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lithium bromide as the working fluids
International Journal of Refrigeration 26 (2003) 315–320 www.elsevier.com/locate/ijrefrig
The thermodynamic performance of a new solution cycle in double absorption heat transformer using water/lithium bromide as the working fluids Zongchang Zhao*, Fangwei Zhou, Xiaodong Zhang, Songping Li Research Institute of Chemical Engineering, Dalian University of Technology, 158 Zhong Shan Road, Dalian, Liaoning Province 116012, PR China Received 8 July 2002; received in revised form 8 October 2002; accepted 16 October 2002
Abstract In this paper, a new solution cycle in the double absorption heat transformer is presented and the thermodynamic performance of this new cycle is simulated based on the thermodynamic properties of aqueous solution of lithium bromide. The results show that this new cycle is superior to the cycle being studied by some researchers. This new solution cycle has a wider range of operation in which the system maintains the high value of COP and has larger temperature lifts and operation stability. The relationship between the absorber and the absorbing evaporator is more independent and this makes the operation and control of the system more easier. # 2003 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Refrigerating system; Absorption system; Water/lithium bromide; Innovation; Design; Performance
Performance thermodynamique du cycle d’un transformateur de chaleur d’une conception nouvelle a` double absorption utilisant de l’eau/bromure de lithium en tant que fluides actifs Mots cle´s : Syste`me frigorifique ; Syste`me a` absorption ; Eau/bromure de lithium ; Modernisation ; Conception ; Performance
1. Introduction In order to reduce the CO2 discharge and to reuse large amounts of industrial waste heat, absorption heat transformers (AHT) which can recover waste heat from a low temperature level to a high temperature level are used in many industries. Because the available temperature lift for single-stage absorption heat transformer (STAHT) is only in the range from 30 to 40 C, a much higher available temperature lift must be obtained by adopting two-stage absorption heat transformer
* Corresponding author. Tel.: +86-411-363-1333-3239. E-mail address: [email protected] (Z. Zhao).
(TSAHT) or double absorption heat transformer (DAHT). Two-stage absorption heat transformer consists of two single-stage absorption heat transformers, so it has more components and more investment in equipment, while double-absorption heat transformer not only is an advanced absorption heat transformer in which it is possible to reach a absorbing temperature as high as that reached by two-stage heat transformer, but it also has the advantage that it is considerably simpler than the two-stage heat transformer. As shown in Fig. 1, only an absorbing evaporator and a pump must be added to a single-stage heat transformer to convert them to a double absorption heat transformer. The industrial waste heat at the intermediate temperature tGE is supplied to the generator for
0140-7007/03/$30.00 # 2003 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(02)00114-7
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Z. Zhao et al. / International Journal of Refrigeration 26 (2003) 315–320
Nomenclature COP FR M P Q t t=tABtGE X X
Subscripts AB AE GE CO EV SE
coefficient of performance flow rate ratio mass flow rate (kg s1) pressure (MPa) heat load (kW) temperature ( C) temperature lift ( C) LiBr mass concentration in solution (mass% LiBr) concentration difference (mass% LiBr)
absorber absorbing evaporator generator condenser evaporator solution heat exchanger
Fig. 1. Schematic diagram of DAHT with an ordinary solution cycle.
evaporating the water from an aqueous solution of lithium bromide. The vaporized water is condensed in the condenser at a low temperature tCO, and the condensed water is split into two streams. One of them is pumped into the evaporator where it is evaporated at an intermediate temperature tEV tGE and a pressure PEV. The other is pumped at a higher pressure PAB and vaporized in the absorbing evaporator heated by an amount of available released heat QAE. The vaporized water is absorbed in the absorber at a high temperature TAB and a pressure PAB by the strong solution coming from the generator. The solution cycle being used in the double absorption heat transformer is plotted in the Fig. 2. The strong solution coming from the generator at a high concentration XGE goes into the absorber to absorb the vaporized water coming from the absorbing evaporator and becomes a weak solution at an intermediate concentration XAB. The weak solution is split into two streams. One goes to the generator to re-heat the strong solution through the heat exchanger. The other is fed to the absorbing evaporator to absorb the vaporized water coming from the evaporator and becomes a weaker solution at a lower concentration XAE. The performance of this cycle has been studied by many researchers [1–4]. However, this cycle has a drawback, the absorption or evaporation temperature in absorbing evaporator cannot be as high as possible, because the weak solution leaving the absorbing evaporator absorbs vaporized water twice, and has the lowest concentration, namely XAE < XAB < XGE. This will not make the absorption temperature in the absorber as high as possible. In order to overcome this drawback, a new solution cycle in the double absorption heat transformer is presented here. Furthermore, its performance is simulated based on the thermodynamic properties of an aqueous solution of lithium bromide.
2. The description of the new solution cycle in the DAHT The new solution cycle in a double absorption heat transformer is shown in Figs. 3 and 4. In this new cycle,
Fig. 2. The ordinary cycle in DAHT.
Fig. 3. Schematic diagram of DAHT with a new solution cycle.
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317
5. The expanding process in the throttling valves is isenthalpic; 6. The temperature difference in the cold end of solution heat exchanger is fixed by 5 C; 7. The energy consumed by the pump is neglected.
The parameters used to determine the performance of the double absorption heat transformer are the following:
Fig. 4. The new solution cycle in DAHT.
the strong solution coming from the generator is split into two streams. One goes to the absorber for absorbing the vaporized water coming from the absorbing evaporator and then goes back to the generator preheating the strong solution through the solution heat exchanger. The other goes to the absorbing evaporator for absorbing the vaporized water coming from the evaporator and then goes back to the generator. Because of absorbing the vaporized water only once, the concentration of the weak solution leaving the absorbing evaporator is higher than that in the cycle shown in Figs. 1 and 2. As a result, a higher temperature in the absorbing evaporator can be obtained. The higher the absorption or evaporation temperature in absorbing evaporator, the higher the absorption temperature in the absorber is in this new solution cycle. Besides the earlier advantage, the weak solution leaving the absorber and that leaving the absorbing evaporator do not affect each other. In other words, it is not necessary that the concentration of the weak solution leaving the absorbing evaporator must be less than that leaving the absorber. Consequently, a wider operating range of the new cycle will be possible. It is convenient to denote the ordinary cycle in Figs. 1 and 2 with ‘‘case one’’ and the new cycle in Figs. 3 and 4 with ‘‘case two’’.
3. The theoretical analysis In order to analyze the performance of this new solution cycle, the following assumptions are made. 1. The analysis is carried out under steady state conditions; 2. The solutions leaving the generator and leaving the absorber and absorbing evaporator are saturated; 3. The condensate leaving the condenser is saturated; 4. Thermal and pressure losses are neglected;
1. The new solution cycle in the double-absorption heat transformer has a wider available range of tAE than that in the ordinary one. The COP keeps a high value in this range. Consequently, the system is more stable and flexible for the operation and the control of the system. 2. When the differences in concentration X1 and X2 in ordinary solution cycle are equal to these in the new solution cycle respectively, to the new solution cycle, the temperature lift is about 5–10 C higher and the COP is about 0.01 lower than those in the ordinary solution cycle being studied by some researchers, respectively. 3. FR2 and X2 are not directly affected by tAB in the new solution cycle, while FR2 and X2 are directly affected by tAB in the ordinary solution cycle being studied by some researchers. As a result, the relationship between the absorber and absorbing evaporator are more independent and this makes the operation and control of the system easier. (1). The bypass ratio is an important parameter since it is directly related to the heat delivered in the absorber. For the condenser, it can be defined as the ratio of the mass flow rate vaporized in the evaporator to the mass flow rate vaporized in the absorbing evaporator BPCO ¼ M2 =M3
ð1Þ
For the absorbing evaporator (case one), it can be defined as the ratio of the mass flow rate of the weak solution which has the intermediate concentration XAB and goes to the generator to that of which goes to the absorbing evaporator. BPAE ¼ M16 =M14
ð2aÞ
For the absorbing evaporator (case two), it can be defined as the ratio of the mass flow rate of the strong solution which has the concentration XGE and goes to the absorber to that of which goes to the absorbing evaporator.
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BPAE ¼ M13 =M14
ð2bÞ
(2). The coefficient of the performance is given by: COP ¼
QAB QGE þ QEV
ð3Þ
(3). For generator, flow rate ratio is defined as the ratio of the mass flow rate of the solution entering the generator to that of refrigerant leaving the generator. For absorber/evaporator, flow rate ratio is defined as the ratio of the mass flow rate of the solution leaving the absorber/evaporator to that of refrigerant going into the absorber/evaporator. They are expressed as the following. FR1 ¼ ðM9 þ M18Þ=M1
ð4Þ
FR2 ¼ M8=M6
ð5Þ
(4). The concentration difference is defined as the concentration difference between the inlet solution and outlet solution of the absorber. For double absorption heat transformer, there are also two concentration difference, and they can be expressed as the following. Case one: X1 ¼ XGE XAB
ð6aÞ
X2 ¼ XAB XAE
ð7aÞ
those of the cycle being studied by some researchers. Figs. 5 and 6 show the variation of coefficients of performance versus the absorption or evaporation temperature tAE. It can be seen that for the new solution cycle (case two) a wider operating range of the temperature of the absorbing evaporator exists. In this range the coefficients of performance decrease very slowly and maintain high value. The lower the temperature tAB of the absorber, the wider the range of the available operating temperature tAE of the absorbing evaporator is. These characteristics of the new solution cycle make the system have more operating elasticity and make the operation and control easier. It is well known that the temperature tAE of the absorbing evaporator is determined by the temperature tEV of the evaporator and the concentration XAE of the weak solution. When the temperature tEV maintains constant, the temperature tAE is only determined by the XAE. The wider the operating range of the tAE, the wider the range of the changing concentration XAE of weak solution. The main reason is that the concentration XAE of the weak solution leaving the absorbing evaporator is not directly affected by that of the weak solution leaving the absorber in case two. On the contrary, the concentration XAE of the weak solution leaving the absorbing evaporator is directly affected by the weak solution coming from the absorber in case one.
Case two: X1 ¼ XGE XAB
ð6bÞ
X2 ¼ XGE XAE
ð7bÞ
(5). Temperature lift is a very important parameter. It is defined as the temperature difference between the absorption temperature in the absorber and generation temperature in the generator, namely, it is expressed as the following t ¼ tAB tGE
Fig. 5. The effect of tAE on COP (case one).
ð8Þ
4. Results and discussion Based on the thermodynamic properties of aqueous solution of lithium bromide [5–7], the earlier assumptions and the balance of material and energy on each of the component in the DAHT, the performance of the new cycle in double-absorption heat transformer is simulated. The results obtained are also compared with
Fig. 6. The effect of tAE on COP (case two).
Z. Zhao et al. / International Journal of Refrigeration 26 (2003) 315–320
Figs. 7 and 8 show the variation of BPCO and BPAE against the temperature tAE of the absorbing evaporator. In Fig. 7 (case one), it can be seen that the BPCO and BPAE decrease with the increase of tAE and the range of the change in tAE is still narrow. However, in Fig. 8 (case two), the BPAE decreases with the increase of tAE and the BPCO decreases slowly with the increase of tAE and increases rapidly when the temperature tAE approaches the limit of about 120 C. The range of the change in tAE is still wider compared with that in case one. Why does the BPCO increase sharply when the tAE approaches 120 C? The reason is the following. When tAE increases, the temperature (t7) and the pressure (P7) of the vapor leaving the absorbing evaporator will all increase. When the temperature (tAB=t16) of the absorber keeps constant, the concentration X16 of the weak solution leaving the absorber must decrease. The flow rate (M13) of the strong solution going into the absorber will decrease, and the flow rate (M14) of the strong solution going into the absorbing evaporator must increase. As a result, BPAE=M13/M14 would also decrease. When tAE approaches 120 C, BPAE will become almost zero. This can be shown clearly in Fig. 8. This means that the M13 will become very small. Most of the strong solution coming from the generator will go into the absorbing evaporator. To keep the material and energy balance of the absorbing evaporator, the flow rate M6 of the vapor coming from the evaporator will
increase greatly. This causes the rapid increase of the value of BPCO. In fact, the absorber AB cannot work normally in this situation (the output heat QAB of the absorber approaches to zero then). Consequently, the double-absorption heat transformer has become a single-stage absorption heat transformer. The 120 C is the highest output temperature of the absorbing evaporator under these conditions (tGE=tEV=70 C, tCO=20 C). It also is almost the highest output temperature of the single-absorption heat transformer. The upper limit of the tGE will vary according to different operating conditions. Figs. 9 and 10 show the variations of differences in concentration of X1 and X2 and flow ratios FR1 and FR2 versus the temperature of the absorbing evaporator at different absorbing temperatures. In Fig. 9 (case one), X1 increases with the increase of tAE, while X2 decreases with the increase of tAE. Generally speaking, X1 is less than X2 at the same tAB. X1 is usually in the range from 2 to 10, while X2 is usually in the range from 4 to 20. FR1 decreases sharply and FR2 increases rapidly with the increase of tAE. It is obvious that FR1 is larger than FR2. In Fig. 10 (case two), FR1 decreases slower with the increase of
Fig. 9. Effect of tAE on FR1 and FR2 (case one). Fig. 7. Effect of tAE on BPAE and BPCO (case one).
Fig. 8. Effect of tAE on BPAE and BPCO (case two).
319
Fig. 10. Effect of tAE on FR1 and FR2 (case two).
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tAE and has a wider range of tAE than that in case one. It is very interesting that X2 and FR2 are not affected by tAB. They vary only with the change in tAE when other temperatures keep constant. The reason is that the concentration of the weak solution leaving the absorbing evaporator does not have direct relationships with that of the weak solution leaving the absorber. The characteristics of the new cycle will make operation and control of the system more stable and easier. Because the FR1 and FR2 are important adjusting parameters, the determination of the suitable ranges of FR1 and FR2 is important for the cycle operating at a range of high COP. Fig. 11 shows the variation of COP, FR1 and FR2 versus the tAE. In Fig. 11, points a, b, c, d and e represent the turning point of the FR1 lines at different tAB, respectively. The COP reaches a maximum value at the turning point. In fact, the corresponding values of FR1 are also the upper limits of available change in FR1. These upper limits are about in the neighborhood of 15. Fig. 12 shows the change in temperature lifts t and the COP versus the temperature tGE of the generator respectively at the different tCO. It can be seen that the temperature lifts in case two are higher than the temperature lifts in case one under the same X1 and X2
conditions. The temperature lifts in case two are about 5–10 C higher than those in case one. Furthermore, the COPs in case two are about 0.01 lower than those in case one.
5. Conclusions
1. The new solution cycle in the double-absorption heat transformer has a wider available range of tAE than that in the ordinary one. The COP keeps a high value in this range. Consequently, the system is more stable and flexible for the operation and the control of the system. 2. When the differences in concentration X1 and X2 in ordinary solution cycle are equal to these in the new solution cycle respectively, to the new solution cycle, the temperature lift is about 5– 10 C higher and the COP is about 0.01 lower than those in the ordinary solution cycle being studied by some researchers, respectively. 3. FR2 and X2 are not directly affected by tAB in the new solution cycle, while FR2 and X2 are directly affected by tAB in the ordinary solution cycle being studied by some researchers. As a result, the relationship between the absorber and absorbing evaporator are more independent and this makes the operation and control of the system easier.
References
Fig. 11. Effect of tAE on COP, FR1 and FR2 (case two).
Fig. 12. Effect of tGE on t and COP.
[1] Rivera W, Best R, Hernandez J, Heard CL, Holland FA. Thermodynamic study of advanced absorption heat transformer—I. Single and two stage configurations with heat exchangers. Heat Recovery Systems & CHP 1994; 14(2):173–84. [2] Rivera W, Best R, Hernandez J, Heard CL, Holland FA. Thermodynamic study of advanced absorption heat transformer—II Double absorption configuration. Heat Recovery Systems & CHP 1994;14(2):185–93. [3] Yin Juan, Shi Lin, Wang Xin, Zhu Mingshan. Performance analysis of double heat transformer. Journal of Fluid and Mechanics 2000;8:50–3 [in Chinese]. [4] Yin J, Shi L, Zhu MS, Han LZ. Performance analysis of the two stage heat transformer. Journal of Tsinghua University 2000;40(10):88–91 [in Chinese]. [5] Patterson MR, Blanco HP. Numerical fits of properties of lithium-bromide water solutions. ASHRAE Trans 1988; 94(2):2059–77. [6] Talbi MM, Agnew B. Exergy analysis: an absorption refrigerator using lithium bromide and water as the working fluids. Applied Thermal Engineering 2000;20(7): 619–30. [7] Sun Dawen. Thermodynamic design data and optimum design maps for absorption refrigeration systems. Applied Thermal Engineering 1997;17(3):211–21.
The thermodynamic performance of a new solution cycle in double absorption heat transformer using water/lithium bromide as the working fluids Zongchang Zhao*, Fangwei Zhou, Xiaodong Zhang, Songping Li Research Institute of Chemical Engineering, Dalian University of Technology, 158 Zhong Shan Road, Dalian, Liaoning Province 116012, PR China Received 8 July 2002; received in revised form 8 October 2002; accepted 16 October 2002
Abstract In this paper, a new solution cycle in the double absorption heat transformer is presented and the thermodynamic performance of this new cycle is simulated based on the thermodynamic properties of aqueous solution of lithium bromide. The results show that this new cycle is superior to the cycle being studied by some researchers. This new solution cycle has a wider range of operation in which the system maintains the high value of COP and has larger temperature lifts and operation stability. The relationship between the absorber and the absorbing evaporator is more independent and this makes the operation and control of the system more easier. # 2003 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Refrigerating system; Absorption system; Water/lithium bromide; Innovation; Design; Performance
Performance thermodynamique du cycle d’un transformateur de chaleur d’une conception nouvelle a` double absorption utilisant de l’eau/bromure de lithium en tant que fluides actifs Mots cle´s : Syste`me frigorifique ; Syste`me a` absorption ; Eau/bromure de lithium ; Modernisation ; Conception ; Performance
1. Introduction In order to reduce the CO2 discharge and to reuse large amounts of industrial waste heat, absorption heat transformers (AHT) which can recover waste heat from a low temperature level to a high temperature level are used in many industries. Because the available temperature lift for single-stage absorption heat transformer (STAHT) is only in the range from 30 to 40 C, a much higher available temperature lift must be obtained by adopting two-stage absorption heat transformer
* Corresponding author. Tel.: +86-411-363-1333-3239. E-mail address: [email protected] (Z. Zhao).
(TSAHT) or double absorption heat transformer (DAHT). Two-stage absorption heat transformer consists of two single-stage absorption heat transformers, so it has more components and more investment in equipment, while double-absorption heat transformer not only is an advanced absorption heat transformer in which it is possible to reach a absorbing temperature as high as that reached by two-stage heat transformer, but it also has the advantage that it is considerably simpler than the two-stage heat transformer. As shown in Fig. 1, only an absorbing evaporator and a pump must be added to a single-stage heat transformer to convert them to a double absorption heat transformer. The industrial waste heat at the intermediate temperature tGE is supplied to the generator for
0140-7007/03/$30.00 # 2003 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(02)00114-7
316
Z. Zhao et al. / International Journal of Refrigeration 26 (2003) 315–320
Nomenclature COP FR M P Q t t=tABtGE X X
Subscripts AB AE GE CO EV SE
coefficient of performance flow rate ratio mass flow rate (kg s1) pressure (MPa) heat load (kW) temperature ( C) temperature lift ( C) LiBr mass concentration in solution (mass% LiBr) concentration difference (mass% LiBr)
absorber absorbing evaporator generator condenser evaporator solution heat exchanger
Fig. 1. Schematic diagram of DAHT with an ordinary solution cycle.
evaporating the water from an aqueous solution of lithium bromide. The vaporized water is condensed in the condenser at a low temperature tCO, and the condensed water is split into two streams. One of them is pumped into the evaporator where it is evaporated at an intermediate temperature tEV tGE and a pressure PEV. The other is pumped at a higher pressure PAB and vaporized in the absorbing evaporator heated by an amount of available released heat QAE. The vaporized water is absorbed in the absorber at a high temperature TAB and a pressure PAB by the strong solution coming from the generator. The solution cycle being used in the double absorption heat transformer is plotted in the Fig. 2. The strong solution coming from the generator at a high concentration XGE goes into the absorber to absorb the vaporized water coming from the absorbing evaporator and becomes a weak solution at an intermediate concentration XAB. The weak solution is split into two streams. One goes to the generator to re-heat the strong solution through the heat exchanger. The other is fed to the absorbing evaporator to absorb the vaporized water coming from the evaporator and becomes a weaker solution at a lower concentration XAE. The performance of this cycle has been studied by many researchers [1–4]. However, this cycle has a drawback, the absorption or evaporation temperature in absorbing evaporator cannot be as high as possible, because the weak solution leaving the absorbing evaporator absorbs vaporized water twice, and has the lowest concentration, namely XAE < XAB < XGE. This will not make the absorption temperature in the absorber as high as possible. In order to overcome this drawback, a new solution cycle in the double absorption heat transformer is presented here. Furthermore, its performance is simulated based on the thermodynamic properties of an aqueous solution of lithium bromide.
2. The description of the new solution cycle in the DAHT The new solution cycle in a double absorption heat transformer is shown in Figs. 3 and 4. In this new cycle,
Fig. 2. The ordinary cycle in DAHT.
Fig. 3. Schematic diagram of DAHT with a new solution cycle.
Z. Zhao et al. / International Journal of Refrigeration 26 (2003) 315–320
317
5. The expanding process in the throttling valves is isenthalpic; 6. The temperature difference in the cold end of solution heat exchanger is fixed by 5 C; 7. The energy consumed by the pump is neglected.
The parameters used to determine the performance of the double absorption heat transformer are the following:
Fig. 4. The new solution cycle in DAHT.
the strong solution coming from the generator is split into two streams. One goes to the absorber for absorbing the vaporized water coming from the absorbing evaporator and then goes back to the generator preheating the strong solution through the solution heat exchanger. The other goes to the absorbing evaporator for absorbing the vaporized water coming from the evaporator and then goes back to the generator. Because of absorbing the vaporized water only once, the concentration of the weak solution leaving the absorbing evaporator is higher than that in the cycle shown in Figs. 1 and 2. As a result, a higher temperature in the absorbing evaporator can be obtained. The higher the absorption or evaporation temperature in absorbing evaporator, the higher the absorption temperature in the absorber is in this new solution cycle. Besides the earlier advantage, the weak solution leaving the absorber and that leaving the absorbing evaporator do not affect each other. In other words, it is not necessary that the concentration of the weak solution leaving the absorbing evaporator must be less than that leaving the absorber. Consequently, a wider operating range of the new cycle will be possible. It is convenient to denote the ordinary cycle in Figs. 1 and 2 with ‘‘case one’’ and the new cycle in Figs. 3 and 4 with ‘‘case two’’.
3. The theoretical analysis In order to analyze the performance of this new solution cycle, the following assumptions are made. 1. The analysis is carried out under steady state conditions; 2. The solutions leaving the generator and leaving the absorber and absorbing evaporator are saturated; 3. The condensate leaving the condenser is saturated; 4. Thermal and pressure losses are neglected;
1. The new solution cycle in the double-absorption heat transformer has a wider available range of tAE than that in the ordinary one. The COP keeps a high value in this range. Consequently, the system is more stable and flexible for the operation and the control of the system. 2. When the differences in concentration X1 and X2 in ordinary solution cycle are equal to these in the new solution cycle respectively, to the new solution cycle, the temperature lift is about 5–10 C higher and the COP is about 0.01 lower than those in the ordinary solution cycle being studied by some researchers, respectively. 3. FR2 and X2 are not directly affected by tAB in the new solution cycle, while FR2 and X2 are directly affected by tAB in the ordinary solution cycle being studied by some researchers. As a result, the relationship between the absorber and absorbing evaporator are more independent and this makes the operation and control of the system easier. (1). The bypass ratio is an important parameter since it is directly related to the heat delivered in the absorber. For the condenser, it can be defined as the ratio of the mass flow rate vaporized in the evaporator to the mass flow rate vaporized in the absorbing evaporator BPCO ¼ M2 =M3
ð1Þ
For the absorbing evaporator (case one), it can be defined as the ratio of the mass flow rate of the weak solution which has the intermediate concentration XAB and goes to the generator to that of which goes to the absorbing evaporator. BPAE ¼ M16 =M14
ð2aÞ
For the absorbing evaporator (case two), it can be defined as the ratio of the mass flow rate of the strong solution which has the concentration XGE and goes to the absorber to that of which goes to the absorbing evaporator.
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BPAE ¼ M13 =M14
ð2bÞ
(2). The coefficient of the performance is given by: COP ¼
QAB QGE þ QEV
ð3Þ
(3). For generator, flow rate ratio is defined as the ratio of the mass flow rate of the solution entering the generator to that of refrigerant leaving the generator. For absorber/evaporator, flow rate ratio is defined as the ratio of the mass flow rate of the solution leaving the absorber/evaporator to that of refrigerant going into the absorber/evaporator. They are expressed as the following. FR1 ¼ ðM9 þ M18Þ=M1
ð4Þ
FR2 ¼ M8=M6
ð5Þ
(4). The concentration difference is defined as the concentration difference between the inlet solution and outlet solution of the absorber. For double absorption heat transformer, there are also two concentration difference, and they can be expressed as the following. Case one: X1 ¼ XGE XAB
ð6aÞ
X2 ¼ XAB XAE
ð7aÞ
those of the cycle being studied by some researchers. Figs. 5 and 6 show the variation of coefficients of performance versus the absorption or evaporation temperature tAE. It can be seen that for the new solution cycle (case two) a wider operating range of the temperature of the absorbing evaporator exists. In this range the coefficients of performance decrease very slowly and maintain high value. The lower the temperature tAB of the absorber, the wider the range of the available operating temperature tAE of the absorbing evaporator is. These characteristics of the new solution cycle make the system have more operating elasticity and make the operation and control easier. It is well known that the temperature tAE of the absorbing evaporator is determined by the temperature tEV of the evaporator and the concentration XAE of the weak solution. When the temperature tEV maintains constant, the temperature tAE is only determined by the XAE. The wider the operating range of the tAE, the wider the range of the changing concentration XAE of weak solution. The main reason is that the concentration XAE of the weak solution leaving the absorbing evaporator is not directly affected by that of the weak solution leaving the absorber in case two. On the contrary, the concentration XAE of the weak solution leaving the absorbing evaporator is directly affected by the weak solution coming from the absorber in case one.
Case two: X1 ¼ XGE XAB
ð6bÞ
X2 ¼ XGE XAE
ð7bÞ
(5). Temperature lift is a very important parameter. It is defined as the temperature difference between the absorption temperature in the absorber and generation temperature in the generator, namely, it is expressed as the following t ¼ tAB tGE
Fig. 5. The effect of tAE on COP (case one).
ð8Þ
4. Results and discussion Based on the thermodynamic properties of aqueous solution of lithium bromide [5–7], the earlier assumptions and the balance of material and energy on each of the component in the DAHT, the performance of the new cycle in double-absorption heat transformer is simulated. The results obtained are also compared with
Fig. 6. The effect of tAE on COP (case two).
Z. Zhao et al. / International Journal of Refrigeration 26 (2003) 315–320
Figs. 7 and 8 show the variation of BPCO and BPAE against the temperature tAE of the absorbing evaporator. In Fig. 7 (case one), it can be seen that the BPCO and BPAE decrease with the increase of tAE and the range of the change in tAE is still narrow. However, in Fig. 8 (case two), the BPAE decreases with the increase of tAE and the BPCO decreases slowly with the increase of tAE and increases rapidly when the temperature tAE approaches the limit of about 120 C. The range of the change in tAE is still wider compared with that in case one. Why does the BPCO increase sharply when the tAE approaches 120 C? The reason is the following. When tAE increases, the temperature (t7) and the pressure (P7) of the vapor leaving the absorbing evaporator will all increase. When the temperature (tAB=t16) of the absorber keeps constant, the concentration X16 of the weak solution leaving the absorber must decrease. The flow rate (M13) of the strong solution going into the absorber will decrease, and the flow rate (M14) of the strong solution going into the absorbing evaporator must increase. As a result, BPAE=M13/M14 would also decrease. When tAE approaches 120 C, BPAE will become almost zero. This can be shown clearly in Fig. 8. This means that the M13 will become very small. Most of the strong solution coming from the generator will go into the absorbing evaporator. To keep the material and energy balance of the absorbing evaporator, the flow rate M6 of the vapor coming from the evaporator will
increase greatly. This causes the rapid increase of the value of BPCO. In fact, the absorber AB cannot work normally in this situation (the output heat QAB of the absorber approaches to zero then). Consequently, the double-absorption heat transformer has become a single-stage absorption heat transformer. The 120 C is the highest output temperature of the absorbing evaporator under these conditions (tGE=tEV=70 C, tCO=20 C). It also is almost the highest output temperature of the single-absorption heat transformer. The upper limit of the tGE will vary according to different operating conditions. Figs. 9 and 10 show the variations of differences in concentration of X1 and X2 and flow ratios FR1 and FR2 versus the temperature of the absorbing evaporator at different absorbing temperatures. In Fig. 9 (case one), X1 increases with the increase of tAE, while X2 decreases with the increase of tAE. Generally speaking, X1 is less than X2 at the same tAB. X1 is usually in the range from 2 to 10, while X2 is usually in the range from 4 to 20. FR1 decreases sharply and FR2 increases rapidly with the increase of tAE. It is obvious that FR1 is larger than FR2. In Fig. 10 (case two), FR1 decreases slower with the increase of
Fig. 9. Effect of tAE on FR1 and FR2 (case one). Fig. 7. Effect of tAE on BPAE and BPCO (case one).
Fig. 8. Effect of tAE on BPAE and BPCO (case two).
319
Fig. 10. Effect of tAE on FR1 and FR2 (case two).
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tAE and has a wider range of tAE than that in case one. It is very interesting that X2 and FR2 are not affected by tAB. They vary only with the change in tAE when other temperatures keep constant. The reason is that the concentration of the weak solution leaving the absorbing evaporator does not have direct relationships with that of the weak solution leaving the absorber. The characteristics of the new cycle will make operation and control of the system more stable and easier. Because the FR1 and FR2 are important adjusting parameters, the determination of the suitable ranges of FR1 and FR2 is important for the cycle operating at a range of high COP. Fig. 11 shows the variation of COP, FR1 and FR2 versus the tAE. In Fig. 11, points a, b, c, d and e represent the turning point of the FR1 lines at different tAB, respectively. The COP reaches a maximum value at the turning point. In fact, the corresponding values of FR1 are also the upper limits of available change in FR1. These upper limits are about in the neighborhood of 15. Fig. 12 shows the change in temperature lifts t and the COP versus the temperature tGE of the generator respectively at the different tCO. It can be seen that the temperature lifts in case two are higher than the temperature lifts in case one under the same X1 and X2
conditions. The temperature lifts in case two are about 5–10 C higher than those in case one. Furthermore, the COPs in case two are about 0.01 lower than those in case one.
5. Conclusions
1. The new solution cycle in the double-absorption heat transformer has a wider available range of tAE than that in the ordinary one. The COP keeps a high value in this range. Consequently, the system is more stable and flexible for the operation and the control of the system. 2. When the differences in concentration X1 and X2 in ordinary solution cycle are equal to these in the new solution cycle respectively, to the new solution cycle, the temperature lift is about 5– 10 C higher and the COP is about 0.01 lower than those in the ordinary solution cycle being studied by some researchers, respectively. 3. FR2 and X2 are not directly affected by tAB in the new solution cycle, while FR2 and X2 are directly affected by tAB in the ordinary solution cycle being studied by some researchers. As a result, the relationship between the absorber and absorbing evaporator are more independent and this makes the operation and control of the system easier.
References
Fig. 11. Effect of tAE on COP, FR1 and FR2 (case two).
Fig. 12. Effect of tGE on t and COP.
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