Computational Mechanics

, Volume 50, Issue 6, pp 695–705

Computational analysis of noise reduction devices in axial fans with stabilized finite element formulations

  • A. Corsini
  • F. Rispoli
  • A. G. Sheard
  • T. E. Tezduyar
Original Paper


The paper illustrates how a computational fluid mechanic technique, based on stabilized finite element formulations, can be used in analysis of noise reduction devices in axial fans. Among the noise control alternatives, the study focuses on the use of end-plates fitted at the blade tips to control the leakage flow and the related aeroacoustic sources. The end-plate shape is configured to govern the momentum transfer to the swirling flow at the blade tip. This flow control mechanism has been found to have a positive link to the fan aeroacoustics. The complex physics of the swirling flow at the tip, developing under the influence of the end-plate, is governed by the rolling up of the jet-like leakage flow. The RANS modelling used in the computations is based on the streamline-upwind/Petrov–Galerkin and pressure-stabilizing/Petrov–Galerkin methods, supplemented with the DRDJ stabilization. Judicious determination of the stabilization parameters involved is also a part of our computational technique and is described for each component of the stabilized formulation. We describe the flow physics underlying the design of the noise control device and illustrate the aerodynamic performance. Then we investigate the numerical performance of the formulation by analysing the inner workings of the stabilization operators and of their interaction with the turbulence model.


Numerical methods Anisotropic Finite element 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Fukano T, Jang C (2004) Tip clearance noise of axial flow fans operating at design and off-design condition. J Sound Vibr 275: 1027–1050CrossRefGoogle Scholar
  2. 2.
    Jang C, Fukano T, Furukawa M (2003) Effects of the tip clearance on vortical flow and its relation to noise in an axial flow fan. JSME Trans B 46: 356–365Google Scholar
  3. 3.
    Quinlan AD, Bent PH (1998) High frequency noise generation in small axial flow fans. J Sound Vibr 218: 177–204CrossRefGoogle Scholar
  4. 4.
    Takata H, Tsukuda Y (1977) Stall margin improvement by casing treatment—its mechanism and effectiveness. J Eng Power 99: 121–133CrossRefGoogle Scholar
  5. 5.
    Smith GDJ, Cumpsty NA (1984) Flow phenomena in compressor casing treatment. J Eng Gas Turbines Power 106: 532–541CrossRefGoogle Scholar
  6. 6.
    Thompson DW, King PI, Rabe DC (1998) Experimental and computational investigation on stepped tip gap effects on the flowfield of a transonic axial-flow compressor rotor. J Turbomach 120: 477–486CrossRefGoogle Scholar
  7. 7.
    Jensen CE (1986) Axial-flow fan. US Patent No. 4,630,993Google Scholar
  8. 8.
    Wadia AR, Szucs PN, Crall DW (1998) Inner workings of aerodynamic sweep. J Turbomach 120: 671–682CrossRefGoogle Scholar
  9. 9.
    Corsini A, Rispoli F (2004) Using sweep to extend stall-free operational range in sub-sonic axial fan rotors. J Power Energy 218: 129–139CrossRefGoogle Scholar
  10. 10.
    Longet CML (2003) Axial flow fan with noise reducing means. US Patent 2003/0123987 A1Google Scholar
  11. 11.
    Mimura M (2003) Axial flow fan. US Patent 6,648,598 B2Google Scholar
  12. 12.
    Uselton RB, Cook LJ, Wright T (2005) Fan with reduced noise generation. US Patent 2005/0147496 A1Google Scholar
  13. 13.
    Corsini A, Sheard AG (2007) Tip end-plate concept based on leakage vortex rotation number control. J Comput Appl Mech 8/1: 21–37Google Scholar
  14. 14.
    Corsini A, Rispoli F, Sheard AG (2007) Development of improved blade tip end-plate concepts for low-noise operation in industrial fans. J Power Energy 221(5): 669–681CrossRefGoogle Scholar
  15. 15.
    Corsini A, Rispoli F, Sheard AG (2010) Shaping of tip end-plate to control leakage vortex swirl in axial flow fans. J Turbomach 132(3): 031005CrossRefGoogle Scholar
  16. 16.
    Ffowcs Williams JE (1977) Aeroacoustics. Ann Rev Fluid Mech 9: 447–468CrossRefGoogle Scholar
  17. 17.
    Corsini A, Rispoli F, Sheard AG (2009) A meridional fan. Patent Application WO/2009/090376Google Scholar
  18. 18.
    Hoffman J, Johnson C (2004) Adaptive DNS/LES: a new agenda in CFD. In: Franca LP, Tezduyar TE, Masud A (eds) Finite element methods: 1970’s and beyond. CIMNE, BarcelonaGoogle Scholar
  19. 19.
    Tezduyar TE, Park YJ (1986) Discontinuity capturing finite element formulations for nonlinear convection–diffusion-reaction equations. Comput Methods Appl Mech Eng 59: 307–325MATHCrossRefGoogle Scholar
  20. 20.
    Tezduyar TE, Park YJ, Deans HA (1987) Finite element procedures for time-dependent convection–diffusion-reaction systems. Int J Numer Methods Fluids 7: 1013–1033MATHCrossRefGoogle Scholar
  21. 21.
    Codina R (1998) Comparison of some finite element methods for solving the diffusion–convection-reaction equation. Comput Methods Appl Mech Eng 156: 185–210MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Franca LP, Valentin F (2002) On an improved unusual stabilized finite element method for the advective–reactive–diffusive equation. Comput Methods Appl Mech Eng 190: 1785–1800MathSciNetCrossRefGoogle Scholar
  23. 23.
    Corsini A, Rispoli F, Santoriello A et al (2004) A new stabilized finite element method for advection-diffusion-reaction equations using quadratic elements. In: Lajos T et al (ed) Modelling fluid flow. Springer, New YorkGoogle Scholar
  24. 24.
    Corsini A, Rispoli F, Santoriello A, Tezduyar TE (2006) Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation. Comput Mech 38: 356–364MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    Hughes TJR (1995) Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Comput Methods Appl Mech Eng 127: 387–401MATHCrossRefGoogle Scholar
  26. 26.
    Hauke G (2002) A simple subgrid scale stabilized method for the advection–diffusion-reaction equation. Comput Methods Appl Mech Eng 191: 2925–2947MathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    Corsini A, Rispoli F, Santoriello A (2005) A variational multiscale high-order finite element formulation for turbomachinery flow computations. Comput Methods Appl Mech Eng 194: 4797–4823MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Gravemeier V, Wall WA (2007) A ‘divide-and-conquer’ spatial and temporal multiscale method for transient convection–diffusion-reaction equations. Int J Numer Meth Fluids 54: 779–804MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 32: 199–259MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28: 1–44MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95: 221–242MATHCrossRefGoogle Scholar
  32. 32.
    Corsini A, Menichini F, Rispoli F, Santoriello A, Tezduyar TE (2009) A multiscale finite element formulation with discontinuity capturing for turbulence models with dominant reaction like terms. J Appl Mech 76: 021211CrossRefGoogle Scholar
  33. 33.
    Corsini A, Iossa C, Rispoli F, Tezduyar TE (2010) A DRD finite element formulation for computing turbulent reacting flows in gas turbine combustors. Comput Mech 46: 159–167MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Corsini A, Rispoli F, Tezduyar TE (2011) finite element computation of NOx emission in aero-engine combustors. Int J Numer Methods Fluids 65: 254–270MathSciNetMATHCrossRefGoogle Scholar
  35. 35.
    Corsini A, Rispoli F, Tezduyar TE (2012) Computer modeling of wave-energy air turbines with the SUPG/PSPG formulation and discontinuity-capturing technique. J Appl Mech 79: 010910CrossRefGoogle Scholar
  36. 36.
    Hughes TJR, Tezduyar TE (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng 45: 217–284MathSciNetMATHCrossRefGoogle Scholar
  37. 37.
    Le Beau GJ, Ray SE, Aliabadi SK, Tezduyar TE (1993) SUPG finite element computation of compressible flows with the entropy and conservation variables formulations. Comput Methods Appl Mech Eng 104: 397–422MATHCrossRefGoogle Scholar
  38. 38.
    Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190: 411–430MATHCrossRefGoogle Scholar
  39. 39.
    Akin JE, Tezduyar T, Ungor M, Mittal S (2003) parameters and Smagorinsky turbulence model. J Appl Mech 70: 2–9MATHCrossRefGoogle Scholar
  40. 40.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575MathSciNetMATHCrossRefGoogle Scholar
  41. 41.
    Akin JE, Tezduyar TE (2004) Calculation of the advective limit of the SUPG stabilization parameter for linear and higher-order elements. Comput Methods Appl Mech Eng 193: 1909–1922MATHCrossRefGoogle Scholar
  42. 42.
    Tezduyar TE, Senga M (2006) Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Comput Methods Appl Mech Eng 195: 1621–1632MathSciNetMATHCrossRefGoogle Scholar
  43. 43.
    Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36: 191–206MathSciNetMATHCrossRefGoogle Scholar
  44. 44.
    Catabriga L, Coutinho ALGA, Tezduyar TE (2005) Compressible Flow SUPG parameters computed from element matrices. Commun Numer Methods Eng 21: 465–476MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    Tezduyar TE, Senga M (2007) SUPG finite element computation of inviscid supersonic flows with YZβ shock-capturing. Comput Fluids 36: 147–159MATHCrossRefGoogle Scholar
  46. 46.
    Catabriga L, Coutinho ALGA, Tezduyar TE (2006) Compressible Flow SUPG parameters computed from degree-of-freedom submatrices. Comput Mech 38: 334–343MATHCrossRefGoogle Scholar
  47. 47.
    Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZβ shock-capturing. Comput Mech 38: 469–481MATHCrossRefGoogle Scholar
  48. 48.
    Rispoli F, Corsini A, Tezduyar TE (2007) Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD). Comput Fluids 36: 121–126MATHCrossRefGoogle Scholar
  49. 49.
    Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2007) YZβ discontinuity-capturing for advection-dominated processes with application to arterial drug delivery. Int J Numer Methods Fluids 54: 593–608MathSciNetMATHCrossRefGoogle Scholar
  50. 50.
    Bazilevs Y, Calo VM, Cottrel JA, Hughes TJR, Reali A, Scovazzi G (2007) multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197: 173–201MATHCrossRefGoogle Scholar
  51. 51.
    Hughes TJR, Scovazzi G, Tezduyar TE (2010) Stabilized methods for compressible flows. J Sci Comput 43: 343–368MathSciNetMATHCrossRefGoogle Scholar
  52. 52.
    Catabriga L, de Souza DAF, Coutinho ALGA, Tezduyar TE (2009) Three-dimensional edge-based SUPG computation of inviscid compressible flows with YZβ shock-capturing. J Appl Mech 76: 021208CrossRefGoogle Scholar
  53. 53.
    Hsu M-C, Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2010) Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. Comput Methods Appl Mech Eng 199: 828–840MathSciNetMATHCrossRefGoogle Scholar
  54. 54.
    Tezduyar TE (2011) Comments on ‘Adiabatic shock capturing in perfect gas hypersonic flows’. Int J Numer Methods Fluids 66: 935–938MathSciNetMATHCrossRefGoogle Scholar
  55. 55.
    Takase S, Kashiyama K, Tanaka S, Tezduyar TE (2010) Space-time SUPG formulation of the shallow-water equations. Int J Numer Methods Fluids 64: 1379–1394MathSciNetMATHCrossRefGoogle Scholar
  56. 56.
    Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid-structure interaction techniques. Comput Mech 48: 247–267MathSciNetMATHCrossRefGoogle Scholar
  57. 57.
    Takizawa K, Henicke B, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48: 333–344MATHCrossRefGoogle Scholar
  58. 58.
    Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Numerical-performance studies for the stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48: 647–657MATHCrossRefGoogle Scholar
  59. 59.
    Takase S, Kashiyama K, Tanaka S, Tezduyar TE (2011) Space-time SUPG finite element computation of shallow-water flows with moving shorelines. Comput Mech 48: 293–306MathSciNetMATHCrossRefGoogle Scholar
  60. 60.
    Kler PA, Dalcin LD, Paz RR, Tezduyar TE (2012) SUPG and discontinuity-capturing methods for coupled fluid mechanics and electrochemical transport problems. Comput Mech. doi:10.1007/s00466-012-0712-z
  61. 61.
    Corsini A, Rispoli F (2005) Flow analyses in a high-pressure axial ventilation fan with a non-linear eddy viscosity closure. Int J Heat Fluid Flow 17: 108–155Google Scholar
  62. 62.
    Craft TJ, Launder BE, Suga K (1996) Development and application of a cubic eddy-viscosity model of turbulence. Int J Heat Fluid Flow 17: 108–155CrossRefGoogle Scholar
  63. 63.
    Bazilevs Y, Hsu M-C, Akkerman I, Wright S, Takizawa K, Henicke B, Spielman T, Tezduyar TE (2011) 3D Simulation of wind turbine rotors at full scale. Part I: geometry modeling and aerodynamics. Int J Numer Methods Fluids 65: 207–235MATHCrossRefGoogle Scholar
  64. 64.
    Hsu M-C, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALE-VMS: validation and the role of weakly enforced boundary conditions. Comput Mech doi:10.1007/s00466-012-0686-x
  65. 65.
    Hsu M-C, Bazilevs Y (2012) Fluid–structure interaction modeling of wind turbines: simulating the full machine. Comput Mech. doi:10.1007/s00466-012-0772-0
  66. 66.
    Inoue M, Kuroumaru M, Furukawa M (1986) Behavior of tip leakage flow behind an axial compressor rotor. J Eng Gas Turbines Power 108: 7–14CrossRefGoogle Scholar
  67. 67.
    Leibovich S (1982) Wave propagation, instability, and breakdown of vortices. In: Hornung HG, Mueller EA (eds) Vortex motion. Vieweg, Braunschweig, pp 50–67Google Scholar
  68. 68.
    Bianchi S, Corsini A, Rispoli F, Sheard AG (2009) Experimental aero-acoustic studies on improved tip configurations for passive control of noise signatures in low-speed axial fans. J Vibr Acoust 131:061007.10Google Scholar
  69. 69.
    Formaggia L, Micheletti S, Perotto S (2004) Anisotropic mesh adaptation in computational fluid dynamics: application to the advection–diffusion-reaction and the Stokes problems. Appl Numer Math 51(4): 511–533MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • A. Corsini
    • 1
  • F. Rispoli
    • 1
  • A. G. Sheard
    • 2
  • T. E. Tezduyar
    • 3
  1. 1.Dipartimento di Ingegneria Meccanica e AerospazialeSapienza University of RomeRomeItaly
  2. 2.Fan Technology, Fläkt Woods LtdEssexUK
  3. 3.Mechanical EngineeringRice UniversityHoustonUSA

Personalised recommendations