2004 Hyundai Sante Fe has hard steering and whining at low idle. Changed Power steering pump and reservoir, and rack and pinion, flushed system. No change

if you are talking power steering system, the whine is a vibration in a problem control valve and could be in the steering valves on the rack

Can't tell from here but your only options are the rack & pinion (if equipped) PS hoses or pump. Sounds like the rack or high pressure hose. fill the PS pump to it's level while running, have someone watching under the hood while you turn the steering wheel hard from side to side (all the way) & see where you leaking from. Good luck

The power steering system includes a P.S. pump which will whine when you turn a hard left or right while in park. There are also power steering hose that can leak. Then there is also a power steering gear box. Unless you have a rack and pinion steering system. Then that is changed as a unit.

No, the power steering is entirely a separate and sealed system, wholly external to the engine. The power steering pump pushes the fluid through a high pressure hose into the rack and pinion-the steering gear mounted below and behind the engine-and holds pressure within the rack that enables power assisted steering. At the same end where the power steering fluid hose enters the gear will be a fitting for a return line back to the fluid reservoir. These two hoses are usually routed close together at least part of the way, some may even be held together with brackets. Leaks could develop at the pump, the fluid reservoir, or the two hoses to and from the rack and pinion, or the seals inside the rack and pinion may have failed. You should be able to find the leak-it will only leak to the outside-to check the rack and pinion for leaks, right where your tie rods come out of the gear and go to the wheels for steering, will be a small rubber boot encasing the tie rod and the end of the rack assembly-on both ends is a boot and a tie rod-peel back the rubber boot from the gear ass\'y, it should be dry. If a lot of fluid, the seals in the rack and pinion are gone. It will have to be replaced.
Hopefully you will find a leaking hose or fractured reservoir, but keep looking, air flow may be blowing the leaking fluid back and under the car. Good luck, hope it\'s not the rack and pinion.

Check the belt first,check the fluid,if low,you have a leak,maybe a hose leak,if not here's a link on how to replace pump.http://www.autozone.com/autozone/repairinfo/repairguide/repairGuideContent.jsp?fromSearchPage=true&pageId=0996b43f8037d718&partName=Removal+%26+Installation&partId=0996b43f8037d718

The bubbles are more or less normal.
I would want to know for sure the noise is coming from the pump and not another pulley on the engine. When you turn the wheels you put load on the pump and the drive belt which loads the other pulleys too.
How about taking a long piece of heater hose and using it to listen around the belt while a helper turns the steering wheel ?

The Power Steering Reservoir is foaming the fluid, causing the noise. Honda's solution is to replace the reservoir with a new one that does not foam the fluid. You can do the same by punching a hole in the screen at the bottom of the reservoir. Then idle the car for a moment or two and flush the fluid. WalMart PS fluid will work fine.

There sre usually two things that make a whining noise.The power steering pump/rack and pinion or the transmission's pump.My guess is the tranny pump

Was it a reman pump and rack? You most likely have a problem with the pump again. If it is hard to steer both ways, it will be the pump. If it is hard to steer only one way, it will be the rack.

the suspect part for a power steering whine is the power steering pump, flush (very important) the system and replace the PS pump..