Effect of streamline curvature on flow non-uniformity in Wind-Tunnel contractions and nozzles

A well-known result due to Prandtl [1] characterises the effect of contraction in wind tunnels and

nozzles, on flow non-uniformity (quantified by the ratio of local velocity variation between a reference

streamline and a neighbouring streamline to the velocity at the reference streamline at a given

streamwise location). According to this classic result, non-uniformity is attenuated at a downstream

location in proportion to the square of the contraction ratio. Corrsin [2 ] extended this to include the

effect of upstream density (temperature) irregularities on working section velocity irregularities in

an incompressible flow and further extended these results to compressible flow, neglecting transverse

streamline curvature effects in the passage. In the present work, Prandtl’s result is extended to

include non-zero transverse streamline curvature effects in the passage. Furthermore,this result is

extended to compressible flows with non-zero streamline curvature, where isentropic flow along the

streamline is assumed.Comparison of present analytical results with CFD simulations shows  good agreement.

References

[1] Prandtl, L., Herstellung einwandfreier Luftströme (Windkanäle), Akademische Verlagsgesellschaft MBH,

1932.

[2] Corrsin, S., “Effect of wind-tunnel nozzle on steady-flow nonuniformities,” Journal of the Aeronautical

Sciences, Vol. 19, No. 2, 1952, pp. 135–136.