I don't really have any answers for you here. My engine popped about 3 months after putting the K04 on the car - cylinder 1 died (this seems to be a common cylinder to die). I broke off a piece of the piston top and blew the rings (shitty picture at the bottom). Upon further inspection the bore for cylinder #1 was a bit oblong, but from my not-very-expert view of things, there wasn't any significant wear on the cylinder wall so read into that what you will. New engine (about 12k miles on it now with K04) and no issues whatsoever (knock on wood), no odd sounds at high load / low rpm, though I avoid that kind of situation like I avoid the plague; it's by far the most stressful thing you can do to your engine (on a turbo'd carl) under otherwise normal driving conditions (e.g. not counting money shifts) -- specially when pushing the engine beyond manufacture specs. Now that you're tuned you need to start driving it like a 1990s turbo car instead of a NA car (in my opinion), don't mash the pedal to the floor at low rpm, hell I won't give it full boost below 3k rpm, in 3rd and up, give it plenty of time to warm up, plenty of time to cool down after a hard run.
Before you start freaking out I will say I have no evidence to say that the engine dying and the sound were related (though I agree, it's a scary and abnormal sound). A couple things that I found interesting, the original engine in the car was an absolute dog at very low rpm, say when making a slow >90* turn in 2nd gear (around 1100 - 1300rpm), it would just sit there and very slowly chug along; this was true for me stock, tuned, and with the k04. First thing I noticed about the new engine was it moved the car decently under those same low rpm / low speed conditions. Not like a v8 obviously, but not like a 1992 ford escort either. Point is, based on that and the cylinder shape I'm not convinced this wasn't an issue from day 1, if I was you I'd probably have all the cylinders scoped to see if you have any obvious issues going on.
A couple of other points, I logged the car extensively and couldn't pick up anything on the logs that changed before, during, or after the sound, though VCDS sampling frequency isn't ideal. The overall timing for the original engine was lower under all circumstances compared to the new engine (and saw higher boost to make up for it), but timing wasn't being pulled around when the sound occurred beyond normal timing pull for high-load low rpm conditions -- the few times I logged those conditions on the new engine the logs looked nearly identical. If the P3 gauge is to be believed, the EGTs were higher for the old engine when pushing it hard, which is inline with lower overall ignition timing. The engine wasn't really an oil burner, though consumption seemed to pick up a bit in the month before it died.
I could basically make the sound happen whenever I wanted, 2k rpm in 3rd though 6th, floor it and as soon as boost built to 15+ psi I'd get that sound. The sound did not appear to be temperature dependent, it would happen in 90* weather and 30* weather. It was more common when the exhaust was relatively cool, i.e. cruising along for a while then flooring it which led me down a path of checking all the exhaust hardware connections thinking that rapid thermal expansion could have been an issue -- didn't find anything there. Changed oil, plugs, coils with no change in behavior. Injector pulse looked fine so didn't bother changing them.
So unfortunately I don't really have any idea what was causing the sound, or if it was related to my engine trouble. I linked the video to APR at one point with a bunch of logs, their response was essentially 'it's hard to hear, probably surging, take it to a tuner', unfortunately the engine died a few days later before I got a chance to bring it in.
Good luck with it, I'd be cautious until you can get things fully checked out though, it's definitely an abnormal sound and it has a cause, somewhere, hopefully you have better luck figuring out just what the hell is causing it.
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