A new approach based on artificial intelligence is proposed here for the exergy assessment of solar adsorption refrigeration system working with activated carbon-methanol pair. Artificial neural network model is used for the prediction of exergy destruction and exergy efficiency of each component of the system. Pressure, temperature and solar insolation are used as input variables for developing the artificial neural network model. The back propagation algorithm with three different variants such as CGP, SCG and LM are used in the network A and network B. The most suitable algorithm and the number of neurons in hidden layer are found as LM with 9 for network A and SCG with 17 for the Network B. The artificial neural network predicted results are compared with the calculated values of exergy destruction and exergy efficiency. The
The conventional refrigeration systems require mechanical energy as the driving source and are responsible for the emission of CO2 and the other greenhouse gases such as CFCs and HFCs which are considered major cause for ozone layer depletion. From this context the adsorption refrigeration system attains a considerable attention in 1970s due to the energy crisis and ecological problems related to the use of CFCs and HFCs. Research has proved that the adsorption refrigeration technology has a promising potential for competing with the conventional vapour compression refrigeration systems. In comparison with the vapour compression refrigeration systems, adsorption refrigeration systems have the benefits of energy savings if powered by waste heat or solar energy, like simpler control, absence of vibration, and low-operation cost.
The major attraction of solar adsorption refrigeration is that its working fluids satisfy the Montreal protocol on ozone layer depletion and the Kyoto protocol on global warming [
Nowadays a more generic approach based on the second law is used for the analysis of thermal energy systems. The conventional energy analysis does not give the qualitative assessment of the various losses occurring in the system components [
The thermodynamic analyses of adsorption systems are complex because of the complex differential equations involved. Instead of solving complex differential equations and applying the limited number of experimental data, faster and simpler solutions can be obtained by using artificial neural network. ANNs are able to learn the key information patterns within multidimensional information domain. The use of ANN for the performance prediction and simulation of complex system has increasingly become popular in the last few years.
The application of artificial neural network for the exergy performance prediction of solar adsorption refrigeration system working at different conditions is necessary nowadays for making the analysis simple. Many earlier studies have reported the application of artificial neural network for the performance predictions of vapour compression refrigeration systems such as for direct expansion heat pump [
Recently some works about the use of ANN in energy systems have been published [
The solar-assisted adsorption refrigeration system consists of a parabolic solar concentrator, water tank, adsorbent bed, condenser, expansion device (capillary tube), and an evaporator as shown in Figure
Specifications of the main components of solar adsorption refrigeration system.
Component | Technical specifications |
---|---|
Condenser | Type: shell and coil |
Capacity: 200 W | |
Water cooled | |
Evaporator | Type: shell and coil |
Material: copper | |
Capacity: 150 W | |
Expansion device | Capillary tube |
Adsorbent bed | Type: rectangular |
Material: stainless steel | |
Parabolic solar concentrator | Solar concentrator of area 3 m2 made of stainless steel |
Adsorbent | Activated carbon |
Adsorbate | Methanol |
Schematic of solar adsorption refrigeration system.
Photographic view of the system.
Water gets heated starting from morning while flowing through the solar concentrator by natural circulation. When the hot water is circulated around the adsorbent bed, the temperature in the adsorbent bed increases. This causes the vapour pressure of the adsorbed refrigerant to reach up to the condensing pressure. The desorbed vapour is liquefied in the condenser. The high-pressure liquid refrigerant is expanded through the expansion device to the evaporator pressure. The low-pressure liquid refrigerant then enters the evaporator where it evaporates by absorbing the latent heat of evaporation. In the evening, the hot water from the tank should be drained off and is refilled with cold water. The temperature of the adsorbent bed reduces rapidly and the pressure in the adsorber drops below the evaporator pressure.
The experiments are carried out keeping the evaporator temperature constant. The same procedure is repeated for the different evaporator loads.
A digital pyranometer with an accuracy of ±5 W/m2 is placed near the solar collector to measure the instantaneous solar insolation. Pressure is measured during heating (desorption) of refrigerant, that is, condensing pressure and during cooling (adsorption), that is, evaporator pressure. The pressure gauges are fixed at the adsorbent bed in order to measure the pressure inside the adsorbent bed at each stages of adsorption and desorption processes. The temperature at various points in the solar adsorption refrigeration system is measured by calibrated T-type (Copper – Constantan) thermocouples. The various temperatures observed are (1) temperature of the adsorbent bed during various processes, (2) temperature of the refrigerant at inlet and outlet of the condenser, expansion device exit, and evaporator outlet, (3) temperature of water entering the water tanks, and (4) temperature of chilled water in the evaporator box.
Uncertainties in the experiments can arise from the selection, condition, and calibration of the instruments, environment, observation, and test planning. A more precise method of estimating uncertainty has been presented by Holman [
The total uncertainties of the various calculated parameters are shown in Table
Uncertainty in different parameters.
Components | Total uncertainty (%) | |
---|---|---|
Exergy destruction | Exergy efficiency | |
Condenser | ±7.6 | ±5.87 |
Expansion device | ±7.3 | ±8.2 |
Evaporator | ±2.68 | ±2.42 |
Adsorbent bed | ±3.57 | ±6.72 |
Solar concentrator | ± 4.67 | ±7.1 |
The total uncertainty arising due to independent variables is given by
The result
The second law of thermodynamics facilitates the assessment of maximum amount of achievable work in a given system with different energy sources. Exergy is the available energy for conversion from an energy source with a reference environmental condition. Therefore exergy represents the thermodynamic quality of an energy carrier. Exergy is an expression used for accounting the loss of available energy due to the entropy generation in the irreversible system or process.
The general exergy balance equation can be written as.
The exergy balance equation in rate form can be written as
The gaseous refrigerant behaves as an ideal gas. Pressure is assumed to be uniform inside the adsorbent bed. The mass transfer inside the adsorbent bed occurs only in the vapour phase. Potential, kinetic, and chemical effects are neglected. Mass flow rate of the refrigerant is assumed as constant. The adsorbent bed consists of uniform size particles; hence the bed porosity is a constant. All the processes are at steady state. The process in the expansion device is assumed to be isenthalpic. Losses in the ducts and valves are neglected.
The specific exergy (ex in kJ/kg) of various components of solar adsorption refrigeration system is calculated by using (
Exergy balance of the different components of solar adsorption refrigeration system.
Component | Exergy received |
Exergy delivered |
Irreversibility (exergy loss) |
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Condenser |
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Expansion device |
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Evaporator |
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Adsorbent bed |
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Solar collector |
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The exergy destruction of overall system is determined as
An artificial neural network tries to recognize an approximate pattern between the inputs and their desired outputs by imitating their brain functions. Their ability of learning by examples makes the ANN more flexible and powerful than the parametric approaches. An ANN compromises interconnected groups of artificial neurons and their respective weight-building blocks. The behavior of the network is largely dependend upon the interaction between these building blocks which are used in training the network in order to perform a particular function. Each neuron accepts a weighted set of inputs and responds with an output or activation function, which can be tangent sigmoid or log-sig function.
A typical ANN consists of the three layers, an input layer, a hidden layer made up of artificial neurons that transform the inputs, and an output layer that stores the results. ANNs are trained to get a specific target output from a particular input using a suitable learning method. Therefore the error between the desired output, and output of the network should be reduced by modifying the weights and biases.
In this study, a back propagation algorithm has been used in feed-forward, single hidden layer network. The ANN model was developed for SAR system with three neurons in the input layer (temperature, pressure, and solar insolation) and six neurons in the output layer (exergy destruction and exergy efficiency of condenser, expansion device, evaporator, adsorbent bed, solar concentrator, and overall system). The architecture of network selected in this work with names of input and output variables are shown in Figures
Network architecture for predicting exergy destruction (network A).
Network architecture for predicting exergy efficiency (network B).
The variants employed in the study are LM, SCG, and CGP. The inputs and outputs are normalized between 0 and 1. Logistic sigmoid (log-sig) transfer function is being used in ANN.
The transfer function used is given by
The neural network tool box in the MATLAB (Version 7.8) is used for ANN modeling of SAR system. The back propagation algorithm optimizes the weight connection by allowing the error to spread from output layers towards the lower layers. The performance of ANN prediction is evaluated by regression analysis between the ANN outputs and experimental values. The criteria used for evaluating the network performance are, correlation coefficient (
In the training, an increased number of neurons from 5 to 10 and from 12 to 18 are used for the networks A and B, respectively. During each step, the performance of network is checked with statistical performance parameters. The statistical performance of networks with different configurations (changing the number of neurons and training function) is shown in Tables
Statistical performance of the different algorithms evaluated for network A (exergy destruction).
Algorithm | Neurons in hidden layer |
|
RMS | COV |
---|---|---|---|---|
LM | 8 | 0.99981 | 0.057 | 0.43 |
LM | 9 | 0.99993 | 0.048 | 0.109 |
LM | 10 | 0.99991 | 0.069 | 0.189 |
SCG | 8 | 0.97941 | 0.098 | 0.476 |
SCG | 9 | 0.98302 | 0.087 | 0.390 |
SCG | 10 | 0.96276 | 0.19 | 0.204 |
CGP | 8 | 0.9869 | 0.0205 | 0.198 |
CGP | 9 | 0.96478 | 0.501 | 0.169 |
CGP | 10 | 0.97916 | 0.023 | 0.183 |
Statistical performance of different algorithms evaluated for network B (exergy efficiency).
Algorithm | Neurons in hidden layer |
|
RMS | COV |
---|---|---|---|---|
LM | 16 | 0.99847 | 0.0504 | 0.714 |
LM | 17 | 0.9980 | 0.042 | 0.684 |
LM | 18 | 0.99089 | 0.0596 | 0.78 |
SCG | 16 | 0.99968 | 0.099 | 0.196 |
SCG | 17 | 0.99980 | 0.051 | 0.176 |
SCG | 18 | 0.99969 | 0.0695 | 0.24 |
CGP | 16 | 0.9689 | 0.0805 | 0.95 |
CGP | 17 | 0.9849 | 0.078 | 0.905 |
CGP | 18 | 0.98914 | 0.058 | 0.802 |
During the training it is found that not all ANN configurations would produce the converged results. Among the converged results the configuration LM-9 and SCG-17 are found to be the most optimal for network A and network B, respectively. The drops in mean square (MSE) with the number of epochs during training, testing, and validation process are shown in Figures
Statistical performance of the network A (exergy destruction).
Component | Algorithm LM-9 | Mean % | ||
---|---|---|---|---|
|
RMS | COV | deviation | |
Condenser | 0.9857 | 0.001269 | 0.2742 | 2.375 |
Expansion device | 0.9843 | 0.003152 | 0.001075 | −2.58 |
Evaporator | 0.9928 | 0.0008298 | 0.2309 | −1.41 |
Adsorbent bed | 0.9971 | 0.001162 | 0.1614 | 0.96 |
Solar concentrator | 0.9867 | 0.007812 | 0.0629 | 0.59 |
Overall system | 0.9908 | 0.0178 | 0.0348 | −0.75 |
Statistical performance of the network B (exergy efficiency).
Component | Algorithm SCG-17 | Mean % | ||
---|---|---|---|---|
|
RMS | COV | deviation | |
Condenser | 0.9973 | 0.0073 | 0.020 | 0.975 |
Expansion device | 0.9846 | 0.00546 | 0.105 | −0.78 |
Evaporator | 0.9981 | 0.00534 | 0.14 | −1.51 |
Adsorbent bed | 0.9996 | 0.000526 | 0.549 | −0.45 |
Solar concentrator | 0.9945 | 0.002743 | 0.357 | 2.78 |
Overall system | 0.9803 | 0.002869 | 0.44 | −1.079 |
Mean square error plot for the LM-9 configuration.
Mean square error plot for SCG-17 configuration.
These results confirmed that the ANN predicted values are close to the experimental results with a maximum correlation coefficient for all the predictions (exergy destructions and exergy efficiency of condenser, expansion device, evaporator, adsorbent bed, solar concentrator, and overall system). The other statistical parameters such as RMS and COV values are found to be low.
The ANN predicted and experimental values of exergy destruction and exergy efficiency of condenser with heat source temperature are shown in Figures
Variation of exergy destruction with heat source temperature (condenser).
Variation of exergy efficiency of with heat source temperature (condenser).
The ANN predictions yield a correlation coefficient of 0.9857, RMS and COV values of 0.001269 and 0.2742, respectively, for exergy destruction, and 0.9973, 0.0073, and 0.20, respectively, for exergy efficiency. The comparison shows that the ANN predicted values are closer to calculated results.
The variation of the ANN predicted and experimental values of exergy destruction and exergy efficiency of expansion device with the heat source temperature is shown in Figures
Variation of exergy destruction with heat source temperature (expansion device).
Variation of exergy efficiency of with heat source temperature (expansion device).
The ANN predicted and experimental values of exergy destruction and exergy efficiency of evaporator are depicted in Figures
Variation of exergy destruction with heat source temperature (evaporator).
Variation of exergy efficiency with heat source temperature (evaporator).
The ANN predictions yield correlation coefficients of 0.9928 and 0.9981 for exergy destruction and exergy efficiency, respectively. The RMS and COV values for each case are found to be 0.0008298, 0.2309 and 0.00534, 0.14, respectively.
The ANN predicted and experimental values of exergy destruction and exergy efficiency of adsorbent bed with heat source temperature are shown in Figures
Variation of exergy destruction with heat source temperature (adsorbent bed).
Variation of exergy efficiency with heat source temperature (adsorbent bed).
The comparison of ANN predicted and experimental results of exergy destruction and exergy efficiency of solar collector with heat source temperature are depicted in Figures
Variation of exergy destruction with heat source temperature (solar concentrator).
Variation of exergy efficiency with heat source temperature (solar concentrator).
The comparison between the ANN predictions and estimated values of exergy destruction and exergy efficiency yields a correlation coefficients of 0.9867 and 0.9945, respectively. The RMS and COV values are 0.007812, 0.0629 and 0.002743, 0.357, respectively.
The comparison between the ANN predicted and experimental results of system exergy destruction and exergy efficiency of SAR are depicted in Figures
Variation of exergy destruction with heat source temperature (overall system).
Variation of exergy efficiency with heat source temperature (overall system).
The comparison between the ANN predictions and experimental values of exergy destruction and exergy efficiency yields correlation coefficients of 0.9908 and 0.9803, respectively. The RMS and COV values are 0.0178, 0.0348 and 0.002869, 0.44, respectively.
The exergy assessment of solar adsorption refrigeration system by using artificial neural network is carried out. The energy and exergy balance equations have been derived using the first and second law of thermodynamics. The exergy loss and exergetic efficiency of each component of the system have also been estimated. In order to gather the data for training and testing the proposed ANN, an experimental system has been set up and tested for its performance at different evaporator loads.
The following conclusions are made from the present work. The exergy destruction and exergy efficiency of each component of solar adsorption refrigeration system has been calculated. The exergy destruction associated with the adsorbent bed is found to be on higher side and it increases with increase in heat source temperature. The operational parameters and material properties of the adsorbent bed should be optimized to reduce the exergy destruction and hence to improve the exergy efficiency. System exergy destruction is found to be increasing with the increase in heat source temperature, whereas the exergy efficiency of the system is found to first increase, reach a maximum, and then decrease. The optimum operating point of the system is at heat source temperature of 72.4°C. Using the three different parameters, namely, temperature, pressure, and solar insolation, an ANN model based on the back propagation algorithm is proposed for predicting the exergy destruction and exergy efficiency of each component of the solar adsorption refrigeration system. The performance of ANN predictions is measured using the three criteria root mean square error, correlation coefficient, and coefficient of variance. The network model demonstrated good results with correlation coefficients in the range of 0.9843 to 0.9971 and 0.9803 to 0.9996 for exergy destruction and exergy efficiency, respectively. The mean percentage of error from 0.59% to 2.375% and 0.45% to 2.78% for network A and network B, respectively. The mean percentage of error in all cases is found to be within ±5%. The comparison of results suggests that the artificial neural network provided results are within the acceptable range. This study reveals that the ANN modelling can be effectively employed for the exergy assessment of solar adsorption refrigeration system with high degree of accuracy.