1Analysis of Flow Field Measurements Obtained in a Large Tow Tank Regarding the Decay of Wake Vortices in the Far- Field for Two- and Four-Vortex Systems

Stereo PIV measurements on a 2- and 4-vortex system have been performed in a large tow tank of SVA in Potsdam. The considered 4-vortex system consists of two counter-rotating vortex pairs generated by wings of a span width ratio of b2/b1 = 0.3 and a circulation ratio of Γ2/Γ1 =-0.3. As reference the corresponding 2-vortex system is also considered. A submersible Stereo PIV system attached to a vertical traversing system was employed. Cross-plane velocity fields are obtained of the descending wake vortex system to access the vortex dynamics well into the wake far field (x/b> 500, τ> 11). The spatio-temporal evolution of the vortex systems are analyzed with respect to the vortex trajectories, circulations and core radii as well as the total kinetic energy contained in the measured flow field. Nomenclature b wing span c root chord cL lift coefficient g acceleration of gravity Ek cross-flow kinetic energy, Eq. (5) N * normalized Brunt-Väisälä frequency, Eq. (1) rc vortex core radius, defined by maximal mean circumferential velocity Re Reynolds number based on chord length, νcV∞ ReΓ Reynolds number based on circulation, νΓ ρ water density t wake evolution time t0 characteristic time constant, Eq. (6) τ non-dimensional wake evolution time, τ = t / t0, T water temperature ∞V towing speed of model v r velocity vector, ( wvu,,) zyx,, wing fixed coordinates with origin at trailing edge α angle of attack Γ circulation, Eq. (3) ν kinematic viscosity ωr vorticity vector Subscripts 0 initial wake condition 1 main wing, outer vortex pair 2 horizontal tail wing, inner counter-rotating vortex pai