I made a design in illustrator but i didn't save the file. After restarting illustrator I search this file and I found this file in data recovery folder but this file doesn't open.
If it didn't crash there won't be a recovery file. The recovery works like so: When Illustrator crashed and created a recovery file, then on the following restart, it will ask you if you want to try a recovery. You have to click OK, otherwise the recovery file will be deleted.
Recovery ≠ autosave
If you don't save your file and you quit Illustrator, then Illustrator won't save your file yor you.
Even if the Recovery file has been created, there is no guarantee that it works. E.g. when the crash is due is a power outage, then saving might still fail. The recovery function is meant for securing the last couple minutes or mabye half an hour that you didn't cover with your backups and regularly saving your file.