Yes its important not only in FLUENT but all CFD simulations to perform grid independent study,  specially if you are trying to present your  results in publications. Typically you will create a sequence of  coarse, medium and fine meshes for the purpose of showing that the solution changes little between medium and fine mesh.

Now if you are not familiar with the flow pattern and/or complexity of the flow at hand, you may have to do even  more than three sequence of meshes. But once you had enough practice you will be able to estimate in future modeling projects approximately what is the appropriate mesh density needed to resolve the flow on similar geometry. This will help you speed up your mesh creation and grid independent study. 

Grid independence study is performed to eliminate/reduce the influence of the number of grids/grid size on the computational results. And it is always good practice to follow this for every individual geometry, which is tedious. The grid independence for one geometry will be applicable only for that geometry. For example if after mesh independence you have 5 nodes along the diameter, using the same 5 nodes for a lower dia will be fine but for a higher dia the physics will not be captured properly.

But all these depends on to what accuracy you need the results.

Yes, you need to do the grid independent study when you change your domain.

In any changes for geometry, meshing grids definitely will changed. When grids changed, we need to ensure the grid independence is applied.

Another good test to do is numerical sensitivity test. The important BC and parameters can be tested to see the the effect of certain conditions to the result.

Other important is parametric studies also may required to ensure the new geometry is giving the expected result as we wish.

Thanks for all of you, I much appreciate that.

What I did in my case is just keep same number of mesh per unit length along the diameter of the smaller pipe.

Yes, the grid independency has to be proved at any simulation. Anyway, you also have to maintain the lowest grid available in order to ease simulation time and keep accuracy. Maybe a non-uniform grid will be the best practice.

Yes, you can keep the same B. C.'s in use.  Change in geometries does not alter B. C.'s  of the problem. As a result of the above, you can observe that there will be only  shifting of the position takes place without affecting B. C.'s.

Yes. I agree for a need of separate grid independence test.

Some regions in flow field respond much on grid size and some other regions respond less. That's why a non-uniform grid with fine mesh around the regions of steep changes are recommended. In those regions if we maintain the same or more number of grid points per unit length, we can expect same level of accuracy, but may not be the least possible grid size. it need more computational time.

If we need both accuracy and less computational time, then we do perform a grid independence test.

Very big thanks, your clarifications are much appreciated. Know it is very clear to me what I have to do...

Thanks

Yes, it is a good practice to always check that your solution does not depend on the grid used. If you have already checked the sensitivity of your mesh for a given pipe size, the work will be a bit easier the next time around. If I were you, I will consider the Reynolds number of my current system and the ratio between the averge size of my mesh elements and the size of the pipe (diameter). If in your next case, the Reynolds number increase I will decrease the sice of your mesh elements with respect to the size of your pipe (increase the density of your grid) in order to properly capture regions of large velocity gradients occurs.

yes its need always , as already explained by other researchers i hope your query resolved.

yes, thanks... actually I much appreciate all the answers above. they are very clear and useful.

Yes its important not only in FLUENT but all CFD simulations to perform grid independent study,  specially if you are trying to present your  results in publications. Typically you will create a sequence of  coarse, medium and fine meshes for the purpose of showing that the solution changes little between medium and fine mesh.

Now if you are not familiar with the flow pattern and/or complexity of the flow at hand, you may have to do even  more than three sequence of meshes. But once you had enough practice you will be able to estimate in future modeling projects approximately what is the appropriate mesh density needed to resolve the flow on similar geometry. This will help you speed up your mesh creation and grid independent study. 

You need to perform the grid independent study when you modify the geometry, unless you are scaling it.