Numerical Modeling of Blunt-Body Flows—Problems and Prospects

  • M. T. Landahl


The problems associated with numerical modeling of blunt-body flows are discussed. An efficient modeling technique should ideally incorporate the interactions between the turbulent boundary layer near the body, the unsteady, highly vortical wake flow behind the body, and the potential-flow regions outside these. The incomplete understanding of vortical unsteady flow fields, in particular, turbulent boundary layers and their separation behavior, will for the foreseeable future preclude accurate modeling; but even coarse modeling methods could serve an important role in establishing cause-and-effect relationships. In particular, one should aim at finding methods which can be used to predict, at least qualitatively, the effect of small local body changes on local flow patterns and on the overall drag. A case is made for flow-field calculation methods based on the vorticity equations. Such methods have proved successful in aeronautical and meteorological applications. The overall drag and lift can be calculated in terms of the vorticity shed into the wake; in particular, the vortex drag associated with longitudinal vortices due to aerodynamic lift can be analyzed.


Turbulent Boundary Layer Vortex Core Separation Line Vortex Sheet Side Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



vortex core radius

A, B

0(1) parameters depending on vorticity distribution in vortex core






unit binormal


radius vector


local radius of curvature of a vortex filament


Reynolds number


velocity vector field


velocity of body


velocity just outside boundary layer

v = ∇φ

potential flow field


circulation around vortex filament




vorticity, ω=(ω1, ω2, ω3)


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  1. Belotserkovskii, S. M. (1969), Calculation of the Flow Around Wings of Arbitrary Planform in a Wide Range of Angles of Attack, NASA TT F-12, 291.Google Scholar
  2. Chorin, A. J. (1973), Numerical Study of Slightly Viscous Flow, J. Fluid Mech., Vol. 57, pp. 785–796.Google Scholar
  3. Ehlers, F. E., Johnson, F. T., & Rubbert, P. E., (1975) Advanced Panel-Type Influence Coefficient Methods Applied to Subsonic and Supersonic Flows, Aerodynamic Analyses Requiring Advanced Computers, Part II, NASA SP-347, pp. 939–984.Google Scholar
  4. Falkner, V. M. (1948), The Solution of Lifting Plane Problems by Vortex Lattice Theory, British A.R.C., R &M2591.Google Scholar
  5. Hedman, S. G. (1966), Vortex Lattice Method for Calculation of Quasi Steady State Loadings on Thin Elastic Wings in Subsonic Flow, FFA Rep. 105, Aeronautical Res. Inst. of Sweden.Google Scholar
  6. Hess, J. L. (1972). Calculation of Potential Flow about Arbitrary Three-Dimensional Lifting Bodies, Rep. No. MDC J5679–01 (Contract N0001 9–71-C-0524), McDonnell Douglas Corp.Google Scholar
  7. Kandil, O. A., Mook, D. T. & Nayfeh, A. H., (1976), New Convergence Criteria for the Vortex-Lattice Models of the Leading-Edge Separation, NASA SP-405, pp. 285–292.Google Scholar
  8. Kinney, R. B. & Cielak, Z. M. (1975), Impulsive Motion of an Airfoil in a Viscous Fluid. Proceedings of Symposium on Unsteady Aerodynamics (March 8–20, 1975) Vol II, ppp. 487–512. Editor R. B. Kinney. U. S. Air Force and University of Arizona, Tucson, Arizona.Google Scholar
  9. Landahl, M. T. & Stark, V. J. E. (1968), Numerical Lifting-Surface Theory - Problems and Progress, AIAAJ., Vol. 6, pp. 2049–2060.Google Scholar
  10. Leonard, A. (1975), Simulation of Unsteady Three-Dimensional Separated Flows with Interacting Vortex Filaments, in NASA SP-347, Aerodynamic Analyses Requiring Advanced Computers, pp. 925–37. (A more accessible reference is Simulation of Three-Dimensional Separated Flows with Vortex Filaments, in Lecture Notes in Physics, Springer-Verlag, 1977).Google Scholar
  11. Lighthill, M. J., (1963), Introduction, Boundary Layer Theory, in Laminar Boundary Layers, (L. Rosenhead, ed.) Ch. II, Oxford University Press.Google Scholar
  12. Palko, R. L. (1976), Utilization of the AEDC Three-Dimensional Potential Flow Computer Program, NASA SP-405, pp. 127–143.Google Scholar
  13. Payne, R. B. (1958), Calculations of Unsteady Viscous Flow past a Circular Cylinder, J. Fluid Mech., Vol. 4, pp. 81–86.Google Scholar
  14. Rubbert, P. E. (1964), Theoretical Characteristics of Arbitrary Wings by a Non planar Vortex Lattice Method. Boeing Report D6–9244. Boeing Commercial Airplane Division, Renton, Washington.Google Scholar
  15. Widnall, S. E. (1975), The Structure and Dynamics of Vortex Filaments, in Annual Review of Fluid Mechanics, Vol. 7, pp. 141–165, Annual Reviews, Palo Alto, California.Google Scholar
  16. Widnall, S. E., Bliss, D. & Zalay, A., (1971) Theoretical and Experimental Study of the Stability of a Vortex Pair, in Aircraft Wake Turbulence and Its Detection, (ed. J. H. Olsen, A. Goldberg and M. Rogers) Plenum Press, New York.Google Scholar
  17. Widnall, S. E. & Sullivan, J. P. (1973), On the Stability of Vortex Rings, Proc. Roy. Soc., Ser. A332, pp. 335–353.Google Scholar
  18. Willmarth, W. W. (1975), Structure of Turbulence in Boundary Layers, in Advances in Applied Mechanics, Vol. 15, pp. 159–254.Google Scholar

Copyright information

© Plenum Press, New York 1978

Authors and Affiliations

  • M. T. Landahl
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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