The method is for converting a vertically standing up-flow tower by inserting a freely insertable pipe into the conical part of the up-flow tower the tower is converted to a down-flow tower where the tower can easily be restored to the up-flow tower and optimized with regards to a minimized stagnation volume in the tower. The upper open end of the pipe is disposed at a first distance (A) from the lower part of the conical inlet part. The first distance (A) is less than the total vertical extension (B) of the conical inlet part. The cellulose pulp establishes a self-forming stagnation zone around the pipe at a lower part of the down-flow tower.