The residuals may diverge because of a lot of reasons. You can follow the below guidelines for troubleshooting:
1. Ensure all your boundary conditions are specified correctly. Double check them. Try changing few of them and see if the residuals still diverge.
2. Ensure a good enough mesh near boundaries.
3. Try changing the turbulence model you've used.
4. After seeing the effect of all of the above if nothing improves you can change the 'Under-relaxation' factors in 'Solution Controls' Panel. Decrease the 'Momentum' value in steps of 0.1 and see the effect.
Try each of the above steps individually to figure out the exact problem.
It's very important for the continuity residuals to go down. If it doesn't, it means that overall continuity is not being satisfied i.e you inflow is not equal to the outflow. Ensuring this is the first check that your CFD results are NOT wrong.