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An air management arrangement for a late lean injection combustor system includes a combustor liner defining a combustor chamber. Also included is a sleeve surrounding at least a portion of the combustor liner, the combustor liner and the sleeve defining a cooling annulus for routing a cooling airfl

An air management arrangement for a late lean injection combustor system includes a combustor liner defining a combustor chamber. Also included is a sleeve surrounding at least a portion of the combustor liner, the combustor liner and the sleeve defining a cooling annulus for routing a cooling airflow from proximate an aft end of the combustor liner toward a forward end of the combustor liner. Further included is a cooling airflow divider region configured to split the cooling airflow into a first cooling airflow portion and a second cooling airflow portion, wherein the first cooling airflow portion is directed to at least one primary air-fuel injector, wherein the second cooling airflow portion is directed to at least one lean-direct injector extending through the sleeve and the cooling annulus for injection of the second cooling airflow portion into the combustor chamber.

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1. A method, comprising: directing an airflow into an airflow passage disposed between a first wall and a second wall surrounding at least a portion of the first wall, wherein the first wall is disposed about a combustor chamber;splitting the airflow from the airflow passage, at an airflow divider r

1. A method, comprising: directing an airflow into an airflow passage disposed between a first wall and a second wall surrounding at least a portion of the first wall, wherein the first wall is disposed about a combustor chamber;splitting the airflow from the airflow passage, at an airflow divider region, into a first airflow portion through a first airflow passage and a second airflow portion through a second airflow passage, wherein the second airflow passage is disposed radially outward from the airflow passage, and the second airflow passage extends between the second wall and a third wall disposed about at least a portion of the second wall;routing the first airflow portion through the first airflow passage a first distance from the airflow divider region to a first air inlet of at least one primary air-fuel injector; androuting the second airflow portion through the second airflow passage a second distance from the airflow divider region to a second air inlet of at least one lean-direct injector, wherein the at least one lean-direct injector extends crosswise through the airflow passage from the second wall to the first wall. 2. The method of claim 1, wherein directing the airflow comprises routing the airflow through the airflow passage in an upstream direction opposite to a downstream direction of combustion gas flow in the combustor chamber, wherein routing the second airflow portion comprises routing the second airflow portion through the second airflow passage in the downstream direction. 3. The method of claim 1, wherein routing the first airflow portion comprises routing the first airflow portion through the first airflow passage in a radially inward direction relative to a central axis of the combustor chamber, wherein routing the second airflow portion comprises routing the second airflow portion through the second airflow passage in a radially outward direction relative to the central axis of the combustor chamber. 4. The method of claim 1, wherein the splitting the airflow comprises splitting the airflow in the airflow divider region at a first offset distance away from the at least one primary air-fuel injector and a second offset distance away from the at least one lean-direct injector. 5. A system, comprising: a first wall disposed about a combustor chamber;a second wall disposed about at least a portion of the first wall, wherein an airflow passage is disposed between the first wall and the second wall;a third wall disposed about at least a portion of the second wall; andan airflow divider region that splits the airflow passage into a first airflow passage and a second airflow passage, wherein the first airflow passage extends a first distance from the airflow divider region to a first air inlet of at least one primary air-fuel injector, wherein the second airflow passage is disposed radially outward from the airflow passage and extends between the second and third walls, wherein the second airflow passage extends a second distance from the airflow divider region to a second air inlet of at least one lean-direct injector, wherein the at least one lean-direct injector extends crosswise through the airflow passage from the second wall to the first wall. 6. The system of claim 5, wherein the airflow passage extends in an upstream direction opposite to a downstream direction of combustion gas flow in the combustor chamber, and the second airflow passage extends in the downstream direction. 7. The system of claim 5, wherein the second air inlet of the at least one lean-direct injector is disposed in the second airflow passage between the second and third walls. 8. The system of claim 6, wherein the second airflow passage is substantially parallel to the airflow passage. 9. The system of claim 5, wherein the airflow passage extends a third distance from the at least one lean-direct injector to the airflow divider region. 10. The system of claim 5, wherein the airflow divider region splits the airflow passage into the first airflow passage extending radially inward relative to a central axis of the combustor chamber, and into the second airflow passage extending radially outward relative to the central axis of the combustor chamber. 11. The system of claim 5, wherein the at least one lean-direct injector is coupled to the first and second walls. 12. The system of claim 5, wherein the first wall comprises a combustor liner, a transition piece, or a combination thereof, wherein the second wall comprises a flow sleeve, an impingement sleeve, or a combination thereof. 13. The system of claim 5, wherein the first wall comprises a combustor liner and the second wall comprises a flow sleeve, wherein the at least one lean-direct injector is coupled to at least one of the combustor liner and the flow sleeve. 14. The system of claim 5, wherein the first wall comprises a transition piece and the second wall comprises an impingement sleeve, wherein the at least one lean-direct injector is coupled to at least one of the transition piece and the impingement sleeve. 15. The system of claim 5, comprising a gas turbine combustor having the first wall, the second wall, and the airflow divider region. 16. The system of claim 15, comprising a gas turbine engine having the gas turbine combustor. 17. A system, comprising: a combustor, comprising: a combustion chamber;a head end chamber separated from the combustion chamber;a first wall disposed about the combustion chamber;a second wall disposed about the first wall;a third wall disposed about the second wall;a passage disposed between the first and second walls;a first fuel injector disposed in the head end chamber;a second fuel injector disposed in the passage;a flow divider region that splits the passage into a first passage and a second passage, wherein the first passage extends a first distance from the flow divider region to a first inlet of the first fuel injector, and the second passage is disposed radially outward from the passage and extends between the second wall and the third wall, and the second passage extends a second distance from the flow divider region to a second inlet of the second fuel injector, wherein the second fuel injector extends crosswise through the passage from the second wall to the first wall. 18. The system of claim 17, wherein the passage extends in an upstream direction opposite to a downstream direction of combustion gas flow in the combustion chamber, and the second passage extends in the downstream direction. 19. The system of claim 18, wherein the second inlet of the second fuel injector is disposed in the second passage between the second and third walls. 20. The system of claim 17, wherein the second passage is substantially parallel to the passage. 21. The system of claim 17, wherein the flow divider region splits the passage into the first passage extending radially inward relative to a central axis of the combustion chamber, and into the second passage extending radially outward relative to the central axis of the combustion chamber.