Relationship between starting vortex ring kinematics and dynamics
Parameter
.
Thrust
.
Efficiency
.
Vortex ring volume
+
+
Vortex ring spacing
–
–
Jet ratio A/D
+
–
Parameter
.
Thrust
.
Efficiency
.
Vortex ring volume
+
+
Vortex ring spacing
–
–
Jet ratio A/D
+
–
Both thrust and efficiency increase in direct proportion with vortex ring volume. By contrast, thrust and efficiency decrease with increasing vortex spacing due to diminished inter-ring interactions. For a fixed volume of ejected fluid, the thrust increases with jet ratio A/D, at the expense of efficiency.
Trends are based on the assumption of negligible vortex formation during the recovery stroke. + indicates a direct relationship and – an inverse relationship (cf. Weihs, 1977; Krueger and Gharib, 2003).