Strouhal number
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.[3][4]
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).
[edit] See also
[edit] References
- ^ White, Frank M. (1999). Fluid Mechanics (4th ed.). McGraw Hill. ISBN 0071168486.
- ^ Sobey, Ian J. (1982). "Oscillatory flows at intermediate Strouhal number in asymmetry channels". Journal of Fluid Mechanics 125: 359–373. Bibcode 1982JFM...125..359S. doi:10.1017/S0022112082003371.
- ^ Kim, K. J.; Durbin, P. A. (1988). "Observations of the frequencies in a sphere wake and drag increase by acoustic excitation". Physics of Fluids 31 (11): 3260–3265. Bibcode 1988PhFl...31.3260K. doi:10.1063/1.866937.
- ^ Sakamoto, H.; Haniu, H. (1990). "A study on vortex shedding from spheres in uniform flow". Journal of Fluids Engineering 112 (December): 386–392. Bibcode 1990ATJFE.112..386S.
