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International Compressor Engineering 
Conference School of Mechanical Engineering 
2024 
Geometric and Numerical Investigation of Twin-Screw Vacuum 
Pumps 
Yang Lu 
yang.lu.8@city.ac.uk 
Sham Rane 
sham.rane@city.ac.uk 
Ahmed Kovacevic 
a.kovacevic@city.ac.uk 
Follow this and additional works at: https://docs.lib.purdue.edu/icec 
Lu, Yang; Rane, Sham; and Kovacevic, Ahmed, "Geometric and Numerical Investigation of Twin-Screw 
Vacuum Pumps" (2024). International Compressor Engineering Conference. Paper 2799. 
https://docs.lib.purdue.edu/icec/2799 
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1126, Page 1 
Geometric and Numerical Investigation of Twin-Screw Vacuum Pumps 
Yang LU 1 *, Sham Rane 1, Ahmed Kovacevic 1 
1 City, University of London, School of Science and Technology, 
London, United Kindoom 
Contact Information (yang.lu.8@city.ac.uk) 
* Corresponding Author 
ABSTRACT 
This paper presents analysis of twin-screw vacuum pumps, encompassing both geometrical calculations and 
numerical simulations. The geometrical calculations include key parameters such as chamber volume, leakage area, 
suction port area, and discharge port area. These parameters are studied across rotational angles for constant pitch, 
and stepped pitch configurations. The leakage areas include radial, axial, and interlobe leakage paths. Computational 
Fluid Dynamics (CFD) is employed to investigate the axial leakage paths. Additionally, the study utilizes the 
SCORG software package, an inhouse simulation tool to calculate thermodynamic processes and integral 
parameters. By integrating the geometric calculations into SCORG, this approach enables extensive calculation and 
design optimization of twin-screw vacuum pumps. Five different combinations of pitch were analyzed to assess their 
impact on both volume flow rate and efficiency. The analysis revealed that reducing the pitch of the second stage 
resulted in a decrease of approximately 2% in volumetric efficiency, while adiabatic efficiency increased by around 
4%. The findings contribute to a more comprehensive understanding of the performance characteristics and design 
considerations for twin screw vacuum pumps. 
1. INTRODUCTION 
Vacuum technology plays a pivotal role in a myriad of industrial applications, spanning from semiconductor 
technology to food packaging and freeze drying (Jousten, 2016). Vacuum pumps for these applications operate at a 
broad pressure range, from 10 superscript -10 Pa for extreme vacuum conditions to 10 superscript 5 Pa at atmospheric pressure. Positive 
displacement machines, such as roots vacuum pumps, scroll vacuum pumps, and twin screw vacuum pumps could 
be used to operate in both rough and fine vacuum regimes (10 superscript 2 to 10 superscript -1 Pa ). Oil-free twin screw vacuum pumps 
have emerged as a popular choice, characterized by features such as variable pitch, large wrap angle, and a discharge 
port plate, enabling operation at lower suction pressures. While previous studies on twin screw vacuum pumps have 
primarily focused on rotor profile design (Li, He, Wu, et al., 2022; Lu et al., 2015; Stosic et al., 2016) and 
performance modelling (Li, He, Sun, et al., 2022; Li et al., 2021; Li, He, Wang, et al., 2022; Li, He, Wu, et al. , 2022; 
Pfaller et al., 2011 ; Pleskun et al. , 2021), it's crucial to note that simulations have typically overlooked axial leakage 
and discharge port considerations. Consequently, the accuracy of simulation results may be compromised, as axial 
leakage losses and discharge losses significantly impact power consumption and volume flow rate. In this paper, all 
leakage paths, including radial, axial, and interlobe leakage flows were addressed. Furthermore, variations in 
discharge port area with rotational angle were calculated. Leveraging the chamber model utilized for twin screw 
compressors, thermodynamic calculations are tailored for twin screw vacuum pumps. Finally, different pitch 
combinations were compared to assess their impact on the volume flow rate and indicated power, offering insights 
into optimizing twin screw vacuum pump performance. 
2. GEOMETRY CALCULATION 
The geometric characteristics of twin-screw vacuum pumps include chamber volume, leakage area and port area. In 
order to construct an accurate performance chamber model , it is imperative to calculate geometric characteristics in 
advance. In this section, it begins by introducing the design parameters of rotor geometry. Subsequently, the 
calculation of chamber volume for both constant pitch and variable pitch configurations is presented. Leakage areas 
27th International Compressor Engineering Conference at Purdue, July 15 - 18, 2024 
1126, Page 2 
are computed, with particular emphasis placed on analyzing the axial leakage path using Computational Fluid 
Dynamics (CFD) methodology. Additionally, the variation in suction port area and discharge port area with 
rotational angle is determined. 
In this section, the introduction of geometrical parameters essential for thermodynamic calculations is detailed. 
These parameters encompass chamber volume, leakage area, and port area. Chamber volume calculations are 
applicable across various pitch configurations, including constant pitch, stepped pitch, and linear pitch. Additionally, 
the intricate calculations involved in determining leakage areas, which comprise radial leakage, axial leakage, and 
interlobe leakage, are explored. Moreover, the variations in suction port area and discharge port area are considered. 
2.2 Chamber volume 
First of all, the cross-section area between rotor and casing is calculated. Then chamber volume is integrated by 
times the area of cross section and Z subscript i - Z subscript i-1 as shown in the following equation. 
      (1) 
In a twin-screw machine, the pitch refers to the distance between corresponding points on adjacent lobes of the 
rotor. It is commonly defined as the axial distance traveled by the rotor for one complete revolution. The pitch can 
either remain constant, meaning it stays the same along the length of the rotors, or it can vary depending on the 
design of the vacuum pumps. In certain instances, the pitch may change gradually or stepwise along the length of the 
rotors to optimize performance for specific operating conditions. The options for rotor pitch type typically include 
uniform, variable, and stepped. While a uniform pitch is easier to manufacture, both variable pitch and stepped pitch 
designs offer gradual compression. Stepped pitch can be optimized for different stages of the working process, 
providing a cost-effective solution. In contrast, variable pitch is ideal for applications that require high efficiency 
and smooth operation. Figure 1 illustrates these three types of pitch. For the purposes of this research, we will focus 
on studying the stepped pitch configuration. 
 
 
       
   
   
 
 
    
   
   
   
   
Figure 1: Chamber volume of different pitch type 
2.3 Leakage area 
Leakage paths encompass radial, axial, and interlobe leakage. Their respective areas can be computed by 
multiplying the length of the leakage path by the gap size as shown in equation (2). Radial leakage area is 
determined by rotor tip length, while interlobe leakage area is calculated based on the sealing line length. In this 
study, axial leakage is investigated using Computational Fluid Dynamics (CFD) methodology. 
      (2) 
For the CFD simulation, the fluid domain of constant pitch main and gate rotors with a wrap angle of 720 degrees 
have been generated as shown in Figure 2. The rotor length is set at 144 mm, while the axial gap size measures 100 
µm with no radial gap present. A mesh comprising five layers is generated at the axial gap. The simulation is 
transient, with 500 timesteps and a timestep size of 1E-05 s. Inlet pressure is specified as 1 bar, while the discharge 
pressure is set at 3 bar. 
27th International Compressor Engineering Conference at Purdue, July 15 - 18, 2024 
(a) Geometry model (b) Mesh at axis gap 
  
    
    
 
 
   
    
 
 
 
    
    
1126, Page 3 
Figure 2: CFD model for axial leakage analysis 
In the configuration of 36 cases with different rotor rotational positions, six featured rotational positions have been 
selected to demonstrate the axial leakage paths. These phases are distinguished based on the contact line: Two range 
of pressure contour are selected to show the pressure difference. Phase 1, where the contact line is at the main rotor's 
outer circle, exhibits two leakage paths spanning the length of the addendum plus dedendum. Phase 2, occurring 
between the two rotors, presents three leakage paths, each with the same length as in Phase 1. Finally, Phase 3, with 
the contact line at the gate rotor's outer circle, showcases two leakage paths of similar length to those in Phase 1. 
Figure 3: CFD results to show axial leakage path 
Interlobe leakage area is determined by analyzing the contact line. Three distinct leakage areas are computed and 
compared in Figure 4. All three leakage paths are configured with identical gap sizes for stepped pitch case. 
Notably, the radial leakage area surpasses the interlobe leakage area, while the axial leakage area registers as the 
smallest among the three. 
27th International Compressor Engineering Conference at Purdue, July 15 - 18, 2024 
2.4 Discharge port area 
  
                             
    
Figure 4: Leakage area 
1126, Page 4 
Discharge port area can be calculated based on the design of the built-in Volume index (Vi). Different port geometry 
can be automatically calculated based on the Vi and given rotor profile as shown in Figure 5. Three distinct 
discharge ports are created based on the provided Vi. As Vi increased, the size of discharge port was reduced. 
    
Figure 5: Discharge port area 
A numerical procedure was employed to compute the time-varying flow area of the discharge port. The flow path 
between the working and discharge chambers initiates when the edge C3 of the rotor lobe intersects the opening 
curves of the discharge port. Initially, the flow area starts at zero and progressively increases to its maximum extent. 
Subsequently, it diminishes until the rotor lobe completely seals off the connection between the working chamber 
and the discharge port. This process is analyzed by defining numerous small elemental areas positioned between 
adjacent radii and the port boundaries, as depicted in Figure 6. The total flow area through the axial discharge port is 
determined by summing all these elemental areas. 
      
Figure 6: Discharge port area 
Suction and discharge port area changing with rotational angle can be calculated as shown in Figure 7. The blue 
curve shows the suction port area changing with rotational angle while green curve shows discharge port area 
changing with rotational angle. Gray curve shows the chamber volume changing with rotational angle. Since the 
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1126, Page 5 
suction port is fully opened for twin screw vacuum pump, the area changing of suction port is same as cross section 
area changing between two rotors and casing. 
Figure 7: Suction and discharge port area 
3. NUMERICAL SIMULATION 
The geometry calculations have been incorporated into SCORG, which houses the thermodynamic model utilized 
for twin screw compressor calculations. This identical thermodynamic model is also applied for twin screw vacuum 
pump calculations (Stosic et al. , 2005). Notably, the simulation does not account for bearing losses or sealing losses. 
The primary objective of this simulation is to explore the influence of pitch combinations on performance outcomes. 
Five cases have been meticulously analyzed utilizing the refined geometry model. In each case, consistent 
parameters such as a wrap angle of 1440 degrees and a Vi (internal volume index) of 3 have been maintained. 
Moreover, to ensure uniform displacement within the vacuum pump, the pitch of the first proportion remains 
unchanged as 100 mm, while the second pitch is systematically reduced across all cases from 100 mm to 65 mm. 
The displacement of the studied twin screw vacuum pump is 0.875 L/rev. To maintain uniform wrap angles across 
the configurations, adjustment is complemented by a proportional reduction in rotor length as shown in Table 1. 
Table 1: Rotor geometry 
Parameters Unit Casel Case2 Case3 Case4 Case5 
Length [mm]  400 360 350 340 330 
Wrap angle [degree] 1440 1440 1440 1440 1440 
Pitch 1 [mm] 100 100 100 100 100 
Pitch 2 [mm] 100 80 75 70 65 
Proportion 1 [/] 0.5 0.56 0.57 0.588 0.606 
Proportion 2 [/] 0.5 0.44 0.43 0.412 0.394 
The operational parameters for thermodynamic calculations are outlined in Table 2. A rotational speed of 8000 rpm 
is maintained, with a suction pressure of 0.1 bar and a discharge pressure of 1 bar. Notably, the suction pressure is 
deliberately set below the fine vacuum pressure range, as the chamber model initially developed for twin screw 
compressors may lack precision under fine vacuum conditions. Additionally, it's worth noting that the gap size for 
all three leakage paths is uniformly set to 50 mu m. 
Table 2: Working condition 
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1126, Page 6 
Parameters Unit Value 
Speed [rpm] 8000 
P_ sue 
P_dis 
[bar] 0.1 
[bar] 1 
T_sue [K] 293 
Vi [/] 3 
Figure 8 illustrates pressure curves of Case 2, providing the pressure changing of variable pitch case. Notably, the 
pressure within the control volume experiences a gradual increase, with small discharge pressure losses when the 
control volume connects with the discharge port. Examination of the pressure-volume curve reveals a distinct 
pressure jump during the compression process. This phenomenon can be attributed to the stepped pitch design, 
which induces variations in pressure levels within the system. 
Figure 8: Pressure curve 
Table 3 presents a comparison of key performance metrics including volume flow rate, indicated power, volumetric 
efficiency, adiabatic efficiency, and specific power across Cases 1 to 5. It is observed that both volume flow rate and 
volumetric efficiency decrease from Case 1 to Case 5. This reduction can be attributed to the higher internal volume 
ratio resulting from the decreased second portion of the pitch. Higher internal volume ratios typically lead to 
increased leakage. However, adiabatic efficiency exhibits an opposite trend, showing an increase across the cases. 
This can be attributed to two primary factors. Firstly, the compression process tends to be more isothermal. The 
enclosed area of pressure volume curve is expected to reduce from Casel to Case 5. Additionally, the lower 
discharge losses associated with larger discharge ports contribute to this observed increase. Notably, specific power 
demonstrates a decreasing trend from Case 1 to Case 5, indicating an improvement in efficiency across the 
configurations. 
Table 3: Performance comparison 
Parameters Unit Casel Case2 Case3 Case4 Case5 
Q [m3/min] 6.79 6.66 6.65 6.65 6.65 
P _ind [kW] 5.93 5.67 5.60 5.55 5.48 
eta v [%] 97.05 95.19 95.01 94.98 94.99 
eta ad [%] 62.13 63.82 64.62 65 .05 65 .82 
Specific power [kW/m3/min] 0.874 0.851 0.843 0.835 0.825 
4. CONCLUSIONS 
This paper undertakes calculations of key geometrical parameters, including chamber volume, leakage area, and 
discharge port area. Leveraging the chamber model employed for thermodynamic calculations in twin screw 
compressors, the application is extended to twin screw vacuum pumps. The study involves comparing five different 
pitch combinations in terms of volume flow rate, indicated power, volumetric efficiency, adiabatic efficiency, and 
specific efficiency. The simulation results demonstrate a noteworthy trend: by reducing the second proportion pitch, 
27th International Compressor Engineering Conference at Purdue, July 15 - 18, 2024 
1126, Page 7 
volumetric efficiency is observed to decrease while adiabatic efficiency tends to increase. Specifically, volumetric 
efficiency experiences a reduction of approximately 2%, whereas adiabatic efficiency sees an increase of around 
4%. These findings underscore the benefits associated with reducing the second proportion of pitch in twin screw 
vacuum pump configurations. 
P_ ind indicated power (kW) 
Q volume flow rate (m3/min) 
Vi volume index (/) 
eta v volumetric efficiency (%) 
eta ad adiabatic efficiency (%) 
NOMENCLATURE 
REFERENCES 
Jousten, K. (2016). Handbook of Vacuum Technology. Wiley-VCR. 
Li, D., He, Z., Sun, S., & Xing, Z. (2022). Dynamic characteristics modelling and analysis for dry screw vacuum 
pumps. Vacuum, 198. https://doi .org/10.1016/ j. vacuum.2022.110868 
Li, D., He, Z., Wang, C. , Guo, Y., Wei, W., Lin, D., & Xing, Z. (2021). Design methodology and performance 
analysis of conical rotors for dry screw vacuum pumps. Vacuum, 185. 
https://doi .org/10.1016/j.vacuum.2020.110025 
Li, D., He, Z., Wang, C., Sun, S., Ma, K., & Xing, Z. (2022). Simulation of dry screw vacuum pumps based on 
chamber model and thermal resistance network. Applied Thermal Engineering, 211. 
https:/ /doi.org/10.1016/j.applthermaleng.2022.118460 
Li, D., He, Z., Wu, W., & Xing, Z. (2022). Study on the Quimby-tooth rotor profile for dry screw vacuum pumps. 
Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical 
Engineering, 236(5), 1947-1957. https://doi.org/10.1177/09544089221081334 
Lu, Y., Guo, B., & Geng, M. F. (2015). Study on Design of Rotor Profile for the Twin Screw Vacuum Pump with 
Single Thread Tooth IOP Conference Series: Materials Science and Engineering, 
Pfaller, D. , Brummer, A., & Kauder, K. (2011 ). Optimized rotor pitch distributions for screw spindle vacuum pumps. 
Vacuum , 85(12), 1152-1155. https://doi.org/10.1016/j.vacuum.2011.03 .002 
Pleskun, H. , Jiinemann, T., Bode, T. , & BrUmmer, A. (2021 ). Modelling of inhomogeneous chamber states in rotary 
positive displacement vacuum pumps. JOP Conference Series: Materials Science and Engineering, 1180(1), 
012009. https://doi .org/10.1088/l 757-899X/l 180/ l/0 12009 
Stosic, N., Rane, S., Kovacevic, A., & Smith, I. K. (2016). Screw Rotor Profiles of Variable Lead Vacuum and 
Multiphase Machines and Their Calculation Models Volume 6A: Energy, 
Stosic, N. , Smith, I. K., & Kovacevic, A. (2005). Screw Compressor Geometry_ Mathematical Modeling and 
Performance Calculation. Springer 
ACKNOWLEDGEMENT 
I would like to thank reviewers for their comments to this paper. My thanks also to Compressor center of City, 
University of London for permission to prepare and publish this paper. Finally, thanks to the Purdue University for 
providing the conference for presentation of this work. 
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