Outflows in starburst galaxies driven by thermal-mechanical energy, cosmic rays, and their mix are investigated with 1D and 2D hydrodynamic simulations. We show that these outflows could reach a stationary state, after which their hydrodynamic profiles asymptotically approach previous results obtained semi-analytically for stationary outflow configurations. The X-rays from the simulated outflows are computed, and high-resolution synthetic spectra and broad-band light curves are constructed. The simulated outflows driven by thermal mechanical pressure and CRs have distinguishable spectral signatures, in particular, in the sequence of the keV K α lines of various ions and in the L-shell Fe emission complex. We demonstrate that broad-band colour analysis in X-rays is a possible alternative means to probe outflow driving mechanisms for distant galaxies, where observations may not be able to provide sufficient photons for high-resolution spectroscopic analyses.