I know that a converged solution is independent of the value of URF's chosen. However, is it acceptable to change URF's in the middle of a solution and then continue iterating?

Yes it is acceptable.

You're right when you say that a converged solution does not depend on the value of URF's, but the convergence of a solution is dependent on their values, and also by the combination of them.

Some authors like Peric, for example, suggests some rule of thumb like

a_velocity + a_pressure = 1

where a represents the URF.

Regards, ap

regarding URF's,can excessive under-relaxation introduce accuracies in unsteady flows. that is, although solution will be converged but not accurate?

Swarup.

Thanks Swarup, You meant "introduce inaccuracies" right?

Thanks for the information ap. Very well worded indeed!