Strouhal number

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In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms. The parameter is named after Vincenc Strouhal, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding and singing in the wind.[1] The Strouhal number is an integral part of the fundamentals of fluid mechanics.

The Strouhal number is often given as

where St is the dimensionless Strouhal number, f is the frequency of vortex shedding, L is the characteristic length (for example hydraulic diameter) and V is the velocity of the fluid.

For large Strouhal numbers (order of 1), viscosity dominates fluid flow, resulting in a collective oscillating movement of the fluid "plug". For low Strouhal numbers (order of 10−4 and below), the high-speed, quasi steady state portion of the movement dominates the oscillation. Oscillation at intermediate Strouhal numbers is characterized by the buildup and rapidly subsequent shedding of vortices.[2]

For spheres in uniform flow in the Reynolds number range of 800 < Re < 200,000 there co-exist two values of the Strouhal number. The lower frequency is attributed to the large-scale instability of the wake and is independent of the Reynolds number Re and is approximately equal to 0.2. The higher frequency Strouhal number is caused by small-scale instabilities from the separation of the shear layer (Kim and Durbin, 1988 and Sakamoto and Haniu, 1990).

In metrology, specifically axial-flow turbine meters, the Strouhal number is used in combination with the Roshko number to give a correlation between flow rate and frequency. The advantage of this method over the freq/viscosity versus K-factor method is that it takes into account temperature effects on the meter.

f = meter frequency, U = flow rate, C = linear coefficient of expansion for the meter housing material

This relationship leaves Strouhal dimensionless, although a dimensionless approximation is often used for C3, resulting in units of pulses/volume (same as K-factor).

See also

References

  • Kim, K. J. and Durbin, P. A. (1988) "Observations of the frequencies in a sphere wake and drag increase by acoustic excitation," Physics of Fluids, 31, pp. 3260-3265.
  • Sakamoto, H. and Haniu, H. (1990) "A study on vortex shedding from spheres in uniform flow," Journal of Fluids Engineering, 112(December), pp. 386-392.

External links

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