Thanks for explaining Almetr.
some comments...
forcibly closing the exhaust pipe with a cork (the sole of my shoes), I got a reduction in noise at idle in the cold.
Yes, when exhaust is blocked there are back pressure and engine breathing is blocked = lower clean air = lower recirculated dirty air = lower MAF/MAP read = lower injection and retarded injection = lower fuel injected and lower cylinder pressure = lower sound
but the quietest option turned out to be the pilot injection setting from the car manufacturer, my change in the phase and pilot amount only made it worse, apart from the fact that it became a little quieter from the main injection shift.
May be, usually manufacturer settings should be the best balance for street use, but not the best for consumption or performance. It's easy to get 3db up/down or 0,5L up/down. It depends on injector technology too.
But why does a demanding engine work smoothly with Reinforced EGR (forced exhaust boost)? For me, the answer is obvious - the injection process is accompanied by ignition without the disappearance of the flame until the entire cyclic supply burns out, which means that areas with an explosive fuel-air mixture do not have time to accumulate. A phased sound level meter helped me see this. When the engine is running quietly, all the noise falls before TDC and lasts a little beyond TDC, and when bubbling, the noise amplitude is increased just beyond TDC and lasts longer. That's why I disagree with your opinion "With the EGR off, combustion is faster and harder, because the pressure the temperature in the cylinder is higher."
Of course, with EGR ON combustion is smoother, cylinder pressure is lower and usually heat release lower, then combustion sound is lower, its one of the basics with recirculated gases as lower NOx, higher HC and so on. EGR increment delay up to 4 times and retard pressure and heat release various grads, noise always follow that, you can not has noise combustion without cylinder activity and with EGR it happens later and lower.
I attach tests from other well known engine 2.7 V6 CRDI Siemens.
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