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Performance of an Organic Rankine Cycle with two expanders at off-design operation
Applied Thermal Engineering 149 (2019) 688–701
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Research Paper
Performance of an Organic Rankine Cycle with two expanders at off-design operation
T
Mercedes Ibarraa,b, , Antonio Rovirab, Diego-César Alarcón-Padillac ⁎
a
Fraunhofer Chile Research, Center for Solar Energy Technologies, Vicuña Mackenna 4860, Santiago, Chile Universidad Nacional de Educación a Distancia (UNED), C/Juan del Rosal 12, 28040 Madrid, Spain c CIEMAT-Plataforma Solar de Almería, Ctra. de Senés s/n, 04200 Tabernas, Almería, Spain b
HIGHLIGHTS
ORC system with two expanders in series at off-design operation is simulated. • An efficiency reached with two expanders was higher than the achieved with one. • Thermal pressure affects more than the volume expansion ratio of the expander. • Intermediate performance of the first expander was mainly affected by leaks. • The • The performance of the second one was more affected by the discharged pressure. ARTICLE INFO
ABSTRACT
Keywords: ORC Scroll expander Simulation Two expanders Exergy analysis
The objective of this work was to simulate the behavior of an Organic Rankine Cycle (ORC) system with two expanders in series at off-design working conditions. The influence of both the intermediate pressure and the volumetric expansion ratio of the expanders on the off-design performance of the ORC was studied and the irreversibilities of the components were analyzed. The performance of the ORC with two expanders for two different designs was also discussed. The thermal efficiency reached using two expanders was higher than the obtained using only one. However, this increase conveyed an increase in the complexity of the design and control of the expanders. As an additional conclusion, it was found that the influence of the intermediate pressure is higher than that of the volume expansion ratio of each expander. The irreversibility of the first expander was mainly due to leaks. However, the performance of the second expander was particularly affected by the difference between the discharged pressure and the condensation pressure. The off-design analysis allowed the definition of a methodology to achieve the desired power with the maximum thermal efficiency, and the identification of the best actuation for the part load operation.
1. Introduction Organic Rankine Cycle (ORC) systems are a good alternative for energy generation from low grade thermal energy. The source could be either renewable or waste thermal energy from industrial or power generation processes. As it is well known, a simple ORC works like a conventional Rankine cycle but it uses an organic fluid instead of water. The use of organic fluids allows low working temperatures as well as simple facilities because the expander exhaust vapor is still dry after the expansion process. One of the challenges of this technology is the selection of the type
⁎
of expander. In this regard, volumetric expanders (i.e. scroll, screw, reciprocating or multivane expanders) are more suitable than dynamic ones as they are characterized by low mass flow rates, moderate pressure ratios and low rotation speeds [1,2]. Among the different devices proposed for low power rates, the scroll expander stands out because of its simplicity, cost and the good results obtained by the experimental experiences and prototypes [3–5]. Scroll expanders consist of two spirals, one fixed and one moving. The fluid enters the expander at the center of the spirals, and, when the moving spiral gyrates, the volume of the gap between the spirals increases, allowing the fluid to expand while moving outwards.
Corresponding author at: Fraunhofer Chile Research, Center for Solar Energy Technologies, Vicuña Mackenna 4860, Santiago, Chile. E-mail address: [email protected] (M. Ibarra).
https://doi.org/10.1016/j.applthermaleng.2018.12.083 Received 31 July 2018; Received in revised form 21 November 2018; Accepted 13 December 2018 Available online 14 December 2018 1359-4311/ © 2018 Published by Elsevier Ltd.
Applied Thermal Engineering 149 (2019) 688–701
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Nomenclature
Aleak, i Esource K P hi I Icond Irec Iexp, i Iploss ISG Ipump Ileak, i Iexp(over
Imix, i
mtot Ni P Pi (1
Pcond Pevap
Pint Pint , gm Pint, max Pint, min
leakage area of expander i (m2 ) energy from the source (kW) pressure loss coefficient (–) enthalpy of the fluid at the point i of the thermal cycle (kJ/kW) irreversibility (kW) irreversibility in the condenser (kW) irreversibility in the recuperator (kW) irreversibility in the expander i (kW) irreversibility due to evaporator pressure loss (kW) irreversibility in the evaporation (kW) irreversibility in the pump (kW) irreversibility in the expander i due to leakeages (kW) irreversibility in the expander i due to over- and , under ), i under-expansion (kW) irreversibility in the expander i due to mixture of all the flows (kW) massic flow rate (kg/s) rotation speed of expander i (min 1) pressure (kPa) 11) pressure of the fluid at the point i of the thermal cycle (kPa) condensation pressure (kPa) evaporation pressure (kPa)
T Tevap Tcond Thigh Tmax Tmin UAhex, i Vswept , i VR WORC, net Wtot Wexp, i Wpump i exp, i exp, glob pump rec
However, scroll expanders have also some technical limitations such as fixed geometry, over and sub-expansion, leaks and friction between the scrolls. As their geometry is fixed, they have a fixed swept volume (Vswept ) and an internal built-in volume ratio (VR). Often, scroll expanders used in ORC are modified scroll compressors, whose swept volume is limited, as well as their VR. Usually, the value of this last parameter is not greater than 5:1 (1.5–3.5:1 for scrolls that come from the refrigeration industry, and 4:1 for those from air compressors), while ORC operate at much greater expansion ratios [6]. To solve this problem, a few solutions have been proposed by several authors. One approach is to design the scroll as an expander from the beginning, adapting it to the ORC requirements. Clemente et al. [7] modelled a scroll expander with large scrolls to increase the VR. Orosz et al. [8] also presented a modified geometry of a scroll expander where the scrolls had variable thickness walls, in order to create more compact geometries and improve the efficiency. Regarding the dynamic expanders, Kang et al. [9] proposed a two-stage radial turbine to improve the performance of the ORC by increasing the pressure ratio. If a new scroll design is not possible, the design of the cycle should be changed to improve the performance. For example, Quoilin et al. [6] proposed the use of two expanders in series in the same cycle, both working in different expansion conditions and having the volumetric ratio adapted to the expansion ratio required by the cycle; however, the authors did not analyze the off-design operation. Ayachi et al. [10] also presented the idea of coupling two or more machines in order to reduce the under-expansion loss, which degraded the efficiency of the ORC they modelled. Kane et al. [11] also proposed the expansion in several stages, but using two ORC in cascade. A cascade ORC consists in two ORC cycles with two different working temperatures, so that the heat dissipated in the condenser of the first cycle is used to evaporate the fluid of the lower temperature cycle. Li et al. [12] also proposed a direct steam generation solar cascade Rankine cycle, to avoid the limitation of the low built-in expansion ratio of the expander, which was a volumetric one, although an screw type. In a similar manner, Rech et al. [13] proposed a two stage ORC with a supercritical high-pressure level, two pumps that operated in parallel and two turbines operating in series.
intermediate pressure (kPa) intermediate pressure equal to the geometry mean (kPa) intermediate pressure that maximizes the efficiency (kPa) intermediate pressure that minimizes the efficiency differences of the expanders (kPa) adapted pressure ratio of expander i (–) temperature (°C) evaporation temperature (°C) condensation temperature (°C) temperature at the outlet of the evaporator (°C) highest temperature of the cycle (°C) lowest temperature of the cycle (°C) heat transfer coefficient of the heat exchanger i (W/K ) swept volume for expander i (m3 ) volume ratio of the expander (–) net power produced by the ORC (kW) total power produced by the ORC (kW) power produced by expander i (kW) power consumed by the pump (kW) density of the fluid at the point i of the thermal cycle (kg/ m3 ) efficiency of the expander i (–) efficiency of the global expansion (both expanders) (–) efficiency of the pump (–) efficiency of the recuperator (–)
They analyzed the off-design performance with a focus on the control of the system. Unfortunately, the authors concluded that the two stage configuration did not result in a stable operation. All of these proposals have also several limitations. For example, geometric modifications of the scroll expanders could increase the manufacturing costs [7]. And up to date there is not any experimental test for ORC with two expanders in series, but only theoretical projects [14,15]. Cascade cycles have only one experimental set up by Kane et al. [11]. Moreover, even if an optimum built-ratio is reached for the design conditions, the differences between the design expansion ratio and the actual expansion ratio at the off-design operating conditions will affect the performance of the expander [16,17]. Ziviani et al. [18] experimentally assessed the performance of an ORC, comparing two fluids (R245fa and SES36) and focusing on the match between the expander (screw) efficiency and the system performance. Their results showed that, when the pressure ratio was maximized, the expander efficiency was higher. They also concluded that the cycle efficiency can be improved by increasing the specific expansion ratio within the expander. In this regard, Yun et al. [19] proposed an ORC with two expanders in parallel, where the operation mode could be changed between single (using one expander) and dual mode (two expanders). As a result of this operation mode, the pressure ratio was increased and the performance of the cycle improved. Wu et al. [20] proposed a single screw expander with slide valves to adjust the built-in ratio so that the expander could be adapted to the changing working conditions. The objective of this work is to analyze the behavior of an ORC system using two expanders in series at off-design operation, and to determine if the benefits of having two expanders in series would be significant. In particular, the objective is the study of how the determination of the design parameters, and specially the intermediate pressure, affects the performance and behavior of the cycle in the offdesign operation. As commented previously, up to date there is not either experimental test for ORC with two expanders in series nor theoretical works considering its part load operation. To achieve the objective, an ORC simulation model developed in a previous work [16] was adapted, introducing some modifications regarding the expansion 689
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model, which is explained in Section 2. Sections 3 and 4 study the influence of the intermediate pressure and the volume expansion ratio of each expander on the off-design performance of the ORC. Finally Section 5 analyzes the performance of the ORC with two expanders for two different designs.
Table 1 ORC design parameters.
Tevap Thigh Tcond Pevap Pcond
2. Description of the numerical model and design parameters To analyze the behavior of an small ORC system with two expanders out of the design conditions, an off-design model must be used. Quoilin et al., Manente et al. and Hu et al. [14,21,22] proposed different offdesign models of an ORC, but they were focused on finding the optimal control strategies. Lecompte et al. [23] also took into account the part load operation of a CHP system using an ORC when optimizing the size of the heat exchanger-staking. Dickens et al. [24] focused on the complexity of heat exchangers modelling, analyzing the influence of heat transfer coefficients and of void fraction on the off-design prediction accuracy of the model for both the heat exchangers and the ORC system. They concluded that a proper estimation of the mass enclosed in the heat exchanger is more important than a slight improvement of the heat transfer predictions. In this work, the model used is based on the one presented in [16] and summarized in the appendix A.
Units
R245fa
°C
124.00
°C kPa
25.00 2080.50
°C
pump
kPa %
rec
%
145.00
147.43 70 80
(evaporation, condensation and the intermediate pressure between the expanders) are other inputs of the model. The first step in the iterative process is to calculate the mass flow rate. For that, the total power produced by the two expanders (Wtot ) is considered as the sum of the produced net power and the power consumed by the pump (Wpump ), which as an initial guess value is considered as a 6% of the net power:
Wtot = WORC, net + Wpump
(1)
In this preliminary iteration, it is assumed that the first expander generates half of the total power, so it is divided between the first and the second one:
2.1. ORC system design
Wexp,1 = Wexp,2 = Wtot /2
The analyzed system (Fig. 1) is a 5 kW ORC with an internal recuperator and two expanders in series, using R245fa as working fluid. The design parameters of the cycle are shown in Table 1.
(2)
The outlet conditions (Pint ) are calculated taking into account four phenomena in the expander: the adiabatic suction, the adiabatic expansion, the sudden expansion at constant volume and the leaks (see appendix A). One of the outlets of this model is also the mass flow rate (mtot,1). The outlet conditions for the second expander are calculated following the same model, but its results are further limited by the assumption that the mass flow rate must be the same for both expanders and the fact that the outlet pressure of the first is the inlet pressure on the last. Thus, the power of the second expander is a result, as well as the outlet conditions of the fluid. Besides, the pump power (Wpump ) is calculated by:
2.2. Description of the on-design simulation model As previously mentioned, the used model is based on the model presented in [16], adapted to the use of two expanders connected in series. It is assumed that both expanders work at the same shaft speed but they have neither the same size nor the same leakage area. Net power production (WORC , net ) is an input value, so the power produced by each expander on-design should be determined, taking also into account the power consumed by the pump. However, this pumping power consumption is defined by the flow rate of the cycle, which is defined by the expanders’ design, so an iterative process is required. Inlet conditions at the first expander and working pressures
Wpump = wpump·mtot
(3)
where wpump is the enthalpy difference between the inlet and outlet of
Fig. 1. Considered ORC with two expander and internal heat exchanger. 690
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the pump: wpump = h2 h1. Next, the net power value is updated:
WORC , net = Wexp,1 + Wexp,2
considering a new total mass flow rate. For the second expander, the adapted pressure is calculated through the volume ratio and the leak mass flow rate through the leakage area; the internal mass flow rate is calculated through the difference between the mass flow rate obtained by the first expander and the leak flow rate. The design volume, calculated through the density of the intermediate state, allows the calculation of the intermediate pressure. This pressure should be equal to that guessed in the previous iteration. Otherwise, it is the new intermediate pressure for the next iteration. Thus, two conditions are required for the iterations to finish: the mass flow rate and the intermediate pressure. Both of them are related each to the other and determine the behaviour of both expanders. The rest of the components of the cycle are calculated as it is described in [16] and summarized in the appendix A.
(4)
Wpump
When the variable WORC , net converges, then the calculation process finishes. Otherwise, Wtot is recalculated using a new value of the mass flow rate. Once the process converges, the on-design calculation finishes and the components of the cycle may be characterized as it is shown in [16] and summarized in the appendix A, i.e. the characterization of each expander ( Aleaks , VR and Vswept ), the characterization of the heat exchangers (UAhex, i ) and the pressure drop coefficient (K P ). 2.3. Description of the off-design simulation model The off-design model allows the calculation of the power production of the expanders, as well as the mass flow rate and intermediate pressure at any part load operation condition. The inputs of the model are the outlet conditions of the evaporator, the condensation pressure, the expanders rotation speed (N) and the characterization of each expander ( Aleaks , VR and Vswept ). As the energy and mass balances can not be explicitly solved, an iteration is required. In a first iteration the mass flow rate is guessed as the design one, which allows the calculation of the pressure drop before the inlet of the first expander:
P7 = P6
mtot · K 6
3. Methodology To analyze the behavior of an ORC system with two expanders in series, the effect of the selected design values of both the intermediate pressure between expanders (Pint ) and the volumetric expansion ratio (VR) on the performance of the ORC system were analyzed. In both cases, a wide range of part load operation was simulated in order to study the variability of the thermal efficiency of the cycle. The combinations of VR considered in this work for the expanders were defined by the total volumetric expansion of the fluid presented in [16], which is 14:1. The values selected were so that the total VR with two expanders was between 8 and 12, which significantly increases that obtained with one single scroll (VR = 5). Each of the VR combinations considered was named with a letter: (A) VR1 = 3, VR2 = 3; (B) VR1 = 4, VR2 = 2 ; (C) VR1 = 2, VR2 = 4 ; (D) VR1 = 3, VR2 = 4 ; (E) VR1 = 4, VR2 = 3. To analyze the influence of the intermediate pressure (Pint ) at the design conditions, Pint was continuously varied for each of the five VR combinations. The resulting design efficiency of each expander ( exp,1, exp,2 ) and the design global expansion efficiency ( exp, glob ) are plotted in Fig. 2, for each VR combination. Three points may be identified for each VR combination, which correspond with the three methods to select the intermediate pressure:
P
(5)
Once the inlet pressure is known, the properties of the fluid can be determined considering that h7 = h6 . The intermediate pressure at the outlet of the first expander and the inlet of the second expander is guessed in this first iteration as the geometric mean between the inlet and the outlet of the expansion pressure.
Pint , i = 1 =
P9· P7
(6)
Then, the mass flow rate and power production of the first expander can be calculated. The internal flow rate is determined through the swept volume, the adapted pressure is calculated through the volume ratio and the leak flow rate through the leakage area, as it is explained in [16]. The sum of the internal flow rate and the leak flow rate must be equal to the total mass flow rate guessed. Otherwise, the model iterates
1. The first option when designing the cycle was to define the Pint value as the geometric mean between the inlet and outlet expansion
Fig. 2. Expander efficiency depending on the design intermediate pressure. 691
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pressure: Pint = Pint , gm . 2. The second option was to select the Pint value as the pressure for which the maximum global expansion efficiency is reached: Pint = Pint, max . 3. The third option was to select as Pint the value that minimizes the difference between the expanders efficiencies: Pint = Pint, min . In cases B and C there are two points where this condition is met and, therefore, an extra cycle is analyzed.
For each VR combination (A, B, C, D, E) the efficiencies reached with every Pint method are plotted, each one in a different color. The statistical summary for the efficiency of each of these cases is also presented in Table 4. To compare the performance of the cycle comprising two expanders to that of only one expander, the results of the work presented in [16] have also been included in Fig. 3 and Table 4, denoted as design R. For case A, the median of A3 (Pint, min ) was the highest (15.11%) and the efficiency distribution was the more compact. A1 (Pint , gm ) and A2 (Pint, max ) distributions were very similar: they reached the highest values of efficiency, with a maximum in 19.68%, but they also reached the lowest ones (0.8%). For case B, the highest efficiency value was reached by B1 (Pint , gm ), at 21.51%. B2 (Pint, max ) reached the lowest value, at 1.01%. Distributions for B3 and B4 (Pint, min ) were again compact. However, B3 had also the highest median (14.98%, the same as B1) while B4 showed the most compact distribution. For case C, the highest efficiency level was reached by C2 (Pint, max ) at 19.45% closely followed by C1 (Pint , gm ) at 19.44%. C3 and C4 (Pint, min ) were again the ones with a more compact distribution. In this case, C4 had the highest median (15.06%) while C3 showed a slightly more compact distribution. For cases D and E, there were fewer differences between the different Pint methods. For case D, the highest efficiency level was reached by D1 (Pint , gm ) at 20.23%. D3 was the most compact distribution and had also the highest median (15.33%). For case E, the highest efficiency level was reached by E2 (Pint, max ) at 20.03%. E3 was the most compact distribution and reached the highest median (15.13%) too. Overall, the highest values were reached by B1 and the highest median by D3. Hence, in all cases, the method to select the design intermediate pressure affects the results obtained in the off-design performance. The selection of the Pint, min method means higher medians and compact efficiency distributions. Pint , gm and Pint, max methods are more similar between them, and lead to the highest efficiencies: Pint , gm for A, B, C and D and Pint, max for case E. The compactness of the efficiency distribution can be understood either as an advantage or as a disadvantage. A compact efficiency distribution ensures low efficiency variability, even though the operating conditions of the cycle change. However, efficiencies are higher with a less compact distribution.
Hence, for the same design conditions, five VR combinations and three (or four) intermediate pressure values (for each combination) were considered, resulting in a total of 17 cases (see Table 2). The performance at off-design conditions was analyzed for those designs. To determine the performance of those ORC designs at offdesign conditions, the model was used to simulate the cycles varying four parameters:
• The temperature at the outlet of the evaporator (T ) was varied from 120 °C to 150 °C. The evaporation pressure (P ) was varied from 500 kPa to • 3000 kPa. • The condensation temperature (T ) was varied from 15 °C to 35 °C. • The expander speed (N) was varied between 1000 and 5000 min . high
evap
cond
−1
Variations of these parameters allowed the analysis of the performance of the ORC under a wide range of part load conditions, which provided a comprehensive set of possible operating points of the cycle. The analysis of the results was made in two parts. First, the variability of the efficiency was evaluated for all the designs. Then, for two representative designs, the performance of the cycles was studied in detail through the evaluation of the cycle and expander performance under these different conditions. For the cycle performance, the variables studied were the thermal and exergy efficiencies, as well as the working pressures and temperatures. For the expander performance, the variables considered were the net power and the isentropic efficiency of the expanders. The simulation model was deployed in Matlab [25] and the properties of the fluid were obtained using the Refprop libraries for R245fa [26]. 4. Analysis of the influence of design parameters in the off-design efficiency
Table 2 Input parameters considered.
All the designs were different and, therefore, their characterization was different too. The characterization for the scrolls of each cycle are shown in Table 3. The total flow rate through the expanders is the same in the two expanders, as well as the rotation speed, but the rest of the parameters that define the expander will be different. For the second expander, the design volume is calculated through the density of the intermediate state, and therefore is affected by the volume of the first expander. It is also much larger than the first. As the design volumes are larger, leakages areas will be larger too, and therefore, leak mass flow rate will increase. For these designs, the efficiency at off-design operation was calculated and its variability analyzed using box diagrams (Fig. 3). These diagrams are usually plotted to represent the statistical distribution of a variable. The box limits are the quantil 25% (1st Q ) and 75% (3rdQ ) of the distribution and the middle of the box is the median. The distances between the tops and bottoms are the interquartile ranges. Thus, the smaller the box, the more uniform the values of the observed variable are. The whiskers are lines extending above and below each box. Whiskers are drawn from the ends of the interquartile ranges to the furthest observations within the whisker length. Observations beyond the whisker length are marked as outliers. An outlier is a value that is more than 1.5 times the interquartile range away from the top or bottom of the box.
VR1 A1
A2 A3
B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 E1 E2 E3
692
3
3 3
4 4 4 4 2 2 2 2 3 3 3 4 4 4
VR2 3
3 3
2 2 2 2 4 4 4 4 4 4 4 3 3 3
Pint (kPa) 545
570 905
545 420 620 840 545 750
1145 1295 545 655 880 545 510 710
exp, glob
0.8132
0.8138 0.7583
0.7830 0.7983 0.7625 0.6821 0.7784 0.8069 0.7611 0.7315 0.8149 0.8256 0.7995 0.8220 0.8231 0.7919
Pint method Pint, gm
Pint,
Pint,
max
min
Pint, gm
Pint,
max
Pint,
min
Pint,
min
Pint, gm
Pint,
max
Pint,
min
Pint,
min
Pint, gm
Pint,
Pint,
max
min
Pint, gm
Pint,
Pint,
max
min
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Table 3 Characterization of the scroll expanders. Vswept,1 A1
A2 A3
B1 B2 B3 B4
C1 C2 C3 C4
D1 D2 D3
E1 E2 E3
Vswept,2
Ndis 50
1.74·10
5
8.36·10
5
1.74·10
5
7.95·10
5
1.90·10
5
5.11·10
5
1.82·10
5
8.72·10
5
1.78·10
5
1.13·10
4
1.88·10
5
7.79·10
5
2.18·10
5
6.36·10
5
1.83·10
5
8.85·10
5
1.76·10
5
5.92·10
5
1.89·10
5
3.85·10
5
2.00·10
5
3.51·10
5
1.73·10
5
8.34·10
5
1.71·10
5
6.70·10
5
1.78·10
5
4.96·10
5
1.72·10
5
8.25·10
5
1.71·10
5
8.86·10
5
1.80·10
5
6.42·10
5
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50
Aleak,1
Aleak,2
Wexp,dis,1
Wexp,dis,2
2.32
2.91
1.51
3.73
3.59·10
6
6.06·10
6
3.59·10
6
5.96·10
6
3.70·10
6
5.14·10
6
3.65·10
6
6.15·10
6
3.62·10
6
6.71·10
6
3.69·10
6
5.92·10
6
3.87·10
6
5.53·10
6
3.66·10
6
6.18·10
6
3.60·10
6
5.40·10
6
3.69·10
6
4.68·10
6
3.76·10
6
4.54·10
6
3.59·10
6
6.06·10
6
3.57·10
6
5.63·10
6
3.62·10
6
5.09·10
6
3.57·10
6
6.03·10
6
3.57·10
6
6.18·10
6
3.63·10
6
5.55·10
6
2.26 2.51 2.89 2.31 1.71 2.15 1.70 1.08 0.85 2.31 2.00 1.48 2.36 2.48 1.88
Table 4 Statistical summary of the off-design efficiencies for each of the cycles considered. 1st Q and 3rdQ are the quantile 25% and 75% of the distribution.
2.97 2.73 2.34 2.93 3.59 3.09 3.53 4.16 4.45 2.91 3.23 3.75 2.87 2.75 3.36
A compact distribution may be interesting for cycles that are going to operate with changing conditions (such as a solar field with a small storage system), and therefore, this cycles may benefit if the intermediate pressure is selected as the Pint, min . Meanwhile, in facilities whose operating conditions are mostly stable (i.e. waste heat from industrial processes or large plants with high storage capacity) this criterion is not suitable. Regarding the VR, it is not so easy to identify a trend on the results of the performance at off-design conditions. However, the use of two expanders in series improves the performance. The distribution of the efficiency reached in the case of one expander (R) is also a compact distribution, with a median of 13.33%, much lower than any of the twoexpander designs considered. The maximum value reached with one expander was 16.32%, also much lower than the one reached with two expanders. Therefore, with an appropriate design (i.e. C4), the values of the
Min
1st Q
Median
Mean
3rdQ
Max
A1 A2 A3
0.0140 0.0080 0.0570
0.1260 0.1267 0.1191
0.1442 0.1453 0.1511
0.1431 0.1441 0.1440
0.1699 0.1700 0.1629
0.1966 0.1968 0.1830
B1 B2 B3 B4
0.0392 0.0101 0.0537 0.0578
0.1224 0.1229 0.1189 0.1052
0.1498 0.1402 0.1498 0.1386
0.1434 0.1405 0.1422 0.1313
0.1654 0.1664 0.1628 0.1489
0.2151 0.1925 0.1838 0.1672
C1 C2 C3 C4
0.0049 0.0007 0.0579 0.0563
0.1134 0.1259 0.1136 0.1187
0.1387 0.1452 0.1467 0.1506
0.1329 0.1424 0.1396 0.1436
0.1608 0.1687 0.1582 0.1632
0.1944 0.1945 0.1777 0.1838
D1 D2 D3
0.0047 0.0074 0.0240
0.1193 0.1260 0.1248
0.1442 0.1458 0.1533
0.1388 0.1439 0.1465
0.1687 0.1728 0.1696
0.2023 0.2009 0.1928
E1 E2 E3
0.0162 0.0155 0.0291
0.1251 0.1236 0.1229
0.1438 0.1438 0.1513
0.1434 0.1421 0.1441
0.1718 0.1711 0.1679
0.1991 0.2003 0.1910
R
0.0616
0.1002
0.1333
0.1250
0.1440
0.1632
efficiency are higher than with one expander, and these high values are maintained all along the off-design operating conditions. 5. Performance analysis at off-design operation As the selection of the intermediate pressure is a key aspect on the off-design performance, a more detailed analysis of the performance for the different approaches was done in order to clarify the conclusions. For that, the case A was selected (VR1 = 3, VR2 = 3). As designs A1 and A2 are quite similar, designs A1 and A3 were selected as representatives of the cases where Pint = Pint , gm and Pint = Pint, min . The analysis of the performance at off-design conditions is presented
Fig. 3. Statistical analysis of the off-design efficiencies for each of the cycles considered. Pgm: Pint = Pint, gm ; Pmax: Pint = Pint, 693
max ;
Pmin: Pint = Pint,
min
.
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in three stages: the first one that analyses the different variables and performance at off-design operation, the second one that studies the irreversibilities and the last one where the best design and operation point are proposed. The variables selected and the structure of the analysis are the same as in [16]: cycle thermal efficiency ( th ), isentropic efficiency of the expanders ( exp,1 and exp,2 ) and the adapted pressure on each expander (PRad,1 and PRad,2 ), to be able to compare the results of this work with the previous one. In addition, a detailed analysis of the stages of the expansion is included, for an improved understanding of the performance of the expanders.
5.1. Performance analysis The performance analysis of the simulation results at off-design conditions for two expander systems is shown in Figs. 4–8. The behaviour of each variable was displayed in nine different plots to illustrate the different changes on the operation conditions: each graph shows the efficiency as a function of the working pressure and temperature, keeping constant the speed of the expanders and the condensation temperature. The evolution of the thermal efficiency for designs A1 and A3 versus
Fig. 4. Off-design thermal efficiency for the ORC with two expanders.
Fig. 5. Off-design isentropic first expander efficiency. 694
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Fig. 6. Off-design isentropic second expander efficiency.
Fig. 7. Off-design first expander adapted pressure ratio.
the evaporation pressure is shown in Fig. 4. As expected, the thermal efficiency increased when the condensation temperature decreased and the superheating temperature increased. As in the case of the cycle with one expander [16], an optimal pressure was identified, located at higher pressure values than when one expander was used. This maximum values moved to higher pressures when the rotation speed of the expander and the condensation temperature increased. This caused (in some graphs) that the maximum is not shown because the total expanders’ volumetric ratio (VR) were better adapted to the real expansion ratio of the cycle.
For design A1 at high condensation temperatures, the efficiency decreased abruptly when the evaporation pressure was low. In the case of A3 the curve of the thermal efficiency was much more flat along the whole range of operating pressures, although the values reached were lower, as seen in the previous section. Figs. 5 and 6 show the isentropic efficiency of each expander ( exp ). In these cases, the behavior of the efficiency of the expanders is quite different to that of the systems with one expander. In the case of the first expander (Fig. 5) the outlet pressure was not imposed by the conditions of the condenser but by the coupling 695
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Fig. 8. Off-design second expander adapted pressure ratio.
Fig. 9. Off-design cycle irreversibilities for Tmax = 150 °C; Tmin = 25 °C; N = 3000 min 1.
between expanders. The irreversibilities due to the difference between the adapted pressure and the outlet pressure were minimum and the efficiency was rather constant. The PR ad of this expander was close to one (Fig. 7). When the irreversibilities caused by the over- or sub-expansions were reduced, the importance of the irreversibilities due to the leaks increased, generating a change in the efficiency of the expander. Hence, the maximum of the efficiency did not happen when PR ad = 1. This behaviour was not defined by the design intermediate pressure, as the same behaviour is observed for both A1 and A3. The behaviour of the second expander was different (Fig. 6), as the outlet pressure was defined by the condensation conditions. The irreversibilities due to the over- or sub-expansions were much more important that in the case of the first expansor. Moreover, the behaviour of the second expander of both selected designs was not similar. In design A1 the efficiency was very variable, reaching very low values at low working pressures. For design A3 this variability only appeared at the most extreme working conditions (high N, high Tcond and very low Pevap ). Hence, the second expander of this design was better adapted to the operating conditions than the one of design A1.
These differences of behavior in the second expander were also reflected in the PR ad values. In design A1, PR ad,2 reached values over 3.5, while in design A3 was always lower than 2, which indicates again that the second expander was better adapted. In both cases, the irreversibilities caused by the leaks have little importance when compared to those due to the over- and sub-expansions. Therefore, the efficiency of the second expander reached its maximum close to the condition of PR ad,2 = 1. The behaviour of A1 cycle efficiency was defined by the behaviour of the second expander. As the first expander maintained its efficiency, the decrease of efficiency of the second expander at low evaporation pressures was the cause of the overall cycle efficiency decrease. 5.2. Irreversibilities at off-design operation Fig. 9 shows the analysis of the irreversibilities of the cycle under different off-design conditions. Table 5 shows the irreversibility associated to the pressure drop and to the expanders. One of the highest irreversibilities was reached in the evaporator, as the heat source was considered as infinite and it provides energy at the highest temperature of the cycle Tmax . The main difference between the 696
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Table 5 Irreversibilities of the expander and of the pressure drop. Tmax = 150 °C; Tmin = 25 °C; Psat = 1800 kPa. N (min 1)
Iexp,1/Esource (%)
Iexp,1/Esource (%)
Iploss /Esource (%)
Sum (%)
A1
1500 3000 4500
11.83 8.74 7.17
7.35 3.41 2.26
0.34 0.81 1.42
19.52 12.96 10.85
A3
1500 3000 4500
7.34 5.18 3.96
16.36 9.00 6.30
0.33 0.81 1.44
24.04 14.98 11.70
Fig. 10. Irreversibilities of the expanders for design A1.
considered designs was the behaviour of the expanders. For the design A1 the irreversibility of the first expander was greater than for design A3, and reached a constant value along the range of evaluated evaporating pressures. The irreversibility of the second expander was greater for design A3 than for design A1. For the latter, the irreversibility increased at lower evaporation pressures, while for design A3 it was greater at higher evaporation pressures. Hence, the behaviour of the expanders at off-design conditions was critical at off-design operation. Due to the importance of the irreversibility in the expander, its sources were analyzed in the following section.
1.27 kW) and they decreased steeply when the working pressures were decreased, reaching a minimum at 1400 kPa (0.1825 kW). This trend was due to the behaviour of the expansion process, since the irreversibility due to the leakages becomes less important at low pressures. This indicated that the second expander may not be adequate for low pressure operating conditions. For design A3 the irreversibilities of the second expander increased from 0.26 up to 2.85 kW from the low to the high pressure values, as also seen in Fig. 9b. These irreversibilities were again governed by the expansion process. The values for the irreversibility of the leaks also increased with the increasing pressure, but was only dominant at lower pressures. Hence, the design strategy for design A3, with Pint, min , optimized the behaviour at off-design conditions, specially when the lower operating pressures were taken into account, and particularly for the first expander.
5.3. Irreversibilities in the expanders The irreversibilities of the expanders are shown by source to understand the differences on the behaviour of the first and second expander. The irreversibilities of a expander (Iexp ) were classified into three different sources: leakages (Ileak ), over- and under-expansion (Iexp(over , under ) ) and the mix of all the flow rates (Imix ). All these values are shown in Figs. 10 and 11, for both expanders and for designs A1 and A3. The most important sources of irreversibility in the first expander were the leakages. Irreversibility due to the over- and sub-expansion was negligible. This was because the outlet pressure was roughly the same as the adapted. For design A1 the irreversibilities were around between 0.30 and 0.85 kW for all the range of working pressures, with a trend to increase when the pressures were increased. The values of the irreversibilities of design A3 were between 0.30 and 0.48 kW. In the case of the second expander, the irreversibilities were more variable. In A1 the irreversibilities were high for high pressures (up to
5.4. Best operation point The relationship between the thermal efficiency and the generated power for different working conditions (temperatures and expander rotation speeds) are shown in Fig. 12. Using this figure, it was possible to reach a maximum efficiency for each demanded level of power for the given working conditions (maximum and minimum temperatures) by adjusting the expander and pump speed (adjusting the pressure). This optimum pressure for each demanded power was even lower than the one identified for each series of results. Hence, this figure suggested an envelope of the family of curves, where the most appropriate operating point for each demanded power was contained. Each point in the envelope corresponded to a certain scroll speed and boiling 697
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Fig. 11. Irreversibilities of the expanders for design A3.
Fig. 12. Best operating point.
pressure. The point where the maximum high temperature, the minimum condensation temperature and the maximum of the envelope curve happens is the point that should be used for the ORC design. There was a branch of the envelope curve that matches with the constant speed curve, at the maximum admissible speed due to the asymptotically efficiency increase with the expander speed. The point with the optimal pressure for the maximum admissible shaft speed should be selected as the operating point. For design A1, this happened on the maximum power considered (8.65 kW). However, for A3 it happened around 7.25 kW, which is not the maximum power possible. Then, three different regions where the ORC could operate were identified in Fig. 12. In the case of A1, if the power demand decreases, this should be accomplished following the envelope curve searching for the adequate pressure-speed combination, which would define the different operation regions: firstly at decreasing pressure and constant speed, and then decreasing also the expander rotation speed. For A3, the two first regions were similar but also levels of power over the design point could be reached by increasing pressure and constant expander speed, which would lead to an efficiency decrease, defining the third operating region. Eventually, higher power values may be reached with the expander at over-speed conditions for both cases.
6. Conclusions The behavior of an Organic Rankine Cycle (ORC) system with two expanders in series at off-design working conditions was studied and the influence of the intermediate pressure and the expanders’ volumetric expansion ratio on the off-design performance of the ORC was determined. The irreversibilities of the components were analyzed and the performance of the ORC with two expanders for two different designs was also discussed. The thermal efficiency that is reached with two expanders was significantly higher than the obtained in the case of one. Of course, this increase came with an increase in the complexity in the design of the expanders. The first challenge in ORC systems with two expanders in series was the selection of a set of volume expansion ratios and intermediate pressure that optimized the performance of the cycle at off-design operation. In particular, the selection of the adequate intermediate pressure was key to the good performance of the cycle. In a first approach, the best option was to choose the group of parameters for which the expansion efficiency in the design condition was the highest. However, it was possible to find a design that presented a more constant operation, which corresponded to the selection of the intermediate pressure that minimizes the isentropic efficiency difference of both expanders. As long as the adequate intermediate 698
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pressure could be chosen, the volumetric expansion ratio would not affect as much. This design methodology (Pint, min ) showed to be advantageous regarding the variability of the efficiency at off-design conditions. The irreversibility of the first expander was mainly due to the leaks. However, the performance of the second expander was more variable and was defined by the difference between the discharged pressure and the condensation pressure. The off-design performance analysis allowed to establish a methodology to obtain the desired power with the maximum thermal
efficiency, and the identification of the best operation point and the three operation regions that each system allowed. Acknowledgments Mercedes Ibarra acknowledges the generous financial support provided by CORFO (Corporación de Fomento de la Producción) under the Project 13CEI2-21803. Antonio Rovira acknowledges the financial support by the Project 2018-IEN28.
Appendix A Here a summary of the model published in [16] is presented. This model is used to determine the performance of an ORC with heat recuperation and superheating at part load operation. The calculations follow three steps: assessment of the reference cycle, characterization of the components of the facility and part load simulation model calculations. A.1. Calculation of the ORC at the design point Thermal efficiency of the cycle: th
(7)
= WORC, net /Qevap
where
Wnet = Wexp
Wbomb = m (H7
H9)
m (H2
(8)
H1)
The heat consumed in the evaporator (Qevap ) is calculated by:
Qevap = m (H6
(9)
H3)
A.2. Characterization of the system The model presented in the previous section was used to define the design conditions of the cycle, and therefore it characterizes the ORC.
• Pressure drop (representative of all the pressure drop of the system): K
P
=
2 P7)/mdis
6 ·(P6
(10)
• Expanders: the equations for this scroll model are based on the model presented by Lemort et al. [27] – admission volume
Vdis = mtot , dis /(Ndis ·
(11)
dis )
– volumetric expansion ratio
VR = vad/ vin =
(12)
ad / in
– leakeage area
Aleak = Aleak, ref
•
3
Vdis Vdis, ref
(13)
being Aleak, ref = 4, 6 mm2 and Vdis, ref = 36.54 cm3 [27] Heat exchangers: (14)
UA = Qin/ DTML
A.3. Calculation of the ORC at the off-design conditions
• Expanders
min = Vdis· N ·
exp, ad
=
is, exp
(15)
exp, in ·VR
(16)
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mleak = Aleak ·
2(hexp, in
leak
hleak )
(17) (18)
mtot = min + mleak
Wexp = min (hexp, in
is, exp
=
hleak ) + min ·
hexp, in
hexp, out
hexp, in
hexp, out , s
exp, out
(Pad
(19)
Pexp, out )
(20)
• Heat exchangers: U mtot = Udis mtot , dis
0.8
(21)
• Pump:
The efficiency of the pump in off-design conditions is determined by the non-dimensional performance curves used by Manente et al. [21] and Calise et al. [28]. Following the same methodology presented by these authors, it is assumed that the maximum efficiency for the pump takes place for the design conditions. For the off-design pump performance, both the flow rate and the pump rotational speed are varied and the pump performance curve varies according to the affinity laws for constant impeller diameter:
q1 q2
=
N1 N2
1
(22)
H1 N1 = H2 N2
2
W1 N1 = W2 N2
3
(23)
(24)
Appendix B. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.applthermaleng.2018.12.083.
[12] J. Li, P. Li, G. Gao, G. Pei, Y. Su, J. Ji, Thermodynamic and economic investigation of a screw expander-based direct steam generation solar cascade Rankine cycle system using water as thermal storage fluid, Appl. Energy 195 (2017) 137–151. [13] S. Rech, S. Zandarin, A. Lazzaretto, C.A. Frangopoulos, Design and off-design models of single and two-stage orc systems on board a lng carrier for the search of the optimal performance and control strategy, Appl. Energy 204 (2017) 221–241. [14] S. Quoilin, M. Orosz, H. Hemond, V. Lemort, Performance and design optimization of a low-cost solar organic Rankine cycle for remote power generation, Sol. Energy 85 (2011) 955–966. [15] G. Kosmadakis, D. Manolakos, G. Papadakis, An investigation of design concepts and control strategies of a double-stage expansion solar Organic Rankine Cycle, Int. J. Sustain. Energy 34 (2015) 446–467. [16] M. Ibarra, A. Rovira, D.-C. Alarcón-Padilla, J. Blanco, Performance of a 5 kW organic Rankine cycle at part-load operation, Appl. Energy 120 (2014) 147–158. [17] Y. Zhu, L. Jiang, V. Jin, L. Yu, Impact of built-in and actual expansion ratio difference of expander on {ORC} system performance, Appl. Therm. Eng. 71 (2014) 548–558. [18] D. Ziviani, S. Gusev, S. Lecompte, E. Groll, J. Braun, W. Horton, M. van den Broek, M.D. Paepe, Optimizing the performance of small-scale organic Rankine cycle that utilizes a single-screw expander, Appl. Energy 189 (2017) 416–432. [19] E. Yun, D. Kim, S.Y. Yoon, K.C. Kim, Experimental investigation of an organic Rankine cycle with multiple expanders used in parallel, Appl. Energy 145 (2015) 246–254. [20] Y. Wu, R. Zhi, B. Lei, W. Wang, J. Wang, G. Li, H. Wang, C. Ma, Slide valves for single-screw expanders working under varied operating conditions, Energies 9 (2016) 478. [21] G. Manente, A. Toffolo, A. Lazzaretto, M. Paci, An Organic Rankine Cycle off-design model for the search of the optimal control strategy, Energy 58 (2013) 97–106. [22] D. Hu, Y. Zheng, Y. Wu, S. Li, Y. Dai, Off-design performance comparison of an organic Rankine cycle under different control strategies, Appl. Energy 156 (2015) 268–279.
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Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1, National Institute of Standards and Technology, Standard Reference Data Program. Gaithersburg, 2013. [27] V. Lemort, S. Quoilin, C. Cuevas, J. Lebrun, Testing and modeling a scroll expander integrated into an Organic Rankine Cycle, Appl. Therm. Eng. 29 (2009) 3094–3102. [28] F. Calise, M.D. dAccadia, M. Vicidomini, M. Scarpellino, Design and simulation of a prototype of a small-scale solar chp system based on evacuated flat-plate solar collectors and organic Rankine cycle, Energy Convers. Manage. 90 (2015) 347–363.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Performance of an Organic Rankine Cycle with two expanders at off-design operation
T
Mercedes Ibarraa,b, , Antonio Rovirab, Diego-César Alarcón-Padillac ⁎
a
Fraunhofer Chile Research, Center for Solar Energy Technologies, Vicuña Mackenna 4860, Santiago, Chile Universidad Nacional de Educación a Distancia (UNED), C/Juan del Rosal 12, 28040 Madrid, Spain c CIEMAT-Plataforma Solar de Almería, Ctra. de Senés s/n, 04200 Tabernas, Almería, Spain b
HIGHLIGHTS
ORC system with two expanders in series at off-design operation is simulated. • An efficiency reached with two expanders was higher than the achieved with one. • Thermal pressure affects more than the volume expansion ratio of the expander. • Intermediate performance of the first expander was mainly affected by leaks. • The • The performance of the second one was more affected by the discharged pressure. ARTICLE INFO
ABSTRACT
Keywords: ORC Scroll expander Simulation Two expanders Exergy analysis
The objective of this work was to simulate the behavior of an Organic Rankine Cycle (ORC) system with two expanders in series at off-design working conditions. The influence of both the intermediate pressure and the volumetric expansion ratio of the expanders on the off-design performance of the ORC was studied and the irreversibilities of the components were analyzed. The performance of the ORC with two expanders for two different designs was also discussed. The thermal efficiency reached using two expanders was higher than the obtained using only one. However, this increase conveyed an increase in the complexity of the design and control of the expanders. As an additional conclusion, it was found that the influence of the intermediate pressure is higher than that of the volume expansion ratio of each expander. The irreversibility of the first expander was mainly due to leaks. However, the performance of the second expander was particularly affected by the difference between the discharged pressure and the condensation pressure. The off-design analysis allowed the definition of a methodology to achieve the desired power with the maximum thermal efficiency, and the identification of the best actuation for the part load operation.
1. Introduction Organic Rankine Cycle (ORC) systems are a good alternative for energy generation from low grade thermal energy. The source could be either renewable or waste thermal energy from industrial or power generation processes. As it is well known, a simple ORC works like a conventional Rankine cycle but it uses an organic fluid instead of water. The use of organic fluids allows low working temperatures as well as simple facilities because the expander exhaust vapor is still dry after the expansion process. One of the challenges of this technology is the selection of the type
⁎
of expander. In this regard, volumetric expanders (i.e. scroll, screw, reciprocating or multivane expanders) are more suitable than dynamic ones as they are characterized by low mass flow rates, moderate pressure ratios and low rotation speeds [1,2]. Among the different devices proposed for low power rates, the scroll expander stands out because of its simplicity, cost and the good results obtained by the experimental experiences and prototypes [3–5]. Scroll expanders consist of two spirals, one fixed and one moving. The fluid enters the expander at the center of the spirals, and, when the moving spiral gyrates, the volume of the gap between the spirals increases, allowing the fluid to expand while moving outwards.
Corresponding author at: Fraunhofer Chile Research, Center for Solar Energy Technologies, Vicuña Mackenna 4860, Santiago, Chile. E-mail address: [email protected] (M. Ibarra).
https://doi.org/10.1016/j.applthermaleng.2018.12.083 Received 31 July 2018; Received in revised form 21 November 2018; Accepted 13 December 2018 Available online 14 December 2018 1359-4311/ © 2018 Published by Elsevier Ltd.
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Nomenclature
Aleak, i Esource K P hi I Icond Irec Iexp, i Iploss ISG Ipump Ileak, i Iexp(over
Imix, i
mtot Ni P Pi (1
Pcond Pevap
Pint Pint , gm Pint, max Pint, min
leakage area of expander i (m2 ) energy from the source (kW) pressure loss coefficient (–) enthalpy of the fluid at the point i of the thermal cycle (kJ/kW) irreversibility (kW) irreversibility in the condenser (kW) irreversibility in the recuperator (kW) irreversibility in the expander i (kW) irreversibility due to evaporator pressure loss (kW) irreversibility in the evaporation (kW) irreversibility in the pump (kW) irreversibility in the expander i due to leakeages (kW) irreversibility in the expander i due to over- and , under ), i under-expansion (kW) irreversibility in the expander i due to mixture of all the flows (kW) massic flow rate (kg/s) rotation speed of expander i (min 1) pressure (kPa) 11) pressure of the fluid at the point i of the thermal cycle (kPa) condensation pressure (kPa) evaporation pressure (kPa)
T Tevap Tcond Thigh Tmax Tmin UAhex, i Vswept , i VR WORC, net Wtot Wexp, i Wpump i exp, i exp, glob pump rec
However, scroll expanders have also some technical limitations such as fixed geometry, over and sub-expansion, leaks and friction between the scrolls. As their geometry is fixed, they have a fixed swept volume (Vswept ) and an internal built-in volume ratio (VR). Often, scroll expanders used in ORC are modified scroll compressors, whose swept volume is limited, as well as their VR. Usually, the value of this last parameter is not greater than 5:1 (1.5–3.5:1 for scrolls that come from the refrigeration industry, and 4:1 for those from air compressors), while ORC operate at much greater expansion ratios [6]. To solve this problem, a few solutions have been proposed by several authors. One approach is to design the scroll as an expander from the beginning, adapting it to the ORC requirements. Clemente et al. [7] modelled a scroll expander with large scrolls to increase the VR. Orosz et al. [8] also presented a modified geometry of a scroll expander where the scrolls had variable thickness walls, in order to create more compact geometries and improve the efficiency. Regarding the dynamic expanders, Kang et al. [9] proposed a two-stage radial turbine to improve the performance of the ORC by increasing the pressure ratio. If a new scroll design is not possible, the design of the cycle should be changed to improve the performance. For example, Quoilin et al. [6] proposed the use of two expanders in series in the same cycle, both working in different expansion conditions and having the volumetric ratio adapted to the expansion ratio required by the cycle; however, the authors did not analyze the off-design operation. Ayachi et al. [10] also presented the idea of coupling two or more machines in order to reduce the under-expansion loss, which degraded the efficiency of the ORC they modelled. Kane et al. [11] also proposed the expansion in several stages, but using two ORC in cascade. A cascade ORC consists in two ORC cycles with two different working temperatures, so that the heat dissipated in the condenser of the first cycle is used to evaporate the fluid of the lower temperature cycle. Li et al. [12] also proposed a direct steam generation solar cascade Rankine cycle, to avoid the limitation of the low built-in expansion ratio of the expander, which was a volumetric one, although an screw type. In a similar manner, Rech et al. [13] proposed a two stage ORC with a supercritical high-pressure level, two pumps that operated in parallel and two turbines operating in series.
intermediate pressure (kPa) intermediate pressure equal to the geometry mean (kPa) intermediate pressure that maximizes the efficiency (kPa) intermediate pressure that minimizes the efficiency differences of the expanders (kPa) adapted pressure ratio of expander i (–) temperature (°C) evaporation temperature (°C) condensation temperature (°C) temperature at the outlet of the evaporator (°C) highest temperature of the cycle (°C) lowest temperature of the cycle (°C) heat transfer coefficient of the heat exchanger i (W/K ) swept volume for expander i (m3 ) volume ratio of the expander (–) net power produced by the ORC (kW) total power produced by the ORC (kW) power produced by expander i (kW) power consumed by the pump (kW) density of the fluid at the point i of the thermal cycle (kg/ m3 ) efficiency of the expander i (–) efficiency of the global expansion (both expanders) (–) efficiency of the pump (–) efficiency of the recuperator (–)
They analyzed the off-design performance with a focus on the control of the system. Unfortunately, the authors concluded that the two stage configuration did not result in a stable operation. All of these proposals have also several limitations. For example, geometric modifications of the scroll expanders could increase the manufacturing costs [7]. And up to date there is not any experimental test for ORC with two expanders in series, but only theoretical projects [14,15]. Cascade cycles have only one experimental set up by Kane et al. [11]. Moreover, even if an optimum built-ratio is reached for the design conditions, the differences between the design expansion ratio and the actual expansion ratio at the off-design operating conditions will affect the performance of the expander [16,17]. Ziviani et al. [18] experimentally assessed the performance of an ORC, comparing two fluids (R245fa and SES36) and focusing on the match between the expander (screw) efficiency and the system performance. Their results showed that, when the pressure ratio was maximized, the expander efficiency was higher. They also concluded that the cycle efficiency can be improved by increasing the specific expansion ratio within the expander. In this regard, Yun et al. [19] proposed an ORC with two expanders in parallel, where the operation mode could be changed between single (using one expander) and dual mode (two expanders). As a result of this operation mode, the pressure ratio was increased and the performance of the cycle improved. Wu et al. [20] proposed a single screw expander with slide valves to adjust the built-in ratio so that the expander could be adapted to the changing working conditions. The objective of this work is to analyze the behavior of an ORC system using two expanders in series at off-design operation, and to determine if the benefits of having two expanders in series would be significant. In particular, the objective is the study of how the determination of the design parameters, and specially the intermediate pressure, affects the performance and behavior of the cycle in the offdesign operation. As commented previously, up to date there is not either experimental test for ORC with two expanders in series nor theoretical works considering its part load operation. To achieve the objective, an ORC simulation model developed in a previous work [16] was adapted, introducing some modifications regarding the expansion 689
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model, which is explained in Section 2. Sections 3 and 4 study the influence of the intermediate pressure and the volume expansion ratio of each expander on the off-design performance of the ORC. Finally Section 5 analyzes the performance of the ORC with two expanders for two different designs.
Table 1 ORC design parameters.
Tevap Thigh Tcond Pevap Pcond
2. Description of the numerical model and design parameters To analyze the behavior of an small ORC system with two expanders out of the design conditions, an off-design model must be used. Quoilin et al., Manente et al. and Hu et al. [14,21,22] proposed different offdesign models of an ORC, but they were focused on finding the optimal control strategies. Lecompte et al. [23] also took into account the part load operation of a CHP system using an ORC when optimizing the size of the heat exchanger-staking. Dickens et al. [24] focused on the complexity of heat exchangers modelling, analyzing the influence of heat transfer coefficients and of void fraction on the off-design prediction accuracy of the model for both the heat exchangers and the ORC system. They concluded that a proper estimation of the mass enclosed in the heat exchanger is more important than a slight improvement of the heat transfer predictions. In this work, the model used is based on the one presented in [16] and summarized in the appendix A.
Units
R245fa
°C
124.00
°C kPa
25.00 2080.50
°C
pump
kPa %
rec
%
145.00
147.43 70 80
(evaporation, condensation and the intermediate pressure between the expanders) are other inputs of the model. The first step in the iterative process is to calculate the mass flow rate. For that, the total power produced by the two expanders (Wtot ) is considered as the sum of the produced net power and the power consumed by the pump (Wpump ), which as an initial guess value is considered as a 6% of the net power:
Wtot = WORC, net + Wpump
(1)
In this preliminary iteration, it is assumed that the first expander generates half of the total power, so it is divided between the first and the second one:
2.1. ORC system design
Wexp,1 = Wexp,2 = Wtot /2
The analyzed system (Fig. 1) is a 5 kW ORC with an internal recuperator and two expanders in series, using R245fa as working fluid. The design parameters of the cycle are shown in Table 1.
(2)
The outlet conditions (Pint ) are calculated taking into account four phenomena in the expander: the adiabatic suction, the adiabatic expansion, the sudden expansion at constant volume and the leaks (see appendix A). One of the outlets of this model is also the mass flow rate (mtot,1). The outlet conditions for the second expander are calculated following the same model, but its results are further limited by the assumption that the mass flow rate must be the same for both expanders and the fact that the outlet pressure of the first is the inlet pressure on the last. Thus, the power of the second expander is a result, as well as the outlet conditions of the fluid. Besides, the pump power (Wpump ) is calculated by:
2.2. Description of the on-design simulation model As previously mentioned, the used model is based on the model presented in [16], adapted to the use of two expanders connected in series. It is assumed that both expanders work at the same shaft speed but they have neither the same size nor the same leakage area. Net power production (WORC , net ) is an input value, so the power produced by each expander on-design should be determined, taking also into account the power consumed by the pump. However, this pumping power consumption is defined by the flow rate of the cycle, which is defined by the expanders’ design, so an iterative process is required. Inlet conditions at the first expander and working pressures
Wpump = wpump·mtot
(3)
where wpump is the enthalpy difference between the inlet and outlet of
Fig. 1. Considered ORC with two expander and internal heat exchanger. 690
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the pump: wpump = h2 h1. Next, the net power value is updated:
WORC , net = Wexp,1 + Wexp,2
considering a new total mass flow rate. For the second expander, the adapted pressure is calculated through the volume ratio and the leak mass flow rate through the leakage area; the internal mass flow rate is calculated through the difference between the mass flow rate obtained by the first expander and the leak flow rate. The design volume, calculated through the density of the intermediate state, allows the calculation of the intermediate pressure. This pressure should be equal to that guessed in the previous iteration. Otherwise, it is the new intermediate pressure for the next iteration. Thus, two conditions are required for the iterations to finish: the mass flow rate and the intermediate pressure. Both of them are related each to the other and determine the behaviour of both expanders. The rest of the components of the cycle are calculated as it is described in [16] and summarized in the appendix A.
(4)
Wpump
When the variable WORC , net converges, then the calculation process finishes. Otherwise, Wtot is recalculated using a new value of the mass flow rate. Once the process converges, the on-design calculation finishes and the components of the cycle may be characterized as it is shown in [16] and summarized in the appendix A, i.e. the characterization of each expander ( Aleaks , VR and Vswept ), the characterization of the heat exchangers (UAhex, i ) and the pressure drop coefficient (K P ). 2.3. Description of the off-design simulation model The off-design model allows the calculation of the power production of the expanders, as well as the mass flow rate and intermediate pressure at any part load operation condition. The inputs of the model are the outlet conditions of the evaporator, the condensation pressure, the expanders rotation speed (N) and the characterization of each expander ( Aleaks , VR and Vswept ). As the energy and mass balances can not be explicitly solved, an iteration is required. In a first iteration the mass flow rate is guessed as the design one, which allows the calculation of the pressure drop before the inlet of the first expander:
P7 = P6
mtot · K 6
3. Methodology To analyze the behavior of an ORC system with two expanders in series, the effect of the selected design values of both the intermediate pressure between expanders (Pint ) and the volumetric expansion ratio (VR) on the performance of the ORC system were analyzed. In both cases, a wide range of part load operation was simulated in order to study the variability of the thermal efficiency of the cycle. The combinations of VR considered in this work for the expanders were defined by the total volumetric expansion of the fluid presented in [16], which is 14:1. The values selected were so that the total VR with two expanders was between 8 and 12, which significantly increases that obtained with one single scroll (VR = 5). Each of the VR combinations considered was named with a letter: (A) VR1 = 3, VR2 = 3; (B) VR1 = 4, VR2 = 2 ; (C) VR1 = 2, VR2 = 4 ; (D) VR1 = 3, VR2 = 4 ; (E) VR1 = 4, VR2 = 3. To analyze the influence of the intermediate pressure (Pint ) at the design conditions, Pint was continuously varied for each of the five VR combinations. The resulting design efficiency of each expander ( exp,1, exp,2 ) and the design global expansion efficiency ( exp, glob ) are plotted in Fig. 2, for each VR combination. Three points may be identified for each VR combination, which correspond with the three methods to select the intermediate pressure:
P
(5)
Once the inlet pressure is known, the properties of the fluid can be determined considering that h7 = h6 . The intermediate pressure at the outlet of the first expander and the inlet of the second expander is guessed in this first iteration as the geometric mean between the inlet and the outlet of the expansion pressure.
Pint , i = 1 =
P9· P7
(6)
Then, the mass flow rate and power production of the first expander can be calculated. The internal flow rate is determined through the swept volume, the adapted pressure is calculated through the volume ratio and the leak flow rate through the leakage area, as it is explained in [16]. The sum of the internal flow rate and the leak flow rate must be equal to the total mass flow rate guessed. Otherwise, the model iterates
1. The first option when designing the cycle was to define the Pint value as the geometric mean between the inlet and outlet expansion
Fig. 2. Expander efficiency depending on the design intermediate pressure. 691
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pressure: Pint = Pint , gm . 2. The second option was to select the Pint value as the pressure for which the maximum global expansion efficiency is reached: Pint = Pint, max . 3. The third option was to select as Pint the value that minimizes the difference between the expanders efficiencies: Pint = Pint, min . In cases B and C there are two points where this condition is met and, therefore, an extra cycle is analyzed.
For each VR combination (A, B, C, D, E) the efficiencies reached with every Pint method are plotted, each one in a different color. The statistical summary for the efficiency of each of these cases is also presented in Table 4. To compare the performance of the cycle comprising two expanders to that of only one expander, the results of the work presented in [16] have also been included in Fig. 3 and Table 4, denoted as design R. For case A, the median of A3 (Pint, min ) was the highest (15.11%) and the efficiency distribution was the more compact. A1 (Pint , gm ) and A2 (Pint, max ) distributions were very similar: they reached the highest values of efficiency, with a maximum in 19.68%, but they also reached the lowest ones (0.8%). For case B, the highest efficiency value was reached by B1 (Pint , gm ), at 21.51%. B2 (Pint, max ) reached the lowest value, at 1.01%. Distributions for B3 and B4 (Pint, min ) were again compact. However, B3 had also the highest median (14.98%, the same as B1) while B4 showed the most compact distribution. For case C, the highest efficiency level was reached by C2 (Pint, max ) at 19.45% closely followed by C1 (Pint , gm ) at 19.44%. C3 and C4 (Pint, min ) were again the ones with a more compact distribution. In this case, C4 had the highest median (15.06%) while C3 showed a slightly more compact distribution. For cases D and E, there were fewer differences between the different Pint methods. For case D, the highest efficiency level was reached by D1 (Pint , gm ) at 20.23%. D3 was the most compact distribution and had also the highest median (15.33%). For case E, the highest efficiency level was reached by E2 (Pint, max ) at 20.03%. E3 was the most compact distribution and reached the highest median (15.13%) too. Overall, the highest values were reached by B1 and the highest median by D3. Hence, in all cases, the method to select the design intermediate pressure affects the results obtained in the off-design performance. The selection of the Pint, min method means higher medians and compact efficiency distributions. Pint , gm and Pint, max methods are more similar between them, and lead to the highest efficiencies: Pint , gm for A, B, C and D and Pint, max for case E. The compactness of the efficiency distribution can be understood either as an advantage or as a disadvantage. A compact efficiency distribution ensures low efficiency variability, even though the operating conditions of the cycle change. However, efficiencies are higher with a less compact distribution.
Hence, for the same design conditions, five VR combinations and three (or four) intermediate pressure values (for each combination) were considered, resulting in a total of 17 cases (see Table 2). The performance at off-design conditions was analyzed for those designs. To determine the performance of those ORC designs at offdesign conditions, the model was used to simulate the cycles varying four parameters:
• The temperature at the outlet of the evaporator (T ) was varied from 120 °C to 150 °C. The evaporation pressure (P ) was varied from 500 kPa to • 3000 kPa. • The condensation temperature (T ) was varied from 15 °C to 35 °C. • The expander speed (N) was varied between 1000 and 5000 min . high
evap
cond
−1
Variations of these parameters allowed the analysis of the performance of the ORC under a wide range of part load conditions, which provided a comprehensive set of possible operating points of the cycle. The analysis of the results was made in two parts. First, the variability of the efficiency was evaluated for all the designs. Then, for two representative designs, the performance of the cycles was studied in detail through the evaluation of the cycle and expander performance under these different conditions. For the cycle performance, the variables studied were the thermal and exergy efficiencies, as well as the working pressures and temperatures. For the expander performance, the variables considered were the net power and the isentropic efficiency of the expanders. The simulation model was deployed in Matlab [25] and the properties of the fluid were obtained using the Refprop libraries for R245fa [26]. 4. Analysis of the influence of design parameters in the off-design efficiency
Table 2 Input parameters considered.
All the designs were different and, therefore, their characterization was different too. The characterization for the scrolls of each cycle are shown in Table 3. The total flow rate through the expanders is the same in the two expanders, as well as the rotation speed, but the rest of the parameters that define the expander will be different. For the second expander, the design volume is calculated through the density of the intermediate state, and therefore is affected by the volume of the first expander. It is also much larger than the first. As the design volumes are larger, leakages areas will be larger too, and therefore, leak mass flow rate will increase. For these designs, the efficiency at off-design operation was calculated and its variability analyzed using box diagrams (Fig. 3). These diagrams are usually plotted to represent the statistical distribution of a variable. The box limits are the quantil 25% (1st Q ) and 75% (3rdQ ) of the distribution and the middle of the box is the median. The distances between the tops and bottoms are the interquartile ranges. Thus, the smaller the box, the more uniform the values of the observed variable are. The whiskers are lines extending above and below each box. Whiskers are drawn from the ends of the interquartile ranges to the furthest observations within the whisker length. Observations beyond the whisker length are marked as outliers. An outlier is a value that is more than 1.5 times the interquartile range away from the top or bottom of the box.
VR1 A1
A2 A3
B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 E1 E2 E3
692
3
3 3
4 4 4 4 2 2 2 2 3 3 3 4 4 4
VR2 3
3 3
2 2 2 2 4 4 4 4 4 4 4 3 3 3
Pint (kPa) 545
570 905
545 420 620 840 545 750
1145 1295 545 655 880 545 510 710
exp, glob
0.8132
0.8138 0.7583
0.7830 0.7983 0.7625 0.6821 0.7784 0.8069 0.7611 0.7315 0.8149 0.8256 0.7995 0.8220 0.8231 0.7919
Pint method Pint, gm
Pint,
Pint,
max
min
Pint, gm
Pint,
max
Pint,
min
Pint,
min
Pint, gm
Pint,
max
Pint,
min
Pint,
min
Pint, gm
Pint,
Pint,
max
min
Pint, gm
Pint,
Pint,
max
min
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Table 3 Characterization of the scroll expanders. Vswept,1 A1
A2 A3
B1 B2 B3 B4
C1 C2 C3 C4
D1 D2 D3
E1 E2 E3
Vswept,2
Ndis 50
1.74·10
5
8.36·10
5
1.74·10
5
7.95·10
5
1.90·10
5
5.11·10
5
1.82·10
5
8.72·10
5
1.78·10
5
1.13·10
4
1.88·10
5
7.79·10
5
2.18·10
5
6.36·10
5
1.83·10
5
8.85·10
5
1.76·10
5
5.92·10
5
1.89·10
5
3.85·10
5
2.00·10
5
3.51·10
5
1.73·10
5
8.34·10
5
1.71·10
5
6.70·10
5
1.78·10
5
4.96·10
5
1.72·10
5
8.25·10
5
1.71·10
5
8.86·10
5
1.80·10
5
6.42·10
5
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50
Aleak,1
Aleak,2
Wexp,dis,1
Wexp,dis,2
2.32
2.91
1.51
3.73
3.59·10
6
6.06·10
6
3.59·10
6
5.96·10
6
3.70·10
6
5.14·10
6
3.65·10
6
6.15·10
6
3.62·10
6
6.71·10
6
3.69·10
6
5.92·10
6
3.87·10
6
5.53·10
6
3.66·10
6
6.18·10
6
3.60·10
6
5.40·10
6
3.69·10
6
4.68·10
6
3.76·10
6
4.54·10
6
3.59·10
6
6.06·10
6
3.57·10
6
5.63·10
6
3.62·10
6
5.09·10
6
3.57·10
6
6.03·10
6
3.57·10
6
6.18·10
6
3.63·10
6
5.55·10
6
2.26 2.51 2.89 2.31 1.71 2.15 1.70 1.08 0.85 2.31 2.00 1.48 2.36 2.48 1.88
Table 4 Statistical summary of the off-design efficiencies for each of the cycles considered. 1st Q and 3rdQ are the quantile 25% and 75% of the distribution.
2.97 2.73 2.34 2.93 3.59 3.09 3.53 4.16 4.45 2.91 3.23 3.75 2.87 2.75 3.36
A compact distribution may be interesting for cycles that are going to operate with changing conditions (such as a solar field with a small storage system), and therefore, this cycles may benefit if the intermediate pressure is selected as the Pint, min . Meanwhile, in facilities whose operating conditions are mostly stable (i.e. waste heat from industrial processes or large plants with high storage capacity) this criterion is not suitable. Regarding the VR, it is not so easy to identify a trend on the results of the performance at off-design conditions. However, the use of two expanders in series improves the performance. The distribution of the efficiency reached in the case of one expander (R) is also a compact distribution, with a median of 13.33%, much lower than any of the twoexpander designs considered. The maximum value reached with one expander was 16.32%, also much lower than the one reached with two expanders. Therefore, with an appropriate design (i.e. C4), the values of the
Min
1st Q
Median
Mean
3rdQ
Max
A1 A2 A3
0.0140 0.0080 0.0570
0.1260 0.1267 0.1191
0.1442 0.1453 0.1511
0.1431 0.1441 0.1440
0.1699 0.1700 0.1629
0.1966 0.1968 0.1830
B1 B2 B3 B4
0.0392 0.0101 0.0537 0.0578
0.1224 0.1229 0.1189 0.1052
0.1498 0.1402 0.1498 0.1386
0.1434 0.1405 0.1422 0.1313
0.1654 0.1664 0.1628 0.1489
0.2151 0.1925 0.1838 0.1672
C1 C2 C3 C4
0.0049 0.0007 0.0579 0.0563
0.1134 0.1259 0.1136 0.1187
0.1387 0.1452 0.1467 0.1506
0.1329 0.1424 0.1396 0.1436
0.1608 0.1687 0.1582 0.1632
0.1944 0.1945 0.1777 0.1838
D1 D2 D3
0.0047 0.0074 0.0240
0.1193 0.1260 0.1248
0.1442 0.1458 0.1533
0.1388 0.1439 0.1465
0.1687 0.1728 0.1696
0.2023 0.2009 0.1928
E1 E2 E3
0.0162 0.0155 0.0291
0.1251 0.1236 0.1229
0.1438 0.1438 0.1513
0.1434 0.1421 0.1441
0.1718 0.1711 0.1679
0.1991 0.2003 0.1910
R
0.0616
0.1002
0.1333
0.1250
0.1440
0.1632
efficiency are higher than with one expander, and these high values are maintained all along the off-design operating conditions. 5. Performance analysis at off-design operation As the selection of the intermediate pressure is a key aspect on the off-design performance, a more detailed analysis of the performance for the different approaches was done in order to clarify the conclusions. For that, the case A was selected (VR1 = 3, VR2 = 3). As designs A1 and A2 are quite similar, designs A1 and A3 were selected as representatives of the cases where Pint = Pint , gm and Pint = Pint, min . The analysis of the performance at off-design conditions is presented
Fig. 3. Statistical analysis of the off-design efficiencies for each of the cycles considered. Pgm: Pint = Pint, gm ; Pmax: Pint = Pint, 693
max ;
Pmin: Pint = Pint,
min
.
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in three stages: the first one that analyses the different variables and performance at off-design operation, the second one that studies the irreversibilities and the last one where the best design and operation point are proposed. The variables selected and the structure of the analysis are the same as in [16]: cycle thermal efficiency ( th ), isentropic efficiency of the expanders ( exp,1 and exp,2 ) and the adapted pressure on each expander (PRad,1 and PRad,2 ), to be able to compare the results of this work with the previous one. In addition, a detailed analysis of the stages of the expansion is included, for an improved understanding of the performance of the expanders.
5.1. Performance analysis The performance analysis of the simulation results at off-design conditions for two expander systems is shown in Figs. 4–8. The behaviour of each variable was displayed in nine different plots to illustrate the different changes on the operation conditions: each graph shows the efficiency as a function of the working pressure and temperature, keeping constant the speed of the expanders and the condensation temperature. The evolution of the thermal efficiency for designs A1 and A3 versus
Fig. 4. Off-design thermal efficiency for the ORC with two expanders.
Fig. 5. Off-design isentropic first expander efficiency. 694
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Fig. 6. Off-design isentropic second expander efficiency.
Fig. 7. Off-design first expander adapted pressure ratio.
the evaporation pressure is shown in Fig. 4. As expected, the thermal efficiency increased when the condensation temperature decreased and the superheating temperature increased. As in the case of the cycle with one expander [16], an optimal pressure was identified, located at higher pressure values than when one expander was used. This maximum values moved to higher pressures when the rotation speed of the expander and the condensation temperature increased. This caused (in some graphs) that the maximum is not shown because the total expanders’ volumetric ratio (VR) were better adapted to the real expansion ratio of the cycle.
For design A1 at high condensation temperatures, the efficiency decreased abruptly when the evaporation pressure was low. In the case of A3 the curve of the thermal efficiency was much more flat along the whole range of operating pressures, although the values reached were lower, as seen in the previous section. Figs. 5 and 6 show the isentropic efficiency of each expander ( exp ). In these cases, the behavior of the efficiency of the expanders is quite different to that of the systems with one expander. In the case of the first expander (Fig. 5) the outlet pressure was not imposed by the conditions of the condenser but by the coupling 695
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Fig. 8. Off-design second expander adapted pressure ratio.
Fig. 9. Off-design cycle irreversibilities for Tmax = 150 °C; Tmin = 25 °C; N = 3000 min 1.
between expanders. The irreversibilities due to the difference between the adapted pressure and the outlet pressure were minimum and the efficiency was rather constant. The PR ad of this expander was close to one (Fig. 7). When the irreversibilities caused by the over- or sub-expansions were reduced, the importance of the irreversibilities due to the leaks increased, generating a change in the efficiency of the expander. Hence, the maximum of the efficiency did not happen when PR ad = 1. This behaviour was not defined by the design intermediate pressure, as the same behaviour is observed for both A1 and A3. The behaviour of the second expander was different (Fig. 6), as the outlet pressure was defined by the condensation conditions. The irreversibilities due to the over- or sub-expansions were much more important that in the case of the first expansor. Moreover, the behaviour of the second expander of both selected designs was not similar. In design A1 the efficiency was very variable, reaching very low values at low working pressures. For design A3 this variability only appeared at the most extreme working conditions (high N, high Tcond and very low Pevap ). Hence, the second expander of this design was better adapted to the operating conditions than the one of design A1.
These differences of behavior in the second expander were also reflected in the PR ad values. In design A1, PR ad,2 reached values over 3.5, while in design A3 was always lower than 2, which indicates again that the second expander was better adapted. In both cases, the irreversibilities caused by the leaks have little importance when compared to those due to the over- and sub-expansions. Therefore, the efficiency of the second expander reached its maximum close to the condition of PR ad,2 = 1. The behaviour of A1 cycle efficiency was defined by the behaviour of the second expander. As the first expander maintained its efficiency, the decrease of efficiency of the second expander at low evaporation pressures was the cause of the overall cycle efficiency decrease. 5.2. Irreversibilities at off-design operation Fig. 9 shows the analysis of the irreversibilities of the cycle under different off-design conditions. Table 5 shows the irreversibility associated to the pressure drop and to the expanders. One of the highest irreversibilities was reached in the evaporator, as the heat source was considered as infinite and it provides energy at the highest temperature of the cycle Tmax . The main difference between the 696
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Table 5 Irreversibilities of the expander and of the pressure drop. Tmax = 150 °C; Tmin = 25 °C; Psat = 1800 kPa. N (min 1)
Iexp,1/Esource (%)
Iexp,1/Esource (%)
Iploss /Esource (%)
Sum (%)
A1
1500 3000 4500
11.83 8.74 7.17
7.35 3.41 2.26
0.34 0.81 1.42
19.52 12.96 10.85
A3
1500 3000 4500
7.34 5.18 3.96
16.36 9.00 6.30
0.33 0.81 1.44
24.04 14.98 11.70
Fig. 10. Irreversibilities of the expanders for design A1.
considered designs was the behaviour of the expanders. For the design A1 the irreversibility of the first expander was greater than for design A3, and reached a constant value along the range of evaluated evaporating pressures. The irreversibility of the second expander was greater for design A3 than for design A1. For the latter, the irreversibility increased at lower evaporation pressures, while for design A3 it was greater at higher evaporation pressures. Hence, the behaviour of the expanders at off-design conditions was critical at off-design operation. Due to the importance of the irreversibility in the expander, its sources were analyzed in the following section.
1.27 kW) and they decreased steeply when the working pressures were decreased, reaching a minimum at 1400 kPa (0.1825 kW). This trend was due to the behaviour of the expansion process, since the irreversibility due to the leakages becomes less important at low pressures. This indicated that the second expander may not be adequate for low pressure operating conditions. For design A3 the irreversibilities of the second expander increased from 0.26 up to 2.85 kW from the low to the high pressure values, as also seen in Fig. 9b. These irreversibilities were again governed by the expansion process. The values for the irreversibility of the leaks also increased with the increasing pressure, but was only dominant at lower pressures. Hence, the design strategy for design A3, with Pint, min , optimized the behaviour at off-design conditions, specially when the lower operating pressures were taken into account, and particularly for the first expander.
5.3. Irreversibilities in the expanders The irreversibilities of the expanders are shown by source to understand the differences on the behaviour of the first and second expander. The irreversibilities of a expander (Iexp ) were classified into three different sources: leakages (Ileak ), over- and under-expansion (Iexp(over , under ) ) and the mix of all the flow rates (Imix ). All these values are shown in Figs. 10 and 11, for both expanders and for designs A1 and A3. The most important sources of irreversibility in the first expander were the leakages. Irreversibility due to the over- and sub-expansion was negligible. This was because the outlet pressure was roughly the same as the adapted. For design A1 the irreversibilities were around between 0.30 and 0.85 kW for all the range of working pressures, with a trend to increase when the pressures were increased. The values of the irreversibilities of design A3 were between 0.30 and 0.48 kW. In the case of the second expander, the irreversibilities were more variable. In A1 the irreversibilities were high for high pressures (up to
5.4. Best operation point The relationship between the thermal efficiency and the generated power for different working conditions (temperatures and expander rotation speeds) are shown in Fig. 12. Using this figure, it was possible to reach a maximum efficiency for each demanded level of power for the given working conditions (maximum and minimum temperatures) by adjusting the expander and pump speed (adjusting the pressure). This optimum pressure for each demanded power was even lower than the one identified for each series of results. Hence, this figure suggested an envelope of the family of curves, where the most appropriate operating point for each demanded power was contained. Each point in the envelope corresponded to a certain scroll speed and boiling 697
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Fig. 11. Irreversibilities of the expanders for design A3.
Fig. 12. Best operating point.
pressure. The point where the maximum high temperature, the minimum condensation temperature and the maximum of the envelope curve happens is the point that should be used for the ORC design. There was a branch of the envelope curve that matches with the constant speed curve, at the maximum admissible speed due to the asymptotically efficiency increase with the expander speed. The point with the optimal pressure for the maximum admissible shaft speed should be selected as the operating point. For design A1, this happened on the maximum power considered (8.65 kW). However, for A3 it happened around 7.25 kW, which is not the maximum power possible. Then, three different regions where the ORC could operate were identified in Fig. 12. In the case of A1, if the power demand decreases, this should be accomplished following the envelope curve searching for the adequate pressure-speed combination, which would define the different operation regions: firstly at decreasing pressure and constant speed, and then decreasing also the expander rotation speed. For A3, the two first regions were similar but also levels of power over the design point could be reached by increasing pressure and constant expander speed, which would lead to an efficiency decrease, defining the third operating region. Eventually, higher power values may be reached with the expander at over-speed conditions for both cases.
6. Conclusions The behavior of an Organic Rankine Cycle (ORC) system with two expanders in series at off-design working conditions was studied and the influence of the intermediate pressure and the expanders’ volumetric expansion ratio on the off-design performance of the ORC was determined. The irreversibilities of the components were analyzed and the performance of the ORC with two expanders for two different designs was also discussed. The thermal efficiency that is reached with two expanders was significantly higher than the obtained in the case of one. Of course, this increase came with an increase in the complexity in the design of the expanders. The first challenge in ORC systems with two expanders in series was the selection of a set of volume expansion ratios and intermediate pressure that optimized the performance of the cycle at off-design operation. In particular, the selection of the adequate intermediate pressure was key to the good performance of the cycle. In a first approach, the best option was to choose the group of parameters for which the expansion efficiency in the design condition was the highest. However, it was possible to find a design that presented a more constant operation, which corresponded to the selection of the intermediate pressure that minimizes the isentropic efficiency difference of both expanders. As long as the adequate intermediate 698
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pressure could be chosen, the volumetric expansion ratio would not affect as much. This design methodology (Pint, min ) showed to be advantageous regarding the variability of the efficiency at off-design conditions. The irreversibility of the first expander was mainly due to the leaks. However, the performance of the second expander was more variable and was defined by the difference between the discharged pressure and the condensation pressure. The off-design performance analysis allowed to establish a methodology to obtain the desired power with the maximum thermal
efficiency, and the identification of the best operation point and the three operation regions that each system allowed. Acknowledgments Mercedes Ibarra acknowledges the generous financial support provided by CORFO (Corporación de Fomento de la Producción) under the Project 13CEI2-21803. Antonio Rovira acknowledges the financial support by the Project 2018-IEN28.
Appendix A Here a summary of the model published in [16] is presented. This model is used to determine the performance of an ORC with heat recuperation and superheating at part load operation. The calculations follow three steps: assessment of the reference cycle, characterization of the components of the facility and part load simulation model calculations. A.1. Calculation of the ORC at the design point Thermal efficiency of the cycle: th
(7)
= WORC, net /Qevap
where
Wnet = Wexp
Wbomb = m (H7
H9)
m (H2
(8)
H1)
The heat consumed in the evaporator (Qevap ) is calculated by:
Qevap = m (H6
(9)
H3)
A.2. Characterization of the system The model presented in the previous section was used to define the design conditions of the cycle, and therefore it characterizes the ORC.
• Pressure drop (representative of all the pressure drop of the system): K
P
=
2 P7)/mdis
6 ·(P6
(10)
• Expanders: the equations for this scroll model are based on the model presented by Lemort et al. [27] – admission volume
Vdis = mtot , dis /(Ndis ·
(11)
dis )
– volumetric expansion ratio
VR = vad/ vin =
(12)
ad / in
– leakeage area
Aleak = Aleak, ref
•
3
Vdis Vdis, ref
(13)
being Aleak, ref = 4, 6 mm2 and Vdis, ref = 36.54 cm3 [27] Heat exchangers: (14)
UA = Qin/ DTML
A.3. Calculation of the ORC at the off-design conditions
• Expanders
min = Vdis· N ·
exp, ad
=
is, exp
(15)
exp, in ·VR
(16)
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mleak = Aleak ·
2(hexp, in
leak
hleak )
(17) (18)
mtot = min + mleak
Wexp = min (hexp, in
is, exp
=
hleak ) + min ·
hexp, in
hexp, out
hexp, in
hexp, out , s
exp, out
(Pad
(19)
Pexp, out )
(20)
• Heat exchangers: U mtot = Udis mtot , dis
0.8
(21)
• Pump:
The efficiency of the pump in off-design conditions is determined by the non-dimensional performance curves used by Manente et al. [21] and Calise et al. [28]. Following the same methodology presented by these authors, it is assumed that the maximum efficiency for the pump takes place for the design conditions. For the off-design pump performance, both the flow rate and the pump rotational speed are varied and the pump performance curve varies according to the affinity laws for constant impeller diameter:
q1 q2
=
N1 N2
1
(22)
H1 N1 = H2 N2
2
W1 N1 = W2 N2
3
(23)
(24)
Appendix B. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.applthermaleng.2018.12.083.
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