Mathematical modeling and performance analysis of a solar assisted vapour absorption refrigeration system ’

. Climate change is the hottest topic today on earth. Traditional HVAC’s harm the environment and stand out to be a major contributor to global warming. One of the many techniques to mitigate the current climate crisis is by utilizing the abundantly available solar radiation. Solar evacuated tube collectors are used to absorb solar radiation. This solar power is used to provide solar cooling technologies. Unlike the conventional HVAC’s thermally driven absorption cooling is a boon in today’s era. In the follo wing research work, the study aims to provide numerical modeling of a solar assisted air-conditioning unit through the first law of thermodynamics using mass balancing equations for the province of Delhi in July. This research work’s aim is to build and ev aluate a Li-Br absorption cooler with a capacity of 1 KW. This paper aims to provide characteristic design features of components and measures the efficiency of the system at operating conditions. PCM based thermal energy storage tank is adopted which helps to supply cold air even at no sunlight hours. As a result of this research study, such solar assisted air conditioners turn out to be a chosen solution for sustainability.


Introduction
Greenhouse gas emissions are directly responsible for the rising temperatures worldwide. Heating, ventilation air conditioners have large energy acquisition and pose a negative impact on the local environment. They have raised tremendous concerns about the current climate threat as they are responsible for ozone depletion and global warming. Many organizations are searching for ways to fight climate change and resorting to sustainable alternatives. Reciprocating sorption chillers can be one method of limiting the usage of conventional systems and hence reducing reliance on fossil fuels. In the 1950s, numerous nations developed tiny sun absorption refrigeration systems. In the area of solar refrigeration employing solar collectors (flat plate), American Professor G.O.G.L. is well known for his contribution [1]. Sorption cooling includes both absorption and adsorption. Absorption machines do not require much of input power (shaft power) as they are thermally driven. In this way, absorption machines offer dependable and efficient cooling in areas with expensive or unreliable power sources, or in areas with access to waste, gas, geothermal, or solar heat. [2]. Traditional systems incorporate mechanical compression machines using electrical energy consumption whereas in absorption cooling thermal compression of refrigerant is employed. This area of research focuses discussion on an absorption system, which uses a refrigerant -absorbent pair that work together. The most commonly chosen working pairs are (1)'lithium bromide -water, where the former is the absorbent and the latter is the refrigerant. It is one of the widely used pairs for space airconditioning applications, (2)'ammonia -water, where the refrigerant is ammonia & absorbent being water, but the lower efficiency of NH3-H2O compared with LiBr-H2O restricts their use. NH3 is poisonous and is not fit for residential applications.
[3] performed a life cycle analysis to examine the viability of the proposed design. COP achieved is bit lower but the system is economically friendly as compared to conventional HVAC's. [4] examined the system through a computational simulation using MATLAB. It incorporates analysis through 1 st and 2 nd law of thermodynamics. Various trends between the COP & temperatures of generator, absorber, and condenser are presented. [5] studies an ammonia -water absorption system for analysis. C-program is developed to find the thermodynamic properties of each component. Effect of various key parameters (eg. concentration effect, change in pressure) on performance of the structure is examined with graphs. [6] study the integration of PCM's with HVAC's to reduce energy consumption leading to maximization of the system's performance. The study also involves the making of 2 different systems and their efficiency is investigated. [7] includes construction and parameter analysis for each component of solar air conditioner. COP is calculated for two different working temperatures of the generator. A small thermal storage tank is also incorporated.
The study's goal is to analyse a'LiBr-H2O'thermally driven absorption cooler which absorbs solar thermal energy using evacuated tube collectors. Practical problems that are faced by such an arrangement include crystallization, pressure drops & air leakage. To prevent crystallization to occur, the pressure of the condenser needs to be maintained at a particular value, irrespective of the temperature of the cooling water. This is achieved by monitoring the cooling water flow rate moving towards the condenser. Sometimes, addition of additives takes place to inhibit crystallization [1]. This paper reports design characteristics of different components of the system and presents a thermodynamic energy analysis of the vapour absorption refrigeration system under varied working conditions.

Geography description
The thermally powered solar absorption air-conditioning unit is planned and implemented for the province of Delhi, India. The site is located at 28.6° north latitude and 77.2° east longitude. In this area the average incident solar radiation is approximately 0.5 KWh/m2/day. In Delhi, for the month of July average ambient air temperature is 35℃ and humidity is 50% for the same. Under the current climatic conditions space air conditioning is required for human comfort.
The solar air conditioning system mainly comprises of evacuated tube solar collectors, a PCM thermal-storage unit & a vapor-absorption machine. The system's design and layout is depicted in Fig. 1. One of the crucial elements of a solar assisted air conditioning system, the solar collector, transforms the solar energy into thermal energy which further helps to drive the absorption chiller [8]. Evacuated tube collectors are used to absorb heat from sun's radiation. The heat transfer fluid incorporated for the solar system array is water because of a large value of thermal conductivity and heat capacity. Solar thermal energy then converts into heat output by the ETC collectors, which then uses that heat to warm water passing through them. In order to lessen losses from convection and re-radiation, the ETC collector is vacuumed [9]. The ETC collectors are placed under the sunlight to reach a temperature of 100℃. Once the given temperature is reached, the cycle starts. The amount of heat absorbed does not equal the actual heat that is transmitted to the heat transfer liquid because of the energy losses associated with the heat-transfer from the absorbent to the tubes.
Heat acquired by the solar collector is the useful heat required as an input to the generator in the absorption cycle. The following assumptions are adopted for the solar cycle system: • Ambient temperature of the environment is 35℃ and the pressure is 1 atm.
• A temperature difference of about 20℃ is considered between the collector and the generator because of the losses that will take place. • Area of each evacuated tube is 0.03 m 2 .
• Efficiency of ETC is 0.70.
• Inlet heating water temperature to the generator is 92℃.
• Outlet temperature of water from generator is 88℃. To find dimensions of the solar collector the following approach is used. The required area for the solar collector per cooling capacity is given as [10]: 1) Incident solar radiation for Delhi (G) = 0.5 KWh/m 2 /day 2) Efficiency of solar collector (η) = 0.7 or 70% 3) Chiller COP = 0.76 or 76% For 1KW absorption chiller, 3.75 m 2 coverage of area of the evacuated tubes is required. Area of each evacuated tube is 0.03 m 2 . ∴ 3.75 ÷ 0.03 = 125"evacuated tubes are required.

PCM storage
PCMs are materials that are ideal for energy transfer and conservation purposes as they are able to absorb, store, and emit a significant quantity of heat energy at fairly consistent temperatures [11], [12]. These are integrated to enhance the operational efficiency of solar assisted air conditioners. A thermal energy storage system is installed between ETC and the vapour absorption system to stock the thermal energy with the aid of PCMs. The primary elements of this unit are a solar collector & a storage tank. A cylindrical vessel which is filled with a dense bed of PCM spheres, serves as the storage unit [13]. Heat transfer during charging & discharging process takes place b/w the PCM and the heat-transfer fluid. Direct cooling occurs in the morning and early afternoon. The excess energy is utilized to create and stock up cooling energy in PCM once the specified temperature is reached and there is enough radiation of sun. The PCM storage is discharged in the night [14].
The heat gained by the heat-transfer fluid in the solar cycle is further utilized by the system's absorption unit for the purpose of cooling. In the generator, high temperature heat transfer fluid transfers its heat to the working pair, LiBr-H2O solution which is pumped from the absorber. Hence, heat gain takes place in the generator. Water (refrigerant) evaporates from solution and this high pressure super-heated steam moves further to the condenser whereas the remaining strong solution with high percentage of Li-Br moves towards the absorber with the help of a solution heat exchanger. Inside the condenser, heat rejection takes place and the refrigerant changes to a high pressure saturated liquid. Pressure decreases as the saturated liquid moves through the expansion valve. Then it further enters the evaporator, where evaporation occurs and cooling takes place. Low pressure saturated-vapour exits through the evaporator, moves and enters the absorber where the solution present absorbs it. The heat gathered in the evaporator is released when the refrigerant vapour gets absorbed and is condensed from vapour to a liquid state. The heat generated by the condensation of vapour of the refrigerant, caused due to the absorption in mixture, is carried away through the cooling water as it moves along the bundle of absorber tubes. The weak absorbent mixture is then pushed towards the generator to drive off the refrigerant by heating it up [15].   Table 1 describes the operating conditions and temperatures of components that are adopted for carrying out the thermodynamic analysis.

{heat rejected} 8) Refrigerant Expansion Valve
Since there is no loss. ̇8 =̇9 and 8 = 9 ∴ ℎ 8 = ℎ 9 The COP for the absorption system is described through the following relation:

Design of the generator heat-exchanger
Latent-heat of'vaporization and sensible heat is obtained as an output when heat is fed into the generator. Experiments reveal that for such systems, the value obtained for heat-transfer coefficient, U ranges between 1600'-7500 W/m 2 -℃. To evaluate the efficiency of a HX, the value of ( . ) is used to represent the best heat transfer rate.
Employing single pass heat exchanger, the temperature b/w hot & cold fluid doesn't remain constant and varies with the distance along the heat-exchanger. For a HX that has two ends at which hot and cold streams enter or exit on either side, the logarithmic mean temperature difference is: Heat transfer is given by: = . .

Results
Results for the above research are tabulated in Table 2 for thermally driven water -libr absorption cooling system. Results for the above research are tabulated in Table 2 for thermally driven water -libr absorption cooling system. At each point h, P and T are specified along with the description of each part present in the absorption system. The COP evaluates the air-conditioner capacity. COP based on generator temperature = 75℃ is calculated to be equal to 0.76.  It is noticed clearly that, as a rise occurs in the generator temperature, the value of coefficient of performance (COP) also increases. This implies that the system's performance is enhanced as the temperature of the generator rises. With Li-Br, the maximum attainable temperature is 100℃ as above that crystallization may take place. Fig. 4 and fig. 5 shows that the system's COP decreases with a rise in the temperature of the absorber and condenser respectively. So, the system performance & the absorption reaction is improved by reducing the absorber temperature, this statement is explained through the fact that since water absorption by Li-Br is a chemical reaction therefore it requires to be cooled down for achieving an improved performance. To achieve a better condensation rate in the condenser, the water vapour ought to be cooled down which is done using cooling towers or through the phenomena of natural air cooling. Since, water -    libr pair is considered for analysis hence, for cooling purposes water will be a better choice than the other because of the problem of crystallization that may occur [16]. Fig. 6, tells that the COP is increased as heat-exchanger effectiveness increases. The amount of energy required for the overall process is reduced before moving into the generator as the HX aids in increasing the strong solution temperature. An improvement in the COP is noticed, with the increase in the heat-exchanger effectiveness and a reduction in the energy requirement of the generator [16].

Conclusions
In this analysis, a mathematical model is articulated by applying the 1 st law of thermodynamics to a vapour absorption refrigeration system. This thermally driven solar absorption air conditioning unit is planned and implemented for the province of Delhi, India. The system is integrated with evacuated tube collectors which absorbs sun's radiation and then transforms it into heat output, which warms the water that is passing through the collectors. A well-defined approach is used to find the dimensions of the collector. Area for each of the collector is calculated to be 3.75 m 2 . A thermal energy storage unit is incorporated to increase the system's operational efficiency. Numerical modeling of the absorption unit is accomplished with the help of energy calculations for each component of the system, at each of the points from thermodynamic characteristics of the working fluid at the given working parameters. The COP evaluates the capacity of the air conditioner and is calculated to be 0.76. Design for the generator heat exchanger is proposed. The value obtained for the coefficient of heat-transfer for heat exchanger is calculated through the LMTD method and the obtained value lies between the mentioned range.
From the results and discussion using appropriate graphical methods it is discovered that the cycle's COP increases as the generator's working temperature rises, indicating an improvement in efficiency and performance. While the COP value is decreased with a rise in temperatures of absorber and condenser. From the graph, it is observed that an increase in the heat exchanger effectiveness occurs with a decrease in the energy needed in the generator which further leads to an improvement in the performance of the system. Additionally, it has been found that raising the generator temperature improves the vapour absorption cycle's COP but, this increase in temperature negatively impacts the system's efficiency and performance. Thus, a special attention must be given to this dominant reverse effect. Finally, this research leads the way to an improved thermal system. Hence, this methodology can be used and applied to a similar suitable system which will be economical and sustainable.