Air Flow over Cylindar (Under Development)

In this chapter we perform the numerical simulations for acoustic field generated by air flowing over a cylinder. This problem is chosen to verify the accuracy of the developed solver. The acoustic fields are calculated for different Reynolds numbers

(1)\[ \begin{align}\begin{aligned}\newcommand{\defeq}{\buildrel{\text{def}}\over{=}}\\\mathrm{Re} \defeq \frac{\rho vD}{\mu}\end{aligned}\end{align} \]

The density of air is \(\rho = 1.2250 \,\mathrm{kg}/\mathrm{m}^3\). The dynamic viscosity is \(\mu = 1.983\times10^{-5} \,\mathrm{kg}/\mathrm{(m\cdot s)}\). Choose the diameter of the cylinder to be \(D = 0.1 \,\mathrm{m}\). Then, at the three given Reynolds numbers, the velocity can be calcuated from (1):

\[v = \frac{\mu\mathrm{Re}}{\rho D}\]
Reynolds number 89,000 46,000 22,000
Velocity (m/s) 14.407102 7.446367 3.561306


In examples/bulk/air run the following commands to obtain the above numbers:

./go velocity --density 1.225 --diameter 0.1 --dvisco 1.983e-5 --reynolds 89000
./go velocity --density 1.225 --diameter 0.1 --dvisco 1.983e-5 --reynolds 46000
./go velocity --density 1.225 --diameter 0.1 --dvisco 1.983e-5 --reynolds 22000

The bulk modulus of air is \(K = 1.42 \times 10^5 \, \mathrm{Pa}\).