 499–509; also AIAA Paper  2011-1227. Google Scholar

  • [23] Guedeney T., Gomar A., Gallard F., Sicot F., Dufour G. and Puigt G., “Non-Uniform Time Sampling for Multiple-Frequency Harmonic Balance Computations,” Journal of Computational Physics, Vol. 236, No. 1, 2013, pp. 317–345.doi: JCTPAH 0021-9991 CrossrefGoogle Scholar

  • [24] Tyler J. M. and Sofrin T. G., “Axial Flow Compressor Noise Studies,” Society of Automotive Engineers Transactions, Vol. 70, No. 1, 1962, pp. 309–332. Google Scholar

  • [25] Ottavy X., Courtiade N. and Gourdain N, “Experimental and Computational Methods for Flow Investigation in High-Speed Multistage Compressor,” Journal of Propulsion and Power, Vol. 28, No. 6, 2011, pp. 1141–1155.doi: JPPOEL 0748-4658 LinkGoogle Scholar

  • [26] Mersinligil M., Brouckaert J. F., Ottavy X. and Courtiade N., “A High Temperature High Bandwidth Fast Response Total Pressure Probe for Measurements in a Multistage Axial Compressor,” Journal of Engineering for Gas Turbines and Power, Vol. 134, No. 6, 2012, p. 134.doi: JETPEZ 0742-4795 CrossrefGoogle Scholar

  • [27] Goncalves E. and Houdeville R., “Reassessment of the Wall Functions Approach for RANS computations,” Aerospace Science and Technology, Vol. 5, No 1, 2001, pp. 1–14. doi: ARSTFZ 1270-9638 CrossrefGoogle Scholar

  • [28] Gourdain N., Ottavy X. and Vouillarmet A., “Experimental and Numerical Investigation of Unsteady Flows in a High-Speed Three Stages Compressor,” 8th European Turbomachinery Conference, von Kármán Inst. for Fluid Dynamics, Turbomachinery & Propulsion Dept., Rhode Saint Genèse, Belgium, 2009, pp. 247–266. Google Scholar

  • [29] Cambier L., Heib S. and Plot S., “The Onera elsA CFD Software: Input from Research and Feedback from Industry,” Mechanics and Industry, Vol. 14, No. 3, Jan. 2013, pp. 159–174. CrossrefGoogle Scholar

  • [30] Cambier L. and Veuillot J. P., “Status of the elsA CFD Software for Flow Simulation and Multidisciplinary Applications,” 48th AIAA Aerospace Science Meeting and Exhibit, AIAA Paper  2008-0664, 2008. LinkGoogle Scholar

  • [31] Roe P. L., “Approximate Riemann Solvers, Parameter Vectors and Difference Schemes,” Journal of Computational Physics, Vol. 43, No. 2, 1981, pp. 357–372. doi: JCTPAH 0021-9991 CrossrefGoogle Scholar

  • [32] Wilcox D. C., “Reassessment of the Scale-Determining Equation for Advanced Turbulence Models,” AIAA Journal, Vol. 26, No. 11, Nov. 1988, pp. 1299–1310.doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [33] Marty J. and Aupoix B., “Interaction of Shrouded Stator Flow and Main Flow and Its Influence on Performances of a Three-Stage High Pressure Compressor,” Journal of Power and Energy, Vol. 226, No. 4, June 2012, pp. 489–500. doi: CrossrefGoogle Scholar

  • [34] Courtiade N., Ottavy X. and Gourdain N., “Modal Decomposition for the Analysis of the Rotor-Stator Interactions in Multistage Compressors,” Journal of Thermal Science, Vol. 21, No. 3, May 2012, pp. 276–285. doi: CrossrefGoogle Scholar

  • [35] Placzek A. and Castillon L., “Aeroelastic Response of a Contrafan Stage Using Full Annulus and Single Passage Models,” Journal of Aeroelasticity and Structural Dynamics, Vol. 3, No. 2, 2014, pp. 1–30. doi: Google Scholar