It should be no surprise that most tunes in open D tuning are played in the key of D. With this in mind, let's take a look at some scale positions for D major. Below are diagrams of the D-major scale at various positions on the neck.
The scales are shown on a fretboard rather than conventional music notation because I believe that you will be more successful if you are able to visualize the note positions on the fretboard. Showing scales in TAB form or standard notation doesn't provide this visualization as easily. When you find the need to improvise, this visualization can prove invaluable, I hope you agree.