problem 2 von karman vortex street 30 points a long cylinder with diam

Question

Problem 2: Von Kármán Vortex Street
30 points
A long cylinder with diameter D = 0.02 m is placed in a uniform flow of speed U. Assume that
fluid density p= 800 kg/m³, and fluid viscosity = 0.08 Pa-s. For a certain range of incoming flow
speeds, an interesting flow pattern will emerge: the cylinder will create a clockwise vortex in its
wake, then a counterclockwise vortex, then another clockwise, then another counterclockwise, and
on and on. This alternating pattern is called the Von Kármán Vortex Street, and there is a constant
frequency of vortex production, f (for a given spoed). A video: https://youtu.be/3mULL606f38
Part a: How many independent dimensionless groups govern this problem?
Part b: Assume that one of the dimensionless groups is the Reynolds number. Find another di-
mensionless group, this one with the shedding frequency / in the numerator. (Hint: it involves
speed and one other parameter.)
Part c: Experimental data is shown below, with the z-axis being Reynolds Number and the y-axis
the dimensionless number called St. (this is what you determined in (b)). Suppose you don't know
exactly what the incoming flow speed U is, other than it is less than 10 m/s. But you can measure
the oscillation in the wake (for example if the cylinder is piezoelectric) and know f= 25.6 Hz. Use
the experimental data in the figure to estimate the incoming flow velocity.
(Hint: May need to guess and check, and of course your answer will be a bit approximate.)
0.22
St
0.20
0.18
0.16
0.14
0.12