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A system, in one embodiment, includes an engine wall. The engine wall includes a cold-side and a hot-side. The engine wall includes one or more dilution holes, wherein each of the one or more dilution holes includes a first opening on the cold-side, a second opening on a hot-side, and a section of t

A system, in one embodiment, includes an engine wall. The engine wall includes a cold-side and a hot-side. The engine wall includes one or more dilution holes, wherein each of the one or more dilution holes includes a first opening on the cold-side, a second opening on a hot-side, and a section of thermal barrier coating (TBC) applied on the cold-side and having an opening that generally circumscribes the first opening.

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1. A system comprising: a turbine engine comprising:a transition section comprising a generally annular transition piece havinga plurality of dilution holes extending radially through the annular transition piece with respect to a longitudinal axis of the transition piece, wherein each of the plural

1. A system comprising: a turbine engine comprising:a transition section comprising a generally annular transition piece havinga plurality of dilution holes extending radially through the annular transition piece with respect to a longitudinal axis of the transition piece, wherein each of the plurality of dilution holes comprises:an entry-side opening on a cold-side of the transition piece;an exit-side opening on a hot-side of the transition piece; anda section of thermal barrier coating (TBC) having a thickness and an innermost edge, wherein the TBC is applied on the cold-side and the innermost edge generally circumscribes the entry-side opening. 2. The system of claim 1, wherein each section of TBC is discrete and limited in surface area to reduce heat transfer in a vicinity of each dilution hole. 3. The system of claim 1, wherein the entry-side opening comprises a chamfer. 4. The system of claim 3, wherein the chamfer comprises an angle that is between approximately 15 to 75 degrees with respect to a radial axis of the transition piece. 5. The system of claim 1, wherein the TBC applied on the cold-side has the thickness of between approximately 0.02 to 1.6 millimeters. 6. The system of claim 1, wherein the TBC applied on the cold-side comprises yttria-stabilized zirconia (YSC), platinum aluminide, or nickel-cobalt, or some combination thereof. 7. The system of claim 1, comprising another layer of TBC applied on the hot-side of the transition piece. 8. The system of claim 7, wherein the TBC applied on the hot-side has a hot-side thickness of between approximately 0.02 to 1.6 millimeters. 9. The system of claim 1, wherein the transition piece has a transition piece thickness of between approximately 0.1 to 1.6 millimeters. 10. A system comprising: a combustor wall comprising:a cold-side;a hot-side; anda plurality of dilution holes passing through the combustor wall, wherein each dilution hole comprises an entry-side opening on the cold-side and an exit-side opening on the hot-side, each dilution hole comprises a chamfer about the entry-side opening, and each dilution hole comprises a discrete thermal barrier coating (TBC) applied on the cold-side, wherein each discrete TBC comprises a thickness and a generally circular shape having an opening with an innermost edge that generally circumscribes the entry-side opening of a respective dilution hole. 11. The system of claim 10, wherein each dilution hole has a diameter between approximately 5 to 70 millimeters. 12. The system of claim 10, wherein the generally circular shape of each discrete TBC has an outer diameter that is between approximately 1.5 to 3 times a hole diameter of the respective dilution hole. 13. The system of claim 10, wherein each discrete TBC covers at least a portion of the chamfer on the entry-side opening of a respective dilution hole. 14. The system of claim 10, wherein each discrete TBC has a separation distance between an innermost edge of the discrete TBC and the entry-side opening of a respective dilution hole. 15. The system of claim 10, wherein the thickness of each discrete TBC has a variable thickness. 16. The system of claim 10, wherein each discrete TBC has a conical surface leading into the entry-side opening of a respective dilution hole. 17. The system of claim 16, wherein each discrete TBC has a curved surface that gradually curves into the entry-side opening of a respective dilution hole. 18. A system comprising: an engine wall comprising a cold-side, a hot-side, and one or more dilution holes,wherein each of the one or more dilution holes comprises:a first opening on the cold-side;a second opening on a hot-side;a section of thermal barrier coating (TBC) having a thickness and an innermost edge, wherein the TBC is applied on the cold-side, and the innermost edge forms an opening that generally circumscribes the first opening. 19. The system of claim 18, wherein the first opening of each of the one or more dilution holes comprises a chamfer, and wherein the section of TBC applied on the cold-side at least partially covers the chamfer.