The problem is you have a leak somewhere most likely the pressure line. You need to get the leak fixed so the system won't suck in air creating bubbles causing the noise you hear. There's also a possibility if the power steering fluid doesn't look agitated(foaming), the bearings in the pump itself are bad (from running it low on fluid) which means you need to have the power steering pump replaced. good luck and hope this helps.

engine warm, level ground, cap off the power steering resiviour. note level "hot". add *** neccessary. turn wheels, full deflection lt/rt several times. check level again. if more is needed, add and repeat the above steps.

still noisy? prolly did damage the pump. additives will not hurt anything. try em as suggested. those additives contian seal conditioners and help lubricate the pump. seals aside, since it did run dry, the pump bushings may have been effected. so when engine is running, do note any pulley wobble. pulley wobble would denote a pump that needs replacing.

iffin the moise just wont go away, and there's no pullet wobble, likely you have an undetermined amount of time/miles to go b4 the pump fails. but i wouldn't ignore it too long. as on some/most platforms, if the pump fails and the belt gets tossed, it will leave you stranded. as the belt that turns that pump may also turn the alternator. possibly other periferals as well.

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EDIT,

respect, @ Stpaulguy. regarding, "That's no longer an approved method and can blow the hoses and damage the pump"

i'd like to see your source/documentation on that. find it hard to believe a system w/air will damage things like hoses. they merely pass fluid. we all know of the pump needing lubrication. not what i'm questioning. hoses blowing? eh. that would mean hoses and pumps would blow just driving and having a leak. leaks allow room for air.

and how does one remove air with a pump?

total respect. but doesn't make sense. if so, i wouldn'y but that platform. as that's not the standard through out the industry.\

and here's how to do bleeding as per the manual on an '02 taurus,

http://www.autozone.com/autozone/repairi...

it says to go lock to lock lt/rt to bleed! there's documentation/source info.

i am curious. so do post your source. pls!!!!

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i'm a USAF trained hydraulic/pneumatic tech. worked on some of th most sophisticated hydraulic systems there are. plus, 3 yrs (vehicle) fleet service. and all around gear head.

Air in the system. The recommended way to remove it is with a hand vacuum pump. Do NOT turn the steering wheel full left and full right. That's no longer an approved method and can blow the hoses and damage the pump

Jack the front frame rails up and support them on jack-stands. Turn the motor on and swing the steering wheel lock to lock at least a dozen times to get the air out.

If this doesn't work you need a re-manufactured power steering pump.

If it was running dry I would think that you damaged the pump so it is going to be loud. You can try an additive like in this video which helps quiet the power steering pump: