Theoretical mass flow (no leakage): Q_th = V_d × n (m^3/s at suction conditions) m_dot_th = Q_th × ρ_suction = Q_th × p1/(R T1)
At pressure ratio = 4.5, speed = 3000 rpm: - Volumetric efficiency = 82.3% - Adiabatic efficiency = 76.1% - Leakage fraction: blowhole = 8.2%, radial = 5.4%
No seal is perfect. Mathematical models must calculate the length of sealing lines and the area of the "blowhole"—the tiny triangular gap where the two rotors and the housing meet. This is a critical factor in volumetric efficiency. 2. Thermodynamic Modelling: The Control Volume Approach Theoretical mass flow (no leakage): Q_th = V_d
The most significant recent trend is the development of hybrid modelling frameworks that combine the strengths of physical modelling with machine learning (ML). A prominent example is the integration of a 1D chamber model with to perform thermodynamic analysis and optimisation of multi-stage compressors. Similarly, an integrated framework uses a conventional chamber model alongside ML techniques to optimise parameters like rotor geometry and fluid injection, achieving high accuracy while significantly reducing computational costs.
$$ \eta_is = 20.1 / 23.65 = 0.85 \text (85%) $$ Theoretical mass flow (no leakage): Q_th = V_d
By utilizing a real gas equation of state (such as Peng-Robinson or Martin-Hou), the differential equations for pressure ( ) and temperature (
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. Theoretical mass flow (no leakage): Q_th = V_d
dUdθ=1ω(∑ḣin−∑ḣout+Q̇)−pdVdθthe fraction with numerator d cap U and denominator d theta end-fraction equals the fraction with numerator 1 and denominator omega end-fraction open paren sum of h dot sub i n end-sub minus sum of h dot sub o u t end-sub plus cap Q dot close paren minus p the fraction with numerator d cap V and denominator d theta end-fraction is the internal energy of the gas. represents the enthalpy of flowing fluid streams. Q̇cap Q dot