Generalized Vortex Lattice Method for Predicting Characteristics of Wings with Flap and Aileron Deflection

A generalized vortex lattice method for complex
lifting surfaces with flap and aileron deflection is formulated. The
method is not restricted by the linearized theory assumption and
accounts for all standard geometric lifting surface parameters:
camber, taper, sweep, washout, dihedral, in addition to flap and
aileron deflection. Thickness is not accounted for since the physical
lifting body is replaced by a lattice of panels located on the mean
camber surface. This panel lattice setup and the treatment of different
wake geometries is what distinguish the present work form the
overwhelming majority of previous solutions based on the vortex
lattice method. A MATLAB code implementing the proposed
formulation is developed and validated by comparing our results to
existing experimental and numerical ones and good agreement is
demonstrated. It is then used to study the accuracy of the widely used
classical vortex-lattice method. It is shown that the classical approach
gives good agreement in the clean configuration but is off by as much
as 30% when a flap or aileron deflection of 30° is imposed. This
discrepancy is mainly due the linearized theory assumption
associated with the conventional method. A comparison of the effect
of four different wake geometries on the values of aerodynamic
coefficients was also carried out and it is found that the choice of the
wake shape had very little effect on the results.

• Mondher Yahyaoui

• Aileron deflection
• camber-surface-bound vortices
• classical VLM
• Generalized VLM
• flap deflection.

[1] Bertin, J.J., and Smith, M.L. Aerodynamics for engineers, 3rd Ed,
Prentice Hall, 1998. [2] Katz, J., and Plotkin A., Low-speed aerodynamics, McGraw-Hill Books
Co., 1991.
[3] Margason, R.J., and Lamar, J.E., "Vortex-Lattice FORTRAN Program
for Estimating Subsonic Aerodynamic Characteristics of complex plan
forms,” NASA TN D66142, 1971.
[4] Donaldon, M.V., and Mueller de Almeida, S.F.,” A vortex lattice
program for steady state aerodynamic analysis of flapped and twisted
uav wing plan forms”, Brazilian symposium on Aerospace Engineering
& Applications, 2009.
[5] Thiart, G.D., "Generalized vortex lattice method for prediction hydrofoil
characteristics”, R&D Journal, 2001.
[6] Neely, R.H., Bollech, T.V., Westrick, J.C., and R.R. Graham,
"Experimental and calculated characteristics of several NACA 44-series
wings with aspect ratios of 8, 10, and 12 and taper ratios of 2.5 and 3.5”,
NACA TN 1270, 1947.
[7] J. Roskam, Methods for estimating stability derivatives of conventional
subsonic aircraft, 1971.
[8] Lowry, G.J., and Polhamus, E.C., "A method for predicting lift
increment due to flap deflection at low angle of attack in incompressible
flow”, NACA TN 3911, 1957.
[9] Abbott, I.H., and Von Doenhoff, A.E., Theory of wing sections, Dover
Publications, 1959.