A multivortex method for axisymmetric bodies at angle of attack.

Abstract

A multivortex model made up of a large number of discrete free vortices has been used to represent the actual vortex sheets shed from the lee side of a slender body at an angle of attack. Circulation, strength, and position of the vortices, together with the induced normal forces, are evaluated at various axial positions along the body axis. The viscous inputs to the analysis are the separation or feeding points which are provided by experiment or semi-empirical theories. A discussion of the numerical computations and a comparison with experimental data are presented.n Re y r Nomenclature body axes d/2 -base or reference radius A r /(0-5p co 1 T 00 2 7ra 2 ) = normal force coefficient MApcoFooVa 3 ) = pitching moment coefficient vortex induced normal force and pitching moment coefficients x = local normal force coefficient sin 2 c*a) = cross-flow drag coefficient total impulse body total length Mach number number of vortices Reynolds number body local radius nondimensional length of the vortex sheet length measured along the vortex sheet from point of separation time frees tream velocity u + iv -complex velocity in the cross-flow plane nondimensional velocities, u' = u/V^ . . . angle of attack relative incidence, /? = tana/tane circulation per unit length of the vortex sheet circulation strength of vortex sheet or discrete vortex semi apex angle of the cone r/27rF 00 r 0 = nondimensional circulation strength, also X' = Xr 0 /a air density £ + it]] a -% -it] -complex coordinate, also or = re id ; a = re~i e <f > + i\I/ = complex velocity potential (or potential function) velocity potential angular orientation of the vortex sheet at the center of vorticity

Calculation of symmetric vortex separation affecting subsonic bodiesat high incidence

“…17 ' 19 However, the applicability of these methods is limited to cases that fit the simplifying assumptions, and additional data are needed if any reasonable results are to be achieved. A more advanced calculation is suggested by taking into consideration the two-dimensional development of the boundary layer and its separation on the body surface in the cross-flow plane.…”