the chassis width is 154 mm (6.06 in.)  that gives you some idea of max cooler height it can accommodate.  NH-D9L is only 110 mm tall so it should work heightwise. most aftermarket cooler of tower style requires user to uninstall Dell motherboard and remove Dell backplate, and install custom backplate.  this is not always an easy job.  for easier cooler update consider those cooler that can use the Dell backplate in situ so you do not have to uninstall mobo etc. Dell backplate typically uses M3 tapped nut. not sure whether the Noctua cooler fan will cause a Dell bios startup error.  If the fan rpm is significantly different from Dell fan, it may cause this nuisance error which you can click a key to pass.
I was wondering would it be possible to install a new cooler into the DI 3891. What are the Maximum physical dimensions and is there anything I'd need in addition to a cooler.   I was thinking of installing the NH-D9L
New CPU cooler in the dell inspiron 3891