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Experimental study and modeling of an Organic Rankine Cycle using scroll expander
Applied Energy 87 (2010) 1260–1268
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Experimental study and modeling of an Organic Rankine Cycle using scroll expander Sylvain Quoilin *, Vincent Lemort, Jean Lebrun Thermodynamics Laboratory, University of Liège, Campus du Sart Tilman, B49, B-4000 Liège, Belgium
a r t i c l e
i n f o
Article history: Received 21 January 2009 Received in revised form 8 June 2009 Accepted 15 June 2009 Available online 6 August 2009 Keywords: Organic Rankine Cycle (ORC) Scroll expander Waste heat recovery Power generation
a b s t r a c t This paper presents both a numerical model of an Organic Rankine Cycle (ORC) and an experimental study carried out on a prototype working with refrigerant HCFC-123, and whose heat sources consist in two hot air flows. The ORC model is built by interconnecting different sub-models: the heat exchanger models, a volumetric pump model and a scroll expander model. Measured performance of the ORC prototype is presented and used to validate the ORC model. This model is finally used to investigate potential improvements of the prototype. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The interest for low grade heat recovery grew dramatically in the past decades. An important number of new solutions have been proposed to generate electricity from low temperature heat sources and are now applied to much diversified fields such as solar thermal power, biological waste heat, engine exhaust gases, domestic boilers, etc. Among the proposed solutions, the Organic Rankine Cycle (ORC) system is the most widely used. Its two main advantages are the simplicity and the availability of its components. In such a system, the working fluid is an organic component, better adapted than water to lower heat source temperatures. Unlike with traditional power cycles, local and small scale power generation is made possible by this technology. A wide range of ORC applications have been investigated in previous works, such as waste heat recovery [1–3], solar energy use [4,5], combined heat and power [6,7], geothermal systems [8], or engine exhaust gases [9–11]. Experimental studies of small scale ORC units demonstrated that the scroll expander is a good candidate for small scale power generation, because of its reduced number of moving parts, reliability, wide output power range, and broad availability [12]. Isentropic effectiveness’s ranging from 48% to 65% were reported, depending on the design of the scroll expander [4,5,7,13,14]. The study of a superposed ORC cycle proposed by Kane et al. [15] is of particular interest, since it uses a technology similar to the one proposed in the present work (selection of HCFC-123 as one of the two working fluids and use of scroll expanders). The flu* Corresponding author. Tel.: +32 4 366 48 22; fax: +32 4 366 48 12. E-mail address: [email protected] (S. Quoilin). 0306-2619/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2009.06.026
ids of the bottoming and of the topping cycles were selected to optimize the overall performance, with a maximum heat source temperature of 165 °C. A net efficiency of 12% was reached. Previous studies also showed the influence of the working fluid thermodynamic properties on the ORC performances [16–21]. On the other hand, only few papers present detailed simulation models of the ORC accounting for the characteristics of each component of the cycle: Kane [4] proposed a semi-empirical model of a small scale ORC with 3-zones heat exchangers, and a scroll expander model accounting for friction losses, intake throttling and internal leakage. Wei et al. [22] proposed a dynamic model of a 100 KWe ORC, focusing mainly on the heat exchangers and using empirical laws for the pump and for the expander. These ORC simulation models are very useful to optimize the operating conditions and the components of the cycle. The first part of this paper describes the simulation model of an ORC system. This model is built by interconnecting the sub-models of the different components: the heat exchangers, the pump and the expander. In the second part, the results of an experimental study are presented: this study aimed at evaluating the performance of an ORC working with refrigerant HCFC-123 and using a scroll expander. The above models are validated experimentally. The last part of the paper investigates, through simulations, the performance of the system and points out some achievable improvements.
2. ORC modeling This section describes the models of the different components of the ORC system under investigation. The modeling approach
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Nomenclature A AU b Bo C Co Cp d Dh k Fr G g h h ifg L _ M N Np Nu p Pr Q_ q r Re s t T v V
area, m2 heat transfer conductance, W/K corrugation depth, m boiling number, Bo = q/Gifg constant convective number, Co ¼ qg =ql ðð1 xÞ=xÞ0:8 specific heat, J/(kg K) diameter, m hydraulic diameter, Dh = 2b, m thermal conductivity, W/(mK) Froude number, Fr = G2/q2gDh 2 _ mass flux, G ¼ M=ððN p 2Þ b WÞ, kg/(m s) acceleration due to gravity, m/s2 convective heat transfer coefficient, W/(m2 K) specific enthalpy, J/kg enthalpy of vaporization, J/kg plate length, from center of inlet port to center of exit port, m mass flow rate, kg/s rotational speed, rpm number of plates Nusselt number, Nu = hDh/k pressure, Pa Prandtl number, Pr = lCp/k heat transfer rate, W heat flux, W/m2 ratio _ Dh Þ=ððNp 2Þ b W lÞ Reynolds number, Re ¼ ðM specific entropy, J/(kg K) temperature, C torque, N m specific volume, m3/kg volume, m3
consists in developing semi-empirical models, instead of deterministic models. Semi-empirical models involve a limited number of physically meaningful parameters that can be easily identified from performance measurements, while deterministic models require an exact knowledge of the geometry of all the components. Semi-empirical models are usually more numerically robust than deterministic models and allow a sharp decrease of the computational time. Therefore, they are more appropriate to be interconnected in such a way to build a simulation model of a larger system. A volumetric pump and a scroll expander models are considered since they are the technologies selected for the ORC prototype presented in this paper. All the models proposed in this section were developed under EES environment [23].
V_ _ W W x X
volume flow rate, m3/s power, W plate width, m vapor quality pump capacity fraction
Greek letters D differential e effectiveness q density, kg/m3 Subscripts amb ambient calc calculated ev evaporator ex exhaust exp expander f working fluid in internal leak leakage loss mechanical losses meas measured n nominal pp pump pred predicted r refrigerant s isentropic, swept sh shaft sf secondary fluid su supply tp two-phase v vapor, volume
_ in is the differAs shown in Eq. (1), the internal mass flow rate M _ entering the expander and the ence between the mass flow rate M _ leak . The internal mass flow rate is the volleakage mass flow rate M ume flow rate V_ s;exp divided by the specific volume of the fluid vr,su,2 after entering cooling-down and pressure drop. The volume flow rate is defined as the product of the swept volume V s;exp with the expander rotational speed Nexp. The swept volume in expander mode is equal to the one in compression mode V s;cp divided by the built-in volume ratio of the machine rv.
2.1. Scroll expander model The scroll expander model was previously proposed and validated by the authors [24]. In this model, the evolution of the refrigerant through the expander is decomposed into the following steps (as shown in Fig. 1): Supply pressure drop (su ? su,1). Supply cooling-down (su,1 ? su,2). Isentropic expansion to the internal pressure imposed by the built-in volume ratio of the expander (su,2 ? in). Expansion at a fixed volume to the exhaust pressure (in ? ex,2). Mixing between suction flow and leakage flow (ex,2 ? ex,1). Exhaust cooling-down or heating-up (ex,1 ? ex).
Fig. 1. Conceptual scheme of the expander model.
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_ _ in ¼ M _ M _ leak ¼ V s;exp ¼ Nexp V s;exp ¼ N exp : V s;cp M mr;su;2 60 mr;su;2 60 mr;su;2 rm
ð1Þ
The leakage mass flow rate can be computed by reference to the flow through a simply convergent nozzle. The fictitious leakage area Aleak is assimilated to the nozzle throat area and must be experimentally identified. In the same manner as for the leakage mass flow rate, the pressure drop is computed by reference to the flow through a simply convergent nozzle, whose throat diameter is the equivalent supply port diameter dsu. _ in is obtained by multiplying The internal expansion power W the internal work win by the internal mass flow rate. This internal work is the sum of the internal work win,s associated to the isentropic part of the expansion and the internal work win,v associated to the isochoric evolution. In Eq. (2), hr,in, vr,in and Pin are, respectively, the specific enthalpy, the specific volume and the pressure of the fluid at the end of the isentropic part of the expansion. The specific volume is the product of the built-in volume ratio rv with the specific volume vr,su,2.
_ in ¼ M _ in win ¼ M _ in ðwin;s þ win;v Þ W _ in ððhr;su;2 hr;in Þ þ v r;in ðPin P ex ÞÞ ¼M _ in ððhr;su;2 hr;in Þ þ r v v r;su;2 ðPin Pex ÞÞ ¼M
ð3Þ
A fictitious envelope of uniform temperature Tw is assumed to be sufficient to represent the three heat transfer modes. Tw is determined by establishing a steady-state heat balance on this envelope, as proposed by Winandy et al. [25]:
_ loss Q_ ex þ Q_ su Q_ amb ¼ 0 W
ð4Þ
Supply and exhaust heat transfers are described by introducing fictitious semi-isothermal heat exchangers characterized by global heat transfer conductances AUsu and AUex [24]. The latter can be correlated to the refrigerant mass flow rate according to the following law:
AU su ¼ AU su;n ex
ex;n
_ M _ Mn
1 1 1 ¼ þ U hr hsf
ð6Þ
The respective heat transfer area of each zone is obtained by imposing the total heat transfer area of the heat exchanger:
Al þ Atp þ Av ¼ ðN p 2Þ L W
2.2.1. Single-phase heat transfer coefficient Forced convection heat transfer coefficients are evaluated by means of the non-dimensional relationship:
ð8Þ
where the influence of temperature-dependent viscosity is neglected. The exponents m and n are set according to Muley’s recommendations for corrugated plate heat exchangers with a 30° Chevron angle [26]: m = 0.5 for the laminar regime (Re < 400), and m = 0.7 for the turbulent regime (Re > 400). In all cases, n = 1/3. The coefficient C is identified with experimental data, by minimizing the difference between predicted and measured values for a set of working points. Because of the large differences between Reynolds numbers, this coefficient is assigned specific values for the vapor and liquid zones on the refrigerant side and for the air and water sides. 2.2.2. Boiling heat transfer coefficient The overall boiling heat transfer coefficient is estimated by the Hsieh correlation [27], established for the boiling of refrigerant R410a in a vertical plate heat exchanger. This heat exchange coefficient is considered as constant during the whole evaporation process and is calculated by:
htp ¼ C hl Bo0:5
!0:8 ð5Þ
2.2. Condenser and evaporator models The condenser and the evaporator are modeled by means of the e-NTU method for counter-flow heat exchangers. The heat exchanger is subdivided into three zones, each of them being character-
ð7Þ
In the present work, the pressure drops are neglected in both the condenser and the evaporator models, since no accurate differential pressure sensors were installed on the heat exchangers in the experimental study. These pressure drops were however very limited. For other fluids and/or other heat exchangers leading to higher pressure drops, a pressure drop model should be included.
Nu ¼ C Rem Prn ð2Þ
The expander mechanical power can be split into the internal _ loss . These losses expansion power and the mechanical losses W can be expressed as a function of a mechanical losses torque Tm and the rotational speed of the expander. The expander mechanical power is given by
_ sh ¼ W _ in W _ loss ¼ W _ in 2 p Nrot T m W
ized by a heat transfer area A and a heat transfer coefficient U. The zone definition is shown in Fig. 2, in the case of the evaporator. The heat transfer coefficient U is calculated by considering two convective heat transfer resistances in series (secondary fluid and refrigerant sides).
ð9Þ
Where Bo is the boiling number and hl is the all-liquid non-boiling heat transfer coefficient. As for the single phase heat transfer coefficient, C is identified experimentally. 2.2.3. Condensation heat transfer coefficient The condensation heat transfer coefficient is estimated by the Kuo correlation [28] (Eq. (10)), established in the case of a vertical plate heat exchanger fed with R410A.
htp ¼ C hl ð0:25 Co0:45 Fr0:25 þ 75 Bo0:75 Þ l
ð10Þ
where Frl is the Froude number in saturated liquid state, Bo the boiling number and Co the convection number. The heat transfer coefficient correlation is quality-dependant. In this modeling, an average heat transfer coefficient is considered. For this reason, the two-phase heat transfer correlations are integrated using the following equation:
htp ¼ Fig. 2. Three-zone modeling of the evaporator.
1 L2 L1
Z
L2
L1
htp dL
ð11Þ
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Assuming that vapor quality variation is linear with length, the average heat transfer coefficient is calculated by:
htp ¼
Z
1
htp dx
ð12Þ
0
2.3. Pump model The pump is characterized by its swept volume and its global isentropic efficiency (gpp). The latter is assumed constant. The pump electrical consumption is given by:
_ _ el;pp ¼ W pp;s W
ð13Þ
gpp
The mass flow rate displaced by the pump is computed as a function of its capacity fraction Xpp by:
_ _ r ¼ V s;pp ¼ X pp V s;pp;max M
v r;su;pp
v r;su;pp
ð14Þ
The capacity fraction Xpp is defined as the ratio between the actual volume flow rate and the maximum volume flow rate of the pump. This variable is an input of the model; it is actually tuned by modifying the swept volume of the pump or its rotating speed.
Fig. 4. Information diagram of the ORC simulation model.
and the cycle efficiency. The parameters to identify with experimental data are indicated in bold. All other parameters are measured or imposed. 3. Experimental study 3.1. Test bench description
2.4. Global model The global model of the cycle is built by interconnecting the models of the different sub-components described above, as shown in Fig. 3. The modeling highlights the following constraints: (a) For a given displacement, the pump imposes the refrigerant mass flow rate. (b) The evaporator imposes the fluid superheating and the pump exhaust pressure. (c) Provided its rotational speed is fixed, the expander imposes the evaporator exhaust pressure. (d) For given secondary fluid mass flow rate and supply temperature, the condenser imposes the pressures at expander exhaust and pump supply (if a description of the refrigerant pressure drop is included in the modeling). This simulation model is not fully predictive, because the liquid subcooling at the condenser exhaust is defined as a model input. In order to predict this subcooling, a refrigerant charge model should be introduced. The information diagram of the Rankine cycle simulation model is given in Fig. 4. The inputs of the model are the mass flow rates and supply temperatures of the secondary fluids in the evaporator and in the condenser, the capacity fraction of the pump and its rotational speed. The main outputs are the expander shaft power
An experimental study was carried out on a prototype of ORC working with HCFC-123. A schematic representation of the test bench is given in Fig. 5. The scroll expander was originally an oilfree open-drive scroll compressor, adapted to operate in reverse. It drives an asynchronous machine through two belt-pulleys couplings and a torque meter. The latter is used to measure the expander shaft power. The heat source consists of a set of three heat exchangers supplied with two hot air flows. The condenser is cooled by water. A diaphragm piston-type pump drives the liquid fluid from the condenser exhaust to the boiler supply. A pulse damper is installed before the Coriolis flow meter in order to attenuate the flow rate fluctuations generated by the volumetric pump. 3.2. Achieved performances In total, 39 steady-state performance points were achieved, by combining the operating parameters listed in Table 1. Three performance indicators are taken into account: the expander shaft power, the expander isentropic effectiveness, and the cycle efficiency. The expander overall isentropic effectiveness is defined by:
_ W
sh es ¼ _ M r ðhr;su;exp hr;ex;exp;s Þ
And the cycle efficiency by:
Fig. 3. Block diagram of the global model of the cycle.
ð15Þ
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Fig. 5. Schematic representation of the test bench.
Table 1 Range of achieved operating conditions. Working condition
Minimum value
Maximum value
First hot air source mean temperature Second hot air source mean temperature Air mass flow rate Refrigerant mass flow rate Condenser water volume flow rate Condenser mean water temperature Expander rotation speed
53.4 °C 101.0 °C 0.071 kg/s 45 g/s 0.13 l/s 13.2 °C 1771 rpm
86.4 °C 163.2 °C 0.90 kg/s 86 g/s 0.70 l/s 15.0 °C 2660 rpm
some other working conditions, such as pressure and temperature levels. The cycle efficiency is mainly limited by a low pump efficiency (about 15%) and by a very high net positive suction head (NPSH), which constrained the tests to a large subcooling at the condenser exhaust (between 20 and 44 K). 4. Verification of the rankine cycle model 4.1. Expander model validation
gcycle ¼
_ sh W _ pp W Q_ evap
ð16Þ
As shown in Fig. 6, an expander isentropic effectiveness ranging from 42% to 68% is reached, corresponding to a maximum cycle efficiency of 7.4%. The pressure ratio over the expander varies from 2.7 to 5.4 and has obviously a clear influence on the system performance. Error bars account for measurement uncertainties. The efficiency curves plotted as a function of the pressure ratio show several irregularities, which is explained by the effects of
The parameters of the expander model are tuned to best fit the three model outputs (supply pressure, exhaust temperature, shaft power) to experimental data. The input variables of this calculation are: the expander rotational speed, the refrigerant mass flow rate, the supply temperature and the exhaust pressure. The parameters of the expander model are identified by minimizing an error-objective function F (using a genetic algorithm) defined as a weighted sum of the errors for each output:
F¼
39 h X
F 1 ðT r;ex; exp ;meas T r;ex; exp ;pred Þ2i
i¼1
þF 2
pr;su; exp ;meas pr;su; exp ;pred pr;su; exp ;meas
!2 þ F3 i
_ sh;meas W _ sh;pred W _ sh;meas W
!2 3 5 i
ð17Þ The weighting factors F1, F2, and F3 are pffiffiffiffiffiffichosen to give each pffiffiffi term the same approximate weight: F 1 ¼ 1= 60; F 2 ¼ 1; F 3 ¼ 1= 2. Comparisons between the prediction by the model and the measurements for the exhaust temperature and the output power are given in Fig. 7. The maximum deviations between the measurements and the predictions by the model are 3 K for the temperature and 6% for the shaft power. 4.2. Heat exchanger model validation
Fig. 6. Measured performance vs. pressure ratio.
The parameters of the condenser and of the evaporator are identified by imposing some measurements as input variables and by minimizing the deviation between the measured and predicted output variables.
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For given refrigerant supply temperature and exhaust subcooling, the condenser model predicts the condensing pressure. Fig. 8a shows that this pressure is predicted with a relative error of about 3%. For given refrigerant supply temperature and saturation pressure, the evaporator model predicts the heat flow rate and the exhaust temperature. Fig. 8b shows that the exhaust temperature is predicted with a maximum absolute error of 7 K, which corresponds to an error of 2.5% in the prediction of the heat flux. All the identified parameters are listed in Table 2. It can be observed that the identified single phase heat exchange coefficients C are very different. This is explained by the simplified modeling approach: the identified correlations not only account for the heat exchange, but also for pressure drops and ambient heat losses (mainly in the evaporator). This leads for example to a very low Cv in the evaporator because the vapor undergoes high ambient heat losses at that point. 4.3. Validation of the global model of the cycle Given all the parameters listed in Table 2, the predicted expander shaft power is compared to the measured one. Fig. 9 shows that all measurements are predicted within 10%. The error is higher for the global cycle model because of the cumulated subcomponent models inaccuracies. 5. Simulation and optimization
Fig. 7. Predicted vs. measured expander model outputs.
Fig. 8. Predicted vs. measured condenser and evaporator outputs.
This section illustrates how the cycle simulation model established and validated in the previous sections can be used in order to optimize the working conditions of the system. The increase of the system performance following this optimization is evaluated hereafter for one of the 39 measured performance points, characPex,exp = 1.84 105 Pa, terized by Psu,exp = 7.91 105 Pa, Tsu,exp = 133 °C and Nexp = 2660 rpm. Fig. 10 shows the T-s diagram for this working point, with superposition of the secondary fluids temperature profiles. Large vapor superheating at the evaporator exhaust and liquid subcooling at the condenser exhaust are observed. A first improvement consists in reducing the liquid subcooling. In the present case, this subcooling is reduced from 27 K (measured value) down to 5 K. The increase in performance can be explained by the location of the pinch point at the condenser exhaust (on the refrigerant side), which prevents the condensing pressure to be lowered. A second improvement is the selection of a more efficient pump. The effectiveness of the pump installed on test bench is 15%. A higher effectiveness should obviously be achieved. A pump effectiveness of 60% is assumed in this simulation. The third parameter to be optimized is the evaporator exhaust superheating. Yamamoto et al. [29] showed that for a working fluid with a low latent heat such as HCFC-123, the saturated vapor at the turbine supply would give the best performance. This can be achieved in two ways, as shown in Fig. 11: 1. Modification of the pump flow rate: Increasing the fluid mass flow rate will lead to a higher pressure at the expander supply, since the latter has to ‘‘increase” the density of the fluid to absorb the total amount of mass flow rate imposed by the pump. Increasing the pressure will lead to a higher evaporation temperature and hence to a lower temperature difference between the two heat sources. The mean logarithmic temperature difference being smaller, the heat flow rate across the evaporator will be reduced and the superheating will be reduced. Fig. 12 gives the evolution of the cycle efficiency and of the expander effectiveness with the flow rate, and shows that a higher flow rate indeed increases the performance.
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Table 2 Summary of the cycle model parameters. Expander
Condenser
Evaporator
Pump
AUamb = 6.38 W/K
Num ¼ 0:84 Re
AUsu = 21.22 W/K
Nuw ¼ 0:72 Re0:7 Pr1=3
Nul ¼ 1:29 Re0:5 Pr1=3
AUex = 34.2 W/K
Nul ¼ 0:4 Re0:5 Pr1=3
Nua ¼ 0:101 Re0:7 Pr1=3
dsu = 0.00591 m
htp ¼ 1:98 hl Bo0:5
htp ¼ 23:7 hl ð75 Bo0:75 þ 0:25 Co0:45 Fr0:25 Þ l
0:7
Pr
1=3
Num ¼ 0:063 Re
0:7
Pr
1=3
gpp = 15% V_ s;pp;max ¼ 58 cm3 =s
Tloss = 0.4067 N m Aleak = 4.858 mm2 rv = 4.005 Vs = 36.39 cm3
Fig. 9. Predicted vs. measured output power with the global model.
Fig. 12. Cycle efficiency and expander effectiveness vs. flow rate.
2. Modification of the expander rotational speed: If the expander rotational speed is decreased, its volumetric flow rate absorbed is decreased, and, for a given mass flow rate, the pressure is increased. Fig. 13 shows that lowering the expander speed indeed increases the performance, but only until a certain point (around 2000 rpm), where the expander effectiveness is reduced to a prohibitive value because of internal leakage.
Fig. 10. T-s diagram and secondary fluid temperatures.
Fig. 11. Required flow rate and speed to achieve a given superheating.
Therefore, reducing the expander rotational speed and increasing the pump mass flow rate both have a similar effect: they yield a higher evaporating pressure and a reduced superheating. Since the reduction of the superheating can be achieved in two ways, it is important to determine which combination of mass flow rate/rotational speed optimizes the cycle’s performance. The following observations should be taken into account while trying to optimize the working conditions:
Fig. 13. Cycle efficiency and expander effectiveness vs. speed.
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Fig. 14. Cycle efficiency for given working conditions.
Fig. 15. T-s diagram and secondary fluid temperatures.
A higher mass flow rate increases the heat transfer in the evaporator and thus the output power (at constant cycle efficiency). There exists a rotational speed that maximizes the expander effectiveness. This is due to the antagonist effects of the rotational speed on the internal leakages and on friction losses and supply pressure drop. A higher pressure in the evaporator may decrease the heat transfer (because of the lower logarithmic mean temperature difference), and increase the under-expansion losses in the expander. In order to determine the optimal working condition, a map of the cycle efficiency is drawn in Fig. 14: the cycle efficiency is plotted as a function of the two working conditions. Each gray cross in the background represent one point calculated by the model and used to establish the isometric curves. These curves should only be read in the area defined by the crosses. The lower right part of the map corresponding to high mass flow rate and low rotational speed is undefined, because superheating is reduced to zero, which would correspond to a two-phase state at the evaporator exhaust. Fig. 14 shows that an optimum working point is obtained around a value of 0.9 kg/s and 2300 rpm. The T-s diagram of this new, optimized working point is presented in Fig. 15. This new cycle is much closer to the theoretical Carnot cycle than the original cycle. Its efficiency has been increased from 5.1% to 9.9%. 6. Conclusions This paper proposes a semi-empirical model of an ORC system, involving a relatively limited number of parameters. The compari-
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son between predicted values and experimental results shows a fairly good agreement (for the cycle model as well as for the different sub-models). The experimental study carried out shows a promising expander isentropic effectiveness and demonstrates the viability of utilizing a mass-produced compressor as an expander in a small scale ORC. This represents an important step towards achieving the cost reductions that would make a kilowatts-sized ORC economical. However, the use of a hermetic expander could at least address two drawbacks encountered with the investigated open-drive expander: the refrigerant release to the ambient (a hermetic machine is fully tight) and the low volumetric performances (a hermetic machine is characterized by smaller operating plays between the moving parts [30]). Moreover, a hermetic machine could be more convenient for applications requiring electricity and not mechanical power as the energy output, since it is equipped with a generator nestled in the expander shell [12]. Limitation of the overall cycle efficiency is partly explained by the low temperature of the heat source and by the low pump efficiency. The former can be rectified by using higher temperature heat sources, while the latter can be addressed by selecting of a pump optimized for the pressure ratio and mass flow rate ranges of the ORC. Optimization of the working conditions is also needed in order to reduce the expander supply superheating and the condenser exhaust subcooling. Cycle improvements are easy to simulate with the proposed model. Simulation can also be used to identify an optimal control strategy, to evaluate new configurations and to compare the performance achieved with different working fluids. References [1] Hung TC, Shai TY, Wang SK. A review of organic Rankine cycles (ORCs) for the recovery of low-grade waste heat. Energy 1997;22:661–7. [2] Gnutek Z, Bryszewska-Mazurek A. The thermodynamic analysis of multicycle ORC engine. Energy 2001;26:1075–82. [3] Larjola J. Electricity from industrial waste heat using high-speed organic Rankine cycle (ORC). Int J Prod Econ 1995;41:227–35. [4] Kane El H. Intégration et optimisation thermoéconomique and environomique de centrales thermiques solaires hybrides. PhD Thesis, Laboratoire d’Energétique Industrielle, Ecole polytechnique Fédérale de Lausanne, Suisse; 2002. [5] Manolakosa D, Papadakisa G, Kyritsisa S, Bouzianasb K. Experimental evaluation of an autonomous low-temperature solar Rankine cycle system for reverse osmosis desalination. Desalination 2007;203:366–74. [6] Schuster A, Karellas S, Kakaras E, Spliethoff H. Energetic and economic investigation of organic Rankine Cycle applications. Appl Therm Eng 2009;29:1809–17. [7] Aoun B, Clodic D. Theoretical and experimental study of an oil-free scroll type vapor expander. In: Proc. the 19th Int. compressor engineering conference at Purdue, paper 1188; 2008. [8] Kanoglu Mehmet. Exergy analysis of a dual-level binary geothermal power plant. Geothermics 2002;31:709–24. [9] Patel PS, Doyle EF, Compounding the truck diesel engine with an organic Rankine cycle system. SAE publication 760343; 1976. [10] Talbi M, Agnew B. Energy recovery from diesel engine exhaust gases for performance enhancement and air conditioning. Appl Therm Eng 2002;22:693–702. [11] Endo T, Kawajiri S, Kojima Y, Takahashi K, Baba T, Ibaraki S, et al. Study on maximizing exergy in automotive engines. SAE World Congress; 2007. [12] Zanelli R, Favrat D. Experimental investigation of a hermetic scroll expandergenerator. In: Proc. the Int. compressor engineering conference at Purdue; 1994. p. 459–464. [13] Peterson RB, Wang H, Herron T. Performance of a small-scale regenerative Rankine power cycle employing a scroll expander. Proc. IMechE. Part A: J Power Energy 2008;vol. 222:271–82. [14] Yanagisawa T, Fukuta Y, Ogi T, Hikichi T. Performance of an oil-free scroll-type air expander. In: Proc. the ImechE Conf. Trans. on compressors and their systems; 2001. p. 167–174. [15] Kane M, Larrain D, Favrat D, Allani Y. Small hybrid solar power system. Energy 2003;28:1427–43. [16] Hung T-C. Waste heat recovery of organic Rankine cycle using dry fluids. Energy Convers Manage 2001;42:539–53. [17] Liu B-T, Chien K-H, Wang C-C. Effect of working fluids on organic Rankine cycle for waste heat recovery. Energy 2004;29:1207–17.
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[25] Winandy E, Saavedra C, Lebrun J. Experimental analysis and simplified modelling of a hermetic scroll refrigeration compressor. Appl Therm Eng 2002;22:107–20. [26] Muley A, Manglik RM. Experimental study of turbulent flow heat transfer and pressure drop in a plate heat exchanger with chevron plates. J Heat Trans, ASME 1999;121:110–7. [27] Hsieh YY, Lin TF. Saturated flow boiling heat transfer and pressure drop of refrigerant R410a in a vertical plate heat exchanger. Int J Heat Mass Trans 2002;45:033–1044. [28] Kuo WS, Lie YM, Hsieh YY, Lin TF. Condensation heat transfer and pressure drop of refrigerant R410a flow in a vertical plate heat exchanger. Int J Heat Mass Trans 2005;48:5205–20. [29] Yamamoto T, Furuhata T, Arai N, Mori K. Design and testing of the organic Rankine cycle. Energy 2001;26:239–51. [30] Lemort V. Contribution to the characterization of scroll machines in compressor and expander modes. PhD Thesis, Université de Liège, Belgique; 2008.
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Experimental study and modeling of an Organic Rankine Cycle using scroll expander Sylvain Quoilin *, Vincent Lemort, Jean Lebrun Thermodynamics Laboratory, University of Liège, Campus du Sart Tilman, B49, B-4000 Liège, Belgium
a r t i c l e
i n f o
Article history: Received 21 January 2009 Received in revised form 8 June 2009 Accepted 15 June 2009 Available online 6 August 2009 Keywords: Organic Rankine Cycle (ORC) Scroll expander Waste heat recovery Power generation
a b s t r a c t This paper presents both a numerical model of an Organic Rankine Cycle (ORC) and an experimental study carried out on a prototype working with refrigerant HCFC-123, and whose heat sources consist in two hot air flows. The ORC model is built by interconnecting different sub-models: the heat exchanger models, a volumetric pump model and a scroll expander model. Measured performance of the ORC prototype is presented and used to validate the ORC model. This model is finally used to investigate potential improvements of the prototype. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The interest for low grade heat recovery grew dramatically in the past decades. An important number of new solutions have been proposed to generate electricity from low temperature heat sources and are now applied to much diversified fields such as solar thermal power, biological waste heat, engine exhaust gases, domestic boilers, etc. Among the proposed solutions, the Organic Rankine Cycle (ORC) system is the most widely used. Its two main advantages are the simplicity and the availability of its components. In such a system, the working fluid is an organic component, better adapted than water to lower heat source temperatures. Unlike with traditional power cycles, local and small scale power generation is made possible by this technology. A wide range of ORC applications have been investigated in previous works, such as waste heat recovery [1–3], solar energy use [4,5], combined heat and power [6,7], geothermal systems [8], or engine exhaust gases [9–11]. Experimental studies of small scale ORC units demonstrated that the scroll expander is a good candidate for small scale power generation, because of its reduced number of moving parts, reliability, wide output power range, and broad availability [12]. Isentropic effectiveness’s ranging from 48% to 65% were reported, depending on the design of the scroll expander [4,5,7,13,14]. The study of a superposed ORC cycle proposed by Kane et al. [15] is of particular interest, since it uses a technology similar to the one proposed in the present work (selection of HCFC-123 as one of the two working fluids and use of scroll expanders). The flu* Corresponding author. Tel.: +32 4 366 48 22; fax: +32 4 366 48 12. E-mail address: [email protected] (S. Quoilin). 0306-2619/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2009.06.026
ids of the bottoming and of the topping cycles were selected to optimize the overall performance, with a maximum heat source temperature of 165 °C. A net efficiency of 12% was reached. Previous studies also showed the influence of the working fluid thermodynamic properties on the ORC performances [16–21]. On the other hand, only few papers present detailed simulation models of the ORC accounting for the characteristics of each component of the cycle: Kane [4] proposed a semi-empirical model of a small scale ORC with 3-zones heat exchangers, and a scroll expander model accounting for friction losses, intake throttling and internal leakage. Wei et al. [22] proposed a dynamic model of a 100 KWe ORC, focusing mainly on the heat exchangers and using empirical laws for the pump and for the expander. These ORC simulation models are very useful to optimize the operating conditions and the components of the cycle. The first part of this paper describes the simulation model of an ORC system. This model is built by interconnecting the sub-models of the different components: the heat exchangers, the pump and the expander. In the second part, the results of an experimental study are presented: this study aimed at evaluating the performance of an ORC working with refrigerant HCFC-123 and using a scroll expander. The above models are validated experimentally. The last part of the paper investigates, through simulations, the performance of the system and points out some achievable improvements.
2. ORC modeling This section describes the models of the different components of the ORC system under investigation. The modeling approach
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Nomenclature A AU b Bo C Co Cp d Dh k Fr G g h h ifg L _ M N Np Nu p Pr Q_ q r Re s t T v V
area, m2 heat transfer conductance, W/K corrugation depth, m boiling number, Bo = q/Gifg constant convective number, Co ¼ qg =ql ðð1 xÞ=xÞ0:8 specific heat, J/(kg K) diameter, m hydraulic diameter, Dh = 2b, m thermal conductivity, W/(mK) Froude number, Fr = G2/q2gDh 2 _ mass flux, G ¼ M=ððN p 2Þ b WÞ, kg/(m s) acceleration due to gravity, m/s2 convective heat transfer coefficient, W/(m2 K) specific enthalpy, J/kg enthalpy of vaporization, J/kg plate length, from center of inlet port to center of exit port, m mass flow rate, kg/s rotational speed, rpm number of plates Nusselt number, Nu = hDh/k pressure, Pa Prandtl number, Pr = lCp/k heat transfer rate, W heat flux, W/m2 ratio _ Dh Þ=ððNp 2Þ b W lÞ Reynolds number, Re ¼ ðM specific entropy, J/(kg K) temperature, C torque, N m specific volume, m3/kg volume, m3
consists in developing semi-empirical models, instead of deterministic models. Semi-empirical models involve a limited number of physically meaningful parameters that can be easily identified from performance measurements, while deterministic models require an exact knowledge of the geometry of all the components. Semi-empirical models are usually more numerically robust than deterministic models and allow a sharp decrease of the computational time. Therefore, they are more appropriate to be interconnected in such a way to build a simulation model of a larger system. A volumetric pump and a scroll expander models are considered since they are the technologies selected for the ORC prototype presented in this paper. All the models proposed in this section were developed under EES environment [23].
V_ _ W W x X
volume flow rate, m3/s power, W plate width, m vapor quality pump capacity fraction
Greek letters D differential e effectiveness q density, kg/m3 Subscripts amb ambient calc calculated ev evaporator ex exhaust exp expander f working fluid in internal leak leakage loss mechanical losses meas measured n nominal pp pump pred predicted r refrigerant s isentropic, swept sh shaft sf secondary fluid su supply tp two-phase v vapor, volume
_ in is the differAs shown in Eq. (1), the internal mass flow rate M _ entering the expander and the ence between the mass flow rate M _ leak . The internal mass flow rate is the volleakage mass flow rate M ume flow rate V_ s;exp divided by the specific volume of the fluid vr,su,2 after entering cooling-down and pressure drop. The volume flow rate is defined as the product of the swept volume V s;exp with the expander rotational speed Nexp. The swept volume in expander mode is equal to the one in compression mode V s;cp divided by the built-in volume ratio of the machine rv.
2.1. Scroll expander model The scroll expander model was previously proposed and validated by the authors [24]. In this model, the evolution of the refrigerant through the expander is decomposed into the following steps (as shown in Fig. 1): Supply pressure drop (su ? su,1). Supply cooling-down (su,1 ? su,2). Isentropic expansion to the internal pressure imposed by the built-in volume ratio of the expander (su,2 ? in). Expansion at a fixed volume to the exhaust pressure (in ? ex,2). Mixing between suction flow and leakage flow (ex,2 ? ex,1). Exhaust cooling-down or heating-up (ex,1 ? ex).
Fig. 1. Conceptual scheme of the expander model.
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_ _ in ¼ M _ M _ leak ¼ V s;exp ¼ Nexp V s;exp ¼ N exp : V s;cp M mr;su;2 60 mr;su;2 60 mr;su;2 rm
ð1Þ
The leakage mass flow rate can be computed by reference to the flow through a simply convergent nozzle. The fictitious leakage area Aleak is assimilated to the nozzle throat area and must be experimentally identified. In the same manner as for the leakage mass flow rate, the pressure drop is computed by reference to the flow through a simply convergent nozzle, whose throat diameter is the equivalent supply port diameter dsu. _ in is obtained by multiplying The internal expansion power W the internal work win by the internal mass flow rate. This internal work is the sum of the internal work win,s associated to the isentropic part of the expansion and the internal work win,v associated to the isochoric evolution. In Eq. (2), hr,in, vr,in and Pin are, respectively, the specific enthalpy, the specific volume and the pressure of the fluid at the end of the isentropic part of the expansion. The specific volume is the product of the built-in volume ratio rv with the specific volume vr,su,2.
_ in ¼ M _ in win ¼ M _ in ðwin;s þ win;v Þ W _ in ððhr;su;2 hr;in Þ þ v r;in ðPin P ex ÞÞ ¼M _ in ððhr;su;2 hr;in Þ þ r v v r;su;2 ðPin Pex ÞÞ ¼M
ð3Þ
A fictitious envelope of uniform temperature Tw is assumed to be sufficient to represent the three heat transfer modes. Tw is determined by establishing a steady-state heat balance on this envelope, as proposed by Winandy et al. [25]:
_ loss Q_ ex þ Q_ su Q_ amb ¼ 0 W
ð4Þ
Supply and exhaust heat transfers are described by introducing fictitious semi-isothermal heat exchangers characterized by global heat transfer conductances AUsu and AUex [24]. The latter can be correlated to the refrigerant mass flow rate according to the following law:
AU su ¼ AU su;n ex
ex;n
_ M _ Mn
1 1 1 ¼ þ U hr hsf
ð6Þ
The respective heat transfer area of each zone is obtained by imposing the total heat transfer area of the heat exchanger:
Al þ Atp þ Av ¼ ðN p 2Þ L W
2.2.1. Single-phase heat transfer coefficient Forced convection heat transfer coefficients are evaluated by means of the non-dimensional relationship:
ð8Þ
where the influence of temperature-dependent viscosity is neglected. The exponents m and n are set according to Muley’s recommendations for corrugated plate heat exchangers with a 30° Chevron angle [26]: m = 0.5 for the laminar regime (Re < 400), and m = 0.7 for the turbulent regime (Re > 400). In all cases, n = 1/3. The coefficient C is identified with experimental data, by minimizing the difference between predicted and measured values for a set of working points. Because of the large differences between Reynolds numbers, this coefficient is assigned specific values for the vapor and liquid zones on the refrigerant side and for the air and water sides. 2.2.2. Boiling heat transfer coefficient The overall boiling heat transfer coefficient is estimated by the Hsieh correlation [27], established for the boiling of refrigerant R410a in a vertical plate heat exchanger. This heat exchange coefficient is considered as constant during the whole evaporation process and is calculated by:
htp ¼ C hl Bo0:5
!0:8 ð5Þ
2.2. Condenser and evaporator models The condenser and the evaporator are modeled by means of the e-NTU method for counter-flow heat exchangers. The heat exchanger is subdivided into three zones, each of them being character-
ð7Þ
In the present work, the pressure drops are neglected in both the condenser and the evaporator models, since no accurate differential pressure sensors were installed on the heat exchangers in the experimental study. These pressure drops were however very limited. For other fluids and/or other heat exchangers leading to higher pressure drops, a pressure drop model should be included.
Nu ¼ C Rem Prn ð2Þ
The expander mechanical power can be split into the internal _ loss . These losses expansion power and the mechanical losses W can be expressed as a function of a mechanical losses torque Tm and the rotational speed of the expander. The expander mechanical power is given by
_ sh ¼ W _ in W _ loss ¼ W _ in 2 p Nrot T m W
ized by a heat transfer area A and a heat transfer coefficient U. The zone definition is shown in Fig. 2, in the case of the evaporator. The heat transfer coefficient U is calculated by considering two convective heat transfer resistances in series (secondary fluid and refrigerant sides).
ð9Þ
Where Bo is the boiling number and hl is the all-liquid non-boiling heat transfer coefficient. As for the single phase heat transfer coefficient, C is identified experimentally. 2.2.3. Condensation heat transfer coefficient The condensation heat transfer coefficient is estimated by the Kuo correlation [28] (Eq. (10)), established in the case of a vertical plate heat exchanger fed with R410A.
htp ¼ C hl ð0:25 Co0:45 Fr0:25 þ 75 Bo0:75 Þ l
ð10Þ
where Frl is the Froude number in saturated liquid state, Bo the boiling number and Co the convection number. The heat transfer coefficient correlation is quality-dependant. In this modeling, an average heat transfer coefficient is considered. For this reason, the two-phase heat transfer correlations are integrated using the following equation:
htp ¼ Fig. 2. Three-zone modeling of the evaporator.
1 L2 L1
Z
L2
L1
htp dL
ð11Þ
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Assuming that vapor quality variation is linear with length, the average heat transfer coefficient is calculated by:
htp ¼
Z
1
htp dx
ð12Þ
0
2.3. Pump model The pump is characterized by its swept volume and its global isentropic efficiency (gpp). The latter is assumed constant. The pump electrical consumption is given by:
_ _ el;pp ¼ W pp;s W
ð13Þ
gpp
The mass flow rate displaced by the pump is computed as a function of its capacity fraction Xpp by:
_ _ r ¼ V s;pp ¼ X pp V s;pp;max M
v r;su;pp
v r;su;pp
ð14Þ
The capacity fraction Xpp is defined as the ratio between the actual volume flow rate and the maximum volume flow rate of the pump. This variable is an input of the model; it is actually tuned by modifying the swept volume of the pump or its rotating speed.
Fig. 4. Information diagram of the ORC simulation model.
and the cycle efficiency. The parameters to identify with experimental data are indicated in bold. All other parameters are measured or imposed. 3. Experimental study 3.1. Test bench description
2.4. Global model The global model of the cycle is built by interconnecting the models of the different sub-components described above, as shown in Fig. 3. The modeling highlights the following constraints: (a) For a given displacement, the pump imposes the refrigerant mass flow rate. (b) The evaporator imposes the fluid superheating and the pump exhaust pressure. (c) Provided its rotational speed is fixed, the expander imposes the evaporator exhaust pressure. (d) For given secondary fluid mass flow rate and supply temperature, the condenser imposes the pressures at expander exhaust and pump supply (if a description of the refrigerant pressure drop is included in the modeling). This simulation model is not fully predictive, because the liquid subcooling at the condenser exhaust is defined as a model input. In order to predict this subcooling, a refrigerant charge model should be introduced. The information diagram of the Rankine cycle simulation model is given in Fig. 4. The inputs of the model are the mass flow rates and supply temperatures of the secondary fluids in the evaporator and in the condenser, the capacity fraction of the pump and its rotational speed. The main outputs are the expander shaft power
An experimental study was carried out on a prototype of ORC working with HCFC-123. A schematic representation of the test bench is given in Fig. 5. The scroll expander was originally an oilfree open-drive scroll compressor, adapted to operate in reverse. It drives an asynchronous machine through two belt-pulleys couplings and a torque meter. The latter is used to measure the expander shaft power. The heat source consists of a set of three heat exchangers supplied with two hot air flows. The condenser is cooled by water. A diaphragm piston-type pump drives the liquid fluid from the condenser exhaust to the boiler supply. A pulse damper is installed before the Coriolis flow meter in order to attenuate the flow rate fluctuations generated by the volumetric pump. 3.2. Achieved performances In total, 39 steady-state performance points were achieved, by combining the operating parameters listed in Table 1. Three performance indicators are taken into account: the expander shaft power, the expander isentropic effectiveness, and the cycle efficiency. The expander overall isentropic effectiveness is defined by:
_ W
sh es ¼ _ M r ðhr;su;exp hr;ex;exp;s Þ
And the cycle efficiency by:
Fig. 3. Block diagram of the global model of the cycle.
ð15Þ
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Fig. 5. Schematic representation of the test bench.
Table 1 Range of achieved operating conditions. Working condition
Minimum value
Maximum value
First hot air source mean temperature Second hot air source mean temperature Air mass flow rate Refrigerant mass flow rate Condenser water volume flow rate Condenser mean water temperature Expander rotation speed
53.4 °C 101.0 °C 0.071 kg/s 45 g/s 0.13 l/s 13.2 °C 1771 rpm
86.4 °C 163.2 °C 0.90 kg/s 86 g/s 0.70 l/s 15.0 °C 2660 rpm
some other working conditions, such as pressure and temperature levels. The cycle efficiency is mainly limited by a low pump efficiency (about 15%) and by a very high net positive suction head (NPSH), which constrained the tests to a large subcooling at the condenser exhaust (between 20 and 44 K). 4. Verification of the rankine cycle model 4.1. Expander model validation
gcycle ¼
_ sh W _ pp W Q_ evap
ð16Þ
As shown in Fig. 6, an expander isentropic effectiveness ranging from 42% to 68% is reached, corresponding to a maximum cycle efficiency of 7.4%. The pressure ratio over the expander varies from 2.7 to 5.4 and has obviously a clear influence on the system performance. Error bars account for measurement uncertainties. The efficiency curves plotted as a function of the pressure ratio show several irregularities, which is explained by the effects of
The parameters of the expander model are tuned to best fit the three model outputs (supply pressure, exhaust temperature, shaft power) to experimental data. The input variables of this calculation are: the expander rotational speed, the refrigerant mass flow rate, the supply temperature and the exhaust pressure. The parameters of the expander model are identified by minimizing an error-objective function F (using a genetic algorithm) defined as a weighted sum of the errors for each output:
F¼
39 h X
F 1 ðT r;ex; exp ;meas T r;ex; exp ;pred Þ2i
i¼1
þF 2
pr;su; exp ;meas pr;su; exp ;pred pr;su; exp ;meas
!2 þ F3 i
_ sh;meas W _ sh;pred W _ sh;meas W
!2 3 5 i
ð17Þ The weighting factors F1, F2, and F3 are pffiffiffiffiffiffichosen to give each pffiffiffi term the same approximate weight: F 1 ¼ 1= 60; F 2 ¼ 1; F 3 ¼ 1= 2. Comparisons between the prediction by the model and the measurements for the exhaust temperature and the output power are given in Fig. 7. The maximum deviations between the measurements and the predictions by the model are 3 K for the temperature and 6% for the shaft power. 4.2. Heat exchanger model validation
Fig. 6. Measured performance vs. pressure ratio.
The parameters of the condenser and of the evaporator are identified by imposing some measurements as input variables and by minimizing the deviation between the measured and predicted output variables.
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For given refrigerant supply temperature and exhaust subcooling, the condenser model predicts the condensing pressure. Fig. 8a shows that this pressure is predicted with a relative error of about 3%. For given refrigerant supply temperature and saturation pressure, the evaporator model predicts the heat flow rate and the exhaust temperature. Fig. 8b shows that the exhaust temperature is predicted with a maximum absolute error of 7 K, which corresponds to an error of 2.5% in the prediction of the heat flux. All the identified parameters are listed in Table 2. It can be observed that the identified single phase heat exchange coefficients C are very different. This is explained by the simplified modeling approach: the identified correlations not only account for the heat exchange, but also for pressure drops and ambient heat losses (mainly in the evaporator). This leads for example to a very low Cv in the evaporator because the vapor undergoes high ambient heat losses at that point. 4.3. Validation of the global model of the cycle Given all the parameters listed in Table 2, the predicted expander shaft power is compared to the measured one. Fig. 9 shows that all measurements are predicted within 10%. The error is higher for the global cycle model because of the cumulated subcomponent models inaccuracies. 5. Simulation and optimization
Fig. 7. Predicted vs. measured expander model outputs.
Fig. 8. Predicted vs. measured condenser and evaporator outputs.
This section illustrates how the cycle simulation model established and validated in the previous sections can be used in order to optimize the working conditions of the system. The increase of the system performance following this optimization is evaluated hereafter for one of the 39 measured performance points, characPex,exp = 1.84 105 Pa, terized by Psu,exp = 7.91 105 Pa, Tsu,exp = 133 °C and Nexp = 2660 rpm. Fig. 10 shows the T-s diagram for this working point, with superposition of the secondary fluids temperature profiles. Large vapor superheating at the evaporator exhaust and liquid subcooling at the condenser exhaust are observed. A first improvement consists in reducing the liquid subcooling. In the present case, this subcooling is reduced from 27 K (measured value) down to 5 K. The increase in performance can be explained by the location of the pinch point at the condenser exhaust (on the refrigerant side), which prevents the condensing pressure to be lowered. A second improvement is the selection of a more efficient pump. The effectiveness of the pump installed on test bench is 15%. A higher effectiveness should obviously be achieved. A pump effectiveness of 60% is assumed in this simulation. The third parameter to be optimized is the evaporator exhaust superheating. Yamamoto et al. [29] showed that for a working fluid with a low latent heat such as HCFC-123, the saturated vapor at the turbine supply would give the best performance. This can be achieved in two ways, as shown in Fig. 11: 1. Modification of the pump flow rate: Increasing the fluid mass flow rate will lead to a higher pressure at the expander supply, since the latter has to ‘‘increase” the density of the fluid to absorb the total amount of mass flow rate imposed by the pump. Increasing the pressure will lead to a higher evaporation temperature and hence to a lower temperature difference between the two heat sources. The mean logarithmic temperature difference being smaller, the heat flow rate across the evaporator will be reduced and the superheating will be reduced. Fig. 12 gives the evolution of the cycle efficiency and of the expander effectiveness with the flow rate, and shows that a higher flow rate indeed increases the performance.
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Table 2 Summary of the cycle model parameters. Expander
Condenser
Evaporator
Pump
AUamb = 6.38 W/K
Num ¼ 0:84 Re
AUsu = 21.22 W/K
Nuw ¼ 0:72 Re0:7 Pr1=3
Nul ¼ 1:29 Re0:5 Pr1=3
AUex = 34.2 W/K
Nul ¼ 0:4 Re0:5 Pr1=3
Nua ¼ 0:101 Re0:7 Pr1=3
dsu = 0.00591 m
htp ¼ 1:98 hl Bo0:5
htp ¼ 23:7 hl ð75 Bo0:75 þ 0:25 Co0:45 Fr0:25 Þ l
0:7
Pr
1=3
Num ¼ 0:063 Re
0:7
Pr
1=3
gpp = 15% V_ s;pp;max ¼ 58 cm3 =s
Tloss = 0.4067 N m Aleak = 4.858 mm2 rv = 4.005 Vs = 36.39 cm3
Fig. 9. Predicted vs. measured output power with the global model.
Fig. 12. Cycle efficiency and expander effectiveness vs. flow rate.
2. Modification of the expander rotational speed: If the expander rotational speed is decreased, its volumetric flow rate absorbed is decreased, and, for a given mass flow rate, the pressure is increased. Fig. 13 shows that lowering the expander speed indeed increases the performance, but only until a certain point (around 2000 rpm), where the expander effectiveness is reduced to a prohibitive value because of internal leakage.
Fig. 10. T-s diagram and secondary fluid temperatures.
Fig. 11. Required flow rate and speed to achieve a given superheating.
Therefore, reducing the expander rotational speed and increasing the pump mass flow rate both have a similar effect: they yield a higher evaporating pressure and a reduced superheating. Since the reduction of the superheating can be achieved in two ways, it is important to determine which combination of mass flow rate/rotational speed optimizes the cycle’s performance. The following observations should be taken into account while trying to optimize the working conditions:
Fig. 13. Cycle efficiency and expander effectiveness vs. speed.
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Fig. 14. Cycle efficiency for given working conditions.
Fig. 15. T-s diagram and secondary fluid temperatures.
A higher mass flow rate increases the heat transfer in the evaporator and thus the output power (at constant cycle efficiency). There exists a rotational speed that maximizes the expander effectiveness. This is due to the antagonist effects of the rotational speed on the internal leakages and on friction losses and supply pressure drop. A higher pressure in the evaporator may decrease the heat transfer (because of the lower logarithmic mean temperature difference), and increase the under-expansion losses in the expander. In order to determine the optimal working condition, a map of the cycle efficiency is drawn in Fig. 14: the cycle efficiency is plotted as a function of the two working conditions. Each gray cross in the background represent one point calculated by the model and used to establish the isometric curves. These curves should only be read in the area defined by the crosses. The lower right part of the map corresponding to high mass flow rate and low rotational speed is undefined, because superheating is reduced to zero, which would correspond to a two-phase state at the evaporator exhaust. Fig. 14 shows that an optimum working point is obtained around a value of 0.9 kg/s and 2300 rpm. The T-s diagram of this new, optimized working point is presented in Fig. 15. This new cycle is much closer to the theoretical Carnot cycle than the original cycle. Its efficiency has been increased from 5.1% to 9.9%. 6. Conclusions This paper proposes a semi-empirical model of an ORC system, involving a relatively limited number of parameters. The compari-
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son between predicted values and experimental results shows a fairly good agreement (for the cycle model as well as for the different sub-models). The experimental study carried out shows a promising expander isentropic effectiveness and demonstrates the viability of utilizing a mass-produced compressor as an expander in a small scale ORC. This represents an important step towards achieving the cost reductions that would make a kilowatts-sized ORC economical. However, the use of a hermetic expander could at least address two drawbacks encountered with the investigated open-drive expander: the refrigerant release to the ambient (a hermetic machine is fully tight) and the low volumetric performances (a hermetic machine is characterized by smaller operating plays between the moving parts [30]). Moreover, a hermetic machine could be more convenient for applications requiring electricity and not mechanical power as the energy output, since it is equipped with a generator nestled in the expander shell [12]. Limitation of the overall cycle efficiency is partly explained by the low temperature of the heat source and by the low pump efficiency. The former can be rectified by using higher temperature heat sources, while the latter can be addressed by selecting of a pump optimized for the pressure ratio and mass flow rate ranges of the ORC. Optimization of the working conditions is also needed in order to reduce the expander supply superheating and the condenser exhaust subcooling. Cycle improvements are easy to simulate with the proposed model. Simulation can also be used to identify an optimal control strategy, to evaluate new configurations and to compare the performance achieved with different working fluids. References [1] Hung TC, Shai TY, Wang SK. A review of organic Rankine cycles (ORCs) for the recovery of low-grade waste heat. Energy 1997;22:661–7. [2] Gnutek Z, Bryszewska-Mazurek A. The thermodynamic analysis of multicycle ORC engine. Energy 2001;26:1075–82. [3] Larjola J. Electricity from industrial waste heat using high-speed organic Rankine cycle (ORC). Int J Prod Econ 1995;41:227–35. [4] Kane El H. Intégration et optimisation thermoéconomique and environomique de centrales thermiques solaires hybrides. PhD Thesis, Laboratoire d’Energétique Industrielle, Ecole polytechnique Fédérale de Lausanne, Suisse; 2002. [5] Manolakosa D, Papadakisa G, Kyritsisa S, Bouzianasb K. Experimental evaluation of an autonomous low-temperature solar Rankine cycle system for reverse osmosis desalination. Desalination 2007;203:366–74. [6] Schuster A, Karellas S, Kakaras E, Spliethoff H. Energetic and economic investigation of organic Rankine Cycle applications. Appl Therm Eng 2009;29:1809–17. [7] Aoun B, Clodic D. Theoretical and experimental study of an oil-free scroll type vapor expander. In: Proc. the 19th Int. compressor engineering conference at Purdue, paper 1188; 2008. [8] Kanoglu Mehmet. Exergy analysis of a dual-level binary geothermal power plant. Geothermics 2002;31:709–24. [9] Patel PS, Doyle EF, Compounding the truck diesel engine with an organic Rankine cycle system. SAE publication 760343; 1976. [10] Talbi M, Agnew B. Energy recovery from diesel engine exhaust gases for performance enhancement and air conditioning. Appl Therm Eng 2002;22:693–702. [11] Endo T, Kawajiri S, Kojima Y, Takahashi K, Baba T, Ibaraki S, et al. Study on maximizing exergy in automotive engines. SAE World Congress; 2007. [12] Zanelli R, Favrat D. Experimental investigation of a hermetic scroll expandergenerator. In: Proc. the Int. compressor engineering conference at Purdue; 1994. p. 459–464. [13] Peterson RB, Wang H, Herron T. Performance of a small-scale regenerative Rankine power cycle employing a scroll expander. Proc. IMechE. Part A: J Power Energy 2008;vol. 222:271–82. [14] Yanagisawa T, Fukuta Y, Ogi T, Hikichi T. Performance of an oil-free scroll-type air expander. In: Proc. the ImechE Conf. Trans. on compressors and their systems; 2001. p. 167–174. [15] Kane M, Larrain D, Favrat D, Allani Y. Small hybrid solar power system. Energy 2003;28:1427–43. [16] Hung T-C. Waste heat recovery of organic Rankine cycle using dry fluids. Energy Convers Manage 2001;42:539–53. [17] Liu B-T, Chien K-H, Wang C-C. Effect of working fluids on organic Rankine cycle for waste heat recovery. Energy 2004;29:1207–17.
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