Thermodynamic modeling and performance analysis of four new integrated organic Rankine cycles (A comparative study)

Accepted Manuscript Thermodynamic modeling and performance analysis of four new integrated organic Rankine cycles (A comparative study) Reza Kheiri, Hadi Ghaebi, Mohammad Ebadollahi, Hadi Rostamzadeh PII: DOI: Reference:

S1359-4311(17)32899-5 http://dx.doi.org/10.1016/j.applthermaleng.2017.04.150 ATE 10299

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

23 September 2016 24 February 2017 29 April 2017

Please cite this article as: R. Kheiri, H. Ghaebi, M. Ebadollahi, H. Rostamzadeh, Thermodynamic modeling and performance analysis of four new integrated organic Rankine cycles (A comparative study), Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/j.applthermaleng.2017.04.150

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Thermodynamic modeling and performance analysis of four new integrated organic Rankine cycles (A comparative study)

Reza Kheiri, Hadi Ghaebi*, Mohammad Ebadollahi, Hadi Rostamzadeh

Department of Mechanical Engineering, Faculty of Engineering, University of Mohaghegh Ardabili, P.O.Box 179, Ardabil, Iran

Abstract Due to environmental pollution and limitation of the fossil fuels, renewable energy resources can be considered as the main alternative for these nonrenewable resources. Since the organic Rankine cycle (ORC) uses organic working fluids and low grade heat sources (LGHSs) to generate power, its usability is limited due to low thermal efficiency in the industry. Thus, in order to improve the thermal efficiency and net power production of the ORC, four new modified ORCs are proposed: ORC with an ejector (EORC), ORC with an ejector and a regenerator (ERORC), ORC with an ejector and a feed fluid heater (EFFHORC), and ORC with an ejector, a regenerator and a feed fluid heater (ERFFHORC). In the EORC, an ejector and a two-stage evaporator has been integrated into the simple ORC. In the ERORC, an ejector, a regenerator with a two-stage evaporator have been integrated into the simple ORC in order to modify two previous cycles. Steam enters to the regenerator prior to the ejector and supply a part of the energy requirement of the first-stage evaporator. The EFFHORC incorporates with an open feed fluid heater, an ejector, and a two-stage evaporator as well as the basic ORC. Steam from the second-stage evaporator enters to ejector as a primary fluid and then its pressure is

*

Corresponding Author: E-mail: [email protected] , Tel & Fax: (+98-45) 33512910

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reduced. This process increases suction of the secondary fluid of the ejector from the turbine and consequently, both of the power generation and the thermal efficiency are increased. In the ERFFHORC, an ejector, a regenerator, and a feed fluid heater are integrated into the simple ORC to surpass all the aforementioned cycles. In addition, various working fluids (i.e., R600, R245fa, R236fa, and cis-2-Butene) are presented to evaluate the thermodynamic performance of the proposed cycles. Later, a thorough parametric study is performed to evaluate the effects of different key parameters, namely, evaporator pressure, condenser temperature, pumps pressure ratio and feed fluid heater pressure on the thermodynamic performance of the prescribed cycles. The results demonstrated that through this state-of-art modification, the thermal efficiency of the EORC, ERORC, EFFHORC, and ERFFHORC is improved by 13.21%, 15.30%, 18.35%, and 19.29%, respectively, compared with that of the simple ORC. Moreover, among all proposed working fluids, R245fa is suggested as a good candidate due to its high thermal efficiency, too. Keywords: Organic Rankine cycle (ORC), Ejector, Regenerator, Feed fluid heater, Thermodynamic performance, Working fluids

Nomenclature A

area specific heat at constant pressure(J

)

energy loss (kW) specific enthalpy (

M

Mach number mass flow rate

P

pressure (kPa) heat rate (kW)

R,r

radius (m) universal gases constant (J

T

temperature(◦C)

V

velocity(m

)

)

main velocity (m

2

specific volume (

)

work(kW)

Greek Symbols

η

thermal Efficiency (%) ejector suction mass flow rate to motive mass flow rate

η

isentropic coefficients of the secondary flow (%)

η

isentropic coefficients of the primary flow (%)

η

isentropic efficiency of diffuser (%)

η

isentropic efficiency (%)

Subscripts C,cond

condenser

cs

isentropic condition of condenser

c.v.

control volume

D

diffuser

E

evaporator

EX

exit

FFH

feed Fluid Heater

HE

heat exchanger

i

inlet

isen

isentropic

m

mixing

N

nozzle

Net

net

P

pump

p

primary

pA

primary flow the A-A section

R

regenerator

s

secondary

sA

secondary flow at the A-A section

T

turbine

TOT

total 3

1. Introduction Industrialization leads to global warming and damage to the environment. In order to provide future energy demands and reduce greenhouse gas emissions as well as fossil fuels dependency, the development of energy systems must be taken into account. Studies show that more than 50% of the total heat generated in the industry is wasted as low-temperature heat sources, where the organic Rankine cycle (ORC) and Kalina cycle (KC) are two main power cycles which use these low grade heat sources. By comparing these two versatile cycles, Kalina cycle needs a higher pressure than the ORC [1]. In recent decades, a great number of researches on the ORC have been conducted. For instance, Munoz et al. [2] and Sanchez et al. [3] concluded that between different technologies, ORC results in a perfect solution for the purpose of LGHSs utilization. Wei et al. [4] proposes two alternative approaches for the design of a dynamic model for an organic Rankine cycle (ORC) which are used for the design of control and diagnostics systems. They concluded that the important features of ORC are high reliability and flexibility. In the similar analysis, Karellas et al. [5] investigate the effects of ORC components on some key parameters, such as the regenerator which had a deep influence on the performance of the whole system. Elsewhere, Guo et al. [6] analyzed the ORC thermodynamically to find the average energy dissipation carried out at different temperatures of the geothermal source. Worek et al. [7] presented a cost-effective optimum design criterion for organic Rankine cycles using low-temperature geothermal heat sources. In this study, the ratio of the total heat exchanger area to the net power output is used as the objective function and optimized using the steepest descent method. The optimum cycle performance is evaluated and compared for different working fluids that include ammonia,

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HCFC123, n-Pentane, and PF5050. They concluded that ammonia has minimum objective function and maximum geothermal water utilization for the optimized geothermal ORC. In the similar work done by Sun et al. [8], the ORC is optimized by Rosen method. This work presented a detailed analysis of an organic Rankine cycle as a heat recovery power plant using R134a as working fluid. Mathematical models for the expander, evaporator, air cooled condenser, and pump are developed to evaluate and optimize the plant performance. As stated by Sun et al. [8], the optimization results revealed that the relationships between controlled variables (optimal relative working fluid mass flow rate, the optimal relative condenser, and fan air mass flow rate) and uncontrolled variables (the heat source temperature and the ambient dry bulb temperature) are nearly linear function for the maximization of the net produced power of the system, while are quadratic function for the maximization of the thermal efficiency. In the other case study, Bahaa et al. [9] proposed a thermodynamic screening of 31 pure component working fluids for organic Rankine cycles, using BACKONE equation of state. The fluids are alkanes, fluorinated alkanes, ethers and fluorinated ethers. Analysis for the heat transfer from the heat carrier with maximum temperature of 120‫ﹾ‬C to the working fluid showed that the largest amount of heat can be transferred to a supercritical fluid and the least to a highboiling subcritical fluid. Roy et al. [10] conducted a comprehensive parametric optimization and performance analysis of a waste heat recovery systems based on organic Rankine cycle, using R12, R-123, and R-134a as working fluids. The cycles are compared with heat source as waste heat of flue gas at 140

and 312 Kg/s/unit mass flow rate at the exhaust of ID fans for 4 * 210

MW, NTPC Ltd. Kahalgaon, India. Results shows the Organic Rankine Cycle with R-123 as working fluid appears to be a choice system for utilizing low-grade heat sources for power generation. Yamada et al. [11] performed energy analysis of a new ORC using the HFO-123yf.

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Li et al. [12] investigated effects of the dry fluids on the net produced power and thermal efficiency of the ORC. An experimental model of a ORC is built and tested by Gang et al. [13], where they proposed three important results: 1. The mass flow rate through the pump is different from that through the turbine in the dynamic test. During the converter frequency adjusting process, the mass flow rate through the pump increased but not in a monotonic way. 2. An isentropic efficiency around 0.65 for the turbine is achieved in the high rotation speed ranges. The heat loss from the turbine to the environment is about two order of magnitudes lower than the enthalpy drop through the turbine even in the small-scale system. 3. The turbine shaft power was about 1 kW, and the ORC thermal efficiency was around 6.8%. Higher system and turbine efficiencies can be speculated on the normal condition for the ORC operation. Schuster et al. [14] proposed a supercritical ORC instead of the simple ORC. The results showed that the heat losses decreased, considerably. In the now-a-days studies, the ejector is introduced as one of the most important components for the energy systems. With this respect, Elrod [15] and Keenan and Neumann [16] proposed onedimensional fundamental theory for energy analysis of the ejector where they demonstrated that the ejector mixing process is an isentropic process. For the properties consideration and the best use of this theory, the mathematical modeling is proposed by Refs. [17] and [18]. Jia et al. [19] studied the behavior of the ejector on the heat absorption and power production potential of the ORC. Hem et al. [20] proposed an ORC with a vapor injector. In this cycle, they used isentropic vapor injector for increasing the thermal efficiency of the ORC. Sadeghi et al. [21] proposed a new two-dimensional model for the ejector analysis by considering the frictional effects on the ejector wall. This model is a combination of 1-D and shock circle model and is closer to the reality. Zhao et al. [22] used the ejector with a separate feed in the ORC, showing that the

6

thermal efficiency can be increased for the proposed system. More investigations for the combination of the ORC with different systems can be found in the following literatures [23-24]. In this study, integration of an ejector, a regenerator, and a feed fluid heater and also combination of them in the simple ORC is proposed to increase the power output and the thermal efficiency, simultaneously. By incorporating the ejector, the pressure will be moderated and reached to the desired level. Using a regenerator, heat loss can be reduced without using of any outsources such as solar energy, where some part of the energy requirement for the evaporator of the ORC is provided. Meanwhile, using of a feed fluid heater in cycles will provide an amount of energy for evaporators without using of any external energy sources. The specific objectives of this study are multifold and are as follows: 

To develop four modified ORCs (ORC with an ejector (EORC), ORC with an ejector and a regenerator (ERORC), ORC with an ejector and a feed fluid heater (EFFHORC), ORC with an ejector, a regenerator and a feed fluid heater (ERFFHORC)



To carry out a comprehensive thermodynamic model for the proposed systems



To perform a parametric study in order to evaluate the effect of the main thermodynamic parameters on the performance of the proposed cycles.



To suggest different working fluids (i.e., R600, R245fa, R236fa, Cis-2-Butene) and evaluate the performance of the proposed cycles using these working fluids.

2. System description 2.1. Basic ORC Figure (1) (a and b) shows a schematic diagram and T-S diagram of the basic ORC, respectively. The basic ORC is in fact the Rankine cycle that incorporates evaporator instead of boiler. This 7

cycle includes mainly a steam turbine, a condenser, an evaporator, and a pump. Since working fluids of the ORC usually have low boiling point, then a low grade heat source (LGHS) can be used for steam production in the evaporator. The heat source can be solar, biogas, geothermal as well as water for the aim of the energy extraction of the LGHS. Because of low thermal efficiency of the ORC, it is required to make a change on its structure. Therefore four novel arrangements for the ORC have been proposed which are illustrated as blow. 2.2. The ORC with an ejector (EORC) A schematic diagram and the T-S diagram of the EORC is depicted in Figs. (2a) and (2b), respectively. This cycle has been proposed by Li et al. [22] to increase the thermal efficiency of the ORC. An ejector and a two-stage evaporator are added to the basic ORC, where the steam of the two-stage evaporator acts as the primary fluid for the ejector. The ejector reduces turbine exhaust pressure (secondary fluid) and tends to increase the turbine power production. The EORC consists of two sub-cycles which are as follows: The first sub-cycle (6-8-9-3-5-6): A part of the saturated liquid from the condenser enters the first-stage evaporator through a pump (6-8) and converts to the superheated or saturated vapor by means of the evaporator (8-9). Then it enters the turbine, where the expanded steam in the turbine produces power output (9-3). Thereafter, the exhaust steam from the turbine enters the ejector as a secondary fluid. The second sub-cycle (6-7-1-5-6): Another part of the saturated liquid enters to the second-stage evaporator by means of pump (6-7) and converts to the saturated steam (7-1). This steam acts as

8

the primary fluid of the ejector, whereas the primary and secondary fluids of the ejector enter to the condenser after mixing (6-7 and 6-8). 2.3. The ORC with an ejector and a regenerator (ERORC) Schematic and T-S diagram of the ORC with an ejector and a regenerator are shown in Figures (3a and 3b), respectively. In this cycle, a heat exchanger (regenerator) is added to the EORC. In the regenerator, some part of the turbine exhaust energy is recovered, and hence the first-stage evaporator duty is decreased. This cycle also consists of two sub-cycles which are as follows: The first sub-cycle (6-8-9-10-11-3-5-6): In this sub-cycle a part of the condensed liquid from the condenser is sent to the regenerator by a pump (6-8). This fluid enters to the first-stage evaporator after heat absorbing, where it is converted to the saturated steam (9-10) and expanded in the turbine (10-11). The turbine exhaust steam then enters the regenerator (11-3) and acts as a secondary fluid of the ejector. The second sub-cycle (6-7-1-3-5-6): In this sub-cycle another part of the condenser exhaust fluid is sent to the second pump (6-7), and then enters the second-stage evaporator (7-1) where it leaves the evaporator as the saturated steam. Finally, this saturated steam enters the ejector as the primary working fluid and draws the secondary fluid into the ejector. 2.4. The ORC with an ejector and a feed fluid heater (EFFHORC) The schematic of the ORC with an ejector and a feed fluid heater as well as the corresponding TS diagram are shown in Figures (4a and 4b). To increase the thermal efficiency of the proposed system, an open feed fluid heater (FFH) is integrated in the EORC. As shown in Figure (4a), the heater is feeding in two ways: one from the turbine and another from the condenser. By this modification although the power generation of turbine decreases, but decreasing of heat

9

requirement of the evaporator tends to have a higher thermal efficiency than that of the EORC. The sub-cycles of this system are as follows: The first sub-cycle (6-7-1-5-6): A part of the condenser outlet liquid is entered to the secondstage evaporator by means of pump III (6-7), and then enters the ejector as the primary fluid (point 1). The second and third sub-cycles ((6-8-10-11-12-3-5-6) and (9-10-11-12-9)): Another part of the condensed liquid is sent to the FFH (6-8). This liquid (state 8) is then mixed with the extracted steam of turbine (state 9) and after adjusting of its temperature and pressure goes to the firststage evaporator by means of pump I (10-11). Finally, after entering to the turbine as a saturated vapor (state 12), the exhaust steam exiting through the turbine (state 3) is then supplied to the ejector as a secondary fluid. 2.5. The ORC with an ejector, a feed fluid heater, and a regenerator (ERFFHORC) Figures (5a) and (5b) illustrates the schematic and T-S diagram of the ERFFHORC, respectively. In this cycle, an ejector, a regenerator, an open FFH as well as a two-stage evaporator are integrated in the basic ORC. The proposed arrangement of these equipments tend to increase the thermal efficiency, significantly. The sub-cycles of this system are as follows: The first sub-cycle (6-7-1-5-6): A part of the condensed liquid is pumped to the second-stage evaporator (6-7), where the liquid is converted to the saturated steam by the evaporator (7-1), and then enters to the ejector as its primary fluid. The second and third sub-cycles (6-8-10-11-12-13-14-3-5-6) and (9-10-11-12-13-9): Here, the rest of the liquid is pumped to the feed fluid heater (6-8), where it is mixed with the extracted steam of the turbine (state 9). After adjusting its temperature and pressure, the saturated liquid is pumped to the heat exchanger (10-11). This fluid reaches to a higher temperature by passing

10

from the proposed heat exchanger (11-12) and enters the first-stage evaporator. The outlet steam of the turbine enters to the heat exchanger (14-3), and then acts as the secondary fluid of the ejector.

3. Thermodynamic modeling For thermodynamic modeling of the proposed cycles, simulation codes are prepared in the Engineering Equation solver (EES). The mass balance and the first law of the thermodynamics are applied to each component of the system which are as follows [25]:

(1) (2) Figure (6) shows a schematic diagram of the ejector which has been considered in this work. In the present work, the model suggested by Sadeghi et al. [21] is used. In this model, it is assumed that there is pressure drop within the constant area section due to the presence of viscosity. Using the following assumption, the principles of mass, momentum and energy conservations are used to analyze the ejector performance: 

The working fluid is an ideal gas with variable properties (Cp, γ).



The flow inside the ejector is steady state.



The kinetic energies at the primary nozzle and suction part inlets and the diffuser exit are negligible.



The inner wall of the ejector is adiabatic.



The entrained flow pressure is uniform and equals to the evaporator pressure.



The isentropic efficiencies for the primary and the secondary flows are 0.85 and 0.95, respectively. This parameter for the mixed flow inside the diffuser is 0.9. 11

The more detailed thermodynamic modeling of the ejector has been brought in Appendix (A). Modeling assumptions are as follows :  All processes are performed at steady state and there is no pressure drop in the components of the systems.  The fluid temperature at the outlet of the condenser is 25 °C.  The pressure of the first- and second-stage evaporators are 599kpa and 420kpa, respectively [22].  Effectiveness of the regenerator is 70% [26].  Isentropic efficiency of the turbine is 80% [26].  The pressure of the feed fluid heater is assumed 340 kPa [27].  Isentropic efficiency of pumps is 80% [26].  Effectiveness of the evaporators are 80% [26].  The working fluid of LGHS is water with inlet temperature of 80 °C. Using the above mentioned equations for the components of the proposed cycles, the equations that needed for thermodynamic modeling of the proposed cycles can be obtained (Table (1)).

4. Results and discussion 4.1. Model validation To validate the developed codes in the EES software, a comparison is made on the results of two different cycles from two different references: 4.1.1. EORC

12

To validate the model developed for the EORC, data reported by the Li et al. [22] is used (see Table (2)), where R600 is assumed as working fluid for this validation. 4.1.2. ORC incorporating with a feed fluid heater and a regenerator This cycle is shown in Figure (7). Simulation results for this cycle is compared with those of reported by Safarian and Aramoun [28] (see Table (3)). Here, R113 is selected as working fluid of the ORC. From Tables (2) and (3) it can be inferred that there are good agreements between the results obtained from the present model and those reported by literature. 4.2. Thermodynamic modeling results Using the codes provided in the EES software, thermodynamic simulation parameters are obtained for all of the aforementioned cycles. Moreover, four different organic working fluids are considered for all proposed cycles which the results are listed in Tables (4-8). To compare the performance improvement of the considered cycles, the increment of their thermal efficiency respect to the basic ORC for different working fluids is also listed in Table (9). By comparing the results of the Tables (4) and (5), it can be seen that the amount of turbine power production in the EORC is more than that of the basic ORC. Using of the ejector tends to reduce turbine exhaust pressure, while increase the power production. On the other hand, the evaporator duty of the EORC is also more than that of the basic ORC. Since the effect of the increasing of the turbine power production is more than decreasing of evaporator duty, hence, the thermal efficiency of the EORC is improved throughout this state-of-art modification. Among the various operating fluids, R245fa has maximum thermal efficiency because of the higher turbine power production. Also, according to the Table (9) R236fa has higher thermal efficiency improvement compared to other working fluids, because its turbine power production increment is more than the other ones (13.21%). 13

Due to the presence of the regenerator, the load of the first-stage evaporator of the ERORC is less than the corresponding value of the EORC. However, because of the decrement of pumps power consumption, the net power production is increased in the ERORC (see Tables (5), (6)). These effects tends that the thermal efficiency of the ERORC would be higher than that of the EORC. According to the Tables (6) and (9), R245fa has the highest thermal efficiency (9.8%) and also, R245fa has the highest thermal efficiency improvement (15.30 %). In the same vein, in order to investigate the performance of the EFFHORC, Tables (5) and (7) are presented. Using FFH tends to significant decrement of the load of the first-stage evaporator, whereas, this reduction is more than the corresponding value in the ERORC. However, the net power production of the EFFHORC is less than that of the EORC, since some part of the steam that extracted from the turbine enters FFH and decreases net power production. As observed in these tables, the reduction in the evaporator load is more than the reduction in the net power production, and hence the thermal efficiency of the EFFHORC is better than that of the EORC. Besides, because of the more net power production and less evaporator load, the thermal efficiency of the EFFHORC is also higher than that of the basic ORC. It is also viewed that, R245fa has the highest thermal efficiency and thermal efficiency improvement (see Tables (7) and (9)). Table (8) presents the thermodynamic modeling results of the ERFFHORC. In this cycle, because of using both of the regenerator and FFH, a signification part of the required energy of the first-stage evaporator is satisfied, and hence tends to a higher thermal efficiency than the basic ORC. The net power production of this cycle is almost equal to that of the EFFHORC, but its first-stage evaporator load is less than the corresponding value in the EFFHORC. Consequently, for all proposed the working fluids, the thermal efficiency of the ERFFHORC is

14

higher than that of the EFFHORC. Similar to the other systems, R245fa has the best performance as well as the highest thermal efficiency improvement in this cycle, too (Tables (8) and (9)). 4.3. Parametric study 4.3.1. Basic ORC 4.3.1.1. The effect of evaporator pressure on performance of the basic ORC Figure (8) illustrates the effect of evaporator pressure on the evaporator load. As it can be viewed, an increase in the evaporator pressure increases the cooling capacity of the evaporator. Besides, R600 and Cis-2-Butene show more variations with the change of the evaporator pressure. This is due to the fact that the absorbed heat by these two working fluids is higher than other ones, since they have high latent enthalpy at the considered range of the pressure. Figure (9) depicts the net power production changes for various evaporator pressure levels for different proposed working fluids. As can be seen, increasing of the evaporator pressure results in an augmentation of the power production. Meanwhile, among all considered working fluids, Cis-2-Butene reveals the highest heat absorption in the evaporator which is also has the highest power production, too. In the same vein, increasing of the evaporator pressure will cause a rise in the turbine power production as well as the heat absorption of the evaporator. Since the increasing of the turbine power production is more than that of the heat absorption by the evaporator, the thermal efficiency is increased by augmentation of the evaporator pressure (Figure (10)). In addition, among the all considered working fluids, R245fa has the highest thermal efficiency. 4.3.1.2. The effect of condenser temperature on performance of the basic ORC Figures (11-13) displays the effect of the condenser temperature variation on the evaporator load, the net power production, and the thermal efficiency, respectively. By increasing of the 15

condenser temperature, the heat that needed for working fluid to reach to the desired temperature and pressure is decreased. In addition, the slop of the evaporator load variation with the condenser temperature for R600 is deeper than the others (Figure (11)). Increasing the condenser temperature tends to increase the turbine outlet pressure, and hence the turbine power production decreases. Also, this phenomenon tends to decrease the pump power consumption. Consequently, the net power production decreases by increasing of the condenser temperature. Furthermore, among all different recommended working fluids, R600 and Cis-2Butene have the greatest variation with the condenser temperature (Figure (12)). As mentioned above, increasing of the condenser temperature decreases both the net power production as well as the heat absorption of the evaporator. But, the total amount of reduction in the power production is more than the heat absorption by the evaporator. As a result, the thermal efficiency will decrease with increasing of the condenser temperature (Figure (13)). Taking the R245fa as working fluid into account, in can also be observed that the slope of this reduction for this fluid is little compared with that of the other working fluids. 4.3.2. The EORC 4.3.2.1. The effect of pumps pressure ratios on performance of the EORC Figures (14) and (15) show the effects of pump (I) and pump (II) pressure ratios on the heat absorption of the first- and second-stage evaporators, respectively. The pressure ratio of Pump(I) only affects the first-stage evaporator in which by increasing of this parameter, heat absorption of the first-stage evaporator is increased (Figure (14)), where among all proposed working fluids, Cis-2-Butene has the highest value.

16

In the same line, pump (II) pressure ratio has not effect on the first-stage evaporator duty, while increasing the pressure ratio of pump (II) increases the pressure of the second-stage evaporator, and hence the heat absorption of evaporator is increased (Figure (15)). Similarly, increasing of the pump (I) pressure ratio leads to a rise in the pump (I) power consumption and turbine power production, simultaneously. As a result, the net power production is increased (Figure (16)). In the same vein, increasing of the pump (II) pressure ratio increases the pressure of the motive steam of the ejector which leads to more pressure decrement at the turbine exhaust, which can in turn increase the net power production (Figure (17)). Referring to the Figures (18) and (19), as the pressure ratios of the pump (I) and pump (II) increase, the thermal efficiency is also augmented. It can also be inferred from these figures that the slope of variations for R600 (in Figure (18)) and Cis-2-Butene (in Figure (19)) are more than other working fluids. 4.3.3. The EFFHORC 4.3.3.1. The effect of FFH pressure on performance of the EFFHORC As mentioned before, the FFH main feed stream comes from the turbine. As pressure of FFH increases (see Figure (4)), the turbine power production decreases due to decrement of the mass flow. This phenomenon also affects pump (I) and pump (II) power consumptions (power consumption of pump (I) and pump (II) decreases and increases, respectively). As a results, the net power production decreases (Figure (20)). The FFH pressure has no effect on the second-stage evaporator heat load. On the other hand, increasing of the FFH pressure decreases the first-stage evaporator load because of the 17

decrement of the terminal temperature difference of this evaporator. It is also easy to notice, all of the studied working fluids have similar variations, too (Figure (21)). Taking Figures (20) and (21) into consideration, increasing of the FFH pressure reduces heat load of the first-stage evaporator as well as the net power production. Accordingly, since the reduction of the heat load of the first-stage evaporator is larger than the net power production, the thermal efficiency is augmented throughout this variation (Figure (22)).

5. Conclusion In this research paper, four modified organic Rankine cycle were proposed to augment of the thermal efficiency as well as the power production. For this purpose, a steam ejector, a feed fluid heater, and a regenerative heat exchanger were integrated into the basic ORC. These modified cycles were: ORC with an ejector (EORC), ORC with an ejector and a regenerator (ERORC), ORC with an ejector and a feed fluid heater (EFFHORC), and ORC with an ejector, a regenerator, and a feed fluid heater (ERFFHORC). Moreover, a parametric study was done to reveal the effects of some operating parameters (i.e., evaporator pressure and condenser temperature for the basic ORC, pumps pressure ratios for the EORC, and feed fluid heater pressure for the EFFHORC) on the thermodynamic performance of the proposed cycles. For all of the considered cycles, different working fluids (i.e., R600, R245fa, R236fa, and Cis-2-Butene) were examined. The significant results obtained from the thermodynamic analysis and parametric studies are as follows: 

Among the considered working fluids and for all of the developed cycle, R245fa and Cis2-Butene had the highest thermal efficiency and net power production, respectively.



Using R245fa as working fluid, the ERFFHORC and basic ORC had the highest and the lowest thermal efficiency, respectively. 18



Using Cis-2-Butene as working fluid, the EORC and had the highest and the lowest net power production, respectively.



For the case of ORC, when the evaporator pressure increased, both of the power and thermal efficiency were increased. However, the net power production and thermal efficiency are decreased by an increase in the condenser temperature.



For the case of EORC, increasing of the pumps pressure ratios tended to the increment of the net power production as well as the thermal efficiency.



For the case of EFFHORC, increasing of the feed fluid heater pressure increases the thermal efficiency and decreases the net power production, respectively.

Appendix (A): Ejector Thermodynamic Modeling Here, the details of the equations used for thermodynamic modeling of the ejector is presented. The ejector consists of three main parts, namely: suction chamber, mixing section, and diffuser (Figure 6). Isentropic flow relations are used to obtain the primary mass flow rate at the nozzle throat by considering the chocking condition which is as follows:

(A.1)

For a given geometry of the nozzle, the fluid properties and Mach number at exit of the nozzle can be calculated: (A.2) (A.3) (A.4)

19

where

and

are the temperature and velocity of the primary flow at exit of the nozzle,

respectively. (A.5) (A.6) (A.7)

(A.8) where A indicates A-A section. Assuming an isentropic expansion for the primary flow, the effective diameter of the primary flow at constant area section is calculated as follows [29]: (A.9)

The mixing of the flows starts when the secondary flow reaches sonic velocity (Mach=1) and is chocked at section A-A. Therefore, there is a very thin layer between the primary and the secondary flows at the cross-sectional A-A. On the other hand, the secondary flow velocity on the ejector wall is zero because of the viscosity effects. Thus, the entrained flow velocity changes from zero on the ejector wall to the sonic velocity in the layer between the primary and the secondary flows. The velocity profile in radial direction is exponential as follows: (A.10) By applying the boundary condition as mentioned above: (A.11)

20

The average velocity and mass flow rate of the secondary flow at the A-A section can be defined as follows [29]: (A.12)

(A.13) Applying the conservation of energy, we have: (A.14) is energy loss of the primary and the secondary flows in the suction chamber and effective area [29]: (A.15) By Applying the conservations of momentum and energy in mixing chamber, the velocity, temperature and Mach number of the mixed flow can be determined as follows [29]: (A.16)

(A.17) (A.18) Assuming the ideal gas model for the flow behavior before the shock, the following relations can be employed to approximate the mixed flow pressure

: (A.19) (A.20)

The ejector back pressure (condenser pressure) is higher than the mixed flow pressure and supersonic shock wave will occur at the end of mixing chamber, and hence the mixed flow 21

velocity decrease to subsonic one. The mixed flow pressure and Mach number, after the shock, can be calculated as [30]: (A.21)

(A.22) The mixed flow pressure and temperature at the diffuser exit can be calculated by the following equations [30]: (A.23) (A.24)

6-References

22

[1]‫ ‏‬P. Bombarda, C.M. Invernizzi, C. Pietra, "Heat recovery from diesel engines: A thermodynamic comparison between Kalina and ORC cycles", Applied Thermal Engineering 30 (2010), 212-219 [2] J. Munoz Escalona, D. Sanchez, R. Chacartegui, T. Sanchez, "Part-load analysis of gas turbine & ORC combined cycles", Applied Thermal Engineering 36 ( 2012), 63-72. [3] R. Chacartegui, J. Munoz Escalona, D. Sanchez, B. Monje, T. Sanchez, "Alternative cycles based on carbon dioxide for central receiver solar power plants", Applied Thermal Engineering 31(2011), 872-879. [4] D. Wei, X. Lu, Z. Lu, J. Gu, "Dynamic modeling and simulation of an Organic Rankine Cycle (ORC) system for waste heat recovery", Applied Thermal Engineering 28(2008), 1216-1224 . [5] S. Karellas, A. Schuster, A. Leontaritis, " Influence of supercritical ORC parameters on plate heat exchanger design", Applied Thermal Engineering 33–34(2012), 70–76. [6] T. Guo, H. Wang, S. Zhang, "Comparative analysis of natural and conventional working fluids for use in transcritical Rankine cycle using low-temperature geothermal source", Energy Research 35(2011), 5049-5062. [7] H. Hettiarachchi, M. Golubovic, M. Worek, Y. Ikegami, "Optimum design criteria for an organic Rankine cycle using low-temperature geothermal heat source", Energy 32 (2007), 16981706. [8] J. Sun, W. Li," Operation optimization of an organic rankine cycle (ORC) heat recovery power plant", Applied Thermal Engineering 31 (2011), 2032-2041. [9] S. Bahaa, K. Gerald, "Working fluids for low temperature organic Rankine cycles", Energy 32 (2007), 1210-1221.

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[10] J. Roy, K. Mishra, A. Misra, "Parametric optimization and performance analysis of a waste heat recovery system using organic Rankine cycle", Energy 35 (2010),5049-5062. [11] N. Yamada, M. Anuar, K. Trung, "Study on thermal efficiency of low-to mediumtemperature organic Rankine cycles using HFO-123yf", Energy 41 (2012), 789-800. [12] W. Li, X. Feng, L. Yu, J. Xu, "Effects of evaporating temperature and internal heat exchanger on organic Rankine cycle", Applied Thermal Engineering 31 (2011), 4014-4023. [13] P. Gang, J. Li, Y. Li, D. Wang, J. Ji, "Construction and dynamic test of a small-scale organic Rankine cycle", Energy 36 (2011), 3215-3223. [14] A. Schuster, S. Karellas, R. Aumann, "Efficiency optimization potential in supercritical organic Rankine cycles", Energy 35 (2010), 1033-1039. [15] H. Elrod, "The theory of ejector", Applied Mechanics 67 (1945), 215-225. [16] J. Keenan, E. Neumann, "A basic air ejector", Applied Mechanics 64(1942), 586-599. [17] H. Narmine, M. Karameldin, M. Shamloul,

"Modeling and simulation of steam jet

ejectors", Desalination 123 (1999), 1-8. [18] B. Saleh,"Performance analysis and working fluid selection for ejector refrigeration cycle", Applied Thermal Engineering 107 (2016), 114–124. [19] X. Li, C. Zhao, Y. Jia, "Increased low-grade heat source power generation capacity with ejector", International conference onmeasuring technology and mechatronics automation (ICMTMA) (2011). [20] R. Xu, Y. Hem, "A vapor injector-based novel regenerative organic Rankine cycle", Applied Thermal Engineering 31 (2011), 1238-1243.

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[21] M. Sadeghi, S.M.S. Mahmoudi, R. Khoshbakhti Saray, " Exergoeconomic analysis and multi-objective optimization of an ejector refrigeration cycle powered by an internal combustion (HCCI) engine", Energy Conversion and Management 96 (2015), 403–417. [22] X. Li, C. Zhao, X. Hu, "Thermodynamic analysis of Organic Rankine Cycle with Ejector", Energy 42 (2012), 342-349. [23] A. Khaliq, K. Basant, R. Kumar, "First and second law investigation of waste heat based combined power and ejector-absorption refrigeration cycle" International Journal of Refrigeration 35 (2012), 88-97. [24] X. Li, Q. Zhang, " The first and second on ac organic Rankine cycle with ejector", solar Energy 93 (2012), 100-108. [25] Van Wylen, Borgnakke, Sonntag, "Thermodynamic Function", 6th, india, (2002). [26] F. Al-Sulaiman, I. Dincer, F. Hamdullahpur," Energy and exergy analyses of a biomass trigeneration system using an organic Rankine cycle", Energy 45 (2012), 975-985. [27] S.M.S. Mahmoudi, M. Yari, " A thermodynamic study of waste heat recovery from GTMHR using organic Rankine cycles", Heat Mass Transfer 47 (2011), 181–196. [28] S. Safarian, F. Aramoun, "Energy and exergy assessments of modified Organic Rankine Cycles", Energy Reports 1(2015), 1-7. [29] Y. Zhu, W. Cai, C. Wen, Y. Li, "Shock circle model for ejector performance evaluation", Energy Conversion and Management 48 (2007), 2533–2541. [30] B.J. Huang, J.M. Chang, C.P. Wang, V.A. Petrenko, "A 1-D analysis of ejector performance", International Journal of Refrigeration 22 (1999), 354–364.

25

Figure Captions Figure 1 The basic ORC: (a) schematic diagram and (b) T-S diagram. Figure 2 The ORC with an ejector (EORC): (a) schematic diagram and (b) T-S diagram. Figure 3 The ORC with an ejector and a regenerator (ERORC): (a) schematic diagram and (b) TS diagram. Figure 4 The ORC with an ejector and a feed fluid heater (EFFHORC): (a) schematic diagram and (b) T-S diagram. Figure 5 The ORC with an ejector, a feed fluid heater, and a regenerator (ERFFHORC): (a) schematic diagram and (b) T-S diagram. Figure 6 Schematic diagram of the ejector. Figure 7 ORC incorporating with turbine bleeding and regeneration [28]. Figure 8 The effect of evaporator pressure on the evaporator heat absorption for the basic ORC. Figure 9 The effect of evaporator pressure on the net power production for the basic ORC. Figure 10 The effect of evaporator pressure on the thermal efficiency for the basic ORC. Figure 11 The effect of condenser temperature on the evaporator heat absorption for the basic ORC. Figure 12 The effect of condenser temperature on the net power production for the basic ORC. Figure 13 The effect of condenser temperature on the thermal efficiency for the basic ORC.

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Figure 14 The effect of pump (I) pressure ratios on the heat absorption of the first-stage evaporator for the EORC. Figure 15 The effect of pump (II) pressure ratios on the heat absorption of the second-stage evaporator for the EORC. Figure 16 The effect of pump (I) pressure ratios on the power production for the EORC. Figure 17 The effect of pump (II) pressure ratios on the net power production for the EORC. Figure 18 The effects of pump (I) pressure ratios on the thermal efficiency for the EORC. Figure 19 The effect of pump (II) pressure ratios on the thermal efficiency for the EORC. Figure 20 The effect of the feed fluid heater pressure on the net power production for the EFFHORC. Figure 21 The effect of feed fluid heater pressure on the first-stage evaporator load for the EFFHORC. Figure 22 The effect of feed fluid heater pressure on the thermal efficiency for the EFFHORC.

27

Figures

a)

b)

Figure 1 28

a)

b)

Figure 2 29

a)

b)

Figure 3 30

a)

b)

Figure 4 31

a)

b)

Figure 5 32

Figure 6

Figure 7

33

Figure 8

34

Figure 9

Figure 10

35

Figure 11

Figure 12

36

Figure 13

37

Figure 14

Figure 15

38

Figure 16

Figure 17 39

Figure 18

Figure 19 40

Figure 20

Figure 21 41

Figure 22

42

Tables Table 1 Energy balance for component of the proposed cycles Components

Equations

Basic ORC cycle Pump(1-2) Evaporator (2-3) Turbine(3-4) Condenser(4-1) = Thermal efficiency

EORC cycle Pump I(6-8) Pump II (6-7) First stage evaporator (8-9) Second stage evaporator(7-1) Turbine (9-3) Condenser(5-6) Appendix( A)

Ejector(1-3-5)

=

Thermal efficiency

43

ERORC cycle Pump I(6-8) Pump II(6-7) Regenerator First stage evaporator (9-10) Second stage evaporator (7-1) Turbine(10-11) Condenser(5-6) Appendix (A)

Ejector(1-3-5)

= Thermal efficiency

EFFHORC cycle Pump I(10-11) Pump II(6-8) Pump III(6-7) First stage Evaporator(11-12) Second stage Evaporator(7-1) Turbine(12-3,12-9) Condenser(5-6) Feed Fluid heater(8-9-10) Appendix (A)

Ejector(1-3-5)

=

Thermal Efficiency ERFFHORC cycle

44

Pump I(10-11) Pump II(6-8) Pump III(6-7) First stage evaporator (12-13) Second stage evaporator(7-1) Turbine(13-14,13-9) Condenser(5-6) Feed fluid heater(8-9-10) Ejector(1-3-5)

Appendix (A)

Regenerator = Thermal efficiency

Table 2 Comparison of the present simulation with those reported by Li et al. [22] for EORC cycle Parameters unit Li et al.[22] Present model

LGHS water’s parameters Mass flowrate

kg/s

1

1

First-stage evaporator inlet temperature

C

80

80

First-stage evaporator outlet temperature

C

59.37

59.42

Second-stage evaporator inlet temperature

C

59.37

59.42

Second-stage evaporator outlet temperature

C

48.1

48.15

First-stage evaporator (Turbine inlet) mass flowrate

kg/s

0.226

0.226

First-stage evaporator (Turbine inlet) temperature

°C

57.48

57.36

First-stage evaporator (Turbine inlet) pressure

Bar

5.99

5.99

0.13

0.13

Cycle parameters (R600)

45

Second-stage evaporator flowrate

kg/s

43.78

43.71

Second-stage evaporator temperature

°C

4.2

4.2

Second-stage evaporator pressure

Bar

36

35.91

Turbine outlet(Secondary fluid of ejector) temperature

°C

2.99

2.99

Turbine outlet(Secondary fluid of ejector) pressure

Bar

0.356

0.356

Condenser inlet flowrate /Condenser outlet flowrate

kg/s °C

38.5/35

38.5/35

Condenser inlet pressure/Condenser outlet pressure

Bar

3.28

3.29

Thermal efficiency(η)

%

7.34

7.27

Condenser inlet temperature /Condenser outlet temperature

Table 3 Comparison of the present simulation with those reported by Safarian and Aramoun[28] States 1 2 3 4 5 6 7 8 9 10 11 12 13 Evaporator duty (kW) Condenser duty (kW) Turbine power production(kW) Pump power consumption (kW) Net power output (kW) Thermal efficiency (%)

Safarian and Aramoun[28] T( C) P(MPa) 25 0.048 25.4 1 40 1 138.3 1 140.2 2.5 195 2.5 157.3 1 92 0.048 74 0.048 300 0.1 189 0.1 25 0.1 35 0.1 252 194.6 61 3.46 57.54 22.83

Present model T( C) P(MPa) 25 0.044 26 1 37.52 1 139.2 1 140.6 2.5 193.7 2.5 155.2 1 87.44 0.044 72.5 0.044 300 0.1 188.9 0.1 25 0.1 35.36 0.1 247.2 195.4 61.3 3.817 57.48 23.25

Table 4 Simulation results for the basic ORC cycle Cycle parameters R600 R236fa Evaporator duty(kW) 95.95 37.15 Condenser duty(kW) 75.44 29.65

46

R245fa 50.61 38.9

Cis-2-Butene 107 83.37

Pump power consumption (kW) Turbine power production(kW) Net power output(kW) Thermal efficiency

0.1466 6.441 6.294 6.56

0.05515 2.08 2.025 5.45

0.077 4.38 4.30 8.5

0.1554 7.748 7.593 7.09

R245fa 50.61 25.07 75.68 53.37 0.077 0.070 7.44 7.29 9.6

cis-2-Butene 107 49.08 156.1 115.4 0.155 0.122 11.51 11.23 7.2

R245fa 49.31 25.07 74.38 52.30 0.0762 0.070 7.44 7.294 1.69 9.8

Cis-2-Butene 105.5 49.08 154.6 113.09 0.1534 0.122 11.51 11.234 2.04 7.27

R245fa 43.02 25.07 68.08 53.37 0.046

Cis-2-Butene 92.04 49.08 141.12 115.4 0.12

Table 5 Simulation results for the EORC cycle Cycle parameters First-stage Evaporator duty(kW) Second-stage Evaporator duty (kW) Total Evaporator duty (kW) Condenser duty (kW) Pump(I) power consumption (kW) Pump(II) power consumption (kW) Turbine power production(kW) Net power Output (kW) Thermal efficiency (%)

R600 95.95 45.53 141.5 106.3 0.1466 0.1089 10.4 10.14 7.17

R236fa 37.15 18.15 55.29 41.92 0.055 0.0377 3.507 3.414 6.17

Table 6 Simulation results for the ERORC cycle Cycle parameters R600 R236fa First-stage Evaporator duty (kW) 93.87 36.33 Second-stage Evaporator duty (kW) 45.53 18.15 Total Evaporator duty (kW) 139.4 54.48 Condenser duty (kW) 104.17 41.08 Pump(I) power consumption (kW) 0.1451 0.054 Pump(II) power consumption (kW) 0.1089 0.0377 Turbine power production (kW) 10.4 3.507 Net power Output (kW) 10.15 3.415 Regenerator duty (kW) 2.73 1.063 7.28 6.27 Thermal efficiency (%)

Table 7 Simulation results for the EFFHORC cycle Cycle parameters First-stage Evaporator duty(kW) Second-stage Evaporator duty(kW) Total Evaporator duty(kW) Condenser duty(kW) Pump(I) power consumption (kW)

R600 89.49 45.53 135 106.3 0.1094

47

R236fa 34.9 18.15 53.05 41.92 0.044

Pump(II) power consumption (kW) Pump(III) power consumption (kW) Turbine power production(kW) Net power output(kW) Thermal efficiency(%)

0.036 0.034 10.1 9.920 7.35

0.0128 0.010 3.4 3.333 6.28

0.023 0.031 6.95 6.85 10.06

0.046 0.0415 10.6 10.392 7.36

R245fa 42.52 25.07 67.59 52.41 0.045 0.023 0.031 6.95 6.851 1.22 10.14

Cis-2-Butene 90.04 49.08 139.12 113.39 0.118 0.046 0.0415 10.6 10.394 1.98 7.47

Table 8 Simulation results for the ERFFHORC cycle Cycle parameters First-stage Evaporator duty(kW) Second-stage Evaporator duty(kW) Total Evaporator duty(kW) Condenser duty(kW) Pump(I) power consumption (kW) Pump(II) power consumption (kW) Pump(III) power consumption (kW) Turbine power production(kW) Net power output(kW) Regenerator duty(kW) Thermal efficiency(%)

R600 87.55 45.53 133 104.47 0.1083 0.036 0.034 10.1 9.922 2.54 7.46

R236fa 34.45 18.15 52.6 41.48 0.043 0.0128 0.010 3.4 3.334 0.99 6.34

Table 9 Comparing thermal efficiency of the proposed cycles to basic ORC Thermal efficiency improvement EORC(%) ERORC(%) EFFHORC(%) ERFFHORC(%)

R600 9.30 10.98 12.0 13.7

48

R236fa 13.21 15.04 15.23 16.33

R245fa 12.94 15.30 18.35 19.29

Cis-2-Butene 1.5 2.5 3.80 5.36

Highlights: 

Four modified ORCs are proposed.



A comprehensive thermodynamic model for the proposed systems is carried out.



Parametric study is performed in order to evaluate the effect of the main thermodynamic parameters on the performance of the proposed cycles.



Different working fluids are examined to evaluate the performance of the proposed cycles.

49