I bought a 2006 XC90 in May.
Recently it has begun to expel coolant when it is running. If I add coolant without it running, it will not leak. If I drive around for a bit, say 15 minutes or so, then park it will expel for a short time - seemingly until the engine is cooled. Then it will stop the purge.

About 30 minutes of driving will drain 3/4 of the reservoir from the MAX FILL line. The red dash light will then come on and I'll have to pull over and add coolant.

The temperature gauge on the dash never goes above the center position.

A check engine light came on and I had the code checked. It was for a MAF Sensor.

I don't see anything else leaking anywhere but the right front. And, it's less of a leak and more of a stream. (I'll attempt to attach video)

 

you are leaking after pressure builds up in the cooling system. You may need to look around some more to see where - radiator or heater hoses, overflow reservoir, reservoir cap, water pump etc - or a shop can pressurize the system to see where the coolant is coming out.