An assembly for a turbine engine 20 is provided that includes a combustor wall 76, 78, which includes an aperture body 100 between a shell 86, 88 and a heat shield 82, 84. The aperture body 100 at least partially forms a cavity 132 and an aperture 72, 74 that extends through the combustor wall 76, 78. An inlet passage 134 extends in the combustor wall 76, 78 to the cavity 132. An outlet passage 136 extends in the combustor wall 76, 78 from the cavity 132 to the aperture 72, 74.