I need to model a valve from fully open to full closed position. I am trying to use the dynamic meshing method in fluent. When the valve is nearly closed the velocities around are expected to be very high (even choking flow in my case)Hence the mesh needs to very fine in this region. How do I solve this problem without having a impractically fine mesh.

Along with your dynamic meshing, you may also want to explore the use of mesh adaption. This will allow you to adapt the mesh based on your gradients. So you will have a finer mesh if there are steeper gradients.