The sound you're talking about is indeed the PTU (Power Transfer Unit).
This is a bidirectional power transfer unit which enables the yellow system to pressurize the green system and vice versa.
The PTU comes into action automatically when the differential pressure between the green and the yellow systems is greater than 500 PSI.
The PTU is inhibited during
the first engine start.
In "my" company (as in most companies) engine 2 is started first. Once eng 2 is started the PTU detects a pressure difference between the yellow system and the green hydr. system and the PTU starts automatically. (The yellow system is normally supplied by an engine driven pump on engine 2 and the green system is supplied by a pump driven by the engine1)
So you will hear this strange noise, and indeed it IS a very strange noise, every time one engine is running and the other is not (yet).
(I liked the way you described the sound
You will hear this sound for quite a long time during a power push. (When the pushback is done with a tug connected to the main landing gear. (see pictures below) In this case the pilot has to steer the airplane during the pushback via the nose wheel steering.)
In this case eng 2 is started at the gate BEFORE the pushback starts. The reason for this is that hydraulic power is needed for the nose wheel steering. In A319/320/321 the nose wheel steering (NSW) uses the green hydraulic power. After the eng 2 is started, hydraulic pressure is provided to the NSW via the PTU and the green hydraulic system. Eng 1 is only started AFTER the pushback is completed because these tugs have limited power and would have a hard time pushing the aircraft back with both engines running at idle.
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Photo © Josh Rawlin
The PTU is situated near the wing roots.
Remember: you will hear this sound whenever only 1 engine is running.
The fact that you continued to hear this sound after the taxi started, indicates to me that UA is one of the companies that allows taxi-out on a single engine. The second engine is started during the taxi or at the holding point. This procedure is used for fuel saving.
I hope this answer is clear enough.
The F/A's in "my" company are used to questions from the passengers about this sound. They get this question on nearly every flight.