Theoretical and experimental analysis of the thermodynamic and economic performance for a packed bed humidifier

Energy Conversion and Management 206 (2020) 112497

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Theoretical and experimental analysis of the thermodynamic and economic performance for a packed bed humidifier ⁎

T

⁎

Junjie Chen, Dong Han , Weifeng He , Yun Liu, Jiming Gu Nanjing University of Aeronautics and Astronautics, College of Energy and Power Engineering, Energy Conservation Research Group (ECRG), Nanjing, Jiangsu 210016, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Packed bed humidifier Heat and mass transfer Mathematical models Finite difference method Parametric analysis Thermodynamic and economic analysis

In this paper, the thermodynamic and economic performance of the humidifier, with a wire mesh corrugated packing, is investigated and evaluated with the defined evaluation criteria experimentally and theoretically. In view of the humidification characteristics of packings, the mathematical models based on mass and energy balance are established. Performance of the packed bed humidifier, evaluated by the unit humidification capacity of volume (UHCV) and the unit humidification capacity of cost (UHCC), is first studied experimentally with fixed packing volume. Moreover, the parametric analysis of the humidification performance is achieved. The maximum values obtained simultaneously from the experiment present as 3.82 × 10−2 kgs−1 m−3 for the UHCV and 12.74 kg$−1 for the UHCC, as the liquid–gas ratio is 2 and the inlet water temperature is 90 °C. The simulation results illustrate that a peak point appears separately at mr = 0.5 for the UHCV and mr = 3 for the UHCC with the increase of liquid-gas ratio. It is also found that a higher value of the inlet air and water temperature, as well as the wet-bulb temperature of inlet humid air, can enhance the UHCV and UHCC in varying extents, while the inlet relative humidity has a reverse influence on them. Furthermore, it is observed that the effects of the specific surface area on the UHCV and UHCC are contradictory, with a best thermodynamic performance of 43.3 × 10−2 kgs−1 m−3, while the maximum economic value presents as 13.3 kg$−1.

1. Introduction Humidifiers, a significant device both for human life and social development, has increasingly attracted more and more attention from researchers at home and abroad in recent years. Many types of humidifiers such as spray towers [1], bubble columns [2], membranes [3] and packed-bed [4] are commonly used, and a lot of remarkable results have been achieved. Numerous researches studied on the humidifiers were performed to augment its heat efficiency tentatively in resent years, including simulations and experiments. Zeng [5] designed an effective multi-string humidifier to afford high interface-to-volume ratios and low pressure drop during spraying for desalination. Comparison results shown that humidification efficiency of the multi-string humidifier is five times as much as the pad humidifiers and spray columns. A novel multi-stage bubble column humidifier driven by solar energy was tested by Abd-UrRehman [6], and the influence of key parameters on the performance of the humidifier was also studied. The results explained that average day round relative humidity is elevated by 9%, 23% and 25% for 2 stage configuration, 3 stage configuration and the integration of Fresnel lens,

⁎

respectively. Solsona [7] designed a membrane humidifier for fuel cell applications and built the control-oriented model for it. The investigation results presented that the control strategy could optimize the performance and stability of the fuel cell. A novel air humidification system using a desiccant wheel to humidify the air atream was proposed and developed by De Antonellis [8] for the building, which the humidification process was achieved by extracting water vapour from environmental air. The findings shown that the power consumption of the proposed system is lower than that of electric steam humidifiers but higher than the one of steam to steam humidifiers. He et al. [9,10] applied successively the packed bed humidifier to the field of humidification-dehumidification (HDH) desalination in order to improve the comprehensive thermal performance of the desalination system. Moreover, in the study of Narayan et al. [11], packed bed tower was found to have a higher effectiveness as a result of the higher dispersion of water droplets, larger contact area and longer contact time compared to other type of humidifier. The packed bed humidifier is mainly composed of the shell and packings, which has been frequently using in gas turbine cycle [12], evaporation and crystallization [13] and other systems in recent years,

Corresponding authors. E-mail addresses: [email protected] (D. Han), [email protected] (W. He).

https://doi.org/10.1016/j.enconman.2020.112497 Received 18 September 2019; Received in revised form 2 December 2019; Accepted 12 January 2020 0196-8904/ © 2020 Elsevier Ltd. All rights reserved.

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Nomenclature

Z

Roman symbols

Greek Letters

a A AZ cp C dp dZ Da f G h hc hd hfg L Lef m mr N p p0 Δp P Re Sc t T V

φ ρ μ η ω

specific surface area (m2m−3) area (m2) cross-sectional area (m2) specific heat capacity (kJkg-1K−1) cost ($) equivalent diameter (m) height of control volume (m) mass diffusivity in gas (m2s−1) geometric coefficient gas specific enthalpy (kJkg−1) heat transfer coefficient (Wm-2K−1) mass transfer coefficient (kgm-2s−1) latent heat of vaporization at 0 °C (kJkg−1) liquid lewis factor mass flow rate (kgs−1) mass flow rate ratio (mwmda-1) power consumption (kW) pressure (Pa) standard atmospheric pressure (Pa) pressure change (Pa) price ($ or $m−3) reynolds number schmidt number running time (h) temperature (°C or K) packing volume (m3)

total packing height (m)

relative humidity density (kgm−3) dynamic viscosity (kgm-1s−1) efficiency humidity ratio (kgkg−1)

Subscripts a b da e i n o p v s ss w wb wp

air air-blower dry air electric heater inlet natural outlet packing vapor saturated supersaturated water wet bulb water pump

Abbreviations HDH UHCV UHCC

humidification-dehumidification unit humidification capacity of volume unit humidification capacity of cost

inlet air enthalpy increased. It was shown that at most experimental conditions, the error between experimental data and simulated data is within ± 12%. From what we have reviewed above, the studies of these new packings will further promote the humidification performance of several humidifiers. The finite difference humidifier model just developed in recent years can calculate the state of the air or water at a specified height within the humidifier, which was constructed from cooling tower analysis performed by Kloppers [20]. The heat and mass transfer methods of Merkel, e-NTU and Poppe were also analyzed and compared, while the difference between them was highlighted. Miller [21] evaluated the effect of multi-extraction on the performance and entropy production of the humidification-dehumidification desalination system by means of the finite difference humidifier models established both at the on-design and off-design conditions. At these conditions, the performance of the HDH system was dramatically improved and the entropy production of the whole system was minimized by balancing the extraction and injection of the water or air flow rate within the humidifier and dehumidifier. Ghalavand [22] established the mathematical models for the packed bed humidifier via the finite difference method to investigate the effect of insulation on the humidifier performance without considering supersaturation in the humid air. The results showed that the model precision in consideration of insulation effect was higher than the model without insulation effect and the absolute error with insulation effect was reduced to 2.4% according to the experimental data. In fact, the supersaturation phenomenon really existed at the air outlet and could seriously affect the performance of humidifier found by Xu et al. [19] experimentally. Chen [23] then reported that enlarging the liquid–gas ratio and reducing the wet-bulb temperature of the inlet air could enhance the supersaturation phenomenon at the humidifier outlet with the unsaturated and supersaturated

especially in desalination [10,14]. Considerable effect of packing material on the humidification performance of the humidifier as well as the performance of the whole system has revealed in the HDH desalination system [15]. The effects of three packing materials including gunny bag cloth, PVC sheets and wooden slates on the comprehensive performance of HDH desalination unit were theoretically and experimentally investigated by Amer et al. [16]. It was found that the humidifier with wooden slates has better mass transfer coefficient and higher productivity at forced air circulation, while the maximum productivity of 5.8 Lh−1 was obtained at the conditions of water mass flow rate of 2.8 kgmin−1 and water temperature at humidifier inlet of 85 °C. Ahmed et al. [17] experimentally studied the performance of a desalination unit with new corrugated aluminum sheets packing in the humidifier. The results indicated that the production of distilled water considerably increases with the increase of the inlet water temperature, the water flow rate, the mass ratio of water and air, and the cooling water flow rate. However, a slight increase in the production of desalinated water was observed by raising the air temperature, while the highest productivity was obtained by a specific air mass rate. The results of cost analysis showed that the total cost per liter of fresh water is about $0.01. He et al. [18] used the polypropylene as the packing material both in the humidifier and dehumidifier to enhance the performance of the HDH desalination system. The simulation results showed that the unit cost of the system was Cu,c = 26.94 ¥th−1 and Cu,t = 68.13 ¥th−1 and the maximum value of gained-output-ratio was for 2.01 corresponding to the minimum irreversible loss of the whole desalination system. Xu et al. [19] developed a mass transfer coefficient correlation for the ceramic foam packing humidifier with the Merkel assumption, and investigated it with the experiment. The study found that the mass transfer coefficient increased with the increase of water or air mass flow rate, but decreased as the inlet water temperature and 2

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humid air during the humidification process is shown in Fig. 2. In general, the exchange of sensible heat is coexistence with latent heat transfer on the surface of packing. The direction of sensible heat transfer can be changed due to the possibility of a temperature difference reversal along the gas–liquid interface. However, the orientation of latent heat transfer is always from saturated side to unsaturated side, as shown in Fig. 2b. In view of Kloppers [20], the Poppe method is more suitable and accurate in cross-flow or counter-flow conditions compared to the Merkel and E-NTU method, taking the water evaporation in the energy balance equations, variation of Lewis factor and supersaturation at air outlet into consideration, while the Reuter method is more likely recommended in cross-counter-flow. For the counter-flow humidification process studied in this paper, the Poppe method is advocated. In order to conduct the thermo-economic analysis for the packed bed humidifier, the following assumptions are given:

models. However, for the humidifier with wire mesh corrugated packing filled, the correlative investigations of the influences both from the inlet conditions as well as the packing properties on the economic performance were not involved from a microscopic perspective, while the relative evaluation objectives for assessing the humidification characteristics of packings have also not been addressed considering the supersaturation. Accordingly, in this paper, taking the supersaturation phenomenon and pressure drop of the packing into consideration, the performance of the humidifier simulated by finite difference method is first evaluated with the experimental data. And then, the pertinent performance evaluated by the proposed criteria are calculated in response to the variation of liquid–gas ratio, inlet air and water temperature, wet-bulb temperature and relative humidity of inlet humid air, as well as the specific surface area of the packing based on the established mathematical models. The relevant evaluation strategy and research results provide significant references for the design and further optimization of the packed bed humidifier particularly in the field of industrial application.

(1) The humidification process operates at the steady-state conditions. (2) The energy loss between the fluid and the ambient is ignored. (3) Kinetic and potential energy terms are not considered in the energy balance. (4) Flow resistances in pipes, water pump and air-blower are neglected. (5) Gas-liquid two-phase fluids contact uniformly in packing region.

2. Experimental setup and principle description A fabricated system setup for the HDH desalination with a packed bed humidifier is shown in Fig. 1, while the humidification subsystem mainly consists of humidifier, air-blower, water pump, electric heater and measurement equipments. The humidifier is made of stainless steel Q245R with a volume of 0.144 m2, inside where the wire mesh corrugated packings 316L, with the dimensions of 0.15 m high, 0.39 m diameter and 700Y specific surface area, are filled. The equipments for measuring temperature, pressure, humidity, flow rate and weight can be seen in detail in Table 1. The humidification process is based on the fact that the capacity of air to carry vapor gradually increases with its temperature. Hence, the inlet water is sprayed over the packing fills drived by the water pump after heating by the electric heater. The power of electric heater is from 1 to 7.5 kW. Then, the ambient air enters from the bottom and has a direct contact with the hot water accompanied by the heat and mass transfer simultaneously, that is, the water vapour from the liquid phase is absorbed by the humid air due to the temperature and humidity difference. After the humidification process, the humid air with high temperature and humidity ratio flows out from the top, while the cooling water dischanges from the bottom of the humidifier. As a result, the temperature-enthalpy diagram of the

3. Mathematical models of the humidification subsystem 3.1. Humidifier 3.1.1. Governing equations for unsaturated case From Poppe assumptions, the humidifier model for simplified calculation from a microscopic perspective can be set up in Fig. 3. The control volume model for the counter-flow packing and air side control volume model can also be built according to the finite difference method, as shown in Fig. 3b and Fig. 3c. Therefore, the differential governing equations to solve the heat and mass transfer process of the humidifier are established. From Fig. 3b, the mass balance equation for water side can be defined as:

dm w dω = mda dZ dZ

(1)

and the energy balance equation of the control volume can be

Fig. 1. Experimental setup. (a) schematic diagram (b)fabricated system. 3

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Table 1 Specifications and information regarding the measurement equipment. Measurement device

Operation range

Accuracy

Resolution

Thermometer WSS-411 Pressure gauge YE-60 Hygrothermoscope KT-TH638

0–100 °C 0–0.4 MPa T = −20–80 °Cφ = 0–100%

Flowmeter G10-15F

G = 0–60 m3h−1 L = 0–200 Lh−1

2.0 °C 0.01 MPa T = 0.1 °C φ = 0.1% G = 2.0 m3h−1 L = 5.0 Lh−1

Electronic scale TCS

0–100 kg

± 1.0 °C ± 800 Pa T= ± 0.5 °C φ = ± 3% G= ± 1.25 m3h−1 L= ± 5 Lh−1 Range: −20–120 °C ± 0.2 g Range: 0–40 °C, 10–85%

20 g

Fig. 2. Psychrometric chat of humidification. (a) without intersection (b) with intersection.

interface can be got as:

obtained by:

hw

dm w dh dh + m w w = mda a dZ dZ dZ

dm w dA = hd (ωsw − ω) dZ dZ

(2)

According to Fig. 3c, the mass transfer equation at the air–water

(3)

and the energy transfer including the sensible heat and latent heat

Fig. 3. Humidifier analysis. (a) humidification scheme (b) differential control volume (c) air side control volume 4

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between gas and liquid phases is given by: 3.1.3. Mass transfer coefficient As mentioned above, the Lewis factor, Lef, is defined as the dimensionless measure of the relative rates of heat and mass transfer. In view of Onda [25], the mass transfer coefficient for gas absorption is given as follows:

(4)

mda dha = [h v hd (ωsw − ω) + hc (Tw − T )] dA −2

−1

s , ωsw is the satuwhere hd is the mass transfer coefficient, kgm rated humidity ratio evaluated at the local water liquid surface temperature, kgkg−1, and dA can be expressed as: (5)

dA = aAZ dZ

1

−2 3 hd = ρv f Re0.7 a Sca (adp ) aDa

and the enthalpy of humid air at unsaturated condition is calculated by:

where

ha = cpa Ta + ω (hfg + cpv Ta)

(6)

mda (1 + ω) AZ aμa

Rea =

By integrating the above formulas, the following differential equations can be found upon rearrangement:

dha h aA = d Z [Lef (hasw − ha) + (1 − Lef ) h v (ωsw − ω)] dZ mda

2

The power consumed by electric heater in order to increase the inlet water temperature can be calculated according to the temperature rise from natural water to spray water, shown as follow:

Ne = cpw m w (Twi − Twn )

)

(10)

hss = cpa Ta + ωsa (hfg + cpv Ta) + (ω − ωsa ) cpw Ta

The power consumption of the air-blower for overcoming the flow resistance within the packing layer is considered in the latter economic model, which can be calculated by the mathematical models according to Gandhidasan [26]. Hence, the power consumed by air-blower can be obtained with the assumed efficiency as ηb = 0.8:

(11)

Nb =

mda (1 + ωi )Δpp

(12)

Nwp =

dTw 1 ⎛ 1 dha dω ⎞ = − Tw ⎜ ⎟ dZ mr ⎝ cpw dZ dZ ⎠

(14)

m w Δpwp 1000ρw ηwp

(22)

3.5. Economic models According to the calculation of humidification performance and configuration size of the packing, the corresponding economic analysis of the packed bed humidifier can be conducted with the price of the main components and packing materials:

ωsw + 0.622 −1 2 ω + 0.622 865 3 sa ωsw + 0.622 ωsa + 0.622

(21)

The power consumption of the water pump can be calculated with the designated pressure rise, ΔPwp = 3 × 105 Pa, and the efficiency, ηwp = 0.8, according to He [10]:

h aA = d Z {Lef [hasw − hss + (ω − ωsa ) cpw Tw] + (1 − Lef ) h v (ωsw − ωsa)} mda

(13)

1000ρa ηb

3.4. Water pump

dha dZ

dω h aA = d Z (ωsw − ωsa) dZ mda

(20)

3.3. Air-blower

and the enthalpy as well as the humidity ratio of air appearing in Eqs. (7), (8), (9) and (10) should be replaced by supersaturation enthalpy and saturation humidity ratio of air, the corresponding equations are obtained upon rearrangement:

(

(19)

3.2. Electric heater

3.1.2. Governing equations for supersaturated case For supersaturated case, the enthalpy of supersaturated humid air must take the excess water vapor into consideration, which will condense as a mist, expressed by:

ln

Ta2.072 p / p0

and where dp is the equivalent diameter of packing, m, f is the corresponding geometric coefficient, 5.23 for dp > 0.015 m and 2 for dp < 0.015 m, and Da is the diffusion coefficient from water to air.

(9)

ωsw + 0.622 −1 ω + 0.622 ωsw + 0.622 ln ω + 0.622

(

(18)

(7)

where the Lewis factor, Lef, represents the indication of the relative rates of heat and mass transfer, which is variable in the process of humidification. The definition, Lef = hc/cpahd, is raised by Klimanek [24]. The empirical relationship for the Lewis factor, Lef, for air–water evaporation system is given in Eq. (9) from Kloppers [20], which has to be specified to solve the value of each node in the discrete equation:

Lef = 0. 865 3

ρa Da

(8)

dTw 1 ⎛ 1 dha dω ⎞ = − Tw ⎜ ⎟ dZ mr ⎝ cpw dZ dZ ⎠

(17)

μa

Sca =

Da = 1.87 × 10−10

dω h aA = d Z (ωsw − ω) dZ mda

Lef = 0.

(16)

)

(15)

Table 2 Price of each component. Components

Air-blower

Water pump

Specifications Prices

Nb = 0.25 kW 77.93 $

Nwp = 0.18 kW 21.25 $

Packing Nwp = 0.75 kW 70.84 $

5

a = 250 m2m−3 828.61 $m−3

a = 500 m2m−3 1104.82 $m−3

a = 700 m2m−3 1487.25 $m−3

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of the total differential method with Eqs. (28) and (29) based on the instrument parameters in Table 1. And the results can be seen in Table 5.

Cb = Pb Cwp = Pwp Cp = Vp Pp

⎧ ⎪

⎨ ⎪C = t (N + N + N ) P e b wp e ⎩ e

(23)

∂UHCV ∂UHCV ∂UHCV dUHCV 1 =⎡ dmda + dωo + dωi ⎤ ⎢ ∂mda ⎥ ∂ ∂ UHCV ω ω UHCV o i ⎣ ⎦ dmda dωo = + mda ωo (28)

where Pb and Pwp are depended on the power consumption of air-blower and water pump, Vp, as the volume of packing required, can be calculated as:

Vp = AZ Zp

(24)

dUHCC UHCC

and Pp is the price of packing 316L, varied with specific surface area, shown in Table 2. Moreover, the total running cost, Ce, is calculated according the running time of 10 years with 7200 h per year, as well as the electrovalence of Pe = 0.085 $kW−1 h−1.

=⎡ ⎣

∂UHCC dmda ∂mda

+

∂UHCC dωo ∂ωo

=

dmda mda

+

+ dωo ωo

∂UHCC dωi ∂ωi

+

+

∂UHCC dCe ∂Ce

1 ⎤ UHCC ⎦

dCe Ce

(29) where

3.6. Overall evaluation criterion

ωo = 0.622

Different from the thermal performance parameters proposed by Tariq [27], a novel thermodynamic evaluation criterion, unit humidification capacity of volume (UHCV), is defined by taking the packing characteristics into account.

UHCV =

mda (ωo − ωi ) Vp

(25)

3600mda (ωo − ωi ) t Cb + Cwp + Cp + Ce

(26)

4. Results and discussion Thermodynamic and economic performance of the packed bed humidifier are first investigated at the experimental conditions, shown in Table 3, which are compared with the simulated results. In order to ensure the accuracy of simulation results from Matlab 2011a software, independence verification of iterative step size is carried out before the simulation with the specific procedures presented in Fig. 4. As shown in Fig. 5 for instance, when the height of control volume is larger than 0.0004 m, the total height of the packing will be unstable, which will result in inaccurate results. The total height of the packing does not reach a stable value until it reduces to 0.0004 m. Therefore, the control volume height chose in the analysis is 0.0004 m. After that, parametric analysis including the main design parameters is conducted to optimize the relevant criteria. The coupled working conditions in parameter analysis are presented in Table 4 detailly.

4.1.2. Effects from inlet water temperature The experiments were investigated at the inlet water temperature of 57 °C, 73 °C and 90 °C for the case of mr = 2. As we can see from Fig. 7a that the outlet air temperature rises continuously with the increase of the inlet water temperature, while the outlet relative humidity of the humid air had a weak negative correlation with it. Obviously, the maximum errors of Tao and φi appear at Twi = 57 °C and Twi = 90 °C, which are 5.37% and 7.64%, respectively. As shown in Fig. 7b, 22.83% for the unit humidification capacity of volume and 22.65% for the unit humidification capacity of cost emerged at Twi = 57 °C are the maximum values of the errors, with a trend of simulated and experimental values keeping synchronously with inlet water temperature positively. Moreover, the maximum values of the UHCV and UHCC are obtained experimentally as UHCV = 3.82 × 10−2 kgs−1 m−3 and

4.1. Comparison between experiments and simulations The experiments were carried out in Nanjing, China in August 2019. With the optimum iteration step size and mathematical model established, the theoretical results are also calculated at the conditions presented in Table 3. Moreover, the absolute errors for the mathematical model can be calculated as:

Error =

|theoretical value − experimental value| × 100% experimental value

(30)

4.1.1. Effects from liquid-gas ratio The experimental results averaged from three experiments at the same conditions can be seen from Fig. 6 compared with the simulated data. Fig. 6a shows the variation of the thermodynamic parameters of humid air, from which it can be found that the maximal errors for the outlet air temperature and outlet relative humidity of the humid air between theoretical results and experimental results are 1.06% at mr = 3 and 5.6% at mr = 1, respectively. It is found that as the liquid–gas ratio increases, gas and liquid can be more evenly contacted, which will cause the outlet air temperature to a higher value. Meanwhile, the relative humidity of the outlet humid air is easier to reach saturation. Moreover, the evaluation criteria for simulation, including the unit humidification capacity of volume and unit humidification capacity of cost, keep pace with the experimental values, which rise from 1.49 × 10−2 kgs−1 m−3 at mr = 1 to 3.14 × 10−2 kgs−1 m−3 at mr = 3 for the former and reduce from 12.5 kg$−1 at mr = 1 to 9.67 kg $−1 at mr = 3 for the latter respectively, presented in Fig. 6b. The maximum errors between the simulated values and experimental results present as 13.69% for UHCV and 22.98% for UHCC at mr = 3. Evidently, higher value of liquid–gas ratio can increase the humidification capacity of the humid air, which is the reason why the UHCV keeps rising. However, an increase in power consumption will result in an increase in operating costs, which is also the main reason for the decrease in UHCC. Therefore, there may be a balance point for the liquid–gas ratio, which is just the significance of the following study.

Considering the investment cost and running cost, unit humidification capacity of cost (UHCC) is also defined as the corresponding economic analysis criterion, shown in Eq. (26).

UHCC =

φo pso pn − φo pso

(27)

The uncertainties both for UHCV and UHCC are estimated by means Table 3 Typical experimental parameters. mda(kgs−1)

mwi(kgs−1)

Twi(°C)

Tai(°C)

φi

P0(kPa)

a(m2m−3)

AZ(m2)

Z(m)

0.0135

0.0135–0.0405

57–90

32.1

0.75

101.325

700

0.12

0.45

6

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Fig. 4. Specific procedure for simulating the packed bed humidifier. (a) off-design condition (b) on-design condition.

UHCC = 12.74 kg$−1 at Twi = 90 °C. A higher value of inlet water temperature is easy to cause an increase in outlet air temperature and hygroscopicity, which will lead to an obvious raise both of UHCC and UHCC. As analyzed above, considering the influence of instrument error,

gas and liquid contact in unfilled region and uniformity of fluid distribution, the simulated results may be considered to be accordant with the experimental results, which can also validate the accuracy of the current mathematical model.

0.2046 0.2044 0.2042

Z/m

0.2040 0.2038 0.2036 0.2034 0.2032 0.0000

0.0002

0.0004

dZ/m

0.0006

0.0008

Fig. 5. Independence verification of the control volume height. 7

0.0010

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Table 4 Coupled working conditions of the humidifier. mda(kgs−1)

mwi(kgs−1)

Twi(°C)

Two(°C)

Tai(°C)

φi

P0(kPa)

a(m2m−3)

AZ(m2)

0.16

0.08–0.64

60–80

40

10–30

0.5–0.9

101.325

250–700

0.12

4.2.2. Effect of inlet air temperature on unit humidification capacity of volume According to the liquid–gas ratio at peak value, Fig. 9 shows the effect of inlet air temperature on the unit humidification capacity of volume with different specific surface area, operated at the conditions of mda = 0.16 kgs−1, mw = 0.08 kgs−1, Twi = 70 °C, Two = 40 °C and φi = 0.7. As we can see that the unit humidification capacity of volume will rise continuously with the increase of the inlet air temperature, while the difference of unit humidification capacity of volume caused by specific surface area is basically stable. For instance, the relevant performance indicator arises as 54.67% from Tai = 10 °C to Tai = 30 °C for the case of a = 700Y, while it is 54.53% for a = 250Y. However, according to the principle of heat transfer, the inlet air temperature cannot increase infinitely due to the outlet temperature of the hot side, so that the increase of the unit humidification capacity of volume is limited.

Table 5 Direct and indirect uncertainty. Terms

dmda/mda

dωo/ωo

dCe/Ce

dUHCV/UHCV

dUHCC/UHCC

Uncertainties

2.1%

4%

3.5%

6.1%

9.6%

4.2. Overall performance analysis 4.2.1. Effect of liquid–gas ratio on unit humidification capacity of volume Different from the experimental conditions, increasing the flow rate of air or water will have a great influence on unit humidification capacity of volume. Fig. 8 shows the effect of liquid–gas ratio on the unit humidification capacity of volume with three cases of a = 250Y, a = 500Y and a = 700Y, operated at the conditions of mda = 0.16 kgs−1, Twi = 70 °C, Two = 40 °C, Tai = 30 °C and φi = 0.7. It is found that the unit humidification capacity of volume varies more obviously with the increase of liquid–gas ratio for all the cases with different specific surface areas, while there is a peak value at mr = 0.5, simultaneously. The peak values are UHCV = 19.98 × 10−2 kgs−1 m−3 at a = 250Y, UHCV = 22.68 × 10−2 kgs−1 m−3 at a = 500Y and UHCV = 31.46 × 10−2 kgs−1 m−3 at a = 700Y, respectively. In addition to the peak values, the unit humidification capacity of volume at a = 700Y always has a sharp superiority from mr = 0.25 to mr = 4. However, with the increase of liquid–gas ratio, the difference of unit humidification capacity of volume caused by specific surface area decreases gradually, which is due to the weakening of the advantages of the contact surface in the packing region. It is found that the three curves approach together at the conditions of high liquid–gas ratio. It can be also seen that although the humidification capacity increases with the promotion of liquid–gas ratio, the longer contact time is required to reach the set outlet water temperature. As a result, the specific packing volume will be ascended, so that the unit humidification capacity of volume is drastically reduced.

4.2.3. Effect of relative humidity at the air inlet on unit humidification capacity of volume As analyzed above, the better value of the unit humidification capacity of volume appears at mr = 0.5 and Tai = 30 °C, respectively. Hence, the investigation schemes of the relative humidity at the air inlet is run at the conditions of mda = 0.16 kgs−1, mw = 0.08 kgs−1, Twi = 70 °C, Two = 40 °C and Tai = 30 °C, as shown in Fig. 10. It is found that the unit humidification capacity of volume at a = 700Y has a huge advantage over the other two packings for all the cases. Meanwhile, there is a reverse trend of the UHCV with the increase of the relative humidity at the air inlet. Furthermore, the unit humidification capacity of volume is optimized by 8.71% at a = 700Y with the downgrade of the relative humidity at air inlet, while it is 8.69% at a = 500Y and 8.77% at a = 250Y, respectively. In detail, the unit humidification capacity of volume of a = 700Y increases from UHCV = 31.46 × 10−2 kgs−1 m−3 at φi = 0.7 to UHCV = 34.2 × 10−2 kgs−1 m−3 at φi = 0.5 for example. Lower inlet relative humidity at constant inlet air temperature means the lower humidity ratio, which will lead to more water vapor being absorbed by humid air. Therefore, the water temperature will be easier to reach the

Fig. 6. Comparison at different liquid–gas ratio. (a) thermodynamic properties of humid air (b) performance criteria. 8

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Fig. 7. Comparison at different inlet water temperature. (a) thermodynamic properties of humid air (b) performance criteria.

35

30

250Y 500Y 700Y

31.5 31.4 31.3 31.2

25

20

-2

-1

UHCV/10 kgs m

-3

31.1 0.2 0.4 0.6 0.8 1.0

15

10

20.0

22.7

19.9

22.6

19.8

22.5

19.7 0.2 0.4 0.6 0.8 1.0

22.4 0.2 0.4 0.6 0.8 1.0

5

0

0

1

2

mr

3

4

Fig. 8. Effect of liquid–gas ratio on unit humidification capacity of volume.

specific surface area can enhance the heat and mass transfer efficiency and the contact time between gas and liquid phases. It is found that the maximum value of the UHCV at a = 700Y can reach 43.3 × 10−2 kgs−1 m−3 at Twi = 80 °C, while it is 31.24 × 10−2 kgs−1 m−3 at a = 500Y and 27.48 × 10−2 kgs−1 m−3 at a = 250Y at the same temperature, respectively. High spraying temperature can greatly improve the humidity ratio at the air outlet, as a result of the enhancement of humidification performance of the packing.

set point, and the volume of packing required will be cut down, resulting in the elevation of the UHCV. 4.2.4. Effect of inlet water temperature on unit humidification capacity of volume Drawing lessons from previous research strategies, the parametric analysis for the inlet water temperature is conducted on five cases from Twi = 60 °C to Twi = 80 °C, averagely. The effect of the inlet water temperature on unit humidification capacity of volume is shown in Fig. 11 at the conditions of mda = 0.16 kgs−1, mw = 0.08 kgs−1, Tai = 30 °C, Two = 40 °C and φi = 0.5. Obviously, it can be seen that the unit humidification capacity of volume increases continuously with the raise of the inlet water temperature within the range of simulation conditions. Meanwhile, the growth rate of the UHCV is almost the same under three specifications of packings. However, the value of the UHCV at a = 700Y is always higher than the other two packings since larger

4.2.5. Effect of wet-bulb temperature at the air inlet on unit humidification capacity of volume Fig. 12 shows the effect of the wet-bulb temperature at the air inlet on the unit humidification capacity of volume at the conditions of mda = 0.16 kgs−1, mw = 0.08 kgs−1, Twi = 80 °C, Two = 40 °C and φi = 1.0. It is found that increasing the specific surface area and wet9

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35

250Y 500Y 700Y

25

-2

-1

UHCV/10 kgs m

-3

30

20

15

10

5

10

15

20

25

30

35

Tai Fig. 9. Effect of inlet air temperature on unit humidification capacity of volume.

4.3. Economic analysis

bulb temperature at the air inlet can enhance the unit humidification capacity of volume, but the enhancement extent decreases gradually. Obviously, increasing the inlet wet-bulb temperature means increasing the inlet humidity ratio and reducing the mass transfer driving force, while it can also increase the heat transfer temperature difference and reduce the packing height. Therefore, the unit humidification capacity of volume will increase slightly with the increase of the wet-bulb temperature at the air inlet.

4.3.1. Effect of liquid–gas ratio on unit humidification capacity of cost In order to quantify the total cost of the packed bed humidifier, taking both of the investment cost and running cost into account, the power consumption of each component needs to be determined first, which plays an important role of the total cost. From Fig. 13, it is found clearly that compared to the power consumed by the electric heater, the power consumption of the air-blower and water pump can be almost ignored. Then, the effect of the liquid–gas ratio on the unit humidification

Fig. 10. Effect of relative humidity at the air inlet on unit humidification capacity of volume. 10

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Fig. 11. Effect of inlet water temperature on unit humidification capacity of volume.

will result in higher cost and higher flow resistance. Therefore, the packing with lower specific surface area at the peak point highlights the economic advantage, as shown in Fig. 14. Meanwhile, it is found that the peak point of the UHCC is different from that of UHCV, which has great reference value for the design and use of the packed bed humidifier.

capacity of cost can be carried out. It is found from Fig. 14 that the influential direction of the liquid–gas ratio can be varied, with a peak value for the three packings, simultaneously. The maximum values of the UHCC emerged at mr = 3 are 12.22 kg$−1 at a = 250Y, 12.21 kg $−1 at a = 500Y and 12.21 kg$−1 at a = 700Y, respectively, from which we can see that the specific surface area has little impact on the unit humidification capacity of cost. The higher liquid–gas ratio will increase the cost of the power consumption and the humidity ratio of the outlet humid air, simultaneously, which will emerge a peak. Furthermore, on the one hand, a higher value of specific surface area can enhance humidification, on the other hand, raising specific surface area

4.3.2. Effect of inlet air temperature on unit humidification capacity of cost The further in-depth investigation of the economic performance can be designated in light of the liquid–gas ratio at peak point. Therefore, the effect of the inlet air temperature on the unit humidification

Fig. 12. Effect of wet-bulb temperature at air inlet on unit humidification capacity of volume. 11

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Fig. 13. Effect of liquid–gas ratio on power consumption of electric heater, water pump and air-blower.

Fig. 14. Effect of liquid–gas ratio on unit humidification capacity of cost.

capacity of cost is calculated at the conditions of mda = 0.16 kgs−1, mw = 0.48 kgs−1, Twi = 70 °C, Two = 40 °C and φi = 0.7, as shown in Fig. 15. It is demonstrated that the inlet air temperature has a positive influence on the unit humidification capacity of cost, while the specific surface area appears a reverse trend. However, the influence from the latter is very slight compared to the former for all the cases. For instance, a distinct advance of the UHCC can be obtained from UHCC = 12.00 kg$−1 at Tai = 10 °C to UHCC = 12.22 kg$−1 at Tai = 30 °C at the case of a = 250Y, while the unit humidification capacity of cost at Tai = 20 °C is UHCC = 12.09 kg$−1 at a = 250Y, UHCC = 12.08 kg$−1 at a = 500Y and UHCC = 12.07 kg$−1 at

a = 700Y. Increasing the inlet air temperature can enhance the unit humidification capacity of volume mentioned above, and hence the unit humidification capacity of cost is improved correspondingly with other economic parameters almost unchanged. However, as the flow resistance of the humid air increases with the increase of specific surface area, more power is consumed, which will result in a slight decrease of the UHCC. 4.3.3. Effect of relative humidity at the air inlet on unit humidification capacity of cost In view of the optimal conditions analyzed above, the effect of the 12

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Fig. 15. Effect of inlet air temperature on unit humidification capacity of cost.

relative humidity at the air inlet on the unit humidification capacity of cost is investigated at the conditions of mda = 0.16 kgs−1, mw = 0.48 kgs−1, Twi = 70 °C, Two = 40 °C and Tai = 30 °C. It is found from Fig. 16 that the variation of the UHCC with the inlet relative humidity of humid air is alike to that of the UHCV, but the reduction rate is slower. Meanwhile, the unit humidification capacity of cost at a = 250Y is always higher than the other two packings, while the difference between each other is always minor.

humidification capacity of cost at the conditions of mda = 0.16 kgs−1, mw = 0.48 kgs−1, Tai = 30 °C, Two = 40 °C and φi = 0.5 according to the current investigation. It can be found that the unit humidification capacity of cost rises sharply with the increase of inlet water temperature, while it is varied from UHCC = 10.65 kg$−1 at Twi = 60 °C to UHCC = 13.30 kg$−1 at Twi = 80 °C at the case of a = 250Y for example. Actually, the difference of the UHCC caused by the specific surface area is still tiny as analyzed above.

4.3.4. Effect of inlet water temperature on unit humidification capacity of cost Fig. 17 presents the effect of the inlet water temperature on the unit

4.3.5. Effect of wet-bulb temperature at the air inlet on unit humidification capacity of cost As we known that the extent of the influence of the wet-bulb

Fig. 16. Effect of relative humidity at the air inlet on unit humidification capacity of cost. 13

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Fig. 17. Effect of inlet water temperature on unit humidification capacity of cost.

4.4. Comparison of humidification performance with previous researches.

temperature at the air inlet on the unit humidification capacity of volume is dwindled as it decreases, while the action is not so obvious to the unit humidification capacity of cost, shown in Fig. 18. The results are obtained at the conditions of mda = 0.16 kgs−1, mw = 0.48 kgs−1, Twi = 80 °C, Two = 40 °C and φi = 1.0. As analyzed above, the unit humidification capacity of cost at a = 250Y has a slight superiority over other packings. Meanwhile, it is found that the variation rate of the UHCC with the inlet wet-bulb temperature of humid air is slower than that with the inlet water temperature, while it is similar to the inlet air temperature.

A comparison of the humidification performance of packings between the current results and those gained by other works is presented in Table 6. It is demonstrated that the packed bed humidifier can operate under various conditions and different packings. Therefore, in order to better compare the humidification performance of multiple packings, the defined criterion, unit humidification capacity of volume, can be effective to evaluate the relevant data. Obviously, it is found that the unit humidification capacity of volume of the current research has a major superiority over the humidifiers studied in previous researches.

Fig. 18. Effect of wet-bulb temperature at the air inlet on unit humidification capacity of cost. 14

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Table 6 Comparison between the current work and previous researches. mda (kgs−1)

mwi (kgs−1)

Tai (°C)

Twi (°C)

0.15

0.53

38.73

49

0.0028

0.0067

74

85

0.04

0.012

43.4

68.9

0.0316

0.031

28

44

0.0135

0.027

32.1

90

Packing specifications 2

−3

Aluminum sheets, a = 50 m m V = 0.65* 0.65* 0.65 Raschig Ring V = π/4* 0.1* 0.1* 1.5 Cellulose paper V = 0.305* 0.305* 0.4 Metal, a = 200 m2m−3 V = 0.33* 0.3* 1.7 Wire mesh, a = 700 m2m−3 V = π/4* 0.39* 0.39* 0.45

Productivity (kgh−1)

UHCV (kgs−1m−3)

References

15

0.015

Ref [17]

1.37

0.032

Ref [22]

1.45

0.011

Ref [28]

3.2

0.0053

Ref [29]

7.39

0.038

Current work

5. Conclusions

Acknowledgements

Based on the experimental test and mathematical analysis, the thermodynamic performance as well as the economic aspect of the humidifier, filled with wire mesh corrugated packing, is investigated and discussed comprehensively. The parametric analysis from the liquid–gas ratio, inlet thermodynamic state of the humid air, inlet water temperature, as well as the specific surface area of packing on the defined evaluation indicators are achieved. Therefore, the following conclusions can be obtained:

The authors gratefully acknowledge the financial support by the National Natural Science Foundation of China (Grant No. 51406081) and the Fundamental Research Funds for the Central Universities (Grant NO.NP2018107). References [1] Houcine I, Benamara M, Guizani A. Pilot plant testing of a new solar desalination process by a multiple-effect-humidification technique. Desalination 2006;196(13):105–24. https://doi.org/10.1016/j.desal.2005.11.022. [2] Rajaseenivasan T, Srithar K. An investigation into a laboratory scale bubble column humidification dehumidification desalination system powered by biomass energy. Energy Convers Manage 2017;139:232–44. https://doi.org/10.1016/j.enconman. 2017.02.043. [3] Yan WM, Chen CY, Jhang Y, et al. Performance evaluation of a multi-stage platetype membrane humidifier for proton exchange membrane fuel cell. Energy Convers Manage 2018;176:123–30. https://doi.org/10.1016/j.enconman.2018.09.027. [4] He WF, Han D, Zhu WP, et al. Thermo-economic analysis of a water-heated humidification-dehumidification desalination system with waste heat recovery. Energy Convers Manage 2018;160:182–90. https://doi.org/10.1016/j.enconman.2018.01. 048. [5] Zeng Z, Sadeghpour A, Ju YS. A highly effective multi-string humidifier with a low gas stream pressure drop for desalination. Desalination 2019;449:92–100. https:// doi.org/10.1016/j.desal.2018.10.017. [6] Abd-Ur-Rehman HM, Al-Sulaiman FA. An experimental investigation of a novel design air humidifier using direct solar thermal heating. Energy Convers Manage 2016;127:667–78. https://doi.org/10.1016/j.enconman.2016.09.053. [7] Solsona M, Kunusch C, Ocampo-Martinez C. Control-oriented model of a membrane humidifier for fuel cell applications. Energy Convers Manage 2017;137:121–9. https://doi.org/10.1016/j.enconman.2017.01.036. [8] De Antonellis S, Intini M, Joppolo CM, et al. Desiccant wheels for air humidification: An experimental and numerical analysis. Energy Convers Manage 2015;106:355–64. https://doi.org/10.1016/j.enconman.2015.09.034. [9] He WF, Wu F, Kong YP, et al. Parametric analysis of a power-water cogeneration system based on single-extraction organic Rankine cycle. Appl Therm Eng 2019;148:382–90. https://doi.org/10.1016/j.applthermaleng.2018.11.070. [10] He WF, Wu F, Wen T, et al. Cost analysis of a humidification dehumidification desalination system with a packed bed dehumidifier. Energy Convers Manage 2018;171:452–60. https://doi.org/10.1016/j.enconman.2018.06.008. [11] Narayan GP, Sharqawy MH, Summers EK, et al. The potential of solar-driven humidification–dehumidification desalination for small-scale decentralized water production. Renew Sustain Energy Rev 2010;14(4):1187–201. https://doi.org/10. 1016/j.rser.2009.11.014. [12] Traverso A. Humidification tower for humid air gas turbine cycles: Experimental analysis. Energy 2010;35(2):894–901. https://doi.org/10.1016/j.energy.2009.07. 021. [13] Han D, He WF, Ji C, et al. Thermodynamic analysis of a novel evaporation and crystallization system based on humidification processes at ambient temperature. Desalination 2018;439:108–18. https://doi.org/10.1016/j.desal.2018.04.016. [14] He WF, Chen JJ, Han D, et al. Energetic, entropic and economic analysis of an openair, open-water humidification dehumidification desalination system with a packing bed dehumidifier. Energy Convers Manage 2019;199:112016https://doi. org/10.1016/j.enconman.2019.112016. [15] Srithar K, Rajaseenivasan T. Recent fresh water augmentation techniques in solar still and HDH desalination–A review. Renew Sustain Energy Rev 2018;82:629–44. https://doi.org/10.1016/j.rser.2017.09.056. [16] Amer EH, Kotb H, Mostafa GH, et al. Theoretical and experimental investigation of humidification–dehumidification desalination unit. Desalination 2009;249(3):949–59. https://doi.org/10.1016/j.desal.2009.06.063. [17] Ahmed HA, Ismail IM, Saleh WF, et al. Experimental investigation of humidification-dehumidification desalination system with corrugated packing in the humidifier. Desalination 2017;410:19–29. https://doi.org/10.1016/j.desal.2017.01.036. [18] He WF, Huang L, Xia JR, et al. Parametric analysis of a humidification

1. The experimental values of the unit humidification capacity of volume and unit humidification capacity of cost present an opposite trend with the increase of liquid–gas ratio, while the magnitude of the increase in the former is greater than the extent of the reduction in the latter, while the values are 112.84% and −24.47% as the liquid–gas ratio rises from 1 to 3, respectively. 2. The unit humidification capacity of volume and unit humidification capacity of cost exist a maximum value of 3.82 × 10−2 kgs−1 m−3 and 12.74 kg$−1 obtained simultaneously at the inlet water temperature of 90 °C and the liquid–gas ratio of 2, while both of them keep pace with the variation of the inlet water temperature experimentally. 3. The peak values for the unit humidification capacity of volume appear simultaneously at the liquid–gas ratio of 0.5 as it are 19.98 × 10−2 kgs−1 m−3, 22.68 × 10−2 kgs−1 m−3 and 31.46 × 10−2 kgs−1 m−3, while the peak values of the unit humidification capacity of cost emerged at the liquid–gas ratio of 3 are 12.22 kg$−1, 12.21 kg$−1 and 12.21 kg$−1 when the specific surface areas are 250Y, 500Y and 700Y, respectively. After the peak point, any elevation in liquid–gas ratio will result in a reduction both of the unit humidification capacity of volume and unit humidification capacity of cost at on-design conditions. 4. In parametric analysis, a lower value of relative humidity at the air inlet can improve the relevant values both of the unit humidification capacity of volume and unit humidification capacity of cost, while the elevation amplitude of the former is much higher than that of the latter. 5. Rising the inlet air and water temperature, as well as the wet-bulb temperature of the inlet air, will result in a higher value of the unit humidification capacity of volume and unit humidification capacity of cost in varying extents, synchronously. Furthermore, a higher value of specific surface area of the packing can cause an increase of the unit humidification capacity of volume, but a reverse influence on unit humidification capacity of cost.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 15

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dehumidification desalination system using a direct-contact dehumidifier. Int J Therm Sci 2017;120:31–40. https://doi.org/10.1016/j.ijthermalsci.2017.05.027. Xu Z, Xie Y, Zhang F. Development of mass transfer coefficient correlation for a ceramic foam packing humidifier at elevated pressure. Appl Therm Eng 2018;133:560–5. https://doi.org/10.1016/j.applthermaleng.2018.01.092. Kloppers JC. A critical evaluation and refinement of the performance prediction of wet-cooling towers. Stellenbosch: University of Stellenbosch; 2003. Miller JA. Numerical balancing in a humidification dehumidification desalination system. Massachusetts Institute of Technology; 2011. Ghalavand Y, Rahimi A, Hatamipour MS. Mathematical modeling for humidifier performance in a compression desalination system: Insulation effects. Desalination 2018;433:48–55. https://doi.org/10.1016/j.desal.2018.01.024. Chen J, Han D, He W, et al. Characteristic analysis of heat and mass transfer process within structured packing humidifier. J Braz Soc Mech Sci Eng 2019;41(9):361. https://doi.org/10.1007/s40430-019-1864-y. Klimanek A. Numerical Modelling of Natural Draft Wet-Cooling Towers. Arch Comput Methods Eng 2013;20(1):61–109. https://doi.org/10.1007/s11831-0139081-9.

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