Research Papers: Gas Turbines: Vehicular and Small Turbomachines

Special Challenges in the Computational Fluid Dynamics Modeling of Transonic Turbo-Expanders

[+] Author and Article Information
Filippo Rubechini

e-mail: filippo.rubechini@arnone.de.unifi.it

Andrea Arnone

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

Roberto Biagi

GE Oil & Gas,
via Felice Matteucci 2,
Firenze 50127, Italy

Contributed by the Vehicular and Small Turbomachines Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June 27, 2013; final manuscript received July 1, 2013; published online August 30, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 135(10), 102701 (Aug 30, 2013) (8 pages) Paper No: GTP-13-1188; doi: 10.1115/1.4025034 History: Received June 27, 2013; Revised July 01, 2013

High pressure ratio turbo-expanders often put a strain on computational fluid dynamics (CFD) modeling. First of all, the working fluid is usually characterized by significant departures from the ideal behavior, thus requiring the adoption of a reliable real gas model. Moreover, supersonic flow conditions are typically reached at the nozzle vanes discharge, thus involving the formation of a shock pattern, which is in turn responsible for a strong unsteady interaction with the wheel blades. Under such circumstances, performance predictions based on classical perfect gas, steady-state calculations can be very poor. While reasonably accurate real gas models are nowadays available in most flow solvers, unsteady real gas calculations still struggle to become an affordable tool for investigating turbo-expanders. However, it is emphasized in this work how essential the adoption of a time-accurate analysis can be for accurate performance estimations. The present paper is divided in two parts. In the first part, the computational framework is validated against on-site measured performance from an existing power plant equipped with a variable-geometry nozzled turbo-expander, for different nozzle positions, and in design and off-design conditions. The second part of the paper is devoted to the detailed discussion of the unsteady interaction between the nozzle shock waves and the wheel flow field. Furthermore, an attempt is made to identify the key factors responsible for the unsteady interaction and to outline an effective way to reduce it.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Dixon, S. L., and Hall, C. A., 2010, Fluid Mechanics and Thermodynamics of Turbomachinery, 6th ed., Butterworth-Heinemann, Waltham, MA.
Japikse, D., and Smith, G. E., 1986, Radial Turbine Design and Performance, 3rd ed., Concepts ETI, White River Junction, VT.
Chen, H., and Baines, N. C., 1994, “The Aerodynamic Loading of Radial and Mixed-Flow Turbines,” Int. J. Mech. Sci., 36(1), pp. 63–79. [CrossRef]
Bloch, H., and Soares, C., 2001, Turboexpanders and Process Applications, 1st ed., Gulf Professional Publishing, Oxford, UK.
Arnone, A., 1994, “Viscous Analysis of Three–Dimensional Rotor Flow Using a Multigrid Method,” ASME J. Turbomach., 116(3), pp. 435–445. [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]
Spalart, P. R., and Allmaras, S. R., 1994, “A One-Equation Turbulence Model for Aerodynamic Flows,” La Recherche Aérospatiale, 1, pp. 5–21.
Spalart, P. R., and Shur, M., 1997, “On the Sensitization of Turbulence Models to Rotation and Curvature,” Aerosp. Sci. Technol., 1(5), pp. 297–302. [CrossRef]
Shur, M. L., Strelets, M. K., Travin, A. K., and Spalart, P. R., 2000, “Turbulence Modeling in Rotating and Curved Channels: Assessing the Spalart-Shur Correction,” AIAA J., 38(5), pp. 784–792. [CrossRef]
Marconcini, M., Rubechini, F., Arnone, A., and Ibaraki, S., 2008, “Numerical Investigation of a Transonic Centrifugal Compressor,” ASME J. Turbomach., 130(1), p. 011010. [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]
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-310.
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]
Boncinelli, P., Rubechini, F., Arnone, A., Cecconi, M., and Cortese, C., 2004, “Real Gas Effects in Turbomachinery Flows: a CFD Model for Fast Computations,” ASME J. Turbomach., 126(2), pp. 268–276. [CrossRef]
Rubechini, F., Marconcini, M., Arnone, A., Cecchi, S., and Dacca, F., 2007, “Some Aspects of CFD Modeling in the Analysis of a Low-Pressure Steam Turbine,” ASME Paper No. GT2007-27235. [CrossRef]
Huber, M. L., 2007, “NIST Thermophysical Properties of Hydrocarbon Mixtures Database (SUPERTRAPP) Version 3.2—Users' Guide,” National Institute of Standards and Technology, Gaithersburg, MD.
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]
Suresh, A., Hofer, D. C., and Tangirala, V. E., 2012, “Turbine Efficiency for Unsteady, Periodic Flows,” ASME J. Turbomach., 134(3), p. 034501. [CrossRef]
Tyler, J. M., and Sofrin, T. G., 1962, “Axial Flow Compressor Noise Studies,” SAE Trans., 70, pp. 309–332.


Grahic Jump Location
Fig. 1

View of the computational mesh

Grahic Jump Location
Fig. 2

Expected, measured, and computed (unsteady) stage performance

Grahic Jump Location
Fig. 3

Unsteadiness at midspan for three different nozzle openings (a) nozzle (b) wheel

Grahic Jump Location
Fig. 4

Impact of computational model on performance at varying nozzle opening

Grahic Jump Location
Fig. 5

Unsteadiness at midspan for two different nozzle geometries (a) nozzle (b) wheel

Grahic Jump Location
Fig. 6

(a) Averaged entropy rise across the stage and (b) instantaneous entropy rise contours on a blade-to-blade surface of the wheel at midspan

Grahic Jump Location
Fig. 7

Space-time diagrams for two different nozzle geometries, static pressure distribution on nozzle–-wheel circumferential interface over a vane passing period

Grahic Jump Location
Fig. 8

Space-time diagrams for two different nozzle geometries, static pressure distribution on wheel blade surface at midspan over a vane passing period

Grahic Jump Location
Fig. 9

Unsteady pressure spectra at nozzle–wheel interface plane, circumferential and time harmonic modes (rotating reference frame)

Grahic Jump Location
Fig. 10

Circumferential distribution of instantaneous static pressure at midspan nozzle–wheel interface t/T = 0



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