Submergence in a flume occurs when downstream conditons combine to reduce free-flow out of the flume to the point where the free-flow discharge equations are no longer suitably accurate.
While submergence corrections can be made for some flumes (Parshall, USGS Portable Parshall, Cutthroat, H flume, Montana), there is added complexity (measuring at the level at two locations) and cost.
Some flumes can not be corrected for submergence (Trapezoidal, Palmer-Bowlus, RBC). Typically this is because the submergence transitons (St) for these flumes is quite high - 80-90% - and attempts to correct the flow are to diffcult / costly / time consuming for the minimal returns.
Remember that submergence can occur at any flow rate. Submergence is determined by the downstream conditons alone.
Any flume can experience submergence - although some types are more resistant (Parshall, Palmer-Bowlus, Cutthroat, Trapezoidal, RBC) to its effects than others (Montana, H flume).
Although there can be advantages to designing an application to experience submergence from the outset, in general, Openchannelflow recommends that flumes be installed for free-flow conditions under all flow rates.
Images: Montana Water Commissioner Training