Drag on a cylinder and shedding frequency

(a) Reynolds number

$$Re=\frac{\rho UD}{\mu}=\frac{1.2\times15\times0.05}{1.8\times10^{-5}}=5.0\times10^{4}$$

This is in the subcritical range (about $10^3$ to $2\times10^5$), where the laminar boundary layer separates near $80^\circ$ and $C_D\approx1.2$, so the given value is reasonable.

(b) Drag force and power

Reference area (projected) $A=DL=0.05\times2=0.10$ m².

$$F_D=\tfrac12\rho U^2C_DA=0.5\times1.2\times15^2\times1.2\times0.10=16.2\ \text{N}$$

Power to overcome drag:

$$P=F_DU=16.2\times15=243\ \text{W}$$

(c) Vortex shedding

$$f_s=\frac{St\,U}{D}=\frac{0.2\times15}{0.05}=60\ \text{Hz}$$

Alternating vortices (von Karman street) produce an oscillating lift force at this frequency, which can excite vibration and noise.

(d) Bluff versus streamlined bodies

 Bluff body                 Streamlined body
   ____                        ______
  /    \  large wake        ---/      \___  thin wake
 |  O   |:::::::::::::       ---\______/
  \____/  low pressure         attached flow

• On a bluff body the boundary layer separates early because of the strong adverse pressure gradient. A broad low-pressure wake forms behind it, so pressure is much lower on the rear than the front: large pressure (form) drag dominates (friction drag is small).
• On a streamlined body the flow stays attached up to the tail, the wake is thin, and drag is mainly skin friction, which is much smaller.

CFD prediction: a 2D/3D domain extending about 10D upstream and 20D downstream is meshed with prism layers; RANS (k-$\omega$ SST) or unsteady URANS/LES is used; $C_D$ is computed by integrating surface pressure and shear stress over the body. Wake resolution and separation prediction are the main sources of error, so validation with experimental $C_D$ is needed.

Answer: $Re=5\times10^4$; $F_D=16.2$ N; $P=243$ W; $f_s=60$ Hz.