Radial Equilibrium

  • Meinhard T. SchobeiriEmail author


In Chapter 4, we briefly described a simple radial equilibrium condition necessary to determine the radial distribution of the stage parameters such as, \(\Phi ,\lambda ,r,\alpha _i\), and \(\beta _i\). Assuming an axisymmetric flow with constant meridional velocity and total pressure distributions, we arrived at free vortex flow as a simple radial equilibrium condition with \(r\nu _u =\) construct.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Wu, Chung-Hua, 1952, “A general Theory of Three-Dimensional Flow in Subsonic and Supersonic Turbomachines of Axial-, Radial, and mixed-Flow Types,” NACA technical Note 2604, Washington, D.C., January 1952.Google Scholar
  2. [2]
    Lakshminarayana, B., 1996, “Fluid Dynamics and Heat Transfer of Turbomachinery,” John Wiley & Sons.Google Scholar
  3. [3]
    Vavra, M. H., 1960, “Aero-Thermodynamics and Flow in Turbomachines,” John Wiley & Sons, Inc.Google Scholar
  4. [4]
    Schobeiri, M. T., 2012 “Turbomachinery Flow Physics and Dynamic Performance,” Second Edition, Springer-Verlag.Google Scholar
  5. [5]
    Novak, R. A., and Hearsey, R. M., “A Nearly Three Dimensional Intra blade Computing System for Turbomachinery, Part I & II,” Journal of Fluid Engineering, Vol 99, pp. 154–166.Google Scholar
  6. [6]
    Wilkinson, D. H., 1972, “Calculation of Blade-to-Blade Flow in Turbomachine by Streamline Curvature,” British ARC R&M 3704.Google Scholar
  7. [7]
    Wennerstrom, A. J., 1974, “On the Treatment of body Forces in the radial Equilibrium Equation of Turbomachinery,” Traupel-Festschrift, Juris-Verlag, Zürich.Google Scholar
  8. [8]
    Hearsey, R. M., 2003, “Computer Program HT 0300 version 2.0,” Hearsey technology, Bellevue, Washington.Google Scholar
  9. [9]
    Horlock, J. H., 1971, “On Entropy Production in Adiabatic Flow in Turbomachines,” ASME Journal of Basic Engineering, pp. 587-593.CrossRefGoogle Scholar
  10. [10]
    Wilkinson, D. H., 1969, Stability, Convergence and Accuracy of 2-Dimensional Streamline Curvature Methods Using Quasi-Orthogonals, Proceedings of the Institution of Mechanical Engineers, Volume 184, 1979–1970.Google Scholar
  11. [11]
    Adkins, G. G., Smith L. H., 1982, “Spanwise Mixing in Axial-Flow Turbomachines,” ASME Journal of Engineering for Gas Turbines and Power, Vol. 104, pp. 97–110.CrossRefGoogle Scholar
  12. [12]
    Gallimore, S. J., 1986, “Spanwise mixing in Multistage Axial Flow Compressors: Part II – Throughflow Calculations Including Mixing,” ASME Journal of Turbomachinery, Vol. 108, pp. 10–16.CrossRefGoogle Scholar
  13. [13]
    Smith, L. H. Jr., 1966, “The Radial-Equilibrium Equation of Turbomachinery,” ASME Journal of Engineering for Power, January, 1966, pp. 1–12.Google Scholar
  14. [14]
    Schobeiri, M. T., Gilarranz, J., and Johansen, E., “Final Report on: Efficiency, Performance, and Interstage Flow Field Measurement of Siemens-Westinghouse HP-Turbine Blade Series 9600 and 5600,” September, 1999.Google Scholar
  15. [15]
    Schobeiri M. T., Gillaranz, J. L., and Johansen E. S., 2000, “Aerodynamic and Performance Studies of a Three Stage High Pressure Research Turbine with 3-D Blades, Design Point and Off-Design Experimental Investigations,” Proceedings of ASME Turbo Expo 2000, 2000-GT-484.Google Scholar
  16. [16]
    Schobeiri, M. T., Suryanaryanan, A., Jerman, C., and Neuenschwander, T., 2004, “A Comparative Aerodynamic and performance study of a three-stage high pressure turbine with 3-D bowed blades and cylindrical blades,” Proceedings of ASME Turbo Expo 2004 Power of Land Air and Sea, June 14-17, 2004, Vienna, Austria, paper GT2004-53650.Google Scholar
  17. [17]
    Treiber, M., Abhari, R. S., and Sell, M., 2002, “Flow Physics and Vortex Evolution in Annular Turbine Cascades,” ASME, GT-2002-30540, Proceedings of ASME TURBO EXPO 2002, June 3-6, 2002, Amsterdam, The Netherlands.Google Scholar
  18. [18]
    Rosic, B. and Xu, L., 2008, “Blade Lean and Shroud Leakage Flows in Low Aspect Ratio Turbines,” Proceedings of ASME Turbo Expo 2008: Power for Land, Sea and Air, June 9-13, 2008, Berlin, Germany, GT2008-50565.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTexas A&M UniversityCollege StationUSA

Personalised recommendations