Modeling of Rotary Desiccant Wheels

Full Papers Modeling of Rotary Desiccant Wheels By Yogesh M. Harshe, Ranjeet P. Utikar, Vivek V. Ranade*, and Deepak Pahwa Rotary desiccant wheels are widely used in dehumidification and energy recovery applications. In this work, we have developed a 2D, steady state model of a rotary desiccant wheel. Mass and energy balance equations for the air streams and the desiccant wheels were developed. The hydraulic diameter and surface area for heat and mass transfer were calculated based on knowledge of the flute geometry. Appropriate correlations for the Sherwood number and Nusselt number were used to estimate heat and mass transfer coefficients. The model is capable of predicting steady state behavior of desiccant wheels having at the most three sections (process, purge, and regeneration). The mathematical model was validated using a real desiccant wheel, and the calculation results are in reasonable agreement with the experimental data. Based on this model, the temperature and humidity profiles in the wheel during both the dehumidification and the regeneration processes are analyzed. The simulated results were used to gain an insight into the operation of desiccant wheels. The model and the presented results will be useful for optimizing dehumidification and energy recovery applications. 1 Introduction Rotary desiccant wheels offer convenience in terms of maintenance and can be driven by low grade heat sources. Rotary wheels are operated with two or three sections, namely the process section where dehumidification occurs, a purge section, and a reactivation section where the desiccant is reactivated by passing hot air. A schematic of a desiccant rotary system is shown in Fig. 1. Figure 1. Schematic of a rotary desiccant wheel (inset shows cross section of a single channel). The overall performance of rotary desiccant wheels is influenced by several design and operating parameters, such as: ± [*] Y. M. Harshe, R. P. Utikar, V. V. Ranade ([email protected]), Industrial Flow Modeling Group, National Chemical Laboratory, Pune 411008, India; D. Pahwa, Desiccant Rotors International (DRI), a division of, Arctic India Engg. Pvt. Ltd., India. Chem. Eng. Technol. 2005, 28, No. 12 DOI: 10.1002/ceat.200500164 ± ± ± ± ± ± The number and area of different regions; Flute geometry; Depth of rotary wheel; Desiccant loading; Adsorption characteristics of the desiccant; Air flow rates (and temperature) through different regions; ± Wheel speed. In order to assess and to optimize the performance of a rotary desiccant dehumidifier for given operating conditions, it is essential to develop a mathematical model describing the operation of such desiccant wheels. Several mathematical models have been used to simulate such desiccant wheels, e.g., [1±3]. The published models can be broadly classified into two approaches. The first approach is based on a 1D transient model to simulate adsorption/desorption processes occurring in a single channel of a desiccant wheel. The mass and energy balance equations, comprising four variables (mass fractions of water in the gas and in the desiccant, and temperatures of the gas and of the desiccant/ matrix), are formulated and solved to simulate transient adsorption/desorption occurring in such a single channel. The boundary conditions needed for such solutions can be specified from knowledge of the rotational speed and the ratio of the dehumidification and regeneration sections. The second approach is based on developing mass and energy balance equations for the entire wheel rather than a single channel. Since there is no flow in a radial direction, variations in that direction can be neglected. Therefore, this type of model involves two spatial variables1): the angle h and the length of the channel z. If the aim is to estimate steady state performance, these governing equations can be written directly for the stea± 1) List of symbols at the end of the paper.  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1473 Full Paper dy state (that is, without considering time derivatives). In such a case, the steady state compositions of the process and regeneration outlet streams can be calculated by averaging over the corresponding process and regeneration zones. A preliminary analysis was done using both of these approaches. The analysis indicated that steady state simulations based on a 2D model are computationally more efficient than unsteady state simulations based on a 1D model. In this work, therefore, we have developed a 2D, steady state model of a rotary desiccant wheel. Mass and energy balance equations for the air streams and the desiccant wheels were developed. The model is capable of predicting steady state behavior of desiccant wheels having at most three sections (process, purge, and regeneration). The details of the mathematical model, numerical solution, and simulated results are discussed in the sections below. the mass of matrix per unit volume, fBesant is a factor introduced by Professor Besant [4] that determines the fraction of heat of adsorption released in the gas, and Cp is the heat capacity. Subscripts d, l, and m denote desiccant, liquid and matrix, respectively. Mass Balance of Water Vapor in the Gas Stream: ¶Y ¶Y ma ¶Y aV ky Ye Y † ‡ 2p N ‡ ˆ ra e ¶t ¶h ra e ¶z where ma, ra, and e are the mass flux of air, density of air, and porosity of the wheel, respectively. z is the axial coordinate. Energy Balance for the Gas Stream: ¶T ¶T ma ¶T ‡ 2p N ‡ ¶t ¶h ra e ¶z ˆ 2 Mathematical Model The following assumptions were made to develop the mathematical model: I. All ducts in the desiccant wheel are made of the same material and are of the same configuration, and desiccant is uniformly distributed in the matrix. II. All ducts are assumed to be adiabatic. III. The rotary speed is uniform and is low enough to neglect the effect of centrifugal force. IV. Axial heat conduction and mass diffusion in both the air stream and the desiccant wall are negligible. V. The effects of adsorption and desorption on the heat and mass boundary layer are negligible. VI. The thermodynamic properties of dry air, vapor, and the desiccant are constants. VII. The heat and mass transfer coefficients between the air stream and the desiccant wall are constant along the air channel. VIII. No leakage occurs between different regions. With these assumptions, one can write mass and energy balances as follows. Mass Balance of Water Content in a Desiccant: ¶W ¶W aV ky Y Ye † ‡ 2p N ˆ Md ¶t ¶h (1) Where W is the water content of desiccant, N the wheel speed, av the surface area for mass transfer per unit volume, ky the mass transfer coefficient, Y is the humidity, and Md the mass of desiccant per unit volume. Ye is the equilibrium humidity, t the time, and h is the angular coordinate. Energy Balance for the Adsorbent:
a h T Tw †‡aV ky Y Ye †Q 1 fBesant @Tw ¶T   ‡ 2p N w ˆ V ¶t ¶h Md Cpd ‡WCpl ‡Mm Cpm (2) where Tw is the wheel temperature, T the gas temperature, h the heat transfer coefficient, Q the heat of adsorption, Mm 1474 (3) aV h Tw T †‡aV ky Y Ye †Q fBesant   ra e Cpa ‡Cpv Y (4) Subscripts a and v denote air and vapor, respectively. As mentioned earlier, the focus of the present work was restricted to obtaining steady state solutions as efficiently as possible. Therefore, the transient terms appearing in Eqs. (1±4) were omitted in the present work, and steady state equations were rewritten in terms of dimensionless groups a, b, d, and w as: Mass Balance of Water Content in a Desiccant: ¶W ˆa Y ¶h Ye
(5) Energy Balance for the Adsorbent: Y Ye † 1 fBesant ¶Tw bh T Tw †‡b  m  ˆ ¶h w0 ‡w1 W
(6) Mass Balance of Water Vapor in the Gas Stream: ¶Y ¶Y d0 Ye Y † ‡ d0 ˆ ¶h ¶z d1 (7) Energy Balance for the Gas Stream: d T T† ¶T ¶T  ‡ bm Y Ye † fBesant ‡ d0 ˆ 0 w ¶h ¶z d 1‡w Y ra Cpa e 1‡w2 Y 2 2 where: aV ky aˆ 2p N Md d0 ˆ ma 2p N ra e bh ˆ aV h 2p N bm ˆ d1 ˆ ma aV ky d2 ˆ w0 ˆ Md Cpd ‡ Mm Cpm w 1 ˆ Md C l (8) aV ky Q 2p N ma Cpa aV h w2 ˆ Cpv Cpa (9) The different symbols used in this section have the conventional meanings. In order to solve this set of equations (Eqs. (5±8)), it is necessary to relate the equilibrium composition Ye, to the water content (W) and temperature of the adsorbent (Tw).  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.de Chem. Eng. Technol. 2005, 28, No. 12 Full Paper Two types of isotherms were incorporated in the present model: 5 P ai W i (10) ± TYPE 1: RH ˆ iˆ0 ± TYPE 2: RH ˆ Rc 1‡ R 1†c since cˆ W Wmax (11) Where RH is the equilibrium relative humidity over the desiccant with water content of W. a0 to a5 are empirical coefficients representing the adsorption isotherm in a polynomial form. R is an isotherm shape parameter and Wmax is the maximum water content of the desiccant. Appropriate boundary and initial conditions were specified as: W z; h† ˆ W z; h ‡ 2p† Tw z; h† ˆ Tw z; h ‡ 2p† Y z; h† ˆ Y z; h ‡ 2p† T z; h† ˆ T z; h ‡ 2p† T 0; h† ˆ TinP T L; h† ˆ TinR h in process h in regeneration (13) In many cases a third section, called a purge section, is used in addition to the process and regeneration sections. The possibility of using a third section was incorporated in the model. Apart from these basic equations, additional correlations were used to estimate the pressure drop and mass and heat transfer coefficients. For this purpose, the hydraulic diameter of a channel was related to the flute geometry as: dh ˆ 8ab P Nu ˆ fNu f Pr Re Stm ˆ Sh ˆ fSh f Sc Re (18) where fNu and fSh are adjustable parameters. Preliminary simulations were carried out to obtain satisfactory values of these parameters. 2.1 Numerical Solution of Model Equations The model equations with specified boundary conditions were solved numerically. The space derivative terms appearing in Eqs. (5±8) were discretized using an implicit upwind difference scheme. Fig. 2 shows the discretization scheme for the solution domain. A generic governing equation was written as: ¶U ¶U ‡X ˆ SU ¶h ¶z (19) where U is any variable (W, Tw, Y, T) and SU is its source term. Integration of Eq. (19) over a computational cell gives: (14) where 2b is the pitch and 2a the height of the channel (see Fig. 1). The perimeter P is calculated as:  2 2b q 3‡ ap 2 (15) P » 2b ‡ 2 b2 ‡ ap†  2 2b 4‡ ap The pressure drop was then calculated as: Dpf ˆ Sth ˆ (12) In addition to these, inlet boundary conditions at the appropriate locations were specified as: Y 0; h† ˆ YinP Y L; h† ˆ YinR heat and mass transfer coefficients for the entire wheel. All the effects due to varying water content and developing flow were combined into adjustable parameters fNu and fSh. Heat and mass transfer coefficients were calculated by assuming that the Stanton numbers for heat (Sth) and mass transfer (Stm) are proportional to the frictional coefficient, f as: 2f rV 2 L 1 ‡ K rV 2 dh 2 Vcell UP Dh
V X US ‡ cell UP Dz  
‡ UP S U UW ˆ Vcell SU P C (20) where Dz and Dh are the widths of the computational cells in the z and h directions, respectively. Subscripts P, S, and W denote variable locations as center, south, and west, respectively. (16) where f is the friction factor, and K represents the velocity heads lost at the entry and exit of the desiccant wheel. The friction factor f is given by [5]:  0:1883  a 0:01 Re (17) f ˆ 12:992 b f ˆ 16 Re The water adsorbed on the desiccant changes the physical characteristics of the surface and may affect the interfacial area and mass transfer coefficient. In a significant part of the channel the flow will not be fully developed. However, in our present model we have assumed a constant value for the Chem. Eng. Technol. 2005, 28, No. 12 http://www.cet-journal.de Figure 2. Discretization of the solution domain.  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1475 Full Paper Eq. (20) was rearranged to give:     X Dh X Dh U SP ˆ US ‡ UW ‡ SU UP 1 ‡ C Dz Dz (21) It should be noted that the source terms appearing in Eqs. (5±8) were linearized while developing Eq. (21). The linearization is relatively straightforward in Eqs. (6±8). For Eq. (5), the equilibrium water content in the gas phase Ye is a complex function of the water content in the adsorbent W. Several alternative ways of linearizing the source term of Eq. (5) were examined and tested. Treating the entire source term U as SC was found to be the best when considering the speed of convergence. The resulting set of algebraic equations was solved iteratively. The updated values of the variables were under-relaxed as: Unew ˆ r Unew ‡ 1 r† Uold Figure 3. Sensitivity to grid size. (22) where r is an under-relaxation parameter. The value of r as 0.2 was found to be suitable though rather conservative. This numerical method was implemented in FORTRAN programs. A dynamic link library (DLL) was developed in FORTRRAN. The library was extensively tested for a wide range of input parameters. A user-friendly program based on this DLL was developed to simulate the performance of rotary desiccant wheels. Typical results obtained from these programs are discussed below. 3 Results and Discussion Preliminary simulations were carried out to examine the effect of the numerical parameters (under-relaxation factor, number of computational cells, and number of iterations) on the accuracy of the results. These simulations were carried out by specifying a polynomial equation (TYPE 1) of the equilibrium relative humidity with respect to the water content of the desiccant. Considering the desired computation time and accuracy, twenty cells in the z direction and thirty six cells in the h direction were found to be adequate (see Fig. 3). Under-relaxation factors were set to 0.2. About two thousand iterations were found to be necessary to obtain converged steady state results. After ensuring numerical accuracy, the model was used to examine the performance of a rotary desiccant wheel. Figs. 4 and 5 show a sample of the predicted results for a wheel speed of 20 rpm. Fig. 4 shows key variables just after the process inlet, while Fig. 5 displays the same variables just before the process outlet. It can be seen that in the process section the water content of the desiccant increases with angle. At the process outlet the water content of the desiccant in the purge section is zero, indicating that the reactivation region is performing satisfactorily to remove water content from the desiccant. 1476 Figure 4. Predicted angular variation of key variables (just after the process inlet). Figure 5. Predicted angular variation of key variables (just before the process outlet).  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.de Chem. Eng. Technol. 2005, 28, No. 12 Full Paper Before using the model to gain a detailed understanding of the behavior of rotary desiccant wheels, model predictions were verified with the experimental data provided by Desiccant Rotors International (DRI) and the experimental data of Kodama [6]. In both the cases the adsorption isotherm data was correlated using a polynomial equation (TYPE 1). The input data used to simulate the experimental data provided by DRI is not listed here for confidentiality reasons. The input data for the case of Kodama [6] is listed in Tab. 1. A comparison of typical predicted results and experimental data for the data obtained from DRI is shown in Fig. 6. The figure shows the influence of rotational speed and gas velocity on the performance of the desiccant wheel. A base case was identified and various adjustable factors (denoted by correction factors in Tab. 1) were tuned to match the experimental observations. It is worth noting that in order to match the model predictions to experimental data it is necessary to relate the Sherwood number to the water content in the desiccant. This relationship is characteristic of a particular desiccant. Once such a relation is established, the model predictions agree satisfactorily with the experimental data over the wide range of design and operating parameters. The model was used to simulate Kodama's experimental data. For all simulations the values of the Sherwood and Nusselt number correction factors listed in Tab. 1 were used. Figure 6. Comparison with experimental data (influence of rotational speed and gas velocity on the performance). No special efforts were made to adjust the values of these parameters to fit the experimental data. Fig. 7 shows the effect of inlet humidity on the fractional residue of water vapor. It can be seen that the residual water content passes through a minima as the rotational speed is increased. At lower feed humidity the fractional residue declines rapidly until an optimum rotational speed is reached, whereas for Table 1. Typical input data for the simulation of Kodama's experiments. Data to be provided by the user Mass flux [kg/m2s] Fractional face area Temperature [K] Humidity [kg/kg of dry air] Process 1.11 0.785 303.0 0.008 Regeneration 1.11 0.215 413.0 0.008 Temperature of reactivation stream = 140 C Operating pressure = 101 000 Pa Rotational spee- fbypass = 0 d = 25 rph Data of specific desiccant wheel Effective Area 0.066 m2 Pitch 0.0032 m Rotor depth 0.05 m Height 0.0018 m Thickness 2´10±4 m Heat of adsorption 2.3´106 J/kg Bulk density of Media 357.14 Kg/m3 Bulk density of desiccant 250.0 Kg/m3 Heat capacity of desiccant 921.0 J/Kg/K Heat capacity of Substrate 1030.0 J/Kg/K Other relevant data Isotherm: RH ˆ 3 P i ai W iˆ0 Coefficients: a0 = 0; a1 = 232.69; a2 = 2061.4; a3 = ±5148.1 Parameters used for the numerical solution of the model equations No. of cells in z direction 20 Friction factor correction 1.0 No. of cells in h direction 36 Sherwood number correction 0.4 Maximum no. of iterations 10 000 Nusselt number correction 0.4 Under-relaxation parameters 0.2 (for W, Tw, Y, and T) Factor for Pressure 4.0 Initial guess From last run Factor for exit correction 1.5 Chem. Eng. Technol. 2005, 28, No. 12 http://www.cet-journal.de  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1477 Full Paper higher feed humidity the decline is gradual and the optimal rotational speed is greater than that for the lower feed humidity. It can be seen that at lower rotational speeds the model predictions agree well with the experimental observations, however, at higher rotational speeds the predictions deviate from the observed results. It is possible to achieve a better agreement with the experimental data by adjusting the tuning parameters. However, due to the lack of adequate data on the desiccant this was not done. Nonetheless, the model adequately captures the correct trends. Fig. 8 shows the effect of the regeneration temperature on the fractional residue of water vapor. It is observed that the performance is improved with higher regeneration temperatures. In this case, at lower regeneration temperatures the model predictions agree reasonably well with the experimental findings. At lower fractional residues, however, the model predictions digress from the experimental findings. One of the reasons for this might be the uncertainty in the adsorption isotherm at lower values of fractional residues of water vapor. The developed software allows the user to explore possible optimizations of rotary desiccant wheels. One such case is illustrated in Fig. 9. It was observed that for a specific desiccant and desiccant loading there is an optimum wheel speed which maximizes the removal of moisture from the process air stream. It can be seen that as the depth of the wheel increases, dehumidification performance of the wheel increases. Similarly, the optimum wheel speed decreases as wheel depth increases. Also, the match between experimental observations and simulation results in this case is very good. Such simulated results can be used to explore the available parameter space and identify appropriate conditions for the most efficient operation of rotary desiccant wheels. Many such optimization studies can be performed with the developed software, making it an effective design and optimization tool for desiccant wheels. Figure 9. Identification of the optimum wheel speed for two different depths of wheels. Figure 7. Effect of the inlet humidity on Yavg/Yin. 4 Conclusions A mathematical model to simulate the performance of a desiccant wheel was developed. The model also accounts for possible heating of the purge stream and reusing it as a regenerating stream. Appropriate numerical techniques to solve these model equations were developed. The model was implemented in user friendly software. The predicted results were in agreement with the prevailing understanding of the operation of desiccant wheels and with the available experimental results and predictions of other available software. It was observed that it is necessary to relate the Sherwood number to the water content in the desiccant for better agreement with the experimental data. With this relationship the agreement with experimental data was found to be satisfactory. The validated model was then used for optimization studies with desiccant. The model and the presented results will be useful for optimizing dehumidification and energy recovery applications. Received: May 17, 2005 [CET 0164] Figure 8. Effect of the regeneration temperature on Yavg/Yin. 1478  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.de Chem. Eng. Technol. 2005, 28, No. 12 Full Paper Symbols used AZ Ah aV [m2] [m2] [m2/m3] Cp dh f fs h ky L ld [J/kg K] [m] [±] [±] [J/m2s K] [kg/m2s] [m] [±] M m Patm ps Q R1 R2 T TW Vcell W [kg/m3] [kg/m2 s] [Pa] [Pa] [J/kg] [m] [m] [K] [K] [m3] [±] Wmax [±] Y [±] Ye [±] Greek Symbols area of face perpendicular to Z area of face perpendicular to h desiccant surface area per unit volume of the wheel heat capacity hydraulic diameter of channel friction factor free area of flow per unit area of wheel heat transfer coefficient mass transfer coefficient depth of the wheel mass of desiccant per kg of matrix, Md/Mm mass per unit volume of wheel mass flux per kg dry air atmospheric pressure saturation pressure heat of adsorption inner radius of wheel outer radius of wheel temperature of gas temperature of wheel volume of computational cell water content of desiccant, kg of water/ kg of desiccant maximum water content of adsorbent, kg of water/kg of desiccant specific humidity of air, kg of water/kg of dry air equilibrium sp. humidity of air @ adsorbent surface, kg of water/kg of air e j r [±] [±] [kg/m3] void fraction, m3 of air/m3 of wheel relative humidity if air, Y/Ysat density Subscripts dry air average of process outlet dry desiccant inlet liquid water dry matrix outlet process section regeneration section regeneration section water vapor purge section a avg d in l m out P reg R v U References [1] [2] [3] [4] [5] [6] X. J. Zhang, Y. J. Dai, R. Z. Wang, Appl. Therm. Eng. 2003, 23 (8), 989. L. Z. Zhang, J. L. Niu, Appl. Therm. Eng. 2002, 22 (12), 1347. W. Tanthapanichakoon, A. Prawarnpit, Chem. Eng. J. 2002, 86, 11. C. J. Simonson, R. W. Besant, Int. J. Heat Mass Trans. 1999, 42 (12), 2161. J. L. Niu, L. Z. Zhang, Int. J. Heat Mass Trans. 2002, 45, 571. A. Kodama, Ph.D. Thesis, Kumamoro University, Japan 1995. ______________________ Chem. Eng. Technol. 2005, 28, No. 12 http://www.cet-journal.de  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1479