A turbine engine combustor wall includes support shell and a heat shield. The support shell includes shell quench apertures, first impingement apertures, and second impingement apertures. The combustor heat shield includes shield quench apertures fluidly coupled with the shell quench apertures, first effusion apertures fluidly coupled with the first impingement apertures, and second effusion apertures fluidly coupled with the second impingement apertures. The shield quench apertures and the first effusion apertures are configured in a first axial region of the heat shield, and the second effusion apertures are configured in a second axial region of the heat shield located axially between the first axial region and a downstream end of the heat shield. A density of the first effusion apertures in the first axial region is greater than a density of the second effusion apertures in the second axial region.