We introduce a HDG method for the convected Helmholtz equation based on the total flux formulation, in which the vector unknown represents both diffusive and convective phenomena. This HDG method is constricted with the same interpolation degree for all the unknowns and a physically informed value for the penalization parameter is computed. A detailed analysis including local and global well-posedness, as well as a superconvergence result is carried out. We then provide numerical experiments to illustrate the theoretical results.