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A system includes a gas delivery disk coupled to a second shaft, wherein the second shaft and the gas delivery disk are disposed about an axis. The gas delivery disk includes an inner axial opening configured to facilitate a first axial flow through a first passage within the second shaft, a duct co

A system includes a gas delivery disk coupled to a second shaft, wherein the second shaft and the gas delivery disk are disposed about an axis. The gas delivery disk includes an inner axial opening configured to facilitate a first axial flow through a first passage within the second shaft, a duct configured to supply a bearing flow in a radial direction toward the axis, and a bearing face disposed within the first passage and radially interior to the inner axial opening. The bearing face is configured to receive the bearing flow, and the bearing face is configured to form a gas bearing between the bearing face and a first shaft disposed about the axis.

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1. A system comprising: a gas delivery disk coupled to a second shaft, wherein the second shaft and the gas delivery disk are disposed about an axis, wherein the gas delivery disk comprises: an inner axial opening configured to facilitate a first axial flow through a first passage within the second

1. A system comprising: a gas delivery disk coupled to a second shaft, wherein the second shaft and the gas delivery disk are disposed about an axis, wherein the gas delivery disk comprises: an inner axial opening configured to facilitate a first axial flow through a first passage within the second shaft;a duct configured to supply a bearing flow in a radial direction toward the axis;a bearing face disposed within the first passage and radially interior to the inner axial opening, wherein the bearing face is configured to receive the bearing flow, and the bearing face is configured to form a gas bearing between the bearing face and a first shaft disposed about the axis; andwherein the gas delivery disk comprises a middle axial opening configured to facilitate a second axial flow through a second passage radially exterior to the second shaft, wherein the duct is configured to extract the bearing flow from the second axial flow. 2. The system of claim 1, wherein the gas delivery disk comprises a plurality of the inner axial openings configured to facilitate the first axial flow through the first passage within the second shaft. 3. The system of claim 1, wherein a second pressure of the second axial flow is greater than a first pressure of the first axial flow. 4. The system of claim 1, wherein the gas delivery disk comprises an outer body, the outer body comprises the middle axial opening, and the duct is configured to extract the bearing flow from the second axial flow upstream of the outer body. 5. The system of claim 1, wherein the gas delivery disk comprises an outer body, the outer body comprises the middle axial opening, and the duct is configured to extract the bearing flow from the second axial flow downstream of the outer body. 6. The system of claim 1, wherein the gas delivery disk comprises: an inner body, wherein the inner body comprises a first axial width and the inner axial opening; anda foot, wherein the foot comprises the bearing face and a second axial width, and the second axial width is greater than the first axial width of the inner body. 7. The system of claim 1, wherein the bearing face comprises at least one groove and a plurality of ridges, wherein the at least one groove is configured to receive the bearing flow, and the plurality of ridges is configured to axially retain a portion of the bearing flow within the at least one groove to form the gas bearing. 8. The system of claim 7, wherein the bearing face comprises a plurality of the grooves, and the gas delivery disk comprises a distribution duct coupled to the duct and to the plurality of the grooves, wherein the distribution duct is parallel to the axis. 9. The system of claim 1, comprising a turbine engine, wherein the turbine engine comprises the first shaft and the second shaft, and the gas delivery disk is disposed about the first shaft at a location between 25 to 75 percent of an axial length of the first shaft. 10. The system of claim 9, wherein the turbine engine comprises a combustor section, and the location of the gas delivery disk is configured to transfer loads from the gas bearing to the combustor section. 11. A system comprising: a first shaft disposed about an axis;a second shaft disposed about the axis and disposed concentrically about the first shaft, wherein the first shaft and the second shaft form a first passage therebetween; anda gas delivery disk coupled to the second shaft, wherein the gas delivery disk comprises: an inner axial opening configured to facilitate a first axial flow through the first passage;a plurality of ducts configured to supply a bearing flow in a radial direction toward the axis, wherein the plurality of ducts is configured to extract the bearing flow from a second axial flow;a bearing face disposed within the first passage and radially interior to the inner axial opening, wherein the bearing face is configured to receive the bearing flow, and the bearing face is configured to form a gas bearing between the bearing face and the first shaft disposed about the axis; andwherein the gas delivery disk comprises a middle axial opening configured to facilitate the second axial flow through a second passage radially exterior to the second shaft. 12. The system of claim 11, wherein the first shaft is coupled to a first compressor stage, the second shaft is coupled to a second compressor stage, and a second pressure of a second airflow from the second compressor stage is greater than a first pressure of a first airflow from the first compressor stage. 13. The system of claim 12, wherein the first shaft is coupled to a low pressure turbine stage, and the second shaft is coupled to a high pressure turbine stage, wherein the second shaft is configured to rotate about the axis at a greater speed than the first shaft. 14. The system of claim 11, wherein the first shaft is configured to rotate counter to the second shaft. 15. The system of claim 11, wherein at least one of the first axial flow and the second axial flow comprises a cooling flow configured to cool a turbine stage of the system, a dilution flow configured to dilute combustion products of the system, or any combination thereof. 16. A method comprising: directing a first gas flow axially through a first passage and an inner axial opening of a gas delivery disk, wherein the first passage is disposed between a first shaft and a second shaft, the first shaft is disposed about an axis, and the second shaft is disposed about the axis;directing a second gas flow axially through a second passage and a middle axial opening of a gas delivery disk, wherein the second passage is disposed radially exterior to the second shaft; anddirecting a bearing flow radially through the gas delivery disk toward the first shaft, wherein the gas delivery disk is configured to form a gas bearing between the gas delivery disk and the first shaft with the bearing flow. 17. The method of claim 16, wherein the bearing flow is extracted from the second gas flow. 18. The method of claim 17, wherein the gas delivery disk comprises a plurality of ducts configured to extract the bearing flow, and the bearing flow through the plurality of ducts is isolated from the first gas flow axially through the inner axial opening.