Screw rotor universality: within-rotor and across-rotor η_v collapse
By DigiEntropy Engineering · 2025-12-25 · 7 min read
The kinematic mass-flow law extends to twin-screw compressors with the rotor swept volume in place of N_cyl × V_cyl. We show that the η_v(Π) curves of every motor variant in a single Bitzer CSH rotor family overlap to within ~3 % CoV, and that the curves across distinct CSH rotors collapse to within ~4 % CoV — tighter than the equivalent reciprocating result.
About this post — Authored by an AI assistant using DigiEntropy's polynomial corpus, the universal compressor predictor, and the project's chart-generation tooling. Charts are produced by Python scripts that read the same database the live site queries; tables and formulas are pulled from the same engineering modules. Findings reflect the project's current dataset and methodology — send corrections or deeper questions to admin@digientropy.com. Abstract The kinematic mass-flow law generalises to twin-screw compressors by substituting the rotor swept volume per revolution for the reciprocating quantity $N{\mathrm{cyl}} \cdot V{d,\mathrm{cyl}}$. We test the resulting form on the Bitzer CSH range using the rotor-displacement value $V{d,\mathrm{rotor}}$ (the shaft drives the male rotor at nameplate speed 2900 rpm at 50 Hz). Two collapses appear: (i) all motor variants of one rotor family share an identical $\etav(\Pi)$ curve to within 3 % CoV, and (ii) the $\etav(\Pi)$ curves of all distinct CSH rotor families collapse to within 4 % CoV — tighter than the equivalent reciprocating result. Hypothesis The kinematic equation specialised for a twin-screw compressor is $\dot m \;=\; \rhos(Te, \mathrm{SH}, \mathrm{ref}) \cdot V{d,\mathrm{rotor}} \cdot N{\mathrm{rev/s}} \cdot \etav(\Pi, \mathrm{ref})$ with $V{d,\mathrm{rotor}}$ the swept volume per revolution of the rotor pair and $N{\mathrm{rev/s}}$ the shaft speed. In a screw compressor the dominant loss mechanism is not clearance-volume re-expansion (there is none) but rotor-tip and end-face leakage past the rotors. A first-order phenomenological form is $\etav \;\approx\; A - B \, \frac{\Pi - \Pii}{N{\mathrm{rev/s}}}$ with $A \approx 0.98$ (ideal $\etav$), $B$ a rotor-tip leakage coefficient, and $\Pii$ the built-in volume ratio set by the rotor profile. We test whether (a) the leakage coefficient $B$ varies between motor variants of one rotor (it should not, since the rotor geometry is the same), and (b) it varies between rotor families (it should, since each rotor profile has a distinct tip-clearance specification). Sample and method Bitzer's CSH range encodes rotor diameter, axial length, and built-in $Vi$ in the model number — CSH7553 denotes a 75-mm-diameter rotor at axial-length code 5 and $Vi$ code 3. The trailing motor code (-50Y, -70Y, …) selects motor rating only; rotor geometry and therefore displacement is invariant under the motor variant. We treat every model sharing a rotor prefix as one rotor family. For each model we fetch the R134a $\dot m$ polynomial at 50 Hz under the available…