Parametric optimization of blowdown operated double-effect vapour absorption refrigeration system

Abstract

Keywords: Double-effect vapour absorption refrigeration system; Exergy; Cogeneration; RSM; ANOVA

Introduction

The combined cooling, heat, and power (CCHP) cycle is used for the production of power, cooling, and heating simultaneously from one primary energy source. The CCHP cycle is advantageous as it limits the use of primary energy which leads to a reduction in load experienced by the power plant. This reduction in the load on the power plant assists the reduction in harmful emissions to the

environment and also decreases the fossil fuel requirement. The most significant aspect of the CCHP cycle is that it utilizes renewable forms of energy or waste energy to operate a refrigeration cycle. Renewable forms of energy can be solar, wind, tidal and geothermal while the waste heat sources include exhaust from the gas turbine, gas-steam combined cycle, automotive vehicle, the flue gas of boiler. Even bleed

*Corresponding author. *E-mail address: ashwanigoyal617@gmail.com This paper was recommended for publication in revised form by Regional Editor Jaap Hoffman Hoffman Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

steam of steam turbines, as well as the heat of blowdown operation, can be used to provide the necessary energy required by the generator of VARS. The multiple benefits of the CCHP cycle made researchers conduct studies to improve its thermodynamic performance. Abed et al. [1] conducted a parametric study to investigate the effect of input variables on the thermodynamic functioning of combined Rankine and absorption refrigeration cycle with propane-decane as the organic dual working fluid through the development of mathematical mode. Fontalvo et al. [2] investigated total exergy destruction and studied the input factors such as ammonia mass fraction and pressure ratio along with their effects. These were studied in terms of absorber and turbine efficiency. An analysis was also carried out to study the influence of internal and external cooling for rectification. Rego et al. [3] experimentally investigated the absorption refrigeration system which was powered by the heat rejected from the automotive vehicles i.e. exhaust heat. Parvez and Khaliq [4] analyzed the second law analysis of the biomass-fuelled cogeneration cycle and found the combustion chamber accountable for 25% exergy destruction. Goyal et al. [5] modified a diesel engine having a single-cylinder of 3.7 kW capacity into a cogeneration system to study the generation of power and cooling process. Yang et al. [6] analyzed the exergy destruction at the ejector in a combined power and ejector refrigeration cycle, concluding it to be more than 40%. Singh [7] conducted a second law analysis of the combined Brayton- Rankine power cycle integrated with the ammonia-water VARS. Talukdar and Gogoi [8] conducted an exergetic analysis of the LiBr-H2O VARS where waste heat from boiler flue gas became the source of heat and concluded a reduction in total exergy destruction when the temperature of the high-pressure generator was increased. Jain et al. [9] used advanced exergy analysis to identify the components on which efforts can be applied to reduce their exergy destructions. In most cases, the objective of the CCHP cycle is space cooling, process heating, and power production from the same primary energy but some researchers felt the need of reducing condenser load by this cycle. Ifaei et al. [10] used bleed steam of steam turbine as a source of heat to run a single-effect vapor absorption refrigeration cycle. The salient feature of this work is that although there is a slight decrease in the thermal efficiency of the steam cycle yet it was compensated by the reduced requirement of the makeup water in the cooling tower. So, such a cycle could be used where water is scarce. One of the major limitations of using waste heat to run the refrigeration cycle is that it fouls the heat exchanger, which leads to a decrease in its effectiveness over a period. The solution to this problem is to utilize a renewable form of energy to run the refrigeration cycle. The most commonly used renewable form of energy is solar energy and geothermal energy. Guo et al. [11] worked on the geothermal source with the cycle of vapor absorption.

The principal aim of this research includes the determination of appropriate working fluid and further optimization of cycle variables. The above-mentioned research works are related to the first law analysis, the second law analysis, and the multi-objective optimization of the system. However, the above-mentioned analyses lack in determining the most influencing decision variables, which affect the performance of the system. Response surface methodology (RSM) is such a statistical optimization technique that can be used to determine the most influencing decision variables. It is a set of mathematical and statistical techniques that can be used to define the effect of independent variables, alone or in combination, on the output by generating a mathematical model. Goyal et al. [12] in their research paper studied the effect of source temperature, sink temperature, mass fraction, isentropic efficiency of the turbine, isentropic efficiency of the pump, and effectiveness of internal heat exchanger (IHE) on the thermal efficiency of organic Rankine cycle by using RSM technique. RSM has many advantages but still, very little work has been done on the CCHP cycle. In the present paper, a series flow double-effect vapor absorption refrigeration system (VARS) run by the waste heat of blowdown operation is thermodynamically analyzed and optimized with the help of RSM to identify the most significant decision variables based on its thermal performance. The second law efficiency is taken as the performance parameter and decision variables are absorber temperature, condenser temperature, evaporator temperature, the temperature of the high-pressure generator, and temperature of the low-pressure generator. Moreover, the CSB analysis of the evaporator is done to determine its sensitivity.

Description Of The System

Figure 1 shows the schematic diagram of the proposed double-effect VARS. The weak solution of Li-Br coming out of the absorber (state 4) is pressurized by pump up to highpressure generator (HPG) Pressure (state 5). Then it passes through solution heat exchanger 1 to recovers heat from the strong Li-Br solution coming out of a low-pressure generator (LPG). This solution then enters (state 6) solution heat exchanger 2 where its temperature is further raised. At state 7, it passes through HPG where external heat is supplied by a steam drum consisting of blowdown water (state 18 to state 19). In HPG, at state 11 the solution splits into refrigerant 1 (water vapor) which passes through LPG, and a strong Li-Br mixture at state 8. LPG recovers the heat from the refrigerant by behaving as an internal heat exchanger to further generate at state 14, the refrigerant 2, and a strong Li-Br mixture. Heat is exchanged at state 9 when the Li-Br mixture from HPG (state 8) passes through solution heat exchanger 2. Further, this mixture flows from the pressure

reducing valve 2 (state 9 to state 10), the LPG (state 15) to solution heat exchanger 1 for the process of heat exchange (state 16). The pressure is reduced to condenser pressure (state 13) when refrigerant 1 after exiting the LPG (state 12) passes through the pressure reducing valve 3. Refrigerant 2 and refrigerant 1 mix in the condenser and the mixed refrigerant is externally cooled by water (state 20 to state 21). Then, it is throttled up to evaporator pressure (state 1 to state 2) and evaporates in the evaporator by cooling external water (state 22 to state 23). At the exit of the evaporator, while passing through the absorber, the mixed refrigerant combines with the strong Li-Br mixture, which is returning from solution heat exchanger 1 through reducing valve 1 (state 16 to state 17). The absorber is externlly cooled by water to dissipate the heat of absorption (state 24 to state 25). This cycle then repeats.

Thermodynamic Modelling

Few assumptions have been considered for the thermodynamic modelling of the proposed system which are listed below [13]:

• Steady-state operating condition. • The concentration of the LiBr-H2O solution is at equilibrium at the respective temperature and pressure. • There is no loss of pressure in the heat exchangers and the connecting piping. • Li-Br solution concentration remains the same when the heat is transferred to the solution heat exchanger. • There are no losses of heat transfer occurring between connecting pipes and the environment. • The state of water is saturated vapor at the exit of the evaporator and is saturated liquid at the exit of the condenser.

Procedure For Modelling A Double Effect Refrigeration System

• Input values of temperatures at cooling load, evaporator, condenser, high-pressure generator, low-pressure generator, blowdown water inlet and outlet, the effectiveness of solution heat Exchangers 1 and 2, and mass of blowdown water available [Table 1] are fed to the system.

Figure 1. Schematic diagram of a double-effect vapor absorption refrigeration system.

Figure 2. State points vs specific entropy and mass flow rate.

• The temperature values at the inlet and outlet of external fluid of condenser, absorber, and evaporator, are also fed [Table 1]. • Determine the properties of refrigerant and solution at relevant state points using engineering equation solver (EES) software (refer to Figures 2,3 and 4) [14]. • Apply conservation equations for mass and concentration, and energy balance equation [15] to determine mass flow rate, the concentration of refrigerant as well as of solution, and the heat transfer for highpressure generator, low-pressure generator, condenser, and absorber [Table 2].

• Calculate the irreversibility for the complete system and also for individual components. Finally, compute the second law efficiency of VARS [Table 3].

Optimization Methodology

We have utilized the principle of steepest ascent-based Response Surface Methodology (RSM) for the parametric optimization [12]. By modelling the often-complex relationship that may exist between a multitude of input variables (X1, X2, … … ., Xn) and their corresponding response/decision-variable, Y, the RSM technique utilizes

a combined mathematical-statistical approach to efficiently compute the optimal values for the input variables. As such, the generic equation describing the mathematical model between the input and output variables is expressed using Equation (1): Y = f(X 1 , X 2 , …… ., X n + ε er )

Where f is output response and εer is the error computed when the model is computed. The corresponding 2nd-order regression model is described by Equation (2) [12] and shown below.

Table 2. Equations dependent on mass, energy, and concentration conservation Components

Equations based on conservation of mass, concentration, and energy

m1 + m15 = m 4 m 4 X 4 = m15 X15 Qabs = m1h 3 + m15 h17 - m 4 h 4 C pw = 4.187 kJ/kg-K Qabs = m 24 C pw (T25 - T24 )

m 8 + m11 = m 4 Q hpg = m11h11 + m 8 h 8 − m 4 h 7 Q hpg = m18 C pw (T18 − T19 )

Q lpg = m11 ( h11 − h12 ) + m8 h10 − m15 h15 − m14 h14 Condenser

m1 = m11 + m14 Q c = m14 h14 + m11h13 − m1h1 Q c = m 20 C pw (T21 − T20 )

Table 3. Mathematical expressions based on the second law of analysis Mathematical Expressions

  T  Iabs = To  (m 4 s 4 − m15 s17 − m 3 s 3 ) + m 24 C pw ln  25    T24   

 T   T  Ishx1 = To  m15 C pw ln  16  + m 4 C pw ln  6    T15   T5   

 T   T  Ishx2 = To  m 8 C pw ln  9  + m 4 C pw ln  7    T8   T6   

  T  Ihpg = To  ( −m 4 s7 + m8 s8 + m11s11 ) + m14 C pw1 ln  19    T18   

  T  Icond = To  ( −m 4 s14 − m11s13 + m1s1 ) + m20 C pw ln  21    T20   

  T  Ievap = To  m1 (s3 − s2 ) + m 22 C pw ln  23    T22    Iexp = To (m1 ∗ (s2 − s1 ))

I = tot Ein Itot = Iabs + Ishx1 + Ishx2 + Ihpg + Iexp + Ilpg + Icond + Ievap  T  Einn =  1 − o  Q hpg  Tavg  Tavg = Thpg + 273

Y = β0 + ∑ i =1 βi Xi + ∑ i =1 βii Xi2 + ∑ i < j βij Xi X j n

Where β0, βi, βii and βij are the interception, linear, quadratic and interaction coefficients, respectively.

Therefore, there are five decision variables and one response variable. For Five decision variables with three levels, the chosen OA design is L27, given in Table 4 [16,17].

Analysis Of Data

In the present work, the second law efficiency is the chosen response variable while high-pressure generator temperature, low-pressure generator temperature, absorber temperature, Condenser temperature, and evaporator temperature are chosen as decision variables.

The data given in Table 5 were analyzed by the RSM module of Minitab 18.1 [18]. This software determines the coefficients of the second-order polynomial Equation (2). Moreover, it provides the contour plots as well as threedimensional surface plots of the model. In addition to

RSM, analysis of variance (ANOVA) is used to check the adequacy of the model.

Table 6. Model validation Sr. Component Quantity Present Reference Percentage No Work [19] Error 1

Result And Discussion

Model Validation The present thermodynamic Model of the proposed system has been validated with the work done by reference [19] under the same input conditions and working fluid. The results of the validation are presented in Table 6.

Analysis And Interpretation Of The Model

ANOVA, a collection of models and procedures, analyses, and estimates various parameters such as probability

plot (nP plot), p-values, F-values, and coefficient of determination to identify the model’s suitability. The validity of ANOVA is governed by the normal probability plot which investigates the residuals. It is worth mentioning that residuals for the response variable of VARS follow a normal distribution. P-values (Table 5) help in identifying the significant effect of decision variables on the output parameters. The effect on the output parameter is said to be significant if the p-value is less than 0.05. These values also estimate the effect of interactions on output variables.

The second-order polynomial Equation (2) can be transformed into a mathematical model that is developed through fitting response data and is given in Equation (3). The least-square methodology, a multi-regression technique, helps in generating this mathematical model. The following terms cannot be estimated and were removed: Tc*Ta, Tc*Tlpg, Tc*Thpg, Ta*Tlpg, Ta*Thpg, Tlpg*Thpg. Regression Equation (3) in uncoded units is given as follows: Second law efficiency = 0.504 − 0.00161 Tc − 0.01101 Ta + 0.00071 Tlpg + 0.01234 Thpg + 0.01532 Te − 0.000054 Tc2 + 0.000067 Ta 2 + 0.000022 Tlpg 2 − 0.000045 Thpg 2 − 0.000321 Te2

+ 0.000441 TcTe + 0.000362 TaTe − 0.000387 TlpgTe − 0.000010 ThpgTe The significance of the model defined by the above Equation (3) can be determined by F-value which governs its statistical significance along with the decision variables and their interactions. The effect of the decision variable on the output parameter is significant if the F-value is high. From Table 5 it is noted that the maximum F value is 2049.43 for absorber temperature and the minimum F value is 495.32 for high-pressure generator. It means that the second law of efficiency is mostly affected by absorber temperature and least affected by high-pressure generator temperature. The R2 value for the present model is 99.8% that again confirms the validity of the results of ANOVA determined above.

GRAPHICAL RESULTS: CONTOUR PLOTS • Contour plots or response surface plots are graphical 2D representations that show the effect of decision variables on the response variable. The following section highlights the inferences drawn from the contour plots on the second law efficiency. Contour Plot of Second Law Efficiency vs TA, TC Figure 5 is the contour plot of second law efficiency for decision variable Tc on the X-axis and Ta on the Y-axis. The area under the dark green color in the plot represents the highest second law efficiency value which is more than 0.18 observed at a low value of Ta and Tc. Conversely, the minimum value which is less than 0.14 is achieved at a high condenser and absorber temperature. Contour Plot of Second Law Efficiency vs TLPG, TC Figure 6 is the contour plot of second law efficiency for decision variable Tc on the X-axis and Tlpg on the Y-axis. The area under the dark green color represents the maximum second law efficiency i.e. more than 0.18. This maximum efficiency is achieved at low Tc and high Tlpg. Conversely, the minimum second law of efficiency is less than 0.15 and is achieved at a high condenser temperature and low temperature of LPG. The significance of this contour plot is that condenser temperature depends upon environmental conditions so, in summer i.e. higher Tc, the value of second law efficiency can be maintained by raising the low-pressure generator temperature. Contour Plot of Second Law Efficiency vs THPG, TC Figure 7 is the contour plot of second law efficiency for decision variables Tc and Thpg on the X-axis and Y-axis respectively. The maximum value is more than 0.175, which

Figure 6. Contour plot of second law efficiency vs Tlpg, Tc.

is represented by the area under a dark green color. This maximum efficiency is achieved at a lower value of Tc and Thpg. Conversely, at a higher condenser temperature and high-pressure generator, a minimum value is obtained i.e. less than 0.145. Contour Plot of Second Law Efficiency vs TE, TC Figure 8 is the contour plot of second law efficiency for decision variable Tc on the X-axis and Te on the Y-axis. In this contour plot, the area under the dark green color represents the second law efficiency at the maximum value that is more than 0.17. This maximum efficiency is achieved by taking a lower value of Tc and a higher value of Te. Conversely, the minimum value is obtained at a higher condenser temperature and lower temperature at Te which is less than 0.14. The significance of this contour plot is that

Figure 7. Contour plot of second law efficiency vs Thpg, Tc.

Figure 9. Contour plot of second law efficiency vs Tlpg, Ta.

for a particular evaporator temperature the system efficiency would be higher in the winter season as compared to summer. Contour Plot of Second Law Efficiency vs TLPG, TA Figure 9 is the contour plot for second law efficiency against the decision variable Ta and Tlpg on the X-axis and Y-axis respectively. As interpreted from the plot, the second law efficiency is maximum that is more than 0.18 which is shown by the area under dark green color. This maximum efficiency is achieved by taking a lower value of Ta and higher Temperature at LPG. Conversely, the second law efficiency is noted lowest (less than 0.15) at a higher absorber temperature and lower temperature at LPG. It also implies that for a fixed absorber temperature, the second law efficiency decrease as Tlpg decrease or at a fixed

Figure 10. Contour plot of second law efficiency vs Thpg, Ta.

value of Tlpg, the second law efficiency would be lower in summer as compared to winter. Contour Plot of Second Law Efficiency vs THPG, TA Figure 10 is the contour plot of second law efficiency for decision variables Ta and Thpg on the X-axis and Y-axis respectively. In this plot, the area under dark green color depicts second law efficiency with a maximum value that is more than 0.18. This maximum efficiency is achieved by taking a lower value of Ta and Thpg. Conversely, the minimum value is achieved at a higher absorber and high-pressure generator temperature. The minimum value represented is less than 0.15. From the figure, it is worth mentioning that area for maximum second law efficiency is insignificant as compared to other areas, and for absorber temperature greater than 36°C the second law efficiency would be up to 18% irrespective of the temperature of LPG. Contour Plot of Second Law Efficiency vs TE, TA Figure 11 is the contour plot of second law efficiency for decision variable Ta on the X-axis and Te on the Y-axis. It is visible in the graph that the second law efficiency is indicated by a peak as represented by the area under dark green color and which is more than 0.18. The area for maximum second law efficiency is quite insignificant. It means practically more than 18 % efficiency is not possible for given values of the decision variable. Contour Plot of Second Law Efficiency vs TE, TLPG Figure 12 is the contour plot of second law efficiency for decision variable Tlpg on the X-axis and Te on the Y-axis. In this contour plot, the area under the dark green color represents the highest value of second law efficiency that is more than 0.170. This maximum efficiency is achieved by taking a higher value of Te and Tlpg. Conversely, the

minimum value is obtained at a lower temperature at the evaporator and low-pressure generator. This value is less than 0.145. The iso-efficiency area can be obtained by reducing the temperature at LPG and simultaneously increasing the temperature of evaporator converse is also true.

CSB Analysis

For CSB analysis of a component, the decision variable of the component is varied for a particular range then irreversibility change of that component as well as irreversibility total of the system is computed in that range and then Change in the irreversibility of CSB =

Table 7. CSB analysis of evaporator Irreversibility Iabs (kW)

Figure 12. Contour plot of second law efficiency vs Te, Tlpg.

In our study F value of absorber temperature is = 2049.4, followed by condenser temperature (F value = 1596.4), and is least affected high-pressure generator temperature(F value = 495).This would further help in the design of the experiment. • In this study, the Iso-second law efficiency curve is plotted against decision variables. The study shows that second law efficiency decrease when Condenser Temperature increase but same value of second law efficiency can be maintained if the temperature of Low-pressure generator increase. Here Condenser Temperature strongly depends upon Coolant temperature which ultimately depends upon ambient temperature thus Condenser temperature is variable so this is the second law of efficiency but this variability can be nullified by altering the temperature of the low-pressure generator.

In the present analysis CSB analysis of evaporator is conducted. Here three values of evaporator temperature is considered namely Te = 6°C, Te = 8°C, Te = 10°C. The irreversibility of the evaporator, as well as the irreversibility total, is computed for the three mentioned values of the evaporator (refer to Table 7). Figure 13 shows irreversibility total on the Y-axis whereas Irreversibility in the evaporator is shown on the X-axis. Therefore, CSB =

The CSB < 1 means that the rate of irreversibility change in the evaporator is more than the rate of irreversibility change of the system. It implies that when evaporator temperature has increased the irreversibility in the evaporator decrease but the irreversibility of the other components except for the evaporator increase.

Conclusions

The present investigation involves RSM-based thermodynamic analysis of VARS which is run by the blowdown heat of a 210 MW thermal power plant situated at Badarpur. The research work yielded significant conclusions which are listed below. • The Heat recovered during blow-down operation can be used as a source of heat for the vapor absorption refrigeration system. In our study waste heat of blowdown water of 210 MW Thermal Power Station, Badarpur is considered. • The RSM method is used to identify the decision variable on which second law efficiency does depend. Higher the F value of the decision variable more strongly would affect second law efficiency

Nomenclature

Specific enthalpy (KJ/kg) Specific heat of Li-Br mixture Temperature (K) Coefficient of Performance Heat transfer (KW) Irreversibility (KW) Low-pressure generator Mass fraction of Li-Br Specific entropy (KJ/kg-K) Specific heat of the water

Greek Symbols Effectiveness of solution heat exchanger 1 ε1 η Efficiency Effectiveness of solution heat exchanger 2 ε2 Subscripts abs Absorber e Evaporator lpg Low-pressure generator c Condenser hpg High-pressure generator p Pump

Authorship Contributions

double effect water-LiBr absorption refrigeration system. Energy Convers. Manag 2016;108:468–477.

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

References

1. The article references can be accessed from the .pdf file.

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