Figure 1.
A pair of counter rotating trailing vortices: At any position outside its core a vortex induces a velocity, which equals the circulation Γ divided by the circumference of the vortex at that position 2πr (free vortex).
In a pair of trailing vortices the mutually induced velocities are therefore calculated for r equals b’, which is the displacement between the vortices. In this case the induced velocities each vortex experiences are directed downwards.
Figure 2.
A pair of NACA 0012 wings was mounted on two tapered aluminium supports, which inserted into tight-fitting slots of variable displacement in a plastic frame. Attached to the base plate via a hinge, the angle of attack of the frame was adjustable by a rearward positioned screw.
Table 1.
Summary of parameter space.
Figure 3.
Vortex interaction in the wake of two paired NACA 0012 wings at Re = 6000.
Angle of attack, 5°; single wing aspect ratio, 1.5; gap width, 1/3 chords. The normalized downstream distance is increased from 1 to 17 chord-lengths. Bottom panel (E) shows how the wake angles were defined.
Figure 4.
Scatter plots of the measured wake angle.
Reynolds number 6000 and 7500 are presented as the upper and lower half respectively. Rows show the two different wing angles of attack at the two Re and columns show different wing aspect ratios. Squares show the smallest gap (1/3 chord length), circles show the medium gap (2/3 chord lengths) and triangles show the largest gap (1 chord length).
Table 2.
Summary of the statistical test with upper and lower bounds based on 95% confidence intervals.
Figure 5.
Diagram of two pairs of counter rotating vortices.
As in Figure 1, induced velocities are calculated for r equals a’ and b’, which are the displacements between the vortices. The major difference from a single vortex pair system is the bi-lateral impact of the induced velocities. Vortex 2 experiences downwards directed velocity induced by vortex 1 and upwards directed velocity induced by vortex 3. If these velocities are of same magnitude, vortex 2 will experience no net displacement.