SOTW Columnist, Distinguished SOTW Member
For a sustained middle D, when he's using the palm key, it's almost certainly for the different timbre using that fingering (as thisidigofyou said). I think Coltrane did the same thing on occasion. It gives a pretty distinct tone quality. Try it and compare it to the standard fingering and you'll hear it.When he's playing a sustained middle D he generally uses the left palm side D alone rather than the standard fingering. When middle D is in the middle of a run he uses the traditional fingering. I'd be curious to know if he does this due to sound/intonation on this particular horn or if it's something he does in general.
That fingering is also sometimes useful for a trill or triplet (i.e. C# D C#) or quick passage. But that's a different reason to use it.