# Bound Vortex

## Bound Vortex

a vortex that is considered to be tightly associated with the body around which a liquid or gas flows, and equivalent with respect to the magnitude of speed circulation to the real vorticity that forms in the boundary layer owing to viscosity.

In calculations of the lift of a wing of infinite span, the wing can be replaced by a bound vortex that has a rectilinear axis and generates in the surrounding medium the same circulation as that generated by the real wing. In the case of a wing of finite span, the bound vortex continues into the surrounding medium in the form of free vortices. Knowledge of the vortex system of a wing permits calculation of the aerodynamic forces acting upon the wing. In particular, the interaction between bound and free vortices gives rise to the induced drag of the wing. The idea of the bound vortex was made use of by N. E. Zhukovskii in the theory of the wing and the screw propeller.

### REFERENCES

Zhukovskii, N. E. “O prisoedinennykh vikhriakh.” Izbr. soch., vol. 2. Moscow-Leningrad, 1948.
Zhukovskii, N. E. Vikhrevaia teoriia grebnogo vinta. Moscow-Leningrad, 1950.
Loitsianskii, L. G. Mekhanika zhidkosti i gaza, 4th ed. Moscow, 1973.
References in periodicals archive ?
According to the classical Prandtl's lifting-line theory, the bound vortex is located along the quarter chord, and the trailing vortex is parallel to the x-axis along the free-stream velocity, as shown in Figure 1.
With the traditional aerodynamic theory on a finite wing with no sweep, the induced velocity generated by its own bound vortex at an arbitrary location along the lifting line can be ignored.
In addition, the bound vortex as well as the trailing vortex generated by the other lifting surface can both produce an induced velocity at an arbitrary location along the lifting line.
where [phi] is the angle between the induced velocity and the z-axis direction as shown in Figure 2, cos ([phi]) = [S'.sub.t]/([S'.sup.2.sub.t] + [G'.sup.2]), [phi] is the angle between the segment of the bound vortex and the line through the point and the vortex segment as shown in Figure 3, sin ([phi]) = [([S'.sup.2.sub.t] + [G'.sup.2]).sup.1/2]/r, r is the distance from the point to the vortex segment, and r = [([([y.sub.2]-[y.sub.1]).sup.2] + [S'.sup.2.sub.t] + [G'.sup.2]).sup.1/2], [S'.sub.t] is the longitudinal separation along the x-axis of the two wings and G' is the vertical distance along the z-axis between the two wings, as shown in Figure 2, and can be calculated with the coordinate transformation as
Applying the Biot-Savart law into the segment of the bound vortex along the lifting line of the other lifting surface and integral along the spanwise, the x-velocity component induced by the bound vortex at an arbitrary point along the lifting line is
Assume that the UAV helicopter has k-blade rotor and the circulation of each blade is [GAMMA]; the circulation of a bound vortex corresponding to d[theta] is (k[GAMMA]/2[pi])d[theta].
The relationship between the bound vortex and cylindrical vortex circulation is given by
Refer to the flapping motion equation combined with blade-element theory and Kutta-Joukowski equation; the components of the bound vortex in first-order Fourier series can be expressed as
The wing is modelled with a bound vortex and two free vortices coming off the wings tips and closing to "rings" when the vertical velocity component is reversed (Fig 1).
Comparison with the stationary case was made, the wing being modelled with a bound vortex and two infinite free vortices (Fig 3).
The aerodynamic force necessary to stay aloft is created solely because of the so-called bound vortex (or circulation), which is complementary to the starting vortex and constitutes a measure of difference in flow speeds over and under the wing.
Therefore, the ring rotation speed, the corresponding bound vortex strength, and their contribution to useful force generation have been increased for the duration of the stroke.

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