I have a 2002 audi a8 When I turn the ignition on after a few seconds there is a noise that starts up. first I thought it was the blower motor. After taking the motor apart i noticed the noise seemed to be coming from two round caps next to the blower motor, and next to the power brakes. i took a picture and circled in red. it is quite loud in the cabin, and stays on most of the time. every so often it stops and the cabin is nice and quiet, any ideas.

 

That is your electric coolant pump/core valves...serves 2 purposes. It helps speed and distribute (dual climate zone) heated coolant to the heater cores, for quicker heat response to the cabin.
It also runs the "restore" feature in your climate control...temporary (few minutes) heat/fan during winter after warm engine is shut off, when you hit the "rest" button.

The car can run without it...but, no restore feature and slightly slower cabin heat response during winter warm-up.

2 cylinder shaped electrical connections power the unit...one for the pump (usually the noise maker) and 1 for the valves (domes). It can be unplugged to kill the noise, if it's failing. The unit is a $1000 piece to replace.