Fuel injector having differential tip cooling system and method

1. A system, comprising:

a fuel injector, comprising:

a fuel conduit configured to inject a fuel;

a first oxygen conduit configured to inject oxygen;

an annular coolant chamber comprising an inner annular wall and an outer annular wall, wherein the outer annular wall comprises a portion of an external wall of the fuel injector;

a cooling coil disposed surrounding the external wall, wherein the cooling coil comprises an entrance coupled to the annular coolant chamber through the external wall, the entrance is configured to convey a coolant to the annular coolant chamber, the cooling coil comprises an exit coupled to the annular coolant chamber through the external wall, and the exit is configured to carry the coolant away from the annular coolant chamber; and

a first annular structural support extending through the annular coolant chamber between the inner annular wall and the outer annular wall, wherein the first annular structural support divides the annular coolant chamber into a first passage and a second passage, and the first annular structural support comprises a first flow divider wall that isolates a first coolant flow in the first passage relative to a second coolant flow in the second passage.

2. The system of claim 1 , comprising a combustion system having the fuel injector.

3. The system of claim 1 , wherein the fuel comprises a dry fuel feedstock, a slurry fuel feedstock, a liquid fuel feedstock, or a combination thereof.

4. The system of claim 1 , comprising a second annular structural support extending through the annular coolant chamber, wherein the first and second annular structural supports collectively divide the annular coolant chamber into the first passage, the second passage, and a third passage.

5. The system of claim 4 , comprising a third annular structural support extending through the annular coolant chamber, wherein the first, second, and third annular structural supports collectively divide the annular coolant chamber into the first passage, the second passage, the third passage, and a fourth passage.

6. The system of claim 1 , wherein the first passage has a smaller axial cross-sectional area than the second passage, the first passage is configured to flow a first coolant with a greater flow velocity than a second coolant flowing in the second passage, or a combination thereof.

7. The system of claim 1 , wherein the entrance is configured to convey the coolant to the annular coolant chamber in a direction crosswise to a longitudinal axis of the fuel injector, and the exit is configured to convey the coolant away from the annular coolant chamber in the direction crosswise to the longitudinal axis of the fuel injector.