Abstract
In this paper we present and discuss results from several investigations of the authors and co-workers over the past three years. The studies are primarily directed at the numerical solution of the Euler equations discretized upon a mesh for the case of vortices shed from the leading edge of a delta wing. The speeds in the various cases range from zero to supersonic. The major discussion of the paper points to the use of Computational Fluid Dynamics as a tool for the understanding of the fundamental fluid mechanical processes in this class of flows. Among the issues discussed are the capturing of a vortex sheet upon a mesh, the mechanism of total pressure loss, the stability of the spiral sheet, the structure of a nearly inviscid vortex core, and the stability of the core. The underlying assumption of course is that flow instability can be studied by numerical methods.
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References
Hoeijmakers, H.W.M: Numerical Computation of Vortical Flows About Wings, NLR Report MP 83073 U, Amsterdam, 1983.
Smith, J.H.B.: Theoretical Modelling of Three-Dimensional Vortex Flows in Aerodynamics. Aero J., April 1984, pp. 101–116.
Moore, D.W., and Griffith-Jones, R: The Stability of an Expanding Circular Vortex Sheet, Mathematika, Vol. 21, 1974, pp. 128–133.
Moore, D.W.: The Stability of an Evolving Two-Dimensional Vortex Sheet, Mathematika, Vol. 23, 1976, pp.35–44.
Hoeijmakers, H.W.M and Vaatstra, W.: A Higher-Order Panel Method Applied to Vortex Sheet Roll-Up. AIAA J. Vol. 21, No. 4, 1983, pp. 516–523.
Krause, E., Shi, X.G., and Hartwich, P.M.: Computation of Leading-Edge Vortices, AIAA Paper 83–1907, 1983.
Rizzi, A., and Eriksson, L.E.: Computation of Inviscid Incompressible Flow with Rotation, J. Fluid Mech, Vol. 153, 1985, pp. 275–312.
Rizzi, A.: Euler Solutions of Transonic Vortex Flows Around the Dillner Wing. J. Aircraft, Vol. 22. April 1985, pp. 325–328.
Rizzi, A.: Multi-Cell Vortices Observed in Fine-Mesh Solutions to the Incompressible Euler Equations, in Super Computers and Fluid Dynamics, ed. K. Kuwahara, Lect. Notes Engineering, Springer, to appear.
Payne, F.M., Ng. T.T., Nelson, R.C. and Schiff, L.B: Visualization and Flow Surveys of the Leading-Edge Vortex Structure on Delta Wing Planform, AIAA-86–0330, Jan 1986.
Murman, E.M. and Powell, K.: Comparison of Measured and Computed Pitot Pressures in Leading-Edge Vortex from a Delta Wing. Technical Report CFDL-TR-86–2, Massachusetts Institute of Technology, Jan 1986.
Monnerie, B. and Werlé, H.: Étude de l’Écoulement Supersonique & Hypersoniqui autour d’une Aile E’lancee en Incidence. In AGARD-CP-30 1968, Paper 23.
Brown, S.N.: The Compressible Inviscid Leading Edge Edge Vortex. Journal of Fluid Mechanics, 22, Part 1, Nov. 1965.
Snow, J.T.: On Inertial Instability as Related to the Multiple-Vortex Phenomenon. J. Atmos Sci, Vol. 35, Sept 1978, pp. 1660–1677.
Hall, M.G.: Vortex Breakdown, Ann Rev Fluid Mech, Vol. 4, 1972, pp. 195–218.
Leibovich, S.: The Structure of Vortex Breakdown, Ann Rev Fluid Mech, Vol. 10, 1978, pp. 221–246.
Hoeijmakers, H.W.M., and Rizzi, A.: Vortex-Fitted Potential Solution Compared with Vortex-Captured Euler Solution for Delta Wing with Leading Edge Vortex Separation. AIAA Paper 84–2144, 1984.
Eriksson, L.E.: Generation of Boundary-Conforming Grids around Wing-Body Configurations using Transfinite Interpolation, AIAA J., Vol. 20, Oct. 1982, pp. 1313–1320.
Rizzi, A.W. and Eriksson, L.E.: Computation of Flow Around Wings Based on the Euler Equations, J. Fluid Mech, Vol. 148, Nov. 1984, pp. 45–71.
Powell, K., Murman, E., Perez, E., and Baron, J.: Total Pressure Loss in Vortical Solutions of the Conical Euler Equations, AIAA Paper 85–1701, 1985.
Murman, E., Rizzi, A., and Powell, K.: High Resolution Solutions of the Euler Equations for Vortex Flows. In Progress and Supercomputing in Computational Fluid Dyn., 1985, pp. 93–113.
Lambourne, N.C. and Bryer, D.W.: The Bursting of Leading-Edge Vortices — Some Observations and Discussion of the Phenomenon. ARC R & M No. 3282, 1961.
Newsome, R.W.: A Comparison of Euler and Navier-Stokes Solutions for Supersonic Flow over a Conical Delta Wing. AIAA-85-0111, Jan. 1985
Newsome, R. and Thomas, J.: Computation of Leading-Edge Vortex Flows. NASA Langley Vortex Flow Aerodynamics Conference, Hampton VA. Oct, 1985.
Rizzi, A.: Separation Phenomena in 2D and 3D Numerical Solutions of the Euler Equations, in Proc. 7th INRIA Conf. Computing Methods in Appl. Sci, Engr., North Holland, to appear.
Hirschel, E.H., and Fornasier, L.: Flowfield and vorticity distribution near wing trailing edges. AIAA paper 84–0421, New York.
Earnhaw, P.B.: An Experimental Investigation of the Struclture of a Leading-Edge Vortex, ARC R & M, No. 3281, 1961.
Rizzi, A.: Modelling Vortex Flowfields by Supercomputers with Super-Size Memory, Aero J. Vol. 89, April 1985, pp. 149–161.
Murman, E.M., and Rizzi, A.: Applications of Euler Equations to Sharp Edge Delta Wings with Leading Edge Vortices, in Proc. AGARD Sym. Appl. Comp. Fluid Dyn. Aero., AGARD-CP-?, to appear.
Rizzi, A.: Three-Dimensional Solutions to the Euler Equations with One Million Grid Points. AIAA Journal, Vol. 23, No. 12, Dec. 1985.
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Rizzi, A., Murman, E.M. (1988). Computation of Flows Containing Edge Vortices. In: Engquist, B., Majda, A., Luskin, M. (eds) Computational Fluid Dynamics and Reacting Gas Flows. The IMA Volumes in Mathematics and Its Applications, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3882-9_15
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DOI: https://doi.org/10.1007/978-1-4612-3882-9_15
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