Selection of adsorptive materials for desiccant cooling systems

Transcription

1 Selection of adsorptive materials for desiccant cooling systems Nóbrega, C.E.L., Brum, N.C.L. 2 Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, CEFET-RIO 2 Universidade Federal do Rio e Janeiro, COPPE-UFRJ. Corresponding nobrega@pobox.com SUMMRY The continuous rise of electric power rates worldwide and environmental issues related to the ozone layer depletion have increased the interest in natural gas cooling technologies over the last years. One of the most promising techniques consists of evaporative cooling aided by solid desiccants. lthough silica-gel has been primarily used in such systems, the requirement of encompassing a greater variety of climatic conditions has led to the development of new materials with selective adsorption properties, some of them being able to adsorb more than one chemical species at the same time (co-sorption. ccordingly, the present work analyses the influence of the isotherm shape of different adsorptive materials over the dehumidifying capacity of a desiccant wheel. mathematical model for the desiccant wheels is developed, and the governing equations for heat and mass transfer are solved employing a totally implicit finite volume technique. The adsorption isotherms are represented by a general equation characterized by a separation factor R, the variation of which allows the behavior of three different materials (silica-gel, molecular sieve and M to be simulated. The results show that the separation factor R has a great influence over the dehumidifying effectiveness, for a given regeneration temperature. INTRODUCTION The adsorption phenomena occur in almost all solid-vapor interfaces, but its effects are negligible unless the solid possess certain properties that allow a great affinity with the vapor. For instance, the internal area of cm 3 of silica-gel is estimated to be 4m 2. The average size of the porous is also of great importance, as it is the factor which determines the size of the molecules to be absorbed. The structural integrity in face of the continuous thermal inversion is also a factor to be considered. One of the earliest works devoted to the dehumidification modeling was performed by Bullock and Trelkheld [], and used a predictor-corrector method to solve a quite simplified model. Maclaine and Cross [2] presented a characteristics potential method, which allowed the coupled problem to be solved in an analogous heat transfer problem. Jurinak, Mitchell and Beckmann [3] proposed alternative design options combining evaporative coolers and desiccant wheels, expanding the range of applicability of such equipment. Zheng and Worek [4] used an explicit finite difference scheme to solve the governing equations, using experimental data for the silica-gel heat of adsorption and isotherm shape. Zhang, Dai and Wang. [5] presents a very accurate model for the cyclic adsorption, which however involves too many parameters. They also provide the experimental data for the heat of adsorption used by the present simulation. The present work uses a totally implicit finite volume technique to solve the non-dimensional governing equations, which contains less parameters when compared to previous efforts. It also proposes the use of a generalized equation for isotherm shape [6], which can be set to represent a particular material (silica-gel, molecular sieve 3 or M by choosing an

2 appropriate value for the separation parameter R. Desiccant wheels consist of a porous disc impregnated with hygroscopic material, which by definition attract and retain water vapor. Figure shows a schematic of a desiccant wheel, operating between two air streams. t the cold side, a fresh air stream (process air is forced through the wheel, giving up its moisture to the hygroscopic material and leaving the wheel at a much lower humidity ratio. s the wheel rotates, the hygroscopic material eventually switches to the regeneration stream, where hot air from a hot source is forced through the wheel, drying the hygroscopic material and dumping the water vapor back to the atmosphere. s depicted in Figure, the porososity pattern is not random, but formed by small channels, evenly distributed throughout the disc. Each channel has a structural layer (usually aluminum and an adsorptive layer, above which the air flows. Figure : Schematic representation of a desiccant wheel METHODS n element of the channel of length Δx, in the direction of the flow, as shown in figure 2, is considered. Figure 2: Elementary Control Volume

3 Some simplifying assumptions are necessary to the establishment of a mathematical model: The flow is hydrodynamic developed. 2 The heat and mass transfer coefficients are constant along the channel. 3 Energy and mass storage within the air are negligible when compared to the solid. 4 Uniform temperature and concentration values in the direction perpendicular to the flow. 5 Symmetry lines represent perfectly adiabatic and impermeable surfaces. 6 Thermal and mass resistances are negligible in the direction perpendicular to the flow. 7 Thermal and mass resistances are infinite in the direction of the flow. ssumption ( is reasonable because of the low viscosity of air and the (small ratio between the air channel height and length. ssumption (2 holds because the flow is usually laminar in the range of interest, whereas assumption (3 reflects the smaller thermal and mass capacitances of air when compared to those of the hygroscopic material. ssumption (4 reflects the typical dimensions of desiccant wheels, in which the channel length is usually a hundred times greater than the channel height and the desiccant layer. ssumption (5 reflects the homogeneity of the porous media, and both assumptions (6 and (7 are consequences of assumption (4. ccordingly, applying a mass balance to the elementary control volume shown on Figure (2, enclosing both the flow channel and the hygroscopic material, Y W m Y Δ xba + fρw Δ xbaw + Y + Δx Y t x n x transient transient withinthe solid net flux withinthechannel ρ in which ρ density of air Δ x elementary length b channel and solid width a channel height Y air absolute humidity W solid humidity content ρ a w density of solid f solid void fraction t time ( using the following definitions m ρ a y u n F m ρ a x y one obtain w w w F F n

4 + + f m Y Y w W m u t x x F t The mass transfer between the solid ant the air stream is given by or W f ρ bδ x a 2h bδx Y Y t ( w w y w f m w W nx y t F F ( 2 h Y Yw (2 y in which m w n x af h y total mass of desiccant in the wheel number of channels length of the wheel mass transfer coefficient pplying a mass balance to the control volume shown on Figure (2, enclosing both the flow channel and the hygroscopic material, H H w m H ρ Δ x yf a + ρw Δ x yf aw + H + Δx H t t n x or transient transient net flux within the channel within the solid H H + + m H w w m u t x x F t (3 The heat transfer between the solid ant the air stream is given by H m H H ρbδ x a + H + Δx H 2hy bδx Y Yw + 2h T T t n x Y heat transfer transient heat released due to net enthalpy between air and within the channel adsorption flux solid ( ( w m H H H + 2hy( Yw Y + 2h( Tw T nb u t x Y (4 in which ( H at + Y d + ct (5 a KJ / Kg C d KJ / Kg c KJ / Kg C

5 Equations ( through (4 are transformed into equivalent dimensionless forms after extensive algebra, Y x W t w hc, Y Y 2 ( Y Yw λ (6 (7 T x T T w T t w hc, ( T T λ ( Y Y + w w (9 (8 where h and c refer to the hot and cold periods, respectively, and C wr λ 2 H f T λ Q H T The heat of adsorption Q is expressed in terms of the latent heat h v and is experimentally obtained [5] as Q h e.28w v ( ( We have now four equations (6 to (9 and five unknowns, Y, Y, W, T and T w. The missing equation is the adsorption isotherm, which relates the humidity content of the hygroscopic material, its temperature and the humidity ratio of the air layer in equilibrium with the solid, W W ( Tw, Yw ( with boundary conditions are given by T (, t T, < t < P (2 hin h Y (, t Y, < t < P (3 hin h T (,, xf t Tcin Ph < t < P (4 Y (,, xf t Ycin Ph < t < P (5 and the periodicity conditions are given by T x P T x (6 wc (, wh (, W x P W x (7 c(, h(, The adsorption isotherm (Eq. is specific for each hygroscopic material. Simonson and Besant [6] suggest that although the humidity content W is a function of both temperature

6 and relative humidity of the air layer, its dependence on the later is much stronger than on the former. ccordingly, a variety of adsorptive materials can be represented by in which W W max R ( R + RH (8 W max R RH maximum humidity content of the solid separation factor relative humidity of the air layer 8 W/Wmax, % R. (M R. (Silica-Gel R. Mol. Sieve Umidade Relativa, % Figure 3: Generalized dsorption Isotherm The separation factor R can be adjusted so as to make the curve a fair representation of selected hygroscopic materials, as illustrated in Figure (3. The definition of effectiveness for a desiccant wheel is not as straightforward as it is in heat exchangers. In a desiccant wheel both heat and mass are being exchanged, and mass and heat transfers have opposite directions. Taking the regenerative stream (hot period as an example, one would note that its temperature decreases as it flows through the channel, which tends to decrease its enthalpy. However, the hot stream is also humidified as it flows, which causes its enthalpy to increase. Moreover, both fresh air and the regeneration streams are supplied by ambient air, so they should have the same inlet humidity ratio (i.e., Y hi Y ci. ccordingly, results are expressed by the dehumidification effectiveness given by d ( Yci Yco ( Y ε (9 ci The domain was discretized using a finite-volume technique, using a fullyimplicit formulation for the transient terms and an upwind formulation for the convective

7 terms. Since both initial mass and temperature distributions are not known a priori, an iterative procedure, which compares the initial fields with the fields calculated at 36 is required. The enthalpy flux of the inlet streams must equal the average enthalpy flux of the outlet streams, as otherwise the wheel wouldn t be operating in a cyclic condition. The heat balance error HBE given below was found to be smaller than,% for all simulations carried out. ph pc m h hhi + m c hci ( m h h ho dt mc h co dt p + h p c HBE (2 m h + m h h hi c ci RESULTS Figures (4 and (5 show the influence of the adsorptive material selection over the effectiveness of dehumidification for two regeneration temperatures. For both cases the best performance is obtained for R, (M. For a moderate value of the regeneration temperature (9 C, silica-gel exhibits a better performance than molecular-sieve, whereas for a higher regeneration temperature (6 C the results are reverted. This result is consistent with the fact that molecular sieves are much stronger adsorbents than silica-gel, and thus require higher regenerative temperatures for desorption to take place. Interesting to note that a relatively weak adsorbent like silica-gel might not be indicated because of the relatively low capacity of removing humidity. Conversely, a strong adsorbent such as a molecular sieve might not be recommended as well, because an excessively high affinity to the water vapor might result in an uncompleted desorption, compromising the cyclic operation of the desiccant wheel. ccordingly, a moderate value for the separation factor seems to be the best choice. The existence of an optimum value of NTU can be explained by considering that an excessively long channel will result in continuous cooling of the regenerative stream with subsequent resorption of the water vapor. The order of magnitude of the optimum value for NTU is consistent with independently obtained results [7]. Figure 4: Dehumidifying effectiveness, T reg 9ºC

8 Figure 5: Dehumidifying effectiveness, T reg 6ºC REFERENCES. Bullock, C.E., Trelkheld, J.L., 966, Dehumidification of Moist ir by diabatic dsorption, SHRE, Transactions, vol. (72, pp Maclaine-Cross, I.L.; Banks, P.J., 972, Coupled Heat and Mass Transfer in Regenerators, Int. Journal of Heat and Mass Transfer, vol. (5, Jurinak, J.J., J.W. Mitchell, W.. Beckman, 984, Open Cycle Solid Desiccant ir Conditioning as an lternative to Vapor Compression Cooling in Residential pplications Journal of Solar Energy Engineering, pp Zheng,W.; Worek, W.M.; 993, Numerical Simulation of Combined Heat and Mass transfer in a Rotary Dehumidifier, Numerical Heat Transfer,, vol.(23 5. Zhang, X.J., et al., 23, Simulation Study of Heat and Mass Transfer in a Honeycomb Rotary Dehumidifier, pplied Thermal Engineering, vol Czachorski, M., Wurm, J. 997, Evaluation of Desiccant Matrices. Gas Research Institute, Report GRI-97/ Zhang, L.Z., Niu, J.L., 22, Performance Comparisons of Desiccant Wheels for ir Dehumidification and Enthalpy Recovery, pplied thermal Engineering, vol. (22, pp 347.