Keep in mind what the CFL number is. It is U*Dt/h, where U is the velocity in a certain direction, Dt is the time step and h is the grid cell size in the direction of U. So in fact, there would be 3 different CFL, one for each direction. Basically, the CFL will tell you how many cells a fluid particle would jump through in one time step (assuming consistent mesh size). To keep the CFL number low, we must stretch the grid cells, meaning make h bigger, but the key is only to do it in the streamwise direction. As the flow moves into the smaller channels, it will speed up, and we need to make sure we have high quality elements that are stretched in the streamwise direction.

What I would do is go back to DesignModeler and slice the geometry, creating a multi-bodied part. When you bring this into meshing, you can then sweep the long constant diameter sections and allow these to have a high aspect ratio. At the moment, I assume that you just have created a Tet-bomb mesh. A sliced model will allow you to create higher quality Hexas that can be stretched to aspect ratios of 1000 without losing accuracy (assuming double precision solve). These stretched cells will reduce the CFL in these cells and hopefully allow your solution to converge better.