# The formula for vorticity

### Vorticity is a crucial quan­tity for an axial fan’s acoustic prop­er­ties.

Oliver Haaf, Group Leader in Proto­type and Func­tion Devel­op­ment for Aero­dy­namics at ebm-papst in Mulfingen

A velocity field’s rota­tion is given by the cross product of the direc­tional deriv­a­tive vector () and the velocity vector (v). It spec­i­fies how fast or how strongly a vortex in a flow field is rotating around its center. The vorticity can be influ­enced by making changes in the blade geom­etry near the gap between the fan and its housing. Noise increases with increasing vorticity.

For axial fans, the pres­sure differ­ence between the intake and outlet sides results in a flow over the fan blades in the vicinity of the housing wall. The flow inter­acts there with the edges, the blade surface and the surrounding housing wall. Vortices form which can raise the noise level by up to 10 dB.

The gap between the blade tip and the fan housing has a major impact on the noise level, with the noise decreasing as the size of the gap is reduced.

Winglets can influ­ence the vortices with different geome­tries. One possi­bility is to reduce the velocity vector v of the vortices. So-called T-winglets increase the flow resis­tance in the gap area, thus reducing the vorticity (ω = × v) and conse­quently the noise gener­ated when the vortices strike solid surfaces.

The other possi­bility is to reduce the vorticityωby changing the blade contours: The blade is rounded off in the gap area and the edges over which the gap flow streams are removed — similar to the winglets on airplane wings. These blades only have an edge on the outlet side of the gap flow, so vortex forma­tion is signif­i­cantly reduced — this influ­ences the gradient vector (del oper­ator = ∂/∂x, ∂/∂y, ∂/∂z) = direc­tional deriv­a­tive vector).

The flow inter­acts in the vicinity of the tip gap with the neigh­boring edges, the blade surface and the surrounding housing wall. The strength of the resulting tip gap vortex depends on the design.

The winglet geom­etry that is best suited to a partic­ular axial fan is deter­mined by the required sepa­ra­tion between the rotating (blade) and stationary (fan housing) compo­nents.

The inter­ac­tion of the two compo­nents is crucial and the geome­tries have to fit in order to achieve optimal results. A good example is provided by the AxiBlade axial fans made of strong, glass-fiber rein­forced plastic that enables the winglet shape to be adapted to the inter­ac­tion with the newly devel­oped housing geom­etry, reducing the noise gener­ated at the gap.