Transient performance of coupled heat and mass transfer in cross-flow hollow fiber membrane module for air dehumidification

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Transient performance of coupled heat and mass transfer in cross-flow hollow fiber membrane module for air dehumidification Ning Zhang , Shao-You Yin , Hong-Hai Yang PII: DOI: Reference:

S0140-7007(19)30381-0 https://doi.org/10.1016/j.ijrefrig.2019.08.032 JIJR 4512

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International Journal of Refrigeration

Received date: Revised date: Accepted date:

6 March 2019 7 August 2019 31 August 2019

Please cite this article as: Ning Zhang , Shao-You Yin , Hong-Hai Yang , Transient performance of coupled heat and mass transfer in cross-flow hollow fiber membrane module for air dehumidification, International Journal of Refrigeration (2019), doi: https://doi.org/10.1016/j.ijrefrig.2019.08.032

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Transient performance of coupled heat and mass transfer in cross-flow hollow fiber membrane module for air dehumidification

Ning Zhang1, Shao-You Yin2, Hong-Hai Yang3* 1. School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510640, China. 2. Heat Pump Engineering and Technology Development Center of Guangdong Universities, Shunde Polytechnic, Foshan 528333, China. 3. College of Environmental Science and Engineering, Donghua University, Shanghai 201620, China. 

Author for correspondence. Tel/fax: 86-21-67792528/86-21-67792522, Email: [email protected]

Abstract Membrane-based liquid desiccant dehumidification has great advantages over traditional method, particularly in avoiding liquid droplets moving into the process air. This paper proposes a simple model to predict the transient performance of the hollow fiber membrane-based dehumidification module. To simplify the fiber-to-fiber influence, the modeled membrane module is assumed to be a parallel-plates heat mass exchanger. The model has been calibrated and validated with a transient experiment reasonably well. Impacts of various parameters on the transient performance were studied by using the proposed model. The results show that the variation of air temperature is more significant than air humidity. The absorption heat of water vapor is the main resistance of heat and mass transfer. It initially restricts the growth of the cooling effectiveness, and then limits the driving potential for moisture transfer. Therefore, it brings the dehumidification effectiveness down. It is found that reducing the heat capacity rate ratio can reduce the equilibrium time, and increase the cooling and

1

dehumidification effectiveness. The high packing density increases the dehumidification effectiveness with a negligible effect of somewhat drop in cooling effectiveness. By contrast, the geometry of the fiber packing arrangement has little influence on dynamic performance of the module formed by numerous fibers. The membrane module can fit the change of weather conditions by varying solution temperature on the inlet of the dehumidifier with the help of this dynamic model. The cooling and dehumidification effectiveness also increase to improve heat and mass transfer performance of the dehumidifier under the adjustment.

Keywords: Transient performance, Hollow fiber membrane contactor, Heat and mass transfer, Air dehumidification

2

1. Introduction Air dehumidification has heightened a necessity to maintain the indoor air environment (Huang et al., 2013; Zhang et al., 2018) in hot and humid areas. The moisture removal using liquid desiccant has coherent advantages of no liquid water droplets condensation, high efficiency and less energy consumption (Ge et al., 2010; Woods, 2014; Yang et al., 2017). In recent years, liquid desiccant air dehumidification technology has drawn many attentions (Ge et al., 2010; Huang et al., 2018; Woods, 2014; Yang et al., 2017; Zhang, 2012a) and this air humidity control method is promising in engineering application (Vali et al., 2015; Zhang et al., 2014, 2016b, 2017). Packed bed columns are common liquid desiccant air dehumidification equipment (Huang et al., 2019). However, the desiccant solution contacts with the process air directly, so liquid desiccant droplets may be carried over to rooms by air stream. It would contaminate the indoor environment and harm occupant health. To overcome these drawbacks, the membrane-based contactors are proposed (Zhang et al., 2012). A bunch of hollow fiber membranes are assembled to form the shell-and-tube shaped module. Desiccant solution flows in the tube side while process air flows across the fibers in the shell side, they are separated from each other by the membranes. Because of selective permeation of the porous membrane, it can only permit the transport of water vapor through the membranes but prevent the liquid desiccant droplets from crossing over to the process air. In general, the operating conditions for a real dehumidifier are always transient. However, the information on its performance, especially the dynamic behaviors is still quite limited. The dynamic transfer characteristics are complex in such a compact membrane module. The daily operation of the dehumidifier is mainly determined empirically by the user (Mohammad et al., 2016; Zhang et al., 2016a, 2018), which is not accurate in performance analysis. The dynamic behaviors should be investigated for better regulation and optimization of the real system. Consequently, a dynamic model of the dehumidifier is needed to set up as a basis. Recently, some researchers have investigated the dynamic heat and mass transfer characteristics on traditional packed towers (Li et al., 2016; Peng et al., 2009; Wang et al., 2017). A non-equilibrium heat and mass transfer model was proposed for the counter flow packed-type dehumidifier (Li et al., 2016). It is a one-dimensional model which is simple for its application on control design and fault diagnosis. To analyze the transient characteristics of packed bed columns, a dynamic model was developed. It was found that thermal mass significantly influences the dynamic response of the 3

dehumidifier (Peng et al., 2009; Wang et al., 2017). The liquid desiccant is usually unsteady flow in direct contact dehumidifiers and it has impact on dynamic characteristics of the module. Hence unsteady solution flow was studied to investigate the transient heat and mass transfer between air and solution (Luo et al., 2014), and the dynamic formation process of unsteady counter-current flow was evaluated (Lu et al., 2016). Besides packed bed columns, the transient performance on plate membrane contactors was also researched. A dynamic mathematical model was developed for the liquid-to-air semipermeable membrane energy exchangers and it was used to investigate the unsteady characteristics under different initial and operating conditions (Seyed-Ahmadi et al., 2009a). The transient responses were predicted by changing structural parameters, and the plate membrane module was adjusted to improve the dehumidification performance by the model (Seyed-Ahmadi et al., 2009b). However, the existing research revealed that the study has not adequately investigated dynamic characteristics of hollow fiber membrane modules. The objective of this study is to develop a dynamic model of hollow fiber membrane modules. The model is validated experimentally and it is used to investigate transient characteristics of the membrane contactor. The dynamic temperature and humidity distribution of air is uncovered by the model. Key parametric analysis on the transient characteristics is discussed and the operation of the dehumidifier is regulated under typical hot and humid weather conditions in China. The results of this study will be helpful for guiding the configuration optimization and daily operation strategies of membrane-based dehumidifiers.

2. Module structures and experimental test Fig. 1.

A hollow fiber membrane module which resembles a shell-and-tube shaped heat exchanger is employed for air dehumidification. As shown in Fig.1, liquid desiccant flows inside the fibers while fresh air flows across the fiber bundle. The fibers are made of semipermeable porous membranes, which selectively allows the permeation of water vapor while prevents the permeation of liquid water from penetration. The physical and transport properties of this hollow fiber membrane module are summarized in Table 1. 4

Table 1. Fig. 2.

In order to study the dynamic heat and mass transfer in the membrane module for liquid desiccant air dehumidification, a test rig has been designed. The real test setup is shown in Fig. 2. As shown, a variable speed blower is used to adjust the air flow rates. The electric heater and electrode humidifier are installed in the air duct to control the air temperature and humidity. A thermostat water bath is fixed to obtain the desired solution temperature. Air flow rates are measured by hot-wire anemometers with accuracies of ±0.15%. Liquid desiccant flow rates are measured by a magnetic flow meter with an accuracy of ±0.5%. Moreover, temperatures of air and solution are measured by temperature sensors (PT100) with accuracies of 0.1 C. Relative humidity of air is measured by humidity sensors (center 313) with accuracies of ±2.5%. LiCl is selected as the liquid desiccant for better dehumidification performance and its properties can be obtained from reference (Zhang, 2008). The liquid desiccant is sampled using a glass hydrometer along the flow direction and the concentrations can be tested by density changes. All the measured experimental values are collected by the data acquisition unit (Agilent 34970A).

3. Dynamic mathematical model 3.1. Overall heat mass transfer coefficients from air stream to liquid desiccant 3.1.1. Geometric parameters The packing density Av (m2/m3), which is the ratio of a mass transfer area per unit volume in the membrane module is Av 

nf  d o x0 z 0

(1)

The packing density presents the structure of the mass exchanger and it is listed in Table 1. The packing fraction of the module is the ratio of total cross sectional area of the fibers to the module and it is defined as



nf d o2 4 x0 z 0

(2)

where nf, d, x0 and z0 are number of fibers, diameter of fibers, module width and module height 5

respectively. Subscript “o” refers to outer. The bundle of fibers is commonly assembled in staggered or aligned arrangement. Longitudinal and transverse pitches are key parameters and they are calculated by the inner diameter of fibers and packing fraction. The longitudinal pitch is expressed by   PL  d o    4 

0.5

(3)

But the transverse pitch is decided according to the module structure. For staggered arrangement,

    PT  d o   2 3 

0.5

(4)

For aligned arrangement, PT  PL

(5)

The longitudinal and transverse pitches are mainly used to calculate the convective coefficients and pressure drop.

3.1.2. Convective coefficients and pressure drop in tube side Liquid desiccant flows in the tube side. For laminar flow in round tubes, the product of friction factor and Reynolds number satisfies (Incropera et al., 2007) f s Re s  64

(6)

in which, subscript “s” represents desiccant solution. For fully developed laminar heat transfer in round tubes (Incropera et al., 2007), Nus  3.66

(7)

According to Chilton-Colburn analogy (Kays et al., 1990), the mass transfer in tube side is

Shs  Nus  Les1/3

(8)

Pressure drop in the tube side Ps  f s

 s us2 y f 2d i

where f, ρ and u are friction factor, density and velocity. Subscript “i” represents inner.

6

(9)

3.1.3. Convective coefficients and pressure drop in shell side Air stream flows across the hollow fiber tube bank in the shell side. Convective heat transfer coefficient across the bundle is 0.33 1 Nua  1.13C1 Re m max Pra

(10)

in which, the correction factors C1 and m1 listed in (Zhang, 2008), and values of them are determined in terms of the bundle geometry. Subscript “a” and “max” mean air and maximum. Re is calculated by the maximum velocity flowing through the tube bank as

Re max 

ua,max d o

a

(11)

where ν is kinematic viscosity. Pressure drop in the shell side Pa  f a N L m2

 a ua,2 max 2

(12)

where NL is the number of fibers along the air flow direction and the constant m2 can be found in (Zhang, 2008).

3.1.4. Overall heat and mass transfer coefficients Resistances in the membrane-based heat and mass transfer are considered as a sum of convective resistances in both of air and solution sides, and the diffusive resistance in membrane (Zhang, 2008). The overall heat transfer coefficient from air to liquid desiccant can be obtained by 1 1 d    do  1     o   htot hi  d i  mem  d m  ho

(13)

where δ is membrane thickness, λmem is heat conductivity of membrane and dm is arithmetic mean diameter of a fiber. The overall mass transfer coefficient can be calculated by 1 1 d    do  1     o   k tot ki  d i  Dvm  d m  k o

in which, Dvm is moisture diffusivity of the membrane.

7

(14)

3.2. Performance indices Dehumidification and cooling effectiveness of the module are important performance indices for heat and mass transfer (Zhang, 2012b), and they can be defined by

m 

h 

a,i  a,o a,i  s,i Ta,i  Ta,o Ta,i  Ts,i

(15)

(16)

where T and ω are temperature and humidity ratio. Subscripts “i” and “o” refer to inlet and outlet.

3.3. Governing equations In most applications, Reynolds numbers of the air and solution stream are usually much less than 2300, therefore both of the flows are considered to be laminar. Other assumptions are: (1) The flows are assumed to be hydrodynamically fully developed while developing both thermally and in concentration. (2) The fluids flow in one direction and axial dispersion of heat and mass is neglected. (3) The fluids are Newtonian fluids with constant thermo-physical properties. (4) Heat and moisture losses through the shell to the surroundings are neglected. Fig. 3.

Based on the above consumptions, governing equations for the dynamic heat and mass transfer through the permeable membrane in a dehumidifier is presented. As shown in Fig.3, the shaded area is selected for the control volume. Numerous fibers are assembled in the membrane module and a conversion approach is taken to simplify the fiber-to-fiber influence for application (Zhang, 2012b). The total membrane area is assumed to be multilayers for a parallel-plates heat mass exchanger by nch 

Atot x0 y 0

(17)

where, Atot is the total membrane area and y0 is the module length. Air stream flows in the x-direction, the change of air temperature and humidity with time is determined by the heat and moisture transfer along the x-direction, and it is calculated by

8

 a cp, a z0

 a z0

Ta  aVa cp, a Ta   nch htot Ta  Ts   0 ta y0 x

(18)

ωa  aVa ωa   nch  a k tot ωa  ωs   0 ta y0 x

(19)

where cp, t and V are specific heat capacity, time and volumetric flow rates respectively. Desiccant solution flows in the tubes and it absorbs water vapor along the y-direction. The energy equation for the liquid side includes heat transfer through the membrane and absorption heat with moisture condensation. Heat and moisture conservation equations in the liquid desiccant side are expressed as s cs z0

Ts sVs cs Ts   nch htot Ts  Ta   nch  a k tot r ωs  ωa   0 ts x0 y

s z0

X sVs X   nch  a k tot ωs  ωa   0 ts x0 y

(20) (21)

in which, r and X are latent heat of phase change and solution concentration. Governing equations (18)-(21) are normalized for further analysis as follows





(22)





(23)

Ta* Ta*  *  NTU sen Ta*  Ts*  0 * ta x ωa* ωa*   NTU Lat ωa*  ωs*  0 ta* x*









Ts* Ts* * *   msen NTUsen Ts*  Ta*  mLat NTU Lat ωs*  ωa*  0 ts* y *





X * X *  *  m* NTU Lat ωs*  ωa*  0 * ts y

(24)

(25)

The dimensionless temperature, humidity and solution concentration are defined by T* 

ω* 

T  Ta,i Ts, i  Ta,i ω  ωa,i

ωs, i  ωa,i

X* 

X Xi

The dimensionless time for the fluid flow of air stream and desiccant solution is expressed by

9

(26)

(27)

(28)

ta* 

tua x0

(29)

ts* 

tus y0

(30)

where t represents time. The module width and module length can be normalized as x* 

x x0

(31)

y* 

y y0

(32)

Number of Transfer Units for heat and mass transfer in the membrane module is calculated by

NTUsen 

htotAtot aVa cp,a

(33)

NTU Lat 

k tot Atot Va

(34)

The dimensionless mass ratio, sensible heat capacity ratio and latent heat capacity ratio are defined by m* 

 aVa s, i  a,i  sVs X s, i

aVa cp,a sVscs

(36)

 aVa r ωs, i  ωa,i  sVs cs Ts, i  Ta,i 

(37)

* msen 

* mLat 

(35)

3.4. Initial and boundary conditions The initial temperature of air and solution are assumed to be equal to indoor temperature: t  0 , Ta  Tin and Ts  Tin

(38)

where subscript “in” refers to indoor. The initial humidity of the air is the indoor humidity, whereas the initial concentration of solution

10

is selected as 0.3 for better dehumidification potential: t  0 , ωa  ωin and X  X 0

(39)

where superscript “0” means initial. Inlet boundary conditions for the air and solution are given as

x  0 , Ta  Ta,i and ωa  ωa,i

(40)

y  0 , Ts  Ts, i and X  X i

(41)

3.5. Numerical solutions The coupled heat and mass transfer for the module are solved by Eqs. (22)-(25) based on the initial and inlet boundary conditions of Eqs. (38)-(41). Governing equations are discretized on a control volume for numerical calculation and they are solved by Alternate Direction Implicit (ADI) finite difference technique. A grid independence test is conducted to check the effects of the grid size. It indicates that 40×40 grids are adequate, which is less than 0.1% difference compared with 50×50 grids.

4. Results and discussion 4.1. Uncertainty analysis Uncertainty analysis for the experimental results was made using the following expressions (Guttman et al., 1965). 2  f  2  f 2   f 2 1  x1     x 2 2     n y    x1   x 2   x n

1

  

2 2 2 2  f y  f1   x1   f 2   x 2                n y  x1   y   x 2   y   x n 

where f is the function of independent variables (x1, x2,…, xn).

2

2 x n 2  

(42)

1

  

2

 x n   y

△x1, △x2,

  

2

2  

etc. are the absolute errors

associated with the variables and △y/y refers to the relative error. A detailed error analysis on the cooling effectiveness was performed as follows

11

(43)

h

h



 

  T   T    T  T  

 T 0 2  T 0 a,i s, i  2 0 0  Ta,i  Ts, i 



2

0 2 a,i 0 a,i

2

12

a, o 2

(44)

a, o

where △ηh/ηh is the relative error of the cooling effectiveness. △T is the absolute errors of temperature. As a result, the uncertainty is obtained and it is less than 8.5% for the cooling effectiveness. Similarly, the uncertainty is less than 9.2% for the dehumidification effectiveness.

4.2 Model validation In the practical application for air dehumidification, if inlet conditions change from the initial values to setting values, parameters of the air on the outlet of the module will become equilibrium state finally. As the outlet variables approach 95% of the difference between the initial state and the final steady state (Namvar et al., 2012), the module is called in quasi-steady state. The time from the initial state to reaching the quasi-steady state during the startup period is defined as the equilibrium time. Fig. 4.

The membrane module is simulated by the model and operating conditions for fluids are listed in Table 1. Air inlet conditions emulate the typical summer conditions in hot and humid Southern China (Zhang et al., 2016a). The inlet temperature and concentration of solution are adjusted to 20 C and 0.3 for higher dehumidification potential. Only the transient performance of the membrane module is investigated in the study, but the whole dehumidification test system contains many devices. To avoid the influence of thermal inertia of other devices on the transient performance, the test system is firstly operated with a vacant module of the same size without hollow fiber membranes. When the whole test system reaches steady-state conditions, the module is replaced quickly by a hollow fiber membrane module to test. Variations of outlet parameters with the time change are shown in Fig.4. It can be seen that the equilibrium time is 18 seconds because of the compact structure and weak thermal inertia of the module. The heat and mass transfer in the module is very fast and it has advantages over the traditional packed tower typed dehumidifier for dynamic regulation and optimization. The maximum relative deviations between the calculated and experimental data are 6.15% and 8.15% for air temperature and humidity respectively. As the membrane module reaches the steady state, the cooling and dehumidification effectiveness is compared between the calculated and tested data listed in Table 12

2. It can be seen that the relative errors are 8.38% and 6.58% respectively. It means that the proposed model can be used to estimate the transition performance of the membrane module. Table 2.

4.3. Transient performance of temperature and humidity distribution Fig. 5(a). Fig. 5(b).

The dynamic model can be used to disclose the transient performance of air temperature and humidity distribution within the membrane contactor. Fig. 5(a) and 5(b) plot the temperature and humidity fields for the air when t*a is equal to 1.0. The air stream flows along x axis and the desiccant solution flows along y axis. Both of air temperature and humidity change because of the heat and mass transfer between the two fluids. As air flows into the module, the isothermal line is basically parallel to the inlet boundary of air. Due to the cooling of cryogenic solution, the temperature distribution on the outlet of air gradually curves to the inlet boundary of the solution. But mass transfer rates usually differ from heat transfer rates in the membrane module. Limited by the moisture diffusivity through membrane, the water vapor transportation is less affected by the liquid desiccant flow. It leads to the result that most of humidity distribution is still mostly parallel to the inlet boundary of air. Fig. 6(a). Fig. 6(b).

As time passes, air temperature and humidity both change very fast and the membrane module reaches quasi-steady state when t*a reaches 2.2. As shown in Fig. 6(a), the air stream meets the desiccant solution in the lower left area and heat transfer can be enhanced with the high temperature difference between two fluids. Thus, the congested temperature contours are observed in this zone. In the upper left area where the intersection of air and solution inlet is, the moisture removal can be enhanced due to the high driving force for mass transfer. The released absorption heat of water vapor causes the solution temperature to rise, and then the air is also heated by the absorption heat. Therefore, the negative dimensionless air temperature is found there, which means the air temperature is higher than the inlet air temperature. As air flows through the module, the sensible cooling prevails over the 13

absorption heat due to more cool desiccant solution. Eventually, the air on the outlet of the module is cooled down. Because NTULat is smaller than NTUsen, the change of mass transfer is slower than that of heat transfer. In Fig. 6(b), it can be seen that the contours of air humidity only gradually incline to the diagonal line on the outlet of air stream.

4.4. Parametric analysis on the transient performance Structural and operating parameters of the membrane module are very important for the transient heat and mass transfer performance. The parametric analysis on the transient performance is also conducted by the proposed model. Dynamic characteristics of the dehumidifier are simulated by varying a structural or operating parameter while other parameters are fixed to Table 1. The change of performance indices with time is displayed from the initial state to the quasi-steady state in the following.

4.4.1. Effect of bundle arrangements on the transient performance Fig. 7.

The effect of different bundle arrangements on transient heat and mass transfer is shown in Fig. 7. In the initial stage, the cooling and dehumidification effectiveness both increase sharply. But the absorption heat inevitably releases to the solution flow during the moisture removal and it has side effect on heat transfer. It results in a decrease in the temperature difference between the air and solution and a drop in cooling effectiveness. After t*a is 0.8, the influence of absorption heat on the cooling effectiveness gradually becomes weak due to the slowing growth in dehumidification effectiveness. Consequently, the cooling effectiveness increases again and the membrane module quickly reaches the quasi-steady state as t*a is 2.2. The absorption heat is also disadvantageous for the mass transfer potential and the dehumidification effectiveness decreases slightly in the last stage. There are numerous fibers employed in the compact module, bundle arrangements have the weak influence on the dynamic heat and mass transfer. As a result, the performance effectiveness in staggered arrangement is only slightly higher than that in aligned arrangement for any time.

14

4.4.2. Effect of packing density on the transient performance Fig. 8.

In general, bundle packing characteristics have the direct influence on transient heat and mass transfer in the module. Fig. 8 plots variations of cooling and dehumidification effectiveness with packing density during the startup period. It is seen that the packing density has more significant influence on transient performance than bundle arrangements. As time goes on, the dehumidification effectiveness increases first and then it decreases slightly. The increasing packing density can expand the mass transfer area and it results in the higher NTULat. Hence, the dehumidification effectiveness grows with closely-packed arrangement for any time. However, the cooling effectiveness decreases with the greater packing density. For one thing, the absorption heat from water vapor limits the driving potential for heat transfer through membranes. For another thing, the heat transfer area expands by increasing packing density and it can improve the heat transfer performance. The disadvantage of absorption heat prevails over the advantage of area expansion of heat transfer. All of these reasons lead to a slight drop in cooling effectiveness with the high packing density. In the compact module, equilibrium time is the same for different fiber number form. It means equilibrium time is almost not affected by the packing density.

4.4.3. Effect of heat capacity rate ratio on the transient performance Fig. 9.

The heat capacity of fluids is also a major factor influencing dynamic characteristics of the membrane contactor. The heat capacity rate ratio is used to non-dimensionalize the heat capacity and it is defined by

C

aVa cp,a sVscs

(45)

As shown in Fig. 9, trends of the cooling and dehumidification effectiveness with different heat capacity rate ratios are similar to those with the packing density. To maintain the required indoor air environment, the volumetric flow rate of air stream is fixed as a constant and the greater value of heat capacity rate ratio indicates the smaller volumetric flow rate of desiccant solution. As the heat capacity 15

rate ratio reduces, the solution flows faster and the heat and mass coefficients in the solution side both increase. It results in the growth of cooling and dehumidification effectiveness. Meanwhile, the high heat capacity rate ratios can also accelerate the transient response. As heat capacity rate ratios change from 1.3 to 0.4, the dimensionless equilibrium time decreases from 2.4 to 1.8 gradually. However, the higher volumetric flow rate of desiccant solution usually leads to more energy consumption on the fluid flow and it is unfavorable for daily operation.

4.5. Transient performance with varying weather conditions Fig. 10.

The dehumidifier usually operates under environment weather conditions which vary from time to time. Accordingly, the transient performance is investigated hour by hour under the operation conditions emulated the typical summer day of Guangzhou in China. The outdoor air temperature and humidity are shown in Fig. 10 and other operation parameters of fluids are specified in Table 1. From Fig. 10, it is found that the outdoor air temperature and humidity increases gradually from early morning to noon. The moisture load increases with the rise of the outdoor air temperature and humidity. As the outdoor air temperature and humidity are higher at noon, the dehumidifier would fail to meet the load without adjustment. Fig. 11. Fig. 12.

To satisfy the need of moisture load, the regulation strategy of the dehumidifier is obtained by the dynamic model. The sensible load can be treated independently by other measures like chilled-ceilings, which will not be elaborated here and details can be found in (Zhang et al., 2016b). It is easy to heat or cool the solution by an auxiliary heat exchanger. So it is feasible to control the solution temperature on the inlet of dehumidifier for daily operation. The regulations of inlet solution temperature and dehumidification rates under the adjustment are plotted hour by hour in Fig. 11 to fit the weather. It can be seen that the inlet solution temperature is regulated to satisfy the demand of the moisture load with variations of outdoor weather conditions. When the outdoor air temperature and humidity are high at noon, the lower solution temperature is controlled to enhance the driving force for moisture 16

transfer. Consequently, the dehumidification rates also increase to meet the moisture load. The cooling and dehumidification effectiveness can also be improved under this adjustment. As discussed in the previous paragraph, the absorption heat has the side effect on heat and mass transfer. When the inlet solution temperature is varied for the moisture load, the undesired absorption heat is also removed from the membrane module by the cool solution at the same time. Therefore, the drawback of absorption heat can be alleviated and enhanced heat and mass transfer is achieved. The cooling and dehumidification effectiveness are compared before and after adjustment in Fig. 12. It is seen that both of the cooling and dehumidification effectiveness increase with the regulation of solution temperature at any time. The cooling and dehumidification effectiveness are still high by varying the solution temperature on the condition of high air temperature and humidity. It means that the dehumidifier can fit the change of weather conditions by the proposed dynamic model.

5. Conclusions A model is developed to characterize the dynamic dehumidification process in the cross-flow hollow fiber membrane module. The model is validated experimentally and is used to investigate the transient performance. The studies performed bring the following conclusions. (1) To simplify the fiber-to-fiber influence, the dynamic model of hollow fiber membrane module is converted equivalently to a parallel-plates cross-flow heat mass exchanger for engineering application. A higher simulation efficiency is obtained by the simple dynamic module compared with the traditional fiber-to-fiber model. The simulation result agrees with the experiments well and the proposed model is satisfactory in predicting transient heat and mass transfer characteristics of the membrane module for the daily system operation optimization. (2) The dynamic temperature and humidity distribution of air can be disclosed by the proposed model at the startup period. Initially, the temperature field is mainly affected by the sensible cooling of liquid desiccant and contours of air temperature are mostly parallel to the inlet of fluids. Over time, the released absorption heat of water vapor prevails over the sensible cooling to heat the air on the inlet and “V” shape contours are observed for the temperature field on the inlet of air stream. Limited by the water vapor permeability, the variations of air humidity are not significant and the air humidity distribution only gradually changes from vertical contours to the diagonal line. (3) The membrane module responds quickly to outside changes and it has advantages over the 17

traditional packed tower typed dehumidifier for dynamic regulation and optimization. It is found that the absorption heat has side effects on the heat and mass transfer at different time. It initially restricts the growth of the cooling effectiveness, and then limits the driving potential for moisture transfer to bring the dehumidification effectiveness down. (4) Parametric analysis on the transient characteristics is performed. Bundle arrangements in the compact module have the weak influence on the heat and mass transfer. The performance effectiveness in staggered arrangement is only slightly higher than that in aligned arrangement in any time. The high packing density is beneficial for moisture removal due to increased mass transfer areas. Meanwhile, it is easy to accumulate absorption heat in narrow space and high packing density leads to the reduction in heat transfer. Reducing the heat capacity rate ratio can bring an increase in the cooling and dehumidification effectiveness, and also shorten the equilibrium time. (5) The dehumidifier can meet the change of weather conditions by varying the solution temperature on the inlet of dehumidifier with the help of the dynamic model. The cooling and dehumidification effectiveness are also increased under this adjustment and the heat and mass transfer performance is improved.

Acknowledgment The project is supported by Natural Science Foundation of China, No. 51506055, No. 51576136 and by the Fundamental Research Funds for the Central Universities No. 2015ZM109.

18

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low flow conditions, Commun. Nonlinear Sci. Numer. Simul. 14, 3599-3607. Seyed-Ahmadi, M., Erb, B., Simonson, C.J., Besant, R.W., 2009a, Transient behavior of run-around heat and moisture exchanger system. Part I: Model formulation and verification, Int. J. Heat Mass Transf. 52, 6000-6011. Seyed-Ahmadi, M., Erb, B., Simonson, C.J., Besant, R.W., 2009b, Transient behavior of run-around heat and moisture exchanger system. Part II: Sensitivity studies for a range of initial conditions, Int. J. Heat Mass Transf. 52, 6012-6020. Vali, A., Ge, G.M., Besant, R.W., Simonson, C.J., 2015, Numerical modeling of fluid flow and coupled heat and mass transfer in a counter-cross-flow parallel-plate liquid-to-air membrane energy exchanger, Int. J. Heat Mass Transf. 89, 1258-1276. Wang, L.S., Xiao, F., Niu, X.F., Gao, D.C., 2017, A dynamic dehumidifier model for simulations and control of liquid desiccant hybrid air conditioning systems, Energy Build. 140, 418-429. Woods, J., 2014, Membrane processes for heating, ventilation, and air conditioning, Renew. Sustain. Energy Rev. 33, 290-304. Yang, B., Yuan, W.X., Shang, Y.H., Wang, J., Wei, B., 2017, Numerical and experimental study of a novel three-fluid membrane dehumidification method applied to spacecraft humidity control, J. Membr. Sci. 530, 112-124. Zhang, L.Z., 2008, Total Heat Recovery: Heat and Moisture Recovery from Ventilation Air, Nova Science Publishers Inc., New York. Zhang, L.Z., 2012a, Progress on heat and moisture recovery with membranes: From fundamentals to engineering applications, Energ. Convers. Manage. 63, 173-195. Zhang, L.Z., 2012b, Coupled heat and mass transfer in an application-scale cross-flow hollow fiber membrane module for air humidification, Int. J. Heat Mass Transf. 55, 5861-5869. Zhang, L.Z., Huang, S.M., Pei, L.X., 2012, Conjugate heat and mass transfer in a cross-flow hollow fiber membrane contactor for liquid desiccant air dehumidification, Int. J. Heat Mass Transf. 55, 8061-8072. Zhang, L.Z., Zhang, N., 2014, A heat pump driven and hollow fiber membrane-based liquid desiccant air dehumidification system: Modeling and experimental validation, Energy 65, 441-451. Zhang, N., Yin, S.Y., Zhang, L.Z., 2016a, Performance study of a heat pump driven and hollow fiber membrane based two-stage liquid desiccant air dehumidification system, Appl. Energy 179, 20

727-737. Zhang, N., Zhang, L.Z., Xu, J.C., 2016b, A heat pump driven and hollow fiber membrane-based liquid desiccant air dehumidification system: A transient performance study, Int. J. Refrig. 67, 143-156. Zhang, N., Yin, S.Y., 2017, Investigation on capacity matching in a heat pump and hollow fiber membrane-based two-stage liquid desiccant hybrid air dehumidification system, Int. J. Refrig. 84, 128-138. Zhang, N., Yin, S.Y., Li, M., 2018, Model-based optimization for a heat pump driven and hollow fiber membrane hybrid two-stage liquid desiccant air dehumidification system, Appl. Energy 228, 12-20. Zhang, W.K., Yang, M., Chen, J.C., Tao, S., Huang, X., Hu, B., Huang, S.M. 2018, Quasi-counter flow parallel-plate membrane contactors (QCPMC) for liquid desiccant air dehumidification: Conjugate heat and mass transfer, Int. J. Therm. Sci. 134, 665-672.

Nomenclature A

area (m2)

Av

packing density (m2/m3)

d

diameter (m)

cp

specific heat capacity (kJ kg-1 K-1)

C

heat capacity rate ratio

C1

constants

Dvm

moisture diffusivity (m2/s)

h

convective heat transfer coefficient (kW m-2 K-1)

f

Darcy friction factor

k

convective mass transfer coefficient (m/s)

Le

Lewis number

m1

constant

m2

constant

m*

dimensionless mass ratio

* mLat

dimensionless latent heat capacity ratio

21

* msen

dimensionless sensible heat capacity ratio

M

dehumidification rate (kg/h)

nf

number of fibers

NL

number of fibers along the flow direction

NTU

Number of Transfer Units

Nu

Nusselt number

PL

longitudinal pitch (m)

PT

transverse pitch (m)

Pr

Prandtl number

r

latent heat of phase change (kJ/kg)

RH

relative humidity

Re

Reynolds number

Sh

Sherwood number

t

time (s)

T

temperature (K)

u

velocity (m/s)

V

volumetric flow rate (m3/s)

x

width coordinate (m)

x0

module width (m)

X

solution concentration

y

length coordinate (m)

y0

module length (m)

z0

module height (m)

△P

pressure drop (Pa)

△T

absolute error of temperature (K)

Greek letters ηh

cooling effectiveness

ηm

dehumidification effectiveness

22

ρ

density (kg/m3)

λ

heat conductivity (kW m-1 K-1)

δ

membrane thickness (m)

φ

packing fraction

ν

kinematic viscosity (m2/s)

ω

humidity ratio (kg/kg)

Subscripts a

air

adj

adjustment

i

inlet, inner

in

indoor

Lat

latent

m

mean

max

maximum

mem

membrane

una

unadjustment

o

outer, outlet

s

solution

sen

sensible

tot

total

Superscript *

dimensionless

0

initial

23

Figure Captions

Fig. 1. Structure of the hollow fiber membrane module for air dehumidification.

Fig. 2. Experimental setup for hollow fiber membrane-based air dehumidification.

24

y0

Air

y x

x0 Liquid desiccant

Fig. 3. Schematic diagram of the hollow fiber membrane for air dehumidification.

40

Ta,o,Calculated Ta,o,Tested a,o,Calculated a,o,Tested

35

Ta,o (℃)

30

35 30

25

25

20

20

15

15

10

10

5

0

5

10

15

a,o (g/kg)

40

5 20

ta (s) Fig. 4. Comparison of calculated and tested air stream temperature and humidity from the dehumidifier.

25

0.2

0.3

1

0. 6 0. 5

0.1

0.8

0. 4

0.7

0. 3

0.6

0.8 0. 6

y*

0.2

0.7

0. 8

0. 4

0. 5

0.1

0.4

0. 7 0.6

0. 8

0.3 0.2

0.2

0.9

0.

0

0

9

0.2

0.4

0.6

x*

Fig. 5(a). Contours of temperature in air stream when t*a =1.0.

26

0.8

1

0 0 0.14

0.2

0.2 0.4 0.26

0.22

0.2

0.16

x* 0.6

Fig. 5(b). Contours of humidity in air stream when t*a =1.0.

27

0.8

0.28

0.36

0.34

0.32

0.3

0.24

0.18

0.1

0.14

0.06

0.26

0.22

0.2

0.16

0.12

0.08

0.6

0.12

0.08

0.4 0.04

0.02

0.34

0.32

0.3

0.24

0.28

0.18

0.1

0.04

0.8

0.06

0.02

y*

0.14

0.06

0.02

0.26

0.22

0.2

0.16

0.12

0.08

1

1

-0. 3

-0.1

1

-0.2

-0.3

1

2 0.

0. 5

0.

-0. 2 -0 .1 0

0.8

0.6

0. 6

0.4 0.

-0.1

y*

4 0.

3 0.

3

0.4 0.2 0. 1

0. 9

0.6

0.4

0.2 0

0. 8

0.7

0.5

0.8

0.

0.3 7

0.9

0

0

0.2

0.4

0.6

0.8

1

x* Fig. 6(a). Contours of temperature in air stream when t*a =2.2.

0.2

0.5 5 0.6

0.4

7 0.

0. 6 5

5 0. 5

0. 7 5

0. 5 5

0.8

0. 7

0.5

0.6 5

0. 6

0. 4

0. 6

0.35 0.4

0

0.2 0.25

0.05 0.1

0.45

0.2

0

0. 3

0. 3

0.15

0.4

5

0.2 0.25

0.1

0.05

y*

0. 4

5

0.6

0. 5

0.3

0.15

0. 3

5

0.2 5

0.8

0.5

0. 4 5

0. 2

0.1

0.05

0.3

1

0.4

0.6

x* Fig. 6(b). Contours of humidity in air stream when t*a =2.2.

28

0.8

1

0.8

η

0.6

0.4

ηh,sta ηh,ali ηm,sta ηm,ali

0.2

0.0 0.0

0.5

1.0

1.5

2.0

2.5

ta* Fig. 7. Effects of bundle arrangements on the cooling and dehumidification effectiveness.

0.8

η

0.6

0.4

ηh,φ=0.2, ηh,φ=0.25, ηh,φ=0.3, ηh,φ=0.35,

0.2

0.0 0.0

0.5

1.0

1.5

ηm,φ=0.2 ηm,φ=0.25 ηm,φ=0.3 ηm,φ=0.35 2.0

2.5

ta* Fig. 8. Effects of packing density on the cooling and dehumidification effectiveness.

29

2.0

ηh,C=0.4, ηh,C=0.7, ηh,C=1.0, ηh,C=1.3,

1.5

0.6

ηm,C=0.4 ηm,C=0.7 ηm,C=1.0 ηm,C=1.3

0.5

1.0

0.3

ηm

ηh

0.4

0.2 0.5 0.1 0.0 0.0

0.5

1.0

1.5

0.0 2.5

2.0

ta* Fig. 9. Effects of heat capacity rate ratio on the cooling and dehumidification effectiveness.

32

0.020

0.019

Ta (℃)

0.018 28 0.017

a (kg/kg)

30

26

Ta a 24

6

8

10

12

14

16

18

0.016

0.015 20

Time (h) Fig. 10. Outdoor air temperature and humidity during the daytime in a typical summer day (Aug 5) of Guangzhou.

30

1.1

30

1.0

28

0.9

26

0.8

24

0.7

22

0.6

Ts Ma

20 18

6

8

10

12

14

16

Ma (kg/h)

Ts (℃)

32

0.5 0.4 20

18

Time (h) Fig. 11. Adjustment of the inlet solution temperature and dehumidification rates to fit the weather.

0.9

0.8

0.8

0.7

h,adj

0.6

m,adj

h,una

m,una

0.6

ηm

ηh

0.7

0.5

0.5 0.4

0.4 0.3

8

10

12

14

16

18

0.3

Time (h) Fig. 12. Comparison of the cooling and dehumidification effectiveness before and after adjustment.

31

Table captions Table 1. Physical and transport properties of the hollow fiber membrane module. Symbol

Unit

Values

Symbol

x0×y0×z0

mm3

150×200×300

Ta,i

di

mm

1.2

RHa,i

do

mm

1.6

Ts,i

nf

3900

φ

Unit 

C

Values 35 80%



C

20

ωs,i

kg/kg

0.0058

0.26

Va

m3/h

100

m3/h

0.1

Av

m2/m3

653

Vs

PT

mm

2.98

NTUsen

8.32

PL

mm

2.58

NTULat

1.35

λmem

Wm-1K-1

0.17

△Pa

Pa

32.5

Dvm

m2/s

7.21×10-7

△Ps

Pa

206.9

Table 2. Comparison of calculated and tested cooling and dehumidification effectiveness of the dehumidifier at the state of steady state. Calculated value Tested value

Relative error

ηh

0.76

0.41

8.38%

ηm

0.69

0.39

6.58%

32