2006 buick ranier engine makes whining noise that gets worse when you accelerate. how do you fix this?

Open the hood. Listen for where the noise is coming from. Fix the thing that is making the noise.

You may have a bad front wheel bearing, have a local shop drive the car and confirm this is the problem

Check your fan belts and Idler

Sounds like a combination of a power steering pump (whine) AND the CV axle (loud clunk noise). Check the fluid level in the power steering pump. The pump is located on the passenger's side towards the firewall. Kind of hard to get at but unscrew the cover and there is a small/short dipstick there. See what it reads. Add Power Steering fluid (NOT transmission fluid, as needed. Don't overfill)
I'd get the "thumping noise" taken care of IMMEDIATELY. Could be a serious problem. Qualified front end shop should be able to diagnose and give you an estimate of cost. Last time I had one done it was about $300 parts and labor...

I am guessing the steering rack is starting to go bad. That is quite expensive to fix. The whining noise is the rack sucking air due to the steering fluid has leaked out. You can check your power steering fluid level and add some with stop leak to see if that helps. The filler cap is at the rear of the engine on the passenger side and is quite hard to get to. Be sure to not reach down to remove the cap unless the engine is cool. There is a high risk of burning yourself on the exhaust manifold.

Check the idler and tensioner pullys for your serpentine belt. I suspect the whining noise heard earlier was due to the fact one was getting a bit stiff or rough turning. When you gave it that extra fuel, the sudden load may have finished it off. Sometimes they lock up, and sometimes they fall apart. Check those items first.

It is the bearing in the idler pully. about $35 and 30 minutes of work and its fixed.

Tie rods have nothing to do with making any kind of noise.You most likely have a bad wheel bearing.Good luck,
ChevRev

Added power steering fluid

If it gets worse when turning the wheel at a stop, then it's the power steering pump. Could be the power steering fluid also. Check your belts for wear or damage. The idle pulley will make a constant noise, sometimes whining sometime screeching. To check idler pulley it is best to remove belts.