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Performance of a triple-pressure-level absorption cycle with R125-N,N′-dimethylethylurea
Applied Energy 71 (2002) 171–189 www.elsevier.com/locate/apenergy
Performance of a triple-pressure-level absorption cycle with R125-N,N0-dimethylethylurea M. Jelinek, A. Levy*, I. Borde Pearlstone Center for Aeronautical Engineering Studies, Mechanical Engineering Department, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel Received 29 October 2001; received in revised form 14 December 2001; accepted 22 December 2001
Abstract In the developed triple-pressure-level (TPL) single stage absorption cycle, a specially designed jet ejector was introduced at the absorber inlet. The device served two major functions: it facilitated pressure recovery and improved the mixing between the weak solution and the refrigerant vapour coming from the evaporator. These effects enhanced the absorption of the refrigerant vapour into the solution drops. To facilitate the design of the jet ejector for such absorption machines, a numerical model of simultaneous heat-and-mass transfers between the liquid and the gas phases in the ejector was developed. The refrigerant pentafluoroethane (R125) and the absorbent N,N0 -dimethylethylurea (DMEU) were used as the working fluid. A computerized simulation program was used to perform a parametric study of the TPL absorption cycle. The influence of the jet ejector on the performance of the TPL absorption cycle was evaluated, and the performance of the TPL absorption cycle was compared with that of a double-pressure level (DPL) cycle. Four cases were studied that represent the improvements in the TPL absorption cycle performances as a result of the incorporation of the jet ejector. The four cases are: the ability to reduce the circulation ratio f, the ability to lower the evaporator temperature, the ability to lower the generator temperature and the ability to use higher-temperature cooling water. # 2002 Published by Elsevier Science Ltd. Keywords: Absorption cycle; Jet ejector; Cycle analysis; COP
1. Introduction Various types of absorption heat-pumps, both single stage and multistage, can exploit a variety of heat sources for cooling and refrigeration (< 0 C). The type of absorption heat pump and the nature of the working fluids are usually determined * Corresponding author. Tel.: +972-8-6477092; fax: +972-8-6472813. E-mail address: [email protected] (A. Levy). 0306-2619/02/$ - see front matter # 2002 Published by Elsevier Science Ltd. PII: S0306-2619(02)00003-X
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Nomenclature Mass transfer area (m2) Cross section of the i-phase (m2) Diffuser cross-section (m2) Drag coefficient () Virtual-mass coefficient () Coefficient of performance (Qe/(Qg+Wp)) Diffusion coefficient (m2/s) Drop diameter (m) The pressure recovered by the ejector divided by the pressure difference between the nozzle inlet and outlet, %. f Circulation ratio (kg strong solution/kg refrigerant) Fgd Inter-phase forces (N/m) h Convective heat-transfer coefficient (W m/K) hm Mass-transfer coefficient (kg m/s) Hi Enthalpy of the i-phase (J/kg) : mgd The mass transfer between the phases (kg/s) Nd Number of the droplets per unit volume [see Eq. (6)] Nu Nusselt number () P Pressure (Pa) Qe Heat rejected by the evaporator (J) Qg Heat transferred to the generator (J) Qgd Heat transfer per unit length (J/m) Qhs Heat transferred at the solution’s heat-exchanger (J) Qhs/Qe The heat transferred at the solution’s heat-exchanger divided by the heat rejected by the evaporator (J/J) Te, Tevp Evaporator temperature ( C) td Residence time (s) Tg Generator temperature ( C) Ti Temperature of the i-phase ( C) Ts Surface temperature of the drop ( C) Tw Cooling-water temperature ( C) ui i-phase velocity (m/s) ur Relative velocity (m/s) Wgd Work transfer per unit length (J/m) Wp Energy supply to the pump (J/kg) x Diffuser length (m) Refrigerant weight fraction in the solution (kg refrigerant/kg solution) * Equilibrium mass concentration (kg refrigerant/kg solution) i i-phase density (kg/m3)
a Ai Atot Cd Cvm COP D Dd dPrec
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Subscripts d Dispersed-phase g Gas-phase gd Gas-droplet interface i i-Phase (g,d) s Drop surface
by the temperature of the heat-source and the cooling or refrigeration demands. Utilization of low-potential heat-sources (70–120 C) for cooling and refrigeration is limited by the properties of the working fluids and the cycle configuration of the heat pump. For utilization of low potential heat sources for cooling and refrigeration to < 0 C, a single-stage absorption heat-pump based on organic working fluids is preferable to absorption heat-pumps based on conventional working fluids such as ammonia–water or water–lithium bromide because of the limitations imposed by the latter type of fluids. The ammonia–water combination requires a heat-source temperature above 120 C for cooling and refrigeration to < 0 C. Such a system is a high-pressure system that requires a rectification column [1]. Ammonia has acceptable thermophysical properties, but it is a flammable toxic and strongly irritant fluid, and is corrosive to copper. The water–lithium bromide solution can be used with a heat-source temperature above 70 C for air-conditioning, but not for cooling and refrigeration because of the limitation for the evaporator temperature ( > 0 C). This system operates under vacuum and does not require a rectification column. The water–lithium bromide solution is highly corrosive and extremely viscous and viscosity-reducing agents are frequently required. The limitations of using common working fluids [2] for utilizing low-potential heat-sources (80–120 C) for cooling and refrigeration (< 0 C) are thus self-evident. With a view to overcoming these limitations, the working fluids used in the studies of our group are based on fluorocarbon (HFC) refrigerants and organic absorbents [3–8]. The refrigerants are not toxic or corrosive, and the organic working fluids are environmentally acceptable. In our high-pressure system, the condenser and the absorber are water cooled, and a rectification column is not needed, since the difference between the normal boiling points of the absorbent and the refrigerant is about 200 C. The performance of these working fluids in a conventional double-pressure level (DPL) single-stage absorption cycle is expressed in terms of a coefficient of performance (COP)1 of about 0.5 and a circulation ratio (f)2 in the range of 3–7. In the present study, an advanced single-stage absorption heat-pump, i.e. a triplepressure-level (TPL) cycle was used to utilize a low-potential-heat source for cooling from 5 to 15 C. Similar absorption cycles have been suggested by Borde and 1
Defined as the heat rejected from the evaporator divided by the heat supply to the generator and the energy supply to the pump. 2 Defined as the ratio between the mass flow rate of the strong solution in the pump to the mass flow of the refrigerant.
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Jelinek [9,10] and Chen [11] in which a jet-ejector was used as a device for mixing and pressure recovery. Borde and Jelinek [9] conducted an experimental study on a heat pump. They showed the suitability to integrate a self-made jet ejector as a mixing unit. Borde and Jelinek [10] conducted a theoretical study on a heat pump with organic working fluids. In their mathematical model, the pressure recovery was not taken into account. Thus the jet ejector was considered only as a mixing device. Chen [11] used a Bernoulli type equation for analysis of the two-phase mixture flow through the ejector, which was based on a single-phase model of pseudo-fluid without taking heat and mass transfer into account. In addition, the momentum balance was not taken into account. To overcome the above-mentioned simplifications, theoretical studies on the performance of the jet ejector parameters were conducted [12– 14]. To facilitate the design of the jet ejector for absorption machines, a two-phase numerical model of simultaneous mass, momentum and heat transfer in the jet ejector was developed [10]. In this study a combination of computerized simulation programs, one for the conventional single-stage absorption cycle (DPL) and the other for the jet ejector, was developed to examine the influence of the jet ejector on the performance of the TPL single-stage absorption cycle.
2. Triple-pressure-level single-stage absorption cycle To utilize a low-potential-heat source for cooling from 5 to 15 C, an advanced single-stage absorption heat pump can be used, i.e. a triple-pressure-level (TPL) cycle. This cycle may be implemented in a number of different ways, for example, by a design known as the compression/absorption cycle [15–18], in which a compressor is inserted between the evaporator and the absorber. The main disadvantage of the latter device is the extra electrical energy required for the compressor. In our TPL single-stage heat-pump, a specially designed jet ejector is introduced at the absorber inlet (Fig. 1), with the purpose of increasing the absorber pressure relative to the evaporator pressure (by partially recovering the high pressure of the generator) and improving the mixing process and the pre-absorption by the weak solution of the refrigerant coming from the evaporator [12–14]. The mixing process in the jet ejector is very intensive as a result of spray generation of the liquid phase and of extensive subcooling of the weak solution in the solution’s heat-exchanger. A schematic representation of the jet-ejector is given in Fig. 2. 2.1. Jet ejector The jet ejector consists basically of a nozzle and a diffuser. The device is characterized by the facts that there are no moving parts and there is no requirement for an additional energy source. At the nozzle outlet, production of a full cone spray of small high-velocity drops of a weak solution serves to transform potential energy (pressure difference between the generator and the evaporator) into kinetic energy. At the diffuser inlet (at the low pressure of the evaporator), the stream of drops mixes with the refrigerant vapour coming from the evaporator. In the diffuser,
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Fig. 1. Schematic representation of a triple-pressure-level single-stage advanced absorption cycle. (Sol. H.E.—solution’s heat-exchanger, Ref. H.E.—refrigerant’s heat-exchanger and P—solution pump.).
Fig. 2. Schematic representation of the jet-ejector.
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pressure recovery (defined as the difference in pressure between the outlet and the inlet of the diffuser) is thus obtained by transforming the droplet kinetic energy to potential energy. As a result, the velocities of both the absorbent drops and the refrigerant gas are reduced. To facilitate the design of the jet ejector for absorption machines, a numerical model of simultaneous mass, momentum and heat transfers between the liquid and gas phases in the jet ejector (Appendix A) was developed on the basis of two-phase mathematical model previously described by Levy et al. [14]. The jet ejector model, as a pre-absorber, was solved numerically for the working fluid pentafluoroethane (R125) as the refrigerant and N,N0 -dimethylethylurea (DMEU) as the absorbent. A solution of R125-DMEU was modelled as the dispersed phase, with R125, as the continuous gas phase. The numerical solution was obtained by means of Gear’s fifth-order BDF method (often called Gear’s stiff method), which is available in the IMSL library [19]. The influences of the jet-ejector design parameters on the pressure recovery, temperature and concentration of the refrigerant in the solution, and velocities of the gas and liquid drops have previously been described by Levy et al. [20]. The parametric study involved an examination and ways of augmentation of the mass transfer process in the diffuser with the ultimate aim of designing a compact and efficient unit. The numerical simulation demonstrated that pressure recovery and pre-absorption in the jet ejector would improve the efficiency of the absorption process and hence the overall efficiency of the refrigeration cycle. 2.2. Application of the TPL absorption cycle In commonly used absorption heat-pumps (when the pressure drop is negligible), the absorber pressure is equal to the evaporator pressure. However, in the TPL cycle, the absorber pressure is higher than evaporator pressure, which leads to an improvement in the cycle performance. This effect can be obtained by decreasing the circulation ratio f (Case 1) or by changing the governing cycle temperatures as follows: lowering the refrigeration temperature, i.e. the evaporator temperature Te (Case 2); lowering the heat-source temperature, i.e. the generator temperature Tg (Case 3); or raising the cooling-water temperature, i.e. the condenser and absorber temperature Tw (Case 4), as summarized in Table 1. Table 1 Comparison between the possibilities provided by the TPL vs. the common single-stage (DPL) absorption cycle in terms of the outside temperatures and the circulation ratio
Case 1 Case 2 Case 3 Case 4 a
Tg ( C)
Te ( C)
Tw ( C)
f
=a = Lower =
= Lower = =
= = = Higher
Lower = = =
=Equal to the value of the common single-stage absorption cycle.
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Implementation of the four cases is explained and analysed in the following sections.
3. System analysis and discussion A combination of the computerized simulation programs, one for the conventional single-stage double-pressure level (DPL) absorption cycle and the other for the jet ejector, facilitated the evaluation of the influence of the jet ejector on the performance of the TPL single-stage absorption cycle. In all cases, calculation of the performances (COP, f, Qhs/Qe3 and dPrec4) of the TPL and DPL cycles was carried out for the R125-DMEU working pair. Calculations for the DPL absorption cycle (absorber pressure=evaporator pressure) and the TPL absorption cycle (absorber pressure=evaporator pressure plus the recovered pressure) were carried out under the following operating conditions: cooling-water temperature 25 C (condenser temperature 32 C and absorber temperature 28 C), generator temperature in the range of 70–140 C, and for evaporator temperatures of 0, 5, 10 or 15 C. For both cycles, the pressure drop along the cycle was taken as zero. 3.1. Influence of the jet ejector on the performance of the TPL cycle The influence of the jet ejector on the performance of the TPL cycle (in comparison with the DPL cycle) was examined for four separate cases in which one operating condition in the TPL was varied and all the other conditions remained the same for both types of cycle. 3.1.1. Case 1—lowering the circulation ratio, f For the same governing cycle temperatures for the DPL and TPL cycles, the higher absorber pressure (by the amount of the pressure recovery) for the TPL at the same absorber outlet temperature results in a higher weight fraction of the refrigerant in the solution. This increase in the weight fraction at the absorber outlet leads to a reduction in f, i.e. a reduction in the mass flow rate of the strong solution in the pump, and consequently to a reduction in the amount of heat to be transferred in the solution’s heat-exchanger. The calculated COP, f and Qhs/Qe for the same evaporator temperatures in the TPL and DPL absorption cycles with R125-DMEU are shown in Figs. 3–5. As can be seen from Fig. 3, the higher values of the COP for the TPL cycle in comparison with those for the DPL cycle can be achieved at lower generator temperatures, for all evaporator temperatures. The improvement in the COP becomes
3
Defined as the heat transferred by the solution heat exchanger divided by the heat rejected by the evaporator. 4 Defined as the pressure recovered by the ejector divided by the pressure difference between the nozzle inlet and outlet, in %.
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Fig. 3. Comparison between the calculated COP for the TPL absorption cycle and for the DPL absorption cycle (full and open symbols, respectively) as a function of the generator temperature for various evaporator temperatures as calculated for R125-DMEU.
more significant as the evaporator temperature falls, and, at the same operating conditions, it increases by about 20%. The values of f in the TPL cycle are much lower than those in the DPL cycle (Fig. 4). At the same operating conditions, the reduction in the values of f can reach 100%. The relative size of the solution’s heat-exchanger can be expressed in terms of Qhs/ Qe. The values of Qhs/Qe in the TPL cycle are lower than those in the DPL cycle (Fig. 5). At the same operating conditions, the reduction in Qhs/Qe becomes more significant as the evaporator temperature falls and can reach 70% of the Qhs/Qe in the DPL cycle. The calculated pressure recovery in the ejector, as expressed by the term dPrec (in %), increases as the generator temperature decreases and decreases as the evaporator temperature falls. Increases of dPrec up to 9% were obtained, as can be seen in Fig. 6. The optimal operating conditions, as a function of the evaporator temperature, are those that achieve the highest COP. The values of the generator temperature and f for these maximum values of the COP as a function of the evaporator temperature are given in Table 2 for the working fluids R125-DMEU. The table illustrates the
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Fig. 4. Comparison between the calculated value of f for the TPL absorption cycle and for the DPL absorption cycle (full and open symbols, respectively) as a function of the generator temperature for various evaporator temperatures as calculated for R125-DMEU.
Table 2 Generator temperature and circulation ratio at maximum calculated COP as a function of the evaporator temperature Triple-pressure-level absorption cycle
Conventional single-stage absorption cycle
Te ( C) COP
Tg ( C)
f
Qhs/Qe
COP
Tg ( C)
f
Qhs/Qe
0 5 10 15
81 91 101 113
3.5 3.9 4.4 5.2
1.78 2.42 3.38 4.84
0.570 0.530 0.485 0.445
90 102 115 132
3.5 4.0 4.6 5.5
2.05 2.91 4.25 6.05
0.595 0.555 0.515 0.480
influence of pressure recovery on the performance of the TPL cycle in comparison with the DPL cycle. At the same evaporator temperature, the main benefit of the TPL cycle at maximum COP is evident in the reduction in the generator temperature by 11–13 C. The maximum COP is increased in the range of 4–8%: the reduction in
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Fig. 5. Comparison between the calculated values of Qhs/Qe for the TPL absorption cycle and for the DPL absorption cycle (full and open symbols, respectively) as a function of the generator temperature for various evaporator temperatures as calculated for R125-DMEU.
the circulation ratio is up to 5% and the reduction in the size of the solution heat exchanger is up to 20%. 3.1.2. Case 2—lowering the evaporator temperature When the values of the generator temperature, the cooling-water temperature (condenser and absorber temperature), the absorber pressure and f for the TPL cycle are the same as those for the DPL cycle, the evaporator pressure in the TPL cycle is lowered by the amount of the pressure recovered, and thus the evaporation temperature falls accordingly. The calculated differences in the evaporator temperature between the DPL and TPL cycles as a function of the generator temperature (with the same COP, f and Qhs/Qe as in the DPL cycle) are shown in Fig. 7. It can be seen that increasing the generator temperature at a constant DPL evaporator temperature decreases the ability to lower the TPL evaporator temperature, while decreasing the DPL evaporator temperature at a constant generator temperature increases the ability to lower the TPL evaporator temperature. In these generator and evaporator temperature ranges, the ability to lower the evaporator temperature in the TPL cycle by 2–5 C was achieved.
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Fig. 6. Variation of the calculated pressure-recovery (%) in the jet ejector with generator temperature for various evaporator temperatures as calculated with R125-DMEU as the working fluid.
3.1.3. Case 3—lowering the generator temperature When the values of the evaporator temperature, the cooling water temperature (condenser and absorber temperature) and f were the same for the TPL and DPL cycles, the generator temperature of the TPL cycle was lowered. The calculated differences in the generator temperature between the TPL and DPL cycles as a function of the DPL generator temperature is shown in Fig. 8. It can be seen that increasing the generator temperature at a constant DPL evaporator temperature increases the ability to lower the TPL generator temperature, while lowering the DPL evaporator temperature at a constant generator temperature increases the ability to lower the TPL generator temperature. In these generator and evaporator temperature ranges, the ability to lower the TPL generator temperature was in the range 10–25 C. That means that a lower temperature heat source can be used with the TPL. 3.1.4. Case 4—raising the cooling-water temperature When the operating conditions for the TPL and DPL cycles are the same in terms of the generator temperature, the evaporator temperature and f, the absorber pressure of the TPL cycle increases by the amount of the pressure recovered, and hence the condenser and absorber temperature may be increased, i.e. a higher coolingwater temperature may be used. Fig. 9 shows the difference in the cooling-water
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Fig. 7. Evaporator temperature differences between the DPL and TPL cycles due to the pressure recovery in the jet-ejector (Case 2) as a function of the generator temperature for various evaporator temperatures as calculated using R125-DMEU as the working fluid.
temperature between the TPL and DPL cycles as a function of the generator and evaporator temperatures. As can be seen in Fig. 9, the ability to raise the coolingwater temperature in the TPL cycle increases upon lowering the evaporator temperature and slightly decreases while the generator temperature increases. This improvement is important in the case of absorption systems used with cooling water obtained from cooling towers in a high-humidity climate. 3.2. Case study Let us take an example for the four cases described above. The following operating conditions were chosen: cooling water temperature 25 C (condenser temperature 32 C and absorber temperature 28 C), generator temperature 100 C, and evaporator temperature of 5 C. Pressure drops along the cycles were taken as zero. From the results summarized in Table 3, it can be seen that Case 1 gives, a 20% reduction in f (from 4.11 in the DPL cycle to 3.27 in the TPL cycle) a 4.6% increase in the COP and a 2.7% reduction in Qhs/Qe. In Case 2, the evaporator temperature could be lowered by 3.6 C, for the same values of the COP, f, Tg and
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Fig. 8. Generator temperature differences between the DPL and TPL cycles due to the pressure recovery in the jet-ejector (Case 3) as a function of the DPL generator temperature for various evaporator temperatures as calculated with R125-DMEU as the working fluid.
Table 3 Improvement in the TPL absorption cycle performances vs. the common single-stage absorption cycle as a result of changing the outside temperature or lowering the circulation ratio
Common Case 1 Case 2 Case 3 Case-4 a
Tg ( C)
Te ( C)
Tw ( C)a
f
COP
Qhs/Qe
100 100 100 88.7 100
5 5 8.6 5 5
25 25 25 25 27.8
4.11 3.27 4.11 4.11 4.11
0.527 0.551 0.527 0.555 0.532
2.99 2.18 2.99 2.51 2.97
Tabsorber=Tw+3 C, Tcondenser=Tw+7 C.
Qhs/Qe. In Case 3, for a constant value of f of 4.11 and the same Tw and Te, lowering of the generator by 11.3 C, gave a 5.3% increase in the COP and a 16% reduction in Qhs/Qe. Finally, for a higher cooling water temperature (by 2.8 C) in the TPL cycle with the same Te and Tg, the COP and Qhs/Qe were essentially the same for the TPL and DPL cycles (Case 4).
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Fig. 9. Cooling water temperature differences between the TPL and DPL cycles due to the pressure recovery in the jet-ejector (Case 4) as a function of the generator temperature for various evaporator temperatures as calculated with R125-DMEU as the working fluid.
4. Conclusions Integrating a specially designed jet ejector at the absorber inlet resulted in an advanced triple-pressure level (TPL) single-stage absorption cycle. The jet ejector facilitated pressure recovery and improved the mixing between the weak solution and the refrigerant vapour coming from the evaporator. The influence of the jet ejector on the performance of the TPL absorption cycle was evaluated, and the performance of the TPL absorption cycle was compared with that of the DPL cycle. Four cases of improvements in the TPL absorption cycle performances were studied. The four cases are: the ability to reduce the circulation ratio f (Case 1), the ability to lower the evaporator temperature (Case 2), the ability to lower the generator temperature (Case 3) and the ability to use higher cooling-water temperature (Case 4). From the four cases studied, it is evident that in the design of a new absorption cycle, Case 1 is the option of choice. In situations in which an improvement of an existing absorption cycle is required or an adaptation to different operating conditions is needed without making changes to the components in the existing cycle, Cases 2–4 have to be considered, each on its own merits.
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Cycle analysis in the generator and the evaporator temperature ranges showed that, in the first case, the COP increased by up to 20%; the reduction in the mass flow rate in the strong solution pump was up to 50%, and a reduction up to 70% was achieved in the amount of heat to be transferred in the solution heat exchanger. In Case 2, the evaporator temperature could be lowered by 2–5 C while all other parameters remained constant. In the third case, the generator temperature could be lowered by 3–15 C by achieving a small improvement in the cycle performance. In Case 4, the condenser and the absorber temperature could be increased by 2–4 C while all other parameters remained almost the same. It should be noted that these improvements are functions of the operating conditions and the thermophysical properties of the working fluids.
Acknowledgements This study was partially supported by the German-Israeli Scientific Cooperation Unit, Ministry of Science, under the program BMBF-MOS, Grant-GR-1718.
Appendix A. Jet-ejector—calculation model A two-phase continuum model was used to describe the steady-state flow of liquid droplets (the dispersed phase) and a gas phase (the continuous phase) through a one-dimensional mixing chamber (diffuser). The governing equations were obtained by macroscopic mass, momentum and energy balances for the two phases in a control volume, with length dx. The model was based on the following assumptions: steady state; mass, momentum and heat transfer only between the two phases; friction forces with the diffuser wall negligible; adiabatic flow; dilute phase flow; droplets comprise a binary mixture of absorbent and refrigerant; constant droplet diameter; and electrical forces and surface tension neglected. Balance equations Based on the above-mentioned assumptions, mass, momentum and energy balance equations for the gas and the dispersed phases were developed. The mass balance equation for the i-phase may be written as: : d dmgd ði ui Ai Þ ¼ dx dx
ð1Þ
where i and ui are the density and the velocity of the i-phase, respectively, Ai is the : cross section occupied by the i-phase and dmgd =dx is the mass transfer per unit length due to absorption. The right-hand side is positive when i=d (dispersed phase) and negative for i=g (gas-phase). The momentum balance equation for the gas phase is expressed as:
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: d 2 dP dm gd g ug Ag þ Atot ¼ Fgd ud dx dx dx
ð2Þ
where Fgd represents all the forces that act on the gas phase due to the dispersed phase, and Atot is the diffuser cross section (i.e. Atot Ag þ Ad ). The momentum balance equation for the dispersed phase is given as: : d 2 dmgd d ud Ad ¼ Fgd þ ud dx dx : where dmgd =dx ud is momentum flux due to the mass transfer. The energy balance equation for the i-phase is given by: : u2 u2 d dmgd pi ui Ai Hi þ i Hgd þ d ¼ Qgd Wgd dx 2 dx 2
ð3Þ
ð4Þ
where Hi and Hgd are the enthalpies of the i-phase and that of the refrigerant at the droplets’ surfaces, respectively; and Qgd and Wgd are the heat and the work transfer per unit length between the two phases during the process, respectively. The last term on the right-hand side of the equation represents the energy flux that is transferred due to absorption. In this equation, the upper sign in the or pertains to i=d and the lower sign to i=g. A number of complementary equations, definitions and empirical correlations are required to solve the set of ordinary differential-equations given above. These will be presented below. It should also be noted that the dispersed phase is a binary mixture, and hence all its thermodynamic properties were calculated upon the basis of weight fraction of the refrigerant in the solution, , and its other thermophysical properties were obtained by applying the mixture theory. Details are given in the publications of Borde et al. [3,4]. Interphase forces The forces acting per unit length between the phases that were taken into account in this model were the forces per unit length due to drag and to virtual mass (first and second terms on the right hand side, respectively). D3d dur D2d 1 Fgd ¼ Atot Nd Cd g ur jur j þ Cvm ud ð5Þ 4 2 6 dx where ur ð ug ud is the relative velocity, and the Nd, number of the droplets per unit volume, can be expressed as follows: Nd ¼
6Ad Atot D3d
ð6Þ
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where Dd is the drop diameter and Cd is the drag coefficient, which is expressed as a function of the Reynolds number, Re, by the correlations of Oseen, Pittet et al. and Stringham et al., as previously described by Clift et al. [21]. The volume of the displaced fluid that contributes to the effective mass of the dispersed phase is usually described by the virtual-mass coefficient, Cvm. In general, this coefficient is a function of the volume fraction of the dispersed phase (which is equal to Ad/Atot in onedimensional flow) and of the shape of the drops, but it is often taken as a constant. It was found that for a spherical droplet Cvm=11/16 [21], and this is the value that was used in the course of this investigation. Work and heat transfer The calculation of the term for work per unit length takes into account only the forces per unit length that act between the two phases, hence: Wgd ¼ Fgd ud
ð7Þ
The heat transfer between the particles and the gas phase was assumed to be governed only by convection. This was expressed by: Qgd ¼ Nd Atot D2d hðTg Ts Þ
ð8Þ
The convective heat-transfer coefficient, h, was expressed as a function of the Nusselt number, Nu (Daltrophe et al. [12,13]). One of the key variables for the mass and heat transfer is the temperature at the surface of the drops Ts, which also defines the equilibrium concentration, ðT; PÞ. This temperature was obtained by assuming that absorption occurs first in a very thin surface layer. Then, the absorbed gas transfers into the drop, while heat is transferred from inside the drop to the surface layer and finally to the gas. The heat balance around the layer was used to calculate the surface temperature. The heat transfer inside the drop was calculated by analogy with mass transfer. Mass transfer The mass transfer source term per unit length can be calculated by: : dmd ¼ hm aðs d Þ dx
ð9Þ
where hm is the mass-transfer coefficient and a is the area for mass transfer per unit length. This was estimated by: a¼
6Ad Dd
ð10Þ
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The correlation for estimating the overall mass transfer was obtained from an approximation of the theoretical solution of Kronig and Brink for one drop, which fits the experimental results of Garner and Lane for a cloud of drops (Clift et al. [21]). rffiffiffiffiffiffiffi : D dmd 6Ad ¼ ð11Þ d o s td dx Dd In this equation, D is the diffusion coefficient in the drop, o is the uniform initial concentration in the drop, and td is the residence time of the drop in the gas phase, which was calculated by: dtd 1 ¼ dx ud
ð12Þ
Note that in the transition from Eq. (9) to (11), the local variable d has vanished and is replaced by the residence time of the drop in the diffuser, td. When the residence time increased and the value of the Fourier number, Fo (=4Dtd =D2d ) reached 0.003, then the Biot number, Bi, is equal to 17.66 and hm was calculated by Biðd D=Dd Þ, and this value was introduced into Eq. (9). The theory of Kronig and Brink for one drop (Clift et al. [21]) assumes no external resistance, constant physical properties of the phases, and an invariant state of the external gas phase. Our model differs from that of Kronig and Brink in that the physical properties of both phases in the present model are functions of pressure and temperature and of the exothermic absorption process. The developed model was verified against a number of cases presented in the literature (Daltrophe et al. [12,13]). References [1] Engler M, Grossman G, Hellman H-M. Comparative simulation and investigation of ammonia–water absorption cycles for heat-pump applications. International Journal of Refrigeration 1997;20(7):504–16. [2] Thioye M. Etude comparative de la performance des machines frigorifiques a absorption utilisant de l’energie thermique a tres faible valeur exergetiqu. International Journal of Refrigeration 1997;20(4): 283–94. [3] Borde I, Jelinek M, Daltrophe NC. Absorption system based on refrigerant R134a. International Journal of Refrigeration 1995;18(6):387–94. [4] Borde I, Jelinek M, Daltrophe NC. Working fluids for absorption refrigeration systems based on R124. International Journal of Refrigeration 1997;20(4):256–66. [5] Borde I, Jelinek M, Daltrophe N.C. Working substances for absorption heat pumps based on R32. In: Proceedings of the 19th International Congress on Refrigeration, The Hague, Netherlands, Vol. 4A, 1995. p. 80–7. [6] Borde I, Jelinek M. Thermodynamic properties of organic working-fluids for absorption heat pumps. In: Proceedings of the 16th European Seminar on Applied Thermodynamics, Abbaye des Premontre’s, Pont-a-Mousson, France, 1997. p. 193–8. [7] Jelinek M., Borde I. Working fluids for absorption heat pumps based on R125 (pentafluoroethane) and organic absorbents. In: International Sorption Heat Pumps Conference, Munich, 1999. p. 205–8. [8] Sawada N, Tanaka T, Mashimo K. Development of organic working-fluids and application to absorption systems. In: International Absorption Heat Pumps Conference, New Orleans, ASME, AES-Vol. 31, 1994. p. 315–20.
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[9] Borde I., Jelinek M. Utilization and recovery of waste heat by absorption heat pumps. Final Scientific Report 1.1.84–31.12.85. Joint German Israel Project. BGUN-ARI-45–86, 1986. [10] Borde I, Jelinek M. Absorption heat pumps with organic refrigerant-absorbent fluid pairs. 2nd International Workshop on Research Activities on Advanced Heat Pumps. Graz, Austria, 1988. [11] Chen LT. A new ejector-absorber cycle to improve the COP of an absorption refrigeration system. Applied Energy 1988;30:37–51. [12] Daltrophe NC, Jelinek M, Borde I. Heat and mass transfer in a two-phase flow of a binary solution and gas. In: 10th International Heat Transfer Conference, Brighton, IChemE, vol. 3, Taylor & Francis, 1995, p. 299–304. [13] Daltrophe NC, Jelinek M, Borde I. Heat and mass transfer in a jet-ejector for absorption systems. In: International Absorption Heat Pumps Conference, New Orleans, ASME, AES-vol. 31, 1994. p. 327– 32. [14] Levy A, Jelinek M, Borde I. Study of design parameters of a jet ejector for absorption systems. In: The 20th International Congress of Refrigeration, Sydney, Australia, vol.III. 1999 [paper 018]. [15] Boer D, Vallas M, Coronas A. Performance of double effect absorption compression cycles for airconditioning using methanol-TEGDME and TFE-TEGDME systems as working pairs. International Journal of Refrigeration 1998;21(7):542–55. [16] Sawada N, Minato K, Kunigi Y, Cycle simulation and COP evaluation of absorption-compression hybrid heat-pumps: heat amplifier type. In: International Absorption Heat Pumps Conference, New Orleans ASME, AES-vol. 31. 1994. p. 471–6. [17] Berlitz T, Cerkvenik B, Hellman HM, Ziegler F. A basis for the energetic assessment of hybrid compression sorption cycles. In: International Sorption Heat Pumps Conference, Munich, 1999. p. 471–5. [18] Boer D, Huor H, Prevots M, Coronas A. Combined vapor compression-double effect absorption cycles for air-conditioning: a new high performance cycle. In: International Absorption Heat Pumps Conference, New Orleans, ASME, AES-vol. 31. 1994. p. 483–6. [19] IMSL, C, FORTRAN Mathematics and statistics libraries. Visual Numerics, Inc., 1997. [20] Levy A, Jelinek M, Borde I. Numerical study on the design parameters of a jet ejector for absorption systems [submitted for publication]. [21] Clift R, Grace JR, Weber ME. Bubbles, drops and particles. New York: Academic Press, 1978.
Performance of a triple-pressure-level absorption cycle with R125-N,N0-dimethylethylurea M. Jelinek, A. Levy*, I. Borde Pearlstone Center for Aeronautical Engineering Studies, Mechanical Engineering Department, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel Received 29 October 2001; received in revised form 14 December 2001; accepted 22 December 2001
Abstract In the developed triple-pressure-level (TPL) single stage absorption cycle, a specially designed jet ejector was introduced at the absorber inlet. The device served two major functions: it facilitated pressure recovery and improved the mixing between the weak solution and the refrigerant vapour coming from the evaporator. These effects enhanced the absorption of the refrigerant vapour into the solution drops. To facilitate the design of the jet ejector for such absorption machines, a numerical model of simultaneous heat-and-mass transfers between the liquid and the gas phases in the ejector was developed. The refrigerant pentafluoroethane (R125) and the absorbent N,N0 -dimethylethylurea (DMEU) were used as the working fluid. A computerized simulation program was used to perform a parametric study of the TPL absorption cycle. The influence of the jet ejector on the performance of the TPL absorption cycle was evaluated, and the performance of the TPL absorption cycle was compared with that of a double-pressure level (DPL) cycle. Four cases were studied that represent the improvements in the TPL absorption cycle performances as a result of the incorporation of the jet ejector. The four cases are: the ability to reduce the circulation ratio f, the ability to lower the evaporator temperature, the ability to lower the generator temperature and the ability to use higher-temperature cooling water. # 2002 Published by Elsevier Science Ltd. Keywords: Absorption cycle; Jet ejector; Cycle analysis; COP
1. Introduction Various types of absorption heat-pumps, both single stage and multistage, can exploit a variety of heat sources for cooling and refrigeration (< 0 C). The type of absorption heat pump and the nature of the working fluids are usually determined * Corresponding author. Tel.: +972-8-6477092; fax: +972-8-6472813. E-mail address: [email protected] (A. Levy). 0306-2619/02/$ - see front matter # 2002 Published by Elsevier Science Ltd. PII: S0306-2619(02)00003-X
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Nomenclature Mass transfer area (m2) Cross section of the i-phase (m2) Diffuser cross-section (m2) Drag coefficient () Virtual-mass coefficient () Coefficient of performance (Qe/(Qg+Wp)) Diffusion coefficient (m2/s) Drop diameter (m) The pressure recovered by the ejector divided by the pressure difference between the nozzle inlet and outlet, %. f Circulation ratio (kg strong solution/kg refrigerant) Fgd Inter-phase forces (N/m) h Convective heat-transfer coefficient (W m/K) hm Mass-transfer coefficient (kg m/s) Hi Enthalpy of the i-phase (J/kg) : mgd The mass transfer between the phases (kg/s) Nd Number of the droplets per unit volume [see Eq. (6)] Nu Nusselt number () P Pressure (Pa) Qe Heat rejected by the evaporator (J) Qg Heat transferred to the generator (J) Qgd Heat transfer per unit length (J/m) Qhs Heat transferred at the solution’s heat-exchanger (J) Qhs/Qe The heat transferred at the solution’s heat-exchanger divided by the heat rejected by the evaporator (J/J) Te, Tevp Evaporator temperature ( C) td Residence time (s) Tg Generator temperature ( C) Ti Temperature of the i-phase ( C) Ts Surface temperature of the drop ( C) Tw Cooling-water temperature ( C) ui i-phase velocity (m/s) ur Relative velocity (m/s) Wgd Work transfer per unit length (J/m) Wp Energy supply to the pump (J/kg) x Diffuser length (m) Refrigerant weight fraction in the solution (kg refrigerant/kg solution) * Equilibrium mass concentration (kg refrigerant/kg solution) i i-phase density (kg/m3)
a Ai Atot Cd Cvm COP D Dd dPrec
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Subscripts d Dispersed-phase g Gas-phase gd Gas-droplet interface i i-Phase (g,d) s Drop surface
by the temperature of the heat-source and the cooling or refrigeration demands. Utilization of low-potential heat-sources (70–120 C) for cooling and refrigeration is limited by the properties of the working fluids and the cycle configuration of the heat pump. For utilization of low potential heat sources for cooling and refrigeration to < 0 C, a single-stage absorption heat-pump based on organic working fluids is preferable to absorption heat-pumps based on conventional working fluids such as ammonia–water or water–lithium bromide because of the limitations imposed by the latter type of fluids. The ammonia–water combination requires a heat-source temperature above 120 C for cooling and refrigeration to < 0 C. Such a system is a high-pressure system that requires a rectification column [1]. Ammonia has acceptable thermophysical properties, but it is a flammable toxic and strongly irritant fluid, and is corrosive to copper. The water–lithium bromide solution can be used with a heat-source temperature above 70 C for air-conditioning, but not for cooling and refrigeration because of the limitation for the evaporator temperature ( > 0 C). This system operates under vacuum and does not require a rectification column. The water–lithium bromide solution is highly corrosive and extremely viscous and viscosity-reducing agents are frequently required. The limitations of using common working fluids [2] for utilizing low-potential heat-sources (80–120 C) for cooling and refrigeration (< 0 C) are thus self-evident. With a view to overcoming these limitations, the working fluids used in the studies of our group are based on fluorocarbon (HFC) refrigerants and organic absorbents [3–8]. The refrigerants are not toxic or corrosive, and the organic working fluids are environmentally acceptable. In our high-pressure system, the condenser and the absorber are water cooled, and a rectification column is not needed, since the difference between the normal boiling points of the absorbent and the refrigerant is about 200 C. The performance of these working fluids in a conventional double-pressure level (DPL) single-stage absorption cycle is expressed in terms of a coefficient of performance (COP)1 of about 0.5 and a circulation ratio (f)2 in the range of 3–7. In the present study, an advanced single-stage absorption heat-pump, i.e. a triplepressure-level (TPL) cycle was used to utilize a low-potential-heat source for cooling from 5 to 15 C. Similar absorption cycles have been suggested by Borde and 1
Defined as the heat rejected from the evaporator divided by the heat supply to the generator and the energy supply to the pump. 2 Defined as the ratio between the mass flow rate of the strong solution in the pump to the mass flow of the refrigerant.
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Jelinek [9,10] and Chen [11] in which a jet-ejector was used as a device for mixing and pressure recovery. Borde and Jelinek [9] conducted an experimental study on a heat pump. They showed the suitability to integrate a self-made jet ejector as a mixing unit. Borde and Jelinek [10] conducted a theoretical study on a heat pump with organic working fluids. In their mathematical model, the pressure recovery was not taken into account. Thus the jet ejector was considered only as a mixing device. Chen [11] used a Bernoulli type equation for analysis of the two-phase mixture flow through the ejector, which was based on a single-phase model of pseudo-fluid without taking heat and mass transfer into account. In addition, the momentum balance was not taken into account. To overcome the above-mentioned simplifications, theoretical studies on the performance of the jet ejector parameters were conducted [12– 14]. To facilitate the design of the jet ejector for absorption machines, a two-phase numerical model of simultaneous mass, momentum and heat transfer in the jet ejector was developed [10]. In this study a combination of computerized simulation programs, one for the conventional single-stage absorption cycle (DPL) and the other for the jet ejector, was developed to examine the influence of the jet ejector on the performance of the TPL single-stage absorption cycle.
2. Triple-pressure-level single-stage absorption cycle To utilize a low-potential-heat source for cooling from 5 to 15 C, an advanced single-stage absorption heat pump can be used, i.e. a triple-pressure-level (TPL) cycle. This cycle may be implemented in a number of different ways, for example, by a design known as the compression/absorption cycle [15–18], in which a compressor is inserted between the evaporator and the absorber. The main disadvantage of the latter device is the extra electrical energy required for the compressor. In our TPL single-stage heat-pump, a specially designed jet ejector is introduced at the absorber inlet (Fig. 1), with the purpose of increasing the absorber pressure relative to the evaporator pressure (by partially recovering the high pressure of the generator) and improving the mixing process and the pre-absorption by the weak solution of the refrigerant coming from the evaporator [12–14]. The mixing process in the jet ejector is very intensive as a result of spray generation of the liquid phase and of extensive subcooling of the weak solution in the solution’s heat-exchanger. A schematic representation of the jet-ejector is given in Fig. 2. 2.1. Jet ejector The jet ejector consists basically of a nozzle and a diffuser. The device is characterized by the facts that there are no moving parts and there is no requirement for an additional energy source. At the nozzle outlet, production of a full cone spray of small high-velocity drops of a weak solution serves to transform potential energy (pressure difference between the generator and the evaporator) into kinetic energy. At the diffuser inlet (at the low pressure of the evaporator), the stream of drops mixes with the refrigerant vapour coming from the evaporator. In the diffuser,
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Fig. 1. Schematic representation of a triple-pressure-level single-stage advanced absorption cycle. (Sol. H.E.—solution’s heat-exchanger, Ref. H.E.—refrigerant’s heat-exchanger and P—solution pump.).
Fig. 2. Schematic representation of the jet-ejector.
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pressure recovery (defined as the difference in pressure between the outlet and the inlet of the diffuser) is thus obtained by transforming the droplet kinetic energy to potential energy. As a result, the velocities of both the absorbent drops and the refrigerant gas are reduced. To facilitate the design of the jet ejector for absorption machines, a numerical model of simultaneous mass, momentum and heat transfers between the liquid and gas phases in the jet ejector (Appendix A) was developed on the basis of two-phase mathematical model previously described by Levy et al. [14]. The jet ejector model, as a pre-absorber, was solved numerically for the working fluid pentafluoroethane (R125) as the refrigerant and N,N0 -dimethylethylurea (DMEU) as the absorbent. A solution of R125-DMEU was modelled as the dispersed phase, with R125, as the continuous gas phase. The numerical solution was obtained by means of Gear’s fifth-order BDF method (often called Gear’s stiff method), which is available in the IMSL library [19]. The influences of the jet-ejector design parameters on the pressure recovery, temperature and concentration of the refrigerant in the solution, and velocities of the gas and liquid drops have previously been described by Levy et al. [20]. The parametric study involved an examination and ways of augmentation of the mass transfer process in the diffuser with the ultimate aim of designing a compact and efficient unit. The numerical simulation demonstrated that pressure recovery and pre-absorption in the jet ejector would improve the efficiency of the absorption process and hence the overall efficiency of the refrigeration cycle. 2.2. Application of the TPL absorption cycle In commonly used absorption heat-pumps (when the pressure drop is negligible), the absorber pressure is equal to the evaporator pressure. However, in the TPL cycle, the absorber pressure is higher than evaporator pressure, which leads to an improvement in the cycle performance. This effect can be obtained by decreasing the circulation ratio f (Case 1) or by changing the governing cycle temperatures as follows: lowering the refrigeration temperature, i.e. the evaporator temperature Te (Case 2); lowering the heat-source temperature, i.e. the generator temperature Tg (Case 3); or raising the cooling-water temperature, i.e. the condenser and absorber temperature Tw (Case 4), as summarized in Table 1. Table 1 Comparison between the possibilities provided by the TPL vs. the common single-stage (DPL) absorption cycle in terms of the outside temperatures and the circulation ratio
Case 1 Case 2 Case 3 Case 4 a
Tg ( C)
Te ( C)
Tw ( C)
f
=a = Lower =
= Lower = =
= = = Higher
Lower = = =
=Equal to the value of the common single-stage absorption cycle.
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Implementation of the four cases is explained and analysed in the following sections.
3. System analysis and discussion A combination of the computerized simulation programs, one for the conventional single-stage double-pressure level (DPL) absorption cycle and the other for the jet ejector, facilitated the evaluation of the influence of the jet ejector on the performance of the TPL single-stage absorption cycle. In all cases, calculation of the performances (COP, f, Qhs/Qe3 and dPrec4) of the TPL and DPL cycles was carried out for the R125-DMEU working pair. Calculations for the DPL absorption cycle (absorber pressure=evaporator pressure) and the TPL absorption cycle (absorber pressure=evaporator pressure plus the recovered pressure) were carried out under the following operating conditions: cooling-water temperature 25 C (condenser temperature 32 C and absorber temperature 28 C), generator temperature in the range of 70–140 C, and for evaporator temperatures of 0, 5, 10 or 15 C. For both cycles, the pressure drop along the cycle was taken as zero. 3.1. Influence of the jet ejector on the performance of the TPL cycle The influence of the jet ejector on the performance of the TPL cycle (in comparison with the DPL cycle) was examined for four separate cases in which one operating condition in the TPL was varied and all the other conditions remained the same for both types of cycle. 3.1.1. Case 1—lowering the circulation ratio, f For the same governing cycle temperatures for the DPL and TPL cycles, the higher absorber pressure (by the amount of the pressure recovery) for the TPL at the same absorber outlet temperature results in a higher weight fraction of the refrigerant in the solution. This increase in the weight fraction at the absorber outlet leads to a reduction in f, i.e. a reduction in the mass flow rate of the strong solution in the pump, and consequently to a reduction in the amount of heat to be transferred in the solution’s heat-exchanger. The calculated COP, f and Qhs/Qe for the same evaporator temperatures in the TPL and DPL absorption cycles with R125-DMEU are shown in Figs. 3–5. As can be seen from Fig. 3, the higher values of the COP for the TPL cycle in comparison with those for the DPL cycle can be achieved at lower generator temperatures, for all evaporator temperatures. The improvement in the COP becomes
3
Defined as the heat transferred by the solution heat exchanger divided by the heat rejected by the evaporator. 4 Defined as the pressure recovered by the ejector divided by the pressure difference between the nozzle inlet and outlet, in %.
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Fig. 3. Comparison between the calculated COP for the TPL absorption cycle and for the DPL absorption cycle (full and open symbols, respectively) as a function of the generator temperature for various evaporator temperatures as calculated for R125-DMEU.
more significant as the evaporator temperature falls, and, at the same operating conditions, it increases by about 20%. The values of f in the TPL cycle are much lower than those in the DPL cycle (Fig. 4). At the same operating conditions, the reduction in the values of f can reach 100%. The relative size of the solution’s heat-exchanger can be expressed in terms of Qhs/ Qe. The values of Qhs/Qe in the TPL cycle are lower than those in the DPL cycle (Fig. 5). At the same operating conditions, the reduction in Qhs/Qe becomes more significant as the evaporator temperature falls and can reach 70% of the Qhs/Qe in the DPL cycle. The calculated pressure recovery in the ejector, as expressed by the term dPrec (in %), increases as the generator temperature decreases and decreases as the evaporator temperature falls. Increases of dPrec up to 9% were obtained, as can be seen in Fig. 6. The optimal operating conditions, as a function of the evaporator temperature, are those that achieve the highest COP. The values of the generator temperature and f for these maximum values of the COP as a function of the evaporator temperature are given in Table 2 for the working fluids R125-DMEU. The table illustrates the
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Fig. 4. Comparison between the calculated value of f for the TPL absorption cycle and for the DPL absorption cycle (full and open symbols, respectively) as a function of the generator temperature for various evaporator temperatures as calculated for R125-DMEU.
Table 2 Generator temperature and circulation ratio at maximum calculated COP as a function of the evaporator temperature Triple-pressure-level absorption cycle
Conventional single-stage absorption cycle
Te ( C) COP
Tg ( C)
f
Qhs/Qe
COP
Tg ( C)
f
Qhs/Qe
0 5 10 15
81 91 101 113
3.5 3.9 4.4 5.2
1.78 2.42 3.38 4.84
0.570 0.530 0.485 0.445
90 102 115 132
3.5 4.0 4.6 5.5
2.05 2.91 4.25 6.05
0.595 0.555 0.515 0.480
influence of pressure recovery on the performance of the TPL cycle in comparison with the DPL cycle. At the same evaporator temperature, the main benefit of the TPL cycle at maximum COP is evident in the reduction in the generator temperature by 11–13 C. The maximum COP is increased in the range of 4–8%: the reduction in
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Fig. 5. Comparison between the calculated values of Qhs/Qe for the TPL absorption cycle and for the DPL absorption cycle (full and open symbols, respectively) as a function of the generator temperature for various evaporator temperatures as calculated for R125-DMEU.
the circulation ratio is up to 5% and the reduction in the size of the solution heat exchanger is up to 20%. 3.1.2. Case 2—lowering the evaporator temperature When the values of the generator temperature, the cooling-water temperature (condenser and absorber temperature), the absorber pressure and f for the TPL cycle are the same as those for the DPL cycle, the evaporator pressure in the TPL cycle is lowered by the amount of the pressure recovered, and thus the evaporation temperature falls accordingly. The calculated differences in the evaporator temperature between the DPL and TPL cycles as a function of the generator temperature (with the same COP, f and Qhs/Qe as in the DPL cycle) are shown in Fig. 7. It can be seen that increasing the generator temperature at a constant DPL evaporator temperature decreases the ability to lower the TPL evaporator temperature, while decreasing the DPL evaporator temperature at a constant generator temperature increases the ability to lower the TPL evaporator temperature. In these generator and evaporator temperature ranges, the ability to lower the evaporator temperature in the TPL cycle by 2–5 C was achieved.
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Fig. 6. Variation of the calculated pressure-recovery (%) in the jet ejector with generator temperature for various evaporator temperatures as calculated with R125-DMEU as the working fluid.
3.1.3. Case 3—lowering the generator temperature When the values of the evaporator temperature, the cooling water temperature (condenser and absorber temperature) and f were the same for the TPL and DPL cycles, the generator temperature of the TPL cycle was lowered. The calculated differences in the generator temperature between the TPL and DPL cycles as a function of the DPL generator temperature is shown in Fig. 8. It can be seen that increasing the generator temperature at a constant DPL evaporator temperature increases the ability to lower the TPL generator temperature, while lowering the DPL evaporator temperature at a constant generator temperature increases the ability to lower the TPL generator temperature. In these generator and evaporator temperature ranges, the ability to lower the TPL generator temperature was in the range 10–25 C. That means that a lower temperature heat source can be used with the TPL. 3.1.4. Case 4—raising the cooling-water temperature When the operating conditions for the TPL and DPL cycles are the same in terms of the generator temperature, the evaporator temperature and f, the absorber pressure of the TPL cycle increases by the amount of the pressure recovered, and hence the condenser and absorber temperature may be increased, i.e. a higher coolingwater temperature may be used. Fig. 9 shows the difference in the cooling-water
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Fig. 7. Evaporator temperature differences between the DPL and TPL cycles due to the pressure recovery in the jet-ejector (Case 2) as a function of the generator temperature for various evaporator temperatures as calculated using R125-DMEU as the working fluid.
temperature between the TPL and DPL cycles as a function of the generator and evaporator temperatures. As can be seen in Fig. 9, the ability to raise the coolingwater temperature in the TPL cycle increases upon lowering the evaporator temperature and slightly decreases while the generator temperature increases. This improvement is important in the case of absorption systems used with cooling water obtained from cooling towers in a high-humidity climate. 3.2. Case study Let us take an example for the four cases described above. The following operating conditions were chosen: cooling water temperature 25 C (condenser temperature 32 C and absorber temperature 28 C), generator temperature 100 C, and evaporator temperature of 5 C. Pressure drops along the cycles were taken as zero. From the results summarized in Table 3, it can be seen that Case 1 gives, a 20% reduction in f (from 4.11 in the DPL cycle to 3.27 in the TPL cycle) a 4.6% increase in the COP and a 2.7% reduction in Qhs/Qe. In Case 2, the evaporator temperature could be lowered by 3.6 C, for the same values of the COP, f, Tg and
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Fig. 8. Generator temperature differences between the DPL and TPL cycles due to the pressure recovery in the jet-ejector (Case 3) as a function of the DPL generator temperature for various evaporator temperatures as calculated with R125-DMEU as the working fluid.
Table 3 Improvement in the TPL absorption cycle performances vs. the common single-stage absorption cycle as a result of changing the outside temperature or lowering the circulation ratio
Common Case 1 Case 2 Case 3 Case-4 a
Tg ( C)
Te ( C)
Tw ( C)a
f
COP
Qhs/Qe
100 100 100 88.7 100
5 5 8.6 5 5
25 25 25 25 27.8
4.11 3.27 4.11 4.11 4.11
0.527 0.551 0.527 0.555 0.532
2.99 2.18 2.99 2.51 2.97
Tabsorber=Tw+3 C, Tcondenser=Tw+7 C.
Qhs/Qe. In Case 3, for a constant value of f of 4.11 and the same Tw and Te, lowering of the generator by 11.3 C, gave a 5.3% increase in the COP and a 16% reduction in Qhs/Qe. Finally, for a higher cooling water temperature (by 2.8 C) in the TPL cycle with the same Te and Tg, the COP and Qhs/Qe were essentially the same for the TPL and DPL cycles (Case 4).
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Fig. 9. Cooling water temperature differences between the TPL and DPL cycles due to the pressure recovery in the jet-ejector (Case 4) as a function of the generator temperature for various evaporator temperatures as calculated with R125-DMEU as the working fluid.
4. Conclusions Integrating a specially designed jet ejector at the absorber inlet resulted in an advanced triple-pressure level (TPL) single-stage absorption cycle. The jet ejector facilitated pressure recovery and improved the mixing between the weak solution and the refrigerant vapour coming from the evaporator. The influence of the jet ejector on the performance of the TPL absorption cycle was evaluated, and the performance of the TPL absorption cycle was compared with that of the DPL cycle. Four cases of improvements in the TPL absorption cycle performances were studied. The four cases are: the ability to reduce the circulation ratio f (Case 1), the ability to lower the evaporator temperature (Case 2), the ability to lower the generator temperature (Case 3) and the ability to use higher cooling-water temperature (Case 4). From the four cases studied, it is evident that in the design of a new absorption cycle, Case 1 is the option of choice. In situations in which an improvement of an existing absorption cycle is required or an adaptation to different operating conditions is needed without making changes to the components in the existing cycle, Cases 2–4 have to be considered, each on its own merits.
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Cycle analysis in the generator and the evaporator temperature ranges showed that, in the first case, the COP increased by up to 20%; the reduction in the mass flow rate in the strong solution pump was up to 50%, and a reduction up to 70% was achieved in the amount of heat to be transferred in the solution heat exchanger. In Case 2, the evaporator temperature could be lowered by 2–5 C while all other parameters remained constant. In the third case, the generator temperature could be lowered by 3–15 C by achieving a small improvement in the cycle performance. In Case 4, the condenser and the absorber temperature could be increased by 2–4 C while all other parameters remained almost the same. It should be noted that these improvements are functions of the operating conditions and the thermophysical properties of the working fluids.
Acknowledgements This study was partially supported by the German-Israeli Scientific Cooperation Unit, Ministry of Science, under the program BMBF-MOS, Grant-GR-1718.
Appendix A. Jet-ejector—calculation model A two-phase continuum model was used to describe the steady-state flow of liquid droplets (the dispersed phase) and a gas phase (the continuous phase) through a one-dimensional mixing chamber (diffuser). The governing equations were obtained by macroscopic mass, momentum and energy balances for the two phases in a control volume, with length dx. The model was based on the following assumptions: steady state; mass, momentum and heat transfer only between the two phases; friction forces with the diffuser wall negligible; adiabatic flow; dilute phase flow; droplets comprise a binary mixture of absorbent and refrigerant; constant droplet diameter; and electrical forces and surface tension neglected. Balance equations Based on the above-mentioned assumptions, mass, momentum and energy balance equations for the gas and the dispersed phases were developed. The mass balance equation for the i-phase may be written as: : d dmgd ði ui Ai Þ ¼ dx dx
ð1Þ
where i and ui are the density and the velocity of the i-phase, respectively, Ai is the : cross section occupied by the i-phase and dmgd =dx is the mass transfer per unit length due to absorption. The right-hand side is positive when i=d (dispersed phase) and negative for i=g (gas-phase). The momentum balance equation for the gas phase is expressed as:
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: d 2 dP dm gd g ug Ag þ Atot ¼ Fgd ud dx dx dx
ð2Þ
where Fgd represents all the forces that act on the gas phase due to the dispersed phase, and Atot is the diffuser cross section (i.e. Atot Ag þ Ad ). The momentum balance equation for the dispersed phase is given as: : d 2 dmgd d ud Ad ¼ Fgd þ ud dx dx : where dmgd =dx ud is momentum flux due to the mass transfer. The energy balance equation for the i-phase is given by: : u2 u2 d dmgd pi ui Ai Hi þ i Hgd þ d ¼ Qgd Wgd dx 2 dx 2
ð3Þ
ð4Þ
where Hi and Hgd are the enthalpies of the i-phase and that of the refrigerant at the droplets’ surfaces, respectively; and Qgd and Wgd are the heat and the work transfer per unit length between the two phases during the process, respectively. The last term on the right-hand side of the equation represents the energy flux that is transferred due to absorption. In this equation, the upper sign in the or pertains to i=d and the lower sign to i=g. A number of complementary equations, definitions and empirical correlations are required to solve the set of ordinary differential-equations given above. These will be presented below. It should also be noted that the dispersed phase is a binary mixture, and hence all its thermodynamic properties were calculated upon the basis of weight fraction of the refrigerant in the solution, , and its other thermophysical properties were obtained by applying the mixture theory. Details are given in the publications of Borde et al. [3,4]. Interphase forces The forces acting per unit length between the phases that were taken into account in this model were the forces per unit length due to drag and to virtual mass (first and second terms on the right hand side, respectively). D3d dur D2d 1 Fgd ¼ Atot Nd Cd g ur jur j þ Cvm ud ð5Þ 4 2 6 dx where ur ð ug ud is the relative velocity, and the Nd, number of the droplets per unit volume, can be expressed as follows: Nd ¼
6Ad Atot D3d
ð6Þ
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where Dd is the drop diameter and Cd is the drag coefficient, which is expressed as a function of the Reynolds number, Re, by the correlations of Oseen, Pittet et al. and Stringham et al., as previously described by Clift et al. [21]. The volume of the displaced fluid that contributes to the effective mass of the dispersed phase is usually described by the virtual-mass coefficient, Cvm. In general, this coefficient is a function of the volume fraction of the dispersed phase (which is equal to Ad/Atot in onedimensional flow) and of the shape of the drops, but it is often taken as a constant. It was found that for a spherical droplet Cvm=11/16 [21], and this is the value that was used in the course of this investigation. Work and heat transfer The calculation of the term for work per unit length takes into account only the forces per unit length that act between the two phases, hence: Wgd ¼ Fgd ud
ð7Þ
The heat transfer between the particles and the gas phase was assumed to be governed only by convection. This was expressed by: Qgd ¼ Nd Atot D2d hðTg Ts Þ
ð8Þ
The convective heat-transfer coefficient, h, was expressed as a function of the Nusselt number, Nu (Daltrophe et al. [12,13]). One of the key variables for the mass and heat transfer is the temperature at the surface of the drops Ts, which also defines the equilibrium concentration, ðT; PÞ. This temperature was obtained by assuming that absorption occurs first in a very thin surface layer. Then, the absorbed gas transfers into the drop, while heat is transferred from inside the drop to the surface layer and finally to the gas. The heat balance around the layer was used to calculate the surface temperature. The heat transfer inside the drop was calculated by analogy with mass transfer. Mass transfer The mass transfer source term per unit length can be calculated by: : dmd ¼ hm aðs d Þ dx
ð9Þ
where hm is the mass-transfer coefficient and a is the area for mass transfer per unit length. This was estimated by: a¼
6Ad Dd
ð10Þ
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The correlation for estimating the overall mass transfer was obtained from an approximation of the theoretical solution of Kronig and Brink for one drop, which fits the experimental results of Garner and Lane for a cloud of drops (Clift et al. [21]). rffiffiffiffiffiffiffi : D dmd 6Ad ¼ ð11Þ d o s td dx Dd In this equation, D is the diffusion coefficient in the drop, o is the uniform initial concentration in the drop, and td is the residence time of the drop in the gas phase, which was calculated by: dtd 1 ¼ dx ud
ð12Þ
Note that in the transition from Eq. (9) to (11), the local variable d has vanished and is replaced by the residence time of the drop in the diffuser, td. When the residence time increased and the value of the Fourier number, Fo (=4Dtd =D2d ) reached 0.003, then the Biot number, Bi, is equal to 17.66 and hm was calculated by Biðd D=Dd Þ, and this value was introduced into Eq. (9). The theory of Kronig and Brink for one drop (Clift et al. [21]) assumes no external resistance, constant physical properties of the phases, and an invariant state of the external gas phase. Our model differs from that of Kronig and Brink in that the physical properties of both phases in the present model are functions of pressure and temperature and of the exothermic absorption process. The developed model was verified against a number of cases presented in the literature (Daltrophe et al. [12,13]). References [1] Engler M, Grossman G, Hellman H-M. Comparative simulation and investigation of ammonia–water absorption cycles for heat-pump applications. International Journal of Refrigeration 1997;20(7):504–16. [2] Thioye M. Etude comparative de la performance des machines frigorifiques a absorption utilisant de l’energie thermique a tres faible valeur exergetiqu. International Journal of Refrigeration 1997;20(4): 283–94. [3] Borde I, Jelinek M, Daltrophe NC. Absorption system based on refrigerant R134a. International Journal of Refrigeration 1995;18(6):387–94. [4] Borde I, Jelinek M, Daltrophe NC. Working fluids for absorption refrigeration systems based on R124. International Journal of Refrigeration 1997;20(4):256–66. [5] Borde I, Jelinek M, Daltrophe N.C. Working substances for absorption heat pumps based on R32. In: Proceedings of the 19th International Congress on Refrigeration, The Hague, Netherlands, Vol. 4A, 1995. p. 80–7. [6] Borde I, Jelinek M. Thermodynamic properties of organic working-fluids for absorption heat pumps. In: Proceedings of the 16th European Seminar on Applied Thermodynamics, Abbaye des Premontre’s, Pont-a-Mousson, France, 1997. p. 193–8. [7] Jelinek M., Borde I. Working fluids for absorption heat pumps based on R125 (pentafluoroethane) and organic absorbents. In: International Sorption Heat Pumps Conference, Munich, 1999. p. 205–8. [8] Sawada N, Tanaka T, Mashimo K. Development of organic working-fluids and application to absorption systems. In: International Absorption Heat Pumps Conference, New Orleans, ASME, AES-Vol. 31, 1994. p. 315–20.
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[9] Borde I., Jelinek M. Utilization and recovery of waste heat by absorption heat pumps. Final Scientific Report 1.1.84–31.12.85. Joint German Israel Project. BGUN-ARI-45–86, 1986. [10] Borde I, Jelinek M. Absorption heat pumps with organic refrigerant-absorbent fluid pairs. 2nd International Workshop on Research Activities on Advanced Heat Pumps. Graz, Austria, 1988. [11] Chen LT. A new ejector-absorber cycle to improve the COP of an absorption refrigeration system. Applied Energy 1988;30:37–51. [12] Daltrophe NC, Jelinek M, Borde I. Heat and mass transfer in a two-phase flow of a binary solution and gas. In: 10th International Heat Transfer Conference, Brighton, IChemE, vol. 3, Taylor & Francis, 1995, p. 299–304. [13] Daltrophe NC, Jelinek M, Borde I. Heat and mass transfer in a jet-ejector for absorption systems. In: International Absorption Heat Pumps Conference, New Orleans, ASME, AES-vol. 31, 1994. p. 327– 32. [14] Levy A, Jelinek M, Borde I. Study of design parameters of a jet ejector for absorption systems. In: The 20th International Congress of Refrigeration, Sydney, Australia, vol.III. 1999 [paper 018]. [15] Boer D, Vallas M, Coronas A. Performance of double effect absorption compression cycles for airconditioning using methanol-TEGDME and TFE-TEGDME systems as working pairs. International Journal of Refrigeration 1998;21(7):542–55. [16] Sawada N, Minato K, Kunigi Y, Cycle simulation and COP evaluation of absorption-compression hybrid heat-pumps: heat amplifier type. In: International Absorption Heat Pumps Conference, New Orleans ASME, AES-vol. 31. 1994. p. 471–6. [17] Berlitz T, Cerkvenik B, Hellman HM, Ziegler F. A basis for the energetic assessment of hybrid compression sorption cycles. In: International Sorption Heat Pumps Conference, Munich, 1999. p. 471–5. [18] Boer D, Huor H, Prevots M, Coronas A. Combined vapor compression-double effect absorption cycles for air-conditioning: a new high performance cycle. In: International Absorption Heat Pumps Conference, New Orleans, ASME, AES-vol. 31. 1994. p. 483–6. [19] IMSL, C, FORTRAN Mathematics and statistics libraries. Visual Numerics, Inc., 1997. [20] Levy A, Jelinek M, Borde I. Numerical study on the design parameters of a jet ejector for absorption systems [submitted for publication]. [21] Clift R, Grace JR, Weber ME. Bubbles, drops and particles. New York: Academic Press, 1978.