  In hydrodynamic approach to relativistic heavy ion collisions, hadrons with
nonzero spin, produced out of the hydrodynamic medium, can acquire polarization
via spin-vorticity thermodynamic coupling mechanism. The hydrodynamical
quantity steering the polarization is the thermal vorticity, that is minus the
antisymmetric part of the gradient of four-temperature field.
  Based on this mechanism there have been several calculations in hydrodynamic
and non-hydrodynamic models for non-central heavy ion collisions in the RHIC
Beam Energy Scan energy range, showing that the amount of polarization of
produced $\Lambda$ hyperons ranges from few percents to few permille, and
decreases with collision energy. We report on an extension of our existing
calculation of global $\Lambda$ polarization in UrQMD+vHLLE model to full RHIC
and LHC energies, and discuss the component of polarization along the beam
direction, which is the dominant one at high energies.
