Exergy Flows inside a One Phase Ejector for Refrigeration Systems

Abstract: The evaluation of the thermodynamic performance of the mutual transformation of different kinds of exergy linked to the intensive thermodynamic parameters of the flow inside the ejector of a refrigeration system is undertaken. Two thermodynamic metrics, exergy produced and exergy consumed, are introduced to assess these transformations. Their calculation is based on the evaluation of the transiting exergy within different ejector sections taking into account the temperature, pressure and velocity variations. The analysis based on these metrics has allowed pinpointing the most important factors affecting the ejector’s performance. A new result, namely the temperature rise in the sub-environmental region of the mixing section is detected as an important factor responsible for the ejector’s thermodynamic irreversibility. The overall exergy efficiency of the ejector as well as the efficiencies of its sections are evaluated based on the proposed thermodynamic metrics.


Introduction
Ejector-based refrigeration systems may be an attractive solution wherever low-grade thermal energy (industrial waste heat or solar energy) is available.Among their advantages are the simplicity in construction, installation and maintenance.However one of the most important shortcomings of these systems is their relatively low coefficient of performance (COP) [1].To understand the main causes of this inefficiency some authors [2][3][4] have undertaken second law thermodynamic analysis of ejectors.Arbel et al. [2] performed an analysis of entropy generation within ejectors.Al-Najem et al. [3] presented one of the possible definitions of ejector exergy efficiency.McGovern et al. [4] showed that many performance measures of ejectors efficiency can be used, but they have not always been clearly defined and the rationale underlying and justifying these measures was often unclear.They also illustrated that the common ground for assessing ejectors performance was to define thermodynamically reversible reference processes against which real processes may be benchmarked.These reversible processes represent the thermodynamic limit of real ejector performance.However the authors proved that even for the relatively simple case of fixed conditions for two identical inlet fluids, 21 reversible reference processes were possible.
In the present paper, a new systematic methodology is proposed to define the efficiency of an ejector and its parts independently of a chosen reversible reference process.The methodology is based on the computation of the transiting exergy flow through a thermodynamic system, a concept first introduced by Brodyansky et al. [5].Two important metrics arise from this analysis, the exergy production and exergy consumption in different parts of the ejector.In the case of identical inlet fluids, analysed in the present paper, each of these metrics is linked to three intensive parameters of the flow inside the ejector, namely pressure, temperature and velocity.

Transiting Exergy in a Process with Pressure, Temperature and Velocity Variations
The Grassmann diagram in Figure 1 illustrates a thermodynamic process where the intensive properties, such as temperature (T), pressure (P) and velocity (V) of a material stream change from their inlet (in) to outlet (out) values.The widths of the bands present the inlet and outlet exergies.The difference between these widths is the lost exergy (D).The specific exergy is defined as e pP, T, Vq " ´"h `0.5 V 2 ı ´h0 ¯´T 0 .ps ´s0 q.The Grassmann exergy efficiency is defined in the Equation (1) as follows: Energies 2016, 9, 212 2 of 11

Transiting Exergy in a Process with Pressure, Temperature and Velocity Variations
The Grassmann diagram in Figure 1 illustrates a thermodynamic process where the intensive properties, such as temperature (T), pressure (P) and velocity (V) of a material stream change from their inlet (in) to outlet (out) values.The widths of the bands present the inlet and outlet exergies.The difference between these widths is the lost exergy (D).The specific exergy is defined as . The Grassmann exergy efficiency is defined in the Equation (1) as follows: According to Brodyansky et al. [5], the transiting exergy of material stream is the lowest exergy value defined by the intensive parameters at the inlet and the outlet of an analysed system or its parts.The following equations illustrate the computation of transiting exergy:

If (T T and T T ) (T T and T T
These equations illustrate the fact that this lowest value of exergy is defined by the minimum values of pressure and velocity chosen among their inlet and outlet values.The situation is quite different for temperature since the transiting exergy is defined by its minimum value if the inlet and outlet conditions are higher than the environmental temperature T0, Equation (1a), by its maximum value for sub-environmental conditions, Equation (1b) and by the value T0 if the environmental temperature has an intermediate value, Equation (1c). Figure 1 visualises the fact that the introduction of the transiting exergy results in a shift of the reference state for exergy calculations.As a result the exergy consumed and produced in a system or its parts are represented by smaller band widths.
The "transiting exergy approach" is different from the traditionally proposed approaches [6][7][8][9][10] in that it does not attempt to individually compute the exergy variations caused by the different factors which may affect any defined thermodynamic system.On the contrary it relies on the unaffected part of the exergy entering and leaving the system [5].As a result this approach provides the grounds for the non-ambiguous definition of exergy consumed (E) and produced (ΔE).As an example of (E) and (ΔE) definitions let us analyse the throttling process taking place at sub-environmental conditions.At first let us assume that for this particular case the kinetic energies of the fluid at the inlet and the outlet of the throttling valve are negligible.Then these two quantities are calculated as: According to Brodyansky et al. [5], the transiting exergy of material stream is the lowest exergy value defined by the intensive parameters at the inlet and the outlet of an analysed system or its parts.The following equations illustrate the computation of transiting exergy: If pT in ą T 0 and T out ą T 0 q : E tr " EpP min , T min , V min q (1a) If pT in ă T 0 and T out ă T 0 q : E tr " EpP min , T max , V min q (1b) If pT in ą T 0 and T out ă T 0 q OR pT in ă T 0 and T out ą T 0 q : E tr " EpP min , T 0 , V min q (1c) These equations illustrate the fact that this lowest value of exergy is defined by the minimum values of pressure and velocity chosen among their inlet and outlet values.The situation is quite different for temperature since the transiting exergy is defined by its minimum value if the inlet and outlet conditions are higher than the environmental temperature T 0 , Equation (1a), by its maximum value for sub-environmental conditions, Equation (1b) and by the value T 0 if the environmental temperature has an intermediate value, Equation (1c). Figure 1 visualises the fact that the introduction of the transiting exergy results in a shift of the reference state for exergy calculations.As a result the exergy consumed and produced in a system or its parts are represented by smaller band widths.
The "transiting exergy approach" is different from the traditionally proposed approaches [6][7][8][9][10] in that it does not attempt to individually compute the exergy variations caused by the different factors which may affect any defined thermodynamic system.On the contrary it relies on the unaffected part of the exergy entering and leaving the system [5].As a result this approach provides the grounds for the non-ambiguous definition of exergy consumed (∇E) and produced (∆E).As an example of (∇E) and (∆E) definitions let us analyse the throttling process taking place at sub-environmental conditions.At first let us assume that for this particular case the kinetic energies of the fluid at the inlet and the outlet of the throttling valve are negligible.Then these two quantities are calculated as: ∇E in´tr " .m ¨pe in ´etr q " .m ¨rep P in , T in q ´ep P out , T in q s " .m ¨p∇e P q T in (2) Energies 2016, 9, 212 3 of 10 ∆E out´tr " . m ¨pe out ´etr q " . m ¨rep P out , T out q ´ep P out , T in q s " .m ¨p∆e T q P out (3) The term (∇e P ) Tin in Equation ( 2) is the decrease of the specific mechanical exergy due to an isothermal pressure drop at constant temperature Tin.The term (∆e T ) Pout in Equation ( 3) is the increase of the specific thermal exergy due to an isobaric temperature drop under sub-environmental conditions at constant pressure Pout.The fluid flow rate is ( .m).The specific exergy losses (d) are also presented on the diagram in Figure 2. As illustrated in Equations ( 4) and ( 5) the values (∇E) and (∆E) allow the computation of two important thermodynamic measures, namely exergy efficiency (η ex, TR ) and exergy losses (D) where (d) represents the specific exergy losses: Energies 2016, 9, 212 3 of 11 The term (eP)Tin in Equation ( 2) is the decrease of the specific mechanical exergy due to an isothermal pressure drop at constant temperature Tin.The term (ΔeT)Pout in Equation ( 3) is the increase of the specific thermal exergy due to an isobaric temperature drop under sub-environmental conditions at constant pressure Pout.The fluid flow rate is (ṁ).The specific exergy losses (d) are also presented on the diagram in Figure 2. As illustrated in Equations ( 4) and ( 5) the values (E) and (E) allow the computation of two important thermodynamic measures, namely exergy efficiency (ƞex, TR) and exergy losses (D) where (d) represents the specific exergy losses: The attention of the reader should be drawn to the fact that all the ambiguities, how to define the consumed and produced exergies [5][6][7], are removed by using the above approach.The values (E) and (ΔE) are defined by Equations ( 2) and ( 3) in a unique way.The interpretation of the results can be easily represented on the specific exergy-enthalpy diagram presented in Figure 2. The path 1-2 represents the change occurring to the stream between the throttling valve inlet and outlet conditions.The same overall result could be achieved by following the composite path 1-2′-2.The segment 1-2′ is (eP)Tin, the segment 2′-2 is (ΔeT)Pout.Given that the throttling takes place under sub-environmental conditions, the lowest exergy content of the fluid is reached at point 2′ which corresponds to the lowest pressure Pout and the highest temperature Tin.This exergy value is the specific transiting exergy of the stream.If the kinetic energy of the stream cannot be neglected, the lowest velocity value should be added to the definition of transiting exergy as illustrated in Figure 1.The expressions (2) and (3) for consumed and produced exergies will be changed accordingly; the subject is important for an ejector analysis and will be discussed in the next section.

The Exergy Consumption and Production in Different Parts of a One-Phase Ejector
The one phase ejector studied in the present paper is the so-called "constant-pressure mixing ejector".It is presented in Figure 3.The exit of the nozzle is located within the suction chamber which is upstream of the constant-area section.The constant-pressure mixing theory of ejector developed by Keenan et al. [11] was frequently used in the analysis of constant-pressure ejectors [12,13].Keenan et al. [11] assumed that the primary and the secondary (entrained) flows at the exit of the nozzle have an identical pressure.Mixing of the two streams begins there and proceeds with constant pressure, until the inlet of the constant-area section.This theory is used as one assumption among others in the new validated ejector model [14] that is used in the present paper to calculate the The attention of the reader should be drawn to the fact that all the ambiguities, how to define the consumed and produced exergies [5][6][7], are removed by using the above approach.The values (∇E) and (∆E) are defined by Equations ( 2) and (3) in a unique way.The interpretation of the results can be easily represented on the specific exergy-enthalpy diagram presented in Figure 2.
The path 1-2 represents the change occurring to the stream between the throttling valve inlet and outlet conditions.The same overall result could be achieved by following the composite path 1-2 1 -2.The segment 1-2 1 is (∇e P ) Tin , the segment 2 1 -2 is (∆e T ) Pout .Given that the throttling takes place under sub-environmental conditions, the lowest exergy content of the fluid is reached at point 2 1 which corresponds to the lowest pressure Pout and the highest temperature Tin.This exergy value is the specific transiting exergy of the stream.If the kinetic energy of the stream cannot be neglected, the lowest velocity value should be added to the definition of transiting exergy as illustrated in Figure 1.The expressions (2) and (3) for consumed and produced exergies will be changed accordingly; the subject is important for an ejector analysis and will be discussed in the next section.

The Exergy Consumption and Production in Different Parts of a One-Phase Ejector
The one phase ejector studied in the present paper is the so-called "constant-pressure mixing ejector".It is presented in Figure 3.The exit of the nozzle is located within the suction chamber which is upstream of the constant-area section.The constant-pressure mixing theory of ejector developed by Keenan et al. [11] was frequently used in the analysis of constant-pressure ejectors [12,13].
Keenan et al. [11] assumed that the primary and the secondary (entrained) flows at the exit of the nozzle have an identical pressure.Mixing of the two streams begins there and proceeds with constant pressure, until the inlet of the constant-area section.This theory is used as one assumption among others in the new validated ejector model [14] that is used in the present paper to calculate the pressure, temperature and velocity at the different cross-sections illustrated in Figure 3.The refrigerant R141b is used as an example for this study.It has been assumed that: the temperature and the pressure of the primary motive fluid entering the primary nozzle are T 4 = 145 ˝C and P 4 = 1000 kPa, the flow rate is .m p = 0.19838 kg/s; the temperature and the pressure of the secondary fluid are T 6 = ´5 ˝C and P 6 = 22.28 kPa, the flow rate is .m s = 0.04959 kg/s.According to information compiled by Liu and Groll [15], it has been assumed that the polytropic efficiencies are: 0.95 for the primary nozzle, 0.85 for the suction chamber and 0.78 for the diffuser.
Energies 2016, 9, 212 4 of 11 pressure, temperature and velocity at the different cross-sections illustrated in Figure 3.The refrigerant R141b is used as an example for this study.It has been assumed that: the temperature and the pressure of the primary motive fluid entering the primary nozzle are T4 = 145 °C and P4 = 1000 kPa, the flow rate is ṁp = 0.19838 kg/s; the temperature and the pressure of the secondary fluid are T6 = −5 °C and P6 = 22.28 kPa, the flow rate is ṁ s = 0.04959 kg/s.According to information compiled by Liu and Groll [15], it has been assumed that the polytropic efficiencies are: 0.95 for the primary nozzle, 0.85 for the suction chamber and 0.78 for the diffuser.To make the exergy analysis representative, the ejector is split into 7 sections: (1) primary stream and the converging part of the nozzle (4-thr); (2) diverging part of the nozzle (thr-7p); (3) suction section of the entrained stream (6-7s), (4) mixing zone (7p-m + 7s-m); (5) zone of the shock (m-d); (6) constant area section (d-8); (7) diffuser and the ejector outlet part (8-1).The calculated parameters such as pressure, temperature, velocity and flow-rates at the inlet and outlet of each section are presented in Table 1 [16].The choice of a suitable working fluid is one of the essential steps in the design of the ejector and, subsequently, in the design and manufacturing of the solar driven refrigeration system.Such a fluid must meet the performance criteria as well as the requirements of safety and environmental protection.It must also be available at an affordable price.In the present study, the refrigerant R141b (CH3CCl2F) was chosen.Previous studies [17,18] have found that it is suitable for ejector applications.Furthermore, R141b has a positive-slope saturated-vapor line in the temperature-entropy diagram and therefore does not require superheating.Its critical temperature and pressure are respectively 204.2 °C and 4205 kPa.Its normal boiling point is 32 °C.Its ODP (Ozon depletion potential) value is 0.1 proving that it has a negligible impact on the environment, while its global warming potential (GWP) value is 725 which is quite acceptable for the application under consideration.The profiles of pressure, temperature and velocity along the ejector are illustrated in Figure 4. To make the exergy analysis representative, the ejector is split into 7 sections: (1) primary stream and the converging part of the nozzle (4-thr); (2) diverging part of the nozzle (thr-7p); (3) suction section of the entrained stream (6-7s), (4) mixing zone (7p-m + 7s-m); (5) zone of the shock (m-d); (6) constant area section (d-8); (7) diffuser and the ejector outlet part (8-1).The calculated parameters such as pressure, temperature, velocity and flow-rates at the inlet and outlet of each section are presented in Table 1 [16].The choice of a suitable working fluid is one of the essential steps in the design of the ejector and, subsequently, in the design and manufacturing of the solar driven refrigeration system.Such a fluid must meet the performance criteria as well as the requirements of safety and environmental protection.It must also be available at an affordable price.In the present study, the refrigerant R141b (CH 3 CCl 2 F) was chosen.Previous studies [17,18] have found that it is suitable for ejector applications.Furthermore, R141b has a positive-slope saturated-vapor line in the temperature-entropy diagram Energies 2016, 9, 212 5 of 10 and therefore does not require superheating.Its critical temperature and pressure are respectively 204.2 ˝C and 4205 kPa.Its normal boiling point is 32 ˝C.Its ODP (Ozon depletion potential) value is 0.1 proving that it has a negligible impact on the environment, while its global warming potential (GWP) value is 725 which is quite acceptable for the application under consideration.The profiles of pressure, temperature and velocity along the ejector are illustrated in Figure 4.By using the definition of transiting exergy from Figure 1 and the simulation results presented in Table 1, it is possible to compute the exergy consumed (E) and produced (ΔE) within each part of the ejector.Let us discuss the mathematical expression and the physical meaning of each of these terms.
Section (4-thr): The exergy consumption is the decrease of thermo-mechanical exergy due to pressure and temperature drops at sup-environmental conditions.The exergy production is the increase of kinetic energy due to the velocity rise from the section's inlet to outlet.
Section (thr-7p): (E) is the decrease of thermo-mechanical exergy due to the pressure drop from inlet to outlet and the temperature drop from its inlet value to T0.The exergy production includes: (1) the increase of thermal exergy due to the temperature drop from T0 to T7p at the sub-environmental conditions and calculated at constant outlet pressure P7p, and (2) the increase of kinetic energy due to the velocity rise from inlet to outlet.By using the definition of transiting exergy from Figure 1 and the simulation results presented in Table 1, it is possible to compute the exergy consumed (∇E) and produced (∆E) within each part of the ejector.Let us discuss the mathematical expression and the physical meaning of each of these terms.
Section (4-thr): ∇E 4´tr " . m p ¨rep P 4 , T 4 , V 4 q ´ep P thr , T thr , V 4 q s " .m p ¨p∇e P, T q ∆E thr´tr " . m p ¨rep P thr , T thr , V thr q ´ep P thr , T thr , V 4 q s " .m p ¨p∆e V q The exergy consumption is the decrease of thermo-mechanical exergy due to pressure and temperature drops at sup-environmental conditions.The exergy production is the increase of kinetic energy due to the velocity rise from the section's inlet to outlet.
Section (thr-7p): ∇E thr´tr " . m p ¨"ep P thr , T thr , V thr q ´ep P 7p , T 0 , V thr q ‰ " .m p ¨p∇e P, T q . m p ¨"ep P 7p , T 7p , V 7p q ´ep P 7p , T 0 , V thr q ‰ " .m p ¨"p∆e T q P 7p `p∆e V q ı Energies 2016, 9, 212 6 of 10 (∇E) is the decrease of thermo-mechanical exergy due to the pressure drop from inlet to outlet and the temperature drop from its inlet value to T 0 .The exergy production includes: (1) the increase of thermal exergy due to the temperature drop from T 0 to T 7p at the sub-environmental conditions and calculated at constant outlet pressure P 7p , and (2) the increase of kinetic energy due to the velocity rise from inlet to outlet.
Section (6-7s): ∇E 6´tr " . m s ¨rep P 6 , T 6 , V 6 q ´ep P 7s , T 6 , V 6 q s " .m s ¨p∇e P q T 6 (10) . m s ¨rep P 7s , T 7s , V 7s q ´ep P 7s , T 6 , V 6 q s " .m s ¨"p∆e T q P 7s `p∆e V q ı (∇E) is the decrease of mechanical exergy due to the pressure drop and calculated at constant inlet T 6 .(∆E) is the sum of: (1) the increase of thermal exergy due to the temperature drop in the sub-environmental region and calculated at constant outlet pressure P 7s , and (2) the increase of kinetic energy due to the velocity rise from inlet to outlet.
Section (7p-m+7s-m): . m p ¨"ep P 7p , T 7p , V 7p q ´ep P 7p , T 0 , V m q ‰ `. m s ¨rep P 7s , T 7s , V 7s q ´ep P 7s , T 0 , V 7s q s " .m p ¨"p∇e T q P 7p `p∇e V q ı `. m s ¨p∇e T q P 7s ( 12) Given that the mixing section deals with two currents ( .m p and .m s ), the transiting exergies in Equations ( 12) and ( 13) are calculated for each current.As a result the consumed exergy is linked to both currents.For the primary stream it is the sum of: (1) the decrease of thermal exergy due to a temperature rise in the sub-environmental region and calculated at constant inlet pressure P 7p , and (2) the decrease of kinetic energy due to the velocity reduction.For the secondary stream it is the decrease of thermal exergy due to a temperature rise in the sub-environmental region and calculated at constant inlet pressure P 7s .The produced exergy is linked to the primary and secondary streams together.For the primary it is the increase of thermal exergy due to a temperature rise in the sup-environmental region and calculated at constant outlet pressure P 7p .For the secondary it is the sum of: (1) the increase of thermal exergy due to the temperature rise in the sub-environmental region and calculated at constant outlet pressure P 7 s, and (2) the increase of kinetic energy due to the velocity rise.
Figure 5 used the diagram of Grassmann applied to the section (7p-m + 7s-m) to illustrate the existing phenomenon in this mixing zone which is given by the two equations ( 12) and (13).
(E) is the decrease of mechanical exergy due to the pressure drop and calculated at constant inlet temperature T6. (ΔE) is the sum of: (1) the increase of thermal exergy due to the temperature drop in the sub-environmental region and calculated at constant outlet pressure P7s, and (2) the increase of kinetic energy due to the velocity rise from inlet to outlet.
Section (7p-m+7s-m): Given that the mixing section deals with two currents (ṁp and ṁ  ), the transiting exergies in Equations ( 12) and ( 13) are calculated for each current.As a result the consumed exergy is linked to both currents.For the primary stream it is the sum of: (1) the decrease of thermal exergy due to a temperature rise in the sub-environmental region and calculated at constant inlet pressure P7p, and (2) the decrease of kinetic energy due to the velocity reduction.For the secondary stream it is the decrease of thermal exergy due to a temperature rise in the sub-environmental region and calculated at constant inlet pressure P7s.The produced exergy is linked to the primary and secondary streams together.For the primary it is the increase of thermal exergy due to a temperature rise in the sup-environmental region and calculated at constant outlet pressure P7p.For the secondary it is the sum of: (1) the increase of thermal exergy due to the temperature rise in the sub-environmental region and calculated at constant outlet pressure P7s, and (2) the increase of kinetic energy due to the velocity rise.
Figure 5 used the diagram of Grassmann applied to the section (7p-m + 7s-m) to illustrate the existing phenomenon in this mixing zone which is given by the two equations ( 12) and (13).Section (m-d): ∇E m´tr " `. m p `. m s ˘¨rep P m , T m , V m q ´ep P m , T m , V d q s " `. m p `. m s ˘¨p∇e V q (14) ∆E d´tr " `. m p `. m s ˘¨rep P d , T d , V d q ´ep P m , T m , V d q s " `. m p `. m s ˘¨p∆e P, T q The exergy consumption (∇E) across the normal shock is the decrease in kinetic energy due to the velocity drop.The exergy production (∆E) is the increase of thermo-mechanical exergy due to the temperature rise from the inlet to the outlet in sup-environmental region and the increase in pressure from the inlet to the outlet.
Section (d-8): ∇E d´tr " `. m p `. m s ˘¨rep P d , T d , V d q ´ep P 8 , T d , V d q s " `. m p `. m s ˘¨p∇e P T d (16) ∆E 8´tr " `. m p `. m s ˘¨rep P 8 , T 8 , V 8 q ´ep P 8 , T 8 , V d q s " `. m p `. m s ˘¨p∆e V q The temperature variation can be neglected in this section, thus (∇E) is the decrease of mechanical exergy due to the pressure drop caused by friction and calculated at constant inlet temperature T d .(∆E) is the increase of kinetic energy due to the velocity rise from the inlet to the outlet.
Section (8-1): ∇E 8´tr " `. m p `. m s ˘¨rep P 8 , T 8 , V 8 q ´ep P 8 , T 8 , V 1 q s " `. m p `. m s ˘¨p∇e V q (18) In this section (∇E) is the decrease in kinetic energy due to the velocity drop.(∆E) is the increase of thermo-mechanical exergy due to the pressure and temperature rise.
The terms (∇E) and (∆E) for the overall ejector may be calculated applying the same methodology.Given that the velocities of the stream in the inlet (states 4, 6) and outlet (state 1) of the ejector are negligible, the terms are: ∇E 46´tr " .m p ¨rep P 4 , T 4 q ´ep P 1 , T 1 qs `. m s ¨rep P 6 , T 6 q ´ep P 6 , T 0 qs " . m p ¨p∇e P, T q `. m s ¨p∇e T q P 6 (20) ∆E 1´tr " . m p ¨rep P 1 , T 1 q ´ep P 1 , T 1 qs `. m s ¨rep P 1 , T 1 q ´ep P 6 , T 0 qs " . m s ¨p∆e P, T q (21) The consumed exergy is linked to both currents.For the primary stream (∇E) is the decrease of thermo-mechanical exergy due to the pressure and temperature drops in the sub-environmental region.For the secondary stream (∇E) is the decrease of thermal exergy due to the temperature rise from the sub-environmental value to T 0 and calculated at constant inlet pressure P 6 .The produced exergy (∆E) is linked to the secondary stream only.The exergy production is the increase of thermo-mechanical exergy due to the pressure rise from the inlet to the outlet and to the temperature rise from T 0 to T 1 .

Analysis of Numerical Results
The numerical values of the above terms are presented in Table 2.The corresponding exergy losses (D), Grassmann exergy efficiencies (η ex, GR ) and exergy efficiencies taking into account the transition streams (η ex, TR ) are calculated according to Equations (1), (4), (5) and are presented in the table as well.
The most important exergy losses take place within the zone of the shock (section m-d).The second important place with the greatest irreversibility is the mixing zone (sections 7p-m + 7s-m).The third one is the diverging part of the nozzle (section thr-7p).Let us now illustrate in which way the newly introduced thermodynamic metrics, exergy consumed (∇E) and produced (∆E) as well as exergy efficiency (η ex, TR ), may be used to complement this analysis.
reason of this discrepancy is the presence of an important transiting exergy flow; this fact is ignored when the Grassman exergy efficiency is applied.
Finally the exergy efficiency (η ex, TR ) of the overall ejector, calculated according to Equations (20), ( 21) and ( 4) is low and equals 18.3%, contrary to the "optimistic" value 37.5% of (η ex, GR ).The main reason of this difference is the presence of an important transiting exergy flow of 3.2 kW.

Conclusions
Calculation of the transiting exergy within different sections of a one phase ejector allows the evaluation of two thermodynamically important metrics, exergy produced and exergy consumed.Their application permitted the evaluation of the mutual transformation of different kinds of exergy linked to three intensive parameters of the flow inside the ejector, namely pressure, temperature and velocity.One of the lowest thermodynamic efficiencies takes place in the mixing zone.The most important factor responsible for this is the temperature rise in the sub-environmental region.Grassmann exergy efficiency is not an appropriate criterion for evaluation of ejectors thermodynamic performance.

Figure 3 .
Figure 3.An ejector model with constant mixing pressure.

Figure 3 .
Figure 3.An ejector model with constant mixing pressure.

Figure 5 .
Figure 5. Diagram of Grassman illustrating transiting exergy in the mixing zone.

Figure 5 .
Figure 5. Diagram of Grassman illustrating transiting exergy in the mixing zone.

Table 1 .
Calculated parameters at different ejector's sections with R141b as working fluid.

Table 1 .
Calculated parameters at different ejector's sections with R141b as working fluid.