Marine Ecosystem Dynamics Modeling Laboratory

Case 10. Flows over a Circular Cylinder

1. Design of the Numerical Experiment

Numerical simulations for uniform flows over a circular cylinder were conducted to examine the laterial boundary conditions implemented in FVCOM.

This problem was tested under a nonrotating and homogenuous density conditions for a rectangular channel with a width of 15m, a length of 60m and a constant depth of 0.5m (Fig. 1). The center of a circular cylinder(D=1m) is located at half witdth of the channel with a distance of 16.5m to the left side which minimizes effects from laterial boundary and outflow conditions. Due to low flowing speed and shallow water, only a horizontal two dimensional FVCOM was set up for the simulations. The model was forced by a unifom, constant flow from west boundary (upstream).

Fig.1: View of the computing domain and zoom view of the grid aroud the cylinder

2. Results

A Reynolds number (Re = UD/ν, where U is the upstream velocity and ν is the molecular kinematic viscosity) can be defined for the above test to characterize the flowing features behind the obstacle. As described in classical fluid dynamics text, if Re<40, a laminar flow with two steady symmetric vortices behind the cylinder is obtained; while for 40<Re<1000, a periodic vortex pairs shed from the downstream side of the cylinder. In case1, case2 and case3, the inflow velocity was adjusted to obtain a desired Reynolds number.

Case1:

Laminar flow with two steady vortices behind the cylinder (Re < 40)

color plot represent relative vorticity

(click the figure for animation)

Case2:

Shear instability occurs at Re around 40

color plot represent relative vorticity 

(click the figure for animation)

Case3:

Kármán vortex street (Re around 300)

color plot represent relative vorticity 

(click the figure for animation)

Case4:

The above test was further extended to a geostrophic scale island wakes problem following the work of Dong et al,(2006). Only Coriolis force was considred at current stage simulation, so again a uniform inflow of 0.2m/s was enforced from boundary. With the inclusion of a constant Coriolis frequency (f=10^-4 s^-1), the results showed the vortex shedding becomes unsymmetric with a deflection to the right direction.

color plot represent relative vorticity

 (click the figure for animation)

«PreviousNext» Posted on November 12, 2013