Theoretical study of the effect of liquid desiccant mass flow rate.pdf

ORIGINAL Theoretical study of the effect of liquid desiccant mass fl ow rate on the performance of a cross fl ow parallel plate liquid desiccant air dehumidifi er Abdulrahman Th Mohammad Sohif Bin Mat M Y Sulaiman K Sopian Abduljalil A Al abidi Received 29 June 2012 Accepted 26 June 2013 Published online 9 July 2013 Springer Verlag Berlin Heidelberg 2013 AbstractA computer simulation using MATLAB is investigated to predict the distribution of air stream parameters humidity ratio and temperature as well as desiccantparameters temperatureandconcentration inside the parallel plate absorber The present absorber consists of fourteen parallel plates with a surface area per unit volume ratio of 80 m2 m3 Calcium chloride as a liquid desiccant fl ows through the top of the plates to the bottom while the air fl ows through the gap between the plates making it a cross fl ow confi guration The model results show the effect of desiccant mass fl ow rate on the perfor mance of the dehumidifi er moisture removal and dehu midifi er effectiveness Performance comparisons between present cross fl ow dehumidifi er and another experimental cross fl ow dehumidifi er in the literature are carried out The simulation is expected to help in optimizing of a cross fl ow dehumidifi er List of symbols cp Specifi c heat kJ kg 1 C DMass diffusivity m2s 1 gAcceleration of gravity m s 2 H Height of dehumidifi er m hHeight of plate m L Thickness of dehumidifi er m Mde Moisture removal rate in dehumidifi er g s 1 m Mass fl ow rate kg s 1 PatAtmospheric pressure bar PwWetted parameter m PwsSaturation pressure bar PwzPartial pressure of water vapor in the solution bar qiMixing heat kJ kg 1 uVelocity m s 1 TTemperature C wWidth channel between two plates m waHumidity ratio of air kgH2O kgdry weEquilibrium humidity ratio of air kgH2O kgdry Greek letters nSolution concentration lViscosity N s m 2 qDensity kg m 3 aThermal diffusivity m2s 1 dsSolution thickness m e Dehumidifi er effectiveness kThermal conductivity W m 1K 1 tKinematic viscosity m2s Subscripts aAir eEquilibrium inInlet sSolution outOutlet 1 Introduction Liquid desiccant dehumidifi cation is a very important process in liquid desiccant air conditioning systems The aim of this process is to attract the water vapor from the air to the liquid desiccant the dehumidifi cation process A Th Mohammad S B Mat M Y Sulaiman K Sopian A A Al abidi Solar Energy Research Institute University Kebangsaan Malaysia 43600 Bangi Selangor Malaysia A Th Mohammad the model used NTU as the input parameter Xiao Hua Liu et al 2 investigated an analytical solution to give air and desiccant parameters as well as enthalpy and moisture effi ciency in a cross fl ow dehumidifi er Yin and Zhang 3 developed an NTU Le model to determine the characteristics of liquid desiccant dehumidifi cation Dai and Zhang 4 built up a mathematical model to predict the performance of a liquid desiccant air dehumidifi er with honeycomb as a packed bed Liu et al 5 estimated the hour hour performance of the dehumidifi er using a sim plifi ed method with empirical correlations Mohammad et al 6 proposed an artifi cial neural network model ANN for predicting the performance of a liquid desiccant dehumidifi er in terms of moisture removal rate and the effectiveness The results show that 6 3 3 1 ANN structure was the best model for predicting the water condensation rate where as the 6 6 6 1 was the best model for predicting the dehumidifi er effectiveness Local volumetric average approach was used by Peng and Pan 7 to investigate the transient heat and mass transfer in liquid desiccant air conditioning process at low fl ow conditions The differential equations of the heat and mass transfer in the liquid desiccant components cannot be solved ana lytically the most basic model is a numerical integration along the height or depth of the dehumidifi er Therefore fi nite difference technique become the most fundamental model available to solve the governing equations of heat and mass transfer process because of observing specifi c details about the dehumidifi er performance Although the fi nite difference use the computer time is prohibitive but reducing the number of iterations with using relaxation reduces the time From the literature most of researchers have investigated experiments on the counter fl ow liquid desiccant dehumidifi ers because their performance tends to be better than the cross fl ow dehumidifi ers But very limited experimental performance data is available on this type of dehumidifi ers arrangements Therefore in this study fi nite difference technique was used to show the distribution of the air and the solution parameters air and solution temperature humidity ratio of air and solution concentration inside a parallel plate liquid desiccant dehumidifi er under the effect of the solution mass fl ow rate The simulation is expected to help in optimizing and designing of new across fl ow dehumidifi er for the air conditioning system The performance of the dehumidifi er was investigated under the effect of solution fl ow rate 2 Dehumidifi er design A parallel plate dehumidifi er consists of a number of ver tical parallel plates with polypropylene material The dis tance between each two adjacent plates is 1 cm Its geometry is presented in Fig 1 All parameters in the design of the dehumidifi er and its specifi cations are sum marized in Table 1 3 Mathematical models The Z axis denotes the direction of air fl ow while the X axis is the direction of the solution perpendicular to the Fig 1 Schematic of the cross fl ow parallel plate dehumidifi er 1588Heat Mass Transfer 2013 49 1587 1593 123 air fl ow which is in a cross fl ow confi guration A theo retical two dimensional analysis of an adiabatic process was developed based on the following assumptions 1 Steady state 2 Two dimensional fl ows 3 No heat transfer from the solution to the plates 4 The interfacial area of heat and mass transfer are equal 5 No heat and mass transfer to or from the surroundings 6 The fi lling fi lm is laminar and fully developed fl ow 7 The thickness of the fi lm is constant 8 The heat and mass transfer coeffi cients are uniform throughout the module 9 The diffusion in the air stream is neglected 10 The tempera ture of the air and the liquid desiccant is equal at the liquid gas interface and the humidity of the air is in equilibrium with that of the liquid desiccant solution 3 1 The basic equations of moist air and fi lling fi lm The heat and mass transfer process which takes place in liquid desiccant dehumidifi er is the same process in cooling tower There is little difference between them while the cooling tower uses the water as the working liquid the process only humidifi es but in liquid desiccant chamber uses a salt water solution can humidify or dehumidify the air depending on the operation conditions The liquid desiccant chamber is fi lled with packing material the solution drips from the top wetting the packing material while air is blows through from the bottom in a counter parallel and cross current arrangement The heat transfer process occurs because of temperature difference between the air and the solution while the mass transfer is driven by a difference between the partial pressure of the water vapor in the air and the vapor pressure of a liquid According to the assumptions the governing equations of the process air can be obtained as follows Momentum conversation is given as op oz la o2ua oy2 2 1 The energy conservation are written respectively as ua oTa oz aa o2Ta oy2 2 2 Moisture conversation in the air is represented by ua oWa oz Da o2Wa oy2 2 3 For laminar fl ow the mean velocity of the fi lling fi lm is given by 8 us qs c dr 3t 4 The thickness of the fi lling fi lm can be estimated as ds 4 ms t qs g 1 3 5 Similarly the equations for the liquid fi lm are Energy balance us oTs ox as o2Ts oy2 1 6 Mass conservation us on ox Ds o2n oy2 1 7 Equations 2 3 6 7 can be written in more compact form as u o oy C o2 oy2 8 where represents Ta Wa Ts and n and the coeffi cient C stands for aa Da as andDs 3 2 Boundary and interfacial matching conditions Boundary conditions of the present model are listed as following Ts Ts in n ninatx 0 9 Ta Ta in wa wa inatz 0 10 us 0 aty1 0 11 In the liquid desiccant fi lm the concentration gradient would vanish near the plate wall and the velocity gradient of the fi lling fi lm is equal to zero close to the liquid fi lm Table 1 Dehumidifi er parameter design Type Dehumidifi er dimensionsProcess Length H cm Width W cm Depth L cm Parallel plate with a cross fl ow752530Adiabatic Plate dimensions Number of platesLength h cm Width L cm Thickness t cm Distance between two plates w cm 1460300 41 Heat Mass Transfer 2013 49 1587 15931589 123 surface In the air stream there is no air fl ow at the liquid gas interface The interfacial matching conditions between the liquid side and the gas side are expressed as 1 Temperature continuity is expressed as Tsjy1 d Tajy2 0 12 2 The humidity ratio of air in equilibrium with CaCL2 solution is calculate according to these equations log10Pws 021254 313619 10 2 T 1 22512 10 4 T2 3 6384 10 7 T3 5 6707 10 10 T4 13 where Pwsis the saturation pressure and T is the solution temperaturebetween 10 C T 80 C Radhwanetal 9 The partial pressure of water vapor in the solution CaCL2is given by Esayed et al 10 Pwz Pws1 146 1 76n 14 Then the equilibrium humidity ratio of air is given by we 0 62185 Pwz Pat Pwz 15 Where Patis the atmospheric pressure Kinsara et al 11 3 Mass balance is given as qsDs on oy1 y1 d qaDa oWa oy2 y2 0 qsus on ox dy1 16 4 Energy balance at the interface implies qsusCps dy1 oTs ox ks oTs oy1 y1 d ka oTa oy2 y2 0 qaDa oWa oy2 y2 0 qi 17 Where qi represents the heat released in the dehumidifi cation process 3 3 The dehumidifi cation effectiveness and moisture removal The rate of water transfer from the air to the liquid desic cant is defi ned as moisture removal dehumidifi cation mass rate and is given by Yin et al 12 Mde ma wa in wa out 18 which can also be described as Mde ms nin nout 1 19 The performance of the dehumidifi er is described in terms of dehumidifi cation effectiveness by Moon et al 13 e wa in wa out wa out we 20 where wa in wa outis the actual change of the humidity ratio and wa out weis the maximum possible change of the humidity ratio 3 4 Solving procedures Distribution of air stream parameters humidity and tem perature and desiccant parameters temperature and con centration as well as the moisture removal rate in the liquid desiccant dehumidifi er can be estimated using the above described model The following is a brief description of the principle steps of the algorithm procedure 1 Input the inlet conditions for both air and desiccant solution massfl owrate temperature airhumidityratio solutionconcentration Thedimensionsoftheplateare representedinTable 1andtheconstantpropertiesofair and calcium chloride are listed in Table 2 2 Specify the dimensions of the channel and assume the wall temperature equal 10 C 3 Calculate the thickness and the velocity of laminar fi lling fi lm Eqs 4 5 4 Assume the interfacial temperature of the fi lling fi lm and calculate the temperature distribution in the liquid desiccant and the air 5 Assume the interfacial temperature of the fi lling fi lm and calculate the temperature distribution in the liquid desiccant and the air 6 From the interfacial temperature calculate the equi librium humidity ratio of air using Eqs 13 15 7 Assume the interfacial concentration of the desiccant fi lling fi lm and calculate the concentration distribu tion in the liquid desiccant 8 From steps 6 and 7 calculate the humidity distribu tion of the moist air using the thermal and physical properties of the liquid desiccant 9 If the condition of Eq 16 is satisfi ed complete the procedure of the program or if not repeat the steps from 7 to 9 until the precision is reached Table 2 Constant properties of air and calcium chloride 14 PropertiesAirCalcium chloride q Kg m3 1 111 394 l Kg m s 1 9 9 10 51 19 9 10 2 Cp J Kg K 9902 330 k W m K 0 02750 525 D m2 s 2 65 9 10 52 5 9 10 5 1590Heat Mass Transfer 2013 49 1587 1593 123 10 If the condition of Eq 17 is satisfi ed complete the procedureoftheprogram orifnot gotostep6andrepeat the steps from 6 to 10 until the precision is reached 11 Calculate the air and liquid desiccant parameters air temperature air humidity ratio solution temperature and solution concentration as well as moisture removal rate and effectiveness 4 Results and discussion The dehumidifi cation performance depends on six input parameters of the air and liquid desiccant including air and solution temperature air and solution mass fl ow rate air humidityratioandsolutionconcentration Thefi nitedifference technique model can give the distribution of air temperature and humidity ratio as well as solution temperature and con centration inside the liquid desiccant dehumidifi er module The outlet parameters moisture removal rate and the effec tiveness caninvestigate whichareimportantforstudyingthe improvementoftheheatandmasstransferinthedehumidifi er The air and desiccant inlet parameters are set as in Table 3 4 1 Effect of desiccant fl ow rate on air temperature and humidity ratio distribution Figure 2 gives the distribution of air temperature and air humidity ratio inside the dehumidifi er under the effect of solution fl ow rate with the above inlet parameters in Table 3 In this case the air is heated and dehumidifi ed along its fl ow direction At the air outlet Z L the air at the top has the highest temperature and lowest humidity ratio the maximum temperature and humidity ratio dif ferences of the air are 3 26 C and 10 5 g Kg with a maximum solution mass fl ow rate of 160 g s while the minimum ratio differences are 2 19 C and 7 7 g Kg with a minimum solution fl ow rate of 30 g s This may be explained as follows increasing solution fl ow rate ensures well contact between the air and the solution and also increases the heat and mass transfer coeffi cients Therefore the moisture removed increases rapidly with solution fl ow rate but it stagnates at high desiccant solution fl ow rate 4 2 Effect of desiccant fl ow rate on the desiccant temperature and concentration distribution At the desiccant outlet X H as shown in Fig 3 the maximumtemperatureandminimumconcentration differences of solution in the direction fl ow of solution are 3 48 C and 0 25 with a maximum solution mass fl ow rate of 160 g s and the minimum temperature and maxi mum concentration differences are 1 19 C and 3 75 with a minimum solution mass fl ow of 30 g s The reason may be explained as follows The desiccant contacted the humid air and more moisture was transferred from the air to the solution since the mass transfer potential was large there Therefore desiccant temperature increased most and thesolutionconcentrationreducesslightlywiththe increasing desiccant fl ow rate According to the results the desiccant concentration differences in the direction of desiccant fl ow can be neglected 4 3 Effect of desiccant fl ow rate on dehumidifi er effectiveness and moisture removal Figure 4 shows the effect of solution mass fl ow rate on the dehumidifi er performance according to the fi gure the moisture removal rate increases rapidly with solution fl ow Table 3 Air and desiccant inlet parameters ma Kg s 1 Ta 0C wa KgH2O Kgdry ma msTs 0C n Input parameters0 16300 0210 18 13440 Air Temperature C Dehumidifier Depth cm Air humidity ratio kgH2O Kg dry Dehumidifier depth cm Fig 2 The effect of solution mass fl ow rate on the air temperature and humidity ratio Heat Mass Transfer 2013 49 1587 15931591 123 rate from 0 619 to 1 21 g s 1 But the moisture removal stagnates at high desiccant solution mass fl ow rates because of the increasing solution mass fl ow rate which increases the mass transfer coeffi cient between the liquid desiccant and the air fl ow but reduces the contact time The dehumidifi er effectiveness also shows similar trend as shown in Fig 5 The fi gure indicates that the effectiveness achieves an increase of 0 32 0 45 when the solution mass fl ow rate increases from 30 to 160 g s 1 This increase may be explained as follows Increasing solution fl ow rate enhances the heat and mass transfer coeffi cients The average water vapor pressure difference between the desiccant and air increased due to the reduced variation of the surface vapor pressure of the desiccant in the dehu midifi er which maintains a good mass transfer between the air and desiccant 4 4 Validation of the model results The performance of the cross fl ow dehumidifi er in terms of the moisture removal rate and the effectiveness in the present study is compared with the other experimental study by Bassuoni 15 Figure 4 shows the trend of the effect of solution fl ow rate on the moisture removal rate and the effectiveness of the dehumidifi er The present work mentions an increasing trend of moisture removal rate with the solution fl ow rate Good agreement between the sim ulation and experimental when the solution temperature increased by 8 C This can be explained as follows The vapor pressure of the solution rises with increasing the solution temperature and it reduces the mass transfer potential between the solution and moisture in the air The dehumidifi er effectiveness increases as the solution fl ow Solution temperature C Dehumidifier height cm Solution concentration Dehumidifier height cm Fig 3 The effect of solution mass fl ow rate on the solution temperature and concentration Moisture removal rate g s Solution mass flow rate gls Fig 4 The effect of solution mass fl ow rate on the moisture removal rate Table 4 Comparison of the operational conditions and outlet results between the present study and experiment in literature Bassuoni 15 Present study Liquid desiccantCaCL2CaCL2 Specifi c area m2m 3 39080 Flow type Cross fl ow Cross fl ow Packing typeStructured packing corrugation angle of