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A vapor injector-based novel regenerative organic Rankine cycle
Applied Thermal Engineering 31 (2011) 1238e1243
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
A vapor injector-based novel regenerative organic Rankine cycle Rong-Ji Xu, Ya-Ling He* Key Laboratory of Thermal Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 September 2010 Accepted 15 December 2010 Available online 30 December 2010
A regenerative organic Rankine cycle (RORC) that uses a vapor injector as the regenerator is proposed. The physical process is theoretically described and the numerical analysis of the injector performance based on a one-dimensional model is also presented. The thermal performance of both the novel cycle and the basic ORC is calculated and compared by using R123 as the working fluid. The results indicate that there exist the inlet vapor pressure regions for the injector that allows the new novel cycle performs better than the basic ORC. The evaporating and condensing temperatures affect the thermal performance and net power output of the cycles. The thermal performance of the RORC is better than the basic ORC for a given extraction pressure of 220 kPa at different evaporating temperatures, and the same result is found for a given extraction pressure of 300 kPa at different condensing temperatures. The influence of the condensing temperature, which affects the inlet liquid parameters of the injector, is more significant. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine cycle Vapor injector Regenerator Thermal performance
1. Introduction Over a half of heat named as the low-grade waste heat in the industrialized behavior is directly rejected to the air, not only lowering the energy efficiency but also causing the environmental problems such as global warming, ozone depletion, and so on [1,2]. To overcome the above-mentioned problems, one attractive alternative solution is to use the organic Rankine cycle (ORC) that converts the low-grade waste heat into the electricity. Over the past decades, many efforts on the ORC are mainly focused on the choice of the working fluid. Saleh et al. [3] and Maizza et al. [4,5] reported nearly all the organic fluids that could be used in the ORC and showed their performance in the ORC. Drescher et al. [6] developed a software to find thermodynamically suitable fluids for ORC in biomass power and heat plants. R123 was selected as the working fluid in that work because of its good performance at low-temperature heat source, nontoxicity and environmental friendliness [6,7]. The other research interests are concentrated on the combination of the ORC and other energy or power cycles [8e11], as well as the improvement or optimization of the ORC [12e15]. One of the useful and simple improvements among them is the regenerative cycle. Mago et al. [16] analyzed both the regenerative ORC (RORC) and basic ORC (BORC) using a combined first and second law analysis and compared the performance with each other to determine the configuration with * Corresponding author. E-mail address: [email protected] (Y.-L. He). 1359-4311/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.12.026
the best thermal efficiency and minimum irreversibility. Mago et al. [17] presented a quantitative estimation of the exergy destroyed in RORC and BORC using exergy topologic method. However, little study on the regenerator used in the ORC is addressed in the literature, mainly because the heat transfer process is usually considered at constant pressure in the past works [3,16,17]. In this work, vapor injector, working like a turbine driven pump, is introduced into the cycle as a regenerator. A vapor injector is a simple and compact device to pump cold liquid to produce an outlet liquid with a higher pressure than the vapor inlet pressure. The latent heat of the inlet vapor is the only energy source to pressurize and heat the liquid, and it does not require any external energy supply [18]. In addition, the injector without moving parts has a heat transfer coefficient as high as 103 kW/(m2 K) for the thermodynamic process in the injector relying on direct contact phenomena [19,20]. Generally, the injector consists of a liquid nozzle, a vapor nozzle, a mixing chamber, and a diffuser as shown in Fig. 1. The vapor nozzle (region II) is a supersonic nozzle, having a converging-diverging shape, through which the vapor isentropically expands. Liquid is distributed by the liquid nozzle (region I) placing on the center of the vapor nozzle. In the mixing chamber (region III) the vapor and the liquid meet together. The mixing process involves complicated heat, momentum and mass exchanges between the vapor and liquid. The vapor completely condenses at the exit of the mixing chamber (region IV), and there would be a shock wave. The outflow possesses relatively high pressure after the wave and then rushes into the diffuser (region V), where the liquid kinetic energy induces a further increase in the
R.-J. Xu, Y.-L. He / Applied Thermal Engineering 31 (2011) 1238e1243
Fig. 1. Schematic of the injector.
pressure. Both the temperature and pressure of the inlet liquid are changed when an injector is introduced into the ORC as a regenerator that is different from the conventional thermodynamic process in the regenerator. The objective of this work is to give the detailed thermodynamic process analysis of the RORC with injector and evaluate the performance of the new RORC. 2. System description and assumptions Fig. 2 illustrates the organic Rankine cycles and the corresponding thermodynamic processes on the Tes diagram. As observed in Fig. 2(a), there exist four different processes for BORC: expansion process (1e2), constant pressure condensing and subcooling (2e30 e3), pumping process (3e6), and constant pressure evaporating (6e1). With regard to the RORC as shown in Fig. 2(b), a steam injector is used as a regenerator. The vapor from the evaporator rushes into the expander and a small part of vapor is extracted from the expander in the expanding process and the others rush into the condenser after expanding. The vapor and the liquid exiting the condenser come into contact in the injector. The vapor releases heat, mass and momentum to the liquid due to the temperature difference, condensation, and the different velocity. Finally, the two parts are completely mixed with an outflowing liquid at a relatively high pressure and temperature. The mixing process in the injector is complicated, and is simply represented by the dotted lines 20 e4 and 3e4 on the Tes diagram. In other words, the injector plays a role like pump where the vapor is the power input. The other processes of the cycle are the same to the BORC.
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The vapor extracted from the expander not only reduces the net power output of the expander but also decreases the pump work input. The percent of the extraction vapor is very important. There may be a proper percentage making better performance than BORC so that the effect of the extraction pressure is analyzed in Section 3. In this work, energy recovery or electricity production from lowgrade heat, such as solar energy, geothermal and waste heat etc., is the main purpose. Low-temperature heat sources, whose temperature is typical about 420 K [12], are by far the most commonly available resource. Hence, the simulation conditions of the cycle can be determined, which are summarized in Table 1, and there are some other assumptions claimed: steady state conditions, adiabatic for all components and pipes, no pressure drop in the evaporator, condenser, feed water heater, and pipes. The isentropic efficiencies for the turbine and pump are unit. The thermodynamic characteristics of fluids are taken from the Refprop 7.0 software [21].
3. Thermodynamic analysis of the ORCs and the injector calculating method 3.1. Thermodynamic analysis of the ORCs The general modeling procedure for the components of the ORC has been established [16] and briefly described in Table 2.
3.2. Injector calculating method For the injector working as a regenerator in the ORC, the following input parameters are independent and known: Inlet vapor temperature and pressure; inlet liquid temperature and pressure; mass flow rate of the cycle. The outlet parameters of the mixed flow are the objects of the injector simulation. Point a in Fig. 1 indicates the inlet position of the injector that is the same to points 20 and 3 in Fig. 2, and point e is the same as point 4.
Fig. 2. Schematic of the organic Rankine cycles and theirs Tes charts.
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R.-J. Xu, Y.-L. He / Applied Thermal Engineering 31 (2011) 1238e1243
3.2.3. Mixing chamber Appling the conservation equations to the mixing chamberglobal volume (III) in Fig.1 leads to the following continuity, momentum, and energy equations.
Table 1 Operating conditions. Heat source temperature (K) Evaporating temperature (K) Environment temperature (K) Environment pressure (kPa) Condensing temperature (K) mass flow rate (kg/s) Expander isentropic efficiency his,e Pump isentropic efficiency his,p
420 403 293 101.35 308 6.3 1 1
1
rc uc ¼ ð1 þ UÞ eb rb ub U with inlet void fraction
eb ¼
In this work, the injector performance simulation is carried out based on the one-dimensional global model reported by Deberne et al. [19]. Rather than using the corrected empirical factors, irreversibilities are taken into account through the pressure variation along the mixing section. Therefore, the model has strong applicability and can be used without any previous experimental data. In addition, the modeling of the vapor nozzle and liquid nozzle, which was not studied by Deberne et al. [19], is added in this work according to the configuration of the nozzle studied. Thus the whole calculation procedure of the injector with a centered liquid supply from inlet parameters to outlet is figured out. 3.2.1. Liquid nozzle Due to the same diameter of the inlet and outlet liquid nozzle, the liquid parameters at point a are the same to that at point b, i.e.:
1 r u
1 þ U rb;v ub;v b;l
Ab;v Ab;v þ Ab;l
¼
b;l
and the area contraction ratio
U¼
Ac Ab;v þ Ab;l
where mass flow rate ratio, U ¼ ml =mv , is deduced from the inlet conditions at the mixing chamber. Momentum
ð1 þ UÞu2 þ
U
1 * P2 þ 1 P
eb rb;v ub;v
¼ ub;v þ Uub;l þ
U
Pb;v eb rb;v ub;v
Zc Pðn$zÞdS
3.2.2. Vapor nozzle In the vapor nozzle, the vapor mass flux mv, velocity uv,b and pressure Pv,b at point b are the objects to obtain from the parameters of inlet steam and the configuration of vapor nozzle. The vapor mass flux can be determined from
(1)
The vapor velocity uv,b can be determined from
uv;b
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 2 hv;a hv;b
(2)
In order to obtain the vapor enthalpy at point b, the vapor pressure at point b must be obtained first. For the constant pressure injector model, we can get Pv,b ¼ Pl,b. Moreover, the flow of the vapor in the nozzle is assumed to be isentropic, hence, the vapor enthalpy can be obtained by the state equation.
hb;v ¼ h Pb;v ; sb;v
(3)
The calculation of the other sections is the same to Ref. [19]. In the following the constant equations are listed, and the solving process can be referred to Ref. [19]. Table 2 Thermodynamic equations to evaluate the BORC and RORC. Component and processes
Equation
BORC
Wt ¼ Wt,idealhis,e ¼ m(h1 h2)his,e Qc ¼ m(h2 h3) Wp ¼ (h6 h3)/his,p Qe ¼ m(h1 h6) hth,B ¼ Wnet/Qe ¼ Wt Wp/Qe
RORC
Expander (1e2) Condenser (2e3) Pump (3e6) Evaporator (6e1) Cycle efficiency 0
Expander (1e2 e2) 0
Injector (2 e4, 3e4) Condenser (2e3) Pump (4e5) Evaporator (5e1) Cycle efficiency
Wt ¼ ðW1e20;ideal þ W20e2;ideal Þhis;e ¼ ½mðh1 h20 Þ þ ml ðh20 h2 Þhis;e (m ml) (h20 h4) ¼ ml(h4 h3) Qc ¼ ml(h2 h3) Wp ¼ (h5 h4)/his,p Qe ¼ m(h1 h5) hth,R ¼ Wnet/Qe ¼ Wt Wp/Qe
(5)
where
Db;l ¼ Da;l ; Pb;l ¼ Pa;l ; hb;l ¼ ha;l ; rb;l ¼ ra;l ; ub;l ¼ ua;l :
mv ¼ rv;b Av;b uv;b
(4)
*
P ¼
b
Zc ðn$zÞdS
1 ¼ ðAc Ab Þ
Zc Pðn$zÞdS ; dS ¼ b
2prðzÞ dz cosðqÞ
b
Energy
! u2b;l u2c ¼ U hb;l þ þ ð1 þ UÞ hc þ 2 2
hb;v þ
u2b;v
!
2
(6)
Equation of state
hc ¼ hðPc ; rc Þ
(7)
3.2.4. Shock wave Continuity
rd ud ¼ rc uc
(8)
with rc ¼ ecrc,v þ (1 ec)rc,l Momentum
rd u2d þ Pd ¼ rc u2c þ Pc
(9)
Energy
rd ud
u2 hd þ d 2
! ¼ rc
u2c þ uc ec rc;v hc;v þ ð1 ec Þrc;l hc;l 2
(10)
Equation of state
hd ¼ hðPd ; rd Þ
(11)
R.-J. Xu, Y.-L. He / Applied Thermal Engineering 31 (2011) 1238e1243
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18.2
18.0 252 17.8
250
17.6
248
BORC efficiency RORC efficiency BORC power output RORC power output
17.4
17.2
246
Net power output (kW)
Cycle thermal efficiency η (%)
254
244
242 17.0 150 200 250 300 350 400 450 500 550 600 650 700 750 800
Extraction pressure (K) Fig. 3. Effect of extraction pressure on the expander power output and thermal efficiency of the RORC compared to BORC.
3.2.5. Diffuser Continuity
Ae ue ¼ Ad ud
(12)
Bernoulli equation
Pe þ
re u2e 2
¼ Pd þ
rd u2d 2
hD rd u2d
(13)
4. Results and discussion In order to find the optimal extraction pressure to achieve the best cycle performance, different extraction pressures are used and both the thermal efficiency and net power output are calculated as shown in Fig. 3. The thermal efficiency of the RORC increases with the vapor extraction pressure increase from 150 to 220 kPa. However, the thermal efficiency decreases when the vapor extraction pressure further increases to 760 kPa. On the other hand, the thermal efficiency of the BORC is constant at 17.8% at the 40
Mass flow ratio U
0.35 30 0.30 25
0.25
20
0.20
15
Vapor mass flow rate mv (kg/s)
0.40
Mass flow ratio Vapor mass flow rate
35
0.15 200
300
400
500
working condition of Table 1. The results indicate that when the extraction pressure is less than 390 kPa, the thermal efficiency of the RORC is better than that of the BORC. The optimal extraction pressure is about 220 kPa, at which the thermal efficiency of the RORC is 18.03%, which is 1.18% higher than that of BORC. It suggests that the injector regenerator is effective and enhances the performance of the BORC. The net power output of the expander decreases with the increase of the vapor extraction pressure: the higher the extraction pressure the more the vapor extracted. The mass of the vapor extracted from the expander and the rate of mass flow rate of the vapor and liquid are plotted against the extraction pressure as shown in Fig. 4. The thermodynamic state of each point for the RORC having the best performance with extraction pressure of 220 kPa and the corresponding BORC are shown in Table 3. The performance of the cycles is given in Table 4. It can be found from Fig. 2 that the state 3 is changed to 4 by the introduction of the injector into the BORC. This means both the pressure and temperature of the condenser outflow are improved and the total heat received from the heat source would be reduced. The corresponding changes in the work of the pumps are shown in Tables 3 and 4. That is the advantage of the RORC. However, the cost is the extracted vapor from the expanding process. The gain and cost are the main factors making the improvement of the thermal performance of the RORC.
600
700
800
Extraction pressure (K) Fig. 4. Mass of the vapor extracted from the expander vs. extraction pressure.
Table 3 Thermodynamic state of each point for the RORC with extraction pressure 220kPa and BORC. State
T (K)
p (kPa)
h (kJ/kg)
s (kJ/(kg K))
1 20 (av) 2 30 3 (al) bv bl cv cl d 4 (e) 5 6
403.00 337.06 322.40 308.00 300.00 322.40 300.00 305.56 303.36 303.62 303.29 302.67 300.46
1453.61 220.00 129.86 129.86 129.86 129.86 129.86 119.31 119.31 673.16 392.67 1453.61 1453.61
454.01 421.76 412.81 235.25 227.04 412.81 227.04 306.33 228.79 230.91 230.48 231.22 227.95
1.6969 1.6969 1.6969 1.1212 1.0942 1.6969 1.0942 1.2594 1.1056 1.1058 1.1050 1.1050 1.0942
u (m/s)
133.80 83.05 90.81 90.81 86.39 21.53
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R.-J. Xu, Y.-L. He / Applied Thermal Engineering 31 (2011) 1238e1243 21.0 300
BORC
RORC
Expander work (kW) Pump work (kW) Net power output (kW) Heat load (kW) Condensing load (kW) Thermal efficiency (%)
259.59 5.71 253.88 1424.2 1170.3 17.83
257.70 4.45 253.10 1403.6 1131.1 18.03
Evaporating and condensing temperatures are the most important parameters determining the performance of ORC. The present work studies the influence of evaporating and condensing temperatures on the thermal performance of the RORC. Fig. 5 shows the thermal efficiency and net power output of the ORCs at different evaporating temperatures but the same extraction pressure of 220 kPa. It can be seen from the figure that the performance of the RORC is better than the BORC, and the injector regenerator is effective at different evaporating temperatures. The net power output of the BORC is a little higher than that of the RORC, and the difference is very small for the case that the amount of extracted vapor is small. The injector performance is the same, which has the best performance with extraction pressure of 220 kPa, because the inlet parameters (state of points 20 and 3) are the same at the different evaporating temperatures. The evaporating temperature only affects the heat load and the net power output. Fig. 6 shows the thermal efficiency and net power output of the ORCs at different condensing temperatures but the same extraction pressure of 300 kPa. The evaporating temperature affects the inlet liquid parameters (state of point 3) of the injector and also the performance of the injector. In other words, there would be a best performance of the injector for a given evaporating temperature of the RORC. The extraction pressure is different from the above analysis, because the injector cannot work when the liquid inlet temperature and pressure are too low. The injector would have a good performance with extraction pressure of 300 kPa at the condensing temperature calculated. It can be further seen that the performance of the RORC is better than the BORC, and the injector regenerator is effective at different condensing temperatures. The net power output of the BORC is higher than RORC, and the difference is more than that for different evaporating temperatures. One reason is that the extraction pressure is higher, and the other reason is that the inlet pressure and temperature of the liquid are lower. Therefore, there would be more vapor extracted and the power output of the expander would be less. 19
Cycle thermal efficiency η (%)
20.5
Performance
RORC efficiency BORC efficiency RORC power output BORC power output
20.0 19.5
280
19.0 18.5
270
18.0 260 17.5 17.0 294
296
298
300
302
304
306
17
5. Conclusion A regenerative organic Rankine cycle that uses vapor injector as regenerator is proposed. Thermodynamic analyses of both new cycle and basic ORCs are conducted. The findings are summarized as follows: (1) The RORC, using vapor injector as the regenerator, has a higher thermal efficiency than the BORC when the extraction pressure is less than 390 kPa. (2) The thermal performance of the RORC is better than the BORC for a given extraction pressure of 220 kPa at different evaporating temperatures. The same result is found for a given extraction pressure of 300 kPa at different condensing temperatures. However, the effect of the condensing temperature on the thermal performance of the RORC is more significant because it affects the inlet liquid parameters of the injector. (3) The injector regenerator is effective and can improve the performance of the BORC. Acknowledgements This work was supported by the Key Project of National Natural Science Foundation of China under Grant No. 50736005, and National Basic Research Program of China (973 Program) under Grant 2010CB227102. Nomenclature
230 220
16
210
15
200
14
190 13 370
375
380
385
390
395
400
405
Evaporating temperature (K) Fig. 5. The thermal efficiency and net power output at different evaporating temperatures.
250
Fig. 6. The thermal efficiency and net power output at different condensing temperatures.
240
Net power output (kW)
Cycle thermal efficiency η (%)
18
308
Condensing temperature (K)
250
RORC efficiency BORC efficiency RORC power output BORC power output
290
Net power output (kW)
Table 4 The performance of the RORC and BORC.
A m D h P Q r s S T u U W z, n
area, m2 mass flow rate, kg/s diameter, m enthalpy, kJ/kg pressure, kPa heat rate, kW radius, m entropy, kJ/(kg K) cross-sectional area of the injector, m2 temperature, K velocity, m/s mass ratio power, kW orientation
R.-J. Xu, Y.-L. He / Applied Thermal Engineering 31 (2011) 1238e1243
Greek letters e void fraction h efficiency, % q angle, r density, kg/m3 U area contraction ratio Subscripts B basic organic Rankine cycle c condenser e evaporator, expander is isentropic l liquid p pump R regenerative organic Rankine cycle th thermal v vapor a, b, c, d, e state points of the injector 1, 2, 20 , 3, 30 , 4, 5, 6 state points of the system References [1] T. Yamamoto, T. Furuhata, N. Arai, K. Mori, Design and testing of the organic Rankine cycle, Energy 26 (3) (2001) 239e251. [2] Y. Chen, P. Lundqvist, A. Johansson, P. Platell, A comparative study of the carbon dioxide transcritical power cycle compared with an organic Rankine cycle with R123 as working fluid in waste heat recovery, Applied Thermal Engineering 26 (17e18) (2006) 2142e2147. [3] B. Saleh, G. Koglbauer, M. Wendland, J. Fischer, Working fluids for lowtemperature organic Rankine cycles, Energy 32 (7) (2007) 1210e1221. [4] V. Maizza, A. Maizza, Working fluids in non-steady flows for waste energy recovery systems, Applied Thermal Engineering 16 (7) (1996) 579e590. [5] V. Maizza, A. Maizza, Unconventional working fluids in organic Rankine-cycles for waste energy recovery systems, Applied Thermal Engineering 21 (3) (2001) 381e390. [6] U. Drescher, D. Bruggemann, Fluid selection for the organic Rankine cycle (orc) in biomass power and heat plants, Applied Thermal Engineering 27 (1) (2007) 223e228.
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[7] T.C. Hung, Waste heat recovery of organic Rankine cycle using dry fluids, Energy Conversion and Management 42 (5) (2001) 539e553. [8] Y.S.H. Najjar, A.M. Radhwan, Cogeneration by combining gas-turbine engine with organic Rankine-cycle, Heat Recovery Systems 8 (3) (1988) 211e219. [9] I. Obernberger, A. Hammerschmid, R. Bini, Combined heat and power production from biomass using the organic Rankine cycle- EU-THERMIE Project Admont (A), Thermal Use of Solid Biomasses 1588 (2001) 283e302. [10] D. Manolakos, G. Kosmadakis, S. Kyritsis, G. Papadakis, On site experimental evaluation of a low-temperature solar organic Rankine cycle system for rodesalination, Solar Energy 83 (5) (2009) 646e656. [11] T. Hung, Triple cycle: a conceptual arrangement of multiple cycle toward optimal energy conversion, Journal of Engineering for Gas Turbines and Power 124 (2) (2002) 429e436. [12] H.D.M. Hettiarachchia, M. Golubovica, W.M. Worek, Y. Ikegami, Optimum design criteria for an organic Rankine cycle using low-temperature geothermal heat sources, Energy 32 (9) (2007) 1698e1706. [13] Y.P. Dai, J.F. Wang, L. Gao, Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery, Energy Conversion and Management 50 (3) (2009) 576e582. [14] A. Schuster, S. Karellas, J. Karl, Innovative applications of organic Rankine cycle. ECOS 2006: Proceedings of the 19th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems, vols. 1e3, 2006, 897e904, 1711. [15] D.H. Wei, X.S. Lu, Z. Lu, J.M. Gu, Performance analysis and optimization of organic Rankine cycle (ORC) for waste heat recovery, Energy Conversion and Management 48 (4) (2007) 1113e1119. [16] P.J. Mago, L.M. Chamra, K. Srinivasan, C. Somayaji, An examination of regenerative organic Rankine cycles using dry fluids, Applied Thermal Engineering 28 (8e9) (2008) 998e1007. [17] P.J. Mago, K.K. Srinivasan, L.M. Chamra, C. Somayaji, An examination of exergy destruction in organic Rankine cycles, International Journal of Energy Research 32 (10) (2008) 926e938. [18] N. Beithou, H. Aybar, A mathematical model for steam-driven jet pump, International Journal of Multiphase Flow 26 (10) (2000) 1609e1619. [19] N. Deberne, J. Leone, A. Duque, A. Lallemand, A model for calculation of steam injector performance, International Journal of Multiphase Flow 25 (5) (1999) 841e855. [20] J. Yan, S. Shao, J. Liu, Z. Zhang, Experiment and analysis on performance of steam-driven jet injector for district-heating system, Applied Thermal Engineering 25 (8e9) (2005) 1153e1167. [21] National Institute of Standards and Technology, Standard reference database 23, Reference fluid thermodynamic and transport properties-Refprop 7.0, US, 2002.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
A vapor injector-based novel regenerative organic Rankine cycle Rong-Ji Xu, Ya-Ling He* Key Laboratory of Thermal Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 September 2010 Accepted 15 December 2010 Available online 30 December 2010
A regenerative organic Rankine cycle (RORC) that uses a vapor injector as the regenerator is proposed. The physical process is theoretically described and the numerical analysis of the injector performance based on a one-dimensional model is also presented. The thermal performance of both the novel cycle and the basic ORC is calculated and compared by using R123 as the working fluid. The results indicate that there exist the inlet vapor pressure regions for the injector that allows the new novel cycle performs better than the basic ORC. The evaporating and condensing temperatures affect the thermal performance and net power output of the cycles. The thermal performance of the RORC is better than the basic ORC for a given extraction pressure of 220 kPa at different evaporating temperatures, and the same result is found for a given extraction pressure of 300 kPa at different condensing temperatures. The influence of the condensing temperature, which affects the inlet liquid parameters of the injector, is more significant. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine cycle Vapor injector Regenerator Thermal performance
1. Introduction Over a half of heat named as the low-grade waste heat in the industrialized behavior is directly rejected to the air, not only lowering the energy efficiency but also causing the environmental problems such as global warming, ozone depletion, and so on [1,2]. To overcome the above-mentioned problems, one attractive alternative solution is to use the organic Rankine cycle (ORC) that converts the low-grade waste heat into the electricity. Over the past decades, many efforts on the ORC are mainly focused on the choice of the working fluid. Saleh et al. [3] and Maizza et al. [4,5] reported nearly all the organic fluids that could be used in the ORC and showed their performance in the ORC. Drescher et al. [6] developed a software to find thermodynamically suitable fluids for ORC in biomass power and heat plants. R123 was selected as the working fluid in that work because of its good performance at low-temperature heat source, nontoxicity and environmental friendliness [6,7]. The other research interests are concentrated on the combination of the ORC and other energy or power cycles [8e11], as well as the improvement or optimization of the ORC [12e15]. One of the useful and simple improvements among them is the regenerative cycle. Mago et al. [16] analyzed both the regenerative ORC (RORC) and basic ORC (BORC) using a combined first and second law analysis and compared the performance with each other to determine the configuration with * Corresponding author. E-mail address: [email protected] (Y.-L. He). 1359-4311/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.12.026
the best thermal efficiency and minimum irreversibility. Mago et al. [17] presented a quantitative estimation of the exergy destroyed in RORC and BORC using exergy topologic method. However, little study on the regenerator used in the ORC is addressed in the literature, mainly because the heat transfer process is usually considered at constant pressure in the past works [3,16,17]. In this work, vapor injector, working like a turbine driven pump, is introduced into the cycle as a regenerator. A vapor injector is a simple and compact device to pump cold liquid to produce an outlet liquid with a higher pressure than the vapor inlet pressure. The latent heat of the inlet vapor is the only energy source to pressurize and heat the liquid, and it does not require any external energy supply [18]. In addition, the injector without moving parts has a heat transfer coefficient as high as 103 kW/(m2 K) for the thermodynamic process in the injector relying on direct contact phenomena [19,20]. Generally, the injector consists of a liquid nozzle, a vapor nozzle, a mixing chamber, and a diffuser as shown in Fig. 1. The vapor nozzle (region II) is a supersonic nozzle, having a converging-diverging shape, through which the vapor isentropically expands. Liquid is distributed by the liquid nozzle (region I) placing on the center of the vapor nozzle. In the mixing chamber (region III) the vapor and the liquid meet together. The mixing process involves complicated heat, momentum and mass exchanges between the vapor and liquid. The vapor completely condenses at the exit of the mixing chamber (region IV), and there would be a shock wave. The outflow possesses relatively high pressure after the wave and then rushes into the diffuser (region V), where the liquid kinetic energy induces a further increase in the
R.-J. Xu, Y.-L. He / Applied Thermal Engineering 31 (2011) 1238e1243
Fig. 1. Schematic of the injector.
pressure. Both the temperature and pressure of the inlet liquid are changed when an injector is introduced into the ORC as a regenerator that is different from the conventional thermodynamic process in the regenerator. The objective of this work is to give the detailed thermodynamic process analysis of the RORC with injector and evaluate the performance of the new RORC. 2. System description and assumptions Fig. 2 illustrates the organic Rankine cycles and the corresponding thermodynamic processes on the Tes diagram. As observed in Fig. 2(a), there exist four different processes for BORC: expansion process (1e2), constant pressure condensing and subcooling (2e30 e3), pumping process (3e6), and constant pressure evaporating (6e1). With regard to the RORC as shown in Fig. 2(b), a steam injector is used as a regenerator. The vapor from the evaporator rushes into the expander and a small part of vapor is extracted from the expander in the expanding process and the others rush into the condenser after expanding. The vapor and the liquid exiting the condenser come into contact in the injector. The vapor releases heat, mass and momentum to the liquid due to the temperature difference, condensation, and the different velocity. Finally, the two parts are completely mixed with an outflowing liquid at a relatively high pressure and temperature. The mixing process in the injector is complicated, and is simply represented by the dotted lines 20 e4 and 3e4 on the Tes diagram. In other words, the injector plays a role like pump where the vapor is the power input. The other processes of the cycle are the same to the BORC.
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The vapor extracted from the expander not only reduces the net power output of the expander but also decreases the pump work input. The percent of the extraction vapor is very important. There may be a proper percentage making better performance than BORC so that the effect of the extraction pressure is analyzed in Section 3. In this work, energy recovery or electricity production from lowgrade heat, such as solar energy, geothermal and waste heat etc., is the main purpose. Low-temperature heat sources, whose temperature is typical about 420 K [12], are by far the most commonly available resource. Hence, the simulation conditions of the cycle can be determined, which are summarized in Table 1, and there are some other assumptions claimed: steady state conditions, adiabatic for all components and pipes, no pressure drop in the evaporator, condenser, feed water heater, and pipes. The isentropic efficiencies for the turbine and pump are unit. The thermodynamic characteristics of fluids are taken from the Refprop 7.0 software [21].
3. Thermodynamic analysis of the ORCs and the injector calculating method 3.1. Thermodynamic analysis of the ORCs The general modeling procedure for the components of the ORC has been established [16] and briefly described in Table 2.
3.2. Injector calculating method For the injector working as a regenerator in the ORC, the following input parameters are independent and known: Inlet vapor temperature and pressure; inlet liquid temperature and pressure; mass flow rate of the cycle. The outlet parameters of the mixed flow are the objects of the injector simulation. Point a in Fig. 1 indicates the inlet position of the injector that is the same to points 20 and 3 in Fig. 2, and point e is the same as point 4.
Fig. 2. Schematic of the organic Rankine cycles and theirs Tes charts.
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R.-J. Xu, Y.-L. He / Applied Thermal Engineering 31 (2011) 1238e1243
3.2.3. Mixing chamber Appling the conservation equations to the mixing chamberglobal volume (III) in Fig.1 leads to the following continuity, momentum, and energy equations.
Table 1 Operating conditions. Heat source temperature (K) Evaporating temperature (K) Environment temperature (K) Environment pressure (kPa) Condensing temperature (K) mass flow rate (kg/s) Expander isentropic efficiency his,e Pump isentropic efficiency his,p
420 403 293 101.35 308 6.3 1 1
1
rc uc ¼ ð1 þ UÞ eb rb ub U with inlet void fraction
eb ¼
In this work, the injector performance simulation is carried out based on the one-dimensional global model reported by Deberne et al. [19]. Rather than using the corrected empirical factors, irreversibilities are taken into account through the pressure variation along the mixing section. Therefore, the model has strong applicability and can be used without any previous experimental data. In addition, the modeling of the vapor nozzle and liquid nozzle, which was not studied by Deberne et al. [19], is added in this work according to the configuration of the nozzle studied. Thus the whole calculation procedure of the injector with a centered liquid supply from inlet parameters to outlet is figured out. 3.2.1. Liquid nozzle Due to the same diameter of the inlet and outlet liquid nozzle, the liquid parameters at point a are the same to that at point b, i.e.:
1 r u
1 þ U rb;v ub;v b;l
Ab;v Ab;v þ Ab;l
¼
b;l
and the area contraction ratio
U¼
Ac Ab;v þ Ab;l
where mass flow rate ratio, U ¼ ml =mv , is deduced from the inlet conditions at the mixing chamber. Momentum
ð1 þ UÞu2 þ
U
1 * P2 þ 1 P
eb rb;v ub;v
¼ ub;v þ Uub;l þ
U
Pb;v eb rb;v ub;v
Zc Pðn$zÞdS
3.2.2. Vapor nozzle In the vapor nozzle, the vapor mass flux mv, velocity uv,b and pressure Pv,b at point b are the objects to obtain from the parameters of inlet steam and the configuration of vapor nozzle. The vapor mass flux can be determined from
(1)
The vapor velocity uv,b can be determined from
uv;b
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 2 hv;a hv;b
(2)
In order to obtain the vapor enthalpy at point b, the vapor pressure at point b must be obtained first. For the constant pressure injector model, we can get Pv,b ¼ Pl,b. Moreover, the flow of the vapor in the nozzle is assumed to be isentropic, hence, the vapor enthalpy can be obtained by the state equation.
hb;v ¼ h Pb;v ; sb;v
(3)
The calculation of the other sections is the same to Ref. [19]. In the following the constant equations are listed, and the solving process can be referred to Ref. [19]. Table 2 Thermodynamic equations to evaluate the BORC and RORC. Component and processes
Equation
BORC
Wt ¼ Wt,idealhis,e ¼ m(h1 h2)his,e Qc ¼ m(h2 h3) Wp ¼ (h6 h3)/his,p Qe ¼ m(h1 h6) hth,B ¼ Wnet/Qe ¼ Wt Wp/Qe
RORC
Expander (1e2) Condenser (2e3) Pump (3e6) Evaporator (6e1) Cycle efficiency 0
Expander (1e2 e2) 0
Injector (2 e4, 3e4) Condenser (2e3) Pump (4e5) Evaporator (5e1) Cycle efficiency
Wt ¼ ðW1e20;ideal þ W20e2;ideal Þhis;e ¼ ½mðh1 h20 Þ þ ml ðh20 h2 Þhis;e (m ml) (h20 h4) ¼ ml(h4 h3) Qc ¼ ml(h2 h3) Wp ¼ (h5 h4)/his,p Qe ¼ m(h1 h5) hth,R ¼ Wnet/Qe ¼ Wt Wp/Qe
(5)
where
Db;l ¼ Da;l ; Pb;l ¼ Pa;l ; hb;l ¼ ha;l ; rb;l ¼ ra;l ; ub;l ¼ ua;l :
mv ¼ rv;b Av;b uv;b
(4)
*
P ¼
b
Zc ðn$zÞdS
1 ¼ ðAc Ab Þ
Zc Pðn$zÞdS ; dS ¼ b
2prðzÞ dz cosðqÞ
b
Energy
! u2b;l u2c ¼ U hb;l þ þ ð1 þ UÞ hc þ 2 2
hb;v þ
u2b;v
!
2
(6)
Equation of state
hc ¼ hðPc ; rc Þ
(7)
3.2.4. Shock wave Continuity
rd ud ¼ rc uc
(8)
with rc ¼ ecrc,v þ (1 ec)rc,l Momentum
rd u2d þ Pd ¼ rc u2c þ Pc
(9)
Energy
rd ud
u2 hd þ d 2
! ¼ rc
u2c þ uc ec rc;v hc;v þ ð1 ec Þrc;l hc;l 2
(10)
Equation of state
hd ¼ hðPd ; rd Þ
(11)
R.-J. Xu, Y.-L. He / Applied Thermal Engineering 31 (2011) 1238e1243
1241
18.2
18.0 252 17.8
250
17.6
248
BORC efficiency RORC efficiency BORC power output RORC power output
17.4
17.2
246
Net power output (kW)
Cycle thermal efficiency η (%)
254
244
242 17.0 150 200 250 300 350 400 450 500 550 600 650 700 750 800
Extraction pressure (K) Fig. 3. Effect of extraction pressure on the expander power output and thermal efficiency of the RORC compared to BORC.
3.2.5. Diffuser Continuity
Ae ue ¼ Ad ud
(12)
Bernoulli equation
Pe þ
re u2e 2
¼ Pd þ
rd u2d 2
hD rd u2d
(13)
4. Results and discussion In order to find the optimal extraction pressure to achieve the best cycle performance, different extraction pressures are used and both the thermal efficiency and net power output are calculated as shown in Fig. 3. The thermal efficiency of the RORC increases with the vapor extraction pressure increase from 150 to 220 kPa. However, the thermal efficiency decreases when the vapor extraction pressure further increases to 760 kPa. On the other hand, the thermal efficiency of the BORC is constant at 17.8% at the 40
Mass flow ratio U
0.35 30 0.30 25
0.25
20
0.20
15
Vapor mass flow rate mv (kg/s)
0.40
Mass flow ratio Vapor mass flow rate
35
0.15 200
300
400
500
working condition of Table 1. The results indicate that when the extraction pressure is less than 390 kPa, the thermal efficiency of the RORC is better than that of the BORC. The optimal extraction pressure is about 220 kPa, at which the thermal efficiency of the RORC is 18.03%, which is 1.18% higher than that of BORC. It suggests that the injector regenerator is effective and enhances the performance of the BORC. The net power output of the expander decreases with the increase of the vapor extraction pressure: the higher the extraction pressure the more the vapor extracted. The mass of the vapor extracted from the expander and the rate of mass flow rate of the vapor and liquid are plotted against the extraction pressure as shown in Fig. 4. The thermodynamic state of each point for the RORC having the best performance with extraction pressure of 220 kPa and the corresponding BORC are shown in Table 3. The performance of the cycles is given in Table 4. It can be found from Fig. 2 that the state 3 is changed to 4 by the introduction of the injector into the BORC. This means both the pressure and temperature of the condenser outflow are improved and the total heat received from the heat source would be reduced. The corresponding changes in the work of the pumps are shown in Tables 3 and 4. That is the advantage of the RORC. However, the cost is the extracted vapor from the expanding process. The gain and cost are the main factors making the improvement of the thermal performance of the RORC.
600
700
800
Extraction pressure (K) Fig. 4. Mass of the vapor extracted from the expander vs. extraction pressure.
Table 3 Thermodynamic state of each point for the RORC with extraction pressure 220kPa and BORC. State
T (K)
p (kPa)
h (kJ/kg)
s (kJ/(kg K))
1 20 (av) 2 30 3 (al) bv bl cv cl d 4 (e) 5 6
403.00 337.06 322.40 308.00 300.00 322.40 300.00 305.56 303.36 303.62 303.29 302.67 300.46
1453.61 220.00 129.86 129.86 129.86 129.86 129.86 119.31 119.31 673.16 392.67 1453.61 1453.61
454.01 421.76 412.81 235.25 227.04 412.81 227.04 306.33 228.79 230.91 230.48 231.22 227.95
1.6969 1.6969 1.6969 1.1212 1.0942 1.6969 1.0942 1.2594 1.1056 1.1058 1.1050 1.1050 1.0942
u (m/s)
133.80 83.05 90.81 90.81 86.39 21.53
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R.-J. Xu, Y.-L. He / Applied Thermal Engineering 31 (2011) 1238e1243 21.0 300
BORC
RORC
Expander work (kW) Pump work (kW) Net power output (kW) Heat load (kW) Condensing load (kW) Thermal efficiency (%)
259.59 5.71 253.88 1424.2 1170.3 17.83
257.70 4.45 253.10 1403.6 1131.1 18.03
Evaporating and condensing temperatures are the most important parameters determining the performance of ORC. The present work studies the influence of evaporating and condensing temperatures on the thermal performance of the RORC. Fig. 5 shows the thermal efficiency and net power output of the ORCs at different evaporating temperatures but the same extraction pressure of 220 kPa. It can be seen from the figure that the performance of the RORC is better than the BORC, and the injector regenerator is effective at different evaporating temperatures. The net power output of the BORC is a little higher than that of the RORC, and the difference is very small for the case that the amount of extracted vapor is small. The injector performance is the same, which has the best performance with extraction pressure of 220 kPa, because the inlet parameters (state of points 20 and 3) are the same at the different evaporating temperatures. The evaporating temperature only affects the heat load and the net power output. Fig. 6 shows the thermal efficiency and net power output of the ORCs at different condensing temperatures but the same extraction pressure of 300 kPa. The evaporating temperature affects the inlet liquid parameters (state of point 3) of the injector and also the performance of the injector. In other words, there would be a best performance of the injector for a given evaporating temperature of the RORC. The extraction pressure is different from the above analysis, because the injector cannot work when the liquid inlet temperature and pressure are too low. The injector would have a good performance with extraction pressure of 300 kPa at the condensing temperature calculated. It can be further seen that the performance of the RORC is better than the BORC, and the injector regenerator is effective at different condensing temperatures. The net power output of the BORC is higher than RORC, and the difference is more than that for different evaporating temperatures. One reason is that the extraction pressure is higher, and the other reason is that the inlet pressure and temperature of the liquid are lower. Therefore, there would be more vapor extracted and the power output of the expander would be less. 19
Cycle thermal efficiency η (%)
20.5
Performance
RORC efficiency BORC efficiency RORC power output BORC power output
20.0 19.5
280
19.0 18.5
270
18.0 260 17.5 17.0 294
296
298
300
302
304
306
17
5. Conclusion A regenerative organic Rankine cycle that uses vapor injector as regenerator is proposed. Thermodynamic analyses of both new cycle and basic ORCs are conducted. The findings are summarized as follows: (1) The RORC, using vapor injector as the regenerator, has a higher thermal efficiency than the BORC when the extraction pressure is less than 390 kPa. (2) The thermal performance of the RORC is better than the BORC for a given extraction pressure of 220 kPa at different evaporating temperatures. The same result is found for a given extraction pressure of 300 kPa at different condensing temperatures. However, the effect of the condensing temperature on the thermal performance of the RORC is more significant because it affects the inlet liquid parameters of the injector. (3) The injector regenerator is effective and can improve the performance of the BORC. Acknowledgements This work was supported by the Key Project of National Natural Science Foundation of China under Grant No. 50736005, and National Basic Research Program of China (973 Program) under Grant 2010CB227102. Nomenclature
230 220
16
210
15
200
14
190 13 370
375
380
385
390
395
400
405
Evaporating temperature (K) Fig. 5. The thermal efficiency and net power output at different evaporating temperatures.
250
Fig. 6. The thermal efficiency and net power output at different condensing temperatures.
240
Net power output (kW)
Cycle thermal efficiency η (%)
18
308
Condensing temperature (K)
250
RORC efficiency BORC efficiency RORC power output BORC power output
290
Net power output (kW)
Table 4 The performance of the RORC and BORC.
A m D h P Q r s S T u U W z, n
area, m2 mass flow rate, kg/s diameter, m enthalpy, kJ/kg pressure, kPa heat rate, kW radius, m entropy, kJ/(kg K) cross-sectional area of the injector, m2 temperature, K velocity, m/s mass ratio power, kW orientation
R.-J. Xu, Y.-L. He / Applied Thermal Engineering 31 (2011) 1238e1243
Greek letters e void fraction h efficiency, % q angle, r density, kg/m3 U area contraction ratio Subscripts B basic organic Rankine cycle c condenser e evaporator, expander is isentropic l liquid p pump R regenerative organic Rankine cycle th thermal v vapor a, b, c, d, e state points of the injector 1, 2, 20 , 3, 30 , 4, 5, 6 state points of the system References [1] T. Yamamoto, T. Furuhata, N. Arai, K. Mori, Design and testing of the organic Rankine cycle, Energy 26 (3) (2001) 239e251. [2] Y. Chen, P. Lundqvist, A. Johansson, P. Platell, A comparative study of the carbon dioxide transcritical power cycle compared with an organic Rankine cycle with R123 as working fluid in waste heat recovery, Applied Thermal Engineering 26 (17e18) (2006) 2142e2147. [3] B. Saleh, G. Koglbauer, M. Wendland, J. Fischer, Working fluids for lowtemperature organic Rankine cycles, Energy 32 (7) (2007) 1210e1221. [4] V. Maizza, A. Maizza, Working fluids in non-steady flows for waste energy recovery systems, Applied Thermal Engineering 16 (7) (1996) 579e590. [5] V. Maizza, A. Maizza, Unconventional working fluids in organic Rankine-cycles for waste energy recovery systems, Applied Thermal Engineering 21 (3) (2001) 381e390. [6] U. Drescher, D. Bruggemann, Fluid selection for the organic Rankine cycle (orc) in biomass power and heat plants, Applied Thermal Engineering 27 (1) (2007) 223e228.
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