I think the interesting question is which program you run is regularly scanning the DVD. That's a desktop/file manager tendency that I don't have on any current systems. I did see that a couple of years ago running Gnome.
Is your drive empty when this happens? Come to think of it, I've never heard an empty disk drive spin up...
Previous section to blacklist a module is interesting, but you have problem of figuring out which module to disable and that it is not needed by other devices that you actually do use.
Unless you need to read DVD very often, I would disable that device in the BIOS. That is is the surest way to get this to really turn off. The second link that @George mentions above says the BIOS does not have that feature, which surprises me. On the systems we have that still have DVD, there is a SATA listing for each device with a button. Oh, well.
If you go down the "disable a module" route, you can find out which modules are loaded by running "sudo /sbin/lsmod". You can unload a module from the command line to test if it really does prevent the disk drive from running still. Syntax is "sudo /sbin/modprobe -r module_name_here". If that does work, then create blacklist entry like others suggest.
But you need to be super cautious because if you disable something needed by your system, then, well, your system will not start. If you notice in the link mentioned on the comment about your question, it is about disabling user access to mount inserted media. It does not necessarily disable the device. Sorry to be so vague, but I think this is dangerous.
echo "blacklist sr_mod" >> /etc/modprobe.d/blacklist-sr_mod.conf