# Theoretical and Numerical Research on High-Speed Small Refrigeration Twin-Screw Compressor
## 5 Results and Analysis
### The Effects of the Rotor Configuration and Wrap Angle  
The analysis demonstrates that leakage losses remain the predominant loss mechanism in high-speed small screw compressor design. While an increasing rotational speed can decrease leakages, this approach reduces the rotor stability and motor efficiency at elevated speeds. For compressors with identical external dimensions, leakage reduction strategies extend beyond clearance minimization to include decreasing the leakage path length through optimized rotor configurations. Specifically, reducing the number of rotor lobes improves the area utilization coefficient while decreasing the leakage proportion, thereby enhancing the overall performance.  
Based on these principles, a 12,000 rpm rated speed was selected, and the rotor geometry was optimized to minimize the leakage area. This optimization resulted in a novel 4/5 lobe rotor profile. Under the conditions of a constant theoretical displacement and built-in volume ratio, Figure 13 illustrates the pressure variation with respect to the normalized volume for both the 4/5 and 5/6 lobe configurations at the design operating conditions. During the compression and discharge processes, the 4/5 lobe configuration demonstrates significantly reduced over-compression phenomena compared to the 5/6 lobe, accompanied by lower discharge pressure fluctuations. These characteristics contribute to enhanced energy efficiency and reduced power consumption.  
The variation in the wrap angle serves as an effective parameter for the optimization of the balance between leakage losses and discharge resistance. Figure 14 presents the discharge port configurations for screw rotors with different wrap angles at a constant  
Figure 12: Comparison of the leakage power loss for rotors with different rated speeds at constant displacement.  
Figure 13: Pressure variation with normalized volume for both 4/5 and 5/6 lobe configurations at design operating conditions.  
built-in volume ratio of 2.8. Utilizing the thermodynamic performance prediction model, Figure 15 illustrates the impact of the wrap angle on the efficiency.  
The analysis reveals that the volumetric efficiency decreases with an increasing wrap angle due to an extended contact line length. In contrast, the adiabatic efficiency demonstrates a non-monotonic relationship with the wrap angle. At lower wrap angles, the reduced discharge port area leads to increased discharge power losses. Conversely, higher wrap angles exhibit diminished discharge power losses but are accompanied by elevated leakage losses. This trade-off relationship results in an optimal wrap angle that maximizes the adiabatic efficiency by balancing these competing loss mechanisms. Figure 16 illustrates the variation in the power losses across different wrap angles, quantitatively demonstrating this efficiency optimization phenomenon.  
Figure 16: Power losses of the rotor with different wrap angles.  
Figure 14: The discharge port with different wrap angles at a constant built-in volume ratio.  
Figure 15: The volumetric and adiabatic efficiencies of rotors with different wrap angles.