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# Numerical simulation of a twin screw expander for performance prediction

Iva Papeš (UGent) , Joris Degroote (UGent) and Jan Vierendeels (UGent)
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Abstract
With the increasing use of twin screw expanders in waste heat recovery applications, the performance prediction of these machines plays an important role. This paper presents a mathematical model for calculating the performance of a twin screw expander. From the mass and energy conservation laws, differential equations are derived which are then solved together with the appropriate Equation of State in the instantaneous control volumes. Different flow processes that occur inside the screw expander such as filling (accompanied by a substantial pressure loss) and leakage flows through the clearances are accounted for in the model. The mathematical model employs all geometrical parameters such as chamber volume, suction and leakage areas. With R245fa as working fluid, the Aungier Redlich-Kwong Equation of State has been used in order to include real gas effects. To calculate the mass flow rates through the leakage paths formed inside the screw expander, flow coefficients are considered as constant and they are derived from 3D Computational Fluid Dynamic calculations at given working conditions and applied to all other working conditions. The outcome of the mathematical model is the P-V indicator diagram which is compared to CFD results of the same twin screw expander. Since CFD calculations require significant computational time, developed mathematical model can be used for the faster performance prediction
Keywords
Redlich-Kwong Aungier EoS, low-order model, Expander

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## Citation

Chicago
Papeš, Iva, Joris Degroote, and Jan Vierendeels. 2015. “Numerical Simulation of a Twin Screw Expander for Performance Prediction.” In IOP Conference Series-Materials Science and Engineering. Vol. 90. IOP Conference Series: Materials Science and Engineering.
APA
Papeš, I., Degroote, J., & Vierendeels, J. (2015). Numerical simulation of a twin screw expander for performance prediction. IOP Conference Series-Materials Science and Engineering (Vol. 90). Presented at the 9th International Conference on Compressors and their Systems, IOP Conference Series: Materials Science and Engineering.
Vancouver
1.
Papeš I, Degroote J, Vierendeels J. Numerical simulation of a twin screw expander for performance prediction. IOP Conference Series-Materials Science and Engineering. IOP Conference Series: Materials Science and Engineering; 2015.
MLA
Papeš, Iva, Joris Degroote, and Jan Vierendeels. “Numerical Simulation of a Twin Screw Expander for Performance Prediction.” IOP Conference Series-Materials Science and Engineering. Vol. 90. IOP Conference Series: Materials Science and Engineering, 2015. Print.
```@inproceedings{6971511,
abstract     = {With the increasing use of twin screw expanders in waste heat recovery applications, the performance prediction of these machines plays an important role. This paper presents a mathematical model for calculating the performance of a twin screw expander. From the mass and energy conservation laws, differential equations are derived which are then solved together with the appropriate Equation of State in the instantaneous control volumes. Different flow processes that occur inside the screw expander such as filling (accompanied by a substantial pressure loss) and leakage flows through the clearances are accounted for in the model. The mathematical model employs all geometrical parameters such as chamber volume, suction and leakage areas. With R245fa as working fluid, the Aungier Redlich-Kwong Equation of State has been used in order to include real gas effects. To calculate the mass flow rates through the leakage paths formed inside the screw expander, flow coefficients are considered as constant and they are derived from 3D Computational Fluid Dynamic calculations at given working conditions and applied to all other working conditions. The outcome of the mathematical model is the P-V indicator diagram which is compared to CFD results of the same twin screw expander. Since CFD calculations require significant computational time, developed mathematical model can be used for the faster performance prediction},
author       = {Pape\v{s}, Iva and Degroote, Joris and Vierendeels, Jan},
booktitle    = {IOP Conference Series-Materials Science and Engineering},
issn         = {1757-8981},
keyword      = {Redlich-Kwong Aungier EoS,low-order model,Expander},
language     = {eng},
location     = {London, UK},
pages        = {9},
publisher    = {IOP Conference Series: Materials Science and Engineering},
title        = {Numerical simulation of a twin screw expander for performance prediction},
url          = {http://dx.doi.org/10.1088/1757-899X/90/1/012059},
volume       = {90},
year         = {2015},
}

```
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