Research Papers: Gas Turbines: Turbomachinery

Preliminary Design Method for Dense-Gas Supersonic Axial Turbine Stages

[+] Author and Article Information
Elio A. Bufi

Laboratoire DynFluid Arts et Metiers ParisTech,
Paris FR-75013, France;
DMMM Politecnico di Bari,
Bari IT-70126, Italy
e-mail: Elio-Antonio.BUFI@ensam.eu

Paola Cinnella

Laboratoire DynFluid Arts et Metiers ParisTech,
Paris FR-75013, France
e-mail: paola.cinnella@ensam.eu

1Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received October 7, 2017; final manuscript received March 25, 2018; published online August 6, 2018. Assoc. Editor: David Sánchez.

J. Eng. Gas Turbines Power 140(11), 112605 (Aug 06, 2018) (11 pages) Paper No: GTP-17-1546; doi: 10.1115/1.4039837 History: Received October 07, 2017; Revised March 25, 2018

A fast preliminary design methodology for supersonic organic Rankine cycle (ORC) stator and rotor axial turbine blades with low degree of reaction is presented. First, the stator and rotor blade mean-line profiles are designed by using the two-dimensional (2D) method of characteristics (MOC), extended to gases governed by general equations of state (EOS). We focus more specifically on working fluids with medium to high molecular complexity, operating at thermodynamic conditions such that the fundamental derivative of gas dynamics Γ is lower than one in a significant portion of the flow field. For rotor blades, MOC is combined with a free-vortex method to achieve a smooth deflection of the supersonic incoming flow. A numerical approach is developed for solving the unique incidence problem in the case of gases governed by general EOS. Both stator and rotor blade geometries designed according to the inviscid MOC model are subsequently corrected to account for the development of viscous boundary layers by solving the compressible integral boundary layer equations extended to dense gases. The resulting blade designs are assessed by means of computational fluid dynamics (CFD) simulations based on a high-order finite volume solver equipped with advanced thermodynamic and transport-property models. Properly accounting for dense gas and viscous effects at an early design stage is found to improve the expected performance of ORC turbine rows significantly and delivers valuable baseline profiles for any further optimization.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Patel, P. , and Doyle, E. , 1976, “Compounding the Truck Diesel Engine With an Organic Rankine-Cycle System,” SAE Paper No. 760343.
Doyle, E. , Dinanno, L. , and Kramer, S. , 1979, “Installation of a Diesel-Organic Rankine Compound Engine in a Class 8 Truck for a Single-Vehicle Test,” SAE Paper No. 790646.
Teng, H. , and Regner, G. , 2009, “Improving Fuel Economy for HD Diesel Engines With WHR Rankine Cycle Driven by EGR Cooler Heat Rejection,” SAE Paper No. 2009-01-2913.
Bourhis, G. , and Leduc, P. , 2010, “Energy and Exergy Balances for Modern Diesel and Gasoline Engines,” Oil Gas Sci. Technol., 65(1), pp. 39–46. [CrossRef]
Kunte, H. , and Seume, J. , 2015, “Experimental Setup of a Small Supersonic Turbine for an Automotive ORC Application Running With Ethanol,” Third International Seminar on ORC Power Systems, Brussels, Belgium, Oct. 12–14, Paper No. 172. http://www.asme-orc2015.be/proceedings/documents/172.pdf
Wheeler, A. , and Ong, J. , 2013, “The Role of Dense Gas Dynamics on ORC Turbine Performance,” ASME Paper No. GT2013-95858.
Verneau, A. , 1987, “Supersonic Turbines for Organic Fluid Rankine Cycles From 3 to1300 kw,” Von Karman Institute, Rhode-Saint-Genèse, Belgium, Von Karman Institute Lecture Series 1987-07.
Redlich, O. , and Kwong, J. , 1949, “On the Thermodynamics of Solutions. V. An Equation of State. Fugacities of Gaseous Solutions,” Chem. Rev., 44(1), pp. 233–244. [CrossRef] [PubMed]
Stryjek, R. , and Vera, J. , 1986, “PRSV: An Improved Peng–Robinson Equation of State for Pure Compounds and Mixtures,” Can. J. Chem. Eng., 64(2), pp. 323–333. [CrossRef]
Martin, J. , and Hou, Y. , 1955, “Development of an Equation of State for Gases,” AIChE J., 1(2), pp. 142–151. [CrossRef]
Lemmon, E. , and Span, R. , 2006, “Short Fundamental Equations of State for 20 Industrial Fluids,” J. Chem. Eng. Data, 51(3), pp. 785–850. [CrossRef]
Thompson, P. , 1971, “A Fundamental Derivative in Gasdynamics,” Phys. Fluids, 14(9), pp. 1843–1849. [CrossRef]
Cramer, M. , and Crickenberger, A. , 1992, “Prandtl-Meyer Function for Dense Gases,” AIAA J., 30(2), pp. 561–564. [CrossRef]
Colonna, P. , Harinck, J. , Rebay, S. , and Guardone, A. , 2008, “Real-Gas Effects in Organic Rankine Cycle Turbine Nozzles,” J. Propul. Power, 24(2), pp. 282–294. [CrossRef]
Congedo, P. , Corre, C. , and Cinnella, P. , 2011, “Numerical Investigation of Dense-Gas Effects in Turbomachinery,” Comp. Fluids, 49(1), pp. 290–301. [CrossRef]
Délery, J. , 2010, Handbook of Compressible Aerodynamics, Wiley, London.
Zucrow, M. , and Hoffman, J. , 1976, Gas Dynamics, Wiley, New York, pp. 1–2.
Aldo, A. , and Argrow, B. , 1995, “Dense Gas Flow in Minimum Length Nozzles,” ASME J. Fluids Eng., 117(2), pp. 270–276. [CrossRef]
Guardone, A. , Spinelli, A. , and Dossena, V. , 2013, “Influence of Molecular Complexity on Nozzle Design for an Organic Vapor Wind Tunnel,” ASME J. Eng. Gas Turbines Power, 135(4), p. 042307. [CrossRef]
Lemmon, E. W. , Huber, M. L. , and McLinden, M. O. , 2013, “NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP Version 9.1,” National Institute of Standards and Technology, Gaithersburg, MD, https://www.nist.gov/srd/refprop/
Goldman, L. , 1968, “Analytical Investigation of Supersonic Turbomachinery Blading. 1/2-Analysis of Impulse Turbine-Blade Sections,” National Aeronautics and Space Administration, Washington, DC, Report No. NASA TN D-4422.
Paniagua, G. , Iorio, M. , Vinha, N. , and Sousa, J. , 2014, “Design and Analysis of Pioneering High Supersonic Axial Turbines,” Int. J. Mech. Sci., 89, pp. 65–77. [CrossRef]
Guardone, A. , Vigevano, L. , and Argrow, B. , 2004, “Assessment of Thermodynamic Models for Dense Gas Dynamics,” Phys. Fluids, 16(11), pp. 3878–3887. [CrossRef]
Bufi, E. , 2016, “Robust Optimization of ORC Turbine Expanders,” Ph.D. thesis, Ecole Nationale Supérieure d'Arts et Métiers, Paris, France.
Chung, T. , Lee, L. , and Starling, K. , 1984, “Applications of Kinetic Gas Theories and Multiparameter Correlation for Prediction of Dilute Gas Viscosity and Thermal Conductivity,” Ind. Eng. Chem. Fundam., 23(1), pp. 8–13. [CrossRef]
Kang, S. , 2012, “Design and Experimental Study of ORC (Organic Rankine Cycle) and Radial Turbine Using R245fa Working Fluid,” Energy, 41(1), pp. 514–524. [CrossRef]
Chen, H. , Goswami, D. , and Stefanakos, E. , 2010, “A Review of Thermodynamic Cycles and Working Fluids for the Conversion of Low-Grade Heat,” Renewable Sustainable Energy Rev., 14(9), pp. 3059–3067. [CrossRef]
Sciacovelli, L. , and Cinnella, P. , 2014, “Numerical Study of Multistage Transcritical Organic Rankine Cycle Axial Turbines,” ASME J. Eng. Gas Turbines Power, 136(8), p. 082604. [CrossRef]
Lakshminarayana, B. , 1995, Fluid Dynamics and Heat Transfer of Turbomachinery, Wiley-Interscience, New York. [CrossRef]
Starken, H. , Yongxing, Z. , and Schreiber, H. , 1984, “Mass Flow Limitation of Supersonic Blade Rows Due to Leading Edge Blockage,” ASME Paper No. 84-GT-233.
Moeckel, W. , 1949, “Approximate Method for Predicting Form and Location of Detached Shock Waves Ahead of Plane or Axially Symmetric Bodies,” National Advisory Committee for Aeronautics, Washington, DC, Technical Report No. NACA-TN-1921. https://ntrs.nasa.gov/search.jsp?R=19930082597
Reshotko, E. , and Tucker, M. , 1957, “Approximate Calculation of the Compressible Turbulent Boundary Layer With Heat Transfer and Arbitrary Pressure Gradient,” National Advisory Committee for Aeronautics, Washington, DC, Technical Report No. NACA TN 4154. http://naca.central.cranfield.ac.uk/reports/1958/naca-tn-4154.pdf
Cinnella, P. , and Congedo, P. , 2005, “Numerical Solver for Dense Gas Flows,” AIAA J., 43(11), pp. 2458–2461. [CrossRef]
Rezgui, A. , Cinnella, P. , and Lerat, A. , 2001, “Third-Order Accurate Finite Volume Schemes for Euler Computations on Curvilinear Meshes,” Comp. Fluids, 30(7–8), pp. 875–901. [CrossRef]
Cinnella, P. , and Congedo, P. , 2005, “Aerodynamic Performance of Transonic Bethe-Zel'dovich-Thompson Flows Past an Airfoil,” AIAA J., 43(2), pp. 370–378. [CrossRef]
Roache, P. J. , 1998, Verification and Validation in Computational Science and Engineering, Vol. 895, Hermosa, Albuquerque, NM.
Bufi, E. , and Cinnella, P. , 2017, “Robust Optimization of Supersonic ORC Nozzle Guide Vanes,” J. Phys. Conf. Ser., 821(1), p. 012014. [CrossRef]
Cinnella, P. , and Bufi, E. , 2017, “Robust Optimization Using Nested Kriging Surrogates: Application to Supersonic ORC Nozzle Guide Vanes,” ERCOFTAC Bull., 110, pp. 1–7. https://www.researchgate.net/publication/317687759_Robust_optimization_using_nested_Kriging_surrogates_application_to_supersonic_ORC_nozzle_guide_vanes


Grahic Jump Location
Fig. 4

Schematic description of the rotor blade design

Grahic Jump Location
Fig. 1

Typical characteristic line patterns and nozzle divergent shape design

Grahic Jump Location
Fig. 3

Sketch of the system of characteristic lines in a rotor vane [21]

Grahic Jump Location
Fig. 2

Sketch of the geometrical postprocessing used for the design of the axial ORC nozzle vane profile

Grahic Jump Location
Fig. 5

Blade designs for R245fa at various operating conditions (see Table 2). Dashed lines represent designs obtained under the perfect gas model.

Grahic Jump Location
Fig. 8

Comparison between inviscid and viscous nozzle vane shapes with view enlargement of the exit section. The operating conditions are specified in Table 4.

Grahic Jump Location
Fig. 7

Unique incidence solution: inlet flow angle, βi,1, as a function of the inlet Mach number M1 for the R245fa fluid. Dense gas conditions: pr0=1.05, Tr0=1.05; dilute gas: pr0=0.01, Tr0=1.15. The solution is calculated for a blade with r/s=0.05 (with r being the leading edge radius and s the cascade pitch) and a stagger angle βs=π/3.

Grahic Jump Location
Fig. 9

Comparison between inviscid and viscous impulse rotor blade shapes. The operating conditions are those of Table5 with βin=βout=60 deg.

Grahic Jump Location
Fig. 6

Characteristic line patterns and expansion fan lines for a supersonic rotor (a); definition of the control volume upstream and downstream of the bow-shock (b)

Grahic Jump Location
Fig. 12

Mach number contour (a) and entropy deviation (b) for DGMOC blades (no boundary layer correction)

Grahic Jump Location
Fig. 13

Mach number contour plot (a) and entropy deviation (b) for RODEC rotors with boundary layer correction

Grahic Jump Location
Fig. 14

Wall pressure distribution on the rotor blade for the viscous simulation with boundary layer correction and comparison with the target design distribution

Grahic Jump Location
Fig. 10

Mach number contour plot for DGMOC nozzle vane without (a) and with (b) boundary layer correction

Grahic Jump Location
Fig. 11

Pressure distribution along the vane axis for DMOG designs with and without boundary layer correction, and comparison with the target inviscid distribution



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