Designg scroll expanders for use heat recovery Ranke cycles Vcent Lemort and Sylva Quoil Thermodynamics Laboratory, University of Liège, Belgium ABSTRACT This paper first vestigates experimentally the performances of a prototype of oil-free open-drive scroll expander workg with water steam and with HCFC-123. Usg experimental data, two different simulation models of the expander are then proposed and validated. These models are fally used to analyze the measured performances with regards to the expander design characteristics. NOMENCLATURE A area, m 2 AU heat transfer coefficient, W/K h specific enthalpy, J/kg M & mass flow rate, kg/s N rotational speed, s -1 ω rotational speed, rad.s -1 P pressure, Pa s specific entropy, J/kg-K t temperature, C T torque, N.m v specific volume, m 3 /kg V & volume flow rate, m 3 /s W & power, W 1 INTRODUCTION Subscripts ad amb calc ex exp leak loss meas sh su adapted ambient calculated exhaust expander ternal leakage mechanical loss measured shaft supply Small-scale heat recovery Ranke cycle systems allow generatg mechanical or electrical energy from local low grade heat sources (1). Systems usg water as workg fluid are particularly suitable for recoverg energy from enge exhaust gas or heat produced by solar concentrators (2, 3, 4). Systems usg an organic fluid (called Organic Ranke Cycles) are more appropriate for lower temperature heat sources (1). The scroll mache is a good candidate for the expansion device of such a system, because of its simplicity of operation and reliability (no valves and few movg parts). Performances of the system strongly correlate with those of the expander, which justifies improvg its design. This paper analyses the performance of an oil-free open-drive expander, with respects to its design characteristics, the case of usg water and HCFC-123.
2 EXPERIMENTAL INVESTIGATION 2.1 Description of the expander The expander prototype is origally an open-drive oil-free air scroll compressor, similar to that tested by Yanagisawa et al. (5) and Aoun and Clodic (4). The only modification made to the origal compressor was the removal of the coolg fan. The expander has a kematically rigid configuration that matas a flank clearance between the scroll wraps. Seals are also nestled the tip of both scrolls to reduced radial leakages. 2.2 Expander fed with steam A first experimental system was constructed to evaluate the performances of the expander for operation with water steam (Figure 1). The system consisted open-loop comprisg 2 electric-steam boilers parallel, a release valve, an electrical super-heater, the expander, a water-cooled condenser and a tank (to collect the condensed water). The expander drove an asynchronous mache through two belt-and-pulley couplgs and a torque-meter. Usg an asynchronous mache (connected to the grid) was a very convenient way to impose the expander rotational speed. The latter was set to different values by modifyg the asynchronous mache pulley diameter. The expander shaft power was determed from the measurements of the torque and of the speed of the torque-meter shaft. The expander supply pressure was controlled by adjustg the steam flow rate feedg the expander (measured by means of a calibrated diaphragm) for a given expander rotational speed. The exceedg steam was released to the ambient through a pneumatically driven release valve. Incondensable gases were extracted from the condenser by means of a vacuum pump allowg the expander exhaust pressure to be stabilized the range of 0.5 to 1 bar. The super-heater was used to adjust the expander supply temperature. Figure 1: Schematic representation of the steam test bench
2.2 Expander fed with HCFC-123 A second experimental system was built to test the expander with refrigerant HCFC-123. The system operated a closed loop, which required the use of a pump. A variable displacement diaphragm pump was selected. It allowed controllg the refrigerant flow rate through the cycle and hence the expander supply pressure. The refrigerant flow rate is measured by means of a Coriolis flow meter stalled at the pump exhaust. The same apparatus as the first experimental system is used to control the expander speed and to measure its shaft power. The boiler of the cycle consisted several heat exchangers fed with hot air, whose flow rates and temperature were varied to control the expander supply temperature. The water flow rate through the condenser was controlled to impose the expander exhaust pressure. Figure 2: Schematic representation of the HCC-123 test bench 3 PERFORMANCE ANALYSIS 2.1 Overall isentropic effectiveness The overall isentropic effectiveness is defed by the ratio of the measured shaft power and the isentropic power (Eq. (1)). Figures 3 (a) and (b) shows that higher isentropic effectiveness are achieved with HCFC-123 than with steam. W& W& W& sh,meas sh,meas sh,meas ε s,meas = = = (1) W& M&.w M&.( h h ) s meas s meas su 2.2 Fillg factor The volumetric performance of the expander is represented by the fillg factor. The latter is defed as the ratio between the measured mass flow rate and the mass flow rate theoretically displaced by the expander (Eq. (2)). As shown Figures 4 (a) and (b), much lower volumetric performances are achieved with steam. The decrease the fillg factor with the rotational speed can be explaed by the lower relative impact of the leakages. ex,s
M&.v meas su φ meas = (2) V& s 0.7 0.7 0.65 0.65 0.6 0.6 εs,meas [-] 0.55 0.5 0.45 0.4 0.35 1513 rpm 2214 rpm 3539 rpm εs,meas [-] 0.55 0.5 0.45 0.4 0.35 1771 rpm 2296 rpm 2660 rpm 0.3 5 7.2 9.4 11.6 13.8 16 P su / P ex [-] 0.3 2.5 3 3.5 4 4.5 5 5.5 P su / P ex [-] (a): Expander fed with water steam (b): Expander fed with HCFC-123 Figure 3: Evolution of the measured isentropic effectiveness with the pressure ratio 2.6 1.4 φmeas [-] 2.4 2.2 2 1513 rpm 2214 rpm 3539 rpm φmeas [-] 1.35 1.3 1.25 1.2 1.8 1.6 450000 500000 550000 600000 650000 P su [Pa] 700000 750000 800000 850000 (a): Expander fed with water steam (b): Expander fed with HCFC-123 Figure 4: Evolution of the measured fillg factor with the expander supply pressure 1.15 1.1 1.05 500000 600000 700000 800000 P su [Pa] 900000 1000000 1771 rpm 2296 rpm 2660 rpm 1.100E6 1.200E6 4 EXPANDER SEMI-EMPIRICAL MODEL 2.1 Description of the model The semi-empirical model of the expander retas the ma physical features of the mache (3). The evolution of the fluid through the expander is decomposed to the followg consecutive steps: an adiabatic supply pressure drop (su su,1); an isobaric supply coolg-down (su,1 su,2); an isentropic expansion to the adapted pressure imposed by the built- volume ratio of the mache (su,2 ad), an adiabatic expansion at a constant mache volume (ad ex,2); an adiabatic mixg between supply and leakage flows (ex,2 ex,1); and an isobaric exhaust coolg-down or heatg-up (ex,1 ex). The mass flow rate swept by the expander is given as a function of the expander swept volume V s,exp, rotational speed N and leakage flow rate by:
M & = M& M& leak V& = v s,exp su, 2 M& leak N V. = v s,exp su, 2 M& leak (3) All the leakage paths are lumped to one unique fictitious leakage path connectg the expander supply and exhaust. The leakage flow rate and the pressure drops are computed by reference to the isentropic flows through a simply convergent nozzle of cross-sectional areas A leak and A su. Under- and over-expansion losses are described by splittg the expansion to an isentropic expansion and constant volume evolutions: ( h h ) + v ( P P )) W & = M & (4) su, 2 ad ad ex,2 Mechanical losses are evaluated on the basis of a lumped mechanical losses torque T loss : N W& 2 sh = W& W& loss = W& π T (5) loss 60 Internal heat transfers are lumped to equivalent supply and exhaust heat transfers between the fluid and a fictitious shell of uniform temperature T w (on the basis of overall heat transfer coefficients AU su and AU ex ). External heat transfer is described by an overall heat transfer coefficient AU amb. 2.1 Parameters identification The semi-empirical model of the expander necessitates 8 parameters that can be identified on the basis of experimental data. The supply and exhaust pressures, the supply temperature, the ambient temperature and the rotational speed were imposed as parameters of the expander model. The parameters of the model are identified by an algorithm that mimizes a function accountg for the errors on the prediction of the mass flow rate, shaft power and exhaust temperature (ma output variables of the model). Parameters were first identified for the tests with HCFC-123. For these tests, the enthalpy at the expander exhaust could be determed (superheated vapour). This allowed a better accuracy of the model parameters, sce ambient heat losses could be estimated. In contrary, for the tests with steam, vapour was saturated at the expander exhaust. Table 1: Identified parameters of the semi-empirical model for the use of HCFC-123 Heat transfer coefficient with the ambient AU amb 6.4 W/K Supply heat transfer coefficient AU su,n ( ). 21. 2 M& 0. 12 8 W/K Exhaust heat transfer coefficient AU ex,n ( ). 34. 2 M& 0. 12 8 W/K Leakage area A leak 4.6 mm 2 Built- volume ratio r v, 4.05 Swept volume V s,exp 36.54 cm 3 Supply port cross-sectional area A su 27.43 mm 2 Mechanical loss torque T loss 0.47 N-m
2.1 Model verification Predictions by the semi-empirical model of the swept mass flow rate are compared to experimental data Figures 5 (a) and (b). The model parameters are those listed Table 1. It can be observed that the model is able to predict with a good accuracy the steam mass flow rate. These results confirm the physical meang of the leakage area identified usg the tests with HCFC-123. Experimental data with steam were not detailed enough to accurately identify the three heat transfer coefficients. In a first approximation, coefficients given Table 2 were considered. A more detailed modellg and experimental validation should answer the question of the fluence of the fluid on the ternal heat transfers. M calc [kg/s] 0.095 0.09 0.085 0.08 0.075 0.07 0.065 0.06 0.055 0.05 0.045 5 % error bars 0.04 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 M meas [kg/s] 1771 rpm 2296 rpm 2660 rpm (a): Expander fed with HCFC-123 M calc [kg/s] 0.014 0.013 0.012 0.011 0.01 0.009 0.008 0.007 5% error bars 0.006 0.006 0.007 0.008 0.009 0.01 0.011 0.012 0.013 0.014 M meas [kg/s] 1513 rpm 2214 rpm 3539 rpm (b): Expander fed with steam Figure 5: Prediction of the mass flow rate (semi-empirical model) The same comparison is given Figures 6 (a) and (b) for the shaft power. For the tests with HCFC-123, the model gives very good results. However the power is underpredicted for the tests with steam (even if mechanical losses were cancelled). It can be shown that the error on the predicted shaft power creases remarkably with the fillg factor. Internal leakages tend to crease the expansion work (by deformation of the P-V diagram), which cannot be described by model. Wsh,calc [W] 2000 1800 1600 1400 1200 1000 800 600 400 5 % error bars 200 200 400 600 800 1000 1200 1400 1600 1800 2000 W sh,meas [W] 1771 rpm 2296 rpm 2660 rpm (a): Expander fed with HCFC-123 W sh,calc [W] 3500 3000 2500 2000 1500 1000 500 T loss = 0.47 N.m T loss = 0 N.m 10% error bars 0 0 500 1000 1500 2000 2500 3000 3500 W sh,meas [W] 1513 rpm 2214 rpm 3539 rpm (b): Expander fed with water steam Figure 6: Prediction of the shaft power (semi-empirical model)
5 EXPANDER DETERMINISTIC MODEL In order to check the physical meang of the identified parameters of the semi-empirical model, a comprehensive model of the expander was developed. This model is adapted from the model proposed by Halm (6) for compressor mode. The modellg is based on control volume analysis, for which differential equations of conservation of mass and energy are established and numerically solved. dm dθ M& su M& ex ω ω = du Q& dv 1 h = P + M& su.h su M& ex dθ ω dθ ω ω (6) (7) The crank angle evolutions of the different control volumes and their derivatives (dv/dθ) rely on a very accurate description of the expander geometry (Figure 7). The built- volume ratio and the swept volume predicted by the determistic model (3.94 and 37.36 cm 3 ) are very close to the value identified with the parameter identification algorithm for the semi-empirical model (Table 1). The model accounts for fluid pressure losses durg suction and discharge processes, for ternal flows between adjacent chambers and for the heat transfer between the fluid and the scrolls. Mechanical losses are described an identical way as for the semi-empirical model. The model only necessitates the followg parameters (Table 2): a radial leakage gap (gap between the tip of a scroll and the plates of the opposite scroll), a flank leakage gap (gap between two scroll wraps), a global heat transfer coefficient, a lumped mechanical losses torque and a correction factor on the exhaust port area to account for discharge pressures losses not implicitly described by the model (7). Up to now, the model has only been validated for the tests with HCFC-123. Results of this validation are shown Figure 10 comparg the predicted and the measured isentropic effectiveness. 6 PERFORMANCE ANALYSIS AND IMPROVEMENTS Both the semi-empirical and the determistic models of the expander are used to analyze the performance of the scroll expander prototype and to dicate how its design might be altered to achieve better performance. Table 2: Identified parameters of the determistic model for the use of HCFC-123 Heat transfer coefficient with the ambient AU amb 4 W/K Radial leakage gap δ r 0 µm Flank leakage gap δ f 70 µm Correction factor on exhaust port area C ex 0.66 - Mechanical loss torque T loss 1.0 N-m
y [m] 0.08 0.06 0.04 0.02 0-0.02-0.04-0.06-0.08 17 14 10 8 6 6 7 9 13-0.1-0.05 0 0.05 0.1 x [m] fixed scroll orbitg scroll Figure 7: Geometrical description of the expander ε s [-] 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 1771 rpm 2296 rpm 2660 rpm measured calculated 0 2.5 3 3.5 4 4.5 5 5.5 r p [-] Figure 8: Prediction of the overall isentropic effectiveness (determistic model) 6.1 Built- volume ratio For the whole tests with steam, the ternal pressure ratio (P su,2 /P ad ) is around 5.2±0.2. Figure 3 (a) shows that much larger pressure ratios were imposed to the expander. Figure 3 clearly dicates that the isentropic effectiveness decreases with the pressure ratio because of the creasg under-expansion losses. For these operatg conditions, usg an expander with a built- volume ratio larger than ~4.0 would yield better performances. For the tests with HCFC-123, the ternal pressure ratio is around 4.2±0.1. As shown Figure 3 (b), maximal pressure ratios of 5.5 were imposed to the expander. For such pressure ratios, under-expansion losses are limited (Figure 9 (a)). In contrary, Figure 3 (b) showed that the isentropic effectiveness drops sharply for the lower pressure ratios, due to over-expansion losses (Figure 9 (b)). x 10 5 6 x 105 7 6 begng of expansion P su P ex 5.5 5 begng of expansion P su 4.5 P ex P [Pa] 5 4 P [Pa] 4 3.5 3 3 2.5 2 2 1.5 1 0 0.5 1 1.5 V [m 3 ] x 10-4 1 0 0.5 1 1.5 V [m 3 ] x 10-4 (a): under-expansion (P su = 6.92 bar, P ex = 1.38 bar, T su = 145.6 C, N = 2296 m -1 ) (b): over-expansion (P su = 5.39 bar, P ex = 2.00 bar, T su = 121.0 C, N = 2295 m -1 ) Figure 9: Representation of the P-V diagram of the expansion of HCFC-123 (determistic model)
6.2 Supply pressure drop As already mentioned by Yanagisawa et al. (6), major supply pressure losses a scroll expander are associated to the two followg phenomena: a) durg part of the suction process, the expander suction port is blocked by the tip of the orbitg scroll, reducg the effective suction port area; b) a the end of the suction process, the flow passage between the central portion of the suction chamber and the two adjacent crescent-shaped portions is progressively reduced to zero. For the operatg pot dicated Figure 7 (a), the determistic model dicates a relative pressure drop of 10.15%. For the same operatg pot, the semi-empirical model predicts a relative pressure drop of 13.24%. The similarity between these two values confirms the physical meang of the equivalent supply port cross-sectional area given Table 1. Figure 10 shows that the relative pressure drop is much larger the case of usg HCFC-123 than steam. 0.35 0.7 (P su - P su,1 )/P su [-] 0.3 0.25 0.2 0.15 0.1 P su = 10 bar P ex = 1 bar DELTAT su = 10 K HCFC-123 water M leak / M [-] 0.6 0.5 0.4 0.3 HCFC-123 water P su = 10 bar P ex = 1 bar DELTAT su = 10 K 0.05 0.2 0 1000 1500 2000 2500 3000 3500 4000 4500 5000 N [m -1 ] Figure 10: Evolution of relative pressure drop with the rotational speed (semi-empirical model) 0.1 1000 1500 2000 2500 3000 3500 4000 4500 5000 N [m -1 ] Figure 11: Evolution of relative leakage with the rotational speed (semiempirical model) 6.3 Internal leakages Validation of the determistic model usg tests with HCFC-123 dicated that the radial leakage gap is equal to zero. This tends to confirm that tip seals worked correctly durg the tests. The identified value of the flank leakage gap (70 µm) is very close to the value identified by Yanagisawa et al. (5) their modellg of a similar expander. This large value can be explaed by the kematically rigid configuration of the expander (that prevents any flank contact). The lumped leakage area troduced the semi-empirical model roughly corresponds to the flow passage between the suction chamber and the adjacent expansion chambers. Under the assumption that ternal leakages are limited to flank leakages, the followg expression can be written: A = 2 δ (8) leak h scroll f For the scroll under vestigation (height of the scroll wrap h scroll of 28.65 mm), Eq. (8) predicts a leakage area of 4.01 mm 2. This value is very close to the value given Table 2 (4.6 mm 2 ), which demonstrates the physical meang of the leakage area troduced the semi-empirical modellg. Figure 11 dicates that, for a given leakage area, the relative
leakage flow rate is much smaller the case of usg HCFC-123 than steam. This explas the differences the achieved fillg factors shown Figures 4 (a) and (b). 6.4 Mechanical losses The mechanical loss torque identified the semi-empirical model is smaller than the one identified the determistic model. The underlyg reason is that the expansion work creases with the flank leakage (by deformation of the P-V digram), which cannot be described by the semi-empirical model. Hence, a smaller mechanical loss torque must be troduced the semi-empirical model order to predict the same shaft power. Further analysis should vestigate whether these losses could be reduced (better adapted tip seals and beargs). 7 CONCLUSIONS This paper compared the performances of a prototype of oil-free open-drive scroll expander, tested with steam and HCFC-123, with regards to its design characteristics. Better overall isentropic performances are achieved with HCFC-123. This is maly explaed by higher volumetric performances (for identical leakage gaps) and the lower under-expansion losses (smaller pressure ratios were imposed to the expander). However, the analysis dicated that suction pressure losses are more detrimental to the performances the case of usg HCFC-123. REFERENCE LIST (1) M. Kane, D. Larra, D. Favrat, Y. Allani, Small hybrid solar power system, Energy 28 (2003) 1427-1443. (2) P. Platell, Displacement expanders for small scale cogeneration, Licentiate Thesis, Department of Mache Design, Royal Institute of Technology, Stockholm, 1993. (3) V. Lemort, I. V. Teodorese, J. Lebrun, Experimental Study of the Integration of a Scroll Expander Into a Heat Recovery Ranke Cycle, : Proceedgs of the International Compressor Engeerg Conference, Purdue, 2006, C105. (4) B. Aoun, D. Clodic, Theoretical and experimental study of an oil-free scroll type vapor expander, : Proceedgs of the Compressor Engeerg Conference, Purdue, 2008, Paper 1188. (5) T. Yanagisawa, M. Fukuta, Y. Ogi, T. Hikichi, Performance of an oil-free scrolltype air expander, : Proceedgs of the ImechE Conference on Compressors and their Systems, 2001, 167-174. (6) N. P. Halm, Mathematical Modelg of Scroll Compressors, Master Thesis, Purdue University, West Lafayette, IN, 1997. (7) Bell, I., V. Lemort, J. Braun, E. Groll. 2008a. Development of Liquid-Flooded Scroll Compressor and Expander Models. Proceedgs of the 19th International Compressor Engeerg Conference at Purdue University: Paper 1283.