Research Papers

An Actuator Disk Model of Incidence and Deviation for RANS-Based Throughflow Analysis

[+] Author and Article Information
Simone Rosa Taddei

Research Assistant
e-mail: simone.rosataddei@polito.it

Francesco Larocca

e-mail: francesco.larocca@polito.it
Aerospace Propulsion Group,
Department of Mechanical and
Aerospace Engineering,
Politecnico di Torino,
C.so Duca degli Abruzzi 24,
Torino 10129, Italy

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received May 24, 2012; final manuscript received July 22, 2013; published online September 26, 2013. Assoc. Editor: Ricardo F. Martinez-Botas.

J. Turbomach 136(2), 021001 (Sep 26, 2013) (9 pages) Paper No: TURBO-12-1052; doi: 10.1115/1.4025155 History: Received May 24, 2012; Revised July 22, 2013

Reynolds-averaged Navier–Stokes (RANS) equations with blade blockage and blade force source terms are solved in the meridional plane of complete axial flow turbomachinery using a finite-volume scheme. The equations of the compressible actuator disk (AD) are introduced to modify the evaluation of the convective fluxes at the leading and trailing edges (LEs and TEs). An AD behaves as a compact blade force which instantaneously turns the flow with no production of unphysical entropy. This avoids unphysical incidence loss across the LE discontinuity and allows for application of all of the desired deviation at the TE. Unlike previous treatments, the model needs no handmade modification of the throughflow (TF) surface and does not discriminate between inviscid and viscous meridional flows, which allows for coping with strong incidence gradients through the annulus wall boundary layers and with secondary deviation. This paper derives a generalized blade force term that includes the contribution of the LE and TE ADs in the divergence form of the TF equations and leads to generalized definitions of blade load, blade thrust, shaft torque, and shaft power. In analyzing a linear flat plate cascade with an incidence of 32 deg and a deviation of 21 deg, the proposed model provided a 105 reduction of unphysical total pressure loss compared to the numerical solution with no modeling. The computed mass flow rate, blade load, and blade thrust showed excellent agreement with the theoretical values. The complete RANS TF solver was used to analyze a four-stage turbine in design and off-design conditions with a spanwise-averaged incidence of up to 2 deg and 43 deg, respectively. Compared to a traditional streamline curvature solution, the RANS solution with incidence and deviation modeling provided a 0.1 to 0.7% accurate prediction of mass flow rate, shaft power, total pressure ratio, and adiabatic efficiency in both the operating conditions. It also stressed satisfactory agreement concerning the spanwise distributions of flow angle and Mach number at LEs and TEs. In particular, secondary deviation was effectively predicted. The RANS solution with no modeling showed acceptable performance prediction only in design conditions and could introduce no deviation.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Denton, J. D., and Dawes, W. N., 1999, “Computational Fluid Dynamics for Turbomachinery Design,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 213(2), pp. 107–124. [CrossRef]
Smith, L. H., 1966, “The Radial-Equilibrium Equation of Turbomachinery,” Trans. ASME J. Eng. Power, 88(1), pp. 1–12. [CrossRef]
Marsh, H., 1966, “A Digital Computer Program for the Through Flow Fluid Mechanics in an Arbitrary Turbo Machine Using a Matrix Method,” ARC R&M Report No. 3509.
Spurr, A., 1980, “The Prediction of 3D Transonic Flow in Turbomachinery Using a Combined Throughflow and Blade-to-Blade Time Marching Method,” Int. J. Heat Fluid Flow, 2(4), pp. 189–199. [CrossRef]
Yao, Z., and Hirsch, C., 1995, “Throughflow Model Using 3D Euler or Navier–Stokes Solvers,” Turbomachinery—Fluid Dynamic and Thermodynamic Aspects, VDI Berichte 1185, Verein Deutscher Ingenieure, Düsseldorf, Germany, pp. 51–61.
Baralon, S., Erikson, L. E., and Hall, U., 1998, “Validation of a Throughflow Time-Marching Finite-Volume Solver for Transonic Compressors,” ASME Paper No. 98-GT-47.
Damle, S. V., Dang, T. Q., and Reddy, D. L., 1997, “Throughflow Method Applicable for All Flow Regimes,” ASME J. Turbomach., 119(2), pp. 256–262. [CrossRef]
Sturmayr, A., and Hirsch, C., 1999, “Throughflow Model for Design and Analysis Integrated in a Three-Dimensional Navier–Stokes Solver,” Proc. Inst. Mech. Eng., Part A: J. Power Energy, 213(4), pp. 263–273. [CrossRef]
Simon, J. F., and Léonard, O., 2005, “A Throughflow Analysis Tool Based on the Navier–Stokes Equations,” Proceedings of ETC 6th European Conference on Turbomachinery, Lille, France, March 7–11.
Croce, G., Gazano, R., Satta, A., and Ratto, L., 2009, “Axisymmetric Navier–Stokes Solution for Turbomachinery Computations,” XIX ISABE Conference, Montreal, Canada, September 7–11, ISABE Paper No. 2009-1227.
Rosa Taddei, S., and Larocca, F., 2013, “CFD-Based Analysis of Multistage Throughflow Surfaces With Incidence,” Mech. Res. Commun., 47, pp. 6–10. [CrossRef]
Simon, J. F., and Léonard, O., 2007, “Modeling of 3-D Losses and Deviations in a Throughflow Analysis Tool,” J. Therm. Sci., 16(3), pp. 208–214. [CrossRef]
Horlock, J. H., 1978, Actuator Disk Theory: Discontinuities in Thermo-Fluid Dynamics, McGraw-Hill, New York.
Pandolfi, M., and Colasurdo, G., 1978, “Numerical Investigations on the Generation and Development of Rotating Stalls,” ASME Paper No. 78-WA/GT-5.
Joo, W. G., Hynes, T. P., and Reddy, D. L., 1997, “The Application of Actuator Disks to Calculations of the Flow in Turbofan Installations,” ASME J. Turbomach., 119(4), pp. 723–732. [CrossRef]
Schmidtmann, O., and Anders, J. M., 2001, “Route to Surge for a Throttled Compressor—A Numerical Study,” J. Fluids Struct., 15, pp. 1105–1121. [CrossRef]
Marsilio, R., and Ferlauto, M., 2009, “Numerical Simulation of Transient Operations in Aeroengines,” Proceedings of ETC 8th European Conference on Turbomachinery, Graz, Austria, March 23–27.
Nigmatullin, R. Z., and Ivanov, M. J., 1994, “The Mathematical Models of Flow Passage for Gas Turbine and Their Components,” Paper No. AGARD-LS-198.
Zannetti, L., and Pandolfi, M., 1984, “Inverse Design Technique for Cascades,” NASA Report No. CR-3836.
Pandolfi, M., 1984, “A Contribution to the Numerical Prediction of Unsteady Flows,” AIAA J., 22(5), pp. 602–610. [CrossRef]
Harten, A., Engquist, B., Osher, S., and Chakravarthy, S. R., 1987, “Uniformly High Order Accurate Essentially Non-Oscillatory Schemes, III,” J. Comput. Phys., 71(2), pp. 231–303. [CrossRef]
Rosa Taddei, S., Larocca, F., and Bertini, F., 2011, “Inverse Method for Axisymmetric Navier–Stokes Computations in Turbomachinery Aerodesign,” Proceedings of ETC 9th European Conference on Turbomachinery, Istanbul, Turkey, March 21–25.
Baldwin, B. S., and Lomax, H., 1978, “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA Paper No. 78-257. [CrossRef]
Rosa Taddei, S., and Larocca, F., 2008, “Axisymmetric Design of Axial Turbomachines: An Inverse Method Introducing Profile Losses,” Proc. Inst. Mech. Eng., Part A, J. Power Energy, 222(6), pp. 613–621. [CrossRef]
Rosa Taddei, S., and Larocca, F., 2012, “Potential of Specification of Swirl in Axisymmetric CFD Methods for Turbine Blade Aerodesign,” Inverse Probl. Sci. Eng., 20(4), pp. 533–551. [CrossRef]
Rosa Taddei, S., and Larocca, F., 2010, “On the Aerodynamic Design of Axial Flow Turbines by an Implicit Upwind Axisymmetric Solver,” Inverse Probl. Sci. Eng., 18(5), pp. 635–654. [CrossRef]
Weinig, F. S., 1964, “Theory of Two Dimensional Flow Through Cascades,” Aerodynamics of Turbines and Compressors, Princeton University Press, Princeton, NJ.
Came, P., 1995, “Streamline Curvature Throughflow Analysis of Axial-Flow Turbines,” Turbomachinery—Fluid Dynamic and Thermodynamic Aspects, (VDI Berichte 1185), Verein Deutscher Ingenieure, Düsseldorf, Germany, pp. 291–307.
Islam, A. M. T., and Sjolander, S. J., 1999, “Deviation in Axial Turbines at Subsonic Conditions,” ASME Paper No. 99-GT-26.
Massardo, A., and Satta, A., 1985, “A Correlation for the Secondary Deviation Angle,” ASME Paper No. 85-IGT-36.


Grahic Jump Location
Fig. 1

Representation of an AD at a LE or TE

Grahic Jump Location
Fig. 4

Four-stage turbine: mesh for the RANS computation

Grahic Jump Location
Fig. 5

Four-stage turbine: convergence history of the RANS solver with incidence and deviation modeling to the off-design conditions

Grahic Jump Location
Fig. 2

Flat plate cascade: pitchwise flow velocity

Grahic Jump Location
Fig. 3

Flat plate cascade: entropy

Grahic Jump Location
Fig. 6

Four-stage turbine: blade angle and spanwise distributions of relative flow angle at the fourth rotor LE

Grahic Jump Location
Fig. 7

Four-stage turbine: blade angle and spanwise distributions of flow angle at the third stator TE

Grahic Jump Location
Fig. 8

Four-stage turbine: spanwise distributions of relative Mach number at the fourth rotor LE

Grahic Jump Location
Fig. 9

Four-stage turbine: spanwise distributions of Mach number at the third stator TE



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In