蒸发冷

Artificial neural network analysis of a refrigeration systemwith an evaporative condenserH.M.Ertunc a ,M.Hosozb,*aDepartment of Mechatronics Engineering,Kocaeli University,41040Kocaeli,Turkey bDepartment of Mechanical Education,Kocaeli University,41380Kocaeli,TurkeyReceived 14December 2004;accepted 7June 2005Available online 3August 2005AbstractThis paper describes an application of artificial neural networks (ANNs)to predict the performance of a refrigeration system with an evaporative condenser.In order to gather data for training and testing the proposed ANN,an experimental refrigeration system with an evaporative condenser was set up.Then,steady-state test runs were conducted varying the evaporator load,air and water flow rates passing through the condenser and both dry and wet bulb temperatures of the air stream entering the condenser.Utilizing some of the experimental data,an ANN model for the system based on standard backpropagation algorithm was devel-oped.The ANN was used for predicting various performance parameters of the system,namely the condenser heat rejection rate,refrigerant mass flow rate,compressor power,electric power input to the compressor motor and the coefficient of performance.The ANN predictions usually agree well with the experimental values with correlation coefficients in the range of 0.933–1.000,mean rel-ative errors in the range of 1.90–4.18%and very low root mean square errors.Results show that refrigeration systems,even complex ones involving concurrent heat and mass transfer such as systems with an evaporative condenser,can alternatively be modelled using ANNs within a high degree of accuracy.Ó2005Elsevier Ltd.All rights reserved.Keywords:Artificial neural network;Refrigeration;Evaporative condenser1.IntroductionThe vapour-compression refrigeration system em-ploys a condenser to reject the heat absorbed by the refrigerant in the evaporator.Depending on the type of the cooling medium,condensers can be classified as air-cooled,water-cooled and evaporative condensers.The evaporative condenser is a compact heat exchanger combining the functions of air and water-cooled con-densers and a cooling tower.In this condenser,thesuperheated vapour pumped by the compressor flows through a bank of tubes.The external surface of the tubes is continually kept wet by a water-distributing system.On the other hand,air is drawn through the condenser casing and sent upwards over the tubes.Absorbing heat from the refrigerant,some of the water on the tubes evaporates into the air.Consequently,the refrigerant vapour gives up its heat and condenses.Because the evaporative condenser offers condensing temperatures limited by ambient wet bulb temperature,which is almost always lower than ambient dry bulb temperature,refrigeration systems employing it can work with lower condensing temperatures.Therefore,these systems are usually more energy-efficient com-pared to ones using air-cooled condensers.Furthermore,initial cost of the evaporative condenser is lower than1359-4311/$-see front matter Ó2005Elsevier Ltd.All rights reserved.doi:10.1016/j.applthermaleng.2005.06.002*Corresponding author.Tel.:+902623032279;fax:+902623032203.E-mail addresses:mhosoz@.tr ,mhosoz@ (M.Hosoz)./locate/apthermengApplied Thermal Engineering 26(2006)627–635that of the water-cooled condenser due to the reduced space and number of the components.While it is relatively simple to accurately model the heat transfer in air and water-cooled condensers,the evaporative condenser presents some difficulties owing to water evaporation into the air stream involved.Based on the early evaporative condenser models[1,2],which usually yielded incorrect results,Peterson et al.devel-oped and tested an analytical condenser model[3].They found that their model underpredicted the heat load by 30%.Goswami et al.[4]investigated the performance of air conditioners with air-cooled condensers using evapo-ratively-cooled ambient air.Ettouney et al.[5]developed correlations for the external heat transfer coefficient of an evaporative condenser.Hwang et al.[6]determined experimental performance of a novel evaporative condenser relying on rotating wet disks to reject heat. Hosoz and Kilicarslan[7]compared performance characteristics of refrigeration systems using evapora-tive,water-cooled and air-cooled condensers.It is seen from the review of the literature that it is too hard to accurately determine the performance of an evaporative condenser and consequently the perfor-mance of a refrigeration system with this condenser using classical modelling techniques.As an alternative, a refrigeration system employing an evaporative con-denser can be modelled using ANNs.This new model-ling technique is based on imitating the structure and mechanisms of the human brain,and being used in more and more engineering applications where classical ap-proaches fail or they are too complicated to be used. ANNs are applied to estimate desired output parameters when enough experimental data is provided.Therefore, ANNs allow the modelling of physical phenomena in complex systems without requiring explicit mathemati-cal representations.ANN modelling of energy systems has been recently studied by numerous investigators,as reviewed by Kal-ogirou[8].Pacheco-Vega et al.[9]applied the ANN to model the heat transfer of afin-tube heat exchanger used for refrigeration applications.Bechtler et al.[10]pre-sented an ANN model for predicting the steady-state performance of a vapour-compression heat pump with various refrigerants.They also modelled dynamic pro-cesses of vapour-compression liquid chillers to predict the coefficient of performance(COP)and compressorNomenclaturea actual outputA0orifice cross-section area(m2)b biasCOP coefficient of performanceCov covariancef activation functionh enthalpy of the refrigerant(kJ kgÀ1)h a enthalpy of the air(kJ kgÀ1)h m orifice differential(mm H2O)I currentflow through the heaters(A)K0flow coefficient_m massflow rate(g sÀ1)MRE mean relative errorn sum of the weighted inputsN number of the points in the data setp predicted outputP number of elements in the input vectorQ cond heat rejection rate in the condenser(W)Q evap refrigeration capacity(W)R correlation coefficientRMSE root mean square errorT a,i dry bulb temperature of the air at the inlet of the condenser(°C)T a,i,w wet bulb temperature of the air at the inlet of the condenser(°C)V voltage across the heaters(V)v a,e specific volume of the air at the exit of the condenser(m3kgÀ1)w interconnection weightW c compressor power(W)W el electric power input to the compressor motor (W)j W p j power absorbed by water in the pump(W) x input of a neuronY expansion factorGreek symbolsg mech mechanical efficiency of the compressorg motor efficiency of the compressor motorq a,e density of the air at the exit of the condenser (kg mÀ3)D P orifice pressure drop(Pa)Subscriptsa airc compressorcond condensere exitel electricevap evaporatori inletr refrigerantw water or wet bulb628H.M.Ertunc,M.Hosoz/Applied Thermal Engineering26(2006)627–635work input[11].Prieto et al.[12]presented an ANN model for predicting the performance of a power plant condenser.Chouai et al.[13]worked on the ANN modelling of the thermodynamic properties of several refrigerants.Swider[14]compared empirically based steady-state models including ANNs for modelling vapour-compression liquid chillers.Sozen et al.[15] compared the results of an ANN model for the analysis of ejector-absorption refrigeration systems with those of analytic functions.Arcaklioglu[16]developed an ANN model for predicting the COP and total irreversibility of a vapour-compression refrigeration system.Arcaklioglu et al.[17]determined the performance of a vapour-com-pression heat pump with different ratios of R12/R22 refrigerant mixtures using ANNs.Islamoglu[18]devel-oped an ANN model for predicting the suction line outlet temperature and massflow rate of a capillary tube suction line heat exchanger used in household refrigerators.In this study,the ANN approach has been applied to a vapour-compression refrigeration system employing an evaporative condenser.Utilizing data obtained from steady-state test runs of an experimental refrigeration system,an ANN model for the system has been devel-oped.The ANN model has been used for predicting var-ious performance parameters of the refrigeration system,namely the condenser heat rejection rate,refrig-erant massflow rate,compressor power,electric power input to the compressor motor and COP.2.Artificial neural networksAn ANN tries to mirror the brain functions in a computerized way by resorting to the learning mecha-nism as the basis of human behaviour.Utilizing the samples from the experiments,ANNs can be applied to the problems with no algorithmic solutions or with too complex algorithmic solutions to be found.Their ability of learning by examples makes the ANNs more flexible and powerful than the parametric approaches [19].An ANN consists of massively interconnected pro-cessing nodes known as neurons.Each neuron accepts a weighted set of inputs and responds with an output. Such a neuronfirst forms the sum of the weighted inputs given byn¼X Pi¼1w i x i!þbð1Þwhere P and w i are the number of elements and the interconnection weight of the input vector x i,respec-tively,and b is the bias for the neuron[20].Note that the knowledge is stored as a set of connection weights and biases.The sum of the weighted inputs with a bias is processed through an activation function,represented by f,and the output that it computes isfðnÞ¼fX Pi¼1w i x i!þb"#ð2ÞBasically,the neuron model represents the biological neuron thatfires when its inputs are significantly excited,i.e.,n is big enough.There are many ways to de-fine the activation function such as threshold function, sigmoid function,and hyperbolic tangent function.ANNs can be trained to perform a particular func-tion by adjusting the values of connections,i.e.,weight-ing coefficients,between the processing nodes.In other words,ANNs are trained to reach from a particular in-put to a specific target output using a suitable learning method until the network output matches the target. The error between the output of the network and the de-sired output is minimized by modifying the weights and biases.When the error falls below a certain value or the maximum number of epochs is exceeded,training pro-cess is ceased.Then,this trained network can be used for simulating the system outputs for the inputs which have not been introduced before.The architecture of an ANN is usually divided into three parts:an input layer,a hidden layer(s)and an output layer.The information contained in the input layer is mapped to the output layer through the hidden layer(s).Each unit can send its output to the units only on the higher layer and receive its input from the lower layer.For a given modelling problem,the numbers of nodes in the input and output layers are determined from the physics of the problem,and equal to the numbers of input and output parameters,respectively.The performance of the ANN-based prediction is evaluated by a regression analysis between the network outputs,i.e.,predicted parameters,and the correspond-ing targets,i.e.,experimental(actual)values.The corre-lation coefficient,mean relative error and root mean square error are the three criterions that can be used in this evaluation.The correlation coefficient is a mea-sure of how well the variation in the output is explained by the targets.This coefficient between the actual versus predicted outputs is defined as follows[21]:Rða;pÞ¼Covða;pÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiCovða;aÞCovðp;pÞpð3Þwhere Cov(a,p)is covariance between a and p sets that refer to the actual output and predicted output sets, respectively.Likewise,Cov(a,a)and Cov(p,p)are the auto covariances of a and p sets,correspondingly.The correlation coefficient ranges betweenÀ1and+1.R val-ues closer to+1indicate a stronger positive linear rela-tionship while R values closer toÀ1indicate a stronger negative relationship.H.M.Ertunc,M.Hosoz/Applied Thermal Engineering26(2006)627–635629The mean relative error,which shows the mean ratio between the errors and experimental values,is evaluated byMREð%Þ¼1NX Ni¼1100ða iÀp iÞa ið4Þwhere N is the number of the points in the data set.Finally,the root mean square error is defined asRMSE¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1NX Ni¼1ða iÀp iÞ2v uu tð5Þ3.Description of the experimental setup and testing procedureThe ANN modelling has been applied to an experi-mental R134a vapour-compression refrigeration unit consisting of a reciprocating compressor,an evaporative condenser,a liquid receiver,afilter–drier,a thermostatic expansion valve and an electrically heated evaporator, as shown in Fig.1.The twin-cylinder open-type com-pressor is driven by a single-phase electric motor.The evaporator consists of copper tube and electric heaters rolled inside the tube.The refrigeration load is supplied to the evaporator by varying the voltage across the elec-tric heaters between0and220V.The evaporative condenser consists of air and water circuit elements along with a bare copper coil having three refrigerant circuits connected in parallel by head-ers.The tube outside diameter and total external surface area of the coil are6.35mm and0.100m2,respectively. The air,water and refrigerant streams exchange heat in a column of150mm·150mm·600mm high.Ambient air is pulled into the column by means of a centrifugal fan at a rate determined by the adjustment of the dam-per setting.Having absorbed heat,the air stream passes through a droplet arrester,and then discharged to the atmosphere via an orifice used for measuring the airflow rate.The water stream is let to fall down the column spreading over the coil surface.Afterwards,the water passes into a tank from where the circulation pump draws it and sends to the top of the column via a control valve determining the waterflow rate in the system.The evaporator,condenser,liquid receiver,expansion valve and pipeline were insulated with either elastomeric insu-lator or polyurethane foam.During tests,the evapora-tive condenser was located inside a special room where dry and wet bulb temperatures could be kept at required values.The locations where mechanical and electrical mea-surements were conducted are also shown in Fig.1. All temperature measurements were performed using K-type thermocouples.Refrigerant thermocouples were located at the inlet and outlet of each component.Both dry and wet bulb temperatures of the air stream entering and leaving the evaporative condenser were measured. Refrigerant pressures were detected at the inlet and out-let of the compressor.Since the length of the pipeline is relatively short,the evaporator and condenser pressures were assumed to be equal to the measured ones.The refrigerant and water massflow rates were measured by variable-areaflow meters.The air massflow rate was determined by measuring orifice differential with an inclined manometer,finding specific volume of the air leaving the condenser with the help of dry and wet bulb temperature measurements,and evaluating them in the followingequation:Fig.1.Schematic diagram of the experimental refrigeration system. 630H.M.Ertunc,M.Hosoz/Applied Thermal Engineering26(2006)627–635_m a¼q a;e K0A0Yffiffiffiffiffiffiffiffiffi2D Pqa;esffi0.0137ffiffiffiffiffiffiffih mv a;esð6ÞThe heat input to the evaporator was found by mea-suring the voltage across the electric heaters and the cur-rent passing through them.The electric power input to the compressor motor was measured by an analogue wattmeter.The evaporator load,i.e.,the refrigeration capacity of the system,can be evaluated for both the heaters side and the refrigerant side.Assuming that the evaporator is insulated perfectly,the evaporator load can be written asQevap¼VIffi_m rðh evap;eÀh evap;iÞð7ÞAs seen in Eq.(7),the evaporator load for the heaters side utilizes voltage and current measurements while that for the refrigerant side uses measurements of the refrigerant massflow rate along with pressures and tem-peratures of the refrigerant at the exit and inlet of the evaporator.The capacity deviation between two sides was usually within±5%,and only the heaters side re-sults were used as the evaporator load due to their hav-ing lower uncertainities.Then,the refrigerant massflow rate in the system based on evaporator load for the heat-ers side was determined from:_m r¼VIh evap;eÀh evap;ið8ÞThe accuracy for the refrigerant massflow rate mea-surements conducted by the variable-areaflow meter, which is equal to±5%,is poorer than the uncertainity for theflow rates determined from Eq.(8).Therefore, only the results of this equation were used as the refrig-erant massflow rate while the results of the direct mea-surements were used for checking purposes.The heat rejection rate in the evaporative condenser for the refrigerant side can be evaluated byQcond¼_m rðh cond;iÀh cond;eÞð9ÞAssuming that the evaporative condenser is perfectly insulated and applying the principle of energy conserva-tion to the condenser,in steady state operation the heat rejected by the refrigerant can be related to the heat absorbed by the air stream as follows:_m rðh cond;iÀh cond;eÞþj W p jffi_m aðh a;eÀh a;iÞð10Þwhere j W p j is the power absorbed by water in the circu-lation pump.As seen in Eq.(10),the heat rejected by the refrigerant is affected by the enthalpy of the air stream entering the condenser.Since it is hard to accurately determine the power absorbed by the water in the pump, the condenser heat rejection rate was determined only from the refrigerant side.However,the air dry and wet bulb temperatures at the inlet of the condenser were measured for developing the ANN because the con-denser heat rejection rate and consequently the perfor-mance of the refrigeration system are considerably influenced by these temperatures.Assuming that the compression process is adiabatic, the compressor power absorbed by the refrigerant can be expressed asW c¼_m rðh comp;eÀh comp;iÞð11ÞThe electric power input to the compressor motor is linked to the compressor power by[22]W el¼W cg mech g motorð12Þwhere g mech is the mechanical efficiency of the compres-sor and g motor is the efficiency of the electric motor, which is a function of the load and speed of the motor.The ratio of the refrigeration capacity to the com-pressor power gives the energetic performance of the system,i.e.,COP¼Qevapcð13ÞIn the experimental study,totally60different steady-state test runs have been conducted to gather data for training the proposed ANN and testing its performance. The inputs varied in the tests were the evaporator load, water and airflow rates,and air dry and wet bulb tem-peratures at the inlet of the condenser.The ranges of these inputs are shown in Table1.Based on the experi-mental results,various performance parameters of the system were determined from the above equations,and used for developing and testing the ANN model.4.Modelling with the ANNIn order to develop the ANN for the experimental refrigeration system,the available data set from the experimental work was divided into training and valida-tion sets.The data set consists of60input–output pairs. While70%of the data set was randomly assigned as the training set,the remaining30%was employed for test-ing/validation of the network.The architecture of the ANN for the refrigeration sys-tem with the names of input and output parameters is schematically illustrated in Fig.2.The inputs to the ANN are the evaporator load(Q evap),air massflow rate (_m a),water massflow rate(_m w)along with air dry bulb Table1Range of the inputs in the experimentsEvaporator load55–486WWater massflow rate 5.5–44.0g sÀ1Air massflow rate45.4–59.3g sÀ1Air dry bulb temperature at the condenser inlet20.5–24.7°CAir wet bulb temperature at the condenser inlet15.3–19.2°CH.M.Ertunc,M.Hosoz/Applied Thermal Engineering26(2006)627–635631(T a,i)and wet bulb(T a,i,w)temperatures at the condenser inlet.The outputs from the ANN are the condenser heat rejection rate(Q cond),refrigerant massflow rate(_m r), compressor power absorbed by the refrigerant(W c), electric power consumed by the compressor motor (W el)and the coefficient of performance(COP).The performance of an ANN is affected by the char-acteristics of the network such as the number of hidden layers and the number of nodes in each hidden layer.By trial and error with different ANN configurations,the network was decided to consist of one hidden layer with four neurons along with input and output layers each withfive neurons.The activation function in the hidden layer was chosen as tangent sigmoid function.Conse-quently,the prediction of thefive output parameters was performed using a three-layer feed forward ANN. Utilizing standard backpropagation algorithm,the most popular algorithm in engineering applications,the input vectors withfive variables and the corresponding target vectors withfive variables from the training set were used for training the network.The training procedure adjusted the weighting coefficients using Levenberg–Marquardt algorithm.The output of the network was compared to the desired output at each presentation, and an error was computed.This error was then back-propagated to the ANN and used for adjusting the weights such that the error decreases with each iteration and the neural model gets closer and closer to producing the desired output.Finally,the training procedure approximates a function between the input and output parameters.Then,the input vectors from the validation data set were presented to the trained network.The responses of the network,i.e.,the predicted output parameters,were compared with the experimental ones for the performance measurement.The computer code used for solving the backpropagation algorithm and measuring the network performance was developed using MATLABÒ7.5.Results and discussionThe predictions of the trained ANN for the perfor-mance parameters of the considered refrigeration system as a function of the experimental values are shown in Figs.3–8.Note that in all graphics the comparisons were made using only values from the test data set, which was not introduced to the network during the training process.In allfigures except the last one,the accuracy of the ANN predictions was evaluated withthe help of a straight line indicating perfect predictionand a ±10%error band.A plot of the predicted versus experimental values for the condenser heat rejection rate is shown in Fig.3.The ANN predictions for this parameter result in a mean rel-ative error (MRE)of 1.90%,a root mean square error (RMSE)of 4.12W and a correlation coefficient of 1.000with the experimental data.These results demon-strate that the ANN excellently predicts the heat rejec-tion rate from the refrigeration system despite wide ranges of operating conditions.A plot of the predicted versus experimental values for the refrigerant mass flow rate is reported in Fig.4.For this parameter,the ANN yields a correlation coefficient of 0.999,a MRE of 2.55%and a RMSE of 0.04g s À1,which are slightly poorer than the previous predictions.It is clear that if a higher number of test runs had beenperformed to provide a larger amount of experimental data for training the ANN,the network predictions would have been better.The ANN predictions versus experimental values for the compressor power absorbed by the refrigerant are indicated in Fig.5.For this parameter,the ANN yields a correlation coefficient of0.998,a MRE of4.18%and a RMSE of2.41W.Although the compressor power in a refrigeration system is a performance parameter of ther-modynamic importance,the user also wants to know the total energy consumed by the system.Therefore,the electric power input to the compressor motor,a major portion of the total energy input to the considered sys-tem,was also predicted by the ANN.As seen in Fig.6,the ANN predictions for the electric power con-sumed by the compressor yield a MRE of2.17%,a RMSE of11.67W and a correlation coefficient of 0.991with the experimental data.The ANN predictions versus experimental values for the COP are shown in Fig.7.Results show that although the ANN yields a MRE of3.03%and a RMSE of0.18,it results in a relatively poor correlation coeffi-cient of0.933.This is probably due to the fact that both the evaporator load and compressor power are required to determine the COP.The performances of the ANN predictions for W el, _m r,Q cond,W c and COP are alternatively presented in Fig.8.It is seen that the tests patterns consist of 18tests,corresponding to30%of totally60tests. Although data from these tests has not been introduced to the ANN before,the ANN remarkably predicts thefive output parameters for the whole range of the experiments.6.ConclusionsIn order to show the applicability of the ANN mod-elling to refrigeration systems,especially to those involv-ing concurrent heat and mass transfer processes,an ANN based on backpropagation algorithm has been developed to predict various output parameters of a refrigeration system with an evaporative condenser.In order to acquire data for training and testing the pro-posed ANN,an experimental system was set up and steady-state test runs were conducted.Based onfive in-put parameters,the trained ANN was used for predict-ing the performance of the refrigeration system in terms of the condenser heat rejection rate,refrigerant mass flow rate,compressor power,electric power input to the compressor motor and the COP.The performance of the ANN predictions was measured using the correla-tion coefficient,mean relative error and root mean square error.The ANN modelling for the refrigeration system usually demonstrated a good statistical perfor-mance with the correlation coefficients in the range of 0.933–1.000and MREs in the range of 1.90–4.18%. Moreover,the RMSE values for the predicted parame-ters were very low compared to the ranges of the experiments.This study reveals that a refrigeration system with an evaporative condenser,probably the hardest one to model using classical techniques,can alternatively be modelled using ANNs within a high degree of accuracy. 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