Once the differential equations are solved (usually via numerical methods like Runge-Kutta), we can calculate the key performance indicators (KPIs): Volumetric Efficiency ( ηveta sub v
Initialize slice states:
Given: inlet p1, T1, discharge p2, speed n, displacement per rev V_d.
Volumetric efficiency is significantly influenced by internal leakages and pressure ratios. For example, in oil-injected air screw compressors, volumetric efficiency improves compared to dry operation because the injected oil acts as a sealant, reducing internal leakages.
Twin-screw compressors consist of male and female rotors meshing within a dual-bore casing. As the rotors turn, the volume between the lobes and the casing changes. This volume variation creates distinct phases: suction, transfer, compression, and discharge.
: The model calculates the instantaneous volume of the working chamber as a function of the rotation angle (
+--------------------------------------------------+ | 1. Input Geometry & Operating Conditions | | (Rotor profiles, clearances, speed, gas) | +--------------------------------------------------+ | v +--------------------------------------------------+ | 2. Pre-calculate Geometric Profiles | | (V(θ), dV/dθ, Leakage Areas A(θ)) | +--------------------------------------------------+ | v +--------------------------------------------------+ | 3. Initialize Chamber Properties | | (Set initial P, T, m at suction closure) | +--------------------------------------------------+ | v +--------------------------------------------------+ | 4. Run Runge-Kutta ODE Solver | | (Solve dm/dθ, dT/dθ, dP/dθ step-by-step) | +--------------------------------------------------+ | v +--------------------------------------------------+ | 5. Convergence Check | | (Do cyclic properties match at wrap angle?) | +--------------------------------------------------+ | | | No | Yes v v +-----------------------------+ +-----------------------------+ | Re-initialize with new end | | 6. Output Performance Data | | states & re-run step 4 | | (Efficiencies, Power) | +-----------------------------+ +-----------------------------+ 8. Conclusion
$$ P v = Z(P,T) R T $$
[ \eta_v = \frac\dotm actual \cdot v suc \cdot n_rotorV_th ]
If chocked (sonic flow at throat), the pressure ratio is replaced by the critical pressure ratio.
(adiabatic efficiency):
Efficiency is largely dictated by what doesn't get compressed. Leakage paths include:
Discharge temperature: T2 = T1 × (p2/p1)^(n−1)/n
Between the rotor tips and the housing casing.
