Abstract: A transition duct in an advanced heavy duty gas turbine engine is cooled by impingement jets formed by apertures in a sleeve spaced a distance from the surface to be cooled. The sleeve is configured so as to duct spent impingement air towards the combustor, where it can be subsequently used for mixing with, and combustion of, the fuel, or for cooling of the combustor. The distance between the impingement sleeve and the transition duct surface is varied to control the velocity of air crossflow from spent impingement air in order to minimize the pressure loss due to crossflow. The cross-sectional areas of the apertures are varied to project impingement jets over the various distances and crossflow velocities. Generally, larger aperture areas are used with larger distances.