[o_mars_2010]

I have developed a code to simulate a flow past a circular cylinder using Immersed Boundary Method.
I set Re=40, and the free stream inlet velocity to 1 and the diameter of the cylinder 0.1.
The resultant streamlines results have no recirculation zone behind the cylinder .
Could any one help me to know what is the reason?

[FMDenaro]

Originally Posted by o_mars_2010

I have developed a code to simulate a flow past a circular cylinder using Immersed Boundary Method.
I set Re=40, and the free stream inlet velocity to 1 and the diameter of the cylinder 0.1.
The resultant streamlines results have no recirculation zone behind the cylinder .
Could any one help me to know what is the reason?

At Re=40 you should have a steady, symmetric separation. Have you reached a full steady state? Are you using upwind discretization? what about your grid?

[o_mars_2010]

i am using AB-CN discretisation on a staggered grid, the mesh size 0.1D, and a time step of 0.01.
I think i reached the steady state because there is no change in the velocity contours or the vorticity contours is taking place.

[o_mars_2010]

an intersting thing happened when i changed the Re to 500 i could watch a steady state recirculation zone ????

is my inlet velocity has to be adjusted according to the Re ??
I mean
if Re =40 then the inlet velocity should be

U=viscosity*Re/(D)
because i specified the inlet velocity to be 1, with no relation to Re

[FMDenaro]

Fix your Re number, then you have to fix two among the parameters U, D, viscosity.

Furthermore, AB-CN is a time integration scheme, but says nothing about the spatial discretization

[o_mars_2010]

sorry, i used second order centeral difference for the spatial discretization.
I will repeat what you say from my understanding to it:
So, for example if i want to make a simulation at Re= 40 around a cylinder with a diameter 0f 0.1 using the kinematic viscosity of water, then the free stream velocity (inlet velocity) will be equal to: (fixing the diameter and viscosity)
U=40*1.04e-6/0.1=4.16e-4 m/s
and in the case of Re=150, the free stream velocity will be:
U=150*1.04e-6/0.1=1.56e-3 m/s

[FMDenaro]

Originally Posted by o_mars_2010

sorry, i used second order centeral difference for the spatial discretization.
I will repeat what you say from my understanding to it:
So, for example if i want to make a simulation at Re= 40 around a cylinder with a diameter 0f 0.1 using the kinematic viscosity of water, then the free stream velocity (inlet velocity) will be equal to: (fixing the diameter and viscosity)
U=40*1.04e-6/0.1=4.16e-4 m/s
and in the case of Re=150, the free stream velocity will be:
U=150*1.04e-6/0.1=1.56e-3 m/s

correct

be sure you respect the stability constraint for the AB-CN scheme with central second order discretization

[o_mars_2010]

Thanks a lot for your help.
About the stability condition, i think because i am using an implicit way for the treatment of the viscous term then, the restrict constrain of time will be relaxed, so:
dt<=dx/U
However, i am not sure about the IBM, may be it add additional constrain on the time step!!!

[o_mars_2010]

I have a very strange results:
When i set the kinematic viscosity as 1.04e-6 i have no recirculation zone.
however, when i set it to 1e-2 i clearly see the recirculation zone.
i calculate the free stream velocity according to the relation i mentioned above in both cases of viscosity.
could you please explain to me why this happened???

[FMDenaro]

by retaining the same reynolds number?

[o_mars_2010]

I am using the non-dimensional form of N-S equation, So i have to set the Reynolds no. and the inlet velocity explicitly, the viscosity does not appear explicitely in the momentum equations.
So, lets say i want to make a simulation of flowing water past a circular cylinder with a diameter D=0.1 at Re=40 and the kinematic viscosity of water is 1.04e-6, then the calculated inlet velocity will be U=40*1.04e-6/0.1=4.16e-4 m/s.
I set the parameters like that in my problem, however i didn't have any circulation.
However, when i changed the kinematic viscosity to 1e-2 (i do not know what fluid have such a value) i got circulation zone!!!!!!!!!!!!
So, my question why i do not have a circulation zone for water???

[o_mars_2010]

Diameter=0.1; % cylinder diameter
%kinematicviscosity=1.04e-6; %water at 20 'C
kinematicviscosity=0.01;
ineltvelocity=Re*kinematicviscosity/Diameter;

[FMDenaro]

I do not understand what you are done... if you have non-dimensional equations (and a non dimensional domain), the only parameter to set is the Reynolds number!

[o_mars_2010]

So, how can i specify the inlet velocity (Dirchilit B.C) on a recatangular domain ?

[FMDenaro]

Originally Posted by o_mars_2010

So, how can i specify the inlet velocity (Dirchilit B.C) on a recatangular domain ?

The non-dimensional inlet is the same as well as the non-dimensional diameter!

[o_mars_2010]

So, if i have a rectangular domain of 40D * 30D, and a grid size 0.05D
then, the non dimensional diameter will be equal to 1
and the non dimensional inlet velocity will be equal to 1
and the rectangular domain will be equal to 40*30
and the grid size will be equal to 0.05

[o_mars_2010]

x*=x/D, u*=u/U, t*=t.(U/D)

[FMDenaro]

.... yes !

[o_mars_2010]

Thank's a lot.

[o_mars_2010]

Dear Dr. Filippo
i have some strange results:
when i set the mesh size to 0.1D, i have a good results for the length of the recirculation zone and the drag coefficient.
l/D=2.33 & Cd=1.55
On the other hand, when i decrease the size of the mesh to 0.05D, which is supposed to give better results, it gives worth results:
l/D=2.03 & Cd=1.39

Could you tell me please what could be the reason ???