A graphical method for the determination of optimum operating parameters in a humidification-dehumidification desalination system

Desalination 455 (2019) 19–33

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A graphical method for the determination of optimum operating parameters in a humidification-dehumidification desalination system

T

Xin Huanga, Xiang Linga,c, , Yang Lia,b, , Weihong Liua, Tingfen Kea ⁎

⁎

a

School of Mechanical and Power Engineering, Nanjing Tech University, No. 30 PuZhu South Road, Nanjing 211816, PR China Jiangsu Key Engineering Laboratory of Process Industrial Energy Conservation and Environmental Protection Technology and Equipment, Jiangsu, PR China c Jiangsu Key Laboratory of Process Enhancement & Energy Equipment Technology, Jiangsu, PR China b

ARTICLE INFO

ABSTRACT

Keywords: Humidification-dehumidification Desalination Graphical method Determination of optimum operating parameters Pinch analysis

Humidification–dehumidification (HDH) technology is an innovative desalination technology which has received considerable attention from researchers in recent years. In this study, the effects of mass flow rate ratio and pinch point temperature difference (PPTD) on the energy consumption of the HDH system are investigated by pinch analysis. A new parameter, pinch point heat capacity rate ratio (PHCR), is introduced to normalise the optimum point for energy consumption. It is found that the specific energy consumption of the system is minimised when the PHCR of the dehumidifier equals to unity. The value of GIR can be achieved 3.978 when the PHCR of dehumidifier equals to unity, at the inlet temperature of the solution in the humidifier equals to 65 °C and PPTD of the humidifier and dehumidifier equals to 1 °C. Based on this discovery, the regression equations are used to predict the optimum value of the mass flow rate ratio at different operating parameters. Combining the regression equations with the evaporation rate contour plots, an efficient graphical method is proposed for the determination of optimum operating parameters of the HDH system. It can be used to determine the operating parameters efficiently according to the performance requirements of the system.

1. Introduction Humidification-dehumidification (HDH) technology is an innovative desalination technology that utilises the moisture carrying capacity of hot air to realise the separation of a solution and pure water [1,2]. It can be widely used in desalination, waste water treatment and other industries [3,4]. Compared to other thermal desalination technologies, HDH technology is simpler in terms of fabrication, operation, and maintenance [5], and it is inexpensive and reliable for small scale applications [2,6]. However, HDH technology is still under research and development. More additional research and development are needed to augment the system efficiency [5]. Besides, better understanding of the thermodynamic process of HDH process is also crucial for the scaling up of the process [1]. Extensive researches have been conducted to investigate the thermodynamic process and improve the efficiency of the system from three aspects, namely, energy, entropy, and exergy. Based on energy analysis, Hou et al. [7] employed pinch technology to demonstrate the existence of optimal values for the liquid-to-air mass flow rate ratio if given the temperature of spraying water and cooling water. However, this value varies with changes in the operating parameters. Therefore, a

⁎

parameter referred to as modified heat capacity rate ratio (HCR) was defined (ratio between the maximum enthalpy change of the cold and hot stream) by Narayan et al. [8] to normalise the optimum point. It was found that the gained output ratio (GOR) was maximised at HCR = 1 (GOR is a parameter that evaluates the energy efficiency of the system, whereby higher GOR values represent higher energy efficiencies). Chehayeb et al. [9] extended the application of HCR to the two-stage humidification dehumidification desalination system. They found that a better balanced HDH system can be achieved by extracting air or water from the humidifier to the dehumidifier and setting HCRd,1 = HCRd,2 = 1. The HCR also was introduced into a HDH system which coupled with a mechanical compression heat pump by He et al. [10]. A maximum value of the produced water appears at HCRd = 1, while the relevant top value of GOR is calculated as GOR = 5.14 based on the energy consumption. Based on entropy analysis, Mistry et al. [11] found that the peak of the GOR corresponds to the minimum specific entropy generation regardless of the operating conditions. Then, the specific entropy generation of HDH systems is regarded as a research object, and the variation of the specific entropy generation has been studied on different system configurations in many studies. For a system with multiple

Corresponding authors at: No. 30 Puzhu South Road, Nanjing, Jiangsu Province 211816, China. E-mail addresses: [email protected] (X. Ling), [email protected] (Y. Li).

https://doi.org/10.1016/j.desal.2018.12.013 Received 25 July 2018; Received in revised form 27 November 2018; Accepted 21 December 2018 0011-9164/ © 2019 Elsevier B.V. All rights reserved.

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Nomenclature cp GIR GOR h hfg H HCR HDH HRR ΔHmax ΔHPP,max m PHCR PPTD Q T ΔTmin w

h ideal PPTD t

specific heat at constant pressure, kJ/kg·K gained input ratio gained output ratio specific enthalpy, kJ/kg latent heat of vaporization, kJ/kg enthalpy, kJ/kgdry air heat capacity rate ratio humidification-dehumidification heat recovery ratio maximum enthalpy rate change, kW maximum enthalpy rate change in consideration of PPTD, kW mass flow rate, kg/s pinch point heat capacity rate ratio pinch point temperature difference heat transfer rate, kW temperature, °C or K pinch point temperature difference, °C or K humidity ratio, kg vapour/kg dry air

Subscripts a c d eva g h H i l o p pre r s Ta v w

Superscripts d

humidifier ideal condition pinch point temperature difference total

dehumidifier

air cold stream dehumidifier evaporation dry air humidifier or hot stream heater inlet liquid outlet pinch point predict ratio saturation air temperature vapour condensate water

regression equations. Evaporation rate contours are plotted based on the energy conservation equations. The regression equations are obtained by the investigation of energy consumption of the system, which can predict the optimum value of mass flow rate ratio of solution and dry air. Then, the usage of the graphical method is explained via a case. The graphical method will only take a short time to determine the optimum operating parameters efficiently according to the performance requirements of the system. It is more appropriate for the engineering application than the numerical optimisation method.

subcomponents, entropy generation is reduced when the value of HCR for a component is brought closer to unity [12]. The performance of an air-heated HDH system powered by low grade waste heat, coupled with plate heat exchangers, is investigated by He et al. [13]. Simulation results showed that the optimal value of the GOR, 3.51, could not be achieved because of a negative specific entropy generation in the dehumidifier, the actual maximum value of GOR is 3.04. However, in a semi-open air, open water HDH desalination system, it was observed that minimising entropy generation does not always improve the performance of the system [14]. Moreover, exergy analyses of HDH systems have also been performed by many other researchers. In most cases, the lower specific exergy loss and greater exergy efficiency resulted in the higher GOR values [15]. Al-Sulaiman et al. [16] found that the exergy destruction of the dehumidifier is the most sensitive parameter affecting the operating or design variables, and further design improvements of the dehumidifier are a priority for the improvement of system performance. In addition, an exergy analysis is performed by Siddiqui [17] to determine the parameters that result in higher exergy destruction in the system. It is found that increasing the pressure ratio increases the irreversibility while maximum temperature has no effect on exergy destruction up to 60 °C. Previous studies have positive impact on the development of HDH technology, whereas past research has mostly focused on the discovery and summarization of certain variation law of system performance in HDH systems with different configurations. The study on the determination of optimum operating parameters according to the certain performance requirements (evaporation rate and specific energy consumption) is rarely involved. Although a few prior studies were proposed to optimise the operating parameters [18,19], the process of optimisation was based on the numerical optimisation, which were complicated and took a lot of computing resources. It may take a long time to get the results. And these methods are cumbersome for use by people without basic programming skills. Moreover, inaccessibility to the source program for the optimisation involves laborious work. The objective of this study is to propose an efficient method for the determination of the optimum operating parameters. It is a graphical method combining of the evaporation rate contour plots and the

2. System description The schematic of a closed-water, open-air HDH desalination system is shown in Fig. 1. The HDH system comprises three components, namely, the humidifier, dehumidifier, and heater. In this study, the focus of the system is the evaporation rate. If the water production is also important, a cooler can be added after the dehumidifier to further cool humid air by using ambient air. In the humidifier, cold air obtained from the ambient environment is directly exposed to the hot solution from the heater so its temperature and capacity of holding water vapour increases. Water from the solution thus evaporates, increasing the air humidity ratio. The humid air is then transferred into the dehumidifier where it transfers heat to the cold incoming solution stream. The temperature of the moist air decreases and some water vapour condenses. The condensate water produced in the dehumidifier is free from salt, therefore condensate water is needed chemical treatment to be fresh/potable water with salinity 500 ppm according to the WHO (World Health Organization) as a recommended value [20–22]. The solution that preheated in the dehumidifier is transported to the heater and heated to a specified temperature followed by its transfer into the humidifier to complete the cycle. Along with the operation of the system, the amount of solution in the system will decrease and the quantity of the salt will increase due to the remove of the water vapour. In order to ensure the continuous and stable operation of the system, the makeup water is added into the system regularly or continuously. The makeup water mixes with the concentrated solution that comes from humidifier and transfer into the dehumidifier. The amount of salt accumulation in the humidifier will 20

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properties used in the study are approximated by pure water properties [4,18]. The effect of salinity is not considered in this work. The makeup water mass flow rate that added into the system should be equal to the evaporation rate in the humidifier, which can be obtained

mmw = mg (waho

Adding the makeup water into the concentrated solution will lead to the change of the solution temperature because the temperatures of them are different. However, the mass flow rate of the makeup water is very small compared to mass flow rate the concentrated solution, which means the temperature changes of the solution is very small. In this study, the temperature changes of the solution due to the addition of the makeup water are neglected. In the dehumidifier, the enthalpy of the air stream is not great. The influence of vapour condensation cannot be neglected. Thus, the process path of air in the dehumidifier is not completely aligned with the curve of saturated air but it is slightly offset. The enthalpy of condensate water contributes to this offset. The temperature can be approximated as the outlet temperature of air in the dehumidifier. To clearly visualize the heat and mass transfer process, the cold and hot stream thermodynamic process paths in the system are drawn in the T-H diagram (Fig. 2). It can help us understand the changing process of the thermodynamic state of air and solution and their relationship. In Fig. 2, 1 to 2 and 6 to 4 represent the thermodynamic process path for air and solution in humidifier, 2 to 3 and 4 to 5 represent the thermodynamic process path for air and solution in dehumidifier, 5 to 6 represents the thermodynamic process path for solution in heater. 3 to 3′ represents the humid air discharged to the ambient. The width of the solution stream line or air stream line indicates the heat exchange quantity in the humidifier or dehumidifier. The height variation indicates the change of temperature. The width of 3 to 3′ indicates the enthalpy loss caused by the discharge of humid air to ambient.

Fig. 1. Schematic of a closed-water, open-air humidification-dehumidification system.

cause scales problems which can be solved by chemical washing regularly and also by using self-cleaning [20,21]. 3. Mathematical model 3.1. Pinch analysis model In the system, the enthalpy of both water and air is defined per unit amount of dry air (air mass flow rate is assumed to be 1 kg/s) [7,23]. The state of air stream is assumed be saturated during humidification and humidification. Making these approximations simplifies the analysis of HDH considerably. The state of the air at any point in the system is fully specified by its temperature [4,24]. In the humidifier, the thermodynamic process path of the solution stream is slightly convex owing to the evaporation of water. However, compared to the total amount of water, the mass of the water evaporated is small and the curvature is not noticeable [4,24]. Therefore, the effect of evaporated water on the energy balance is neglected. The thermodynamic process path of solution stream in the humidifier is assumed to be a straight line. In the pinch analysis, pinch point is the point at which the temperature difference between cold stream and heat stream is minimised. Due to the shape of the saturation curve, the pinch point is not at the inlet or outlet of the humidifier but within the humidifier. At the pinch point in the humidifier, the solution stream line must be parallel to the tangent of the air saturation curve at the pinch point. In other words, the slope of air at the pinch point can be obtained by

3.1.1. Humidifier In the humidifier, the relationship between the pinch point temperature of air, Tahp, and the pinch point temperature of solution, Tlhp, can be expressed by h Tlhp = Tahp + Tmin

where ΔTmin is the pinch point temperature difference (PPTD) in the humidifier. The energy balance for the part of the humidifier below the pinch point yields

120

100

cpl mr

(1)

where cpl is the specific heat capacity of the solution, mr is the mass flow rate ratio of solution and dry air

mr = ml / mg

(4)

h

Temperature ( C)

h (Tahp) =

(3)

wahi )

Enthalpy loss Condensate

Moist air

Heat input

Heat recovered

6 Hot air stream

80

60

2

5

4

PPTD in humidifier

Solution stream

40

2

3

PPTD in dehumidifier

Cold air stream

(2) 20

Thus, the pinch point temperature of air, Tahp, is equal to the temperature at the tangent point. In this study, the time of removing scales depends on the humidifier and the amount of accumulated salts which is not considered in the present work. The humidification efficiency in the humidifier is assumed to be independent on the water characteristics (seawater or brackish water) [20,21]. The thermodynamic

3' 1500

1 2000

2500

3000

3500

4000

Enthalpy (kJ/kgdry air) Fig. 2. Temperature-enthalpy profiles of the closed-water, open-air HDH desalination system. 21

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mr cpl (Tlhp

Tlho ) = hahp

(5)

hahi

The energy balance for the part of humidifier above the pinch point yields

mr cpl (Tlhi

Tlhp) = haho

where hahi, haho, hahp are the saturated specific enthalpy of the moist air at inlet, outlet and pinch point temperatures in the humidifier. The specific enthalpy is expressed by (7)

ha = cpg Ta + w (hfg + cpv Ta )

where cpg, cpv is the specific heat capacity of dry air and vapour, Ta is the temperature of air, w is the humidity ratio of air, hfg is the latent heat of vaporization of water. The inlet air state in the humidifier is determined by the environment, which is different at different places and times. Generally, the effects of varying the inlet air temperatures are not high [25]. In this study, the inlet temperature of ambient air is assumed to be 20 °C. Correspondingly, the outlet state parameters of the air and solution can then be obtained from Eqs. (5) and (6).

GOR =

HRR =

(8)

d Tmin

(9)

d Tmin

ΔTmind

where is the PPTD in the dehumidifier. The energy conservation equation for the dehumidifier is as follows

ml cpl (Tldo

Tldi ) = mg (hadi

hado)

HCR =

(10)

m w cpw Tw

Tldi ) = (hadi

hado)

cpw Tw (wadi

wado)

Tldo)

(12)

(13)

The evaporation rate of the system is obtained by (14)

The water production rate is given by

mcond = mg (wadi

wado)

(20)

In order to ensure the accuracy of the obtained numerical simulation results, the proposed thermodynamic model must be validated by the existing data. McGovern [4] conducted a comparative study for the performance of an open-water closed-air HDH system without extractions or with a single extraction. The PPTD at each pinch point are set to equal. The values of GOR for an open-water closed-air HDH system are obtained by utilising the current model and compared with the simulation results from McGovern [4]. The results of the comparison are presented in Fig. 3. It is found that the maximum deviation between the current results and the referred values is < 3%, which verified the reliability of the proposed thermodynamic model for the HDH system.

3.2. Performance parameters

wahi )

mo hoideal|

4. Model validation

A computer program is developed in MATLAB for the solution of the above governing equations. And all process in the system is assumed to be steady-state.

meva = mg (waho

(19)

where is the specific enthalpy at the lowest (to be cooled) or the highest temperatures (to be heated), Toideal, that the stream can reach with PPTD equal to zero. For the cold stream, Toideal is equal to the hot stream's inlet temperature. For the hot stream, Toideal is equal to the cold stream's inlet temperature. The concept and application of HCR is explained in detail in [8].

3.1.3. Energy consumption in heater According to energy conservation, the energy consumption in heater is given by

QH = cpl ml (Tlhi

(18)

hoideal

where wadi and wado are the humidity ratio of air at the inlet and outlet in the dehumidifier. Substitution of Eq. (11) into Eq. (10) leads to

mr cpl (Tldo

Hmax, c Hmax, h

Hmax = |mi hi

(11)

wado )

Qd Qd = Qh QH + Qd

The maximum possible changes, ΔHmax, is expressed by

where cpw is the specific heat capacity of condensate water, Tw is the temperature of condensate water, mw is the mass flow rate of condensate water, which can be given by

m w = mg (wadi

(17)

QH

where Qh and Qd are the heat transfer rate in the humidifier and dehumidifier. The heat capacity rate ratio (HCR) is defined as the ratio between the maximum enthalpy change of the cold and hot stream [8].

If the pinch point is located on the air outlet side,

Tado = Tldi

hfg mcond

The difference between the two parameters lies in the fact that GOR focuses on water production but GIR focuses on the evaporation rate. In the air-closed HDH system, the inlet air temperature in the humidifier and the outlet air temperature in the dehumidifier are identical, the water production is equal to the evaporation rate. So the value of GOR is equal to the value of GIR. In this study, the main purpose of the system is used to remove the water from the solution. The evaporation rate is the focus. Thus, GIR is the research focus. The heat recovery ratio (HRR) is defined as the ratio of the heat recovered in the dehumidifier to the total heat exchange in the humidifier:

3.1.2. Dehumidifier The pinch point in the dehumidifier may be located on either side of the dehumidifier, which is determined by mr and PPTD in the dehumidifier. If the pinch point is located on the air inlet side,

Tldo = Tadi

(16)

QH

As the value of GIR increases, the heat needed to evaporate a unit mass of water decreases, thus corresponding to a system with higher energy efficiency. GIR is slightly different from the commonly used parameter in thermal desalination systems, namely, the gained output ratio (GOR), which is defined as the ratio of the latent heat of the pure water to the net heat input:

(6)

hahp

hfg meva

GIR =

5. Results and discussion (15)

5.1. Evaporation rate

To assess the performance of the system under different operating conditions, the energy efficiency of the system should be evaluated. The gained input ratio (GIR) is defined to evaluate the energy efficiency of the system, which is the ratio between the total latent heat of evaporated water and the net heat input into the system:

The variation of the evaporation rate with the mass flow rate ratio (mr) at different PPTD (ΔTminh) and inlet temperature of the solution in the humidifier (Tlhi) is demonstrated in Fig. 4. It can be observed that the increase of Tlhi results in the increase of evaporation rate. However, 22

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quantity in the humidifier is maximised. If mr continues to increase, the solution stream line cannot remain tangent to the air stream line owing to the limit of the inlet solution temperature. The pinch point location is always at the right endpoint of the solution stream line. The width of the solution stream line (Qh) cannot change due to the limit of Tlhi and Tahi. Therefore, the evaporation rate remains unchanged as well.

McGovern et al. [4] Current model

3.3

GOR

3.0 2.7

5.2. Gained input ratio

2.4

The effects of the mass flow rate ratio of solution and dry air on GIR at different PPTD and inlet solution temperatures in humidifier are illustrated in Fig. 7. It is obvious that the smaller the values of ΔTminh and ΔTmind are, the higher the value of GIR is. Furthermore, it can also be observed that there are optimal values of the mass flow rate ratio at which the GOR peaks at different values of Tlhi, ΔTminh and ΔTmind. This is found to be true for all values of operating parameters. Despite the fact that in the case when Tlhi is 75 °C, the optimal values of mr under different PPTD are very close, they are obviously different when Tlhi is 85 °C. The effects of the PPTD in the humidifier and dehumidifier on GIR is shown in Fig. 8. The value of GIR increases with the decrease of PPTD in the humidifier and dehumidifier. This is because the effectiveness of the component increases with the decrease of PPTD. The higher effectiveness implies the higher evaporation rate in the humidifier and the higher heat recovery in the dehumidifier, which results in the higher GIR consequently. These results agree with the finding for the effects of humidifier and dehumidifier effectiveness as in the work of Fouda et al. [22]. It also can be found that the influence of PPTD on the GIR is very small when the value of mr is < 3. The effectiveness of both the humidifier and dehumidifier are > 90% when the value of mr is < 3, which means much less performance improvement can be gained by decreasing the PPTD of the component (increasing the effectiveness) [9]. In addition, the values of ΔTminh and ΔTmind have an influence on the optimal value of mr, despite the influence is not very great. Overall, the optimal value of mr decreases gradually with the increase of ΔTminh and ΔTmind. Although, the optimum point for GIR occurs at a particular value of mr, this value varies with changes in the operating parameters. Therefore, for the convenience of research, HCR was introduced by Narayan [8,26] to normalise the optimum point. It is suggested that the performance of the dehumidifier dominates the system performance and the GOR of the system is maximised at HCRd = 1 but not at HCRh = 1. The HCRd is somewhat indicative of the HDH system energy consumption. Thus, only the HCR of the dehumidifier is presented in Fig. 9. As seen, the optimum point for GIR is close to the point where

2.1 1.8 0

1

2

3 PPTD (ºC)

4

5

Fig. 3. Comparison of GOR obtained from the current model with the results from McGovern [4] (Tldi = 25 °C, Tadi = 70 °C).

1.0

Evaporation rate (kg/s)

0.8

h Tlhi=75ºC, ∆Tmin =1ºC

h Tlhi=85ºC, ∆Tmin =1ºC

h Tlhi=75ºC, ∆Tmin =3ºC h Tlhi=75ºC, ∆Tmin =5ºC

h Tlhi=85ºC, ∆Tmin =3ºC h Tlhi=85ºC, ∆Tmin =5ºC

0.6

0.4

0.2

0.0 0

10

20

30

40

50

mr Fig. 4. Variation of the evaporation rate as a function of the mass flow rate ratio.

the increase of ΔTminh leads to a decrease in the evaporation rate. This is because the average temperature and concentration difference between air and solution increase with the increase of Tlhi. This leads to the increase of driving force for heat and mass transfer. On the contrary, the increase of ΔTminh results in the decrease of average temperature and concentration difference, the driving force decreases. Moreover, the evaporation rate increases rapidly for low values of mr until it reaches asymptotically a certain upper limit. It can be found that there is an upper limit for all curves. The existence for the upper limit of the evaporation rate can be explained with the help of T-H diagram in humidifier (Fig. 5). The evaporation rate is only related to the thermodynamic process in the humidifier. Therefore, the stream lines in the dehumidifier are not drawn in the diagram. The pinch point line in Fig. 5 is generated by shifting the moist air stream line up by the value of ΔTminh. The solution stream line is tangent to the pinch point line in general. The tangent point is the pinch point in the humidifier. The width of the solution stream indicates the heat exchange quantity in the humidifier. The changing process of the stream line with the variation of mr is illustrated in Fig. 6. As shown in Fig. 6, the slopes of the solution stream lines decrease with the increase of mr, which implies the increases of the heat exchange capacity in the humidifier. However, when the value of mr exceeds the critical value (mr = 13.1 in Fig. 6), the heat exchange

h Qmax

Qh

80 Temperature ( C)

Tlhi h Tmin

60

Solution stream

Moist air stream Pinch point

40

20

Moist air stream Solution stream Pinch point

0 0

200

400 600 800 Enthalpy (kJ/kgdry air)

1000

Fig. 5. Thermodynamic process paths of streams in the humidifier. 23

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A

h Qmax

80

3.5

75°C

h =1ºC ∆ Tmin h =2ºC ∆ Tmin

3.0

h =3ºC ∆ Tmin

40

h =4ºC ∆ Tmin

2.5

Critical line (mr=13.1) GIR

Temperature ( C)

mr=30 60 mr=14

mr=5

h =5ºC ∆ Tmin

2.0 1.5

20

mr=1

Moist air stream Solution stream Pinch point Critical line

1.0

0

0.5

0

200

400

600

800

1000

0

10

20

30

40

50

mr

Enthalpy (kJ/kgdry air)

B

Fig. 6. Changing process of stream line as a function of the mass flow rate ratio.

d ∆ Tmin =1ºC

3.5

d ∆ Tmin =2ºC

A

d =4ºC ∆ Tmin

h d =2ºC, ∆Tmin =3ºC ∆ Tmin

GIR

h d ∆ Tmin =4ºC, ∆Tmin =1ºC

GIR

2.5

d ∆ Tmin =5ºC

2.5

h d ∆ Tmin =2ºC, ∆Tmin =5ºC

3.0

d =3ºC ∆ Tmin

3.0

h d =2ºC, ∆Tmin =1ºC ∆ Tmin

3.5

2.0

h d ∆ Tmin =4ºC, ∆Tmin =3ºC h d =4ºC, ∆ Tmin =5ºC ∆ Tmin

1.5

2.0

1.0 1.5

0.5 1.0

0

10

20

30

40

50

mr 0.5 10

20

30

40

Fig. 8. Effects of the PPTD in the humidifier and dehumidifier on GIR at (A) Tlhi = 75 °C and (B) Tlhi = 85 °C.

50

mr

B

h d =1ºC, ∆ Tmin =2ºC ∆ Tmin

2.00

h d ∆ Tmin =5ºC, ∆ Tmin =2ºC

3.0

3.0 1.75

h d =1ºC, ∆ Tmin =4ºC ∆ Tmin

2.5

h d =3ºC, ∆ Tmin =4ºC ∆Tmin

2.5

h d =5ºC, ∆ Tmin =4ºC ∆Tmin

GIR

GIR

2.25

3.5

h d ∆ Tmin =3ºC, ∆ Tmin =2ºC

3.5

1.50 1.25

2.0 1.00

2.0 1.5

0.75

1.5

GIR HCRd PHCRd

1.0

1.0

0.50 0.25

0.5

0.00 0

0.5 0

10

20

30

40

HCRd / PHCRd

0

10

20

30

40

50

mr

50

mr

Fig. 9. Variation of HCRd and PHCRd as a function of the mass flow rate ratio (Tlhi = 85 °C, ΔTminh = 1 °C, ΔTmind = 2 °C).

Fig. 7. Effects of the mass flow rate ratio of solution and dry air on GIR at (A) Tlhi = 75 °C and (B) Tlhi = 85 °C.

characterise the optimum point for GIR. The pinch point heat capacity rate ratio is given as

HCRd = 1 but not completely at the point HCRd = 1, which means that HCRd cannot characterise the efficiency of the energy utilisation very precisely. A new performance parameter, namely, the pinch point heat capacity rate ratio (PHCR), is defined, attempt to accurately

PHCR =

HPP,max, c HPP,max, h

(21)

where ΔHPP,max is defined as the maximum possible enthalpy change of 24

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stream in consideration of PPTD, which is expressed by

HPP,max = |mi hi

mo hoPPTD|

The variation of GIR at fixed HRR is plotted in Fig. 14. It can be seen that, at a fixed HRR value, the variation of the GIR curve at different operating parameters (Tlhi, ΔTminh) is similar. GIR increases gradually and approaches a specific value. In general, when mr is > 5, the value of GIR can be regarded as a constant. Furthermore, it is obvious that the higher the value of HRR is, the higher the value of GIR is. The value of GIR is nearly equal to 3 at HRR = 0.7 but only equal to 1.5 at HRR = 0.4, differing by a factor of two. This result seems counterintuitive since the GIR should keep changing with the variation of mr rather than approach a constant value. The principle behind this phenomenon can be explained in theory, as follows. Eq. (16) can be rewritten as

(22)

For the cold stream, hoPPTD is the specific enthalpy of the stream at the temperature of Thi − ΔTmin. For the hot stream, hoPPTD is the specific enthalpy of the stream at the temperature of Tci + ΔTmin. As shown in Fig. 9, the optimal point for GIR occurs when PHCRd = 1. And the value of PHCRd is proportional to mr. The variation of GIR as a function of PHCRd at different Tlhi and PPTD values is presented in Fig. 10. The optimal point for GIR always occurs at PHCRd = 1 regardless of the operating parameters. It is obvious that PHCRd can be used to accurately characterise the optimal point for GIR. In other words, PHCRd is more appropriate than HCRd to characterise the efficiency of the energy utilisation within the entire HDH system. In the following section, PHCRd is discussed instead of HCRd. The specific operating parameters of the point PHCRd = 1 are listed in Appendix A. The value of GIR can be achieved 3.978 at the point of PHCRd = 1 when ΔTminh = 1 °C, ΔTmind = 1 °C and Tlhi = 65 °C. At this point, the value of mr equals to 2.87. The phenomenon whereby GIR is maximised at the point PHCRd = 1 can be explained with the help of Fig. 11. The pinch point location and the inlet and outlet temperature differences between hot and cold stream in the dehumidifier are demonstrated in Fig. 11. When PHCRd increases to unity, the pinch point location transfers from the air inlet to the air outlet in the dehumidifier. The point at which PHCRd = 1 is the point at which the pinch point position transfers. At this moment, the temperature differences at the air inlet and outlet in the dehumidifier are same and all equal to the PPTD in dehumidifier. The heat quantity provided by humid air can just preheat the cold solution to the highest temperature (Tadi − ΔTmind). If PHCRd < 1, part of energy in humid air will be wasted (be discharged to the ambient). If PHCRd > 1, the energy is insufficient to preheat the cold solution to the ideal temperature. The point PHCRd = 1 corresponds to the situation in which all available heat from the humid air is recovered by the cold solution, reducing the required heating power in the heater.

GIR =

hfg meva Qh

=

hfg mg (waho

wahi ) (23)

Qh

After its re-arrangement, Eq. (18) can be expressed as

1

Qh mg (haho hahi )

HRR =

(24)

Substitution of Eq. (24) into Eq. (23) leads to

GIR =

1

1 waho HRR haho

wahi hfg hahi

(25)

According to Eq. (25), the relationship between GIR and HRR is only related to the air inlet and outlet states in the humidifier. If the value of (waho − wahi) / (iaho − iahi) is fixed, the relationship between GIR and HRR is unique. The relationship is appropriate for all different configurations of HDH system since the derivation of Eq. (25) is irrelevant to the system configuration. The relationship between the humidity ratio and enthalpy of saturated air is presented in Fig. 15. As shown in Fig. 15, the humidity ratio is nearly linear as a function of the saturated air enthalpy when the humidity ratio becomes > 0.05 kg/kgdry air [24]. When the humidity ratio is < 0.05 kg/kgdry air, the value of (waho − wahi) / (iaho − iahi) increases gradually as a function of the humidity ratio. According to Eq. (25), the variation of GIR is the same as the variation of (waho − wahi) / (iaho − iahi) at the fixed HRR. Therefore, GIR increases gradually and approaches a particular value in Fig. 14.

5.3. Comparison of GIR and GOR The variation of GIR and GOR (with cooler or without cooler) as a function of PHCRd are presented in Fig. 12. The cooler is assumed to cool the humid air to the temperature that 5 °C higher than ambient temperature. It can be seen that the varying tendencies of GIR and GOR are identical. The GOR and GIR all peak when PHCRd = 1. That is, PHCRd can be used to characterise the optimum point for both GIR and GOR. Moreover, the value of GOR with cooler is close to the value of GIR. This is because the slope of saturated air humidity ratio at the low temperature (< 40 °C) is very small. The saturated humidity ratio of air at 20 and 25 °C are 0.0147 kg/kgdry air and 0.0201 kg/kgdry air respectively. The humidity ratio difference is 0.0054 kg/kgdry air, which can be neglected when compared to the evaporation rate or water production. The evaporation rate and water production rate is nearly same.

h d Tlhi=75°C, ∆Tmin =2ºC, ∆Tmin =1ºC

3.5

h d Tlhi=75°C, ∆Tmin =2ºC, ∆Tmin =5ºC h d Tlhi=85°C, ∆Tmin =1ºC, ∆Tmin =4ºC

3.0

h d Tlhi=85°C, ∆Tmin =3ºC, ∆Tmin =4ºC

GIR

2.5 2.0 1.5

5.4. Relation between HRR and GIR

1.0

The variation of GIR and HRR with mr are illustrated in Fig. 13. The variation trend of GIR and HRR are identical and increase first before they decrease. Additionally, GIR and HRR reach maximum values simultaneously for the same mr value. To perform further research on the relation between HRR and GIR, a comparative GIR analysis at a fixed HRR value is required to be performed as well.

0.5 0.0

0.5

1.0

1.5

2.0 2.5 PHCRd

3.0

3.5

Fig. 10. Variation of GIR as a function of PHCRd.

25

4.0

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Air inlet Air outlet

4.0

h d GIR ∆ Tmin =3°C, ∆Tmin =1°C

0.7

h d GIR ∆ Tmin =3°C, ∆Tmin =3°C

3.5

h d HRR ∆Tmin =3°C, ∆Tmin =1°C

3.0

Air inlet Air outlet

20

0.6 0.5

2.5

0.4

2.0

0.3 0.2

1.5

18

0.1

16

1.0 0.0

14

0.5 0

12

10

20

30

40

50

mr

10

B

4.5

8 4.0

6

3.5

4 2

h d GIR ∆Tmin =1°C, ∆Tmin =2°C

0.9

h d GIR ∆Tmin =4°C, ∆Tmin =2°C h d HRR ∆Tmin=1°C, ∆Tmin =2°C h d HRR ∆Tmin =4°C, ∆Tmin =2°C

0.8

0.6

3.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

GIR

0.0

PHCRd

Fig. 11. Pinch point location and air inlet and outlet temperature differences in the dehumidifier (Tlhi = 85 °C, ΔTminh = 3 °C, ΔTmind = 4 °C).

2.5

0.5 2.5 0.4 2.0

0.3

1.5

0.2

1.0

GIR GOR (without cooler) GOR (with cooler)

3.0

0.7

HRR

Temperature difference (°C)

d ∆Tmin =3°C

GIR

22

0.1

0.5

0.0 0

10

20

30

40

50

mr

Fig. 13. Variation of GIR and HRR with mass flow rate ratio at (A) Tlhi = 75 °C and (B) Tlhi = 85 °C.

2.0

GIR

HRR

h ∆Tmin =3°C,

HRR

A

Pinch point location

1.5 3.9

1.0

3.6 3.3

0.5

h Tlhi=75°C, ∆ Tmin =1 C

h Tlhi=85°C, ∆ Tmin =1 C

h Tlhi=75°C, ∆ Tmin =3 h Tlhi=75°C, ∆ Tmin =5

C

h Tlhi=85°C, ∆ Tmin =3 C

C

h Tlhi=85°C, ∆ Tmin =5 C

HRR=0.7

3.0

0.0

0.5

1.0

1.5 2.0 PHCRd

2.5

3.0

GIR

0.0 3.5

2.7 2.4

HRR=0.6

2.1

Fig. 12. Variation of GIR and GOR as a function of PHCRd (Tlhi = 75 °C, ΔTminh = 2 °C, ΔTmind = 3 °C).

HRR=0.5

1.8

HRR=0.4

1.5 1.2

5.5. Graphical method for the determination of the operating parameters

0

In the previous section, PHCRd and HRR were introduced and investigated. PHCRd was introduced to determine whether the operating point occurred at the optimum point or not. HRR is applied to simplify the functional relationship between the evaporation rate and GIR. The above study is the basis of the graphical method. In this section, a graphical method is evaluated, in an effort to efficiently estimate the optimum operating parameters with the help of PHCRd and HRR, subject to the requirements of the evaporation rate and specific energy consumption (GIR). According to Section 5.2, the point at which PHCRd = 1 is the optimum point for GIR. Whether a set

10

20

30

40

50

mr Fig. 14. Variation of GIR as a function of the mass flow rate at a fixed HRR value.

of operating parameters is optimum or not, is judged by whether PHCRd = 1 at the point-of-interest without calculating the relevant index values of the other points around. This can reduce the calculation effort and simplify the process of judgment. In addition, HRR is used

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that the regression function can predict the optimum value of mr exactly at different ΔTminh and HRR values. If HRR is known, a series of combinations of ΔTminh and mr are obtained using regression functions. However, unique values of ΔTminh and mr cannot be obtained only using regression functions. Accordingly, the contours of the evaporation rate are introduced to obtain the unique values of the optimum parameters. The contours of the evaporation rate can be plotted using the governing equations in Section 3. The evaporation rate of the system is only related to the parameters in the humidifier (ΔTminh and mr). The horizontal and vertical coordinates of the contours of the evaporation rate are ΔTminh and mr, respectively. Fig. 16 shows the contours of the evaporation rate at Tlhi = 75 °C. The contours at other temperature can be found in Appendix B. We should choose the contour at corresponding Tlei according to different requirements of evaporation rate. The recommended range of evaporation rate for different contours at different Tlei is shown in Table 2. The recommended range and the scale of the vertical coordinate of the contours are determined by the data in Appendix A. The contour can be used to obtain the optimum operating parameters. The usage of the contour is explained in a subsequent section in accordance to a case. In this case, the requirement for the evaporation rate is 0.24 kg/s, the requirement for GIR (specific energy consumption) is 3. According to the recommended range listed in Table 2, the contour of Tlei = 75 °C is selected.

2250 Specific enthalpy (kJ/kgdry air)

2000 1750 1500 1250 1000 750 500 250 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Humidity ratio (kg/kgdry air) Fig. 15. Relationship between specific enthalpy and humidity of the saturated air in the temperature range of 0–90 °C.

instead of ΔTmind to simplify the optimisation process. Rearranging Eq. (25) leads to,

HRR = 1

waho haho

wahi hfg hahi GIR

(26)

Case: Evaporation rate: 0.24, GIR: 3.

Eq. (26) is appropriate for all systems of different configurations. The evaporation rate and specific energy consumption (GIR) are the major and most significant performance indices in the system. There are different requirements for the evaporation rate and GIR in different applications. If the evaporation rate and GIR are given, the corresponding value of HRR can be obtained from Eq. (26). In order to identify the optimum point of PHCRd = 1 quickly, regressions are performed to predict the optimum value of mr at different ΔTminh and HRR, based on the data listed in Appendix A. ΔTminh and HRR are the input variables, the mass flow rate ratio is the output variables. Eqs. (27) to (31) are respectively the regression functions at the Tlhi values of 65 °C, 70 °C, 75 °C, 80 °C and 85 °C. The values of R2 of Eqs. (27) to (31) are 0.9996, 0.9994, 0.9994, 0.9992 and 0.9987 respectively, which means that the prediction of these functions have sufficient precision.

mr =

h h 0.2865 Tmin + 0.2283 Tmin HRR

1.109HRR2

0.4151

h Tmin

+ 0.3489

h Tmin

HRR

1.521HRR2

h h 0.6287 Tmin + 0.558 Tmin HRR

5.66HRR

9.287HRR (29)

+ 12.87 mr =

h h 1.065 Tmin + 1.008 Tmin HRR

1.617HRR2

17.15HRR (30)

+ 20.04 mr =

h h 2.006 Tmin + 2.044 Tmin HRR

+ 34.14

Table 1 Real values of PHCRd for predicted operating parameters.

(28)

1.848HRR2

1.177HRR2

(32)

h 0.2342 Tmin + 5.3804

The corresponding operating line is drawn on top of the evaporation rate contour at Tlei = 75 °C (Fig. 17). The intersection point of the operating line and the contour line of the rated evaporation rate (0.24 kg/

(27)

+ 8.995 mr =

mr =

3.656HRR

+ 6.536

mr =

The outlet temperature of air in the humidifier can be obtained by the psychrometric chart of saturated air in accordance to the evaporation rate. And the value of (waho − wahi) / (iaho − iahi) can also be obtained. The required value of HRR, which is equal to 0.707 in this case, can be estimated using the known evaporation rate and GIR by means of Eq. (26). Substitution of HRR = 0.707 into Eq. (29), leads to

35.37HRR (31)

Whether the optimum point can be predicted accurately or not is vital to the optimisation process. In order to further verify the accuracy of the prediction, twenty points were randomly selected and their PHCRd values were calculated. The results are listed in Table 1. The real values of the twenty PHCRd points are all close to unity, which indicates

27

Tlhi

ΔTminh

HRR

mr,pre

PHCRd

65 65 65 65 70 70 70 70 75 75 75 75 80 80 80 80 85 85 85 85

3.62 1.29 2.63 3.67 2.67 4.89 4.95 4.46 4.53 4.65 3.23 3.40 4.75 4.32 4.40 2.50 4.62 4.05 4.53 2.14

0.767 0.706 0.542 0.678 0.494 0.527 0.423 0.692 0.374 0.750 0.525 0.403 0.597 0.736 0.767 0.634 0.349 0.632 0.361 0.504

2.677 3.243 3.800 3.063 5.177 4.458 5.002 3.575 7.231 3.888 6.398 7.458 7.031 5.142 4.655 7.452 15.683 8.419 15.463 13.937

0.998 1.000 0.997 1.001 0.994 1.000 0.997 0.999 0.992 0.994 0.996 0.989 1.000 0.995 0.992 1.001 0.985 0.971 0.984 0.974

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7.0

0.27

0.26

4.8

0.24

0.25

4.6

6.5

0.23

4.4

6.0

4.2 0.22

5.0

0.21

4.5

0.20

t ∆Tmin

mr

5.5

4.0 3.8 3.6 3.4

0.19

4.0

h mr=5.03, ∆Tmin =1.47

3.2 0.18

3.5

3.0 0.17

2.8

3.0 0.5

1.0

1.5

2.0

2.5

3.0 3.5 h Tmin

4.0

4.5

5.0

0.0

5.5

Table 2 Recommended range of evaporation rate at different Tlei. Evaporation rate (kg/s)

65 70 75 80 85

0.10–0.15 0.15–0.20 0.20–0.26 0.26–0.36 0.36–0.52

0.28

7

0.27

0.26

1.5 2.0 h ∆ Tmin

2.5

3.0

3.5

that the optimum point is non-existent in this case. Under this circumstance, the requirement of the evaporation rate or GIR should be decreased to ensure that the optimum point is attained. 5.6. Validation of the graphical method In the last section, a graphical method was proposed for the determination of the optimum operating parameters. To verify that the operating parameters identified by the graphical method are optimum, the other operating parameters that meet the requirement are calculated and compared with those for the optimum operating parameters obtained using the graphical method. All the operating parameters that meet the requirements are all on the corresponding evaporation rate contour line and the corresponding HRR values are always the same. The variation of the total PPTD corresponding to operating parameters that meet the requirements is illustrated in Fig. 18. The total PPTD is the sum of ΔTminh and ΔTmind. It is obvious that the total PPTD is maximised at the point of the operating parameters obtained by graphical method. From the design perspective, the value of the total PPTD is expected to be as high as possible for the same total heat transfer. Therefore, the graphical method is considered as a valid approach for the estimation of the optimum operating parameters.

0.24

0.25

0.23

6 0.22

mr

1.0

Fig. 18. Variation of the total PPTD of the operating parameters that meet the requirements (evaporation rate is 0.24 kg/s).

Fig. 16. Contours of the evaporation rate at Tlei = 75 °C.

Tlhi

0.5

0.21

5

0.20 0.19

4

0.18

6. Conclusions

0.17

In this study, the thermodynamic performance of an HDH desalination system was investigated using pinch analysis. The variations of the evaporation rate and GIR are studied. Additionally, an efficient graphical method, combing the regression equations and the evaporation rate contour plots, is proposed for the determination of the optimum operating parameters based on specified performance requirements in an HDH system. The following conclusions can be drawn:

3 0.5

1.0

1.5

2.0

2.5

3.0 3.5 h ∆ Tmin

4.0

4.5

5.0

5.5

Fig. 17. Contours of the evaporation rate at Tlei = 75 °C. The operating line are superimposed and shown in red colour.

(1) As mr increases, the evaporation rate increases gradually and then reaches an upper limit owing to the limits of Tlhi and Tahi. The evaporation rate stops increase when the pinch point location in the humidifier reaches the top of the humidifier.

kgdry air) is the optimum point we look for, and the corresponding operating parameters are the optimum operating parameters. The corresponding operating parameters are mr = 5.03, ΔTminh = 1.48 °C, and HRR = 0.707. If there is no intersection point in the figure, this means

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(2) The new parameter PHCR is introduced for evaluating the specific energy consumption of the system. It is found that when PHCRd is exactly equal to unity, the specific energy consumption of the system (GIR and GOR) is minimised. It can provide more accurate assessment than HCR. (3) The value of GIR can be achieved 3.978 at the point of PHCRd = 1 when ΔTminh = 1 °C, ΔTmind = 1 °C and Tlhi = 65 °C. At this point, the value of mr equals to 2.87. (4) The variation tendencies of GIR and HRR are identical. The relation between GIR and HRR is almost linear when mr is > 5. The value of GIR is nearly equal to 3 at HRR = 0.7 but is only equal to 1.5 at HRR = 0.4, differing by a factor of two. According to the theory derivation, the relationship between HRR and GIR is only related to

the air inlet and outlet states in the humidifier. (5) The regression equations obtained by regression analysis can predict the exact optimum value of mr at different ΔTminh and HRR values. The proposed graphical method will only take a short time to determine the optimum operating parameters. It is more appropriate for the engineering application than the numerical optimisation method. Acknowledgements The authors acknowledge the financial support by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX18_1089, KYCX18_1090).

Appendix A. Optimal operating parameters Table A.1

Operating parameters of the point at which PHCRd = 1 at different Tlhi. Tlhi (°C)

ΔTminh (°C)

ΔTmind (°C)

HRR

mr

me (kg/kgdry

65

1

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

0.786 0.762 0.735 0.708 0.678 0.763 0.736 0.708 0.678 0.647 0.737 0.708 0.678 0.646 0.612 0.709 0.678 0.645 0.610 0.573 0.677 0.644 0.609 0.571 0.530 0.778 0.754 0.730 0.704 0.676 0.756 0.731 0.705 0.677 0.647 0.732 0.706 0.677 0.647 0.614 0.707 0.678 0.647 0.614 0.579 0.678 0.647 0.614 0.578 0.539

2.870 2.995 3.128 3.271 3.424 2.877 3.003 3.137 3.280 3.434 2.885 3.011 3.145 3.289 3.443 2.892 3.019 3.154 3.298 3.453 2.900 3.027 3.162 3.307 3.462 3.533 3.706 3.892 4.093 4.310 3.544 3.718 3.905 4.107 4.325 3.555 3.730 3.918 4.121 4.340 3.567 3.742 3.930 4.134 4.355 3.577 3.753 3.943 4.148 4.369

0.131 0.134 0.137 0.140 0.143 0.127 0.130 0.133 0.135 0.138 0.123 0.125 0.128 0.131 0.133 0.118 0.121 0.123 0.126 0.128 0.114 0.116 0.119 0.121 0.123 0.172 0.177 0.181 0.186 0.191 0.167 0.171 0.176 0.180 0.185 0.162 0.166 0.170 0.174 0.178 0.157 0.161 0.164 0.168 0.172 0.152 0.155 0.159 0.162 0.166

2

3

4

5

70

1

2

3

4

5

29

air)

GIR 3.978 3.569 3.221 2.919 2.656 3.578 3.222 2.915 2.648 2.413 3.221 2.910 2.639 2.402 2.191 2.903 2.629 2.389 2.177 1.988 2.617 2.375 2.162 1.973 1.803 3.871 3.511 3.196 2.918 2.670 3.524 3.203 2.921 2.670 2.445 3.209 2.922 2.668 2.441 2.237 2.923 2.666 2.436 2.230 2.044 2.661 2.430 2.223 2.036 1.865

(continued on next page)

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Table A.1 (continued) Tlhi (°C)

ΔTminh (°C)

ΔTmind (°C)

HRR

mr

me (kg/kgdry

75

1

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

0.768 0.746 0.723 0.698 0.671 0.748 0.724 0.699 0.672 0.643 0.726 0.701 0.673 0.644 0.612 0.702 0.675 0.645 0.613 0.578 0.676 0.646 0.614 0.579 0.541 0.757 0.735 0.712 0.687 0.659 0.738 0.714 0.689 0.662 0.631 0.716 0.691 0.664 0.634 0.601 0.693 0.666 0.636 0.604 0.567 0.668 0.638 0.606 0.570 0.530 0.745 0.723 0.699 0.672 0.643 0.726 0.702 0.676 0.647 0.614 0.705 0.679 0.651 0.619 0.582 0.682 0.654 0.623 0.588 0.547 0.657 0.627 0.592 0.553 0.507

4.448 4.695 4.964 5.259 5.583 4.465 4.713 4.984 5.280 5.606 4.481 4.731 5.003 5.301 5.629 4.497 4.748 5.022 5.323 5.653 4.513 4.766 5.042 5.344 5.676 5.843 6.230 6.660 7.142 7.685 5.869 6.258 6.692 7.179 7.727 5.895 6.287 6.725 7.216 7.770 5.921 6.317 6.758 7.253 7.812 5.947 6.346 6.791 7.291 7.855 7.999 8.653 9.405 10.280 11.313 8.041 8.702 9.464 10.350 11.390 8.084 8.753 9.524 10.422 11.485 8.129 8.805 9.585 10.496 11.575 8.174 8.858 9.648 10.571 11.667

0.228 0.235 0.242 0.249 0.257 0.222 0.228 0.235 0.242 0.249 0.215 0.221 0.228 0.234 0.241 0.209 0.215 0.220 0.226 0.232 0.202 0.208 0.213 0.219 0.224 0.307 0.317 0.329 0.341 0.353 0.298 0.309 0.319 0.331 0.342 0.290 0.300 0.310 0.321 0.331 0.282 0.291 0.300 0.310 0.320 0.273 0.282 0.291 0.300 0.309 0.422 0.441 0.461 0.482 0.505 0.411 0.429 0.448 0.468 0.489 0.400 0.417 0.434 0.453 0.473 0.389 0.404 0.421 0.439 0.457 0.377 0.392 0.407 0.424 0.441

2

3

4

5

80

1

2

3

4

5

85

1

2

3

4

5

30

air)

GIR 3.759 3.437 3.150 2.891 2.657 3.454 3.162 2.900 2.663 2.447 3.173 2.908 2.668 2.450 2.251 2.914 2.672 2.452 2.252 2.067 2.674 2.453 2.251 2.067 1.896 3.615 3.324 3.058 2.814 2.589 3.346 3.077 2.831 2.604 2.393 3.095 2.846 2.618 2.406 2.209 2.860 2.629 2.417 2.219 2.034 2.639 2.426 2.228 2.043 1.870 3.478 3.208 2.957 2.721 2.498 3.236 2.983 2.746 2.524 2.312 3.007 2.769 2.547 2.336 2.135 2.790 2.567 2.357 2.157 1.966 2.585 2.375 2.177 1.987 1.805

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Appendix B. Contours of the evaporation rate at different inlet temperatures in the humidifier 0.16

5.0

0.15

0.14

4.5

0.13

4.0 3.5

mr

0.12

3.0 0.11

2.5 0.10

2.0

0.09 0.08

1.5 0.5

1.0

1.5

2.0

2.5

3.0 3.5 h Tmin

4.0

4.5

5.0

5.5

Fig. B.1. Contours of the evaporation rate at Tlhi = 65 °C. 0.21

0.22

6.0

0.20

0.19

0.1

5.5 5.0

0.17

mr

4.5 0.16

4.0 0.15

3.5

0.14

3.0 0.13

2.5

0.12 0.11

2.0 0.5

1.0

1.5

2.0

2.5

3.0 3.5 h Tmin

4.0

4.5

5.0

5.5

Fig. B.2. Contours of the evaporation rate at Tlhi = 70 °C. 0.28

7.0

0.27

0.26

0.24

0.25

6.5

0.23

6.0 0.22

mr

5.5 5.0

0.21

4.5

0.20 0.19

4.0

0.18

3.5 0.17

3.0 0.5

1.0

1.5

2.0

2.5

3.0 3.5 h Tmin

4.0

4.5

5.0

Fig. B.3. Contours of the evaporation rate at Tlhi = 75 °C.

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0.40

10

0.39

0.37

0.38

0.36

0.34

0.35

0.33

0.32

9

0.31

8

mr

0.30

7

0.29 0.28

6

0.27 0.26 0.25

5

0.24 0.23 0.22 0.21

4 0.5

1.0

1.5

2.0

2.5

3.0 3.5 h Tmin

4.0

4.5

5.0

5.5

Fig. B.4. Contours of the evaporation rate at Tlhi = 80 °C.

15

0.58 0.57

0.56 0.55

0.54

0.53

0.52

0.51

0.50

0.49

0.48

14

0.47 0.46 0.45

13

0.44

12

0.43

mr

11

0.42 0.41

10

0.40 0.39 0.38 0.37 0.36 0.35 0.34 0.33 0.32 0.31 0.30

9 8 7 6 5 0.5

1.0

1.5

2.0

2.5

3.0 3.5 h Tmin

4.0

4.5

5.0

5.5

Fig. B.5. Contours of the evaporation rate at Tlhi = 85 °C.

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