Common flow problems for modal analysis implemented in OpenFOAM

Dependencies

• OpenFOAM-v2406

Test cases

To run a simulation case, create a folder called run, create a copy of the simulation setup in the run folder, and execute the Allrun script.

2D laminar flow past a cylinder in a narrow channel at $Re=100$

The case setup folder is cylinder_2D_Re100. The main simulation parameters are:

• parabolic inlet velocity profile with $U_\mathrm{max} = 1.0m/s$
• $Re=U_\mathrm{max}d/\nu=1\cdot 0.1/10^{-3}=100$ ($d$ - cylinder diameter, $\nu$ - kinematic viscosity)
• convective time scale: $t_\mathrm{conv} = d/U_\mathrm{max} = 0.1/1 = 0.1s$
• simulation end time $t_\mathrm{end}=200t_\mathrm{conv} = 20s$
• velocity, pressure, and force coefficients are sampled every $\Delta t_\mathrm{write} = t_\mathrm{conv}/50 = 2\times10^{-3}s$

To run the simulation with a different mesh resolution, comment/uncomment the corresponding lines in the Allrun script The notebook cylinder_2D_Re100.ipynb contains results for the mesh dependency of the force coefficients, the shear stress velocity at the cylinder's surface, and the singular value decomposition of the vorticity field.

3D turbulent flow at $Re=3900$

• uniform inlet velocity of $u_x = U_\mathrm{in} = 39m/s$
• $Re=U_\mathrm{max}d/\nu=39\cdot 0.1/10^{-3}=3900$ ($d$ - cylinder diameter, $\nu$ - kinematic viscosity)
• $t_\mathrm{conv} = d/U_\mathrm{in} = 0.1/39.0 \approx 2.5641\times 10^{-3}s$
• simulation end time $t_\mathrm{end}=3900t_\mathrm{conv} = 10s$
• snapshots with velocity and pressure are sampled every $\Delta t_\mathrm{write} = t_\mathrm{conv}/10.25 = 2.5\times10^{-4}s$
• force coefficients are sampled every $\Delta t_\mathrm{write} = t_\mathrm{conv}/51.2 = 1\times10^{-5}s$
• the transient phase is completed after $t_\mathrm{end}=75t_\mathrm{conv} = 0.19225s$
• mean and prime2Mean quantities are sampled every $\Delta t_\mathrm{write} = t_\mathrm{conv}/0.1025 = 2.5\times10^{-2}s$

References

• 2D laminar flow past a cylinder in a narrow channel at $Re=100$:
  • Schäfer, M., Turek, S., Durst, F., et al.: “Benchmark Computations of Laminar Flow Around a Cylinder”. In: Flow Simulation with High-Performance Computers II. Ed. by Hirschel, E. H. Vol. 48. Notes on Numerical Fluid Mechanics (NNFM). Wiesbaden: Vieweg+Teubner Verlag, 1996, pp. 547–566. doi: 10.1007/978-3-322-89849-4_39.
• 3D turbulent flow at $Re = 3900$:
  • Lehmkuhl O. Lehmkuhl, I. Rodrı́guez, R. Borrell, and A. Oliva. “Low-frequency unsteadiness in the vortex formation region of a circular cylinder”. In: Physics of Fluids 25.8 (2013), p. 085109. doi: 10.1063/1.4818641,