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A system, in one embodiment, includes a turbine engine. The turbine engine includes a combustor that includes a hollow annular wall having a combustor liner. The turbine engine also includes first flow path in a first direction through the hollow annular wall. The turbine engine further includes a s

A system, in one embodiment, includes a turbine engine. The turbine engine includes a combustor that includes a hollow annular wall having a combustor liner. The turbine engine also includes first flow path in a first direction through the hollow annular wall. The turbine engine further includes a second flow path in a second direction that is opposite the first direction through the hollow annular wall. The second flow path may include one or more film holes configured to supply a cooling film to a downstream end portion of the combustor liner.

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1. A system comprising: a turbine engine comprising: a combustor comprising a hollow wall having a sleeve disposed about a combustor liner, wherein the combustor liner comprises an inner surface facing inwardly toward a combustion chamber and a plurality of axial cooling channels arranged circumfere

1. A system comprising: a turbine engine comprising: a combustor comprising a hollow wall having a sleeve disposed about a combustor liner, wherein the combustor liner comprises an inner surface facing inwardly toward a combustion chamber and a plurality of axial cooling channels arranged circumferentially about a downstream end portion, wherein the plurality of axial cooling channels are defined by alternating axial grooves and axial protrusions about a circumference of the combustor liner;a first air flow path in a first direction through the hollow wall, wherein the first air flow path comprises a bypass opening extending through the combustor liner to the inner surface; anda second air flow path in a second direction opposite the first direction through the hollow wall, wherein the second air flow path comprises one or more film holes extending radially through the alternating axial grooves of the combustor liner to the inner surface, the one or more film holes are arranged in a series of groups wherein the one or more film holes of each group of the series of groups is spaced together along each of the alternating axial grooves closer than spacing between each group, and the one or more film holes are configured to supply a cooling film to a downstream end portion of the combustor liner. 2. The system of claim 1, wherein the second air flow path is defined by passages formed by the plurality of axial cooling channels on the downstream end portion of the combustor liner and an inner surface of a wrapper coaxially disposed generally about the downstream end portion. 3. The system of claim 2, wherein the wrapper comprises one or more radial openings configured to supply a portion of an air flow along the first air flow path into the plurality of axial cooling channels. 4. The system of claim 3, wherein wherein another portion of the air flow supplied to the plurality of axial cooling channels flows through the one or more film holes arranged in the series of groups to provide the cooling film on the inner surface of the combustor liner at the downstream end portion. 5. The system of claim 1, wherein the first air flow path is at least partially defined by a first passage between a transition piece and a transition sleeve that surrounds the transition piece. 6. The system of claim 5, wherein the first passage is fluidly coupled to a second passage between the combustor liner and the sleeve, wherein the second passage is upstream from the first passage relative to a flow direction of combustion gases within the combustor liner. 7. The system of claim 6, wherein the first passage comprises a plurality of inlets to receive a first portion of air from a compressor, wherein the first portion of air is discharged from the first passage into the second passage as the first portion of air flows along the first air flow path in the first direction. 8. The system of claim 7, wherein the second passage comprises a plurality of inlets to receive a second portion of air from the compressor, wherein the second portion of air and the first portion of air discharged from the first passage flow through the second passage in the first direction. 9. The system of claim 8, wherein the turbine engine comprises one or more fuel nozzles, wherein the fuel nozzles receive the air flowing in the first direction through the annular passage and mix the air with a fuel, and wherein a resulting air-fuel mixture is distributed into the combustor liner for combustion. 10. The system of claim 2, wherein the plurality of axial cooling channels comprises a plurality of surface features disposed on a surface of the plurality of axial cooling channels, wherein the plurality of surface features are configured to enhance the cooling of the combustor liner. 11. A system comprising: a turbine combustor liner comprising: a plurality of axial cooling channels defined by alternating axial grooves and axial protrusions about a circumference of the turbine combustor liner, andan inner surface facing inwardly towards a combustion chamber,wherein the plurality of axial cooling channels are arranged circumferentially about a downstream end portion relative to a downstream direction of combustion along a longitudinal axis of the turbine combustor liner, wherein the turbine combustor liner comprises an inner surface facing inwardly toward a combustion chamber, each of the plurality of axial cooling channels comprises one or more film holes extending radially through the alternating axial grooves into an interior of the turbine combustor liner, the one or more film holes are configured to supply a cooling film to the inner surface of the turbine combustor liner at the downstream end portion, and the one or more film holes are arranged in a series of groups wherein the one or more film holes of each group of the series of groups is spaced together along each of the alternating axial grooves closer than spacing between each group. 12. The system of claim 11, wherein an interior of the turbine combustor liner has a combustion path with a flow of combustion gases in the downstream direction, an exterior of the turbine combustor liner has a first air path with an upstream direction of flow opposite to the downstream direction, and the exterior of the turbine combustor liner has the plurality of cooling channels with a second air path in the downstream direction. 13. The system of claim 12, comprising a first flow sleeve disposed concentrically about the turbine combustor liner to define a first hollow wall, and a second flow sleeve disposed concentrically about a transition piece to define a second hollow wall, wherein the first and second hollow walls are coupled to one another at the downstream end portion, the first and second hollow walls define the first air path with the upstream direction, and the second air path in the downstream direction is disposed radially between the plurality of cooling channels and the transition piece. 14. The system of claim 11, wherein the one or more film holes extend radially through the alternating axial grooves at an angle of approximately 90 degrees. 15. The system of claim 11, wherein the one or more film holes extend radially through the alternating axial grooves at an angle between approximately 30 to 60 degrees. 16. The system of claim 11, wherein each film hole of the one or more film holes has a geometry that converges or diverges through one of the alternating axial grooves into the interior of the turbine combustor liner. 17. The system of claim 15, wherein the geometry comprises a conical shaped passage. 18. The system of claim 11, wherein an axial length of the downstream end portion is less than or equal to approximately 20 percent of a total axial length of the turbine combustor liner, an axial channel length of each of the plurality of cooling channels is less than or equal to the axial length of the downstream end portion, and the cooling channels have a depth of approximately 0.05 to 0.30 inches and a width of approximately 0.25 to 1.0 inches. 19. The system of claim 11, wherein the turbine combustor liner comprises one or more bypass openings extending through the turbine combustor liner to the inner surface. 20. The system of claim 11, wherein each channel of the plurality of axial cooling channels comprises a plurality of surface features disposed on a surface of the channel, wherein the plurality of surface features are configured to enhance the cooling of the turbine combustor liner. 21. A system comprising: a turbine engine comprising: one or more fuel nozzles; anda combustor comprising: a flow sleeve; anda combustor liner surrounded by the flow sleeve and defining a flow path therebetween configured to receive an air flow in a first direction towards the one or more fuel nozzles, wherein the turbine combustor liner comprises an inner surface facing inwardly toward a combustion chamber and the combustor liner comprises a plurality of axial cooling channels arranged circumferentially about a downstream end portion of the combustor liner;wherein each of the plurality of axial cooling channels is defined by alternating axial grooves and axial protrusions about a circumference of the turbine combustor liner, each of the plurality of axial cooling channels comprises one or more film holes extending radially through the combustor liner to the inner surface in a series of groups wherein the one or more film holes of each group of the series of groups is spaced together along each of the alternating axial grooves closer than spacing between each group, and wherein each of the plurality of cooling channels is configured to receive a portion of the air flow from the flow path, direct a first portion of the received air along the axial length of the cooling channel in a second direction away from the one or more fuel nozzles, and direct a second portion of the received air through the one or more film holes to supply a cooling film to the inner surface of the combustor liner at the downstream end portion. 22. The system of claim 21, wherein the combustor liner comprises one or more bypass openings extending through the downstream end portion of the combustor liner to the inner surface at an offset from the plurality of axial cooling channels, and the one or more bypass openings are configured to direct a third portion of the received air to supply a cooling film to the inner surface of the combustor liner. 23. The system of claim 21, wherein each channel of the plurality of axial cooling channels comprises a plurality of surface features disposed on a surface of the channel, wherein the plurality of surface features are configured to enhance the cooling of the combustor liner.