Turbomachinery

1. A turbomachine configured to compress supercritical carbon dioxide, the turbomachine comprising, in fluid flow series:

an inlet;

an inducerless radial impeller having a plurality of backswept blades each of which have a blade exit angle (χ 2 ) of from −50 to −70 degrees;

a fully vaneless diffuser; and

a volute comprising a tongue and having a flow area at the tongue equal to that of the diffuser,

wherein a hub hade angle of the impeller at an entry thereto (γ 1hub ) is from 50 to 70 degrees,

wherein the hub hade angle is defined by an axial line of the inlet and a tangent line that is tangent to a point of the impeller where the blade of the impeller begins,

wherein the inlet is radially flared at a downstream end of the inlet adjacent to the impeller to induce a radial component in flow prior to an entry to the impeller,

wherein only the diffuser is located between the impeller and the volute,

wherein the plurality of blades comprises:

a set of main blades; and

a set of splitter blades,

wherein a meridional chord length of the splitter blades (c s ) is 70 percent of a meridional chord length of the main blades (c m ), and

wherein a radius of the diffuser (r 3 ) is from 1.2 to 1.8 times larger than a radius of the impeller (r 2 ).

2. The turbomachine of claim 1 , in which the backswept blades have a blade exit angle (χ 2 ) of −60 degrees.

3. The turbomachine of claim 1 , in which said hade angle (γ 1hub ) is 60 degrees.

4. The turbomachine of claim 1 , in which each of the plurality of blades is a backswept blade.

5. The turbomachine of claim 1 , in which the impeller comprises one splitter blade for each main blade.

6. The turbomachine of claim 1 , in which a radius of the inlet (r 0 ) is from 25 to 50 percent of the radius of the impeller (r 2 ).

7. The turbomachine of claim 6 , in which the radius of the inlet (r 0 ) is from 30 to 50 percent of the radius of the impeller (r 2 ).

8. The turbomachine of claim 1 , in which the has a height (b 2 ) at an entry of the diffuser and a height (b 3 ) at an exit of the diffuser, with an annulus height ratio and the entry and the exit of the diffuser (b 3 /b 2 ) being 1.

9. The turbomachine of claim 1 , in which the radius of the diffuser (r 3 ) is from 1.3 to 1.7 times larger than the radius of the impeller (r 2 ).

10. The turbomachine of claim 1 , having the inlet, the impeller and the diffuser configured to achieve a design point stagnation pressure ratio of 2 or greater when the impeller is rotated at a speed of at least 50000 revolutions per minute.

11. A method of operating the turbomachine of claim 1 , comprising:

supplying supercritical carbon dioxide to the inlet of the turbomachine; and

rotating the impeller.

12. The method of claim 11 , in which the supercritical carbon dioxide is supplied at 306 kelvin and at 7.7 megapascals, and the impeller is rotated at a speed of at least 50000 revolutions per minute.

13. A system that is a closed, indirect-heated Brayton cycle having a carbon dioxide working fluid and comprising the turbomachine of claim 1 .