Screw Compressors- Mathematical Modelling And Performance Calculation -

: Mathematical equations describe the position of any point on the rotor in a coordinate system as a function of the rotation angle Volume Calculation : The working chamber volume

Modern designs use asymmetric profiles to minimize "leakage triangles" and improve efficiency. Volume Calculation: The instantaneous volume ( ) is a function of the rotation angle (

While conventional twin-screw machines with side-by-side rotors dominate the industry, alternative configurations are gaining research attention. Internally Geared Screw Machines (IGSMs), where one rotor operates inside another on parallel offset axes, are a novel concept. Detailed numerical geometry models for IGSMs are being developed and coupled with existing performance prediction frameworks to assess their potential advantages over conventional designs. These models are essential for understanding how radical changes in geometry influence key parameters like sealing and leakage.

Use when detailed geometry or computational resources are limited. Assumptions: uniform polytropic exponent n, volumetric efficiency correlation, constant leakage fraction.

The model must calculate the heat exchange between the gas and the oil droplets. This keeps the discharge temperature low and allows for higher pressure ratios in a single stage.

These include the clearances between the rotors themselves, and between the rotors and the housing. Orifice Flow: Detailed numerical geometry models for IGSMs are being

To accurately calculate an oil-injected compressor, the model must include an oil mass balance equation and split the heat transfer into gas-to-wall and gas-to-oil components:

Let’s break down the core logic behind screw compressor modelling. 🧵👇

Indicated power: $$ \dotW ind = \fracn \cdot z_160 \cdot W ind $$ Assumptions: uniform polytropic exponent n

mcvdTdt=−T(𝜕p𝜕T)vdVdt+∑ṁinhin−∑ṁouthout−hAw(T−Tw)+Q̇injm c sub v the fraction with numerator d cap T and denominator d t end-fraction equals negative cap T open paren the fraction with numerator partial p and denominator partial cap T end-fraction close paren sub v the fraction with numerator d cap V and denominator d t end-fraction plus sum of m dot sub i n end-sub h sub i n end-sub minus sum of m dot sub o u t end-sub h sub o u t end-sub minus h cap A sub w open paren cap T minus cap T sub w close paren plus cap Q dot sub i n j end-sub = Specific heat capacity at constant volume = Pressure = Enthalpy of the respective fluid streams = Heat transfer through the housing and rotor walls ( is the heat transfer coefficient, Awcap A sub w is the wall area, and Twcap T sub w is the wall temperature) Q̇injcap Q dot sub i n j end-sub

dmdt=ṁin−ṁout+ṁleak,in−ṁleak,out+ṁinjd m over d t end-fraction equals m dot sub i n end-sub minus m dot sub o u t end-sub plus m dot sub l e a k comma i n end-sub minus m dot sub l e a k comma o u t end-sub plus m dot sub i n j end-sub = Mass flow through suction and discharge ports ṁleakm dot sub l e a k end-sub