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. The Strouhal number is an integral part of the fundamentals of fluid mechanics.

The Strouhal number is often given as

\[ \mathrm{St}= {f L\over V}, \]

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. In certain cases like heaving (plunging) flight, this characteristic length is the amplitude of oscillation. This selection of characteristic length can be used to present a distinction between Strouhal number and Reduced Frequency.

\[ \mathrm{St}= {k a\over c}, \]

where \(k\) is the reduced frequency and \(a\) is amplitude of the heaving oscillation.

File:Srrrpd.png

Strouhal number as a function of the Reynolds number for a long cylinder

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.

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.

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.

\[ \mathrm{St}= {f\over U}{C^3} \]

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

• Froude number
• Mach Number
• Weber Number
• Aeroelastic Flutter

External links

• Vincenc Strouhal, Ueber eine besondere Art der Tonerregung

ca:Nombre de Strouhal