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

The present work investigates the thermodynamic optimality of a double-effect vapor absorption refrigeration system (VARS) driven by blowdown heat of a 210 MW thermal power plant at Badarpur using response surface methodology (RSM). RSM helps to develop a relation amongst the decision variables and the second law efficiency via second-order nonlinear polynomial regression equation. In addition, the analysis of variance technique (ANOVA) is applied to identify the decision variables having a significant effect on the system’s thermal performance. Moreover, coefficient of structural bond (CSB) analysis of the evaporator is carried out. The decision variables are the temperatures of the high-pressure generator, low-pressure generator, condenser, absorber, and evaporator. Results conclude that the second law efficiency is affected significantly by absorber temperature (F value = 2049.4), followed by condenser temperature (F value = 1596.4), and is least affected by high-pressure generator temperature (F value = 495). CSB value of the Evaporator is 0.5851.


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 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-H 2 O 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-H 2 O 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 EF-FECT 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.• 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 (X 1 , X 2 , … … ., X n ) 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): Where f is output response and ε er is the error computed when the model is computed.The corresponding 2 nd -order regression model is described by Equation ( 2) [12] and shown below.
Where β 0 , β i , β ii and β ij are the interception, linear, quadratic and interaction coefficients, respectively.

ORTHOGONAL ARRAY (OA)
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.
Therefore, there are five decision variables and one response variable.For Five decision variables with three levels, the chosen OA design is L 27 , given in Table 4 [16,17].

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

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 various parameters such as probability  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.
Regression Equation ( 3) in uncoded units is given as follows: Second law efficiency 0.  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 R 2 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 T A , T C
Figure 5 is the contour plot of second law efficiency for decision variable T c on the X-axis and T a 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 T a and T c .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 T LPG , T C
Figure 6 is the contour plot of second law efficiency for decision variable T c on the X-axis and T lpg 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 T c and high T lpg .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 T c , the value of second law efficiency can be maintained by raising the low-pressure generator temperature.

Contour Plot of Second Law Efficiency vs T HPG , T C
Figure 7 is the contour plot of second law efficiency for decision variables T c and T hpg on the X-axis and Y-axis respectively.The maximum value is more than 0.175, which is represented by the area under a dark green color.This maximum efficiency is achieved at a lower value of T c and T hpg .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 T E , T C
Figure 8 is the contour plot of second law efficiency for decision variable T c on the X-axis and T e 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 T c and a higher value of T e .Conversely, the minimum value is obtained at a higher condenser temperature and lower temperature at T e which is less than 0.14.The significance of this contour plot is that 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 T LPG , T A
Figure 9 is the contour plot for second law efficiency against the decision variable T a and T lpg 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 T a 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 T lpg decrease or at a fixed  value of T lpg , the second law efficiency would be lower in summer as compared to winter.

Contour Plot of Second Law Efficiency vs T HPG , T A
Figure 10 is the contour plot of second law efficiency for decision variables T a and T hpg 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 T a and T hpg .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 T E , T A
Figure 11 is the contour plot of second law efficiency for decision variable T a on the X-axis and T e 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 T E , T LPG
Figure 12 is the contour plot of second law efficiency for decision variable T lpg on the X-axis and T e 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 T e and T lpg .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 CSB Change in the irreversibility of that particular compo = n nent Change in irreversibility total of the system (4)  In the present analysis CSB analysis of evaporator is conducted.Here three values of evaporator temperature is considered namely T e = 6°C, T e = 8°C, T e = 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 dy dx = =0 5851 .
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 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.

AUTHORSHIP CONTRIBUTIONS
Authors equally contributed to this work.

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

Figure 2 .Figure 3 .
Figure 2. State points vs specific entropy and mass flow rate.Figure 3. State points vs temperature and pressure.

Figure 4 .C
State points vs specific enthalpy.Table 2. Equations dependent on mass, energy, and concentration conservation Components Equations based on conservation of mass, concentration, and energy Absorber m m m m X = m X Q = m h + m h -m h

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

Figure 5 .
Figure 5. Contour plot of second law efficiency vs T a , T c . Figure 6.Contour plot of second law efficiency vs T lpg , T c .

Figure 6 .
Figure 5. Contour plot of second law efficiency vs T a , T c . Figure 6.Contour plot of second law efficiency vs T lpg , T c .

Figure 7 .
Figure 7. Contour plot of second law efficiency vs T hpg , T c . Figure 8. Contour plot of second law efficiency vs T e , T c .

Figure 9 .Figure 10 .
Figure 9. Contour plot of second law efficiency vs T lpg , T a .Figure 10.Contour plot of second law efficiency vs T hpg , T a .

Figure 11 .Figure 12 .
Figure 11.Contour plot of second law efficiency vs T e , T a .Figure 12.Contour plot of second law efficiency vs T e , T lpg .

Figure 13 .
Figure 13.CSB analysis of the evaporator.

Table 1 .
Data used as input for simulation Sr. No. Description (Abbreviation) Value(s)1 Ambient temperature (T o ) 25

Table 5 .
Analysis of Variance

Table 6 .
Model validation

Table 7 .
CSB analysis of evaporator • 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.