From David Avellan:
I remember when I first learned this back in high school I thought it was a bull crap move. It looked like it wouldn’t work.
That is until I actually drilled it and quickly learned it works quite well!
The key to the Cross Knee Block is to get the opponent to move towards the knee you will block. This doesn’t work statically – you have to create momentum by turning your opponent.
As a bonus, you can easily land right in an arm bar after the take down.