, 93:101 | Cite as

Global stability analysis of axisymmetric boundary layer: Effect of axisymmetric forebody shapes

  • Ramesh BhoraniyaEmail author
  • Vinod Narayanan


This paper presents the effect of axisymmetric forebody shapes on the global stability characteristics of axisymmetric boundary layer developed on a circular cylinder. Axisymmetric forebodies like sharp-cone, ellipsoid, and paraboloid with a fineness ratio (FR) of 2.5, 5.0 and 7.5 are considered. The boundary layer starts to develop at a stagnation point on the forebody geometry and grows in spatial directions. The inflow velocity component is parallel to the axis of the cylinder, and hence the angle of attack is zero. The base flow is axisymmetric, non-parallel and non-similar. The linearised Navier–Stokes equations are derived in the cylindrical polar coordinates for the disturbance flow components. The discretised linearised Navier–Stokes equations along with appropriate boundary conditions form a general eigenvalue problem and it has been solved using Arnoldi’s algorithm. The global temporal modes have been computed by solving the two-dimensional eigenvalue problem. The extent of a favourable pressure gradient developed in streamwise direction depends on the shape of axisymmetric forebody. The temporal and spatial growth of the disturbances has been computed for axisymmetric (\(N = 0\)) mode for different Reynolds numbers (Re). The forebody shapes have a significant effect on the base flow and stability characteristics at low Re.


Forebody global stability axisymmetric boundary layer 


47.20.Ft 47.20.Ib 47.20.−k 


  1. 1.
    J S Parsons and R E Goodson, Technical report H, Automatic Control Center, School of Mechanical Engineering (Purdue University, 1972)Google Scholar
  2. 2.
    V Narayanan and R Govindarajan, Pramana – J. Phys. 64(3), 323 (2005)Google Scholar
  3. 3.
    M Casarella, T C Shen and B E Bowers, Ship Acoustic Dept. R & D Report 77 (1977)Google Scholar
  4. 4.
    R L James, B H Navran and R A Rozenddal, NASA CR-166051 (1984)Google Scholar
  5. 5.
    B J Holmes, C J Obara and L P Yip, NASA TP-2256 (1984)Google Scholar
  6. 6.
    B H Carmichael, Underwater missile propulsion (Compass Publications, 1966)Google Scholar
  7. 7.
    V Theofilis, Prog. Aerosp. Sci. 39, 249 (2003)CrossRefGoogle Scholar
  8. 8.
    F Alizard and J C Robinet, Phys. Fluids 19, 114105 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    E Akervik, U Ehrenstein, F Gallaire and D S Henningson, Eur. J. Mech. B \(/\)Fluids 27, 501 (2008)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    G N V Rao, J. Appl. Math. Phys. 25, 63 (1974)Google Scholar
  11. 11.
    O R Tutty and W G Price, Phys. Fluids 14, 628 (2002)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    V Narayanan, Stability and transition in boundary layer: Effect of transverse curvature and pressure gradients, Ph.D. thesis (Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, 2005)Google Scholar
  13. 13.
    R Bhoraniya and V Narayanan, Theor. Comput. Fluid Dyn. 32, 425 (2018)MathSciNetCrossRefGoogle Scholar
  14. 14.
    R Bhoraniya and V Narayanan, J. Phys.: Conf. Ser. 822, 012018 (2017)Google Scholar
  15. 15.
    R Bhoraniya and V Narayanan, Phys. Rev. Fluids 2, 063901 (2017)CrossRefGoogle Scholar
  16. 16.
    U Ehrenstein and F Gallaire, J. Fluid Mech. 536, 209 (2005)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    H Fasel, U Rist and U Konzelmann, AIAA J. 28, 29 (1990)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    G Swaminathan, K Shau, A Sameen and R Govindarajan, Theor. Comput. Fluid Dyn25, 53 (2011) CrossRefGoogle Scholar
  19. 19.
    R S Lin and M R Malik, J. Fluid Mech. 311, 239 (1996)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    R S Lin and M R Malik, J. Fluid Mech. 333, 125 (1997)ADSCrossRefGoogle Scholar
  21. 21.
    V Theofilis, P W Duck and J Owen, J. Fluid Mech. 505, 249 (2004)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    V Theofilis, Theor. Comput. Fluid Dyn. 31, 623 (2017) CrossRefGoogle Scholar
  23. 23.
    M R Malik, J. Comput. Phys. 86(2), 372 (1990)ADSCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMarwadi Eduation Foundation Group of InstitutionsRajkotIndia
  2. 2.Department of Mechanical EngineeringIndian Institute of TechnologyPalaj, GandhinagarIndia

Personalised recommendations