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Performance analysis of a combined system for cold and power
Accepted Manuscript Title: Performance analysis of a combined system for cold and power Author: H. Landoulsi, M. Elakhdar, E. Nehdi, L. Kairouani PII: DOI: Reference:
S0140-7007(15)00240-6 http://dx.doi.org/doi:10.1016/j.ijrefrig.2015.07.033 JIJR 3121
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
20-3-2015 7-7-2015 29-7-2015
Please cite this article as: H. Landoulsi, M. Elakhdar, E. Nehdi, L. Kairouani, Performance analysis of a combined system for cold and power, International Journal of Refrigeration (2015), http://dx.doi.org/doi:10.1016/j.ijrefrig.2015.07.033. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Performance analysis of a combined system for cold and power H. Landoulsi, M. Elakhdar, E. Nehdi, L. Kairouani* Unité de Recherche Energétique et Environnement, Ecole Nationale d’Ingénieurs de Tunis, Tunis, Tunisie Université Tunis El Manar
Highlights
We resumed and improved language We have improved the quality of the figures We have reformulated the conclusion We responded to the remarks of referees
Abstract
This paper presents a theoretical study of a combined thermal system, which combines the Rankine cycle and the ejector refrigeration cycle. This combined cycle produces power and refrigeration simultaneously. The thermal system could use low temperature heat sources. A simulation was carried out to evaluate the cycle performance using several working fluids as R123, R141b, R245fa, R601a and R600a. A one-dimensional mathematical model of the ejector was developed using the equations governing the flow and thermodynamics based on the constant area ejector flow model. The ejector is studied in optimal operating regime. The influence of thermodynamic parameters on system performance is studied. The results show that the condenser temperature, the evaporation temperature, the extraction ratio, the fluid nature and the generating temperature have significant effects on the system performances (the coefficient of performance of the combined cycle and the entrainment ratio of the ejector).
Keywords: Coefficient of performance, Ejector, Entrainment ratio, Modeling, Simulation, Turbine.
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* Corresponding author. Tel.: 216 71874700; Fax: 216 71872729 E-mail address: [email protected] Nomenclature A
Area of cross-section
a*
Sound speed
BB
Expansion ratio of the turbine
COP
Coefficient of Performance
COPr
Ratio of the new and the conventional cycle
Cp
Specific heat of gas at constant pressure (kJkg-1K-1)
D
Diameter of the mixing chamber (m)
d
Diameter of the diverging outlet section of the nozzle motor (m)
dD
Diameter of the diverging outlet of the secondary nozzle portion (m)
d*
Diameter of the Col of the nozzle motor (m)
F
Coefficient of wall friction
V
Velocity ( ms-1)
h
Enthalpy (kJkg-1)
k
Ratio of specific heats (= Cp/Cv)
L
Length of the mixing chamber (m)
M
Dimensionless velocity
m
Mass flow rate (kgs-1)
p
Pressure (Pa)
Q
Heat load (kW)
R
Ideal gas constant (J kg-1K-1)
Rext
The extraction rate
r
The compression ratio
T
Temperature (K)
s
Entropy (J kg-1K-1)
U
Entrainment ratio of the ejector
X
Position of the driving nozzle relative to the throat of the mixer (m)
W
Mechanical work (kW)
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3 Greek letters Φ
(PHI) is the geometric relation between the section of the mixing chamber on the Col de la motor nozzle= (D/dx)2
ξ
The ratio engine
Δ
Related to the variation of a parameter Ratio of the outlet section of the nozzle on the side of the mixing chamber
d D
/ D
2
ρ
Density (kg m-3)
η
Isentropic efficiency (%)
Exponents and Subscripts
evap ger turb ext cond * ′ ′′ p sp Net D
Evaporator Generator Turbine Extraction Condenser Critical state of the fluid Primary fluid (or working fluid) Secondary fluid (or fluid aspirated) Pump Preheater Net Diffuser
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1. INTRODUCTION
Renewable energy sources, such as solar, geothermal energy and industrial waste heat are potentially promising energy sources capable to reduce fossil fuel and meet the world electricity demand. Most of these sources require new energy conversion technologies in order to use these waste heats and renewable energy without generating environmental pollution. The low grade and waste heat can be recovered by using Organic Rankine Cycle (ORC), many studies conducted a thermal and economic optimization of basic ORC [1] and regenerative ORC systems [2,3] for various applications.ORC systems can be easily combined with other thermodynamic cycles, such as seawater desalination system [4], thermoelectric generator [5] and internal combustion engine [6]. In addition, it can be used as in a combined heat and power [7] and combined power and refrigeration system. Some studies of the latter cycle are summarized in the next paragraph. Recently, combined power and refrigeration cycles have been explored to make better use of them and improve overall energy conversion efficiency. Goswami cycle, proposed by Goswami et al. [8] uses binary mixture to produce power and refrigeration. This cycle is a combination of Rankine power cycle and an absorption cooling cycle. It could provide the production of power and cooling in the same cycle. It allows an efficient conversion of moderate temperature heat sources, and the possibility of improved resource utilization compared to separate power and cooling systems. The proposed cycle was analyzed theoretically and experimentally by many researchers [9-13]. However, the refrigeration output was relatively small. In fact, this cycle employed the ammonia-rich vapor in the turbine to generate power, and the turbine exhaust passed through a heat exchanger transferring sensible heat to the chilled water. In order to produce more refrigeration output, the fluid should go through a phase change in the cooler. Zheng et al. [14] proposed a combined power/cooling cycle based on the Kalina cycle. Zhang et al. [15] proposed several combined power and refrigeration cycles with both parallel and series-connected configurations and using ammonia-water as working fluid. The cycle has large refrigeration capacity. However, it is incompatible with low temperature heat sources. Wang et al. [16] also
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investigated a combined power and refrigeration system which combined Rankine cycle and absorption refrigeration cycle. The proposed cycles show higher energy and exergy efficiency but the systems are relatively complicated resulting in a higher capital investment. A little attention has been paid to the combination of Rankine cycle and the ejector refrigeration cycle. The ejector refrigeration cycle is another refrigeration cycle which many studies [17,18,19] have been devoted to. Ejector systems using natural or renewable thermal energy to entrain environment-friendly refrigerants can be a promising alternative to current systems.1 Compared to absorption systems, ejector systems have advantages because of their simplicity, reliability, and low installation and operational costs. Dai et al. [20] presented a new cycle which combines power and refrigeration cycle. This cycle combined the Rankine cycle with the ejector refrigeration cycle by adding an extraction turbine between heat recovery vapor generator (HRVG) and the ejector. The vapor from boiler could be expanded through turbine to generate power, and the turbine exhaust can drive the ejector. This combined cycle could produce both power output and refrigeration. They conducted an exergy analysis to evaluate the system’s performances, and they studied the effect of thermodynamic parameters on the cycle efficiency. Wang et al. [21] proposed a modified version of the combined power and refrigeration cycle proposed by Dai et al. [20]. The new cycle combine the Rankine cycle with the ejector refrigeration cycle and could produce power output and refrigeration simultaneously. In this new version, the high pressure and temperature vapor is expanded through the turbine to generate power but only the extracted vapor from the turbine enters the converging–diverging nozzle of the ejector as the primary vapor. The rest expanded in the turbine is mixed with the stream coming from the ejector. A parametric analysis and exergy analysis was conducted to investigate the effects of key thermodynamic parameters on the performance and exergy destruction in each component. It was also shown that the biggest exergy destruction occurs in the heat recovery vapor generator, followed by the ejector and turbine. A combined power and ejector refrigeration cycle using R245fa as a working fluid was studied by Zheng et al. [22]. Simulation results have shown that this cycle has a considerable thermal efficiency. It has also been shown that the most exergy losses take place in the ejector. The author suggested several methods to improve system efficiency such as increasing the area of heat transfer, the coefficient of heat transfer in the HRVG and the optimization design parameters in the ejector and turbine.
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Habib zadeh et al [23] studied the performance of the cycle analyzed by Wang et al. [21] for several working fluids. They presented a comparison for a base case combination of operating conditions as well as the results of parametric studies which show the effects of the heat source temperature, the evaporation temperature, the cooling water temperature and the expansion ratio of the turbine. They also determined the optimum values of the turbine and pump inlet pressures which minimize the total thermal conductance of the system for the working fluids considered. Rashidi et al. [24], in their work, based on a combination of first and second law analysis, evaluated the performance of a regenerative Rankine cycle with two feed water heaters for water and R717 as working fluids and developed a parametric optimization based on a new procedure that combines the artificial neural network (ANN) and the artificial bees colony (ABC). This study presents a thermodynamic analysis ofa combined Rankine and ejector refrigeration cycle. Unlike the other works, the ejector has been studied in optimal operating regime. A one-dimensional mathematical model in the transition regime of the ejector was developed using the equations governing the flow and thermodynamics based on the constantarea ejector flow model. The ejector model includes effects of friction at the constant area mixing chamber. The refrigerants properties are evaluated by using REFPROP [25]. The results are found for various operating conditions.
2. System description and assumptions
Fig.1 illustrates the combined Rankine and ejector refrigeration cycle and Fig.2 shows the T-s and p-h diagrams of the combined cycle.
The system consists of a vapor generator, a turbine, an ejector, an evaporator, a condenser, a pump, a preheater and an expansion valve. At the generator, the high vapor temperature and pressure is generated by the absorption of heat from heat sources such as solar energy, etc. The superheated vapor that escapes from the generator (state 2) is introduced into the turbine to be expanded isentropically, and therefore it will produce power. The partially expanded
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extracted vapor from the turbine (state 3) called primary fluid flows through the driving nozzle of the ejector and leads the secondary fluid leaving the evaporator at high speed (state 9). Then the primary fluid and the secondary fluid are mixed into the mixing chamber. The mixture is compressed through the diffuser. A new pressure, between the pressure of the extraction turbine and the evaporating pressure, is established (state 4). The fully expanded vapor exiting the turbine (state 13) is mixed with that leaving the ejector (state 10). The combined vapor is cooled in the preheater to state 12 and is condensed at the condenser to state 5. Then a part of the condensate flows into the pump (state 6) and the rest (state 7) is expanded towards the expansion valve. Before being sprayed again through the generator, the high pressure fluid (state 11) is heated in the preheater to state 1. Concerning the low pressure and temperature fluid, it enters the evaporator (state 8), and is evaporated by absorbing heat from the cooled media.
3. Mathematical modeling of the ejector
The ejector (Fig.3) consists of a primary nozzle, a secondary nozzle, a mixing chamber and a diffuser. The refrigerant vapour at high pressure is supplied to the ejector primary inlet. This vapour expands in a convergent-divergent nozzle, thereby creating a depression and drawing in low pressure vapour through the ejector secondary inlet. The two flows come into contact in the mixing chamber and entering the diffuser where the pressure increases. The diameters and lengths of various parts forming the nozzle, the diffuser and the suction chamber, together with the fluid flow rate and properties, define the ejector capacity and performance. The entrainment ratio (U) is the flow rate of the entrained vapour divided by the flow rate of the motive vapour. As for the expansion ratio ( ), it is defined as the ratio of the motive vapour pressure to the entrained vapour pressure. The compression ratio (r) gives the pressure ratio of the compressed vapour to the entrained vapour. The driving pressure ratio (ξ) is defined as the ratio of the motive vapour pressure to the back pressure. Fabri and Siestrunck [26] defined three different flow regimes for ejectors. The three flow regimes appointed are based on the dependence of the ratio of the mass flow between the primary and the secondary flow and the pressure at the outlet of the ejector. These regimes are: the supersonic regime (SR), the transition regime (TR) and the mixed regime (MR).
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The performance analysis of an ejector consists of determining the formation conditions of these regimes. During the operation of the ejector in the SR, since the primary static pressure at section 1 shown in Fig. 3, is higher than that of the secondary vapour, the primary fluid expands against the secondary fluid and causes the velocity of the secondary fluid to reach supersonic speed at the aerodynamic throat formed by it. As a consequence of this secondary stream choking phenomenon, the secondary mass flow rate becomes independent of the back pressure. The MR includes all the cases for which the secondary flow is not choked. The secondary flow cannot reach sonic speed within the mixing chamber, and therefore, its mass flow rate changes depending on the back pressure. The TR is a special case of the SR. In the TR, the secondary vapour reaches supersonic speed at the point of confluence of the primary and secondary vapours. It gives the best performance of the ejector, [27-28-29]. For this reason, the ejector is analyzed in the TR. We can consider the following assumptions:
The flow inside the ejector is steady and one dimensional.
The thermodynamic constants: k, cp, R of the two fluids are equal in all sections of the ejector.
Fluid is considered as an ideal gas.
The isentropic relations are used to simplify the model.
At the exit of the mixing chamber, the two fluids are completely mixed.
The primary exit nozzle does not coincide with the mixing chamber inlet (X # 0).
The TR assures the transition of the MR to the SR. The TR is the launching regime of the SR. The model in TR is based on two hypothesis related to the position of the aerodynamic throat and the equality of pressures at this section. According to the hypothesis of Fabri [26], in SR, a sonic throat exists for the secondary fluid; and the closer the regime comes to the transition, the more this sonic throat moves toward the upstream. In the case where we have a non-zero distance X, the flow in convergent part is sonic which implies that the aerodynamic throat is situated in the cylindrical part of the mixing chamber. So while baring in mind the two previous conditions, we deduce that, for TR with a non-zero distance X, the aerodynamic throat is located at the entry of the mixing chamber. Therefore: ′′
(1)
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Where: Where
is the dimensionless velocity is the sound speed at the nozzle throat and it is given by:
To form the sonic throat of the secondary fluid at the section 2, the motive flow must expand, which imposes P2'>P2". After the section 2, we can only have P2' > P2", since the case P2' P2", the primary fluid is going to continue to expand, the sonic throat is situated then downstream the section 3 and the regime becomes supersonic. Therefore, the TR is characterized by: (2) By applying the mass, momentum and energy balances to the control volume defined between section 2 and section 3 (Fig.3), we can write the following equations.
Continuity equation (3) With
, the equation (3) can be expressed as follows: (4)
Energy equation (5) Dividing both sides of the equation by
, the energy equation can be expressed as
follows: (6) Where
is defined as: (7)
Momentum equation (8)
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: Expresses friction losses inside the mixing chamber and is obtained from the following equation: (9) With the assumption
, equation (9) can be expressed as follows: (10)
Using the dimensionless velocity M (
) and the function
, we can write, [30]: (11)
Where
is the sound speed at the nozzle throat and it is given by:
And after a series of transformations of the expression
, we can obtain: (12)
Using equations (10), (12) and dividing the equation of momentum conservation by
, equation (8) can be expressed as: (13)
Where x is defined as:
The distance L (Fig.3) in TR is assumed to be 10D [31]. By using the isentropic relations, the momentum equation becomes: (14)
Calculating the stagnation pressure, pressure P0 3 in the section 3 The mass flow of the primary fluid is written: (15) The mass flow rate in the section 3 is: (16) Where A*3the fictitious throat in the mixing chamber can be calculated by using isentropic relation: (17) Where (18)
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Using equations (15) and (16), we can obtain: ′
′
Where
′
(19)
′
′
And Therefore: (20) Where:
Calculation of pressure
in the Section 4
By using the isentropic relationship, we can write: (21) Where (22) We can also write: (23) Where
is the pressure coefficient in the diffuser of the ejector and is expressed by: (24)
By using a relation similar to (15) the mass flow at the exit of the diffuser may be expressed as: (25) Combining equations (16), (17) and (25), we can obtain: (26) Where Substituting equations (20) and (26) into equation (23), we can find a relation between output parameters (
and input parameters
: (27)
Entrainment ratio U By similarity to the equation (19), the entrainment ratio U can be expressed as:
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(28) Finally, using , we obtain: (29) On the other hand, by using the hypothesis cited in equation (2) and similarity to equation (23), we have:
and
so: (30)
By combining equations (29) and (30), we obtain:
(31)
System of equations Finally we can obtain the system of equations cited bellow:
In which: (33) (34) or
(35)
1
In this system of equations, we have nine parameters U 2 , , , , , M2’, M2", M 3, M4 (by supposing that the pressure coefficient in the diffuser D and the friction factor F
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(therefore x) are fixed). The most important parameters are thermodynamic parameters U 2 , , ,and geometric parameters: , . To have the solution of the system, it is necessary to fix four initial parameters. Thus, the system of equations (32a-32e) translates the relation between five variables among the set of 9 parameters in which 4 are fixed. In our case, the four fixed variables are: M2", , and . The five unknown parameters 1
are: U 2 , , M2’, M 3, M4. The aim of the ejector modeling is to find the back pressure of the ejector and the entrainment ratio. 4. Performance of the combined cycle
Performances of our system are evaluated by the coefficient of performance (COP) given by the following expression: (36) With (37) And at:
The evaporator: (38)
The turbine: (39)
The vapor generator: (40)
The pump: (41) Taking into account equation (36) and by neglecting the work of the pump, the COP can also be written in the following form: (42) With:
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,
: The extraction ratio of the turbine.
(43)
5. RESULTS AND DISCUSSION
The simulation of the combined cycle was carried out. The refrigerants thermodynamics properties are evaluated by using NIST database subroutines REFPROP V 9.0 [25] and the calculating program is written with Fortran Language. Several environment friendly refrigerants like as R123, R141b, R245fa, R601a and R600a are applied to the above computation models for the simulation of the novel system. The model includes operating parameters (generating temperature, evaporating temperature, extraction ratio) and geometric parameter . The ratio of cylindrical chamber length to diameter is assumed to be 10. The coefficients F and D are assumed to be: F = 0.06, ηD = 0.96 [32]. The model determines the thermodynamic properties of each point for the power and the ejector refrigeration cycle identified in Fig.1. It also calculates the performance of the combined cycle such as the entrainment ratio of the ejector, the coefficient of performance of the system, the turbine power and the heat input. From the data cited below and by using the equations developed previously we can examine the influence of fluid nature, thermodynamic parameters and geometric ratio Φ on the system performances. The main assumptions for the simulation of the combined cycle are summarized in Table 1. 5.1. The effect of the fluid nature on the system performances Fig.4 represents the variation of the COPr (the COPr ratio of the new and the conventional cycle) for several refrigerants. It can be seen that the combined cycle has a remarkable improvement in COP over the conventional cycle. Figs.5,6 represent the variation of COP and U with the fluid nature.
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It can be seen that the performance of the system varies with the refrigerant nature. Fig.5 shows that R601a gives the uppermost value of COP. The same result about R601a performances in the combined cycle was obtained by [23]. After R601a, R141b give a high COP. Several studies as Huang et al. [33] indicate that R141b is a good working fluid for an ejector since R141b has a positive-slop saturated vapor line in the thermodynamic T-s diagram. This will not produce condensation of the vapor during an isentropic expansion in the ejector. Thus it reduces loss. The effect of thermal parameters and geometric parameter on the performances is studied here for R601a because it gives better performances and it has a relatively low GWP.
5.2. The effect of the generating temperature on the system performances
Fig.7 shows the influence of generating temperature Tger on the coefficient of performance COP and the turbine power Wturb. Generating temperature varies from 115 to 140 °C.Other working conditions are assumed to be the same as specified in table 1. The results in Fig.7 show that the coefficient of performance decreasesand the turbine power increases with theincreasing generating temperature. Since the turbine output is principallyrelated to the expansion process across the turbine, the net power curve can be explained by the increaseof the expansion ratio. The mass flow rate through the evaporator remains constant since the enthalpy at the inlet and outlet of evaporator do not change and the refrigeration capacity Qevap is constant. Therefore the entrainment ratio of the ejector U, decreases sensitively as the generating temperature increases (Fig.8).
5.3. The effect of the evaporator temperature on the system performances
The value of Tevap is varied between -20°C and 0°C while the values of the other inputs are those specified in table 1. Figs.9,10 show the effect of evaporator temperature respectively on the coefficient of performance, the turbine power and the entrainment ratio.
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As the evaporator temperature increases, the turbine power decreases, the coefficient of performance increases and the entrainment ratio increases. On the one hand, at a higher value of evaporating temperature, the evaporator pressure is high and therefore a small amount of motive vapor is sufficient to create suction and entrain the required quantity of secondary vapor in the ejector. From which, the value of entrainment ratio is more important at a higher evaporating temperature and this result is shown in Fig.10. On the other hand, the turbine power decreases by increasing the evaporator temperature Tevap, Fig.9. In fact, as Tevap increases, the enthalpy rise (h9- h8) when the evaporation of the working fluid decreases. By maintaining the same value of refrigeration capacity Qevap, there will be an automatic increase in the secondary flow circulating in the evaporator, and as the turbine work depends on this flow, so it will increase. This result is interesting for the selection of operating conditions for the ejector refrigeration systems since the coefficient of performance COP is better if the temperature of the evaporator is higher. 5.4. The effect of the geometry of the ejector on the system performances
Figs.11,12 depict the influence of the geometric parameter ɸ on the system performances. In fact, ɸ is the most influential parameter in the ejector performances [29].
From Figs.11,12, it can be seen that the variation of the coefficient of performance COP and entrainment ratio U depending on Φ for constant evaporation and generator temperatures is a strongly increasing curve. The turbine power output decreases when the mass flow rate across the turbine is not changed.
5.5. The effect of the expansion ratio on the system performances
Fig.13 shows the influence of the expansion ratio BB on the coefficient of performance COP and the turbine power.
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In this study the ratio P2/P3 is varied between 0.15 and 0.45 while the values of all the other inputs are those specified in Table1. The values of P3 are in all cases between the condenser pressure P5 and the evaporator pressure P9. The Fig.13 shows that the coefficient of performance increases as the expansion ratio increases. At the same time, the turbine power decreases by increasing the extraction ratio of the turbine. Therefore, while the expansion ratio increases, the primary fluid inlet pressure decreases correspondingly. Nevertheless, the second fluid inlet pressure and the mixed fluid outlet pressure of the ejector do not change. About the variation of entrainment rate U, Fig.14, the entrainment ratio decreases as the expansion ratio increases.
6. Validation of model results
The model was validated with the results of the combined power and ejector refrigeration cycle using R123 as the working fluid presented by Dai and al. [21]. The comparisons presented in Table 2 show high agreement between these previously published results and the present study. 7. Conclusion
In this work, we conducted an energy study of a hybrid system which combines the Rankine cycle and the ejector refrigeration cycle. The system can produce power and refrigeration simultaneously using low temperature heat sources. A simulation was carried out to analyze the cycle performance using several working fluids as R123, R141b, R245fa, R601a and R600a.The established model permits to study the influence of thermodynamic parameters on the system performances in order to optimize its operation into the best conditions. The ejector model is a one-dimensional mathematical model. It was developed by using the equations governing the flow and thermodynamics based on the constant area ejector flow model. The model includes effects of the friction at the constant-area mixing chamber. From the discussions above, it can be concluded the improvement of the coefficient of performance COP depends mainly on the entrainment ratio U. It was found that, for the same operating temperatures of the ejector refrigeration systems, R600a gives the most
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advantageous relative coefficient of performance. The parametric study shows that condenser temperature, evaporating temperatures, generating temperature, the extraction ratios and the geometric parameter ɸ have significant effects on the coefficient of performance, the entrainment ratio, the turbine power and the refrigeration capacity.
Acknowledgments We express our thanks to the anonymous referees for their constructive reviews of the manuscript and for helpful comments.
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[20] Dai Y, Wang J, Gao L. Exergy analysis, parametric analysis and optimization fora novel combined power and ejector refrigeration cycle, Appl ThermEng, 29 (2009) 1983–90. [21] Wang J, Dai Y, Sun Z. A theoretical study on a novel combined power and ejector refrigeration cycle, International Journal of Refrigeration 32 (2009) 1186–94. [22] Zheng B, Weng YW. A combined power and ejector refrigeration cycle for low temperature heat sources, Sol Energy 84 (2010) 779–84. [23] A. Habibzadeh, M.M. Rashidi , N. Galanis. Analysis of a combined power and ejectorrefrigeration cycle using low temperature heat, Energy Conversion and Management 65 (2013) 381–391 [24] Rashidi MM, Galanis N, Nazari F, BasiriParsa A and ShamekhiL. Parametric analysis and optimization of regenerative Clausius and organic Rankine cycles with two feedwater heaters using artificial bees colony and artificial neural network, Energy, 36 (2011) 5728– 5740. [25] REFPROP. Thermodynamic Properties of Refrigerant Mixtures, Version 8 National Institute of Standards and Technology (2002). [26] E. Le Grives, J. Fabri. Divers régimes de mélange de deux flux d’enthalpie d’arrêt différentes, Astronautica acta, Vol 14 (1969) 203-213 . [27] Lu LT, (1986).“Etudes théorique et expérimentale de la production de froid par machine tritherme à éjecteur de fluide frigorigène”, thèse de doctorat, Institut national polytechnique, Grenoble, France. [28] E Nehdi, (1989).“Etude paramétrique expérimentale des caractéristiques du système tritherme à éjecteur”, thèse de doctorat, Institut national des sciences appliquées, Lyon, France . [29] M. Elakhdar, E. Nehdi, L. Kairouani, N. Tounsi. Simulation of an ejector used in refrigeration systems, International Journal of Refrigeration Vol. 34 ( 2011) 1657-1667.
[30] Abramovich, G.N.. Applied Gas Dynamics. Ch. 9: Gas Ejectors. Foreign Technology Division, Air Force Systems Command, OH, USA. No. F33657-70-D-0607-P002 (1970). [31] Paliwoda, P.. A review paper on the experimental study on low-grade heat and solar energy operated halocarbon vapor-jet refrigeration systems. Topical studies. IIR Bull. (1968) 1003. [32] L. Kairouani, M. Elakhdar, E. Nehdi, N. Bouaziz. Use of ejectors in a multi-evaporator refrigeration system for performance enhancement, International Journal of refrigeration 32 (2009) 1173–1185.
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[33] Huang, B.J., Chang, J.M.. Empirical correlation for ejector design, International Journal of Refrigeration 22 (1999) 379.
Figure captions
Fig. 1. Schematic of the combined system. Fig. 2. a) Schematic cycle T-sdiagram. b) Schematic cycle P-h diagram. Fig. 3. Configuration of the ejector and geometrical parameters. Fig. 4. COPr for various fluids. Fig. 5. Effect of fluid nature on the COP and turbine power. Fig. 6. Effect of fluid nature on entrainment ratio. Fig. 7. Effect of generating temperature on the COP and turbine power. Fig. 8. Effect of generating temperature on entrainment ratio. Fig. 9. Effect of evaporator temperature on the COP and turbine power.
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Fig. 10. Effect of evaporator temperature on entrainment ratio. Fig. 11. Effect of geometry of ejector on the COP and turbine power. Fig. 12. Effect of geometry of the ejector on entrainment ratio. Fig. 13. Effect of the expansion ratio on the COP and turbine power. Fig. 14. Effect of expansion ratio on entrainment ratio.
Table captions
Table 1: Main assumptions of the simulation for the combined cycle.
Parameters Evaporator temperature Tevap(C°)
Value 0
Generating temperature Tger(C°)
140
Extraction ratio Rext
0.4
Expansion ratio of turbine BB=p2/p3 The geometry of the ejector Φ Working fluid Evaporator cooling capacity Qevap(kW)
2 7.84 R601a 30
Turbine isentropic efficiency(%)
0.82
Pump isentropic efficiency(%)
0.75
Table 2: Validation of the model. Comparisons for R123
Wang and al. This work [16]
(a) Inputs
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23 Generating temperature(K) Evaporating temperature (K) Generating Pressure (bar)
403.15 268.15 7.00
(b) Results Condensing temperature (K) Turbine work(kW) Refrigeration capacity (kW) Pump work (kW) Heat input (kW) Coefficient of performance%
298.15 116.54 21.01 2.44 905.69 14.92
403.15 268.15 7.00
296.08 119.35 21.01 1.38 904.51 15.36
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S0140-7007(15)00240-6 http://dx.doi.org/doi:10.1016/j.ijrefrig.2015.07.033 JIJR 3121
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
20-3-2015 7-7-2015 29-7-2015
Please cite this article as: H. Landoulsi, M. Elakhdar, E. Nehdi, L. Kairouani, Performance analysis of a combined system for cold and power, International Journal of Refrigeration (2015), http://dx.doi.org/doi:10.1016/j.ijrefrig.2015.07.033. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
Performance analysis of a combined system for cold and power H. Landoulsi, M. Elakhdar, E. Nehdi, L. Kairouani* Unité de Recherche Energétique et Environnement, Ecole Nationale d’Ingénieurs de Tunis, Tunis, Tunisie Université Tunis El Manar
Highlights
We resumed and improved language We have improved the quality of the figures We have reformulated the conclusion We responded to the remarks of referees
Abstract
This paper presents a theoretical study of a combined thermal system, which combines the Rankine cycle and the ejector refrigeration cycle. This combined cycle produces power and refrigeration simultaneously. The thermal system could use low temperature heat sources. A simulation was carried out to evaluate the cycle performance using several working fluids as R123, R141b, R245fa, R601a and R600a. A one-dimensional mathematical model of the ejector was developed using the equations governing the flow and thermodynamics based on the constant area ejector flow model. The ejector is studied in optimal operating regime. The influence of thermodynamic parameters on system performance is studied. The results show that the condenser temperature, the evaporation temperature, the extraction ratio, the fluid nature and the generating temperature have significant effects on the system performances (the coefficient of performance of the combined cycle and the entrainment ratio of the ejector).
Keywords: Coefficient of performance, Ejector, Entrainment ratio, Modeling, Simulation, Turbine.
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* Corresponding author. Tel.: 216 71874700; Fax: 216 71872729 E-mail address: [email protected] Nomenclature A
Area of cross-section
a*
Sound speed
BB
Expansion ratio of the turbine
COP
Coefficient of Performance
COPr
Ratio of the new and the conventional cycle
Cp
Specific heat of gas at constant pressure (kJkg-1K-1)
D
Diameter of the mixing chamber (m)
d
Diameter of the diverging outlet section of the nozzle motor (m)
dD
Diameter of the diverging outlet of the secondary nozzle portion (m)
d*
Diameter of the Col of the nozzle motor (m)
F
Coefficient of wall friction
V
Velocity ( ms-1)
h
Enthalpy (kJkg-1)
k
Ratio of specific heats (= Cp/Cv)
L
Length of the mixing chamber (m)
M
Dimensionless velocity
m
Mass flow rate (kgs-1)
p
Pressure (Pa)
Q
Heat load (kW)
R
Ideal gas constant (J kg-1K-1)
Rext
The extraction rate
r
The compression ratio
T
Temperature (K)
s
Entropy (J kg-1K-1)
U
Entrainment ratio of the ejector
X
Position of the driving nozzle relative to the throat of the mixer (m)
W
Mechanical work (kW)
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3 Greek letters Φ
(PHI) is the geometric relation between the section of the mixing chamber on the Col de la motor nozzle= (D/dx)2
ξ
The ratio engine
Δ
Related to the variation of a parameter Ratio of the outlet section of the nozzle on the side of the mixing chamber
d D
/ D
2
ρ
Density (kg m-3)
η
Isentropic efficiency (%)
Exponents and Subscripts
evap ger turb ext cond * ′ ′′ p sp Net D
Evaporator Generator Turbine Extraction Condenser Critical state of the fluid Primary fluid (or working fluid) Secondary fluid (or fluid aspirated) Pump Preheater Net Diffuser
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1. INTRODUCTION
Renewable energy sources, such as solar, geothermal energy and industrial waste heat are potentially promising energy sources capable to reduce fossil fuel and meet the world electricity demand. Most of these sources require new energy conversion technologies in order to use these waste heats and renewable energy without generating environmental pollution. The low grade and waste heat can be recovered by using Organic Rankine Cycle (ORC), many studies conducted a thermal and economic optimization of basic ORC [1] and regenerative ORC systems [2,3] for various applications.ORC systems can be easily combined with other thermodynamic cycles, such as seawater desalination system [4], thermoelectric generator [5] and internal combustion engine [6]. In addition, it can be used as in a combined heat and power [7] and combined power and refrigeration system. Some studies of the latter cycle are summarized in the next paragraph. Recently, combined power and refrigeration cycles have been explored to make better use of them and improve overall energy conversion efficiency. Goswami cycle, proposed by Goswami et al. [8] uses binary mixture to produce power and refrigeration. This cycle is a combination of Rankine power cycle and an absorption cooling cycle. It could provide the production of power and cooling in the same cycle. It allows an efficient conversion of moderate temperature heat sources, and the possibility of improved resource utilization compared to separate power and cooling systems. The proposed cycle was analyzed theoretically and experimentally by many researchers [9-13]. However, the refrigeration output was relatively small. In fact, this cycle employed the ammonia-rich vapor in the turbine to generate power, and the turbine exhaust passed through a heat exchanger transferring sensible heat to the chilled water. In order to produce more refrigeration output, the fluid should go through a phase change in the cooler. Zheng et al. [14] proposed a combined power/cooling cycle based on the Kalina cycle. Zhang et al. [15] proposed several combined power and refrigeration cycles with both parallel and series-connected configurations and using ammonia-water as working fluid. The cycle has large refrigeration capacity. However, it is incompatible with low temperature heat sources. Wang et al. [16] also
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investigated a combined power and refrigeration system which combined Rankine cycle and absorption refrigeration cycle. The proposed cycles show higher energy and exergy efficiency but the systems are relatively complicated resulting in a higher capital investment. A little attention has been paid to the combination of Rankine cycle and the ejector refrigeration cycle. The ejector refrigeration cycle is another refrigeration cycle which many studies [17,18,19] have been devoted to. Ejector systems using natural or renewable thermal energy to entrain environment-friendly refrigerants can be a promising alternative to current systems.1 Compared to absorption systems, ejector systems have advantages because of their simplicity, reliability, and low installation and operational costs. Dai et al. [20] presented a new cycle which combines power and refrigeration cycle. This cycle combined the Rankine cycle with the ejector refrigeration cycle by adding an extraction turbine between heat recovery vapor generator (HRVG) and the ejector. The vapor from boiler could be expanded through turbine to generate power, and the turbine exhaust can drive the ejector. This combined cycle could produce both power output and refrigeration. They conducted an exergy analysis to evaluate the system’s performances, and they studied the effect of thermodynamic parameters on the cycle efficiency. Wang et al. [21] proposed a modified version of the combined power and refrigeration cycle proposed by Dai et al. [20]. The new cycle combine the Rankine cycle with the ejector refrigeration cycle and could produce power output and refrigeration simultaneously. In this new version, the high pressure and temperature vapor is expanded through the turbine to generate power but only the extracted vapor from the turbine enters the converging–diverging nozzle of the ejector as the primary vapor. The rest expanded in the turbine is mixed with the stream coming from the ejector. A parametric analysis and exergy analysis was conducted to investigate the effects of key thermodynamic parameters on the performance and exergy destruction in each component. It was also shown that the biggest exergy destruction occurs in the heat recovery vapor generator, followed by the ejector and turbine. A combined power and ejector refrigeration cycle using R245fa as a working fluid was studied by Zheng et al. [22]. Simulation results have shown that this cycle has a considerable thermal efficiency. It has also been shown that the most exergy losses take place in the ejector. The author suggested several methods to improve system efficiency such as increasing the area of heat transfer, the coefficient of heat transfer in the HRVG and the optimization design parameters in the ejector and turbine.
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Habib zadeh et al [23] studied the performance of the cycle analyzed by Wang et al. [21] for several working fluids. They presented a comparison for a base case combination of operating conditions as well as the results of parametric studies which show the effects of the heat source temperature, the evaporation temperature, the cooling water temperature and the expansion ratio of the turbine. They also determined the optimum values of the turbine and pump inlet pressures which minimize the total thermal conductance of the system for the working fluids considered. Rashidi et al. [24], in their work, based on a combination of first and second law analysis, evaluated the performance of a regenerative Rankine cycle with two feed water heaters for water and R717 as working fluids and developed a parametric optimization based on a new procedure that combines the artificial neural network (ANN) and the artificial bees colony (ABC). This study presents a thermodynamic analysis ofa combined Rankine and ejector refrigeration cycle. Unlike the other works, the ejector has been studied in optimal operating regime. A one-dimensional mathematical model in the transition regime of the ejector was developed using the equations governing the flow and thermodynamics based on the constantarea ejector flow model. The ejector model includes effects of friction at the constant area mixing chamber. The refrigerants properties are evaluated by using REFPROP [25]. The results are found for various operating conditions.
2. System description and assumptions
Fig.1 illustrates the combined Rankine and ejector refrigeration cycle and Fig.2 shows the T-s and p-h diagrams of the combined cycle.
The system consists of a vapor generator, a turbine, an ejector, an evaporator, a condenser, a pump, a preheater and an expansion valve. At the generator, the high vapor temperature and pressure is generated by the absorption of heat from heat sources such as solar energy, etc. The superheated vapor that escapes from the generator (state 2) is introduced into the turbine to be expanded isentropically, and therefore it will produce power. The partially expanded
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extracted vapor from the turbine (state 3) called primary fluid flows through the driving nozzle of the ejector and leads the secondary fluid leaving the evaporator at high speed (state 9). Then the primary fluid and the secondary fluid are mixed into the mixing chamber. The mixture is compressed through the diffuser. A new pressure, between the pressure of the extraction turbine and the evaporating pressure, is established (state 4). The fully expanded vapor exiting the turbine (state 13) is mixed with that leaving the ejector (state 10). The combined vapor is cooled in the preheater to state 12 and is condensed at the condenser to state 5. Then a part of the condensate flows into the pump (state 6) and the rest (state 7) is expanded towards the expansion valve. Before being sprayed again through the generator, the high pressure fluid (state 11) is heated in the preheater to state 1. Concerning the low pressure and temperature fluid, it enters the evaporator (state 8), and is evaporated by absorbing heat from the cooled media.
3. Mathematical modeling of the ejector
The ejector (Fig.3) consists of a primary nozzle, a secondary nozzle, a mixing chamber and a diffuser. The refrigerant vapour at high pressure is supplied to the ejector primary inlet. This vapour expands in a convergent-divergent nozzle, thereby creating a depression and drawing in low pressure vapour through the ejector secondary inlet. The two flows come into contact in the mixing chamber and entering the diffuser where the pressure increases. The diameters and lengths of various parts forming the nozzle, the diffuser and the suction chamber, together with the fluid flow rate and properties, define the ejector capacity and performance. The entrainment ratio (U) is the flow rate of the entrained vapour divided by the flow rate of the motive vapour. As for the expansion ratio ( ), it is defined as the ratio of the motive vapour pressure to the entrained vapour pressure. The compression ratio (r) gives the pressure ratio of the compressed vapour to the entrained vapour. The driving pressure ratio (ξ) is defined as the ratio of the motive vapour pressure to the back pressure. Fabri and Siestrunck [26] defined three different flow regimes for ejectors. The three flow regimes appointed are based on the dependence of the ratio of the mass flow between the primary and the secondary flow and the pressure at the outlet of the ejector. These regimes are: the supersonic regime (SR), the transition regime (TR) and the mixed regime (MR).
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The performance analysis of an ejector consists of determining the formation conditions of these regimes. During the operation of the ejector in the SR, since the primary static pressure at section 1 shown in Fig. 3, is higher than that of the secondary vapour, the primary fluid expands against the secondary fluid and causes the velocity of the secondary fluid to reach supersonic speed at the aerodynamic throat formed by it. As a consequence of this secondary stream choking phenomenon, the secondary mass flow rate becomes independent of the back pressure. The MR includes all the cases for which the secondary flow is not choked. The secondary flow cannot reach sonic speed within the mixing chamber, and therefore, its mass flow rate changes depending on the back pressure. The TR is a special case of the SR. In the TR, the secondary vapour reaches supersonic speed at the point of confluence of the primary and secondary vapours. It gives the best performance of the ejector, [27-28-29]. For this reason, the ejector is analyzed in the TR. We can consider the following assumptions:
The flow inside the ejector is steady and one dimensional.
The thermodynamic constants: k, cp, R of the two fluids are equal in all sections of the ejector.
Fluid is considered as an ideal gas.
The isentropic relations are used to simplify the model.
At the exit of the mixing chamber, the two fluids are completely mixed.
The primary exit nozzle does not coincide with the mixing chamber inlet (X # 0).
The TR assures the transition of the MR to the SR. The TR is the launching regime of the SR. The model in TR is based on two hypothesis related to the position of the aerodynamic throat and the equality of pressures at this section. According to the hypothesis of Fabri [26], in SR, a sonic throat exists for the secondary fluid; and the closer the regime comes to the transition, the more this sonic throat moves toward the upstream. In the case where we have a non-zero distance X, the flow in convergent part is sonic which implies that the aerodynamic throat is situated in the cylindrical part of the mixing chamber. So while baring in mind the two previous conditions, we deduce that, for TR with a non-zero distance X, the aerodynamic throat is located at the entry of the mixing chamber. Therefore: ′′
(1)
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Where: Where
is the dimensionless velocity is the sound speed at the nozzle throat and it is given by:
To form the sonic throat of the secondary fluid at the section 2, the motive flow must expand, which imposes P2'>P2". After the section 2, we can only have P2' > P2", since the case P2'
Continuity equation (3) With
, the equation (3) can be expressed as follows: (4)
Energy equation (5) Dividing both sides of the equation by
, the energy equation can be expressed as
follows: (6) Where
is defined as: (7)
Momentum equation (8)
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: Expresses friction losses inside the mixing chamber and is obtained from the following equation: (9) With the assumption
, equation (9) can be expressed as follows: (10)
Using the dimensionless velocity M (
) and the function
, we can write, [30]: (11)
Where
is the sound speed at the nozzle throat and it is given by:
And after a series of transformations of the expression
, we can obtain: (12)
Using equations (10), (12) and dividing the equation of momentum conservation by
, equation (8) can be expressed as: (13)
Where x is defined as:
The distance L (Fig.3) in TR is assumed to be 10D [31]. By using the isentropic relations, the momentum equation becomes: (14)
Calculating the stagnation pressure, pressure P0 3 in the section 3 The mass flow of the primary fluid is written: (15) The mass flow rate in the section 3 is: (16) Where A*3the fictitious throat in the mixing chamber can be calculated by using isentropic relation: (17) Where (18)
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Using equations (15) and (16), we can obtain: ′
′
Where
′
(19)
′
′
And Therefore: (20) Where:
Calculation of pressure
in the Section 4
By using the isentropic relationship, we can write: (21) Where (22) We can also write: (23) Where
is the pressure coefficient in the diffuser of the ejector and is expressed by: (24)
By using a relation similar to (15) the mass flow at the exit of the diffuser may be expressed as: (25) Combining equations (16), (17) and (25), we can obtain: (26) Where Substituting equations (20) and (26) into equation (23), we can find a relation between output parameters (
and input parameters
: (27)
Entrainment ratio U By similarity to the equation (19), the entrainment ratio U can be expressed as:
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(28) Finally, using , we obtain: (29) On the other hand, by using the hypothesis cited in equation (2) and similarity to equation (23), we have:
and
so: (30)
By combining equations (29) and (30), we obtain:
(31)
System of equations Finally we can obtain the system of equations cited bellow:
In which: (33) (34) or
(35)
1
In this system of equations, we have nine parameters U 2 , , , , , M2’, M2", M 3, M4 (by supposing that the pressure coefficient in the diffuser D and the friction factor F
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(therefore x) are fixed). The most important parameters are thermodynamic parameters U 2 , , ,and geometric parameters: , . To have the solution of the system, it is necessary to fix four initial parameters. Thus, the system of equations (32a-32e) translates the relation between five variables among the set of 9 parameters in which 4 are fixed. In our case, the four fixed variables are: M2", , and . The five unknown parameters 1
are: U 2 , , M2’, M 3, M4. The aim of the ejector modeling is to find the back pressure of the ejector and the entrainment ratio. 4. Performance of the combined cycle
Performances of our system are evaluated by the coefficient of performance (COP) given by the following expression: (36) With (37) And at:
The evaporator: (38)
The turbine: (39)
The vapor generator: (40)
The pump: (41) Taking into account equation (36) and by neglecting the work of the pump, the COP can also be written in the following form: (42) With:
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,
: The extraction ratio of the turbine.
(43)
5. RESULTS AND DISCUSSION
The simulation of the combined cycle was carried out. The refrigerants thermodynamics properties are evaluated by using NIST database subroutines REFPROP V 9.0 [25] and the calculating program is written with Fortran Language. Several environment friendly refrigerants like as R123, R141b, R245fa, R601a and R600a are applied to the above computation models for the simulation of the novel system. The model includes operating parameters (generating temperature, evaporating temperature, extraction ratio) and geometric parameter . The ratio of cylindrical chamber length to diameter is assumed to be 10. The coefficients F and D are assumed to be: F = 0.06, ηD = 0.96 [32]. The model determines the thermodynamic properties of each point for the power and the ejector refrigeration cycle identified in Fig.1. It also calculates the performance of the combined cycle such as the entrainment ratio of the ejector, the coefficient of performance of the system, the turbine power and the heat input. From the data cited below and by using the equations developed previously we can examine the influence of fluid nature, thermodynamic parameters and geometric ratio Φ on the system performances. The main assumptions for the simulation of the combined cycle are summarized in Table 1. 5.1. The effect of the fluid nature on the system performances Fig.4 represents the variation of the COPr (the COPr ratio of the new and the conventional cycle) for several refrigerants. It can be seen that the combined cycle has a remarkable improvement in COP over the conventional cycle. Figs.5,6 represent the variation of COP and U with the fluid nature.
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It can be seen that the performance of the system varies with the refrigerant nature. Fig.5 shows that R601a gives the uppermost value of COP. The same result about R601a performances in the combined cycle was obtained by [23]. After R601a, R141b give a high COP. Several studies as Huang et al. [33] indicate that R141b is a good working fluid for an ejector since R141b has a positive-slop saturated vapor line in the thermodynamic T-s diagram. This will not produce condensation of the vapor during an isentropic expansion in the ejector. Thus it reduces loss. The effect of thermal parameters and geometric parameter on the performances is studied here for R601a because it gives better performances and it has a relatively low GWP.
5.2. The effect of the generating temperature on the system performances
Fig.7 shows the influence of generating temperature Tger on the coefficient of performance COP and the turbine power Wturb. Generating temperature varies from 115 to 140 °C.Other working conditions are assumed to be the same as specified in table 1. The results in Fig.7 show that the coefficient of performance decreasesand the turbine power increases with theincreasing generating temperature. Since the turbine output is principallyrelated to the expansion process across the turbine, the net power curve can be explained by the increaseof the expansion ratio. The mass flow rate through the evaporator remains constant since the enthalpy at the inlet and outlet of evaporator do not change and the refrigeration capacity Qevap is constant. Therefore the entrainment ratio of the ejector U, decreases sensitively as the generating temperature increases (Fig.8).
5.3. The effect of the evaporator temperature on the system performances
The value of Tevap is varied between -20°C and 0°C while the values of the other inputs are those specified in table 1. Figs.9,10 show the effect of evaporator temperature respectively on the coefficient of performance, the turbine power and the entrainment ratio.
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As the evaporator temperature increases, the turbine power decreases, the coefficient of performance increases and the entrainment ratio increases. On the one hand, at a higher value of evaporating temperature, the evaporator pressure is high and therefore a small amount of motive vapor is sufficient to create suction and entrain the required quantity of secondary vapor in the ejector. From which, the value of entrainment ratio is more important at a higher evaporating temperature and this result is shown in Fig.10. On the other hand, the turbine power decreases by increasing the evaporator temperature Tevap, Fig.9. In fact, as Tevap increases, the enthalpy rise (h9- h8) when the evaporation of the working fluid decreases. By maintaining the same value of refrigeration capacity Qevap, there will be an automatic increase in the secondary flow circulating in the evaporator, and as the turbine work depends on this flow, so it will increase. This result is interesting for the selection of operating conditions for the ejector refrigeration systems since the coefficient of performance COP is better if the temperature of the evaporator is higher. 5.4. The effect of the geometry of the ejector on the system performances
Figs.11,12 depict the influence of the geometric parameter ɸ on the system performances. In fact, ɸ is the most influential parameter in the ejector performances [29].
From Figs.11,12, it can be seen that the variation of the coefficient of performance COP and entrainment ratio U depending on Φ for constant evaporation and generator temperatures is a strongly increasing curve. The turbine power output decreases when the mass flow rate across the turbine is not changed.
5.5. The effect of the expansion ratio on the system performances
Fig.13 shows the influence of the expansion ratio BB on the coefficient of performance COP and the turbine power.
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In this study the ratio P2/P3 is varied between 0.15 and 0.45 while the values of all the other inputs are those specified in Table1. The values of P3 are in all cases between the condenser pressure P5 and the evaporator pressure P9. The Fig.13 shows that the coefficient of performance increases as the expansion ratio increases. At the same time, the turbine power decreases by increasing the extraction ratio of the turbine. Therefore, while the expansion ratio increases, the primary fluid inlet pressure decreases correspondingly. Nevertheless, the second fluid inlet pressure and the mixed fluid outlet pressure of the ejector do not change. About the variation of entrainment rate U, Fig.14, the entrainment ratio decreases as the expansion ratio increases.
6. Validation of model results
The model was validated with the results of the combined power and ejector refrigeration cycle using R123 as the working fluid presented by Dai and al. [21]. The comparisons presented in Table 2 show high agreement between these previously published results and the present study. 7. Conclusion
In this work, we conducted an energy study of a hybrid system which combines the Rankine cycle and the ejector refrigeration cycle. The system can produce power and refrigeration simultaneously using low temperature heat sources. A simulation was carried out to analyze the cycle performance using several working fluids as R123, R141b, R245fa, R601a and R600a.The established model permits to study the influence of thermodynamic parameters on the system performances in order to optimize its operation into the best conditions. The ejector model is a one-dimensional mathematical model. It was developed by using the equations governing the flow and thermodynamics based on the constant area ejector flow model. The model includes effects of the friction at the constant-area mixing chamber. From the discussions above, it can be concluded the improvement of the coefficient of performance COP depends mainly on the entrainment ratio U. It was found that, for the same operating temperatures of the ejector refrigeration systems, R600a gives the most
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advantageous relative coefficient of performance. The parametric study shows that condenser temperature, evaporating temperatures, generating temperature, the extraction ratios and the geometric parameter ɸ have significant effects on the coefficient of performance, the entrainment ratio, the turbine power and the refrigeration capacity.
Acknowledgments We express our thanks to the anonymous referees for their constructive reviews of the manuscript and for helpful comments.
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Figure captions
Fig. 1. Schematic of the combined system. Fig. 2. a) Schematic cycle T-sdiagram. b) Schematic cycle P-h diagram. Fig. 3. Configuration of the ejector and geometrical parameters. Fig. 4. COPr for various fluids. Fig. 5. Effect of fluid nature on the COP and turbine power. Fig. 6. Effect of fluid nature on entrainment ratio. Fig. 7. Effect of generating temperature on the COP and turbine power. Fig. 8. Effect of generating temperature on entrainment ratio. Fig. 9. Effect of evaporator temperature on the COP and turbine power.
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Fig. 10. Effect of evaporator temperature on entrainment ratio. Fig. 11. Effect of geometry of ejector on the COP and turbine power. Fig. 12. Effect of geometry of the ejector on entrainment ratio. Fig. 13. Effect of the expansion ratio on the COP and turbine power. Fig. 14. Effect of expansion ratio on entrainment ratio.
Table captions
Table 1: Main assumptions of the simulation for the combined cycle.
Parameters Evaporator temperature Tevap(C°)
Value 0
Generating temperature Tger(C°)
140
Extraction ratio Rext
0.4
Expansion ratio of turbine BB=p2/p3 The geometry of the ejector Φ Working fluid Evaporator cooling capacity Qevap(kW)
2 7.84 R601a 30
Turbine isentropic efficiency(%)
0.82
Pump isentropic efficiency(%)
0.75
Table 2: Validation of the model. Comparisons for R123
Wang and al. This work [16]
(a) Inputs
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23 Generating temperature(K) Evaporating temperature (K) Generating Pressure (bar)
403.15 268.15 7.00
(b) Results Condensing temperature (K) Turbine work(kW) Refrigeration capacity (kW) Pump work (kW) Heat input (kW) Coefficient of performance%
298.15 116.54 21.01 2.44 905.69 14.92
403.15 268.15 7.00
296.08 119.35 21.01 1.38 904.51 15.36
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