Purdue University Purdue e-pubs International Compressor Engineering Conferene Shool of Mehanial Engineering 2014 Analysis of a Twin Srew Expander for ORC Systems using Computational Fluid Dynamis with a Real Gas Model Iva Papes Ghent University, Belgium, iva.papes@ugent.be Joris Degroote Ghent University, Belgium, joris.degroote@ugent.be Jan Vierendeels Ghent University, Belgium, jan.vierendeels@ugent.be Follow this and additional works at: http://dos.lib.purdue.edu/ie Papes, Iva; Degroote, Joris; and Vierendeels, Jan, "Analysis of a Twin Srew Expander for ORC Systems using Computational Fluid Dynamis with a Real Gas Model" (2014). International Compressor Engineering Conferene. Paper 2350. http://dos.lib.purdue.edu/ie/2350 This doument has been made available through Purdue e-pubs, a servie of the Purdue University Libraries. Please ontat epubs@purdue.edu for additional information. Complete proeedings may be aquired in print and on CD-ROM diretly from the Ray W. Herrik Laboratories at https://engineering.purdue.edu/ Herrik/Events/orderlit.html
1478, Page 1 Analysis of a Twin Srew Expander for ORC Systems using Computational Fluid Dynamis with a Real Gas Model Iva Papes*, Joris Degroote, Jan Vierendeels Ghent University, Department of Flow, Heat and Combustion Mehanis, Ghent, 9000, Belgium E-mail: iva.papes@ugent.be ABSTRACT With the inrease in energy pries and environmental onstraints, reovering the energy from low grade waste heat presents an important hallenge. The Organi Ranke Cyles (ORCs) are widely used, but there is still need to improve their effiieny (espeially for small sale energy prodution). This paper presents the Computational Fluid Dynamis (CFD) analysis of a twin srew expander whih is used for power generation in an ORC system with refrigerant R245fa. The deforming mesh motion is handled by an in-house ode whih generates a blok-strutured grid with the help of the solutions of Laplae problems. The properties of refrigerant R245fa are derived from the Augnier Redlih-Kwong ubi equation of state whih is inorporated in the omputational model. From the results of a CFD analysis, the pressure-volume diagram, mass flow rates and power output for different pressure ratios and different designs were obtained. In order to evaluate the effets of individual learane gaps on the performane of the expander, time dependent mass flow diagrams for eah of them are provided and studied. It an be onluded that the influene of the leakage flows inreases with derease in rotational speed or with the inrease in pressure ratio. To avoid losses during the filling, an optimized design of the inlet port is neessary. 1. INTRODUCTION Small sale ORC systems have a big potential for waste heat reovery. The ORC is named for its use of an organi, high moleular mass fluid whih is haraterized by low saturation temperatures. Although these ORC systems are now well developed, researh efforts are inreasingly direted towards higher effiienies and powers. Thermodynami mahines for the expansion of the organi fluids are the key element for the power generation in the ORC. The srew expander is a speial type of rotary displaement mahine, in whih two srews rotate inside two overlapping ylinders. The urrent generation of srew expanders is in fat designed as ompressors used the other way around. Moving the mesh surrounding the rotor surfaes is omplex and therefore a powerful grid manipulator is neessary for CFD alulations. In this paper an in-house ode presented in Vande Voorde (2004) is used. The validation of CFD alulations using this grid generator for a twin srew ompressor has been reported in Vande Voorde (2005). Sine the validation showed good agreement between the experimental results and CFD alulations, the same proedure is used in this work, for the simulations of an expander where only the sense of rotation is hanged. Several papers have been published using the zero-dimensional hamber model, based on the ideal gas law and standard thermodynami relations for ompressors and expanders. Seshaiah (2006) presented a model for twin srew oil injeted ompressor and Bruemmer and Hutker (2009, 2012) a model for the expander. Reently, the influene of the learane sizes on the performane of a srew expander has been investigated by means of CFD alulations by Rane (2013). Despite these investigations, there is no detailed analysis of the flow through the learanes as a funtion of the rotation angle. Sine the leakage flows have a signifiant influene on srew expander effiieny, it is of great importane to alulate these flows orretly. The srew expanders are haraterized by a fixed built-in volume ratio, determined by the form of the inlet and outlet surfaes. Paul (2011) determined the internal pressure ratio as. For the best performane, the built-in volume ratio should math the operating onditions in order to limit the over- and under-expansion losses. If the internal volume ratio is too high for a given set of operating onditions, the fluid remains trapped longer than
1478, Page 2 neessary, leading to a pressure drop below the disharge pressure (over-expansion). On the ontrary, if the internal volume ratio is too low, the fluid in the hamber remains above the disharge pressure when the disharge/outlet port starts to open (under-expansion). Therefore, depending on the internal pressure ratio, under- or over-expansion losses an derease the effiieny of a srew expander. Apart from over- and under-expansion, the effiieny of a srew expander is mainly governed by the leakage flows through the learanes and sution pressure losses. In this paper, the performane of a srew expander is studied for different pressure ratios and for two different expander designs. The differene between these two designs is additional injetion ports. The leakage flows inside the srew expander and the sution losses are desribed. Based on this study, a better expander an be designed. 2. CFD ANALYSIS The geometry used in CFD alulations, is shown in Figure 1. The CFD alulations were performed for two designs, with and without additional injetion ports. 2.1 Grid generation Figure 1: Geometry of the twin srew expander The domain for CFD alulations is deomposed into three bloks, namely inlet, outlet and injetion ports. The grid in the inlet, outlet, and oil injetion ports is stationary, sine the only moving boundaries to the flow domain are the rotors surfaes. The grid in the asing is built by staking two-dimensional strutured grids in slies of the asing (Figure 2). Before the CFD simulation, 2D strutured meshes are onstruted in slies orresponding with different rotation of profiles, with steps of 1.5 degrees of the male rotor. These 2D meshes are generated using the Laplae potential equation. During the entire simulation the ells definitions are the same (the same faes and nodes). So, the nodes of the grid are moved in the housing (ALE, Arbitrary Langrangian-Eulerian method). For eah time step in the alulation, a new position of the grid nodes an be found by interpolating between two supplied grids. The size of the gaps between the rotors and between the rotors and the asing is extremely small (order tens of mirons versus rotor diameter of about 70 mm). To reah suffiient numerial auray, the number of ells in radial diretion is set to 8 (zoomed view in Figure 2).
1478, Page 3 Figure 2: Grid in the rotor domain All bloks are joined together by using sliding interfaes between the rotor domain and stationary grid. The omplete 3D mesh of the twin srew expander onsists of 2060515 ells. 2.2 Boundary onditions and simulation parameters The fluid flow inside the srew expander is ompressible and is desribed by the set of momentum, energy and mass onservation equations, whih are aompanied by the equation of state and the turbulene model. The governing differential equations are solved by a ommerial pakage with use of user-defined funtions to handle the grid movement and real gas behavior. The boundary onditions used in alulations for two different designs of the expander are presented in Table 1. During the simulations, the inlet temperature of the working fluid was. Only the effets of a variation in the pressure ratio are studied. The spatial disretization that is used for the alulations is first-order upwind for the onvetive terms. The temporal disretization is first-order impliit. The solver alulates the pressure and veloity simultaneously. Table 1: Boundary onditions and simulation parameters Design Without additional injetion ports With additional injetion ports Evaluated pressure ratios Rotors speed (male/female) 6, 5, 4 6000/4000 6,5,4,3,2 6000/4000 Boundary onditions Pressure inlet Pressure outlet Turbulene model k-ε Solver Coupled R245fa is one of the most ommonly used fluids in ORC systems with a low temperature heat soure. Sine the ideal gas equation of state shows big deviations in the ORC working onditions as presented in Luján (2012), an appropriate real gas equation of state should be used. In this paper the Aungier Redlih-Kwong equation of state presented in Aungier (1995) is inorporated in the real gas model through user-defined funtions. It represents a modified form of the Redlih-Kwong equation of state. This new orrelation inludes an aentri fator and the ritial point ompressibility fator as additional parameters to improve its auray. The Aungier Redlih-Kwong equation of state is defined with the following equations: RT ~ a( T) p (1) v b ) V ( V b ) ( 0 Where: 1 T V, a( T ) a0, a T RT b0 0.08664, 0 p p n 0 R T 0.42747 p 0 2 2 RT b a0 V ( V b ) 0 ~ V, b b 0 0
1478, Page 4 However, it is important that the flow onditions in every ell are always in the gas phase region. If they fall outside that region, the partial derivative of pressure at onstant temperature with respet to speifi volume beomes positive. Sine the mesh motion is omplex and the volume of some ells an be extremely small (gap region), this an ause onvergene problems during the start up. 2.3 Geometrial parameters The onfiguration of the rotor lobes is 4/6 (male/female). The outer diameter of the male and female rotors is approximately 70 mm. The volume urve of the srew expander is shown in Figure 3. The formation of a hamber starts when the male and female lobes are in onnetion with the inlet port (zero degrees in Figure 3). As the rotors rotate, the volume of the hamber is rising together with the inrease in inlet surfae area. But, it is only for a short time that the surfae of the inlet port is ompletely available for the filling (zoomed view in Figure 3). Sine a signifiant pressure drop ours during the filling (Setion 3.1), the inlet port should be designed in suh a way that filling ours only during a small part of the growing phase of the volume with maximum inlet surfae area available. Figure 3: Volume urve with inlet and outlet surfae area as a funtion of the rotational angle of the male rotor 3. PERFORMANCE ANALYSIS The design with additional injetion ports ould also be used for the oil injeted twin srew expander with small perentage of oil mixed with the working fluid and injeted through the injetion ports. Therefore it was of great importane to investigate the influene of the injetion of additional working fluid through the injetion ports. The performane analysis is done for both onfigurations in order to indiate how its design influenes the performane of the twin srew expander. The performane of the expander an be evaluated by omparing the mass flow rates and power output for different pressure ratios and different designs. In Figure 4, the mass flow rates and the power output (torque on the rotors walls multiplied by rotational speed) from the CFD alulations are averaged over one period (360 degrees male rotation) whih orresponds with 4 expansion yles. When inreasing the pressure ratio, the output power inreases together with the mass flow rate.
1478, Page 5 Figure 4: Power vs. Mass Flow Rate at different filling pressures and two different designs 3.1 Pressure-Volume Diagram P-V diagrams for different pressure ratios and two different designs are presented in Figure 5 and Figure 6. Figure 5: P-V diagram of the expansion proess (design with additional injetion ports) In both figures, only a female working hamber is represented. Looking from the high pressure side, fluid starts to fill an expanding hamber formed between the lobes of the rotor profiles and the asing of the expander. Sine it is only for a short time that the inlet is ompletely open for working fluid to enter the working hamber (Figure 3), throttling losses and a pressure drop will our (first pressure drop in a P-V diagram). Closing of the inlet (derease in inlet surfae area) in onnetion with the inrease in volume of the hamber will ause the so alled preexpansion (seond pressure drop in a P-V diagram). One the hamber is disonneted from the inlet the volume inreases until the maximum volume is reahed. Addition of the working fluid through the injetion ports will ause an inrease in pressure in a hamber, despite it's inreasing volume. This affets the slope of the P-V urve. As the hamber meets the outlet port, the fluid in the hamber is disharged. Depending on the pressure ratio, over- or under-expansion an be seen (e.g. for pressure ratio 2 and pressure ratio 6, respetively).
1478, Page 6 Figure 6: P-V diagram of the expansion proess (design without additional injetion ports) Comparing Figure 5 and Figure 6, it an be seen that with additional injetion of the working fluid, the slope of the P-V urve an be hanged in a way that it overomes the over- and under-expansion losses. 3.2 Leakage analysis In this paper speial fous is on a study of mass flow rates through the learanes whih are forming leakage paths. Depending on the internal pressure ratio, leakage flows from adjaent hambers an ause re-filling and onsequently, affet the volumetri effiieny of the expander as reported in Rane (2011). On the other hand, during the sution, inlet throttling ours beause the inlet surfae is bloked by the tips of the rotor and the filling is redued, whih will derease the volumetri effiieny. Therefore, it is paramount that these leakage flows are assessed orretly. In the twin srew expander there are four types of leakage paths. It is possible to identify every one of them as it is shown in Figure 7: 1. Clearanes between the rotor tips and the housing allow the flow between two adjaent hambers with different pressures (m tip in Figure 7). 2. Between the meshing rotors, a sealing line is formed, where leaking ours (m sealing in Figure 7). 3. Blowholes are triangular gaps that are formed at the usps between two rotors and the housing (m blowhole in Figure 7). Beause of manufaturing reasons, it is impossible to have a sealing line that reahes to the usp of the housing. As a onsequene, when looking at a 2D ross setion at the end of the sealing line, a triangular region (blowhole) is formed between this end and the nearest positions of the tip learanes between both rotors and the housing. 4. Leaks through the learanes at the end planes our both on the inlet and outlet side (m end plane in Figure 7).
1478, Page 7 Figure 7: Different leakages during the expansion proess In this paper the fous was only on tip and sealing leakage flows. The total mass flow rates in Figure 8 and Figure 9 are the sum of all mass flows that are going through the leading and trailing learanes of the working hamber on the female side (Figure 7). Figure 8: Leakage flows through (a) tip and (b) sealing learane gaps (design with additional injetion ports) With an inrease in pressure ratio, the internal leakage flows are rising, as depited in Figure 8 and Figure 9. In these figures, a positive value means that the flow is leaving the urrent hamber. During the filling (until 80 degrees of male rotation), the outflows via both leakage paths are rising. During the expansion, the inflow through learanes inreases, sine the pressure in an adjaent hamber (whih in this moment is onneted with the inlet) is higher. If in this moment, additional working fluid is injeted through injetion ports (Figure 8 (a)), the outflow through learanes will inrease. After the hamber is onneted with the outlet, two ases are possible. In the ase of high pressure ratios (between and ), the inflow is dominating (sine the pressure in the adjaent hamber is still muh higher than at the outlet port). In the ase of over-expansion with imposed pressure of at the inlet, the outflow will inrease (sine the pressure in the adjaent hamber is lower than the pressure at the outlet port).
1478, Page 8 Figure 9: Leakage flows through (a) tip and (b) sealing learane gaps (design without additional injetion ports) 3.3 Influene of rotational speed on mass flow through learanes The variation of the rotational speed has a signifiant influene on the performane of the twin srew expander. Ideally, the output power should rise linearly with the rotational speed. However, with inrease of the rotational speed, the time for filling derease and throttling losses rise. Therefore there is a small deline (omparing to an ideal linear rise) in output power for higher rotational speed. Figure 10: Power vs. Mass Flow Rate at different rotational speed with pressure ratio 6, and for the design with additional injetion ports The influene of the leakages is also affeted by a hange in rotational speed. In Figure 11, the mass flow rates for two types of leakages and for different rotational speeds are presented. It an be onluded, that with a derease in the rotation speed the influene of the leakage flows is higher.
1478, Page 9 (a) (b) Figure 11: Leakage flows through (a) tip and (b) sealing learane gaps (design with additional injetion ports and pressure ratio of 6) 4. CONCLUSION In this paper, transient 3D CFD analysis of a twin srew expander with R245fa as a working fluid is presented. The alulations are performed with the use of a grid manipulation algorithm and a ommerial CFD solver aompanied by user-defined funtions. It is shown that during the filling proess signifiant pressure drops our. In terms of different pressure ratios, overor under- expansion an our depending on the design of the expander. It is shown that with additional injetion of the working fluid, the output power inreases. In the analysis of the leakage flows, mass flow rates as the funtion of rotational angle are presented for two different types of leakage paths. With the inrease in the pressure ratio or derease in rotational speed the influene of the leakage flows is more signifiant. The study presented in this paper will be used to improve the performane of the expander and optimize the design. NOMENCLATURE v k π n built in volume ratio speifi heat ratio pressure ratio rotational speed V P T R speifi volume pressure temperature gas onstant Subsript ritial value REFERENCES Aungier, R. H., 1995, A fast, aurate real gas equation of state for fluid dynami analysis appliations. Journal of Fluids Engineering, vol. 117, pp. 277-281. Brummer, A., Hutker, J., 2009, Influene of geometri parameters on inlet-losses during the filling proess of srewtype motors. Developments in mehanial engineering, vol. 4, pp. 105-121. Hutker, J., Brummer, A., 2012, Thermodynami Design of Srew Motors for Constant Heat Flow at Medium Temperature Level. Pro. Int. Compressor Conf. at Purdue, pp. 1478.
1478, Page 10 Fujiwara, M., Osada, Y., 1995, Performane analysis of an oil-injeted srew ompressor and its appliation. International Journal of Refrigeration, Number 4, vol. 18, pp. 220-227. Luján, J.M., Serrano, J.R., Dolz, V., Sánhez, J., 2012, Model of the expansion proess for R245fa in an Organi Rankine Cyle (ORC). Applied Thermal Engineering, vol. 40, pp. 248-257. Paul, C. H., 2011, Compressors Hand Book, MGraw Hill. Kovaevi, A., Rane, S., 2013, 3D CFD analysis of a twin srew expander, 8th International Conferene on Compressors and their Systems, pp. 417-429, City University London, 9-10 September. Smith, I.K., Stosi, N., 2006, Cost effetive small sale ORC systems for power reovery from low grade heat soures. Proeedings of ASME International Mehanial Engineering Congress and Exposition, Chiago, Illinois, USA, pp. 1-7. Seshaiah, N., Ghosh, S.K., Sahoo, R.K., Sarangi, S.K., 2006, Performane Analysis of Oil Injeted Twin Srew Compressor. 18th National and 7th ISHMT-ASME Heat and Mass Transfer Conferene, India. Vande Voorde, J., Vierendeels, J., Dik, E., 2004, Development of a Laplaian-based mesh generator for ALE alulations in rotary volumetri pumps and ompressors. Computer Methods in Applied Mehanis and Engineering, vol. 193, 39-41, pp. 4401-4415. Vande Voorde, J., Vierendeels, J. and Dik, E., 2005, ALE Calulations of Flow Through Rotary Positive Displaement Mahines. In Pro. of the ASME Fluids Engineering Divison Summer Meeting and Exhibition, FEDSM2005-77353, ISBN 0-7918-3760-2, Huston, USA. ACKNOWLEDGEMENT This study is part of the ORCNext projet with finanial support of IWT Flanders. This work was arried out using the STEVIN Superomputer Infrastruture at Ghent University, funded by Ghent University, the Flemish Superomputer Center (VSC), the Herules Foundation and the Flemish Government (department EWI). J. Degroote gratefully aknowledges a post-do fellowship of the Researh Foundation Flanders (FWO).