A cooling circuit of a gas turbine passes an airflow through a combustor section that includes a plurality of mixing tubes for transporting a fuel/air mixture and a perforated plate including a plurality of impingement holes and a plurality of tube holes for accommodating the mixing tubes. The tube holes and the mixing tubes form a plurality of annulus areas between the perforated plate and the mixing tubes. The impingement holes and the annulus areas are configured to pass the airflow through the perforated plate. A flow management device modifies an effective size of the annulus areas to control a distribution of the airflow through the impingement holes and the annulus areas of the perforated plate to enhance cooling efficiency.