Complex screw rotors with a central circular cross section connecting right-hand and left-hand sections of the rotors

A screw compressor or expander comprising:

• a female rotor including a first section having a right-hand first groove and a second section having a left-hand second groove, wherein the first groove has a first variable helix, the second groove has a second variable helix, and the female rotor has a first variable profile and a first variable outer diameter;
• and
• a male rotor including a third section having a left-hand first lobe and a fourth section having a right-hand second lobe, wherein the first lobe has a third variable helix, the second lobe has a fourth variable helix, and the male rotor has a second variable profile and a second variable outer diameter,
• wherein the female rotor includes a first central section positioned between the first section and the second section and the male rotor includes a second central section positioned between the third section and the fourth section, and wherein the female rotor transitions to a substantially circular cross section at the first central section and the male rotor transitions to a substantially circular cross section at the second central section.