By means of three-dimensional hydrodynamical simulations, we investigate the formation of second-generation (SG) stars in young globular clusters of different masses. We consider clusters with a first generation of the asymptotic giant branch (AGB) stars with mass $10^5$ and $10^6M_{\odot}$ moving at constant velocity through a uniform gas with density $10^{-24}$ and $10^{-23}$ g cm$^{-3}$. Our setup is designed to reproduce the encounter of a young cluster with a reservoir of dense gas, e. g. during its orbital motion in the host galaxy. In the low-density cases, as a result of the cooling AGB ejecta, weakly perturbed by the external ram pressure, a compact central He-rich SG stellar component is formed, and this occurs on a smaller timescale ($<10$ Myr) in the larger mass cluster. Our high-density cases are subject to a stronger ram pressure, which prevents the retention of the He-rich AGB ejecta in the lower mass cluster ($10^5M_{\odot}$), whereas in the more massive cluster ($10^6M_{\odot}$), the gravitational potential can still overcome the ram pressure and a more extended and less He-enhanced SG can form.
By combining our results with previous simulations, we are able to study relevant cluster-related scaling relations across a dynamical range of two orders of magnitude in mass (from $10^5 M_{\odot}$ to $10^7 M_{\odot}$).
In agreement with existing observations, we find positive correlations between the SG-to-total mass ratio and maximum He fraction in SG stars as a function of the initial cluster mass.