  Multiple stellar populations are observed in almost all globular-clusters,
but the origin of this phenomenon is still debated. We investigate the role
cool supergiants may have played. To do this, we combine two investigative
methods: state-of-the-art massive stellar evolution and calculations of the
hydrodynamic structure of the cluster-gas. This approach allows us to study how
star-formation in young massive clusters depends on the energy- and mass-input
of the first-generation of stars, while predicting the chemical composition of
the second-generation. We find that the presence of massive (9-500 M$_{\odot}$)
metal-poor supergiants in the young cluster leads to a star-formation episode
within the first 4 Myr of the cluster's lifetime, that is, before the first
core-collapse supernovae explode or the gas is expelled. The stellar winds
accumulate in the cluster center, forming the second-generation there. Its
composition is predicted to show variations in O & Na abundances, consistently
with observations. The abundance of helium is, similarly to other scenarios
involving massive stars, higher than what is referred from observations.
Supposing dynamical removal of stars from the outskirts of the cluster, or
applying a top-heavy initial-mass-function, we can predict a number ratio of
the second-generation as high as 20-80%. The effect of metallicity is shown to
be important, as the most luminous supergiants are only predicted at
low-metallicity, thus limiting $-$ but not excluding $-$ the extent of a
polluted second-generation at high-metallicity. These massive stars becoming
black-holes suggests globular-clusters hosting gravitational-wave progenitors.
Our scenario predicts a correlation between the mass of the cluster and the
extent of the multiple population phenomenon.
