Research Papers: Gas Turbines: Turbomachinery

Accounting for Unsteady Interaction in Transonic Stages

[+] Author and Article Information
Filippo Rubechini

Department of Industrial Engineering,
University of Florence,
via di Santa Marta, 3,
Firenze 50139, Italy
e-mail: filippo.rubechini@arnone.de.unifi.it

Michele Marconcini, Matteo Giovannini, Juri Bellucci, Andrea Arnone

Department of Industrial Engineering,
University of Florence,
via di Santa Marta, 3,
Firenze 50139, Italy

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 24, 2014; final manuscript received August 5, 2014; published online November 25, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(5), 052602 (May 01, 2015) (9 pages) Paper No: GTP-14-1433; doi: 10.1115/1.4028667 History: Received July 24, 2014; Revised August 05, 2014; Online November 25, 2014

This paper discusses the importance of the unsteady interaction in transonic turbomachinery stages. Although the flow in a turbomachine is inherently unsteady, most current calculations for routine design work exploit the steady state assumption. In fact, unsteady flow effects are often taken into account for mechanical integrity checks, such as blade flutter or forced response, or heat transfer issues associated with circumferential nonuniformities, whereas steady state calculations are usually selected for the aerodynamic design. In this work, some cases are discussed in which significant departures are found between steady and time-averaged results, and the basic fluid mechanisms responsible for them are examined. Finally, a current perspective of unsteady computational fluid dynamics (CFD) calculations for the aerodynamic design is given.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Arnone, A., 1994, “Viscous Analysis of Three-Dimensional Rotor Flow Using a Multigrid Method,” ASME J. Turbomach., 116(3), pp. 435–445. [CrossRef]
Spalart, P. R., and Allmaras, S. R., 1994, “A One-Equation Turbulence Model for Aerodynamic Flows,” La Rech. Aérosp., 1, pp. 5–21.
Wilcox, D. C., 2008, “Formulation of the k–ω Turbulence Model Revisited,” AIAA J., 46(11), pp. 2823–2838. [CrossRef]
Menter, F. R., 1994, “Two-Equations Eddy Viscosity Turbulence Models for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605. [CrossRef]
Arnone, A., Liou, M. S., and Povinelli, L. A., 1992, “Navier–Stokes Solution of Transonic Cascade Flow Using Non-Periodic C-Type Grids,” J. Propul. Power, 8(2), pp. 410–417. [CrossRef]
Arnone, A., Carnevale, E., and Marconcini, M., 1997, “Grid Dependency Study for the NASA Rotor 37 Compressor Blade,” ASME Paper No. 97-GT-384.
Pacciani, R., Rubechini, F., Arnone, A., and Lutum, E., 2012, “Calculation of Steady and Periodic Unsteady Blade Surface Heat Transfer in Separated Transitional Flow,” ASME J. Turbomach., 134(6), p. 061037. [CrossRef]
Schmitt, S., Eulitz, F., Wallscheid, L., Arnone, A., and Marconcini, M., 2001, “Evaluation of Unsteady CFD Methods by Their Application to a Transonic Propfan Stage,” ASME Paper No. 2001-GT-0310. [CrossRef]
Bonaiuti, D., Arnone, A., Hah, C., and Hayami, H., 2002, “Development of Secondary Flow Field in a Low Solidity Diffuser in a Transonic Centrifugal Compressor Stage,” ASME Paper No. GT2002-30371. [CrossRef]
Marconcini, M., Rubechini, F., Arnone, A., and Ibaraki, S., 2010, “Numerical Analysis of the Vaned Diffuser of a Transonic Centrifugal Compressor,” ASME J. Turbomach., 132(4), p. 041012. [CrossRef]
Marconcini, M., Rubechini, F., Arnone, A., Scotti Del Greco, A., and Biagi, R., 2012, “Aerodynamic Investigation of a High Pressure Ratio Turbo-Expander for Organic Rankine Cycle Applications,” ASME Paper No. GT2012-69409. [CrossRef]
Rubechini, F., Marconcini, M., Arnone, A., Scotti Del Greco, A., and Biagi, R., 2013, “Special Challenges in the Computational Fluid Dynamics Modeling of Transonic Turbo-Expanders,” ASME J. Eng. Gas Turbines Power, 135(10), p.102701. [CrossRef]
Denton, J. D., 1992, “The Calculation of Three-Dimensional Viscous Flow Through Multistage Turbomachines,” ASME J. Turbomach., 114(1), pp. 18–26. [CrossRef]
Giles, M. B., 1988, “UNSFLO: A Numerical Method for Unsteady Inviscid Flow in Turbomachinery,” MIT, Cambridge, MA, GTL Report No. 195.
Pianko, M., and Wazelt, F., 1982, “Propulsion and Energetics Panel Working Group 14 on Suitable Averaging Techniques in Non-Uniform Internal Flows,” Advisory Group for Aerospace Research and Development, Neuilly Sur Seine, France, AGARD Advisory Report No 182.
Wyss, M. L., Chima, R. V., and Tweedt, D. L., 1993, “Averaging Techniques for Steady and Unsteady Calculation of a Transonic Fan Stage,” AIAA Paper No. 93-3065. [CrossRef]
Cumpsty, N. A., and Horlock, J. H., 2006, “Averaging Nonuniform Flow for a Purpose,” ASME J. Turbomach., 120(1), pp. 120–129. [CrossRef]
Suresh, A., Hofer, D. C., and Tangirala, V. E., 2012, “Turbine Efficiency for Unsteady, Periodic Flows,” ASME J. Turbomach., 134(3), p. 034501. [CrossRef]
Holmes, D. G., 2008, “Mixing Planes Revisited: A Steady Mixing Plane Approach Designed to Combine High Levels of Conservation and Robustness,” ASME Paper No. GT2008-51296. [CrossRef]
Denton, J., 2010, “Some Limitations of Turbomachinery CFD,” ASME Paper No. GT2010-22540. [CrossRef]
Arnone, A., Liou, M. S., and Povinelli, L. A., 1995, “Integration of Navier–Stokes Equations Using Dual Time Stepping and a Multigrid Method,” AIAA J., 33(6), pp. 985–990. [CrossRef]
Jameson, A., 1991, “Time Dependent Calculations Using Multigrid With Applications to Unsteady Flows Past Airfoils and Wings,” AIAA Paper No. 91-1596. [CrossRef]
Arnone, A., and Pacciani, R., 1996, “Rotor–Stator Interaction Analysis Using the Navier–Stokes Equations and a Multigrid Method,” ASME J. Turbomach., 118(4), pp. 679–689. [CrossRef]
Giovannini, M., Marconcini, M., Arnone, A., and Bertini, F., 2014, “Evaluation of Unsteady Computational Fluid Dynamics Models Applied to the Analysis of a Transonic High-Pressure Turbine Stage,” Proc. Inst. Mech. Eng., Part A–J. Power Energy, 228(7), pp. 813–824. [CrossRef]
Van Zante, D. E., Chen, J. P., Hathaway, T. H., and Randall, C., 2008, “The Influence of Compressor Blade Row Interaction Modeling on Performance Estimates From Time-Accurate, Multistage, Navier–Stokes Simulations,” ASME J. Turbomach., 130(1), p.011009. [CrossRef]
de la Loma, A., Paniagua, G., Verrastro, D., and Adami, P., 2007, “Transonic Turbine Stage Heat Transfer Investigation in Presence of Strong Shocks,” ASME Paper No. GT2007-27101. [CrossRef]
Sieverding, C. H., 1985, “Axial Turbine Performance Prediction Methods,” Thermodynamics and Fluid Mechanics of Turbomachinery (NATO ASI Series 639 E, No. 97A, Vol. 1), Nijhoff, Dordrecht, The Netherlands, pp. 737–784.
Denton, J. D., 1993, “The 1993 IGTI Scholar Lecture—Loss Mechanisms in Turbomachines,” ASME J. Turbomach., 115(4), pp. 621–656. [CrossRef]
Miller, R. J., Moss, R. W., Ainsworth, R. W., and Harvey, N. W., 2003, “Wake, Shock, and Potential Field Interactions in a 1.5 Stage Turbine—Part I: Vane–Rotor and Rotor–Vane Interaction,” ASME J. Turbomach., 125(1), pp. 33–39. [CrossRef]
Denton, J. D., and Dawes, W. N., 1999, “Computational Fluid Dynamics for Turbomachinery Design,” Proc. Inst. Mech. Eng., Part C, 213(2), pp. 107–124. [CrossRef]
Arnone, A., and Pacciani, R., 1998, “IGV–Rotor Interaction Analysis in a Transonic Compressor Using the Navier–Stokes Equations,” ASME J. Turbomach., 120(1), pp. 143–155. [CrossRef]
Prasad, A., 2003, “Evolution of Upstream Propagating Shock Waves From a Transonic Compressor Rotor,” ASME J. Turbomach., 125(1), pp. 133–240. [CrossRef]


Grahic Jump Location
Fig. 1

Instantaneous density gradient for different expansion ratios: (a) M2,is = 1.0; (b) M2,is=1.1; and (c) M2,is = 1.3

Grahic Jump Location
Fig. 2

Stage operating conditions at varying the expansion ratio

Grahic Jump Location
Fig. 3

Nozzle profile losses versus nozzle discharge Mach

Grahic Jump Location
Fig. 4

Impact of computational model on performance at varying expansion ratio

Grahic Jump Location
Fig. 5

Averaged entropy rise across the stage for different expansion ratios. Steady and unsteady results.

Grahic Jump Location
Fig. 6

Nozzle Mach number—steady and time-averaged results: (a) M2,is = 1.0; (b) M2,is = 1.1; and (c) M2,is = 1.3

Grahic Jump Location
Fig. 7

Pitchwise pressure nonuniformity at the vane discharge: steady and unsteady results

Grahic Jump Location
Fig. 8

Instantaneous static pressure contours: (a) near stall; (b) peak efficiency; and (c) choke

Grahic Jump Location
Fig. 9

Rotor and overall efficiency versus mass flow

Grahic Jump Location
Fig. 11

Pitchwise relative Mach number at rotor inlet, at full and part load. Time-averaged results.

Grahic Jump Location
Fig. 12

Instantaneous pressure contours at midspan [11]

Grahic Jump Location
Fig. 13

Load distribution on the nozzle (a) and on the blade (b) at midspan, and spanwise distribution of exit swirl angle (c). Comparison between steady and time-averaged results [11].

Grahic Jump Location
Fig. 14

Measured and computed stage performance

Grahic Jump Location
Fig. 15

Impact of computational model on performance at varying nozzle opening [12]

Grahic Jump Location
Fig. 10

Overall performance at full and part load



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