Designing scroll expanders for use in heat recovery Rankine cycles

Transcription

1 Deigning croll expander for ue in heat recovery Rankine cycle V Lemort, S Quoilin Thermodynamic Laboratory, Univerity of Liège, Belgium ABSTRACT Thi paper firt invetigate experimentally the performance of a prototype of oilfree open-drive croll expander working with water and with HCFC-123. Uing experimental data, two different imulation model of the expander are then propoed and validated. Thee model are finally ued to analyze the meaured performance with regard to the expander deign characteritic. NOMENCLATURE A area, m 2 AU heat tranfer coefficient, W/K h pecific enthalpy, J/kg M ma flow rate, kg/ N rotational peed, -1 P preure, Pa t temperature, C T torque, N.m v pecific volume, m 3 /kg V volume flow rate, m 3 / W power, W Subcript ad adapted amb calc ex in leak lo mea h u ambient calculated exhaut internal leakage mechanical lo meaured ientropic, wept haft upply Greek letter pecific heat ratio, - efficiency, - filling factor, - 1 INTRODUCTION Small-cale heat recovery Rankine cycle ytem allow generating mechanical or electrical energy from local low grade heat ource (1). Sytem uing water a working fluid are particularly uitable for recovering energy from engine exhaut ga or heat produced by olar concentrator (2, 3, 4). Sytem uing an organic fluid are more appropriate for lower temperature heat ource (1). The croll machine i a good candidate for the expanion device of uch a ytem, becaue of it implicity of operation and reliability (no valve and few moving part). Performance of the ytem trongly correlate with that of the expander, which jutifie improving it deign. Thi paper analye the performance of an open-drive oil-free expander, with repect to it deign characteritic, in the cae of uing water and HCFC-123. IMechE,

2 2 EXPERIMENTAL INVESTIGATION 2.1 Decription of the expander The expander prototype i originally an open-drive oil-free air croll compreor, imilar to thoe teted by Yanagiawa et al. (5) and Aoun and Clodic (4). The only modification made to the original compreor wa the removal of the cooling fan. The expander ha a kinematically rigid configuration that maintain a flank clearance between the croll wrap. Seal are alo netled in the tip of both croll to reduced radial leakage. 2.2 Steam driven expander A firt experimental ytem wa contructed to evaluate the performance of the expander for operation with water team (Figure 1). The ytem conited in an open-loop compriing 2 electric-team boiler in parallel, a releae valve, an electrical uper-heater, the expander, a water-cooled condener and a tank (to collect the condened water). The expander drove an aynchronou machine through two belt-and-pulley coupling and a torque-meter. Uing an aynchronou machine (connected to the grid) wa a very convenient way to impoe the expander rotational peed. The latter wa et to different value by modifying the aynchronou machine pulley diameter. The expander haft power wa determined from the meaurement of the torque and of the peed of the torque-meter haft. The expander upply preure wa controlled by adjuting the team flow rate feeding the expander (meaured by mean of an orifice plate meter) for a given expander rotational peed. The exce team wa releaed to the ambient through a pneumatically driven releae valve. Incondenable gae were extracted from the condener by mean of a vacuum pump allowing the expander exhaut preure to be tabilized in the range of 0.5 to 1 bar (abolute). The uper-heater wa ued to adjut the expander upply temperature. Figure 1: Schematic repreentation of the team tet bench 4

3 2.3 HCFC driven expander A econd experimental ytem, operating in a cloed loop, wa built to tet the expander with refrigerant HCFC-123. A variable diplacement diaphragm pump wa ued to control the refrigerant flow rate through the cycle and hence the expander upply preure. The refrigerant flow rate wa meaured by mean of a Corioli flow meter intalled at the pump exhaut. The ame apparatu a in the firt experimental ytem wa ued to control the expander peed and to meaure it haft power. The boiler of the cycle conited in everal heat exchanger fed with hot air, whoe flow rate and temperature were varied to control the expander upply temperature. The water flow rate through the condener wa controlled to regulate the expander exhaut preure. Figure 2: Schematic repreentation of the HCFC-123 tet bench 3 PERFORMANCE ANALYSIS 3.1 Overall ientropic efficiency The overall ientropic efficiency i defined by the ratio of the meaured haft power and the ientropic power (Eq. (1)). Figure 3 (a) and (b) how that higher ientropic efficiencie are achieved with HCFC-123 than with water team. W h, mea W h, mea W h, mea, mea W M. w M.( h h ) mea mea u ex, (1) 3.2 Filling factor The volumetric performance of the expander i repreented by the filling factor. The latter i defined a the ratio between the meaured ma flow rate and the ma 5

4 flow rate theoretically diplaced by the expander (Eq. (2)). A hown in Figure 4 (a) and (b), a much lower volumetric performance i achieved with team. The decreae in the filling factor with the rotational peed can be explained by the lower relative impact of the leakage. mea M mea.v u V (2) (a): Expander fed with team (b): Expander fed with HCFC-123 Figure 3: Evolution of the meaured ientropic efficiency with the preure ratio (a): Expander fed with team (b): Expander fed with HCFC-123 Figure 4: Evolution of the meaured filling factor with the expander upply preure 4 EXPANDER SEMI-EMPIRICAL MODEL 4.1 Decription of the model The emi-empirical model of the expander retain the main phyical feature of the machine (3). The evolution of the fluid through the expander i decompoed into the following conecutive tep: an adiabatic preure drop (u u,1) and an iobaric cooling-down by contact with the metal ma of the machine (u,1 u,2) during the uction proce; an ientropic expanion to the adapted preure impoed by the built-in volume ratio of the machine (u,2 ad), an adiabatic expanion at a contant machine volume (ad ex,2); an adiabatic mixing between upply and leakage flow (ex,2 ex,1); and an iobaric exhaut cooling-down or heating-up (ex,1 ex). 6

5 The ma flow rate wept by the expander i given a a function of the expander wept volume V, rotational peed N and leakage flow rate by: V N. V M M M M M (3) in leak leak leak vu,2 vu,2 All the leakage path are lumped into one unique fictitiou leakage path connecting the expander upply and exhaut. The leakage flow rate and the preure drop are computed by reference to the ientropic flow through a imply convergent nozzle of cro-ectional area A leak and A u. Under- and over-expanion loe are decribed by plitting the expanion into an ientropic expanion and contant volume evolution: in in u,2 ad ad ad ex,2 W M ( h h ) v P P (4) Mechanical loe are evaluated on the bai of a lumped mechanical loe torque T lo : W W W W 2 N T (5) h in lo in lo Internal heat tranfer are lumped into equivalent upply and exhaut heat tranfer between the fluid and a fictitiou hell of uniform temperature T w (on the bai of overall heat tranfer coefficient AU u and AU ex ). External heat tranfer i decribed by an overall heat tranfer coefficient AU amb. 4.2 Parameter identification The emi-empirical model of the expander neceitate 8 parameter that can be identified on the bai of experimental data. The upply and exhaut preure, the upply temperature, the ambient temperature and the rotational peed were impoed a input variable of the expander model. The parameter of the model are identified by an algorithm that minimize a function accounting for the error on the prediction of the ma flow rate, haft power and exhaut temperature (main output variable of the model). Parameter were firt identified for the tet with HCFC-123. For thee tet, the enthalpy at the expander exhaut could be determined (uperheated vapour). Thi allowed a better accuracy of the model parameter, ince ambient heat loe can be etimated. In contrary, for the tet with team, vapour wa aturated at the expander exhaut. Table 1: Identified parameter of the emi-empirical model (tet with HCFC-123) Heat tranfer coefficient with the ambient AU amb 6.4 W/K Supply heat tranfer coefficient AU u 21.2 M W/K Exhaut heat tranfer coefficient AU ex 34.2 M W/K Leakage area A leak 4.6 mm 2 Built-in volume ratio r v,in Swept volume V,exp cm 3 Supply port cro-ectional area A u mm 2 Mechanical lo torque T lo 0.47 N-m 4.3 Model verification Prediction by the emi-empirical model of the wept ma flow rate are compared to experimental data in Figure 5 (a) and (b). The model parameter are thoe 7

6 lited in Table 1. It can be oberved that the model i able to predict with a good accuracy the team ma flow rate. Thee reult confirm the phyical meaning of the leakage area identified uing the tet with HCFC-123. Experimental data with team were not detailed enough to accurately identify the three heat tranfer coefficient. In a firt approximation, coefficient given in Table 2 were conidered. A more detailed modelling and experimental validation hould anwer the quetion of the influence of the fluid on the internal heat tranfer. (a): Expander fed with HCFC-123 (b): Expander fed with team Figure 5: Prediction of the ma flow rate (emi-empirical model) The ame comparion i given in Figure 6 (a) and (b) for the haft power. For the tet with HCFC-123, the model give very good reult. However the power i under-predicted for the tet with team (even if mechanical loe were cancelled). It can be hown that the error on the predicted haft power increae remarkably with the filling factor. Internal leakage tend to increae the expanion work (by deformation of the P-V diagram), which cannot be decribed by model. (a): Expander fed with HCFC-123 (b): Expander fed with team Figure 6: Prediction of the haft power (emi-empirical model) 5 EXPANDER DETERMINISTIC MODEL In order to check the phyical meaning of the identified parameter of the emiempirical model, a comprehenive model of the expander wa developed. Thi model i adapted from the model propoed by Halm (6) for compreor mode. The modelling i baed on control volume analyi, for which differential equation of conervation of ma and energy are etablihed and numerically olved. 8

7 dm d 2 1 Mu N ex M (6) du Q 1 P dv M u. h h u M ex (7) d 2 N d 2 N 2 N The crank angle evolution of the different control volume and their derivative (dv/d) rely on a very accurate decription of the expander geometry (Figure 7). The built-in volume ratio and the wept volume predicted by the determinitic model (3.94 and cm 3 ) are very cloe to the value identified with the parameter identification algorithm for the emi-empirical model (Table 1). The model account for fluid preure loe during uction and dicharge procee, for internal flow between adjacent chamber and for the heat tranfer between the fluid and the croll. Mechanical loe are decribed in an identical way a for the emi-empirical model. The model only neceitate the following parameter (Table 2): a radial leakage gap (gap between the tip of a croll and the plate of the oppoite croll), a flank leakage gap (gap between two croll wrap), a global heat tranfer coefficient, a lumped mechanical loe torque and a correction factor on the exhaut port area to account for dicharge preure loe not implicitly decribed by the model (7). Up to now, the model ha only been validated for the tet with HCFC-123. Reult of thi validation are hown in Figure 8 comparing the predicted and the meaured ientropic efficiencie given a a function of the preure ratio over the expander. Table 2: Identified parameter of the determinitic (tet with HCFC-123) Heat tranfer coefficient with the ambient AU amb 4 W/K Radial leakage gap r 0 µm Flank leakage gap f 70 µm Correction factor on the exhaut port area C ex Mechanical lo torque T lo 1.0 N-m y [m] x [m] fixed croll orbiting croll Figure 7: Geometrical decription of the expander [-] rpm 2296 rpm 2660 rpm meaured calculated r p [-] Figure 8: Prediction of the overall ientropic efficiency (determinitic model) 9

8 6 PERFORMANCE ANALYSIS AND IMPROVEMENTS Both the emi-empirical and the determinitic model of the expander are ued to analyze the performance of the croll expander prototype and to indicate how it deign might be altered to achieve better performance. 6.1 Built-in volume ratio For the whole tet with team, the internal preure ratio (P u,2 /P ad ) i around 5.2±0.2. Figure 3 (a) how that much larger preure ratio were impoed to the expander. Figure 3 clearly indicate that the ientropic efficiency decreae with the preure ratio becaue of the increaing under-expanion loe. For thee operating condition, uing an expander with a built-in volume ratio larger than ~4.0 would yield a better performance. For the tet with HCFC-123, the internal preure ratio i around 4.2±0.1. A hown in Figure 3 (b), maximal preure ratio of 5.5 were impoed to the expander. For uch preure ratio, under-expanion loe are limited (Figure 9 (a)). In contrary, Figure 3 (b) howed that the ientropic efficiency drop harply for the lower preure ratio, due to over-expanion loe (Figure 9 (b)). x x beginning of expanion P u P ex beginning of expanion P u 4.5 P ex P [Pa] 5 4 P [Pa] V [m 3 ] (a): under-expanion (P u = 6.92 bar, P ex = 1.38 bar, T u = C, N = 2296 min -1 ) x V [m 3 ] (b): over-expanion (P u = 5.39 bar, P ex = 2.00 bar, T u = C, N = 2295 min -1 ) Figure 9: Repreentation of the P-V diagram of the expanion of HCFC-123 (determinitic model) x Supply preure drop A already mentioned by Yanagiawa et al. (5), major upply preure loe with a croll expander are aociated to the two following phenomena: a) during part of the uction proce, the expander uction port i blocked by the tip of the orbiting croll, reducing the effective uction port area; b) at the end of the uction proce, the flow paage between the central portion of the uction chamber and the two adjacent crecent-haped portion i progreively reduced to zero. For the operating point indicated in Figure 9 (a), the determinitic model indicate a relative preure drop of 10.15%. For the ame operating point, the emi-empirical model predict a relative preure drop of 13.24%. The imilarity between thee two value confirm the phyical meaning of the equivalent upply port croectional area given in Table 1. Figure 10 how that the relative preure drop i much larger in the cae of uing HCFC-123 than team, which can be explained by the much larger pecific volume 10

9 of team (at imilar preure and temperature). Thi i jutified by Eq. (8) that give, in a firt approximation, the relative upply preure drop a a function of the pecific volume of the fluid at the expander upply. Pu Pu 1 1 V Pu 2 Pu v u A u 2 (8) Figure 10: Evolution of the relative preure drop with the rotational peed (emi-empirical model) Figure 11: Evolution of the relative leakage flow rate with the rotational peed (emi-empirical model) 6.3 Internal leakage Validation of the determinitic model uing tet with HCFC-123 indicated that the radial leakage gap i equal to zero. Thi tend to confirm that tip eal worked correctly during the tet. The identified value of the flank leakage gap (70 µm) i very cloe to the value identified by Yanagiawa et al. (5) in their modelling of a imilar expander. Thi large value can be explained by the kinematically rigid configuration of the expander (that prevent any flank contact). The lumped leakage area introduced in the emi-empirical model roughly correpond to the flow paage between the uction chamber and the adjacent expanion chamber. Under the aumption that internal leakage are limited to flank leakage, the following expreion can be written: A 2h (9) leak croll f For the croll under invetigation (height of the croll wrap h croll of mm), Eq. (9) predict a leakage area of 4.01 mm 2. Thi value i very cloe to the value given in Table 2 (4.6 mm 2 ), which demontrate the phyical meaning of the leakage area introduced in the emi-empirical modelling. Figure 11 indicate that, for a given leakage area, the relative leakage flow rate i much maller in the cae of uing HCFC-123 than team. Thi explain the difference in the achieved filling factor hown in Figure 4 (a) and (b). Here alo, the underlying reaon i the much larger pecific volume of water (at imilar preure and temperature). Thi i demontrated by Eq. (10) that give, in a firt approximation, the relative leakage flow rate a a function of the pecific volume of the fluid at the expander upply. M M leak in 1 1 Aleak 2 2 Pu v V 1 1 u (10) 11

10 6.4 Mechanical loe The mechanical lo torque identified in the emi-empirical model i maller than the one identified in the determinitic model. The underlying reaon i that the expanion work increae with the flank leakage (by deformation of the P-V diagram), which cannot be decribed by the emi-empirical model. Hence, a maller mechanical lo torque mut be introduced in the emi-empirical model in order to predict the ame haft power. Further analyi hould invetigate whether thee loe could be reduced (better adapted tip eal and bearing). CONCLUSIONS Thi paper compared the performance of a prototype of oil-free open-drive croll expander, teted with water and HCFC-123, with regard to it deign characteritic. Better overall ientropic performance i achieved with HCFC-123. Thi i mainly explained by higher volumetric performance (for identical leakage gap) and the lower under-expanion loe (maller preure ratio were impoed to the expander). However, the analyi indicated that uction preure loe are more detrimental to the performance in the cae of uing HCFC-123. Note that the latter fluid will be phaed out in a near future. Further work hould invetigate the performance of the machine with replacement fluid uch a R245fa. REFERENCE LIST (1) M. Kane, D. Larrain, D. Favrat, Y. Allani, Small hybrid olar power ytem, Energy 28 (2003) (2) P. Platell, Diplacement expander for mall cale cogeneration, Licentiate Thei, Department of Machine Deign, Royal Intitute of Technology, Stockholm, (3) V. Lemort, I. V. Teodoree, J. Lebrun, Experimental Study of the Integration of a Scroll Expander Into a Heat Recovery Rankine Cycle, In: Proceeding of the International Compreor Engineering Conference, Purdue, 2006, C105. (4) B. Aoun, D. Clodic, Theoretical and experimental tudy of an oil-free croll type vapor expander, In: Proceeding of the Compreor Engineering Conference, Purdue, 2008, Paper (5) T. Yanagiawa, M. Fukuta, Y. Ogi, T. Hikichi, Performance of an oil-free crolltype air expander, In: Proceeding of the ImechE Conference on Compreor and their Sytem, 2001, (6) N. P. Halm, Mathematical Modeling of Scroll Compreor, Mater Thei, Purdue Univerity, Wet Lafayette, IN, (7) Bell, I., V. Lemort, J. Braun, E. Groll. 2008a. Development of Liquid-Flooded Scroll Compreor and Expander Model. In: Proceeding of the 19th International Compreor Engineering Conference at Purdue Univerity: Paper