Modeling of Conjugated Heat and Mass Transfer in Solid Sorbents

Transcription

1 Modeling of Conjugated Heat and Mass Transfer in Solid Sorbents C.E.L. NOBREGA Departamento de Engenharia Mecânica Centro Federal de Educação Tecnológica CEFET-Rio Av. Maracanã, 229, Bloco E, ZC: BRAZIL N.C.L. BRUM Programa de Engenharia Mecânica Universidade Federal do Rio de Janeiro COPPE/UFRJ Rio de Janeiro, Cidade Universitária, P.O: BRAZIL Abstract: - Although the content of ater vapor ithin atmospheric air is usually comprised of a fe grams per kilogram of dry air, the control of humidity is of crucial importance in HVAC design, due to the high latent heat of ater. Accordingly, air dehumidification can account for as much as 40% of the total energy consumption of an air conditioning unity. The use of solid sorbents for air dehumidification has increased over the last decades, as some materials can be prepared as a coating for porous matrices used as heat and mass exchangers. Since the adsorption is an exothermic phenomenon, the mass transfer significantly affects the heat transfer process. The present paper is dedicated to the modeling and solution of the conjugated heat and mass transfer in a solid sorbent layer. Key-Words: - adsorption, desiccant, dehumidification, heat and mass transfer. Introduction The concern ith indoor air quality has led to increased air ventilation rates in modern building design. As a consequence, cooling units ith larger capacity have to be employed, since outdoor air has to be cooled and dehumidified to the comfort condition. This increase in the thermal load can be minimized by using an enthalpy heel, described in Fig.. It consists of a porous cylindrical matrix, usually made ith fiber-glass or aluminum. The matrix is coated ith a desiccant material, usually silica-gel or an artificial zeolite. The enthalpy heel continuously rotates beteen the supply and exhaust air ducts of the building. Heat is transferred form the supply side to the exhaust side, as the exhaust stream is colder than the supply air stream. In addition, some moisture contained ithin the supply air stream is captured by the desiccant coat, as it flos through the enthalpy heel. This moisture ill be released on the exhaust side, since the exhaust stream is dryer than the supply air stream. Accordingly, the enthalpy heel allos simultaneous heat and mass transfer to the exhaust stream, hich is sub sequentially dumped back to the atmosphere. Fig. shos the detail of typical cell. The air flos through the channel, exchanging heat and mass ith the desiccant felt. The knoledge of the temperature and mass distributions along the flo direction is of great importance to airconditioning engineers. A number of assumptions are required to obtain a solvable mathematical model, hile retaining physical reasoning [, 5]: The physical domain is bounded by symmetry lines, hich represent perfectly insulated and impermeable surfaces. All air and desiccant physical properties are constant. The air flo is thermally developed The temperature and mass concentrations in y direction are disregarded. Accordingly, only distributions in the x direction are considered. The adsorption heat is represented by a heat source ithin the desiccant felt. Initial temperature and mass distributions are unknon but the heel operates in cycles, hich characterizes the problem as periodic. The heat of adsorption is comprised by the sum of the ater latent heat of vaporization and the ettability heat, hich accounts for reducing one degree of movement freedom of an adsorbed vapor molecule. ISBN:

2 Defining a non-dimensional position x 2hyAF x H m T (5) And a non-dimensional time t hy xt (6) mc 2 AF B WR Equations () to (4) can be reritten as Figure : Schematic of an enthalpy heel 2 Problem Formulation Figure (2.a) shos a control volume in the flo direction, enclosing a differential length of the desiccant felt and the flo channel. The mass conservation principle is expressed as [6,8] Y Y f m W 0 m u t x L t () Y x W t T x T t Y Y Y Y 2 T T T T Y Y (7) (8) (9) (0) Figure (2.b) shos a control volume in the flo direction, enclosing exclusively a differential length of the desiccant felt. The mass conservation principle is expressed as f m Ly AF W t y 2 h Y Y (2) Figure (3.a) shos a control volume in the flo direction, enclosing exclusively a differential length of the desiccant felt. The energy conservation principle is expressed as H H m H 0 m u t x L t (3) Figure (3.b) shos a control volume in the flo direction, enclosing exclusively a differential length of the flo channel. The energy conservation principle is expressed as m H H H 2hy Y Y 2h T T yaf u t x Y (4) ith 2 C r H f T H H Y f W Q H H T T () (2) The adsorption of a gas on a solid surface is an exothermic process, since the degrees of freedom of gas molecules movement are reduced. The heat liberated is called heat of adsorption, and in the case of ater vapor is comprised of the latent heat of evaporation plus the heat of etting. The folloing expressions for the heat of adsorption and the isotherm for ater vapor and regular density silicagel ere obtained experimentally [9]: Q2400W 3500, W 0.05 Q400W 2950, W 0.05 (3) ISBN:

3 W W W W 3 4 (4) Figure 2: Mass Balance on a control volume Figure 4: fluxogram for iterative solution The convergence criteria requires a pre-established agreement for both temperature and concentration fields, Crit. T( x,0) T( guess)( x,0) Conv. temp T ( x,0) (5) Crit. W( x,0) W( guess)( x,0) Conv. mass W( x,0) (6) As required by a periodic regime, the inlet of enthalpy must equal the average outlet enthalpy at the end of each cycle. An indication of the numerical accuracy of the solution is provided by the heat and mass balance error (HMBE), Figure 3: Energy Balance on a control volume 3 Problem Solution The solution of the problems requires Eqs. (7) to (0) to be discretized, using the finite-volume technique [0]. The convective terms ere represented by an upind scheme, hereas the time-dependent terms ere represented by a fully implicit scheme. The periodic nature of the problem requires an interactive solution. The initial temperature and concentration distributions ithin the desiccant felt are guessed, and the problem is solved up to the pre-defined nondimensional period P. The distributions in P are required to match the initially guessed distributions, as otherise the calculated distributions at P are used as a ne guess. A fluxogram is given in Fig. (4). ph pc Hhi Hci ( H ) 0 ho dt H 0 codt p h p c HMBE H H hi ci (7) All the calculations in the present ork exhibited HBE values smaller than 0.0%. The air enthalpy is given by H at Y d ct (8) a KJ / Kg C d KJ / Kg c KJ / Kg C Table shos typical temperature and concentration distributions along the flo direction, for t = 0.0 and t = P. ISBN:

4 t = 0.0 t = P x T(ºC) W T(ºC) W Table : Typical mass and temperature distributions at the beginning and end of a cycle The purpose of the equipment is to recover enthalpy form exhaust air stream, accordingly, it is opportunely to define enthalpy recovery effectiveness, Hhi Hho ER H H (9) hi ci The first analysis considers the simulation for three different values for the non-dimensional period of revolution P, as a function of the enthalpy heel non-dimensional length X. The results are shon in Fig. (5). It can be seen that loer periods of revolution ould lead to increasing enthalpy recovery effectiveness. ER by considering Figures (6) and (7), hich respectively depicts the temperature and humidity distributions along the desiccant felt, at the end of the desorption cycle. Figure (6) shos that the moisture removal capacity is small, as there is little difference beteen the humidity concentrations at the beginning and at the end of the adsorption process. The impact on the enthalpy recovery is hoever important, due to the significant value of the heat of adsorption. By comparing Figs. (6) and (7), it can be learned that the greater variation in the humidity content occurs by the middle of the section, here the temperature variation is also higher. Humidity Concentration, W NON-DIMENSIONAL POSITION, X Figure 6: Humidity concentration along the desiccant felt at selected angular positions, P = 8.0, L = Figure (7) shos that the desiccant felt temperature increases during the adsorption process, as heat is transferred form the supply air stream. Hoever, the rise in temperature negatively affects the adsorption process, hich is exothermic by nature. Accordingly, a rise in temperature of the surrounding medium inhibits the required heat release. Accordingly, the sensible and latent energy recoveries have competing effects over the enthalpy recovery effectiveness NON-DIMENSIONAL LENTGH, X Figure 5: Enthalpy recovery effectiveness The influence of the non-dimensional period of revolution over the effectiveness is further explained ISBN:

5 TEMPERATURE OF DESICCANT FELT, T W ( C) NON-DIMENSIONAL POSITION, X Figure 7: Temperature distribution along the desiccant felt at selected angular positions, P = 8.0, L = This is an interesting feature, since it makes the enthalpy recovery effectiveness fairly insensitive to the atmospheric conditions, as described by Fig. (8). ER L = 20.0 L = OUTSIDE AIR ABSOLUTE HUMIDITY, Y hi Figure 8: Enthalpy recovery effectiveness as a function of atmospheric conditions. The curve relative to L = 5.0 shos a little decrease in the enthalpy recover effectiveness as the atmospheric humidity increases. This effect shos to be overcome for a higher value of L. 4 Conclusion A simple mathematical model for the conjugated heat and mass transfer ithin a solid desiccant material as developed and numerically solved. The problem consists of a set of four partial differential equations, hich represent mass and energy balances ithin the air and the desiccant material, and one algebraic equation, hich stands for the desiccant adsorption isotherm. Although the conclusions are restricted to silica-gel, other materials could be easily fitted in the presented methodology. The governing equations ere composed by familiar non-dimensional parameters, so as to supply equipment designers ith typical figures. It as observed that sensible and latent energy recovery have contradictory effects over the enthalpy recovery effectiveness. It as also shon that the enthalpy recovery effectiveness is independent of the atmospheric conditions, as long as sufficient desiccant length is provided for both sensible and latent heat recovery. 5 Nomenclature a constant c constant cop coefficient of performance C r all specific heat (kj/kg K) d constant f desiccant mass fraction h heat transfer coefficient (KW/m 2 ) h y convective mass transfer coefficient (kg/m 2 s) H enthalpy of air (kj/kg) L length of the heel (m) m air mass flo rate (kg/s) m mass of the all (kg) P period of revolution P atm atmospheric Pressure (Pa) P t etted perimeter (m) P s saturation pressure (Pa) Q heat of adsorption (kj/kg) t time (s) T temperature (C) u air flo velocity (m/s) Y air absolute humidity (kg/kg air) Y L adsorbed air layer absolute humidity (kg/kg air) W desiccant humidity (kg of moisture/kg of desiccant) x coordinate (m) flo channel idth (m) y AF ISBN:

6 Greek letters 2 auxiliary parameter auxiliary parameter relative humidity of air layer effectiveness Subscripts ci cold inlet co cold outlet ER heat heel hi hot inlet ho hot outlet sat saturation all air Superscript non-dimensional Wheels, Energy, 2009, (34): doi:0.06/j.energy [7]Chung, J.D.; Lee, D.Y., Effect of Desiccant Isotherm on the Performance of Desiccant Wheel, International Journal of Refrigeration, 2009 ;( 32): doi: 0.06/ j.ijrefrig [8] Nobrega, C.E.L.; Brum, N.C.L., Influence of Isotherm Shape over Desiccant Cooling Cycle Performance, Heat Transfer Engineering, 2009, 30(4): doi:0.080./ [9] Pesaran, A.A., Mills, A.F..; Moisture Transport in silica Gel Packed Beds-Part I, International Journal of Heat and Mass Transfer, 987; (30): [0] Patankar, S. Numerical Heat Transfer and Fluid Flo. Boston, Ma: Hemisphere Publishing Co., 980. References: [] Bullock, C.E., Trelkheld, J.L., 966, Dehumidification of Moist Air by Adiabatic Adsorption, ASHRAE, Transactions, vol. (72), pp 30. [2] Maclaine-Cross, I.L.; Banks, P.J., 972, Coupled Heat and Mass Transfer in Regenerators, Int. Journal of Heat and Mass Transfer, vol. (5), 972. [3] Jurinak, J.J., J.W. Mitchell, W.A. Beckman, 984, Open Cycle Solid Desiccant Air Conditioning as an Alternative to Vapor Compression Cooling in Residential Applications Journal of Solar Energy Engineering, pp 252. [4] Zheng, W.; Worek, W.M.; 993, Numerical Simulation of Combined Heat and Mass transfer in a Rotary Dehumidifier, Numerical Heat Transfer, A, vol. (23) [5] Zhang, X.J., et al., 2003, A Simulation Study of Heat and Mass Transfer in a Honeycomb Rotary Dehumidifier, Applied Thermal Engineering, vol.23. [6] Nobrega, C.E.L.; Brum, N.C.L., Modeling and Simulation of Heat and Enthalpy Recovery ISBN: