A turbine rotor adapted and configured to be rotationally driven, about a rotation axis that extends in an axial direction, by a flowing fluid that spirals circumferentially about, radially inwardly toward, and axially along said rotation axis, said rotor comprising a rotor core and a plurality of rotor vanes uniformly circumferentially distributed about said rotor core, wherein:
- said rotor has a configuration bounded by a peripheral envelope configured as a surface of revolution about said rotation axis, and has an axial length extending along said rotation axis from a base end of said rotor to an outlet end of said rotor;
- said rotor includes a first rotor stage being a first portion of said rotor adjoining said base end and extending along said rotation axis along a first portion of said axial length, and a second rotor stage being a second portion of said rotor adjoining said outlet end and extending along said rotation axis along a second portion of said axial length;
- bounding surfaces of said rotor core and of said plurality of said rotor vanes define and bound a corresponding plurality of open rotor channels that each respectively communicate from a respective rotor channel inlet on said peripheral envelope to a respective rotor channel outlet on said outlet end of said rotor;
- all of said respective rotor channel inlets together form a rotor inlet, and all of said respective rotor channel outlets together form a rotor outlet;
- said bounding surface of said rotor core is defined as a further surface of revolution about said rotation axis, with a radius that diminishes continuously along a curve throughout said first portion of said axial length in said first rotor stage from a maximum radius at said base end to a minimum radius at a downstream end of said first rotor stage, and that remains approximately constant at said minimum radius throughout said second portion of said axial length in said second rotor stage, such that said rotor channels have a cross-sectional area perpendicular to said axis, which cross-sectional area increases successively on successive section planes perpendicular to said axis successively along said axis in said first rotor stage;
- said rotor is configured and adapted to rotate at a target rotational peripheral speed in an operational rotation direction about said rotation axis, with said fluid flowing from said rotor inlet to said rotor outlet at a target fluid flow speed through said rotor channels;
- said bounding surfaces of said rotor core and of said rotor vanes are configured to define and follow smoothly along a respective rank of transformed streamlines extending along said bounding surfaces respectively in each one of said rotor channels from said respective rotor channel inlet to said respective rotor channel outlet thereof;
- each said respective rank of transformed streamlines is based on a rotational transformation of a respective rank of stationary streamlines into a rotating reference system for rotation of said rotor at said target rotational peripheral speed by helically twisting said stationary streamlines about said rotation axis in a twist direction opposite said operational rotation direction of said rotor by twist angles that increase progressively from a zero twist at said base end to a maximum twist at said outlet end corresponding to a rotation angle through which said rotor will rotate at said target rotational peripheral speed when said fluid flows from said rotor inlet to said rotor outlet at said target fluid flow speed through said rotor channels;
- each respective one of said stationary streamlines respectively has the same length as all others of said stationary streamlines from respective inlet ends thereof at said rotor inlet to respective outlet ends thereof at said rotor outlet;
- said outlet ends of said stationary streamlines each respectively exit said rotor outlet parallel to said rotation axis;
- respective inlet ends of said stationary streamlines and respective inlet ends of said transformed streamlines are respectively spaced uniformly from one another in said axial direction along a radially outer free edge of each respective one of said rotor vanes at said rotor inlet adjacent to said peripheral envelope;
- respective outlet ends of said stationary streamlines and respective outlet ends of said transformed streamlines respectively terminate in respective annular rings of respectively equal cross-sectional area normal to said rotation axis at said outlet end of said rotor;
- each said respective rank of stationary streamlines makes a smooth banked rolling turn through a respective one of said rotor channels from said rotor channel inlet to said rotor channel outlet of said respective rotor channel;
- said inlet end of a first one of said transformed streamlines and said inlet end of a first one of said stationary streamlines are respectively located adjacent to said base end of said rotor;
- said inlet end of a last one of said transformed streamlines and said inlet end of a last one of said stationary streamlines are respectively located adjacent to said downstream end of said first rotor stage;
- said outlet end of said first one of said transformed streamlines and said outlet end of said first one of said stationary streamlines are respectively located on a radially innermost first one of said annular rings of equal cross-sectional area;
- said outlet end of said last one of said transformed streamlines and said outlet end of said last one of said stationary streamlines are respectively located on a radially outermost last one of said annular rings of equal cross-sectional area;
- said stationary and transformed streamlines each respectively progress from said respective inlet end thereof to said respective outlet end thereof with a radial position of said respective stationary or transformed streamline that has a respective maximum at said respective inlet end thereof and a respective minimum at said respective outlet end thereof and that monotonically decreases and/or stays constant, and never increases, along said respective stationary or transformed streamline from said inlet end to said outlet end thereof;
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- said respective inlet ends of said stationary streamlines enter into said rotor channel inlet at respective entry angles relative to a tangent of said peripheral envelope, said entry angles have entry angle values that decrease monotonically along said axial direction from a steepest entry angle value for said first stationary streamline adjacent to said base end of said rotor to a shallowest entry angle value for said last stationary streamline adjacent to said downstream end of said first rotor stage.