[kingmaker]

I am trying to simulate a cylinder in flow problem (2D).

Case 1 :

Flow around a cylinder 
Turbulence Model : LES (all default values)
Wall Function : nutUSpaldingWallFunction (for nuSgs)
solver : pimpleFoam

Case 2 :

All physics same as Case 1. 
No Displacement on the mesh
solver : pimpleDyMFoam

OpenFOAM version 2.2.1

I know the Turbulence models LES should not have any effect in 2D case, I setup a generic 3D case.

Now when I plot the forces(Lift and Drag) on the cylinder they are completely different.
Here I am posting the plots. I am totally confused. I am doing this because I want to use the pimpleDyMFoam for FSI simulations (because of mesh motion possibility). So I want to make sure that pimpleDyMFoam, with mesh motion set to 0 on relevant patches, gives same result as pimpleFoam . But apparently this is not the case.

Any hints to as what is happening is really helpful.

[floquation]

Is there any particular reason for using v2.2.1?
Much newer versions are available, including many bug fixes. Perhaps that will resolve your issue.

Otherwise, you'll have to open the two solvers and compare them.
For instance, I noted the following difference in OF v4.0 in interFoam vs interDyMFoam yesterday:

interDyMFoam:
    if (p_rgh.needReference()) // Statement irrelevant for mesh motion??
    {
        fvc::makeRelative(phiHbyA, U);
        adjustPhi(phiHbyA, U, p_rgh);
        fvc::makeAbsolute(phiHbyA, U);
    }

interFoam:
    adjustPhi(phiHbyA, U, p_rgh);

You can play with such differences (edit them) and see if it resolves your issue. Especially in the old version you're using, there could very well be a bug somewhere.
(P.S.: Your bug might disappear if you set a non-zero very small mesh motion. Perhaps the fact that it is precisely zero is the reason you see this happening.)