-> 2D code:

    In this section, we give all the results that we have obtained with a 2D code; we ran this code for two different initial angle of fluid velocity: 0° & 45°.
We did calculus on a domain 128*128 and with a number of Reynolds: Re=200.

        -> 0 degree:

                We have done a simulation with a time end of 40 sc. You can look simulation parameters in file params0dg. If we observe drag, we see that during the first second, it's very high; after, it begins to oscillate during two seconds around a constant value. After six sc., we can consider that the drag doesn't evolve and stay constant. However, we must be careful because after 18scd, the drag begins a new time to oscillate and to grow up (that corresponds to the increase of the lift).
For the lift, like we work with a in-line array, we can observe the beginning of oscillations around 14 sc.
 
 

Drag	Lift

                We display twenty pictures of vorticity (one picture for each second until 20 sc) with exactly the same color palette. After that, we have done a little animation with eighty pictures (two per second) in order to well see vorticity evolution and to understand where and when turbulences appear.
                 The flow has a characteristic jet shear-layer structure and there isn't any sign of vortex behind the cylinders. However, vortices are generated by a shear-layer instability at the edge of the shear-layer, between the cylinders.
 
 

t=1s	t=2s	t=3s
t=4s	t=5s	t=6s
t=7s	t=8s	t=9s
t=10s	t=11s	t=12s
t=13s	t=14s	t=15s
t=16s	t=17s	t=18s
t=19s	t=20s	Animation

 
 
 

            -> 45 degrees:

                    Here, we did a simulation with a time end of 20 sc. You can look simulation parameters in file  params45dg.
                    On the first graph, we plotted drag which admits a period where it is very high (2sc-5sc). After this, it decreases and oscillates around a constant value and begins a periodic oscillation. This decrease and this change corresponds to the apparition of the lift (turbulences) and the increase of its value.
After 7 sc, when drag and lift evolve periodically, we can see that lift is twice higher than drag. In comparison with previous simulation, lift is also higher and develops earlier in the rotated array.
 
 

Drag	Lift

 

                       We display twenty picture of vorticity (one picture for each second) with exactly the same color palette. After that, we have done a little animation with eighty pictures (four per second) in order to well see vorticity evolution and to understand where and when turbulences appear.
                       Until four sc, fluid flowing is not at all turbulent. From the fifth sc, turbulences appear, leave cylinder contour and breed other turbulences near other cylinders. The fifth sc is exactly period when drag decreases and lift increases a lot. After this period, we can observe that lift is less important than before and that drag and lift are in a periodic evolution. The plots of vorticity suggest that more vorticity is produced in the rotated array (the flow past the rotated array exhibits a completely different flow regime).
 
 
 

t=1s	t=2s	t=3s
t=4s	t=5s	t=6s
t=7s	t=8s	t=9s
t=10s	t=11s	t=12s
t=13s	t=14s	t=15s
t=16s	t=17s	t=18s
t=19s	t=20s	Animation

 
 
 
 

Results of parallelisation

Graphic Results 3D