partitioning - Unallocated space instead of LUKS partition with gparted

I have unplugged a USB with valuable data with a mounted LUKS partition which destroyed the partition table.

Running testdisk does not recognized the partition: it claim it as unallocated space instead of a LUKS partition. From parted:

Number  Start   End     Size    Type     File system  Flags
 1      1049kB  3222MB  3221MB  primary               boot
 2      3222MB  3224MB  2097kB  primary

There should be a third LUKS type partition

Number  Start   End     Size    Type     File system  Flags
 1      1049kB  3222MB  3221MB  primary               boot
 2      3222MB  3224MB  2097kB  primary
 3      3224MB  16.0GB  12.8GB  primary

I tried adding a new partition with testdisk for this apparent unallocated space but didn't found the crypt_LUKS type in the list:

>List of partition type 
[...]                                                  
 1e hid. FAT16 LBA       87 HPFS FT mirror-V/S set f0 Linux/PA-RISC boot
 20 Willowsoft OFS1      8e Linux LVM            f1 Storage Dimensions
[...]

Hence my first question:

1. Is Linux LVM the right type for a LUKS encrypted partition? Which method should be used to force to recognize the unallocated space as a LUKS partition

Choosing Linux LVM does not allow to run cryptsetup luksOpen (I get Device /dev/sdb1 is not a valid LUKS device.)

2. Which other method would you use in order to recover my LUKS partition recognized as unallocated space ?

Linux doesn't care about partition types. Just give it any type which is not a Windows type; Linux LVM works well, or 0xDA (Non-FS Data). To check whether a device, for example, /dev/sdc3 is a LUKS container:

sudo cryptsetup isLuks /dev/sdc3 && echo LUKS container || echo Not a LUKS container

The best way is to recreate the partition as it was and, if necessary, restore the LUKS header from backup. Backup the first 2 MiB of the partition first.