I'd call the above a purifier, and a clarifier similar, but with no discharge for separated milk. It would essentially just remove sludge rather than sludge/water.
And yes, I run two purifiers in my day job. One removes water/sludge from lube oil for two very large diesels. The other removes water/sludge from fuel oil before being stored in tanks which then feed the above engines.
In both cases, the product (lube oil/fuel oil) is heated to about 70 degrees to increase the density difference between water/product and aid separation.
Water is removed continuously from the equivalent of the 'separated milk' outlet on the diagram above, whilst the separated product comes from the cream outlet.
After a certain interval, the bowl opens to dispel all sludge/water down a sludge outlet.
A good explanation is here:
http://www.marineengineering.org.uk/. It won't let me post a direct link so you'll have to scroll down on the left bar to Utilities/Fuel Treatment/Purifiers.
Next time I've got one in bits I'll get some photos if you're interested.
Edit: The act of purifying the lube oil on the diesels is that it essentially makes it last indefinitely. As I'm sure you'll appreciate, if you're talking 3000 litres of lube oil, it's kinda expensive to do an oil change! The sludge and water is removed from suspension in the oil which maintains the oils performance. The only thing that we need to watch the the total base number - this will decrease when running on high sulphur fuels due to the formation of sulphuric acid as part of the combustion process.
However, due to the trend towards low sulphur fuels this means our oil is lasting longer and longer. I've personally seen about 6000 hours on these engines which is rapidly approaching the equivalent of about 500,000 miles - and no oil change yet.