I has found one recipe 'logwood for barrels' in one book from 1926.
Its for fluid barrels, not damascus.
First of all traditional rust bluing 10-12 times using Fe2SO4 * 7H2O (ferrous sulphate, green crystals) and FeCl2 (iron chloride 1 1/2) solution. The final color dark chocolate with blue nuance.
Then 1,8 liter of spring water, 38.4 grams of logwood extract, 0.2 grams ferrous sulphate. Heat solution till boiling and put barrels in solution for 10 minutes.
The final color dark blue.

Geno.