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Research Papers: Design of Energy, Fluid, and Power Handing Systems

Integral Modeling of a Twin-Screw Compressor

[+] Author and Article Information
Sarah Van Erdeweghe

Applied Mechanics and Energy
Conversion (TME) Section,
Department of Mechanical Engineering,
KU Leuven—University of Leuven,
Leuven B-3001, Belgium
e-mail: sarah.vanerdeweghe@kuleuven.be

Joris De Schutter

Professor
Production Engineering,
Machine Design and Automation
(PMA) Section,
Department of Mechanical Engineering,
KU Leuven—University of Leuven,
Leuven B-3001, Belgium
e-mail: joris.deschutter@kuleuven.be

Eric Van den Bulck

Professor
Applied Mechanics and Energy
Conversion (TME) Section,
Department of Mechanical Engineering,
KU Leuven—University of Leuven,
Leuven B-3001, Belgium

1Deceased October 9, 2015.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 15, 2016; final manuscript received May 14, 2016; published online June 6, 2016. Assoc. Editor: Yu-Tai Lee.

J. Mech. Des 138(7), 073401 (Jun 06, 2016) (10 pages) Paper No: MD-16-1035; doi: 10.1115/1.4033694 History: Received January 15, 2016; Revised May 14, 2016

In this paper, an integral methodology for the modeling of a twin-screw compressor is presented. Starting from a known rotor profile, all the algorithms to calculate the second rotor profile, the size of the control volume, and the compressor's performance are presented. The proposed modeling approach can be applied in an optimization procedure to find the optimal rotor profiles for a given application, with corresponding working conditions. Furthermore, based on the modeling results and substantiated with measurements on different compressor types, a similarity law for positive displacement compressors seems to exist. The existence of a similarity law has large application potential as it could be used to predict the performance of a positive displacement compressor in other than the (lab) tested working conditions. Further investigation of the similarity law for positive displacement compressors is therefore proposed as a key topic for future research.

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References

Fleming, J. S. , Tang, Y. , and Cook, G. , 1998, “ The Twin Helical Screw Compressor—Part 1: Development, Applications and Competitive Position,” Proc. Inst. Mech. Eng., Part C, 212(5), pp. 355–367. [CrossRef]
Stosic, N. , Smith, I. , and Kovacevic, A. , 2005, Screw Compressors—Mathematical Modelling and Performance Calculation, Springer-Verlag, Berlin.
Seshaiah, N. , 2006, “ Experimental and Computational Studies on Oil Injected Twin-Screw Compressor,” Ph.D. thesis, National Institute of Technology, Rourkela, India.
Stosic, N. , 2015, “ On Heat Transfer in Screw Compressors,” Int. J. Heat Fluid Flow, 51, pp. 285–297. [CrossRef]
Stosic, N. , 1998, “ On Gearing of Helical Screw Compressor Rotors,” Proc. Inst. Mech. Eng., Part C, 212(7), pp. 587–594. [CrossRef]
Litvin, F. L. , and Fuentes, A. , 2004, Gear Geometry and Applied Theory, 2nd ed., Cambridge University Press, Cambridge, UK.
Fleming, J. , Thang, Y. , and Cook, G. , 1998, “ The Twin Helical Screw Compressor—Part 2: A Mathematical Model of the Working Process,” Proc. Inst. Mech. Eng., Part C, 212(5), pp. 369–380. [CrossRef]
Seshaiah, N. , Ghosh, S. K. , Sahoo, R. K. , and Sarangi, S. K. , 2007, “ Mathematical Modeling of the Working Cycle of Oil Injected Rotary Twin Screw Compressor,” Appl. Therm. Eng., 27(1), pp. 145–155. [CrossRef]
Tang, Y. , 1995, “ Computer Aided Design of Twin Screw Compressors,” Ph.D. thesis, University of Strathclyde, Glasgow, UK.
Wu, H. , Xing, Z. , and Shu, P. , 2004, “ Theoretical and Experimental Study on Indicator Diagram of Twin Screw Refrigeration Compressor,” Int. J. Refrig., 27(4), pp. 331–338. [CrossRef]
Fujiwara, M. , and Osada, Y. , 1995, “ Performance Analysis of an Oil-Injected Screw Compressor and Its Application,” Int. J. Refrig., 18(4), pp. 220–227. [CrossRef]
Stosic, N. , Smith, I. K. , and Kovacevic, A. , 2003, “ Optimisation of Screw Compressors,” Appl. Therm. Eng., 23(10), pp. 1177–1195. [CrossRef]
Szarkowicz, D. , and Firnhaber, M. A. , 1980, “ Modeling and Simulation of Rotary Screw Compressors,” International Compressor Engineering Conference, Vol. 348, pp. 304–310.
Peng, X. , Xing, Z. , Cui, T. , and Li, L. , 2002, “ Analysis of the Working Process in an Oil-Flooded Screw Compressor by Means of an Indicator Diagram,” Proc. Inst. Mech. Eng., Part A, 216(6), pp. 465–470. [CrossRef]
Van Erdeweghe, S. , 2015, “ Integrale Modellering van een Schroefcompressor,” Master's thesis, University of Leuven (KU Leuven), Leuven, Belgium.
Emmecom, 2012, “ Airmoving Datasheet RL_A,” Emmecom, Carugate, Italy, Last accessed Jan. 14, 2016, http://www.emmecomsrl.com/en/assets/rl.pdf
Hsieh, S. H. , Shih, Y. C. , Hsieh, W. H. , Lin, F. Y. , and Tsai, M. J. , 2011, “ Calculation of Temperature Distributions in the Rotors of Oil-Injected Screw Compressors,” Int. J. Therm. Sci., 50(7), pp. 1271–1284. [CrossRef]

Figures

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Fig. 1

Illustration of the compression process [1]

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Fig. 4

Different steps in the geometric model. (a) Main rotor profile in the reference plane r2,0(θ2). (b) Gate rotor profile generation according to the main rotor profile of (a), results of Eqs. (7) and (8) for ζ2∈(0,(π/2)). (c) Validation of the generated gate rotor profile r1,0(θ1) (full curve) against the measurement results (dots). (d) Calculated gate (left) and known main (right) rotor profiles in the reference plane. The symmetry plane is indicated by the dashed line. (e) Surface algorithm: two triangles with the same (small) enclosed angle. Example for the gate rotor side. (f) Result of the geometric model: V(α2).

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Fig. 3

Two-dimensional rotor profiles r1,0(θ1) and r2,0(θ2) from 3D laser scanner measurements and inverse screw transformations (Eqs. (1) and (2))

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Fig. 2

Definition of the coordinate systems

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Fig. 5

Flowchart for control volume algorithm →V(α2)

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Fig. 6

Subprocesses in the overall compression process and indication of the state variables

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Fig. 7

Performance results at nominal working conditions (see Table 2). (a) M(α2). The control volume loses mass because of leakages. (b) Indicator diagram.

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Fig. 8

Performance characteristics for nnnom ± 1500 rpm and P3P3,nom ± 0.5 bar. (a) Dimensional performance diagram: w(Q˙). (b) Nondimensional performance diagram: Ψ(Φ).

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Fig. 9

Flowchart of the optimization procedure

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Fig. 10

Performance results for a screw and lobe compressor. (a) Screw, from Ref. [15]. (b) Lobe, own calculations on the data set of an Emmecom RL2130/DN 300 type lobe compressor in Ref. [16].

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