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.
24 - distinct CSH rotor families - one representative model per rotor
Figure 2 overlays the ηv(Π) curves for 24 distinct CSH rotor families (one representative model per rotor).
2.6 % - within-rotor CoV - two motor variants of the CSH7553 rotor
The two curves agree to within 2.6 % CoV. The residual difference is consistent with small differences in motor speed (motor-load-dependent slip at 50 Hz) and minor catalogue-fit noise; rotor leakage itself is structurally identical.
4 % - across-rotor CoV - tighter than the reciprocating result
The 24 curves spread within a 4 % CoV envelope across the pressure-ratio range we test.
2900 rpm - nameplate male-rotor speed - at 50 Hz, N = 48.3 rev/s
The shaft drives the male rotor at nameplate speed 2900 rpm at 50 Hz.
0.98 - A, the ideal ηv - in the first-order leakage form
A first-order phenomenological form is ηv ≈ A − B (Π − Πi) / N, with A ≈ 0.98 (ideal ηv), B a rotor-tip leakage coefficient, and Πi the built-in volume ratio set by the rotor profile.
fifth - tier of the collapse hierarchy - after frequency, cylinder, geometry, predictor
The CSH/CSW screw result is the fifth tier of our internal collapse hierarchy. Earlier tiers — frequency, cylinder, geometry, predictor — are covered in the preceding posts in this series.
Hypothesis
The kinematic equation specialised for a twin-screw compressor is
$\dot m \;=\; \rhos(Te, \mathrm{SH}, \mathrm{ref}) \cdot V{d,\mathrm{rotor}} \cdot N{\mathrm{rev/s}} \cdot \etav(\Pi, \mathrm{ref})$
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