A CFD-based throughflow method with an explicit body force model and an adaptive formulation for the S2 streamsurface

Abstract

The paper describes the development and validation of a novel CFD-based throughflow model. It is based on the axisymmetric Euler equations with tangential blockage and body forces and inherits its numerical scheme from state-of-the-art CFD solver (TRAF code), including real-gas capabilities. A crucial aspect of the numerical procedure is represented by an adaptive approach for the meridional flow surface, which employs a new time-dependent equation to accommodate incidence and deviation effects, and which allows the explicit calculation of the blade body force. A realistic distribution of entropy along the streamlines is proposed in order to compute dissipative forces on the basis of a distributed loss model. The throughflow code is applied to the investigation of the NASA rotor 67 transonic fan and of a four stage low-pressure steam turbine at design conditions. The performance of the method is evaluated by comparing predicted operating characteristics and spanwise distributions of flow quantities with the results of CFD, steady, viscous calculations and experimental data.

Keywords

Throughflow model axisymmetric Euler equations blade body force models S2 stream surface turbomachinery steam turbine

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References

Rubechini

Schneider

Arnone

. A redesign strategy to improve the efficiency of a 17-stage steam turbine. J Turbomach 2012; 134: 031021.

Pasquale

Persico

Rebay

. Optimization of turbomachinery flow surfaces applying a CFD-based throughflow method. J Turbomach 2012; 136: 031013.

Smith

. The radial-equilibrium equation of turbomachinery. J Eng Gas Turb Power 1966; 88: 1–12.

Novak

. Streamline curvature computing procedures for fluid flow problems. J Eng Gas Turb Power 1967; 89: 478–490.

Casey

Robinson

. A new streamline curvature method for radial turbomachinery. J Turbomach 2010; 132: 031021.

Sturmayr A and Hirsch C. Shock representation by Euler throughflow models and comparison with pitch-averaged Navier–Stokes solutions. In: ISABE paper 99–7281, ISABE XIV, Florence, Italy, 5–10 September 1999.

Simon JF and Leonard O. A throughflow analysis tool based on the Navier–Stokes equations. In: Proceedings of the 6th European Turbomachinery Conference, Lille, France, 7–11 March 2005.

Yao Z and Hirsch C. Throughflow model using 3D Euler or Navier-Stokes solvers. In: Turbomachinery-Fluid Dynamic and Thermodynamic Aspects, VDI Berichte 1185, 1995, pp. 51–61.

Baralon S, Erikson LE and Hall U. Viscous throughflow modelling of transonic compressors using a time-marching finite volume solver. In: ISABE paper.ISABE XIII, Chattanooga, TN, 7–12 September 1997.

10.

Wu CH. A general theory of three-dimensional flow in subsonic and supersonic turbomachines of axial-, radial-, and mixed-flow types. NACA TN 2604, Washington, DC, January 1952.

11.

Persico

Rebay

. A penalty formulation for the throughflow modeling of turbomachinery. Comput Fluid 2012; 60: 86–98.

12.

Rosa Taddei S, Larocca F and Bertini F. Treatment of the leading edge discontinuity in time marching throughflow models. In: ISABE paper 09–1134, ISABE XIX, Montrèal, Canada, 7–11 September 2009.

13.

Rosa Taddei

Larocca

. An actuator disk model of incidence and deviation for RANS-based throughflow analysis. ASME J Turbomach 1997; 119: 256–262.

14.

Nigmatullin RZ and Ivanov MJ. The mathematical models of flow passage of gas turbine engines and their components. AGARD-LS-198. AGARD publications, December 1994.

15.

Dangle

Dang

Reddy

. Throughflow method for turbomachines applicable for all flow regimes. ASME J Turbomach 1997; 119: 256–262.

16.

Arnone

. Viscous analysis of three–dimensional rotor flow using a multigrid method. J Turbomach 1994; 116: 435–445.

17.

Accornero A, Doria G, Maretto L, et al. Flow in a 320 MW low-pressure section: Theoretical and experimental evaluation. Belgium: von Karman Institute, Sint-Genesius-Rode, 1980.

18.

Accornero A and Maretto L. Aerodynamics and streamwetness fraction of a multi-stage turbine–Comparison of prediction with experimental data. Belgium: von Karman Institute, Sint-Genesius-Rode, 1983.

19.

Jameson A, Schmidt W and Turkel E. Numerical solutions of the Euler equations by finite volume methods using Runge–Kutta time–stepping schemes. In: AIAA 14th fluid and plasma dynamics conference, 23–25 June 1981, Palo Alto, CA.

20.

Martinelli L and Jameson A. Validation of a multigrid method for Reynolds averaged equations. In: AIAA 26th aerospace sciences meeting, Reno, NV, January 1998.

21.

Swanson RC and Turkel E. Artificial dissipation and central difference schemes for the Euler and Navier–Stokes equations. In: AIAA 8th computational fluid dynamics conference, Honolulu, HI, 9–11 June 1987.

22.

Roe

. Approximate Riemann solvers, parameter vectors and difference schemes. J Comput Phys 1981; 43: 357–372.

23.

Brandt

. Multi-level adaptive computations in fluid dynamics, Williamsburg, VA: AIAA, 1979.

24.

Denton

. Throughflow calculations for transonic axial flow turbines. J Eng Gas Turb Power 1978; 100: 212–218.

25.

Boncinelli

Rubechini

Arnone

. Real gas effects in turbomachinery flows: A CFD model for fast computations. J Turbomach 2004; 126: 268–276.

26.

Rubechini F, Marconcini M, Arnone A, et al. Some aspects of CFD modeling in the analysis of a low-pressure steam turbine. In: ASME Turbo Expo, ASME paper No GT2007-27235, Montrèal, Canada, 14–17 May 2007.

27.

Pierzga

Wood

. Investigation of the three-dimensional flow field within a transonic fan rotor: Experiment and analysis. ASME J Turbomach 1985; 107: 436–449.

28.

Lieblein S. Analysis of experimental low-speed loss and stall characteristics of two-dimensional compressor blade cascades. NACA RM E57A28, Washington, DC, March 1957.

29.

Carter ADS and Hughes HP. A theoretical investigation of the effect of profile shape on the performance of aerofoils in cascade. Aeronaut Res Council R&M 2384; London, UK, 1950.

30.

Anderson MR and Bonhaus DL. A comprehensive through-flow solver method for modern turbomachinery design. In: ASME Turbo Expo ASME paper GT2015–43763, Montrèal, Canada, 15–19 June 2015.

31.

Sturmayr

Hirsch

. Throughflow model for design and analysis integrated in a three-dimensional Navier–Stokes solver. Proc IMechE, Part A: J Power and Energy 1999; 213: 263–273.

32.

Arnone A and Benvenuti E. Three-dimensional Navier–Stokes analysis of a two-stage gas turbine. In: ASME Turbo Expo, ASME paper 94–GT–88, The Hague, The Netherlands, 13–16 June 1994.

33.

Harvey

Peskin

Klein

. NIST/ASME steam properties, Gaithersburg, MD: National Institute of Standards and Technology, 2000.

34.

IAPWS. IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam. IAPWS Release, IAPWS Secretariat, 1997.

35.

Traupel W. Termische Turbomaschinen. Berlin, Germany: Springer-Verlag, ISBN 978-3-540-67377-4, 1958.

36.

Zhu J and Sjolander SA. Improved profile loss and deviation correlations for axial-turbine blade rows. In: ASME Turbo Expo, ASME paper GT2005–69077, Reno–Tahoe, NV, 6–9 June 2005.