Turbine engine combustor wall with non-uniform distribution of effusion apertures

An axial flow combustor for a turbine engine with an axial centerline, comprising:

• a first combustor wall;
• a second combustor wall including a support shell and a heat shield;
• and
• an annular combustor bulkhead extending radially between an upstream end of the first combustor wall and an upstream end of the second combustor wall;
• wherein the shell includes a plurality of shell quench apertures, a plurality of first impingement apertures, and a plurality of second impingement apertures;
• wherein the heat shield includes a plurality of shield quench apertures fluidly coupled with the shell quench apertures, a plurality of first effusion apertures fluidly coupled with the first impingement apertures, and a plurality of second effusion apertures fluidly coupled with the second impingement apertures;
• wherein the shield quench apertures and the first effusion apertures are configured in a first axial region of the heat shield, the second effusion apertures are configured in a second axial region of the heat shield, and the first axial region is located axially between the upstream end of the second combustor wall and the second axial region;
• and
• wherein 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.