Sounds like you have air in the system, did you bleed it properly after the pump replacement?

You're likely seeing a bunch of foam/bubbles in the reservoir accompanied by the noise.

 

it sounds like the pump was not primed correctly when changed. To prime the pump the front wheels must be raised off the ground. the system is filled with the correct fluid and without starting the car turn the steering wheel from right to left. End to end. Do that about six times and let sit for about ten minutes. repeat this five to seven times before you start the car. After doing this start the car run for 30sec turn off. check level and see if the fluid has foamed up, I'd it did let sit for 1hr for the air to escape. After the hour has gone by start the car and turn the steering left to right again (end to end). this is how you prime the steering pump in all Audi's