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2 22 Heat and Mass Transfer in Desiccant Weels Celestino Ruivo 1,2, José Costa 2 and António Rui Figueiredo 2 1 University of Algarve, 2 ADAI-University of Coimbra Portugal 1. Introduction 1.1 Background Nowadays te interest in eating, ventilation, air-conditioning and refrigerating systems (HVAC&R) based on desiccant weels is increasing due to te possibility of using renewable energy sources, making tem an attractive alternative or complement to conventional systems. Te termally driven desiccant systems can potentially reduce te peak electricity demand and associated electricity infrastructure costs. Tey generally incur in iger initial cost compared wit equivalent conventional systems, but cost reduction can be acieved at te design stage troug careful cycle selection, flow optimisation and size reduction. Te performance of tese systems can be evaluated by experimental or numerical approaces. To date tere still exists a lack of data of real manufactured weels enabling to perform a dynamic energy analysis of suc alternative systems wit reasonable accuracy at design stage. Te data given by te manufacturers of desiccant weels are usually restricted to particular sets of operating conditions. Besides, te available software for sizing is usually appropriate to run only stationary operating conditions. For tese reasons, it is recognized te importance of te use of a simple predicting metod to perform te dynamic simulation of air andling units equipped wit desiccant weels. In tis capter, te results of a detailed numerical model are used to determine te effectiveness parameters for te coupled eat and mass transfer processes in desiccant weels, allowing te use of te effectiveness metod as an easy prediction tool for designers. 1.2 General caracterization and modelling aspects Desiccant weels are air-to-air eat and mass excangers used to promote te deumidification of te process airflow. Te rotor matrix, as illustrated in Fig. 1, is compact and mecanically resistant, and consists of a ig number of cannels wit porous desiccant walls. Te rotation speed of te weel is relatively low. Te ygroscopic matrix is submitted to a cyclic sequence of adsorption and desorption of water molecules. Te regeneration process of te matrix (desorption) is imposed by a ot airflow. In eac cannel of te matrix, a set of pysical penomena occurs: eat and mass convection on te gas side as well as eat and mass diffusion and water sorption in te desiccant wall. Te regeneration airflow sould be eated by recovering energy from te system and using renewable energy sources wenever possible.

3 514 Advanced Topics in Mass Transfer Fig. 1. Desiccant weel and detail of te porous structure of te matrix In te scematic representation of a desiccant weel in Fig. 2, airflow 1 (process air) and airflow 2 (regeneration air) cross te matrix in a counter-current configuration, wit equal or different mass flow rates. Te desorption zone is generally equal or smaller tan te adsorption zone. 2 out 2 in 1 in 1 out Fig. 2. Desiccant weel ( - Adsorption zone; - Desorption zone) Te approacing airflows in eac zone can present instabilities and eterogeneities and are generally turbulent. However, te relatively low values of ydraulic diameter of te cannels (frequently less tan 5 mm) togeter wit moderate values of te frontal velocity (usually between 1 and 3 m s 1 ) impose laminar airflows. Besides, in very sort matrixes, te entrance effects can be relevant, particularly for larger ydraulic diameters of te cannels. During te adsorption/desorption cycle, te matrix exibits non uniform distributions of adsorbed water content and temperature, and te angular gradients depend on te constitution of te wall matrix and also on te rotation speed. Te desiccant weels are mainly used in deumidification systems to control te umidity of airflows or te indoor air conditions in process rooms of some industries. Fig. 3.a scematically represents a system wit a eating coil, operating by Joule effect, or actuating as a eat excanger, to eat te regeneration airflow. In Fig. 3.b, a desiccant ybrid system wit two stages of air deumidification is sown. Te first stage occurs in a cooling coil of te compression vapour system and te second corresponds to te adsorption in te desiccant weel. Te eat released by te condenser is recovered to eat te regeneration airflow, improving te global efficiency of te system.

4 Heat and Mass Transfer in Desiccant Weels 515 a) Fig. 3. Deumidification systems based on desiccant weels: a) simple deumidification system and b) ybrid deumidification system b) Anoter possible interesting application, altoug less common, is for air cooling operations, combining te evaporative cooling wit te solid adsorption deumidification, as scematically represented in Fig. 4. Fig. 4. Desiccant evaporative cooling system Te moisture removal capacity of te desiccant weel can exibit significant time variations according to te load profile and weater conditions, a fact tat must be taken into account at design stage. On te oter and, te operational costs depend on te control strategy cosen for te system. Te capacity control alternatives can be based on: a) fan modulation, b) by-pass of te process airflow or of te regeneration airflow, c) modulation of te eating device for regeneration or d) modulation of te rotation speed of te weel. Te strategies based on variable airflow by fan modulation are generally more efficient, presenting iger potential to reduce te running costs.

5 516 Advanced Topics in Mass Transfer Different numerical modelling metods of solution supported by different simplified treatments of te flow and te solid domains ave been used. Several numerical difficulties are related wit te coupling between te different penomena and te computational time consumption, mainly in detailed numerical models. One crucial aspect is te caracterization of te matrix material of te desiccant weel, namely te knowledge of its termal properties, diffusion coefficients, pase equilibrium laws, ysteresis effects, etc. In Pesaran (1983), te study of water adsorption in silica gel particles is focussed on te importance of te internal resistances to mass transfer. Te investigation of Kodama (1996) deals wit te experimental caracterization of te matrix of a desiccant rotor made of a composite desiccant medium, a fibrous material impregnated wit silica gel. It is recognized te importance of validating te numerical models by comparison wit experimental data, necessarily covering a wide range of conditions, but te publised data on tis matter are scarce. In some cases, te degree of accuracy of te measured results is not indicated and, in oter works, a poor degree of accuracy is reported. Moreover, some examples of exaustive experimental researc on te beaviour of a desiccant weel (Cejudo et al., 2006) sow significant mass and energy imbalances between te regeneration and te process air streams. 1.3 Real and ideal psycrometric evolutions An example of te psycrometric evolutions in bot air flows is scematically represented in Fig. 5. A decrease of te water vapour content and a temperature increase of te process air are observed and opposite canges are observed in te regeneration air. 1 in 2out 1out 2in wv T Fig. 5. Psycrometric evolutions of te airflows in a desiccant weel Te outlet states of bot airflows are influenced by te rotation speed, te airflow rates, te transfer area in te adsorption and te desorption zones of te weel, te tickness of cannel wall and its properties. Te expected influence of te cannel lengt and of te adsorption/desorption cycle duration on te outlet states of bot airflows is scematically represented in Fig. 6, for te particular case of equal mass flow rates. Te outlet state of eac

6 Heat and Mass Transfer in Desiccant Weels 517 airflow is defined by te interception of te isolines of te cannel lengt Lc and of te cycle duration τ cyc. Te solid curves L c1, L c2 and L c3 correspond to rotor matrix wit sort, medium-lengt and long cannels, respectively. Te solid curves τ cyc1, τ cyc2 and τ cyc3 correspond to low, medium and ig cycle durations, respectively. For eac cannel lengt an optimum value of te cycle duration exists, i.e. te optimum rotation speed tat maximizes te deumidification rate. Tis optimal rotation diminises wit te cannel lengt. τcyc3 τcyc2 τ cyc1 2out,id 2out 1in L c3 Lc2 Lc1 Lc1 Lc2 Lc3 2in 1 out τcyc1 τcyc2 τcyc3 wv T 1out,id Fig. 6. Influence of te cannel lengt and of te cycle duration on te psycrometric evolutions Te ideal beaviour of a desiccant weel corresponds to cases wit infinite transfer area of te cannel. It is common to take te maximum ideal deumidification rate as a reference, te corresponding outlet states being represented in Fig. 6 by 1 out,id and 2 out,id. Te identification of te ideal outlet states requires te knowledge of te equilibrium curves of te ygroscopic matrix, i.e. te sorption isoterms. Suc information is scematically represented in Fig. 7 by te adsorbed water content X as a function of te water vapour content w v and of te temperature T. Te adsorbed water content in te ygroscopic matrix at te equilibrium condition imposed by te inlet state of te process airflow corresponds to te ideal maximum value. Te minimum value of te adsorbed water content tat can be acieved in ideal operating conditions is dictated by te inlet conditions of te regeneration airflow. Te orizontal lines c1out and c 2out in Fig. 7 represent tose minimum and maximum values, respectively, and correspond to te dased curves c 1out and c 2out in Fig. 8. In most ygroscopic

7 518 Advanced Topics in Mass Transfer matrices, tose curves correspond to constant or quite constant values of te ratio of te water vapour partial to saturation pressure ( pv p vs ). Tis ratio corresponds strictly to te relative umidity concept of te moist air only in te cases were te temperature of te moisture air is lower tan te water saturation temperature at local atmosperic pressure (ASHRAE, 1989) c 2out 2 out 2in 1in in 1 out X (kg kg -1 ) in c 1out T w v (kg kg -1 ) Fig. 7. Representation of te equilibrium curves between te desiccant and te moist air Te ideal outlet state of te process air ( 1 out,id ) is defined by te interception of te curve c1out wit te line of constant specific entalpy 1in. In a similar way, te ideal outlet state of te regeneration air ( 2 out,id ) is defined by te interception of te curve c 2out wit te line of constant specific entalpy 2in. Consequently, te ideal (maximum) mass transfer rates are in a first step estimated as: and ( ) m = m w w (1.a) w1,id' 1 1in 1out,id ( ) m = m w w, (1.b) w2,id' 2 2out,id 2 in wic can most probably present different values, te lower value indicating te limiting airflow (ereafter called critical airflow). Te equality between te mass transfer rates in bot airflows is imposed by te principle of mass conservation, wic implies te redefinition of te outlet ideal sate of te non-critical airflow ( 1 out,id or 2 out,id ). Tis rationale is illustrated in Fig. 8, a case were te critical airflow is te process air (airflow 1).

8 Heat and Mass Transfer in Desiccant Weels 519 c 2out 2 out,id c2out 2 out,id 1in 1in 2in c1out c 1out 2in 1 out,id 1 out,id Fig. 8. Ideal air evolutions in a desiccant weel, were te critical airflow is te process air 1.4 Pair of effectiveness parameters Following te classical analysis of te beaviour of eat excangers, te concept of effectiveness results from te comparison between a real eat excanger and an ideal one adopted as a reference. Te application of te so-called effectiveness metod to a desiccant weel requires te use of two effectiveness independent parameters due to te existence of te simultaneous and coupled processes of eat and mass transfer. Furtermore, tose parameters sould be quite independent of te inlet states of bot airflows or, at least, easily correlated wit tem. Te use of te effectiveness metod as practical interest, mainly to perform quick simulations of desiccant weels, but it needs te prior knowledge of te ideal outlet conditions or of te ideal transfer rates, as described in te previous section. Te deviation of te outlet states of bot airflows relatively to te ideal ones, as illustrated in Fig. 6, is an indicator of te effectiveness of te eat and mass transfer penomena in te desiccant weel. So, te state canges registered in bot airflows in a real application sould be compared wit tose of te ideal operation. Taking into account te analogy wit te classical analysis of eat excangers, te following generic definition for te effectiveness is purposed: φ φ φ φ η φ = = φ φ φ φ 1in 1out 2in 2out 1in 1out,id 2in 2out,id, (2) were te generic variable φ can assume different meanings suc as te adsorbed water content at equilibrium between te moist air and te desiccant.

9 520 Advanced Topics in Mass Transfer According to preliminary investigation, te recommended independent parameters for a desiccant weel are tose based on te canges of adsorbed water content X (kg of adsorbed water/kg of dry desiccant,) and of te specific entalpy (J/kg of dry air), respectively, ηx and η. Taking into account, for example, te canges occurring in te process airflow, η can be calculated by: X η = X X X,1in,1in X X,1out,1out,id, (3) were X,1out,id = X,2in 1out,id. Concerning te evaluation of η, it is not possible to consider tat =. So te following definition is proposed, by convenience: 1in η = 1in 1in 1out 2in. (4) At real conditions, it is expected tat bot effectiveness parameters exibit a dependence on te airflow rates, cannel lengt and rotation speed, as well on te inlet states of bot airflows. In an optimized case, operating near te ideal conditions, te effectiveness parameter η sould be low, near zero, wile ηx sould be as ig as possible, near te unity, te dependence on te operating parameters and conditions being quite negligible. Te application of te effectiveness metod is igly elpful in perform quick energy dynamic simulations of HVAC&R systems integrating desiccant weels at te design stage, tus promoting te use of more efficient systems tat allow te incorporation of renewable energy or waste energy recovery. 2. Modelling of desiccant weels 2.1 Objectives and outline Te aim of tis capter consists mainly of te use of a detailed numerical model to study te beaviour of desiccant weels. Focused on a representative cannel of a compact matrix, wic is ypotetically treated as a parallel-plate cannel, te detailed matematical formulation takes into account te important canges of properties in bot te porous solid and airflow domains tat generally occur in transient sorption processes. Altoug te detailed model is not an appropriate tool to perform te dynamic simulation of a real desiccant weel, due to its complexity and te required computational effort, it is an interesting complementary tool to be used in te product optimization by te manufacturer, in te investigation of te validity of te assumptions supporting simplified models (e.g., te lumped capacitance metod) and also to evaluate te dependence of te effectiveness parameters on te operating parameters and conditions. 2.2 Detailed numerical modelling of a representative cannel Te pysical domain of te ygroscopic weel can be considered as a set of small angular slices, te cannels in eac slice aving te same beaviour. Te transient tree-dimensional problem is too complex to be solved in a very detailed way and, terefore, it is necessary to adopt a set of simplifications. Te most common simplification about te pysical domain is te consideration of two-dimensional airflow between desiccant parallel plates. Te

10 Heat and Mass Transfer in Desiccant Weels 521 ypotesis of two-dimensionality, togeter wit te consideration of cyclic inlet conditions, real wall tickness and ratio of airflow rate to wetted perimeter is frequently adopted wen modelling te beaviour of desiccant weels (Dai et. al, 2001 and Zang et al., 2003). Te wall domain of a cannel of te ygroscopic matrix is modelled in a detailed way, by taking into account te simultaneous eat and mass transfer togeter wit te adsorption/desorption process. Fig. 9 illustrates te pysical domain of te cannel to be modelled. Two pases co-exist in equilibrium inside te desiccant porous medium, te equilibrium being caracterized by sorption isoterms. Te ordinary diffusion of vapour is neglected due to te small dimension of te pores (Pesaran, 1983). Terefore, only two mecanisms of mass transport are considered: surface diffusion of adsorbed water and Knudsen diffusion of water vapour. For simplification purposes, te wall is considered to be a omogeneous desiccant porous material. Te upper boundary of te domain is considered impermeable and adiabatic. Te treatment of te airflow as a bulk flow and te use of suitable convective eat and mass transfer coefficients are considered to evaluate te excanges occurring at te interface between te airflow and te desiccant wall surface. L c y= y c y Desiccant porous medium x Airflow Fig. 9. Pysical domain of te modelled cannel For te wall domain, te complete set of conservation equations to be solved by te model can be reduced to te general form: H p H c x x = c φ ( ρφφ ) + Γφ Sφ = 0, (4) t x j x j were te density ρ φ, te diffusion coefficient Γ φ and te source-term S φ assume different meanings depending on te nature of te generic variable φ considered ( φ= X - mass conservation equation of adsorbed water, φ = T - energy conservation equation, φ=ϕv - mass conservation equation of water vapour). According to te local equilibrium condition assumption, only one of te two differential mass conservation equations is solved, te mass conservation equation for water adsorbed water. Te mass fraction of water vapour inside te porous medium ϕ v is calculated troug te knowledge of te sorption isoterm. For te airflow domain, te simplified one-dimensional conservation equation is considered: ( ρfφ ) + ( ρfufφ) Sφ = 0 t x (5) were te source-term S φ assumes also different meanings depending on te nature of te generic variable φ considered ( φ = 1 - global mass conservation equation, φ=ϕ v - mass conservation equation of water vapour, φ = T - energy conservation equation, φ= u - f

11 522 Advanced Topics in Mass Transfer momentum conservation equation). At te interface ( y = y c ), te mass and eat convection transfers are modelled assuming tat te low mass transfer rate teory is valid (Bird, 1960 and Mills, 1994). Te eat convection coefficient is estimated after te Nusselt number Nu for developed laminar cannel flow. As for te mass convection coefficient m, te Serwood number S is related to Nu according to te Cilton-Colburn analogy. Te convective fluxes at te interface are calculated as: j ϕv,f ϕ = ρ 1 ϕ v,gs m f v,i v,i (6) ( ) j = T T (7),gs f i were ϕ v,i and T i are values at te interface, respectively, for te vapour mass fraction and te temperature. Te water vapour content in te airflow or inside te pores of te desiccant medium is related wit te mass fraction of water vapour by w v = ϕv /(1 ϕ v). Te modelling of a cannel requires te definition of te initial conditions and of te conditions of te airflow entering te cannel. Te initial conditions are imposed by specifying uniform distributions of T and X in te desiccant wall. Te airflow domain is assumed to be initially in termodynamic equilibrium wit te desiccant wall. Te condition of te airflow entering te cannel is imposed by specifying te inlet velocity of te airflow u = uin (or te corresponding mass inlet velocity, F m = F m,in ), as well te inlet temperature T in and te water vapour fraction ϕ v,in. Te total pressure is assumed to be constant and its value is imposed. Te numerical solution procedure is based on te solution of te discretized partial differential equations using te finite volume metod. Te values of te diffusion coefficients at te control-volume interfaces are estimated by te armonic mean, tus allowing te conjugate and simultaneous solution in bot gas and solid domains (Patankar, 1980). Te energy and te vapour mass transport equations are solved in a conjugate procedure tat covers simultaneously bot sub-domains. Witin te desiccant wall subdomain, te equilibrium value of te vapour mass fraction is locally specified. Additional data and te complete description of te formulation of different versions of te model can be found in previous works (Ruivo et al, 2006; Ruivo et al, 2007 a,b ; Ruivo et al, 2008 a,b and Ruivo et al. 2009). Te numerical model as been used in simulating te cyclic beaviour of a typical cannel of desiccant weels and also te beaviour of a wall element of te cannel, namely to inspect te validity of some assumptions tat support simplified numerical metods. 2.3 Prediction of te beaviour of desiccant weels Te beaviour of te modelled cannel enables te prediction of te global beaviour of te desiccant weel crossed by two airflows at steady state conditions. Te adsorption mode corresponds to te adsorption zone of te rotor matrix, were te deumidification of te process airflow occurs, wile te desorption mode corresponds to te desorption zone, were te rotor matrix is regenerated. Te cyclic process wit a duration τ cyc is divided into te adsorption and te desorption modes, wit durations τ ads and τ des. From te point of

12 Heat and Mass Transfer in Desiccant Weels 523 view of te modelled cannel, te desorption and te adsorption processes occur, respectively, wen 0< t τ des and τ des < t τ cyc. Te modelled cannel tat is representative of te matrix is submitted to an initial transient process tat must be started at a certain condition. Te transition of mode, from desorption to adsorption, or vice-versa, is done by suddenly canging te inlet airflow conditions and reversing te airflow direction in te cannel. After a certain number of desorption/adsorption cycles, te differences between two consecutive cycles are negligible, meaning tat te stationary cyclic regime was acieved. Te initial condition for te sequence of te cycles corresponds to te beginning of one of te modes of te cycle (desorption or adsorption), imposing uniform distributions for temperature and adsorbed water content in te desiccant and assuming tat te airflows are initially in termodynamic equilibrium wit te desiccant medium. At steady state conditions, te mass transfer rate occurring in te desorption zone is equal to tat occurring in te adsorption zone. Terefore, considering te desorption mode, te following expressions can be deduced, respectively, for te mass and eat transfer rates between bot airflows, per unit of transfer area of te matrix: x c 1 Jv,gs = jv,gsdx x (8) c 0 x c 1 J,gs = j,gsdx x (9) c 0 Te global mass and eat transfer rates in te desiccant weel at steady state operating conditions, per unit of transfer area of te matrix, are: J τdes v,gs Jm = dt (10) 0 τcyc J τdes,gs J = dt (11) 0 τcyc At te outlet of eac zone, te air state exibits a non uniform angular distribution. Te downstream average of temperatures and of water vapour contents at te outlet of te cannel in eac operation mode are evaluated, te acieved values representing te outlet states of te regeneration and process airflows crossing te desiccant weel at steady state condition (Ruivo, 2007 b ). 2.4 Properties and coefficients Te numerical model takes into account te canges occurring in te airflow properties and in te convection and diffusion coefficients. Te major part of te relations for te dry air, water vapour and liquid water was derived from termodynamics tables (Çengel, 1998) in te form of polynomial expressions (Ruivo, 2005). Te properties of te air-mixture suc as te specific eat and te termal conductivity are weigted averages based on te dry air and water vapour mass fractions. Similarly, te specific eat and te termal conductivity of

13 524 Advanced Topics in Mass Transfer te wet desiccant medium are weigted averages based on te mass fraction of eac component (dry-air, water vapour, adsorbed water and dry desiccant). Te properties of silica gel RD, te relations for te equilibrium condition, te eat of wetting, te adsorbed water entalpy and te adsorption eat are indicated in Ruivo et al. (2007 a ). Te dependences of te mass diffusion coefficients on te temperature and on te adsorbed water content are also presented in Ruivo et al. (2007 a ), and were derived after te expressions in Pesaran (1983). Te equilibrium curve for te pair silica gel-moist air is represented in Fig X (kg kg -1 ) p v / p vs Fig. 10. Equilibrium curve for te pair silica gel-moist air 3. Study cases and results 3.1 Prediction of te performance of desiccant weels One of te potentialities of te present numerical model is te calculation of te transient evolutions of te internal fields of temperature and of water vapour content, bot in te airflow and in te cannel wall domains. Different parametric studies ave been conducted using te numerical model to investigate te influence of a set of parameters, namely te rotation speed, te cell dimensions, te wall tickness, as well as te inlet conditions of bot airflows, on te beaviour of desiccant weels (Ruivo, 2005 and Ruivo et al b ). Te researc done by using suc detailed numerical model gives to te manufacturers important guidelines to te optimization of te desiccant deumidification equipments. Moreover after calibration by comparison wit experimental data, te detailed numerical models are also an interesting tool to generate data of global performance of desiccant weels, namely te outlet state of bot airflows or te eat and mass transfer rates for a large set of operating conditions. Te acieved global beaviour data can be displayed in a cart or in a table, represented by correlations or be used to test te validity of easy and quick predicting metods. Tis information is very elpful for a more accurate sizing of te deumidification

14 Heat and Mass Transfer in Desiccant Weels 525 and/or cooling installations and to analyse dynamically different solutions, namely to investigate te control strategies tat lead to a better energy use. w v (kg kg -1 ) T (ºC) t (s) x= 0 m a) T i T f x= 0 m w v,i w v,f t (s) Fig. 11. Cyclic evolutions of te interface and of te airflow states: (a) temperature and (b) water vapour content b) 0.3

15 526 Advanced Topics in Mass Transfer Te data plotted in Fig. 11 concern to te internal beaviour of a desiccant weel composed by a compact corrugated matrix wit sinusoidal cross section cannels. Te specific transfer area and te porosity of te matrix are 3198 m 2 m -3 and 0.84, respectively. According to Ruivo et al. (2007 b ), te cosen matrix corresponds to cell B3 ( Hcell = 1.5 mm, Pcell = Psin = 3 mm, Ep = 0.1 mm, Hsin = 1.27 mm), te representative cannel of te matrix being modelled wit Hp = 0.05 mm and Hc = mm. Te cannel lengt is Lc = 0.3 m. Te rotor speed is 7.2 rotations per our, tat corresponds to τ cyc = 500 s. Te desiccant weel is divided into two equal parts, te adsorption and desorption zones being crossed by counter-current airflows. Te desiccant is silica gel. Te inlet temperatures of te process and regeneration airflows are 30 ºC and 100 ºC, respectively. Equal values of te inlet water vapour content (0.01 kg kg 1 ) and of te mass inlet velocity (1.5 kg s 1 m 2 ) are imposed to bot airflows. Te illustrated time evolutions of te states of te interface and of te bulk airflow evidence te abrupt variations in te mode transition. From te temperature and te moisture content evolutions (Figs. 11.a and 11.b), it can be observed tat te airflow and te wall are closely in termodynamic equilibrium in most of te rotor domain, a condition tat is sometimes taken as a simplifying ypotesis in te beaviour analysis of ideal desiccant weels (v., e.g., Van den Bulk, (1985)). It can also be seen tat only in te desorption mode te cannel wall surface acieves equilibrium wit te incoming air, an indication tat te regeneration process is completed. Tis suggests tat it is possible to optimise te deumidification performance of te rotor troug te canges of te rotation speed and of te adsorption and desorption zones. Oter cases wit different cycle durations were simulated. Te registered influence of τ cyc on te global eat and mass transfer rates is sown in Fig. 12. Te eat transfer rate exibits a monotonic decreasing trend wit te cycle duration wile a maximum value of te mass transfer rate is observed Jm 10 6 (kg s -1 m -2 ) J 10 6 (W m -2 ) τ cyc (s) Fig. 12. Heat and mass transfer rates per unit of transfer area of te desiccant weel

16 Heat and Mass Transfer in Desiccant Weels Test of simplifying assumptions for numerical modelling Several studies ave been carried out to predict te beaviour of desiccant weels using simplified matematical models (e.g. Zeng, 1993; Dai et al., 2001; Zang et al and Gao et al. 2005). In most of tem, te eat and mass transfers inside te desiccant medium are not described in a detailed way, simplified approaces being adopted instead. Te range of validity of suc models can be investigated by using experimental tecniques and by detailed numerical modelling. Te air stream beaviour and its interaction wit te desiccant medium are also often treated in a simplified way, namely by assuming a fictitious bulk flow pattern, as well as fictitious eat and mass convection coefficients for te gas side. Wen advanced numerical metods are used, solving te complete set of differential transport equations, a number of critical issues still remain, suc as te lack of suitable functions to describe te variation of te porous medium properties and te complexity of numerically solving te intrinsically coupled penomena witin te porous desiccant solid and te great time consumption of computational calculations. In te present section, te numerical detailed model is used to simulate te pysical beaviour of te desiccant layer of a wall element of te cannel. It is also supposed tat te desiccant layer belongs to te cannel wall of a compact desiccant matrix, wic is crossed by a moist air flow. Te ypotesis of one-dimensionality assumed in tis study is mainly intended to better identify te effects to be analysed, namely te importance of neglecting te internal eat and mass diffusive resistances. Te pysical model is scematically represented in Fig. 13. Desiccant wall element y= y c y Airflow Tf, ϕv,f ;, m H p x x = x c Fig. 13. Scematic representation of te cannel wall element For te assessment of te internal resistances of te porous medium in te cross direction, tere is no interest to consider te streamwise variation of te flow properties. Terefore te pysical domain is reduced to an element of te cannel wall, wic is considered as a omogeneous desiccant medium, aving te properties of silica-gel and an infinitesimal lengt in te flow direction. Te eat and mass transfer penomena inside te porous medium are considered only in te y direction. Te air stream in contact wit te infinitesimal-lengt wall element is treated as a well mixed flow (bulk flow), caracterised by constant and uniform properties (pressure, temperature and vapour content), tus dispensing te need of solving any conservation equation in te flow domain. Results of te investigation about two simplifying approaces based on te lumpedcapacitance metod (Ruivo et al., 2008 b ) are ere presented. Te first approac corresponds to te teoretical analysis of te system wit negligible internal resistances to te eat and mass diffusion, commonly known as te global lumped-capacitance metod (approac A- null resistances ). It is numerically simulated by specifying enoug great values of te

17 528 Advanced Topics in Mass Transfer diffusion coefficients (te termal conductivity and te coefficients of Knudsen diffusion and of surface diffusion). Te oter approac corresponds only to te termal lumpedcapacitance metod (approac B- null termal resistance ). It is numerically simulated by imposing an enoug great value to te termal conductivity of te desiccant medium y (mm) t=0 s T (ºC) a) y (mm) t=0 s X (kg kg -1 ) Fig. 14. Time-varying profiles of te dependent variables along te desorption process in a desiccant layer of H = 1 mm: (a) temperature and (b) adsorbed water content X p b) Te numerical tests of bot simplifying approaces consists of te analysis of te response of te desiccant wall to a step cange of te airflow conditions, starting from a given initial 96.9

18 Heat and Mass Transfer in Desiccant Weels 529 desiccant state and finising wen te desiccant wall acieves te equilibrium wit te moist airflow. Te results ere presented are for te simulation of te transient process of desorption, were te initial temperature and adsorbed water content in te desiccant were 30ºC and kg kg -1, respectively. Te airflow conditions were 100ºC and 0.01 kg kg -1, respectively for te temperature and te water vapour content. Te process pressure was assumed as Pa T (ºC) H p = 0.01 mm t (s) Fig. 15. Predicted temperature at te convective interface considering normal internal resistances ( ), null termal and mass resistances ( approac A) and null termal resistance ( approac B) Te value 2.45 was assigned to te Nusselt number corresponding to eat convection between a uniform temperature wall and a fully-developed laminar flow inside a corrugate sinusoidal-type cannel of a compact excanger (Zang et al., 2003). Te cannel crosssection area was 4.5 mm 2, wit an internal perimeter of 10.6 mm and a ydraulic diameter of 1.69 mm, approximately. Te conducted runs covered a wide range of values of te layer tickness in order to study te validity of neglecting internal termal and mass resistances and only te termal resistance. Te properties of te desiccant medium were referred also to silica gel RD (Pesaran, 1983). A particular case was selected for te analysis of te transient evolutions of te main variables inside a desiccant layer wit 1 mm of tickness. Time-evolving profiles are sown in Figs. 14.a and 14.b as calculated wit te normal

19 530 Advanced Topics in Mass Transfer internal resistances. It is seen tat te temperature field presents small gradients, meaning tat te internal resistance to eat diffusion is almost insignificant, contrarily to tose restricting te mass diffusion. Te gradients of te adsorbed water content are significant during almost all te transient process, mainly near te convective surface. Te diagrams in Figs. 15 and 16 sow te time evolutions of te temperature and of te adsorbed water content at te interface determined by te detailed model for te tree different scenarios: wit normal internal resistances, witout internal resistances to te eat and mass and witout internal resistance to eat conduction. It can be observed tat te results of approac A (dased lines) sow an increasing deviation relatively to tose of te detailed model (full lines) for desiccant layers wit Hp 0.1 mm. Moreover, te results of approac B agree reasonably well wit te detailed model for all studied wall ticknesses, unlike tose of approac A. Tis indicates tat significant inaccuracies may result wen te internal resistance to mass diffusion is neglected, leading to unrealistic estimation of te convection fluxes at te interface. It can be concluded tat te eat and mass lumped capacitance assumption supporting te pseudo gas-side model is acceptable for desiccant layers tinner tan about 0.1 mm X (kg kg -1 ) H p = 0.01 mm t (s) Fig. 16. Predicted adsorbed water content at te convective interface considering normal internal resistances ( ), null termal and mass resistances ( approac A) and null termal resistance ( approac B)

20 Heat and Mass Transfer in Desiccant Weels Assessment of effectiveness parameters Several assessments of te desiccant weel effectiveness parameters ave been recently conducted based on experimental and numerical modelling data. Te cases ere presented were generated by te detailed numerical model to investigate te influence of te regeneration temperature on te effectiveness parameters. Different inlet states of te regeneration airflow were considered, corresponding to 80, 100 and 120ºC of temperature, all wit te same value of te water vapour content 0.01 kg kg 1. Te value of 1.5 kg s 1 m 2 is considered for te mass inlet velocity of bot airflows. Te inlet state of te process airflow is defined by a temperature of 30ºC and water vapour content of 0.01 kg kg 1. Te desiccant weel is symmetric. Te desiccant is silica gel. Te rotor matrix corresponds also to cell B3, i.e, te specific transfer area and porosity of te matrix are 3198 m 2 m -3 and 0.84, respectively. According to Ruivo et al. (2007 b ), te representative cannel of te matrix being modelled wit H p =0.05 mm, H c =0.263 mm. Te cannel lengt is L c =0.3 m. Te rotation speed corresponds to cycle duration of 500 s, close to te optimum value tat maximises te deumidification rate (see Fig. 12). Te output results of te detailed numerical model for te different simulated cases are indicated in Table 1. Te effectiveness parameters η and η presented in Table 2 were calculated, respectively, by te Eqs. 3 and 4. X Case T 1in [ºC] w v,1in [kg kg 1 ] T 2in [ºC] w v,2in [kg kg 1 ] T 1out [ºC] w v,1out [kg kg 1 ] Table 1. Output results of te detailed numerical model Case η ηx Table 2. Calculated effectiveness parameters η and ηx. Te registered inlet regeneration temperature dependence of η and ηx is small, being te constant value corresponding to te average of te values acceptable to use in te in te effectiveness metod. It sould be remarked tat te set of analysed cases does not

21 532 Advanced Topics in Mass Transfer represent an exaustive study. Furter researc sould be done based on additional numerical or experimental modelling data. 4. Conclusions Tis Capter gives an overview of te researc towards te prediction of te beaviour of desiccant weels. Ideal and real psycrometric evolutions of process and regeneration airflows were analysed, and te general trend of te influence of te cannel lengt of te matrix and te cycle duration was presented, as well as te procedure to determine te ideal outlet states of bot airflows. Tis procedure takes into account te curves of equilibrium between te moist-air and te desiccant medium as well as te relation between bot airflow rates, and enables te identification of te airflow tat limits te process of eat and mass transfer (critical airflow). A new pair of independent parameters for te effectiveness of te coupled eat and mass transfer in desiccant weels is proposed, te values at ideal operating conditions being pysically intuitive, i.e. η = 0 and η =1, and independent of te operating conditions. A numerical model for simulating te cyclic adsorption/desorption process in a representative cannel of te desiccant matrix was briefly referred. Te model is based on te solution of te differential equations for te conservation of mass and energy. Te airflow is treated as a bulk flow, te interaction wit te wall being evaluated by using appropriated convective coefficients. Te wall domain is treated in detail, considering te internal time-varying fields of variables and properties. To illustrate te potentialities of te model in predicting te internal beaviour of a desiccant weel, data tat are useful for te manufacturer to product optimization, te results of a particular case were presented. Results of a parametric study were also presented, sowing te dependence of te global beaviour of te desiccant weel on te rotation speed. An expected optimum point maximizing te deumidification rate was determined. An adapted version of te model to simulate te detailed eat and mass transfer during te adsorption process in a wall element of te cannel was used to investigate te validity of simplifying assumptions, namely tose tat neglect te internal eat and mass diffusive resistances. Te results of te parametric study sow tat te internal resistance to mass diffusion is muc more important tat te internal termal resistance. Tis justifies te use of a simplified metod assuming no internal termal gradients in te desiccant wall in te direction normal to te airflow. Te use of a lumped capacitance metod for te coupled eat and mass transfer is acceptable only for very tin desiccant wall layers. Anoter parametric study of te global beaviour of a desiccant weel at different regeneration temperatures was presented and its results were used to calculate te effectiveness values, a quite negligible dependence of η and η relatively to te regeneration temperature being observed. Te adoption of te effectiveness metod seems to be an interesting tool, at te same time easy and intuitive, for design purposes. 5. References ASHRAE Handbook. Fundamentals (1989). American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., ISBN , Atlanta GA X X

22 Heat and Mass Transfer in Desiccant Weels 533 Bird, R.; Stewart, W. & Ligfoot, E. (1960). Transfer penomena, Jon Wiley & Sons, Inc., New York and London Cejudo, J; Moreno, R. & Carrillo, A. (2002). Pysical and neural network models of a silicagel desiccant weel. Energy and Buildings, Vol. 34, No. 8, (September 2002) pp , ISSN Çengel, Y. (1998). Heat Transfer- A practical approac, McGraw-Hill, ISBN Dai, Y.; Wang, R. & Zang, H. (2001). Parameter analysis to improve rotary desiccant deumidification using a matematical model. International Journal of Termal Sciences, Vol. 40, No. 4, (April 2001) pp , ISSN Gao, Z.; Mei, V. & Tomlinsom, J. (2005). Teoretical analysis of deumidification process in a desiccant weel. Heat and Mass Transfer, Vol. 41, No. 11, (July 2005) pp , ISSN Kodama, A. (1996). Experimental study on optimization of a oneycomb rotor continuous adsorber operated wit termal swing, P.D tesis, Faculty of Engineering, Kumamoto University, Japan Mills, A. (1994). Heat and mass transfer, CRC Press, ISBN Patankar, S. (1980). Numerical eat transfer and fluid flow, McGraw-Hill, Wasington Pesaran, A. (1983). Moisture transport in silica gel particle beds, P.D tesis, University of California, Los Angels Ruivo, C. (2005). Modelação numérica dos fenómenos de transferência de calor e de massa em rodas igroscópicas, P.D tesis, University of Coimbra, Coimbra, Portugal, ISBN Ruivo, C.; Costa, J. & Figueiredo, A. (2006). Analysis of simplifying assumptions for te numerical modeling of te eat and mass transfer in a porous desiccant medium. Numerical Heat Transfer, Part A Applications, Vol. 49, No. 9, (October 2006) pp , ISSN Ruivo, C.; Costa, J. & Figueiredo, A. (2007) a. On te beaviour of ygroscopic weels: Part I cannel modelling. International Journal of Heat and Mass Transfer, Vol. 50, No , (November 2007) pp , ISSN Ruivo, C.; Costa, J. & Figueiredo, A. (2007) b. On te beaviour of ygroscopic weels: Part II rotor performance. International Journal of Heat and Mass Transfer, Vol. 50, No , (November 2007) pp , ISSN Ruivo, C.; Costa, J. & Figueiredo, A. (2008) a. Numerical study of te beavior of an elementary desiccant layer of a ygroscopic rotor. Numerical Heat Transfer, Part A Applications, Vol. 53, No. 10, (January 2008) pp , ISSN Ruivo, C.; Costa, J. & Figueiredo, A. (2008) b. On te validity of lumped capacitance approaces for te numerical prediction of eat and mass transfer in desiccant airflow systems. International Journal of Termal Sciences, Vol. 47, No. 3, (Marc 2008) pp , ISSN Ruivo, C.; Costa, J. & Figueiredo, A. (2009). Validity of pseudo-gas-side-controlled models to predict te beaviour of desiccant matrices. International Journal of Termal Sciences, Vol. 48, No. 11, (November 2009) pp , ISSN Van Den Bulk, E.; Mitcell, J. & Klein, S. (1985). Design teory for rotary eat and mass excangers - I. Wave analysis of rotary eat and mass excangers wit infinite transfer coefficients. International Journal of Heat and Mass Transfer, Vol. 28, No. 8, (August 1985) pp , ISSN

23 534 Advanced Topics in Mass Transfer Zang, X.; Dai, Y. & Wang, R. (2003). A simulation study of eat and mass transfer in a oneycomb rotary desiccant deumidifier. Applied Termal Engineering, Vol. 23, No. 8, (June 2003) pp , ISSN Zeng, W. & Worek, W. (1993). Numerical simulation of combined eat and mass transfer processes in a rotary deumidifier. Numerical Heat Transfer, Part A Applications, Vol. 23, No. 2, (Marc 1993) pp , ISSN

24 Advanced Topics in Mass Transfer Edited by Prof. Moamed El-Amin ISBN Hard cover, 626 pages Publiser InTec Publised online 21, February, 2011 Publised in print edition February, 2011 Tis book introduces a number of selected advanced topics in mass transfer penomenon and covers its teoretical, numerical, modeling and experimental aspects. Te 26 capters of tis book are divided into five parts. Te first is devoted to te study of some problems of mass transfer in microcannels, turbulence, waves and plasma, wile capters regarding mass transfer wit ydro-, magnetoydro- and electro- dynamics are collected in te second part. Te tird part deals wit mass transfer in food, suc as rice, ceese, fruits and vegetables, and te fourt focuses on mass transfer in some large-scale applications suc as geomorpologic studies. Te last part introduces several issues of combined eat and mass transfer penomena. Te book can be considered as a ric reference for researcers and engineers working in te field of mass transfer and its related topics. How to reference In order to correctly reference tis scolarly work, feel free to copy and paste te following: Celestino Ruivo, José Costa and António Rui Figueiredo (2011). Heat and Mass Transfer in Desiccant Weels, Advanced Topics in Mass Transfer, Prof. Moamed El-Amin (Ed.), ISBN: , InTec, Available from: ttp:///books/advanced-topics-in-mass-transfer/eat-and-mass-transferin-desiccant-weels InTec Europe University Campus STeP Ri Slavka Krautzeka 83/A Rijeka, Croatia Pone: +385 (51) Fax: +385 (51) InTec Cina Unit 405, Office Block, Hotel Equatorial Sangai No.65, Yan An Road (West), Sangai, , Cina Pone: Fax: