Between the rotor tips and the housing casing.
One of the most insightful outputs of a screw compressor model is the indicator diagram, which shows the pressure inside a working chamber as a function of its volume (or, equivalently, of the rotor rotation angle). The indicator diagram reveals the suction, compression and discharge processes, and it clearly shows whether under‑compression or over‑compression occurs at the discharge port. The area enclosed by the indicator curve represents the indicated work per cycle. New mathematical models for calculating the indicator diagram have been proposed and successfully verified against experimental data.
: Contemporary designs often utilize asymmetric rotor profiles , which can reduce the "blow-hole" area (a major source of internal leakage) by up to 90% compared to older designs.
is the flow discharge coefficient (experimentally determined, typically between 0.6 and 0.85). Aclearcap A sub c l e a r end-sub is the cross-sectional area of the clearance gap. are upstream pressure and temperature. Pdowncap P sub d o w n end-sub is the downstream pressure. is the isentropic exponent of the gas. Between the rotor tips and the housing casing
ηs=ṁactual⋅(hdischarge,isentropic−hsuction)Wshafteta sub s equals the fraction with numerator m dot sub a c t u a l end-sub center dot open paren h sub d i s c h a r g e comma i s e n t r o p i c end-sub minus h sub s u c t i o n end-sub close paren and denominator cap W sub s h a f t end-sub end-fraction Computational Algorithm for Simulation
Performance calculation typically involves evaluating key parameters such as:
For chamber models that consider non‑uniform pressure distributions, more advanced numerical methods are required. A recent development treats each working unit of a screw compressor as a one‑dimensional compressible transient flow with two moving pistons, allowing fluid to pass through. Numerical methods for such models have been verified by shock wave tests. The area enclosed by the indicator curve represents
Geometric modeling serves as the fundamental cornerstone for any performance analysis. It translates the complex, continuous helical contact lines of the rotors into discrete algebraic variables.
Leakage is the primary source of inefficiency in screw compressors. Gas flows from high-pressure chambers to low-pressure chambers through gaps (clearances).
The story of screw compressors is one of continuous improvement, driven by advances in mathematical modeling and performance calculation. From humble beginnings to the sophisticated designs of today, screw compressors have become a vital component in many industries. As research and development continue, we can expect even more efficient and compact screw compressors to emerge, powering the machinery of tomorrow. powering the machinery of tomorrow.
Screw compressors are a cornerstone of modern industrial systems, ranging from refrigeration to high-pressure air production. Their effectiveness is largely defined by their internal rotor geometry and the thermodynamic efficiency of the compression cycle. 1. Mathematical Modelling of Geometry
These include the clearances between the rotors themselves, and between the rotors and the housing. Orifice Flow:
For short clearances with minimal friction, the flow is modeled as an isentropic expansion through an orifice: