  We consider scenarios for non-thermal particle acceleration and
re-acceleration in the central cores of compact massive star clusters, aided by
insights from high resolution hydrodynamic simulations. We show that i)
particles are unlikely to interact with many shocks during their lifetimes in
the core; ii) colliding flows do not produce hard spectra; iii) turbulent
re-acceleration in the core is suppressed. Inefficient re-acceleration
mechanisms are not expected to produce hard components nor to increase the
maximum energy within the cores of massive star clusters. Models in which the
observed ultra-high energy gamma rays originate in the core of massive stellar
clusters are thus disfavoured.
