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Modeling and performance investigation on the counter-flow ultrasonic atomization liquid desiccant regenerator
Applied Thermal Engineering 165 (2020) 114573
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Modeling and performance investigation on the counter-flow ultrasonic atomization liquid desiccant regenerator
T
Ye Yaoa, , Wei Lia, Yixiong Hub ⁎
a b
Institute of Refrigeration and Cryogenics Engineering, Shanghai Jiao Tong University, Shanghai 200240, China School of Energy Science and Engineering, Central South University, Changsha, Hunan Province 410083, China
HIGHLIGHTS
ultrasonic atomization liquid desiccant regenerator (UALDR) is studied. • Counter-flow model for the counter-flow UALDR has been developed. • AEffects of inlet parameters on the performance of the counter-flow UALDR are studied. • Comparisons between the concurrent-flow and the counter-flow UALDR are made. • ARTICLE INFO
ABSTRACT
Keywords: Counter-flow Ultrasonic atomization Liquid desiccant Regenerator Modeling
As the key components in a liquid desiccant dehumidification system, liquid desiccant regenerator produces great effect on the whole system’s performance. This paper studies the counter-flow ultrasonic atomization liquid desiccant regenerator. Firstly, a mathematical model for the regenerator has been established and experimentally validated with finite difference method. Two performance indicators, i.e., the moisture removal rate and the regeneration thermal efficiency, were suggested to evaluate the performance of the counter-flow regenerator, and the influences of inlet parameters on the regeneration performance of the counter-flow regenerator have been investigated by the established model in this study. Decreasing temperature difference and increasing humidity difference between air and solution can improve regeneration performance. With the temperature of air and solution increasing, the regeneration efficiency increases, but the energy loss also increases. The regeneration efficiency decreases with the increase of solution concentration. The regeneration efficiency increases nonlinearly with the increase of gas-liquid ratio. Finally, there exists an optimum droplet size for the best regeneration performance. Compared with the parallel-flow configuration, the counter-flow has better regeneration performance, which is attributed to the more uniform distribution of moisture transfer driving force and the longer residence time of droplets in the regenerator. The study contributes to the development and the better applications of the counter-flow ultrasonic atomization liquid desiccant regenerator.
1. Introduction As a promising alternative approach, liquid desiccant dehumidification (LDD) has been attracting more and more attention in recent years [1–6]. The LDD system uses a kind of hygroscopic salt solution (such as LiBr, LiCl and CaCl2) as absorbent. Since there exists water vapor partial pressure difference between the surface of the hygroscopic salt solution and the air to be treated, this drives the water vapor in the air to pass through the absorbent solution, enabling the processing of air humidity. The absorbed moisture will reduce the dehumidifying ability of the desiccant solution. To recycle the desiccant, the solution
⁎
must be regenerated after the air dehumidification process. Compared with the solid desiccant dehumidification (SDD) system, the LDD system has several advantages including: (1) The higher energy efficiency because liquid desiccants are easier to be cooled, and the isothermal dehumidification process can be acquired; (2) The larger energy storage capability (up to 500 MJ/m3 [5]) which is conducive to utilizing the intermittent renewable energy (such as solar energy and industrial waste heat) for the air dehumidification all the time of the day [7,8]; (3) More flexible form which makes it possible for the waste heat far away from the air-handling units to be utilized for the desiccant regeneration [9].
Corresponding author. E-mail address: [email protected] (Y. Yao).
https://doi.org/10.1016/j.applthermaleng.2019.114573 Received 9 February 2019; Received in revised form 14 October 2019; Accepted 20 October 2019 Available online 22 October 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 165 (2020) 114573
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Nomenclature
Av Cd cp D ds h hc hd H Le m md m NTU Nu p p Pr Q Re Sr
Sh T u V X
y
calculation height (m)
Greek symbols
specific area between air and solution droplets (m2 /m3) drag coefficient specific heat capacity (kJ/kg °C) diffusion coefficient (m2 /s) droplet diameter (m) enthalpy (kJ/kg) heat transfer coefficient (W/m2 °C) mass transfer coefficient (kg/m2s) regenerator height (m) Lewis number (dimensionless) molality of LiCl aqueous solution (mol/kg) mass of desiccant solution droplet (kg) mass flow rate (kg/s) number of transfer unit (dimensionless) Nusselt number (dimensionless) pressure (kPa) pressure drop (kPa) Prandtl number (dimensionless) power (W) Reynolds number (dimensionless) cross sectional area of regenerator (m2) Schmidt number (dimensionless) Sherwood number (dimensionless) temperature (°C) velocity (m/s) volume of regenerator (m3) solution concentration (weight fraction)
µa
efficiency thermal conductivity (W/m °C) viscosity of air (Ns/m2) density (kg/m3) time (s) humidity ratio (kg/kgdryair)
Subscripts
a am d guess h in l m out r s ts ts, sat v 0
The regenerator in the liquid desiccant system is the component consuming heating energy for regenerating the weak desiccant solution delivered from the absorber, so its efficiency directly effects the LDD performance. Many earlier studies focused on packed regenerator due to its large heat and mass transfer area between the air and the liquid desiccant. Martin et al. [10] made an experimental study on a packed regenerator using triethylene glycol (TEG) as the liquid desiccant and presented effects of inlet parameters of the air and desiccant on humidity effectiveness of the regeneration. Fumo et al. [11] carried out an experimental study on the counter-flow packed regenerator using aqueous lithium chloride (LiCl-H2O) as the liquid desiccant. Longo et al. [12,13] experimentally studied a packed-bed regenerator using LiBrH2O and a new solution KCOOH-H2O and made a further study on the structured and the random packed regenerator. Liu et al. [14] developed an NTU-based model to simulate the heat and mass transfer processes in a cross-flow liquid desiccant regenerator, and the model can predict the air and desiccant parameters inside the regenerator as well as outlet parameters at any running conditions. They also conducted experimental research on the regenerator with LiBr solution and compared the regeneration performances of cross-flow regenerator with other counter-flow configurations [15]. To prevent the liquid desiccant regeneration decaying in the packed regenerator, the internally heated regenerators were recommended by researchers. Yin and Zhang [16] compared the internally heated and adiabatic regenerator, and the results indicated that the regenerate rate and energy utilization efficiency of the internally heated regenerator are higher than the adiabatic one. Some new-type regenerators have been studied and developed based on technologies in other fields. For example, Bai et al. [17] investigated the membrane-based flat-plate heat and mass exchanger used for liquid desiccant regeneration. The results showed that the boundary conditions of the membrane surface changed along the membrane diagonal line and the increase of NTU and m improved the regeneration performance. Yon et al. [18,19] proposed a novel liquid desiccant regeneration system operating in vacuum condition. The
air ambient droplet guess value heater inlet loss moist air outlet regeneration desiccant solution at solution temperature air saturated at solution temperature vapor at 0 °C
regeneration temperature of this system was lower to 20–35 °C at vacuum pressure from 1000 to 2000 Pa, and the power consumption was reduced by 40.66% compared to conventional packed-bed regenerator. Guo et al. [20] evaluated the potential of using electrodialysis (ED) technology to regenerate liquid desiccant. The efficiency of the ED in two hours for all experiments ranged from 55.17 to 73.54%, and the concentration difference produced important effect on the regeneration performance of ED. Cheng et al. [21,22] investigated the stability and the performance of the ED regeneration technology with different desiccant solution concentrations. It was found that excessive current would be harmful to the dehumidification capacity of the liquid desiccant. Chen et al. [23] evaluated the vacuum multi-effect membrane distillation system for liquid desiccant regeneration with thermodynamic model and proposed a new configuration, of which the specific energy consumption was reduced by 10–50%. The method of ultrasonic atomizing for the solution regeneration may become a promising way to develop a kind of new regenerator in which the solution is atomized into droplets of 40–50 μm by the special effect of cavitation of power ultrasound [24]. The new structure configuration will greatly enlarge the air-desiccant contacting area and reduce the air flow resistance, and hence, the performance and regeneration efficiency can be significantly improved [25]. In the previous study [26], the mathematical model for the ultrasonic atomization regenerator with parallel-flow configuration has been developed and explored. In this study, the ultrasonic atomization regenerator with counter flow configuration is to be investigated. This paper is mainly concerned about the following contents: (1) A mathematical model is developed for the liquid desiccant regeneration process in the counter-flow ultrasonic atomization liquid desiccant regenerator (UALDR) based on the principle of energy and mass conservation between the air and the desiccant solution. (2) An experimental system is designed for validating the proposed model of the counter-flow UALDR. 2
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(3) Effects of air and desiccant inlet parameters on the performance of the counter-flow UALDR are investigated by using the developed model. Plus, the regeneration performance of the counter-flow UALDR is compared to the parallel-flow one,
cross sectional area of regenerator; ud a is droplet velocity relative to the regenerating air; h v,0 is the enthalpy of water vapor at 0 °C; pa is atmospheric pressure; pv is surface vapor pressure of desiccant solution at given temperature [28].
2. Mathematical model 2.1. Assumptions
Nu = 2 + 0.6Re 0.5 Pr 0.33
(11)
Sh = 2 + 0.6Re 0.5 Sc 0.33
(12)
where Re is Reynold number, Re = |ud + ua | ds a / µg ; Pr is Prandtl number, Pr = µa cpa/ ; is Schmidt number, Sc = µa / a D ; The momentum conservation equation of a solution droplet is given by:
The heat and moisture transfer process of the ultrasonic atomization regenerator is different from the packed-bed regenerator. In the ultrasonic atomization regenerator, the desiccant solution is atomized in fine droplets to exchange heat and moisture with process air. The heat and moisture transfer process in the counter-flow UALDR is schematically shown in Fig. 1. To simplify the heat and mass transfer process in the regenerator, some assumptions are made for the mathematical model development:
md
dud = md g dt
1 Cd 2
a
Cd = 18.5/ Re3/5 1.9
Cd = 0.44 508
Re < 508
Re
200000
3 Cd 4 ds
Energy, water and solute conservation equations in a differential element are written by:
2.3. Numerical solution
(2)
a
Heat and mass transfer equations between the air and the desiccant solution are given by:
ma dha = hc Av dV (Ts ma d
a
= hd
m A v dV
Ta ) + h v, ts ma d (
ts, sat
a)
a
a
(u d + u a ) 2
s
(15)
The mathematical model of the counter-flow UALDR consists of Eqs. (1)–(5), which can be solved by the finite difference method with inlet boundary conditions of the solution droplets (Eq. (16)) and the air (Eq. (17)). Inlet boundary conditions of the solution droplets: y = 0 : Ts = Ts, in , ms = m s, in , Xs = Xs, in (16) Inlet boundary conditions of the air:
(3)
d (ms X ) = 0
(14)
where md = ds3 s /6. y is the differential height of regenerator; ud is expressed as ud = dy /dt .
dud 1 = g dy ud
dms = ma d
(13)
Cd = 24/ReRe < 1.9
2.2. Governing equations
(1)
ds2 (ud + ua )2
where the first term in the right-hand of the above equation is gravity, and the second term is drag force. md is the mass of droplet; a is air density. ua and ud are velocity of air and droplet, respectively. Cd is the drag coefficient, which is shown as follows [29]:
(1) The regeneration process in the regenerator is considered as adiabatic. (2) Heat and mass transfer inside the solution droplet is neglected. (3) The droplets are spherical, and deformation is neglected. (4) The effect of the collisions between droplets and the regenerator wall is neglected. (5) The direction of heat and moisture transfer is one dimensional along the regenerator height.
ma dha = d (ms hs )
4
(4) (5)
where m is mass flow rate; h is enthalpy; a is air humidity ratio; X is solution concentration; hc and hd are heat and mass transfer coefficients, respectively; Av is specific transfer area of unit volume, expressed by Eq. (8); dV is volume element; T is temperature; h v, ts is the enthalpy of water vapor at solution temperature, defined in Eq. (9); m is the density of moist air; Ts, sat is the humidity ratio of air in equilibrium with desiccant solution, calculated by Eq. (10).
hc =
Nu· ds
(6)
hd =
Sh ·D ds
(7)
Av =
6 ms d s, in s Sr ud
(8)
a
(9)
h v, ts = h v,0 + cpv Ts ts, sat
= 0.622
pv pa
pv
(10)
In Eqs. (6) and (7), Nu and Sh are Nusselt and Sherwood numbers, respectively. For the case of Re < 5, Nu and Sh are expressed by Eqs. (11) and (12) [27], respectively; is thermal conductivity of air; D is mass diffusion coefficient of vapor into air; ds is droplet diameter; Sr is
Fig. 1. Schematic diagram for the heat and mass transfer process in the counter flow UALDR. 3
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y = H : Ta = Ta, in , ma = m a, in , a = a, in (17) The difference equations for the mathematical model are given by Eqs. (18)–(23).
hai+ 1
hai y
i+1 a
=
NTU · Le i hTs, sat H
=
NTU ( H
i a
y
msi + 1
msi = ma (
ma (hai+ 1
i Ts, sat
i+1 a
hai +
1 Le
1 h v, ts (
i Ts , sat
i a)
udi y
=
1 g udi
cp, m = cpa +
(18)
(21)
msi hsi
(22) a
(udi + ua ) 2
(23)
s
hm
m Av V
ma
a cpv
(26)
(1) Input boundary conditions, including inlet temperatures of air and solution, inlet air humidity, inlet solution concentration, mass flow rate of air and solution and parameters of regenerator. (2) Assume the outlet air temperature and humidity. (3) Repeat the following for each grid:
where NTU is number of transfer unit; Le is Lewis number.
NTU =
(25)
The calculation flow chart is presented in Fig. 2. In the following model validation, the regenerator is divided into 100 grids ( y = 0.01 m) along the height. The gird independence test shows that 100 grids are enough for numerical accuracy (less than 0.2% difference compared to 200 grids). For the counter-flow arrangement, it needs to calculate parameters from one side to the other side. Therefore, the solution inlet was chosen as the starting point, so the outlet air temperature and humidity were assumed.
(20)
i a)
3 Cd 4 dsi
m cp, m
where cp, m is the specific heat of moist air.
(19)
msi + 1 X i + 1 = msi X i udi+ 1
h hm
2.4. Numerical procedure
i a)
hai ) = msi + 1 hsi + 1
Le =
(24)
Fig. 2. Calculation flow chart for the model solution. 4
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(a) Calculate the enthalpy of air (Eq. (18)). (b) Calculate the air humidity (Eq. (19)). (c) Calculate the air temperature according the calculated air enthalpy and humidity. (d) Calculate the solution mass flow rate (Eq. (20)). (e) Calculate the enthalpy of solution (Eq. (21)). (f) Calculate the solution concentration (Eq. (22)). (g) Calculate the solution droplet velocity (Eq. (23)). (h) Calculate the solution temperature since the solution enthalpy and concentration are known. (4) Iterate until the difference between the calculated values of the inlet air temperature and humidity and the given values meet requirement.
and the temperature of the weak solution was kept constant by using an electrical heater. The solution was atomized into tiny droplets with an average diameter of 300 μm by an ultrasonic atomization device (Type: YPW59). The solution flow rate was adjusted by a regulating valve and measured by a rotameter. Air was delivered by a variable-speed axial fan, and the inlet air temperature and humidity of the counter-flow UALDR were regulated by air heater and humidifier, respectively. Specifications of main equipment and measurement instruments in the experimental system are listed in Tables 1 and 2, respectively. The temperature & humidity sensor was used for the air temperature and humidity testing, the hot-wire anemometer for the air velocity testing in the regenerator, the PT100 temperature sensor for the solution temperature testing and the glass rotor flow meter for the solution mass flow testing.
3. Model validation
3.1. Uncertainty analysis
An experimental system has been built for the model validation, which is shown in Fig. 3. The experimental counter-flow UALDR has the diameter of 0.34 m and the height of 1.0 m. The LiCl aqueous solution was used as the liquid desiccant in this study. The weak LiCl solution in storage tank was fed to the regeneration tower by a magnetic pump,
The temperatures of air and solution were directly measured by sensors, so the uncertainty for air temperature is 0.2%, for solution temperature is 0.3%. The air humidity ratio is calculated by air temperature and relative humidity measured by sensors, and it is processed
Fig. 3. Experimental set-up for the counter-flow UALDR. (a) Schematic diagram; (b) Field photo. 5
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Table 1 Specifications of main equipment in the experimental system. Equipment
Properties
Manufacturer
Ultrasonic atomizer
Power: 50 W Maximum capacity: 50 L/min Sauter mean diameter: 300 μm Power: 65 W Maximum capacity: 45 L/min Power :75 W Maximum capacity: 540 m3/h Power :1500 W Power :800 W Control accuracy: ± 0.5 °C
Hangzhou Chenggong Ultrasonic Equipment Co., Ltd.
Magnetic pump Variable speed fan PTC air heater Solution heater
Shanghai Xinxishan Pumps Co., Ltd. Leqing Hongke Electrical Co., Ltd. Suzhou Weire Electrical Co., Ltd. Shanghai Oumeng Industrial Co., Ltd.
where h v,0 is latent heat of water, Qs, h and Qa, h are energy consumption for heating the desiccant solution (Eq. (30)) and the regenerating air (Eq. (31)), respectively.
Table 2 Specifications of measurement instruments for the experimental study. Instruments
Measurement range
Accuracy
Temperature & humidity sensor (Type: Rotronic HC2A-S) Hot wire anemometer (TES 1341) Temperature sensor (Type: PT100) Glass rotor flow meter
−50 to + 100 °C, 0–100% RH 0–20 m/s −50 to +450 °C 6–60 L/h
± 0.2%, ± 0.8% ± 1% ± 0.3% ± 2.5%
Qs, h = cps ms (Ts, out , h Qa, h = cpa ma (Ta, out , h
f1 x1
x1 y
2
f2
+
x2
x2 y
2
+
+
fn xn
xn y
2
(27)
Ql = cps ms, out (Ts, out
where Uxi is the uncertainty of measured value x i . f is the function of measured value; x1, x2 xn are measured values; x is the absolute error of measured values; y/ y is relative error. The comparison of the model results and the experimental data are shown in Fig. 4. Horizontal error bars represent the error of the experimental data. 20 groups of experiments were conducted to validate the mathematical model. As shown in Fig. 4, the maximum relative errors for the outlet air temperature, the outlet air humidity and the outlet solution temperature are less than 6%, 8% and 6%, respectively. It indicates that the proposed model can effectively predict the parameter changes of the air and the desiccant solution in the counter-flow UALDR under any inlet conditions.
a, in )
=
ma h v,0 ( a, out Qs, h + Qa, h
Tam)
(32)
Fig. 5 shows the influence of inlet air temperature (from 25 to 60 °C) on the performance of the counter-flow UALDR. As shown in Fig. 5(a), the influence of the inlet air temperature on the regeneration thermal efficiency is nonlinear. There seems to exist an inlet air temperature which results in the lowest regeneration thermal efficiency. For this case, the lowest regeneration thermal efficiency appears at the inlet air temperature of about 41 °C. The reason for this trend can be explained as follows: The energy for water evaporating increases more slowly than total energy with the inlet air temperature less than 41 °C, and it increases faster than total energy with the inlet air temperature greater than 41 °C. Moreover, the extreme point is dependent on the initial temperatures of the air and solution. The moisture removal rate increases linearly with the inlet air temperature increasing. The moisture removal rate increases by about 80% as the inlet air temperature rises from 25 to 45 °C. The increase of inlet air temperature reduces the temperature difference between air and solution, which decreases the sensible heat transfer and increases the moisture driving force between air and solution droplets. Therefore, both outlet air and solution temperature increase with inlet air increasing (Fig. 5(b)). The increasing moisture driving force enhances the moisture transfer rate from the solution droplets to the air, so the moisture removal rate, outlet air humidity and solution mass concentration all increase (Fig. 5(c)). 4.2. Influence of inlet air humidity
(28)
Fig. 6 exhibits the influence of inlet air humidity (from 5 to 15 g/kg dry air) on the performance of the counter-flow UALDR. Obviously, the higher inlet air humidity is not conducive to the solution regeneration. Therefore, the moisture removal rate and the regeneration thermal efficiency both decrease with the inlet air humidity increasing. The lower
where ma is air mass flow rate, kg/s; a, in and a, out are air humidity ratios at inlet and outlet of the regenerator, respectively. r
Tam ) + cpa ma (Ta, out
4.1. Influence of inlet air temperature
By using the validated model, the regeneration performances of the counter-flow UALDR are theoretically investigated under different operating conditions. In the simulation, the basic conditions are listed as below: Ta, in = 25 °C, a, in = 15 g/kg, ma, in = 0.0558 kg/s, Ts, in = 60 °C, Xin = 0.3, ms, in = 0.0136 kg/s and d = 300 μm. The inlet air temperature (Ta, in ) changes from 25 to 60 °C, the inlet air humidity ( a, in ) from 5 to 15, the inlet solution temperature (Ts, in ) from 50 to 80 °C, the inlet solution concentration from 0.3 to 0.35, the solution mass flow rate from 0.00558 to 0.558 kg/s and the solution droplet diameter (ds ) from 300 to 1000 μm. The moisture removal rate (mr ) and the regeneration thermal efficiency ( r ) are adopted to evaluate the performance of the counter-flow UALDR, which are defined by Eqs. (28) and (29), respectively. a, out
(31)
a, h
where subscript am denotes ambient air.
4. Simulation and discussions
mr = ma (
Ta, in, h )/
(30)
s, h
where subscripts s and a represent the desiccant solution and the regeneration air, respectively; h denotes heater for heating solution and air; h is the heating efficiency of heater; in and out represent inlet and outlet of the regenerator, respectively. Since the regenerated desiccant solution will be cooled to ambient temperature before it is reused for dehumidification, the outlet energy loss of the counter-flow UALDR (Ql ) can be obtained by Eq. (32).
with uncertainty analysis.
y = y
Ts, in, h)/
a, in )
(29)
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Fig. 5. Variations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with inlet air temperature.
of the inlet air humidity, the change trend of the outlet air humidity and the outlet solution mass concentration versus the inlet air humidity in Fig. 6(c) can be easily understood. From the above analysis results of Sections 4.1 and 4.2, decreasing the temperature difference and increasing humidity difference between air and solution contribute to improving regeneration efficiency. 4.3. Influence of inlet solution temperature The solution temperature is one of the key control variables in a counter-flow UALDR. As shown in Fig. 7, the higher inlet solution temperature results in the larger moisture removal rate and the higher regeneration thermal efficiency. The increase of inlet solution temperature causes the solution moisture pressure to increase. Therefore, the moisture removal rate increases with the increase of the inlet solution temperature, and so do the outlet air humidity and the outlet solution concentration with the inlet solution temperature (Fig. 7(c)). The higher inlet solution temperature will result in more sensible heat transfer amount from the solution to the air, and hence, the outlet air temperature increases with the inlet solution temperature increasing (Fig. 7(b)). It can be noticed that the higher inlet solution temperature is conducive to improving the performance of the counter-flow UALDR. But, the higher inlet solution temperature means the more energy loss,
Fig. 4. Comparison of model results and experimental data; (a) Outlet air temperature; (b) Outlet air humidity; (c) Outlet solution temperature.
moisture removal rate means the smaller amount of latent heat transfer from the solution to the air, and this causes the outlet solution temperature to rise under the higher inlet air humidity as shown in Fig. 6(b). The higher solution temperature will result in the larger amount of sensible heat transfer from the solution to the air. So, the outlet air temperature increases with the inlet air humidity increasing (Fig. 6(b)). Since the moisture removal rate decreases with the increase 7
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Fig. 6. Variations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with inlet air humidity.
Fig. 7. Variations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with inlet solution temperature.
which is not preferred considering the system energy efficiency. So, the inlet solution temperature of the counter-flow UALDR should be as low as possible provided that the moisture removal rate of the counter-flow UALDR can satisfy the actual system requirement.
4.5. Influence of gas-liquid ratio Fig. 9 gives the influence of gas-liquid ratio (from 0.5 to 5) on the performance of the counter-flow UALDR. In this case, the air mass flow rate is fixed. The larger gas-liquid ratio means the smaller solution flow rate and the smaller number of droplets in the counter-flow UALDR. As shown in Fig. 9(a), the moisture removal rate decreases with the gasliquid ratio increasing, while the trend of regeneration efficiency is opposite. It is because the decrease of solution flow rate reduces the moisture transfer amount to the air. The humidity difference between the air and solution increase, which causes the solution concentration to increase. Meanwhile, the increase of solution concentration improves the thermal regeneration efficiency. It can be seen from Fig. 9 (a) and (c) that with the gas-liquid ratio greater than 2.5, all parameters increase slowly. Hence, there is no obvious improvement on the regeneration performance with the gas-liquid ratio greater than 2.5.
4.4. Influence of inlet solution concentration The influence of inlet solution mass concentration (from 0.3 to 0.35) on the performance of the counter-flow UALDR is show in Fig. 8. It can be seen the higher inlet solution concentration results in the smaller moisture removal rate and the lower regeneration thermal efficiency. For the given conditions, the moisture removal rate and the regeneration thermal efficiency both decrease by about 60% as the inlet solution concentration rises from 0.3 to 0.35. The higher inlet solution concentration has the lower surface moisture pressure, and hence, it reduces the moisture removal rate and the regeneration thermal efficiency of the counter-flow UALDR, which results in the higher outlet temperature of air and solution (Fig. 8(b)) and the lower outlet air humidity (Fig. 8(c)). For the same parameter, the inlet value affects the outlet one mostly. Hence, the outlet solution mass concentration increases with the inlet one increasing.
4.6. Influence of droplet diameter The solution droplet size, which can be controlled by the acoustic frequency of the ultrasonic atomizer, produces great effect on the performance of the counter-flow UALDR. As indicated in Fig. 10, there
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Fig. 8. Variations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with solution concentration.
Fig. 9. Variations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with gas-liquid ratio.
should be a best droplet size at which the maximum moisture removal rate and regeneration thermal efficiency of the counter-flow UALDR can be achieved. For this case, the moisture removal rate and the regeneration thermal efficiency of the UALDR both increase with the solution droplet size increasing from 300 to about 420 μm, and the situations are the opposite when the solution droplet size is larger than 420 μm. According to the previous study [30], the mass transfer coefficient increases with the decrease of the droplet size. When the droplet size is too small (e.g., smaller than 420 μm in this case), the solution droplets reach moisture equilibrium with the air before the outlet of the counter-flow UALDR, and they even adsorb moisture due to temperature reduction in the solution droplets. Fig. 11 shows the variations of the humidity ratio of air and solution along flow direction. Marker square and circle represent air and solution, respectively. The marker of square and circle with the same color represent the variation of air and solution under same condition. Subfigure in Fig. 11 shows the outlet air humidity ratio. The second and third red circles show that the air humidity is greater than the equilibrium humidity of solution, which indicates dehumidification occurs after the cross points. For a given solution mass flow rate, the contact area between air and solution droplets decreases with the increase of droplet diameter. Therefore, with the droplet size increasing, the outlet air temperature decreases, and the outlet solution temperature increases as shown in Fig. 10(b). The change pattern of the outlet air humidity and the outlet
solution mass concentration against the droplet size in Fig. 10(c) can be explained by the same reason as used for Fig. 8. 4.7. Comparison with the parallel-flow configuration By using the mathematical model for the UALDR of parallel-flow configuration [10], the comparisons of regeneration performance between the counter-flow and the parallel-flow configurations under same basic conditions are made, which is presented in Fig. 12. The results manifest that the moisture removal rate and the regeneration thermal efficiency of the counter-flow UALDR are obviously higher than that of the parallel-flow one. The moisture removal rate and regeneration thermal efficiency for the counter-flow configuration are 24% and 28% greater than the parallel-flow one, respectively. It can be explained by the following two reasons: (1) the residence time of solution droplets in the counter-flow UALDR is longer than the parallel-flow one, which increases the reaction time for the heat and moisture transfer between the air and the solution droplets. (2) the humidity ratio difference between the air and the solution along flow direction in the counter-flow UALDR is more uniform than that of parallel-flow configuration.
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5. Conclusions The mathematical model for the counter-flow ultrasonic atomization liquid desiccant regenerator was first developed and experimentally validated in this study. The moisture removal rate and the regeneration thermal efficiency were suggested to evaluate the performance of the new counter-flow regenerator. With the developed model, the effects of various parameters on the performance of the counter-flow regenerator were investigated, and the following conclusions can be achieved: (1) To improve regeneration performance, it needs to decrease the temperature difference between the air and solution to reduce sensible heat transfer. (2) Although the increase of the inlet air and the inlet solution temperature can significantly improve the regeneration performance of the counter-flow regenerator, the temperatures should be determined based on the consideration of energy efficiency of the whole dehumidification system. (3) The increase of the inlet air humidity and the inlet solution concentration reduces the regeneration efficiency of the counter-flow regenerator. (4) The regeneration efficiency increases nonlinearly with the increase of gas-liquid ratio. With the gas-liquid ratio larger than a certain value, the improvement is not obvious. (5) The increase of gas-liquid ratio can improve the regeneration performance of the counter-flow regenerator, and the improvement is not obvious when the gas-liquid ratio (6) There exists a best droplet size at which the best regeneration performance of the counter-flow regenerator can be achieved for specific conditions. Dehumidification can occur as the droplet diameter is smaller than the best droplet size during regeneration process. (7) Since the residence time of droplets and the mean humidity difference between the air and solution for the counter-flow configuration are greater than that of parallel-flow one, the regeneration performance of the counter-flow regenerator is obviously better than that of the parallel-flow configuration.
Fig. 10. V. ariations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with droplet diameter.
Fig. 11. Variations of air humidity and equilibrium humidity of solution along the height of regenerator under different conditions of droplet diameters. 10
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Fig. 12. Comparison of UALDR with counter flow and parallel flow configuration. (a) moisture removal rate; (b) regeneration thermal efficiency.
Declaration of Competing Interest [8]
None.
[9]
Acknowledgement This work is financially supported by National Natural Science Foundation of China (Grant No. 51876115).
[10] [11]
Appendix A. Supplementary material
[12]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114573.
[13]
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Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Modeling and performance investigation on the counter-flow ultrasonic atomization liquid desiccant regenerator
T
Ye Yaoa, , Wei Lia, Yixiong Hub ⁎
a b
Institute of Refrigeration and Cryogenics Engineering, Shanghai Jiao Tong University, Shanghai 200240, China School of Energy Science and Engineering, Central South University, Changsha, Hunan Province 410083, China
HIGHLIGHTS
ultrasonic atomization liquid desiccant regenerator (UALDR) is studied. • Counter-flow model for the counter-flow UALDR has been developed. • AEffects of inlet parameters on the performance of the counter-flow UALDR are studied. • Comparisons between the concurrent-flow and the counter-flow UALDR are made. • ARTICLE INFO
ABSTRACT
Keywords: Counter-flow Ultrasonic atomization Liquid desiccant Regenerator Modeling
As the key components in a liquid desiccant dehumidification system, liquid desiccant regenerator produces great effect on the whole system’s performance. This paper studies the counter-flow ultrasonic atomization liquid desiccant regenerator. Firstly, a mathematical model for the regenerator has been established and experimentally validated with finite difference method. Two performance indicators, i.e., the moisture removal rate and the regeneration thermal efficiency, were suggested to evaluate the performance of the counter-flow regenerator, and the influences of inlet parameters on the regeneration performance of the counter-flow regenerator have been investigated by the established model in this study. Decreasing temperature difference and increasing humidity difference between air and solution can improve regeneration performance. With the temperature of air and solution increasing, the regeneration efficiency increases, but the energy loss also increases. The regeneration efficiency decreases with the increase of solution concentration. The regeneration efficiency increases nonlinearly with the increase of gas-liquid ratio. Finally, there exists an optimum droplet size for the best regeneration performance. Compared with the parallel-flow configuration, the counter-flow has better regeneration performance, which is attributed to the more uniform distribution of moisture transfer driving force and the longer residence time of droplets in the regenerator. The study contributes to the development and the better applications of the counter-flow ultrasonic atomization liquid desiccant regenerator.
1. Introduction As a promising alternative approach, liquid desiccant dehumidification (LDD) has been attracting more and more attention in recent years [1–6]. The LDD system uses a kind of hygroscopic salt solution (such as LiBr, LiCl and CaCl2) as absorbent. Since there exists water vapor partial pressure difference between the surface of the hygroscopic salt solution and the air to be treated, this drives the water vapor in the air to pass through the absorbent solution, enabling the processing of air humidity. The absorbed moisture will reduce the dehumidifying ability of the desiccant solution. To recycle the desiccant, the solution
⁎
must be regenerated after the air dehumidification process. Compared with the solid desiccant dehumidification (SDD) system, the LDD system has several advantages including: (1) The higher energy efficiency because liquid desiccants are easier to be cooled, and the isothermal dehumidification process can be acquired; (2) The larger energy storage capability (up to 500 MJ/m3 [5]) which is conducive to utilizing the intermittent renewable energy (such as solar energy and industrial waste heat) for the air dehumidification all the time of the day [7,8]; (3) More flexible form which makes it possible for the waste heat far away from the air-handling units to be utilized for the desiccant regeneration [9].
Corresponding author. E-mail address: [email protected] (Y. Yao).
https://doi.org/10.1016/j.applthermaleng.2019.114573 Received 9 February 2019; Received in revised form 14 October 2019; Accepted 20 October 2019 Available online 22 October 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
Av Cd cp D ds h hc hd H Le m md m NTU Nu p p Pr Q Re Sr
Sh T u V X
y
calculation height (m)
Greek symbols
specific area between air and solution droplets (m2 /m3) drag coefficient specific heat capacity (kJ/kg °C) diffusion coefficient (m2 /s) droplet diameter (m) enthalpy (kJ/kg) heat transfer coefficient (W/m2 °C) mass transfer coefficient (kg/m2s) regenerator height (m) Lewis number (dimensionless) molality of LiCl aqueous solution (mol/kg) mass of desiccant solution droplet (kg) mass flow rate (kg/s) number of transfer unit (dimensionless) Nusselt number (dimensionless) pressure (kPa) pressure drop (kPa) Prandtl number (dimensionless) power (W) Reynolds number (dimensionless) cross sectional area of regenerator (m2) Schmidt number (dimensionless) Sherwood number (dimensionless) temperature (°C) velocity (m/s) volume of regenerator (m3) solution concentration (weight fraction)
µa
efficiency thermal conductivity (W/m °C) viscosity of air (Ns/m2) density (kg/m3) time (s) humidity ratio (kg/kgdryair)
Subscripts
a am d guess h in l m out r s ts ts, sat v 0
The regenerator in the liquid desiccant system is the component consuming heating energy for regenerating the weak desiccant solution delivered from the absorber, so its efficiency directly effects the LDD performance. Many earlier studies focused on packed regenerator due to its large heat and mass transfer area between the air and the liquid desiccant. Martin et al. [10] made an experimental study on a packed regenerator using triethylene glycol (TEG) as the liquid desiccant and presented effects of inlet parameters of the air and desiccant on humidity effectiveness of the regeneration. Fumo et al. [11] carried out an experimental study on the counter-flow packed regenerator using aqueous lithium chloride (LiCl-H2O) as the liquid desiccant. Longo et al. [12,13] experimentally studied a packed-bed regenerator using LiBrH2O and a new solution KCOOH-H2O and made a further study on the structured and the random packed regenerator. Liu et al. [14] developed an NTU-based model to simulate the heat and mass transfer processes in a cross-flow liquid desiccant regenerator, and the model can predict the air and desiccant parameters inside the regenerator as well as outlet parameters at any running conditions. They also conducted experimental research on the regenerator with LiBr solution and compared the regeneration performances of cross-flow regenerator with other counter-flow configurations [15]. To prevent the liquid desiccant regeneration decaying in the packed regenerator, the internally heated regenerators were recommended by researchers. Yin and Zhang [16] compared the internally heated and adiabatic regenerator, and the results indicated that the regenerate rate and energy utilization efficiency of the internally heated regenerator are higher than the adiabatic one. Some new-type regenerators have been studied and developed based on technologies in other fields. For example, Bai et al. [17] investigated the membrane-based flat-plate heat and mass exchanger used for liquid desiccant regeneration. The results showed that the boundary conditions of the membrane surface changed along the membrane diagonal line and the increase of NTU and m improved the regeneration performance. Yon et al. [18,19] proposed a novel liquid desiccant regeneration system operating in vacuum condition. The
air ambient droplet guess value heater inlet loss moist air outlet regeneration desiccant solution at solution temperature air saturated at solution temperature vapor at 0 °C
regeneration temperature of this system was lower to 20–35 °C at vacuum pressure from 1000 to 2000 Pa, and the power consumption was reduced by 40.66% compared to conventional packed-bed regenerator. Guo et al. [20] evaluated the potential of using electrodialysis (ED) technology to regenerate liquid desiccant. The efficiency of the ED in two hours for all experiments ranged from 55.17 to 73.54%, and the concentration difference produced important effect on the regeneration performance of ED. Cheng et al. [21,22] investigated the stability and the performance of the ED regeneration technology with different desiccant solution concentrations. It was found that excessive current would be harmful to the dehumidification capacity of the liquid desiccant. Chen et al. [23] evaluated the vacuum multi-effect membrane distillation system for liquid desiccant regeneration with thermodynamic model and proposed a new configuration, of which the specific energy consumption was reduced by 10–50%. The method of ultrasonic atomizing for the solution regeneration may become a promising way to develop a kind of new regenerator in which the solution is atomized into droplets of 40–50 μm by the special effect of cavitation of power ultrasound [24]. The new structure configuration will greatly enlarge the air-desiccant contacting area and reduce the air flow resistance, and hence, the performance and regeneration efficiency can be significantly improved [25]. In the previous study [26], the mathematical model for the ultrasonic atomization regenerator with parallel-flow configuration has been developed and explored. In this study, the ultrasonic atomization regenerator with counter flow configuration is to be investigated. This paper is mainly concerned about the following contents: (1) A mathematical model is developed for the liquid desiccant regeneration process in the counter-flow ultrasonic atomization liquid desiccant regenerator (UALDR) based on the principle of energy and mass conservation between the air and the desiccant solution. (2) An experimental system is designed for validating the proposed model of the counter-flow UALDR. 2
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(3) Effects of air and desiccant inlet parameters on the performance of the counter-flow UALDR are investigated by using the developed model. Plus, the regeneration performance of the counter-flow UALDR is compared to the parallel-flow one,
cross sectional area of regenerator; ud a is droplet velocity relative to the regenerating air; h v,0 is the enthalpy of water vapor at 0 °C; pa is atmospheric pressure; pv is surface vapor pressure of desiccant solution at given temperature [28].
2. Mathematical model 2.1. Assumptions
Nu = 2 + 0.6Re 0.5 Pr 0.33
(11)
Sh = 2 + 0.6Re 0.5 Sc 0.33
(12)
where Re is Reynold number, Re = |ud + ua | ds a / µg ; Pr is Prandtl number, Pr = µa cpa/ ; is Schmidt number, Sc = µa / a D ; The momentum conservation equation of a solution droplet is given by:
The heat and moisture transfer process of the ultrasonic atomization regenerator is different from the packed-bed regenerator. In the ultrasonic atomization regenerator, the desiccant solution is atomized in fine droplets to exchange heat and moisture with process air. The heat and moisture transfer process in the counter-flow UALDR is schematically shown in Fig. 1. To simplify the heat and mass transfer process in the regenerator, some assumptions are made for the mathematical model development:
md
dud = md g dt
1 Cd 2
a
Cd = 18.5/ Re3/5 1.9
Cd = 0.44 508
Re < 508
Re
200000
3 Cd 4 ds
Energy, water and solute conservation equations in a differential element are written by:
2.3. Numerical solution
(2)
a
Heat and mass transfer equations between the air and the desiccant solution are given by:
ma dha = hc Av dV (Ts ma d
a
= hd
m A v dV
Ta ) + h v, ts ma d (
ts, sat
a)
a
a
(u d + u a ) 2
s
(15)
The mathematical model of the counter-flow UALDR consists of Eqs. (1)–(5), which can be solved by the finite difference method with inlet boundary conditions of the solution droplets (Eq. (16)) and the air (Eq. (17)). Inlet boundary conditions of the solution droplets: y = 0 : Ts = Ts, in , ms = m s, in , Xs = Xs, in (16) Inlet boundary conditions of the air:
(3)
d (ms X ) = 0
(14)
where md = ds3 s /6. y is the differential height of regenerator; ud is expressed as ud = dy /dt .
dud 1 = g dy ud
dms = ma d
(13)
Cd = 24/ReRe < 1.9
2.2. Governing equations
(1)
ds2 (ud + ua )2
where the first term in the right-hand of the above equation is gravity, and the second term is drag force. md is the mass of droplet; a is air density. ua and ud are velocity of air and droplet, respectively. Cd is the drag coefficient, which is shown as follows [29]:
(1) The regeneration process in the regenerator is considered as adiabatic. (2) Heat and mass transfer inside the solution droplet is neglected. (3) The droplets are spherical, and deformation is neglected. (4) The effect of the collisions between droplets and the regenerator wall is neglected. (5) The direction of heat and moisture transfer is one dimensional along the regenerator height.
ma dha = d (ms hs )
4
(4) (5)
where m is mass flow rate; h is enthalpy; a is air humidity ratio; X is solution concentration; hc and hd are heat and mass transfer coefficients, respectively; Av is specific transfer area of unit volume, expressed by Eq. (8); dV is volume element; T is temperature; h v, ts is the enthalpy of water vapor at solution temperature, defined in Eq. (9); m is the density of moist air; Ts, sat is the humidity ratio of air in equilibrium with desiccant solution, calculated by Eq. (10).
hc =
Nu· ds
(6)
hd =
Sh ·D ds
(7)
Av =
6 ms d s, in s Sr ud
(8)
a
(9)
h v, ts = h v,0 + cpv Ts ts, sat
= 0.622
pv pa
pv
(10)
In Eqs. (6) and (7), Nu and Sh are Nusselt and Sherwood numbers, respectively. For the case of Re < 5, Nu and Sh are expressed by Eqs. (11) and (12) [27], respectively; is thermal conductivity of air; D is mass diffusion coefficient of vapor into air; ds is droplet diameter; Sr is
Fig. 1. Schematic diagram for the heat and mass transfer process in the counter flow UALDR. 3
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y = H : Ta = Ta, in , ma = m a, in , a = a, in (17) The difference equations for the mathematical model are given by Eqs. (18)–(23).
hai+ 1
hai y
i+1 a
=
NTU · Le i hTs, sat H
=
NTU ( H
i a
y
msi + 1
msi = ma (
ma (hai+ 1
i Ts, sat
i+1 a
hai +
1 Le
1 h v, ts (
i Ts , sat
i a)
udi y
=
1 g udi
cp, m = cpa +
(18)
(21)
msi hsi
(22) a
(udi + ua ) 2
(23)
s
hm
m Av V
ma
a cpv
(26)
(1) Input boundary conditions, including inlet temperatures of air and solution, inlet air humidity, inlet solution concentration, mass flow rate of air and solution and parameters of regenerator. (2) Assume the outlet air temperature and humidity. (3) Repeat the following for each grid:
where NTU is number of transfer unit; Le is Lewis number.
NTU =
(25)
The calculation flow chart is presented in Fig. 2. In the following model validation, the regenerator is divided into 100 grids ( y = 0.01 m) along the height. The gird independence test shows that 100 grids are enough for numerical accuracy (less than 0.2% difference compared to 200 grids). For the counter-flow arrangement, it needs to calculate parameters from one side to the other side. Therefore, the solution inlet was chosen as the starting point, so the outlet air temperature and humidity were assumed.
(20)
i a)
3 Cd 4 dsi
m cp, m
where cp, m is the specific heat of moist air.
(19)
msi + 1 X i + 1 = msi X i udi+ 1
h hm
2.4. Numerical procedure
i a)
hai ) = msi + 1 hsi + 1
Le =
(24)
Fig. 2. Calculation flow chart for the model solution. 4
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(a) Calculate the enthalpy of air (Eq. (18)). (b) Calculate the air humidity (Eq. (19)). (c) Calculate the air temperature according the calculated air enthalpy and humidity. (d) Calculate the solution mass flow rate (Eq. (20)). (e) Calculate the enthalpy of solution (Eq. (21)). (f) Calculate the solution concentration (Eq. (22)). (g) Calculate the solution droplet velocity (Eq. (23)). (h) Calculate the solution temperature since the solution enthalpy and concentration are known. (4) Iterate until the difference between the calculated values of the inlet air temperature and humidity and the given values meet requirement.
and the temperature of the weak solution was kept constant by using an electrical heater. The solution was atomized into tiny droplets with an average diameter of 300 μm by an ultrasonic atomization device (Type: YPW59). The solution flow rate was adjusted by a regulating valve and measured by a rotameter. Air was delivered by a variable-speed axial fan, and the inlet air temperature and humidity of the counter-flow UALDR were regulated by air heater and humidifier, respectively. Specifications of main equipment and measurement instruments in the experimental system are listed in Tables 1 and 2, respectively. The temperature & humidity sensor was used for the air temperature and humidity testing, the hot-wire anemometer for the air velocity testing in the regenerator, the PT100 temperature sensor for the solution temperature testing and the glass rotor flow meter for the solution mass flow testing.
3. Model validation
3.1. Uncertainty analysis
An experimental system has been built for the model validation, which is shown in Fig. 3. The experimental counter-flow UALDR has the diameter of 0.34 m and the height of 1.0 m. The LiCl aqueous solution was used as the liquid desiccant in this study. The weak LiCl solution in storage tank was fed to the regeneration tower by a magnetic pump,
The temperatures of air and solution were directly measured by sensors, so the uncertainty for air temperature is 0.2%, for solution temperature is 0.3%. The air humidity ratio is calculated by air temperature and relative humidity measured by sensors, and it is processed
Fig. 3. Experimental set-up for the counter-flow UALDR. (a) Schematic diagram; (b) Field photo. 5
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Table 1 Specifications of main equipment in the experimental system. Equipment
Properties
Manufacturer
Ultrasonic atomizer
Power: 50 W Maximum capacity: 50 L/min Sauter mean diameter: 300 μm Power: 65 W Maximum capacity: 45 L/min Power :75 W Maximum capacity: 540 m3/h Power :1500 W Power :800 W Control accuracy: ± 0.5 °C
Hangzhou Chenggong Ultrasonic Equipment Co., Ltd.
Magnetic pump Variable speed fan PTC air heater Solution heater
Shanghai Xinxishan Pumps Co., Ltd. Leqing Hongke Electrical Co., Ltd. Suzhou Weire Electrical Co., Ltd. Shanghai Oumeng Industrial Co., Ltd.
where h v,0 is latent heat of water, Qs, h and Qa, h are energy consumption for heating the desiccant solution (Eq. (30)) and the regenerating air (Eq. (31)), respectively.
Table 2 Specifications of measurement instruments for the experimental study. Instruments
Measurement range
Accuracy
Temperature & humidity sensor (Type: Rotronic HC2A-S) Hot wire anemometer (TES 1341) Temperature sensor (Type: PT100) Glass rotor flow meter
−50 to + 100 °C, 0–100% RH 0–20 m/s −50 to +450 °C 6–60 L/h
± 0.2%, ± 0.8% ± 1% ± 0.3% ± 2.5%
Qs, h = cps ms (Ts, out , h Qa, h = cpa ma (Ta, out , h
f1 x1
x1 y
2
f2
+
x2
x2 y
2
+
+
fn xn
xn y
2
(27)
Ql = cps ms, out (Ts, out
where Uxi is the uncertainty of measured value x i . f is the function of measured value; x1, x2 xn are measured values; x is the absolute error of measured values; y/ y is relative error. The comparison of the model results and the experimental data are shown in Fig. 4. Horizontal error bars represent the error of the experimental data. 20 groups of experiments were conducted to validate the mathematical model. As shown in Fig. 4, the maximum relative errors for the outlet air temperature, the outlet air humidity and the outlet solution temperature are less than 6%, 8% and 6%, respectively. It indicates that the proposed model can effectively predict the parameter changes of the air and the desiccant solution in the counter-flow UALDR under any inlet conditions.
a, in )
=
ma h v,0 ( a, out Qs, h + Qa, h
Tam)
(32)
Fig. 5 shows the influence of inlet air temperature (from 25 to 60 °C) on the performance of the counter-flow UALDR. As shown in Fig. 5(a), the influence of the inlet air temperature on the regeneration thermal efficiency is nonlinear. There seems to exist an inlet air temperature which results in the lowest regeneration thermal efficiency. For this case, the lowest regeneration thermal efficiency appears at the inlet air temperature of about 41 °C. The reason for this trend can be explained as follows: The energy for water evaporating increases more slowly than total energy with the inlet air temperature less than 41 °C, and it increases faster than total energy with the inlet air temperature greater than 41 °C. Moreover, the extreme point is dependent on the initial temperatures of the air and solution. The moisture removal rate increases linearly with the inlet air temperature increasing. The moisture removal rate increases by about 80% as the inlet air temperature rises from 25 to 45 °C. The increase of inlet air temperature reduces the temperature difference between air and solution, which decreases the sensible heat transfer and increases the moisture driving force between air and solution droplets. Therefore, both outlet air and solution temperature increase with inlet air increasing (Fig. 5(b)). The increasing moisture driving force enhances the moisture transfer rate from the solution droplets to the air, so the moisture removal rate, outlet air humidity and solution mass concentration all increase (Fig. 5(c)). 4.2. Influence of inlet air humidity
(28)
Fig. 6 exhibits the influence of inlet air humidity (from 5 to 15 g/kg dry air) on the performance of the counter-flow UALDR. Obviously, the higher inlet air humidity is not conducive to the solution regeneration. Therefore, the moisture removal rate and the regeneration thermal efficiency both decrease with the inlet air humidity increasing. The lower
where ma is air mass flow rate, kg/s; a, in and a, out are air humidity ratios at inlet and outlet of the regenerator, respectively. r
Tam ) + cpa ma (Ta, out
4.1. Influence of inlet air temperature
By using the validated model, the regeneration performances of the counter-flow UALDR are theoretically investigated under different operating conditions. In the simulation, the basic conditions are listed as below: Ta, in = 25 °C, a, in = 15 g/kg, ma, in = 0.0558 kg/s, Ts, in = 60 °C, Xin = 0.3, ms, in = 0.0136 kg/s and d = 300 μm. The inlet air temperature (Ta, in ) changes from 25 to 60 °C, the inlet air humidity ( a, in ) from 5 to 15, the inlet solution temperature (Ts, in ) from 50 to 80 °C, the inlet solution concentration from 0.3 to 0.35, the solution mass flow rate from 0.00558 to 0.558 kg/s and the solution droplet diameter (ds ) from 300 to 1000 μm. The moisture removal rate (mr ) and the regeneration thermal efficiency ( r ) are adopted to evaluate the performance of the counter-flow UALDR, which are defined by Eqs. (28) and (29), respectively. a, out
(31)
a, h
where subscript am denotes ambient air.
4. Simulation and discussions
mr = ma (
Ta, in, h )/
(30)
s, h
where subscripts s and a represent the desiccant solution and the regeneration air, respectively; h denotes heater for heating solution and air; h is the heating efficiency of heater; in and out represent inlet and outlet of the regenerator, respectively. Since the regenerated desiccant solution will be cooled to ambient temperature before it is reused for dehumidification, the outlet energy loss of the counter-flow UALDR (Ql ) can be obtained by Eq. (32).
with uncertainty analysis.
y = y
Ts, in, h)/
a, in )
(29)
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Fig. 5. Variations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with inlet air temperature.
of the inlet air humidity, the change trend of the outlet air humidity and the outlet solution mass concentration versus the inlet air humidity in Fig. 6(c) can be easily understood. From the above analysis results of Sections 4.1 and 4.2, decreasing the temperature difference and increasing humidity difference between air and solution contribute to improving regeneration efficiency. 4.3. Influence of inlet solution temperature The solution temperature is one of the key control variables in a counter-flow UALDR. As shown in Fig. 7, the higher inlet solution temperature results in the larger moisture removal rate and the higher regeneration thermal efficiency. The increase of inlet solution temperature causes the solution moisture pressure to increase. Therefore, the moisture removal rate increases with the increase of the inlet solution temperature, and so do the outlet air humidity and the outlet solution concentration with the inlet solution temperature (Fig. 7(c)). The higher inlet solution temperature will result in more sensible heat transfer amount from the solution to the air, and hence, the outlet air temperature increases with the inlet solution temperature increasing (Fig. 7(b)). It can be noticed that the higher inlet solution temperature is conducive to improving the performance of the counter-flow UALDR. But, the higher inlet solution temperature means the more energy loss,
Fig. 4. Comparison of model results and experimental data; (a) Outlet air temperature; (b) Outlet air humidity; (c) Outlet solution temperature.
moisture removal rate means the smaller amount of latent heat transfer from the solution to the air, and this causes the outlet solution temperature to rise under the higher inlet air humidity as shown in Fig. 6(b). The higher solution temperature will result in the larger amount of sensible heat transfer from the solution to the air. So, the outlet air temperature increases with the inlet air humidity increasing (Fig. 6(b)). Since the moisture removal rate decreases with the increase 7
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Fig. 6. Variations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with inlet air humidity.
Fig. 7. Variations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with inlet solution temperature.
which is not preferred considering the system energy efficiency. So, the inlet solution temperature of the counter-flow UALDR should be as low as possible provided that the moisture removal rate of the counter-flow UALDR can satisfy the actual system requirement.
4.5. Influence of gas-liquid ratio Fig. 9 gives the influence of gas-liquid ratio (from 0.5 to 5) on the performance of the counter-flow UALDR. In this case, the air mass flow rate is fixed. The larger gas-liquid ratio means the smaller solution flow rate and the smaller number of droplets in the counter-flow UALDR. As shown in Fig. 9(a), the moisture removal rate decreases with the gasliquid ratio increasing, while the trend of regeneration efficiency is opposite. It is because the decrease of solution flow rate reduces the moisture transfer amount to the air. The humidity difference between the air and solution increase, which causes the solution concentration to increase. Meanwhile, the increase of solution concentration improves the thermal regeneration efficiency. It can be seen from Fig. 9 (a) and (c) that with the gas-liquid ratio greater than 2.5, all parameters increase slowly. Hence, there is no obvious improvement on the regeneration performance with the gas-liquid ratio greater than 2.5.
4.4. Influence of inlet solution concentration The influence of inlet solution mass concentration (from 0.3 to 0.35) on the performance of the counter-flow UALDR is show in Fig. 8. It can be seen the higher inlet solution concentration results in the smaller moisture removal rate and the lower regeneration thermal efficiency. For the given conditions, the moisture removal rate and the regeneration thermal efficiency both decrease by about 60% as the inlet solution concentration rises from 0.3 to 0.35. The higher inlet solution concentration has the lower surface moisture pressure, and hence, it reduces the moisture removal rate and the regeneration thermal efficiency of the counter-flow UALDR, which results in the higher outlet temperature of air and solution (Fig. 8(b)) and the lower outlet air humidity (Fig. 8(c)). For the same parameter, the inlet value affects the outlet one mostly. Hence, the outlet solution mass concentration increases with the inlet one increasing.
4.6. Influence of droplet diameter The solution droplet size, which can be controlled by the acoustic frequency of the ultrasonic atomizer, produces great effect on the performance of the counter-flow UALDR. As indicated in Fig. 10, there
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Fig. 8. Variations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with solution concentration.
Fig. 9. Variations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with gas-liquid ratio.
should be a best droplet size at which the maximum moisture removal rate and regeneration thermal efficiency of the counter-flow UALDR can be achieved. For this case, the moisture removal rate and the regeneration thermal efficiency of the UALDR both increase with the solution droplet size increasing from 300 to about 420 μm, and the situations are the opposite when the solution droplet size is larger than 420 μm. According to the previous study [30], the mass transfer coefficient increases with the decrease of the droplet size. When the droplet size is too small (e.g., smaller than 420 μm in this case), the solution droplets reach moisture equilibrium with the air before the outlet of the counter-flow UALDR, and they even adsorb moisture due to temperature reduction in the solution droplets. Fig. 11 shows the variations of the humidity ratio of air and solution along flow direction. Marker square and circle represent air and solution, respectively. The marker of square and circle with the same color represent the variation of air and solution under same condition. Subfigure in Fig. 11 shows the outlet air humidity ratio. The second and third red circles show that the air humidity is greater than the equilibrium humidity of solution, which indicates dehumidification occurs after the cross points. For a given solution mass flow rate, the contact area between air and solution droplets decreases with the increase of droplet diameter. Therefore, with the droplet size increasing, the outlet air temperature decreases, and the outlet solution temperature increases as shown in Fig. 10(b). The change pattern of the outlet air humidity and the outlet
solution mass concentration against the droplet size in Fig. 10(c) can be explained by the same reason as used for Fig. 8. 4.7. Comparison with the parallel-flow configuration By using the mathematical model for the UALDR of parallel-flow configuration [10], the comparisons of regeneration performance between the counter-flow and the parallel-flow configurations under same basic conditions are made, which is presented in Fig. 12. The results manifest that the moisture removal rate and the regeneration thermal efficiency of the counter-flow UALDR are obviously higher than that of the parallel-flow one. The moisture removal rate and regeneration thermal efficiency for the counter-flow configuration are 24% and 28% greater than the parallel-flow one, respectively. It can be explained by the following two reasons: (1) the residence time of solution droplets in the counter-flow UALDR is longer than the parallel-flow one, which increases the reaction time for the heat and moisture transfer between the air and the solution droplets. (2) the humidity ratio difference between the air and the solution along flow direction in the counter-flow UALDR is more uniform than that of parallel-flow configuration.
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5. Conclusions The mathematical model for the counter-flow ultrasonic atomization liquid desiccant regenerator was first developed and experimentally validated in this study. The moisture removal rate and the regeneration thermal efficiency were suggested to evaluate the performance of the new counter-flow regenerator. With the developed model, the effects of various parameters on the performance of the counter-flow regenerator were investigated, and the following conclusions can be achieved: (1) To improve regeneration performance, it needs to decrease the temperature difference between the air and solution to reduce sensible heat transfer. (2) Although the increase of the inlet air and the inlet solution temperature can significantly improve the regeneration performance of the counter-flow regenerator, the temperatures should be determined based on the consideration of energy efficiency of the whole dehumidification system. (3) The increase of the inlet air humidity and the inlet solution concentration reduces the regeneration efficiency of the counter-flow regenerator. (4) The regeneration efficiency increases nonlinearly with the increase of gas-liquid ratio. With the gas-liquid ratio larger than a certain value, the improvement is not obvious. (5) The increase of gas-liquid ratio can improve the regeneration performance of the counter-flow regenerator, and the improvement is not obvious when the gas-liquid ratio (6) There exists a best droplet size at which the best regeneration performance of the counter-flow regenerator can be achieved for specific conditions. Dehumidification can occur as the droplet diameter is smaller than the best droplet size during regeneration process. (7) Since the residence time of droplets and the mean humidity difference between the air and solution for the counter-flow configuration are greater than that of parallel-flow one, the regeneration performance of the counter-flow regenerator is obviously better than that of the parallel-flow configuration.
Fig. 10. V. ariations of moisture removal rate, regeneration thermal efficiency (a), outlet air and solution temperature (b), outlet air humidity and solution concentration (c) with droplet diameter.
Fig. 11. Variations of air humidity and equilibrium humidity of solution along the height of regenerator under different conditions of droplet diameters. 10
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Fig. 12. Comparison of UALDR with counter flow and parallel flow configuration. (a) moisture removal rate; (b) regeneration thermal efficiency.
Declaration of Competing Interest [8]
None.
[9]
Acknowledgement This work is financially supported by National Natural Science Foundation of China (Grant No. 51876115).
[10] [11]
Appendix A. Supplementary material
[12]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114573.
[13]
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