Coupled heat and mass transfer analysis of an adiabatic dehumidifier – unique approach

Coupled Heat and Mass Transfer Analysis of an Adiabatic Dehumidifier – Unique Approach 1876 6102 © 2016 The Authors Published by Elsevier Ltd This is an open access article under the CC BY NC ND licen[.]

1876-6102 © 2016 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of ICAER 2015

doi: 10.1016/j.egypro.2016.11.198

Energy Procedia 90 ( 2016 ) 305 – 315

ScienceDirect

2015, Mumbai, India Coupled Heat and Mass Transfer Analysis of an Adiabatic

a Deparment of Mechanical Engineering, Indian Institue of technology Guwahati, Guwahati-781039, India

Abstract

Liquid desiccant dehumidifier is one of the most desirable systems for dehumidification of air when compared to conventional refrigeration system and solid desiccant based dehumidifier In the present study, a finite difference model is developed to simulate the coupled heat and mass transfer processes occur in a counter flow adiabatic dehumidifier employing lithium chloride (LiCl) as a desiccant solution Mat-lab R13 is used as a simulation package for solving the aforementioned model This model has taken into the consideration of thermal effectiveness, effective height and moisture effectiveness as variable parameters for obtaining the correlation of the desired operating parameters The predicted numerical parameters for absorption process have good agreement with the experimental data reported in the literature This model is unique and can be extended to any type of liquid desiccant solution by changing the solution properties The performance analysis of adiabatic counter flow dehumidifier is also carried out by varying the operating parameters and the detailed results are presented in the full manuscript

© 2016 The Authors Published by Elsevier Ltd

Peer-review under responsibility of the organizing committee of ICAER 2015

Keywords: Desiccant; dehumidification; heat and mass transfer; moisture effectiveness; condensation rate;

1 Introduction

In the traditional vapour compression or vapour absorption refrigeration system, process air is dehumidified by cooling below its dew point temperature and then reheating to the desired comfort temperature (required indoor

* Corresponding Author Tel.: (+91) 361-2582673; Fax: (+91) 361-2690762

E-mail address: pmkumar@iitg.ernet.in

© 2016 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of ICAER 2015

conditions) This method is more energy consuming and is limited to lower cooling load capacity The best and economical way of dehumidification is by means of liquid desiccant solution This method is very popular due to its capability of removing latent load thereby minimizing the energy demand Dehumidifier is one of the important component of a liquid desiccant air conditioning system in which the concentrated solution is diluted The schematic

of heat and mass transfer process that occurs across the dehumidifier is shown in Fig 1 Initially, the concentrated solution is sprayed from the top of the packed tower and air (high RH) is circulated from bottom of the tower (in a counter flow direction) When the process air comes in contact with concentrated solution, desorption of moisture present in the process air occurs During this process, latent heat is released due to condensation of water vapor to solution side and chemical heat is released due to exothermic reaction (water vapor absorption by desiccant solution) Therefore remarkable rise in temperature of both air and desiccant solution takes place

Nomenclature

at specific surface area per unit volume (m2/ m3)

cp specific heat at constant pressure (kJ/kg-K)

G specific mass flow rate (kg/m2-s)

h specific enthalpy (kJ/kg)

z height of the tower (m)

Greek letters

β concentration of the desiccant by mass (%)

γ solution to air flow rate ratio

ξ effectiveness

λ condensation rate (kg/m2-s)

δ latent heat of vaporization (kJ/kg)

ω air specific humidity ratio (kgv /kgda)

m mass transfer coefficient (kg/m2-s)

h heat transfer coefficient (W/m2-K)

Subscripts

a air

e equilibrium

i inlet

m moisture

o outlet

s liquid desiccant solution

T thermal

During absorption (dehumidification) process, heat and mass interactions occur between the air and the liquid desiccant solution The driving force for heat transfer is due to temperature difference whereas for mass transfer is their vapour pressure difference [1] The complicity of heat and mass transfer dealt way back from 1969 and Treybal [2] was the first person to describe the heat and mass transfer process occurred during dehumidification process by proposing a simple mathematical model From then, many researchers have developed various mathematical models for predicting the coupled heat and mass transfer characteristics occurred during dehumidification process using finite difference model [3-5], ɛ-NTU model [6-7] and simplified models [8-9] Fumo and Goswami [3], Babakhani et

al [4] and Liu et al [5] compared their analytical solution with the experimental data and concluded that their

models were valid only with some reasonable assumptions Gandhidasan [8] introduced the dimensionless parameters such as moisture and thermal effectiveness and formulated the condensation rate in terms of heat exchanger effectiveness, mass flow rate of air and thermal effectiveness The proposed model has been compared with the experimental findings and found that the prediction matched within 10.5% with the experimental data Chung et al [10] developed a model for obtaining dimensionless heat and mass transfer correlations for both structured and random packing’s They found that the heat transfer coefficients were stronger function of the air flow rate than the solution flow rate Also, increasing the desiccant concentration reduces the heat transfer coefficients

Fig 1 Energy and mass balance across the dehumidifier

Many researchers developed the finite difference model for predicting the coupled heat and mass transfer characteristics of an adiabatic dehumidifier [2-5] The uniqueness of the proposed model is the development of a correlation between the heat transfer coefficient and thermal effectiveness as well as for mass transfer coefficient and moisture removal effectiveness No one has correlated the moisture effectiveness and thermal effectiveness with the height of the dehumidifier which defines the performance as well as desired design conditions of a dehumidifier Also, using these correlations one can predict the exit parameters with known operating conditions very precisely

2 Heat and mass transfer analysis of liquid desiccant dehumidifier

A schematic of a counter flow heat and mass transfer processes occurred between air and desiccant solution is represented in Fig.1

To simplify the analysis, the following assumptions are made;

• Dehumidification process is adiabatic

• Change in mass flow rate of air is negligible

• Properties of desiccant solution and ambient air is assumed to be constant with respect to the temperature

• Heat and mass transfer interaction at the interface area are equal to the specific area of packing

2.1 Air side

The enthalpy on air side is given by

On differentiation Eq 1

a p a p v a p v a

Energy balance across the air side flow is written as

Combining Eqs (2) & (3), the air temperature gradient is obtained as

α

ω

−

=

Eq 4 can be integrated as

,

a o

a i

a s a pa pv

T

dZ

α ω

−

=

After integrating Eq 5, final equation can be obtained as

1 exp

a i s i a pa pv

α ω

The most common performance measures for evaluating the dehumidifier potential to dehumidify the ambient air

are thermal and moisture effectiveness

2.1.1 Thermal effectiveness

A dimensionless parameter given by Gandhidasan [8] in terms of outlet air temperature and inlet temperatures of

ambient air and solution is

a i a o

T

a i s i

T T

T T

ξ = −

From Eqs.6 & 7, the thermal effectiveness (ξT) in terms of heat transfer coefficient (αh), height (h) and flow rate of

air is formulated as

1 exp

h t T

a pa pv

a z

α ξ

ω

+

(8)

2.1.2 Heat transfer coefficient

From Eq.8, heat transfer coefficient in terms of thermal effectiveness and height is introduced as

ln 1

a p a p v

h

a z

ω

α

ξ

−

(9)

2.1.3 Mass balance for air side

The mass transfer rate across the interface is equal to the change in humidity ratio and the equation is written as

a m t e

Eq 10 is integrated as

,

, ( ) 0

a o

a i

z

m t

a d

dZ G

ω

ω

α ω

After integrating Eq.11, final equation can be obtained as

1 exp

a z G

2.1.4 Moisture effectiveness

The moisture effectiveness based on specific humidity difference across the dehumidifier is given as follows [8]

i o

m

i e

ω ω

ξ

ω ω

−

=

From Eqs 12 & 13 the moisture effectiveness (ξm) in terms of mass transfer coefficient (αm), height (h), specific surface area of packing (at) and flow rate of air (Ga) is formulated as

m

a

a z G

α

ξ = − ⎛ ⎜ − ⎞ ⎟

(14)

2.1.5 Mass transfer coefficient

From Eq.14, mass transfer coefficient in terms of moisture effectiveness and height is introduced as

1

ln

1

a

m

G

a z

α

ξ

−

2.2 Solution side

Energy balance across the solution side flow is written as

(G s+dG s)(h s+dh s)−G h s s =αh a T t( a−T dZ s) −G d a ω(C T p v a+δ) (16)

The enthalpy on the solution side is given by

,

s p s s

2.2.1 Condensation rate

The rate of water vapour condensed (absorbed) from the ambient air to the solution side is referred as condensation rate (λ) and is given by

a

The change in the solution side flow rate is equal to the rate of water vapour condensed from the ambient air, it is written as

s

By combining Eqs (16), (17) & (19) the solution side temperature gradient is obtained as

,

1

p a p v p s s p v a

p s

ω

γ

where s

a

G

G

(20)

2.2.2 Mass balance for solution side

Since the mass of the desiccant is constant during the desorption process, the mass balance across the solution side is written as

s i i s o o

The rate of water vapour condensed from the ambient air is transferred to the desiccant solution by a process known

as absorption Simply, the condensation rate represents the amount by which the desiccant solution diluted So, Eq

21 can be formulated as

s i i s i a o o

From Eq.22, the solution concentration at the outlet in terms of inlet flow rate, solution concentration and condensation rate is given by

,

1

1

a i o

s i

G

G

=

(23)

3 Validation of model

In order to use the developed mathematical model, with confidence, a proper validation is essential A comparison

is made between the predicted values calculated from the developed mathematical model and experimental values

presented by the Chung and Gosh [10] During the experimental studies, a packed column of height 0.41m with the specific area of 223 m2/m3 was considered Table 1 lists the inlet parameters considered for validating the developed model [10] and a comparison of typical experimental data for 16 cases [10] with the results obtained from the present study is presented in Table 2 With reference to the results presented in Table 2, it is found that the predicted results obtained from the present model match well with the experimental data reported by Chung and Gosh [10] for the desiccant solution outlet temperature, the ambient air outlet temperature and humidity ratio and the water condensation rate In all the cases, the present mathematical model yields the air outlet temperature and specific humidity ratio and the desiccant solution outlet temperature slightly less than the experimental values The maximum and mean difference for air outlet temperature are -0.92 °C and -0.4 °C The specific humidity of air at the outlet and the solution outlet temperature differ as much as -4.35 % and -0.78 °C, whereas the average difference is about -1.84 % and -0.41 °C Developed model can’t be applied for predicting the desired outlet parameters when the inlet temperature of the solution and the process air are equal

Table 1 Inlet parameters that are used for validating the developed mathematical model [10]

(kg/s) (°C) (kg wv /kg da ) (kg/s) (°C) (% by mass)

Table 2 Comparison of present outlet parameters with the predicted outlet parameters of Chung and Gosh [10]

Exp Present diff Exp Present diff Exp Present % Error Exp Present % Error 17.8 18.130 -0.33 16.9 16.982 -0.29 0.0064 0.0065 -1.56 0.1109 0.1086 2.07 17.6 18.170 -0.57 16.6 17.172 -0.57 0.0063 0.0064 -1.59 0.1248 0.1222 2.08 17.3 17.430 -0.13 16.6 16.715 -0.12 0.0066 0.0067 -1.52 0.1495 0.1387 7.22 17.8 18.072 -0.27 17.2 17.429 -0.23 0.0067 0.0068 -1.49 0.1649 0.1558 5.51 19.1 19.533 -0.43 18.3 18.604 -0.31 0.0080 0.0081 -1.25 0.2210 0.2162 2.17 19.1 19.426 -0.33 18.6 18.748 -0.15 0.0077 0.0078 -1.30 0.2226 0.2194 1.44 19.1 19.320 -0.22 18.5 18.675 -0.18 0.0075 0.0076 -1.34 0.2290 0.2258 1.40 18.9 19.128 -0.23 18.0 18.578 -0.58 0.0073 0.0074 -1.37 0.2353 0.2321 1.36 20.6 21.199 -0.60 19.8 20.168 -0.37 0.0058 0.0059 -1.72 0.1551 0.1571 -1.29 19.9 20.075 -0.18 19.0 19.218 -0.22 0.0058 0.0059 -1.72 0.1768 0.1742 1.47 19.8 20.126 -0.33 19.4 20.126 -0.73 0.0051 0.0052 -1.96 0.1445 0.1416 2.01 19.5 19.829 -0.33 19.2 19.616 -0.42 0.0052 0.0053 -1.92 0.1685 0.1654 1.84 18.9 19.521 -0.62 18.4 19.133 -0.73 0.0049 0.0050 -2.04 0.1697 0.1685 0.71 18.6 19.091 -0.49 18.2 18.981 -0.78 0.0047 0.0048 -2.13 0.1751 0.1749 0.11 18.5 19.418 -0.92 18.1 18.623 -0.52 0.0046 0.0048 -4.35 0.1813 0.1749 3.53 18.4 19.017 -0.62 18.0 18.699 -0.70 0.0045 0.0046 -2.23 0.1831 0.1813 0.98

Fumo & Goswami [3], Gandhidasan [8] and Babakhani & Soleymani [4] studied the effects of various design parameters such as the inlet air temperature and humidity ratio, the inlet desiccant temperature and concentration, the air and the desiccant flow rate on the condensation rate in detail Hence, in this paper, the influences of air flow rate and the inlet temperature on both thermal effectiveness and moisture effectiveness during the dehumidification

process is presented in Figs 2(a) & 2(b) and 3(a) & 3(b), respectively A comparison between the experimental results presented by Chung and Gosh [10] and the present model is shown in aforementioned Figs Further, the effects of moisture effectiveness and thermal effectiveness and relative humidity on the condensation rate as well as the influence of solution to air flow ratio on the desiccant solution concentration are investigated using the present model Slope of thermal effectiveness and moisture effectiveness curve provides an estimation of the influence of these variables on the thermal and moisture effectiveness The thermal effectiveness and moisture effectiveness increase with the decrease in air flow rate with a slope of -1.0 & -0.9 (Figs 2(a) & 2(b)) It may be noted that at high flow rate, the air will be in contact with the desiccant solution for a shorter period of time, giving a lower change in temperature and specific humidity difference ratio (Figs 2(a) & 2(b)) The thermal effectiveness and moisture effectiveness enhance with the decrease of air inlet temperature with a slope of -0.42 & -0.6 (Figs 3(a) & 3(b)) and there is a linear increment of air inlet temperature for lower temperature and specific humidity difference ratio Since the temperature of the air and solution are highly dependent on the vapour pressures, at lower air inlet temperatures, the difference in vapour pressure of ambient air and desiccant solution is high therefore higher tendency of heat transfer from the ambient air to the solution side

Fig 2 Comparison of present model with the experimental data of Chung and Gosh [10]: a) Influence of thermal effectiveness on air flow rate

and b) Influence of moisture effectiveness on air flow rate

Fig.3 Comparison of present model with the experimental data of Chung and Gosh [10]: a) Influence of thermal effectiveness on air inlet

temperature and b) Influence of moisture effectiveness on air inlet temperature

4 Results and discussions

The operating parameters that are kept constant during the analysis are listed in Table 3 Fig 4 illustrates the moisture effectiveness obtained for different mass transfer coefficients at different tower height from 0.1 to 0.6 m In Fig 4, the variation of moisture effectiveness is determined using a new correlation developed in terms of mass transfer coefficient, tower height, air mass flow rate and specific area (Eq 14) For the given operating conditions,

as the mass transfer coefficient increases, the moisture effectiveness is also found to increase Low the mass transfer from the ambient air to the solution side yields the lower value of moisture effectiveness This is due to the fact that

as the mass transfer coefficient decreases the change in the solution concentration is also decrease and hence there is

a decrease in the moisture effectiveness From Fig 4, it is also observed that the moisture effectiveness increases exponentially as a function of mass transfer coefficient with the increase in tower height This may be explained, as the height increases, contact time between the ambient air and solution side increases Hence, increase in moisture effectiveness takes place For a given αm of 0.4 g/m2-s, increasing the tower height from 0.1 to 0.6 m, increases the moisture effectiveness by 69 %

Table 3 Dehumidifier parameters used in the analysis Operating parameters Unit Operating range

Desiccant inlet temperature °C 17.7 Desiccant flow rate at the inlet kg/s 0.2783 Desiccant concentration % by mass 34

0

10

20

30

40

50

60

70

80

90

100

0.04 0.14 0.24 0.34 0.44 0.54 0.64

Tower height (m)

h - 0.6 (W/m 2 K)

h - 0.5 (W/m 2 K)

h - 0.4 (W/m 2 K)

0 10 20 30 40 50 60 70 80 90 100

Tower height (m)

m - 0.6 (g/m 2 s)

m - 0.5 (g/m 2 s)

m- 0.4 (g/m 2 s)

Fig 4 Effect of heat transfer coefficient on thermal effectiveness Fig 5 Effect of mass transfer coefficient on moisture effectiveness

The effect of heat transfer coefficient on the thermal effectiveness is illustrated in Fig 5, by varying the tower height (0.1 to 0.6 m) for different heat transfer rates (0.4 to 0.6 W/m2-K) A new correlation which has been developed for thermal effectiveness (Eq 8) in terms of heat transfer coefficient, air mass flow rate, specific area and tower height is used for determining the variation of temperature difference ratio across the height of the

dehumidifier Two defined tendencies have been observed from Fig 5 One tendency is the apparent exponential increment of the thermal effectiveness for an increase in the tower height This is due to the fact that, as the tower height increases, the ambient air temperature (function of vapour pressure) increases, giving a lower change in heat transfer rate For a given αh of 0.6 W/m2-K, increasing the tower height from 0.1 to 0.6 m, increases the thermal effectiveness by 61 % The second defined tendency is the apparent increase in thermal effectiveness with increase

in heat transfer rate This can be explained from Fig 5 that lower the thermal effectiveness, lower the change in ambient air temperature and hence there is an apparent decrease in heat transfer coefficient

The influence of relative humidity (R.H.) on the condensation rate (λ) is shown in Fig 6 To investigate this effect, the relative humidity is varied from 70 % to 90 % that can be obtained during the peak summer seasons in a humid climate As illustrated, when the relative humidity is increased, the condensation rate is increased It happens because higher the R.H implies a higher air vapour pressure and consequently higher potential mass transfer From Fig 6, it is also observed that for a length 0.5 m, the condensation rate is constant in case of a relative humidity

90 % or 80 % or 70 % This is due to the fact that as the height increases, the difference in humidity ratio approaches

to zero, which results in apparent decrease of heat and mass interactions between the ambient air and the desiccant solution and hence there is a constant condensation rate beyond a particular tower height for different relative humidity’s Therefore, it is advisable to have an optimum tower height depending upon the operating conditions Figure 7 shows the results obtained for the concentration at different solution to air flow rate (L/G ratio) ratios, by varying the tower height from 0.1 to 0.6 m For any given flow rate ratio, as the height increases the solution concentration decreases Since the concentration is highly dependent on vapour pressure, the higher the solution vapour pressure, the lower the condensation rate and consequently gives the lower potential for mass transfer interaction From Fig 7, it is also observed that as the flow rate ratio increases desiccant solution concentration decreases This happens because as the flow rate ratio increases, the solution to air contact will be for shorter period

of time, giving a lower change in concentration For a given γ = 0.5, increasing the tower height from 0.1 to 0.6 m, decreases the solution concentration by 3.3 %

0

0.05

0.1

0.15

0.2

0.25

0.04 0.14 0.24 0.34 0.44 0.54 0.64

2 s)

Tower height (m)

R.H - 90 % R.H - 80 % R.H - 70 %

32.5 32.7 32.9 33.1 33.3 33.5 33.7 33.9 34.1 34.3 34.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

g Li

Tower height (m)

γ - 1.5

γ - 1

γ - 0.5

Fig 6 Influence of relative humidity on condensation rate Fig.7, Effect of concentration on solution to air flow ratio

5 Conclusions

Ambient air dehumidification process using strong desiccant solution (LiCl- H2O) has been studied by proposing a unique mathematical model using dimensionless parameters such as thermal effectiveness and moisture effectiveness in terms of heat and mass transfer coefficient The developed mathematical model has been shown very good agreement with the available experimental data [10] It is observed that operating variables such as solution to air flow rate ratio, air inlet temperature, relative humidity and heat and mass transfer coefficients have greater impact on dehumidifier performance It is also found that for a constant area beyond a certain tower height, the condensation rate for any relative humidity is nearly the same For a detailed study of absorption process across