What about this.
You have drawn a primary carbocation which you labeled as secondary. I think ring expansion should be concerted with the loss of water as a leaving group, to avoid formation of the primary cation.
Ultimately this is all going to depend on the exact conditions, how acidic things really are, what the temperature is, etc. Generally we try to avoid drawing primary cation though, and instead draw funny things like concerted hydride or alkyl shifts to avoid it.