A detailed study on simultaneous heat and mass transfer in an in-tube vertical falling film absorber

Accepted Manuscript Title: A detailed study on simultaneous heat and mass transfer in an in-tube vertical falling film absorber Author: Mehdi Aminyavari, Marcello Aprile, Tommaso Toppi, Silvia Garone, Mario Motta PII: DOI: Reference:

S0140-7007(17)30187-1 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.04.029 JIJR 3631

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

18-1-2017 8-4-2017 30-4-2017

Please cite this article as: Mehdi Aminyavari, Marcello Aprile, Tommaso Toppi, Silvia Garone, Mario Motta, A detailed study on simultaneous heat and mass transfer in an in-tube vertical falling film absorber, International Journal of Refrigeration (2017), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.04.029. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

A detailed study on simultaneous heat and mass transfer in an in-tube vertical falling film absorber

Mehdi Aminyavari1, Marcello Aprile, Tommaso Toppi, Silvia Garone, Mario Motta Department of Energy, Politecnico di Milano, Via Lambruschini 4, 20156, Milano, Italy

Highlights 

A lumped element model of a vertical in-tube falling film absorber was built



Tests have been performed on an existing Heat Transformer for validation



The model has been validated by the experimental data obtained from the tests



Sensitivity of the model with respect to the inlet condition has been evaluated



Insight is given to simultaneous heat and mass transfer along the falling film

Abstract In the present study, a numerical model of a vertical in-tube falling film absorption heat exchanger utilizing N H 3  H 2 O pair as working fluid, is developed. At first, the results of the simulations are validated with experimental data obtained from the absorber of an Absorption Heat Transformer (AHT). Then, in order to comprehend the effect of measurements errors on the results of the model, the sensitivity of the model with respect to the measured inlet conditions is investigated. Furthermore, simultaneous heat and mass transfer along the interface throughout the pipes length is studied. Results indicate that the main resistances for heat and mass transfer are the ones between gas and interface. It has been also found that the majority of the gas gets absorbed by the film in the top segments of the pipes since the driving forces along the interface are higher in these segments.

1

Corresponding author, PhD candidate in energy department of Politecnico di Milano Tel.: +390223998653 E-mail address: [email protected]

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Keywords: ammonia; water; absorption; falling film; heat transfer; mass transfer

Nomenclature

A: area ( m 2 ) Cp

: specific heat ( kJ kg  1 K  1 )

Cp

: partial molar specific heat ( kJ km ol  1 K  1 )

D h : hydraulic diameter ( m ) D

: mass diffusivity ( m 2 s  1 )

F

: mass transfer coefficient ( km o l m  2 s  1 )

g

: gravity acceleration ( m s  2 )

h

: enthalpy ( kJ kg  1 )

h

: partial molar enthalpy ( kJ km o l  1 ) : molecular weight ( kg km o l  1 )

M

: mass flowrate ( kg s  1 )

m n

: molar flux ( km o l m  2 s  1 )

P

: pressure ( kP a )  Cp     

: Prandtl number 

Pr

q

: heat flux ( kW m  2 )

R

: conduction resistance ( m 2 K kW  1 )

Re :

Sc

T

  VD h     

Reynolds number 

     D 

: Schmidt number 

: temperature ( K )

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U

: overall heat transfer coefficient ( kW m  2 K  1 )

V

: velocity ( m s  1 )

X : mole fraction of ammonia (-)

: absorbed/desorbed ammonia to total molar flux ratio (-)

Z

Greek symbols  : Heat transfer coefficient ( kW m  2 K  1 ) 1

 : mass flowrate per unit periphery ( kg m s

1

)

 : falling film thickness ( m )  : thermal conductivity ( kW m K  1 )  : dynamic viscosity ( N s m  : density ( kg m

3

2

)

)

 : rate factor 

: correction factor

Subscripts C

: coolant

G

: gas

Gb

: gas bulk

Gi

: gas interface

h

: related to heat transfer

i:

interface

j : control volume indicator L

: liquid

Lb

: liquid bulk

Li

: liquid interface

m

: related to mass transfer

sat : saturation W

: wall

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Superscript *: modified for finite rate

1. Introduction Since early 1870s when Zénobe Gramme invented the first commercial scale power plant Thomspon (1888), up to today, vast quantities of heat energy are being dumped to the atmosphere as waste in different industries. This energy that for instance is estimated as 1 9 .2 TW h yr  1 in Norway in 2009 (Enova 2009), 8 7 .8 TW h yr  1 in Germany in 2010 (IFEU 2010), and 3 6 TW h yr  1 in UK in 2014 (DECC 2014), is being considered as waste due to its low temperature and the fact that plants cannot further utilize it in any part of the cycle. An option to get advantages of this enormous source of heat is upgrading it to a useful temperature level through the adoption of Absorption Heat Transformers (AHTs). Additionally, AHTs can also be used to upgrade lowtemperature renewable energy sources, such as geothermal and solar. In absorption heat pumps, the absorber is acknowledged to be the most critical component in terms of cost, sizing and cycle performance (Fernández-Seara et al., 2007 and Goel and Goswami, 2005). Besides, due to the simultaneous heat and mass transfer between the gas and the liquid phases occurring during the absorption process which influences the system’s performance significantly, the mathematical modeling of absorption phenomena is considered as a problematic matter. Thus, the ability to predict the behavior of the absorber is crucial in the design and optimization phases of absorption systems and the need for further investigation on the absorption process and validation of the specific modelling approach used for the different classes of absorbers is being sensed. Falling film absorber is one of the possible alternative configurations that can be integrated in AHTs along with other options such as bubble absorber, packed bed absorber, tube-in-tube or shell

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and tube absorber. The issue of heat and mass transfer in falling film absorbers has been the focus of many previous researches and different approaches have been presented. Kang et al. (1998) and Kang et al. (2000) considered mass transfer resistance in both the gas and liquid phase and their results indicate that the mass transfer resistance in the solution side is the dominant one. Different results have been found by Potnis et al. (1997) and Gommed et al. (2001) who investigated the same situation, concluding that gas phase has more effect on the overall mass transfer. In a review paper conducted by Killion and Garimella (2001) it is also confirmed that in falling film absorption modeling there is a disagreement among the authors upon the choice of dominant mass transfer resistance. Concerning the heat transfer phenomena along the gas-liquid interface, in earlier works, including the study carried out by Iedema et al. (1995), the heat transfer equations have not been corrected in order to take into account the simultaneous effect of the mass transfer flux on the thermal boundary layer. Later (Bird et al. (2006)), it was proved that this effect needs to be considered to properly model the phenomenon. Kang et al. (1999) performed an experimental analysis on ammonia-water falling film absorption process in a plate heat exchanger with enhanced surfaces. They examined the effect of solution and gas flow characteristics and inlet concentrations. They proposed Sherwood and Nusselt number correlations as a function of Reynolds number of the flows, inlet sub-cooling and inlet concentration difference. Goel and Goswami (2005) performed an analytical investigation on the combined heat and mass transfer process in a counter-current N H 3  H 2 O lamella plate absorber. In their work, the correlations proposed by a a et al. (1987) and Yih (1987) were employed to calculate the heat transfer coefficients (  ), for gas-interface and liquid-interface respectively; the correlation extracted from Wilke (1962) was applied to obtain the heat transfer coefficient between the liquid film and the tube wall. They revealed that the absorption rate increases when the coolant and solution inlet temperature is reduced, while it decreases when the coolant flow rate is reduced. Lin et al. (2011) conducted an analysis on a two-stage air-cooled ammonia-water absorption refrigeration system which was designed to deliver 5 kW cooling capacity. They also used the same

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set of correlations as the ones employed by Goel and Goswami (2005). Based on their observations, mass transfer resistance mainly exists in the solution stream while the heat transfer resistance is mainly due to the cooling air side. Sieres and Fernández-Seara (2007) presented a general differential mathematical model in order to simplify the simultaneous heat and mass transfer analyzes in different components of ammonia-water absorption system. They suggested a map of possible solutions of the mass transferred composition z depending on the interface temperature range. This paper presents a finite difference model for a co-current in-tube vertical falling film absorption system to predict the simultaneous heat and mass transfer phenomena in the absorber. The hypothesis and related set of equations for developing the mathematical model along with the solving procedure are presented. Given the uncertainty of the relative magnitude of the thermal resistance in the liquid and gas phases, both the contributions are calculated. The model is validated against the experimental data obtained from an AHT’s absorber and to prove the reliability of the results, a sensitivity analysis has been carried out which shows that they are not affected by the uncertainty in the measurement of the inputs. Finally, a set of very detailed results about the interface properties and the effect of different parameters on the performance of the machine has been provided in order to give a further insight into the simultaneous heat and mass transfer phenomena.

2. Mathematical Model A mathematical model is developed for the vertical falling film absorber schematically represented in Fig. 1. As depicted, the system consists of an array of vertical pipes that pass through two perforated round plates, one at the bottom and the other at the top. The two plates are welded to the pipes and the shell, so that the coolant stream between the shell and the tubes is separated from the ammonia-water mixture. The coolant water enters the shell side of the absorber from the bottom, while gas is entering the absorber vertical pipes from the top, along with the weak liquid solution that flows downward thanks to gravity. Page 6 of 27

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Initially, the rich in ammonia gas and weak in ammonia liquid solution come in contact in the top pool of the absorber. Here, due to the sub-cooled state of the liquid solution, part of the gas is absorbed. Consequently, at the entrance of the pipes, a variation of the flowrates of gas and liquid solution, respectively in reduction and increase with respect to the entrance of the absorber, occurs. Additionally, since the pool section is completely isolated from the environment, this absorption is adiabatic and the released heat of absorption increases the temperature of both gas and liquid solution. Afterwards, the saturated liquid solution flows in each pipe as a liquid film and being cooled by the water flowing in the outer side of the pipes, the solution further absorbs the gas along its path towards the bottom and gets richer in ammonia. It is noteworthy that since absorption is an exothermic process, in order to sustain the absorption and keep the liquid solution far from boiling (i.e., in sub-cooled state), the released heat should be rejected from the liquid solution film through the wall of the pipes by means of the coolant flowing in the shell. When developing the numerical model for the heat and mass transfer calculation, the absorber is discretized along the length. The pipes are considered to be identical and the flow of cooling water, liquid solution and gas are assumed to be equally distributed among them. Under this hypothesis, the model can focus on a single pipe, which is divided in N

pipe elem ents

control volumes. Fig. 2

shows the discrete control volume with the sign convention adopted for heat and mass fluxes. The following assumptions, mostly applied in the modelling of falling film absorbers by other authors (Fernández-Seara et al., 2005 and Goel and Goswami, 2005 and Sieres and FernándezSeara, 2007), are made in the construction of the mathematical model of the system. (1) The flow is one-dimensional and in steady-state condition. (2) The thermal losses towards the environment are neglected because the envelope has been

insulated and it is calculated that the heat losses does not exceed

70

W, which corresponds

to less than 2 % of the heat duty. (3) No chemical reaction is taking place at the interface.

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(4) The gas and liquid are in equilibrium at the interface (Lewis and Whitman, 1924). (5) The internal wall of the pipe is homogeneously wetted by the thin liquid solution film;

therefore there is no direct contact between the gas and cooling wall. (6) The heat and mass transfer surfaces are equal and the heat and mass transfer resistances are

confined to a thin region close to the interface, as described by Bird et al. (2006). (7) The only driving force for the mass transfer is the concentration difference between the liquid solution and the gas (i.e., mass transfer due to pressure and thermal difference is

neglected). (8) Gas and liquid solution at the inlet of the heat exchanger go through an adiabatic mixing

before entering the pipes. (9) Pressure inside the pipes is considered homogenous and equal to the inlet pressure and the

gas and liquid solution are equally distributed in all the pipes. (10) The effect of non-absorbable gases is neglected. Unlike for H 2 O  LiBr appliances, the inlet of air from the environment is not an issue for N H 3  H 2 O heat transformers, as all sections operate at pressures higher than the atmospheric pressure. Non absorbable gases can be found at the beginning of the activities, as a consequence of the filling of the circuit with the solution. Once such gases have been removed, they have not been found in the following periodical checks. (11) Longitudinal conduction is neglected in both the pipe and the fluid domains.

Referring to assumption 3 and taking into account that the interface itself contains no significant mass (Bird et al., 2006), one can consider continuity in the total mass flux at the interface for any species being transferred. Therefore, for the control volume shown in Fig. 2, it can be written: n N H 3 ,G i  n N H 3 , L i  n N H 3 ,i

(1a)

n H 2 O ,G i  n H 2 O , L i  n H 2 O ,i

(1b)

The positive value for the molar flux indicates that mass is entering the liquid solution from the interface (subscript “Li”) and leaving the gas stream towards the interface (subscript “Gi”). The

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ammonia molar flux entering the liquid can be calculated on the basis of a mass transfer coefficient *

FLi

, as follows: (2)

*

n N H 3 , L i  F L i ( X L i  X L b )  X L i ( n total ,i )

and consequently for the gas side as: *

n N H 3 , G i   FG i ( X G i  X G b )  X G i ( n total ,i )

(3)

It is worth noting that the change in the sign is due to outward molar flux convection adopted with respect to the gas volume. In equation (2) and (3) the total molar flux through the interface is the sum of ammonia and water molar flux getting absorbed: n total , i  n N H 3 , i  n H 2 O , i

(4)

Herewith, it is useful to mention that the ammonia molar flow rate transferred through the interface, n N H 3 ,i ,

following (Treybal, 1968 and Sieres and Fernández-Seara, 2007 and Goel and Goswami,

2005 and Lin et al., 2011), can also be expressed as:

 Z  X Gi  n N H 3 , G i  FG . Z . L n    Z  X Gb 

(5)

 Z  X Lb  n N H 3 , L i  F L .Z . L n    Z  X Li 

(6)

where Z 

(7)

n N H 3 ,i n total , i

However, using these correlations may cause two potential difficulties in the numerical solving procedure of the mass balance: (1) There should be a specific division on the domain in which one looks for the proper value of Z which satisfies equation (1) as suggested by Sieres and Fernández-Seara (2007) in order to skip the asymptotic discontinuity of n N H

3

,Li

and n N H

3

,G i

.

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(2) Even though one makes the division, mentioned above, in some specific cases where FG is

much smaller than F L , numerical problems may arise in approaching solutions near the asymptotic values. Therefore, the authors chose to apply the basic equation (2) and (3), presented by (Bird et al., 2006 and Treybal, 1968) and used e.g. by Kim et al. (2003), in order to skip the mentioned problems. Applying the right correlation for heat and mass transfer in the falling film absorption is key for a successful analytical study. Once a proper correlation for either heat or mass transfer is chosen, the *

Chilton and Colburn (1934) analogy can be adopted to obtain the other. The parameters F L i and *

FG i in equation (2) and (3), are the mass transfer coefficients between liquid-interface and gas-

interface for finite flux, respectively, which can be calculated as below: *

(8)

*

(9)

F L i  F L i m L FG i  FG i m G

where FL i and FG i are the mass transfer coefficients at low mass transfer rates obtained from the literature and  m L and m G are the mass transfer coefficient correction factors for finite mass transfer that can be calculated as defined by Bird et al. (2006): 

 mL

e

 mL

 mL  



 mG  

 mG

1 e

(10)

  1

  mG

(11)

  

Where  mL and  m G are called rate factor and are defined by equation (12) and (13) respectively.  mL 

 mG 

(12)

n total , i FL i  n total , i

(13)

FG i

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The liquid-side mass transfer coefficient, FL i , was obtained from the correlation developed by Yih (1987). His simplified model was developed to describe the heat and mass transfer through a gasliquid or solid-liquid interface of a wavy or turbulent falling liquid film over a wide range of Reynolds as presented below:

FL i

1  2 3  (0.01099 R e 0.3955 Sc 0.5 )( D L  L )  g   film L   2  ML     1  2 DL  L  g   3  0.2134 0.5   (0.02995 R e film Sc L )( ) 2  ML     1  2 3    D  g  0.6804 0.5 L L (0.0009777 R e Sc )( )  film L  2  ML     

49  R e film  300

(14)

300  R e film  1600

1600  R e film  10500

where R e film 

4

(15)



being  the mass flow rate per unit periphery. The gas-side mass transfer coefficient, FG i , instead, has been derived by applying the ChiltonColburn analogy on the heat transfer coefficient between the bulk gas and the interface given in (Rohsenow and Hartnett, 1973 and a a et al., 1987). This coefficient is developed for laminar flow conditions inside a duct with a uniform surface heat flux. (16)

 G    di 

 G i  4.364 

Therefore FG i can be written as: FG i 

 Gi C P , G M G  Sc G P r G

(17)



2 3

In a similar manner, by applying Chilton-Colburn analogy, the convective heat transfer coefficient between the liquid solution and the interface can be expressed as:

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 Li

  

 F C p M  Sc P r  2 3 L L L L  Li  2 3   F L i C p L M L  Sc L P r L    F C p M  Sc P r  2 3 L L L L  Li

  

49  R e film  300 300  R e film  1600

(18)

1600  R e film  10500

The heat transfer between the bulk gas and the liquid solution is consisting of two parts, the sensible heat transfer due to the mass transfer across the interface and the convective heat transfer due to the temperature gradient between the two phases. Since heat and mass transfer occurs simultaneously, the convective part of the heat transfer should be modified by a correction factor called “ h ” which will take into account the effect of the mass transfer on the convective heat transfer part. q L i  q L i , sensible  q L i , convective

(19)

where (20)

q Li , sensible  n N H 3 ,i hLi , N H 3  n H 2 O ,i hLi , H 2 O q L i , co n vective   L i

hL

 Ti

 TLb 

(21)

And likewise, it can be also written for the gas phase that, q G i  q G i , sensible  q G i , convective

(22)

In which (23)

q G i , sensible  n N H 3 ,i hG i , N H 3  n H 2 O ,i hG i , H 2 O q G i , co n vective   G i

hG

 TG b

 Ti 

(24)

Considering the energy continuity across the gas-liquid interface, it can be said that: q Li  q G i  q i

(25)

In equation (21) and (24),  hL and hG which are respectively the convective heat correction factor for liquid and gas phase can be calculated as follows (Bird et al., 2006 and Treybal, 1968): 

 hL

e

 hL

 hL  



 hG  

 hG

1 e

(26)

  1

  hG

(27)

  

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Where  hL and  hG are the parameters depending on the partial molar specific heats, the molar flux of the species and also the heat transfer coefficient of the stream and can be computed as:  hL 

(28)

n N H 3 ,i C p L i , N H 3  n H 2 O ,i C p L i , H 2 O

 Li

and  hG 

(29)

n N H 3 ,i C p G i , N H 3  n H 2 O ,i C p G i , H 2 O

 Gi

It is worth mentioning that partial enthalpies and partial molar specific heats should be calculated at the interface condition as a function of temperature, concentration and pressure as shown below: h Li , N H 3  f ( X Li , Ti , P )

(30)

hG i , N H 3  g ( X G i , Ti , P )

(31)

C p Li , N H 3  r ( X Li , Ti , P )

(32)

C p G i , N H 3  y ( X G i , Ti , P )

(33)

Where, as declared in assumption 5: X L i  f L , sat (Ti , P )

(34)

X G i  f G , sat (Ti , P )

(35)

Similarly, equation (30) to (35) can be written for water as well. Based on the control volume and the positive sign convention shown in Fig.2, one may write the mass and energy balance for the j th gas control volume as below: m G ( j  1)  m G ( j )  ( m N H 3 , i  m H 2 O , i )

(36)

m G ( j  1) hG ( j 1)  m G ( j ) hG ( j )  q i Ai

(37)

Accordingly for the liquid volume: m L ( j  1)  m L ( j )  ( m N H 3 , i  m H 2 O , i )

(38)

m L ( j 1) h L ( j 1)  m L ( j ) h L ( j )  q i Ai  qW AW

(39)

In these equations m G stands for the total mass flow rate of the bulk gas and m L for the bulk liquid

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solution, A is the heat transfer surface and qW indicates the heat flux rejected from the solution by the coolant through the wall, which can be calculated as: qW  U total (T Lb  TC )

(40)

Here U total is the overall heat transfer coefficient through the wall, which brings together the various thermal resistances between the solution liquid film and the coolant: U total 

(41)

1 1

 LW

 RW 

1

C

In the expression above, RW is the conductive resistance of the pipe,  LW stands for the heat transfer coefficient between the solution liquid film and the inner wall of the tube, calculated according to Gesellschaft (2010):

 LW

1     L 3 1.43 R e film       film   2  0.344 5 0.0136 R e Pr film  

R e film  400

(42)   L    film

   

R e film  400

where

 film

1  1 2 3   3  L  Re3 film  2     gL   1 8 2   3 L  3  0.302 R e 15film  2    gL  

R e film  400

(43) R e film  400

and  C is the cooling heat transfer coefficient between the coolant and outer wall of the tube that can be calculated by Dittus Boelter correlation (Incropera and DeWitt, 1990) valid for a forced flow inside an annulus:   C  0.8 0.33  0.023 R e P r     Dh  c      0.8 0.4 0.023 R e P r  C    Dh  

cooling

(44)

heating

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And therefore one can write the energy balance for the coolant with respect to the Fig. 2 as below: m C ( j  1) hC ( j  1)  qW AW  m C ( j ) hC ( j )

(45)

3. Solving procedure In the present model, a finite difference method is used to solve the system of nonlinear equations based on what Goel and Goswami (2005) suggested as the steps of performing energy and mass balances. The model consists of two main functions; the first function gets the liquid solution and gas inlet conditions and calculates the unknown values for all the differential segments marching downward until the bottom. In this procedure, in order to write the energy and mass balance of each segment, the conditions of the parallel neighbor coolant segment need to be known. Therefore as a first try, a value will be assigned to the variables of each segment of coolant, so that function 1 can proceed all the way down to the end of the absorber. Afterward, function 2, which is in charge of calculating the unknowns of coolant segments, will march upward, having the input conditions of coolant at the bottom, and considers the most recent results of function 1 to perform the mass and energy balances. Once function 2 has reached the top segment, it will pass the updated values of coolant to function 1 and this function will start its calculation again. This loop will be continued until all the unknown values of each segment converge to a specific value within a tolerance of less than 10  8 . More in detail, regarding the energy and mass balances across the interface for each differential segment presented in Fig. 2, considering that Ti , n N H

3

,i

and n H

2 O ,i

are all unknown, the following

steps have been considered in function 1: (1) Guess a Ti for j th segment. (2) Find the value of n to ta l , i in equation (2) and (3) that satisfies equation (1a).

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(3) Considering the calculated n N H value of n H

2 O ,i

3

,i

in step (2) and utilizing eq. (4), calculate corresponding

.

(4) Having the values of Ti , n N H

3

,i

and n H

2 O ,i

, employing equation (19) and (22), check the

validity of equation (25). (5) If equation (25) is not satisfied, go back to step (1) and guess a new value for Ti , if it is satisfied, proceed to element j  1 . The complete flowchart of the solving procedure is demonstrated in Fig. 3. 4. Experimental methodology 4.1. Experimental setup The results of the model were compared against the experimental results obtained from the absorber of a prototype single-stage water-ammonia heat transformer shown in Fig. 4. The absorber consists of 3 7 tubes of 1 m length, while outer and inner diameters are 1 5 .8 mm and 1 3 .8 mm respectively. The tubes are placed in a triangle arrangement with 1 6 mm center to center distance. The bundle forms a hexagon with side length of 5 7 .5 8 mm, surrounded by a shell 2 mm away from the outer tubes. The data points are obtained at fixed inlet conditions: the coolant temperature and flow rate are kept constant by a hydraulic circuit providing the set values with  0 .0 5  C and  10 l h  1 stability. Constant gas and solution inlet conditions (points 3 and 4 according to Fig. 1) were obtained through stable operation of the absorption heat transformer: the standard deviation of the temperatures is below 0 .1  C on the whole acquisition period (eight minutes, started at least after five minutes of stability). Coolant inlet and outlet temperatures (points 1 and 2) are measured by PT100 thermoresistances, while the flow rate is provided by a magnetic flow meter. The temperature influence on the water properties (density and specific heat capacity) is considered when

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calculating the exchanged power on volumetric flow rate and temperature difference which will result in an uncertainty on the heat duty always below 5%, usually under 3.5%. Gas and solution temperatures in points 3, 4 and 5 are measured by T-type thermocouples placed in contact with the steel tubes properly isolated to minimize heat transfer towards the environment and improve the accuracy. Capacitive pressure transducer provides the pressure in the absorber, while the solution outlet mass flow rate (point 5) is measured by a Coriolis flow meter which also provides a density reading that can be used to calculate the concentration. The probes used for the measurement are reported in Table 1, together with the overall uncertainty associated with the measure, is obtained as combined uncertainty of the sensor, the data acquisition chain and signal digitalization. For what concerns the remaining inputs, the refrigerant concentration and flowrate (point 3), are to be measured with good accuracy. Therefore, together with the concentration and mass flow rate of point 4, they are obtained indirectly from a thermodynamic model of the heat transformer, following the procedure presented in Aprile et al. (2015). The cycle relevant temperatures, the pressures and the heat duty at the external heat exchangers, together with the already mentioned mass flow rate of rich solution have been measured. The position of the temperature sensor installed on the heat transformer is reported in Fig. 5, where the cycle scheme is also reported. The relevant state points for the absorber modelling, have been numbered according to Fig. 1. The measured data have been used to tune a steadystate model of the heat transformer, where balances of mass, species and energy for each components have been solved under the hypotheses of phase equilibrium of two-phase points, negligible pressure drop in the connecting pipes as well as negligible kinetic and potential energy differences. The numerical model has been tuned for each working condition modifying parameters such as the UA value of the heat exchangers or the sub-cooling at some components outlet, until the calculated state point match the available experimental measures with a deviation smaller than the measurement accuracy. Once the identification process is complete, it

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returns a good estimation of the unknown mass flow rate and concentrations required as input to the absorber model. 4.2. Experimental data In the present paper, nine experimental tests at different operating conditions are presented for the sake of validation of the model. In Table 2, the inlet conditions of coolant, gas and liquid solution are reported for the nine cases which has been identically set as the input data of the mathematical model as well. 5. Model validation The numerical model has been validated by comparing the calculated outlet of the liquid solution (point 5), outlet of coolant water (point 2), and total rejected absorption heat with corresponding experimental data. Table 3 presents these data, obtained from the experiment as well as the deviation of the results of the model from these data. It is noteworthy that the errors on temperatures and concentrations have been reported as a direct subtraction  y experim ental  y m od el  while concerning the mass flowrates and heats, these values have been expressed as percentages:   y experim ental  y m od el     100    y experim ental  

As demonstrated in Table 3, overall, it can be seen that the present simulation results are in a very good agreement with the experimental ones. To begin, the outlet temperature of point 2 and 5 has been predicted mainly with an accuracy of less than half a degree and regarding the ammonia concentration of point 5, this accuracy varies between 0 .0 0 1 5 to 0 .0 1 8 9 . Solution sub-cooling of point 5, which can be considered as a good indicator of the mass transfer along the film, has also been predicted very well with an accuracy of 0 .0 1  C to 0 .8 8  C . Last but not the least, it can be noted that the mass flowrate of liquid solution at point 5 has been predicted with almost 2 .1 % accuracy on average. The reported data demonstrate that the developed

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model has a good accuracy in simulating the performance of the in-tube falling film absorption heat exchangers. 6. Results and discussion In this section, the input conditions of test 5, which has the minimum root mean square error with respect to the other tests, have been chosen for a further study of the model results in order to enhance the understanding of the absorption process inside the tubes. However, these results and discussions can be extended to all the other tests, reported in this article. First of all, the effect of the inlet data (explained in section 4.1) on the results of the model has been investigated; Table 4 reports the sensitivity of the model to variations of the inputs in a certain range. This range is equal to the measurement error for the measured values, while for those variables which are calculated through the thermodynamic model, an estimated model accuracy was used. It is a range of variation of the parameter that allows the overall combined error of the thermodynamic model to stay within a range which is defined as providing a good identification of the whole cycle. Moreover, in the cases examining the effect of reducing m G and x G as well as increasing m S , the changes of inlet values are banded by the critical values that model can function without returning an unphysical result ( m G becoming negative at the bottom of the tubes). To this end, each inlet conditions listed in Table 2 is altered by the defined values, while keeping the other inlet conditions unchanged and the effect of the changed variable on the same set of data that had been used for validation is reported (see Table 4). It can be seen that these ranges of error in reading the inlet values has almost negligible effect on the results of the model. Fig. 6 compares the temperature profiles of gas, liquid solution film, interface and the coolant water. It is worth noting that, due to the adiabatic mixing of the gas and liquid solution in the top pool of the absorber, the temperature of both streams increase respectively from 5 9 .5  C (circle) and 7 2 .1  C

(diamond) at the inlet of the absorber to 8 8 .9  C at the inlet of the pipes. As shown in this

line graphs, the temperature of liquid solution film decreases rapidly in the top portion of the pipes Page 19 of 27

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and it reaches 5 0 % of its total temperature decrease in the first 1 6 .2 cm . Concerning the interface temperature, it follows the trend of liquid solution film while sustaining a positive value difference all along the absorber length. It is noteworthy that due to lower thermal conductivity of gas with respect to liquid solution film, the temperature fall of gas stream is less steep and all three profiles meet at the bottom of the absorber where the majority of the gas flowrate supplied at the inlet is already absorbed by liquid solution film. The released heat of absorption from the pipes is rejected by the coolant water of the shell side which results in an increase of its temperature from 7 2 .0  C at the bottom to 7 9 .2  C on top of the absorber. Fig. 7 demonstrates the mass flowrate profiles of the gas and liquid solution film. It can be noticed that as the two streams proceed towards the bottom of the absorber, the gas will continuously get absorbed by the liquid film, which will result in a decreasing and an increasing trend for gas and liquid solution film flowrates, respectively. As expected, since the interface itself contains no significant mass (Bird et al., 2006), the decrease in mass flowrate of gas ( 9 .6 1 1 9 kg h  1 ) is equal to the increase of the mass flowrate of liquid solution film. Regarding the concentrations, the gas which is almost pure in ammonia ( 99.85% ) at the inlet of absorber (circle), after going through the adiabatic mixing process with liquid solution pool, enters the pipes with 9 8 .4 3 % ammonia concentration and correspondingly the concentration of ammonia in liquid solution increases from 4 6 .4 8 % (diamond) to 5 1 .5 4 % . These results can be observed in Fig. 8, where the trend of development of concentration profiles along the pipes are also presented. As it can be seen, all profiles show a rapid increase at the entrance of the pipes which is followed by a moderate increase throughout the length of the pipes toward bottom. It can also be underlined how the ammonia concentration at the liquid interface is always higher than liquid solution film ([ x Li  x Lb ]  0) and similarly the concentration at the gas interface keeps a higher value than the one in the bulk gas stream ([ xGi  xGb ]  0) along the length of the pipes. This situation is what commonly happens in absorbers as mentioned by Sieres and Fernández-Seara

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(2007). The bar chart in Fig. 9 compares the heat duty of different portions of the pipes divided in 2 0 sections of 5 cm long each. It can be observed that the exchanged heat is maximum at the top section of the absorber and decreases gradually along the axial direction. As a result, the top 1 0 cm rejects almost 2 2 % of the total heat duty and the first 3 0 cm rejects about half of the total absorption heat. However this contribution reaches an almost steady situation in the lowest 2 0 cm . Taking into account equation (19) and (22) and the constraint presented in equation (25), it can be seen that part of the absorption heat is the sensible heat carried by the absorbed molecules of the gas into the liquid. Therefore the behavior in Fig. 9 would be justifiable by looking at Fig. 10. This diagram illustrates that the ammonia and water absorption flowrates from gas to liquid phase show a very significant increase in the first 5cm and reach their peak of 0 .1 0 8 7 6 kg m  2 s  1 and 0 .0 0 3 9 5 2

kg m s

1

, respectively. Nevertheless, absorption of ammonia is of a more importance than that of

water, being about two orders of magnitude higher. On the other hand, the driving potential of mass transfer is the difference between concentration of interface and gas and also between interface and liquid (see equation (2) and (3)). This driving force is presented in Fig. 11 along the length of the pipes and it can be effortlessly comprehended that this parameter has higher average value in the top portion of the pipes which augments the mass transfer and therefore the released heat of absorption. It is noteworthy that the change in trend of the graphs presented in Fig. 10 and Fig. 11 near the bottom section of the pipes is due to the fact that the heat transfer coefficient of coolant is higher at the inlet of the shell (point 1), caused by the entrance length effect. Furthermore, the rest of heat of absorption is the share of convective heat transfer that strongly depends on the temperature difference between the gas and liquid solution film (see equation (21) and (24)). This driving force is also attainable in Fig. 11 along the length of the pipes and it can be realized that this parameter also favors the absorption more at the entrance section than the rest

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parts of the tubes. Additionally, the values of heat and mass transfer coefficients between the gas and interface and also between the liquid solution film and interface are presented in Fig. 12. It is perceptible from the graphs that the main resistance for heat transfer is the one between the gas and interface, being two orders of magnitude greater than the one corresponding to liquid solution film to interface. This confirms the result introduced by Potnis et al. (1997) and Gommed et al. (2001) of negligible thermal resistance between liquid and interface. Similarly, the mass transfer coefficient between gas and interface is lower than the one between liquid solution film and interface, although only by a factor of about 2. It is noteworthy that the equivalent local heat transfer coefficient between the interface and the inner wall of the tubes varies between 1.21 [kW m  2 K  1 ] and 1.48 [kW m  2 K  1 ] which is in agreement with experimental film heat transfer coefficients reported by Hoffmann and Ziegler (Hoffmann L. and Ziegler F., 1996) and also Kang et al. (Kang et al., 1999). The trends for the heat transfer coefficient reported in Fig. 12 can be commented referring to the values of Reynolds and Prandtl corresponding to gas and liquid film streams which are demonstrated in Fig. 13. It is noteworthy that due to the reduction of temperature from top to bottom of the absorber, the value of kinematic viscosity of gas and liquid film are decreasing and increasing, correspondingly. This change should normally favor the increase of Reynolds value of gas and the decrease of Reynolds value of liquid; but as the figure reveals, instead, there is a steep fall in Reynolds of the gas stream due to the absorption and reduction of its mass flowrate which correspondingly causes a small increase in Reynolds of the liquid film by increasing its mass flow rate. 7. Conclusion In the present study, a model of an in-tube vertical falling film absorber was put forward to investigate the simultaneous heat and mass transfer phenomena along the interface of gas and liquid solution after validating the model with experimental data, achieved from the absorber of an AHT.

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Results indicate that the main resistances for heat and mass transfer along the film are the ones between the gas and interface. Moreover it has been shown that the gas and liquid solution that enter the absorber from the top go through an adiabatic mixing process before entering the pipes which results in an increase in TG , T L , m L , X L and a decrease in m G and X G . Furthermore, it was found that since both heat and mass transfer driving forces along the interface are higher in the top segments of the pipes, majority of the gas gets absorbed by the film in these sections (e.g. 5 0 % of m G in the top 3 5 .2 cm).

References Aprile, M., Toppi, T., Guerra, M., Motta, M., 2015. Experimental and numerical analysis of an aircooled double-lift NH3–H2O absorption refrigeration system. International Journal of Refrigeration 50, 57-68. Bird, B., Stewart, W., Lightfoot, E., 2006. Transport Phenomena, Revised 2nd Edition. John Wiley & Sons, Inc. Chilton, T.H., Colburn, A.P., 1934. Mass Transfer (Absorption) Coefficients Prediction from Data on Heat Transfer and Fluid Friction. Industrial & Engineering Chemistry 26, 1183-1187. DECC, 2014. The potential for recovering and using surplus heat from industry. Enova, 2009. “Investigation of waste heat potential from industry in Norway (In Norwegian: Utnyttelse av spillvarme fra norsk industri - en potentialstudie),” Enova, Trondheim. Fernández-Seara, J., Sieres, J., Rodríguez, C., Vázquez, M., 2005. Ammonia–water absorption in vertical tubular absorbers. International Journal of Thermal Sciences 44, 277-288. Fernández-Seara, J., Uhía, F.J., Sieres, J., 2007. Analysis of an air cooled ammonia–water vertical tubular absorber. International Journal of Thermal Sciences 46, 93-103. Gesellschaft, 2010. VDI Heat Atlas. Springer Berlin Heidelberg. Goel, N., Goswami, D.Y., 2005. Analysis of a counter-current vapor flow absorber. International Journal of Heat and Mass Transfer 48, 1283-1292. Gommed, K., Grossman, G., Koenig, M.S., 2001. Numerical study of absorption in a laminar falling film of ammonia-water, ASHRAE Transactions, pp. 453-462. Hoffmann L., Ziegler F., 1996. Experimental Investigation of Heat and Mass Transfer With Aqueous Ammonia, Proc., International Absorption Heat Pump Conference September, 1, Montreal, Canada, pp. 383–392. Iedema, P., Liem, S., Van der Wekken, B., 1995. Heat and mass transfer in vapour and liquid phase of a H2O/NH3-refrigerator., 15th International congress of refrigeration, Trondheim. IFEU, 2010. “The use of industrial waste heat - techno-economic potential and energy policy implementations,” Institute for Energy and Environmental Research (IFEU), Heidelberg, arlsruhe. Incropera, F.P., DeWitt, D.P., 1990. Fundamentals of heat and mass transfer. Wiley. a a , S., Aung, W., Shah, R.K., 1987 Handbook of single-phase convective heat transfer. Wiley, New York. Kang, Y.T., Akisawa, A., Kashiwagi, T., 1999. Experimental correlation of combined heat and mass transfer for NH3–H2O falling film absorption. International Journal of Refrigeration 22, 250262. Kang, Y.T., Kashiwagi, T., Christensen, R.N., 1998. Ammonia-water bubble absorber with a plate heat exchanger, ASHRAE Transactions, Pt 1B ed, pp. 1565-1575. Page 23 of 27

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Kang, Y.T., Fujita, Y., Akisawa, A., Kashiwagi, T., 1999. Combined heat and mass transfer under different inlet subcooling modes during NH3-H2O falling film absorption process. American Society of Mechanical Engineers, New York, NY (US); Tokyo Univ. of Agriculture and Tech. (JP). Killion, J.D., Garimella, S., 2001. A critical review of models of coupled heat and mass transfer in falling-film absorption. International Journal of Refrigeration 24, 755-797. Kim, H.Y., Saha, B.B., Koyama, S., 2003. Development of a slug flow absorber working with ammonia–water mixture: part II—data reduction model for local heat and mass transfer characterization. International Journal of Refrigeration 26, 698-706. Lewis, W.K., Whitman, W.G., 1924. Principles of Gas Absorption. Industrial & Engineering Chemistry 16, 1215-1220. Lin, P., Wang, R.Z., Xia, Z.Z., 2011. Numerical investigation of a two-stage air-cooled absorption refrigeration system for solar cooling: Cycle analysis and absorption cooling performances. Renewable Energy 36, 1401-1412. Potnis, S.V., Anand, G., Gomezplata, A., Erickson, D.C., Papar, R.A., 1997. GAX component simulation and validation, ASHRAE Transactions, 1 ed, pp. 454-459. Rohsenow, W.M., Hartnett, J.P., 1973. Handbook of heat transfer. McGraw-Hill. Sieres, J., Fernández-Seara, J., 2007. Modeling of simultaneous heat and mass transfer processes in ammonia–water absorption systems from general correlations. Heat and Mass Transfer 44, 113-123. Tae Kang, Y., Akisawa, A., Kashiwagi, T., 2000. Analytical investigation of two different absorption modes: falling film and bubble types. International Journal of Refrigeration 23, 430-443. Thomspon, S.P., 1888. Dynamo-electric machinery: a manual for students of electrotechnics London: E. & F.N. Spon. p. 140. Treybal, R.E., 1968. Mass-transfer operations. McGraw-Hill, New York. Wilke, W., 1962. Wärmeübergang an Rieselfilme. VDI-Verlag. Yih, S.M., 1987. Modeling heat and mass transfer in wavy and turbulent falling liquid films.

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Fig. 1. Schematic of the falling film absorption heat exchanger Fig. 2. Differential control volume with the positive sign convention Fig. 3. Solving procedure’s flowchart Fig. 4. Absorption Heat Transformer machine using N H 3  H 2 O and falling film absorber Fig. 5. Heat transformer cycle scheme and sensors’ position Fig. 6. Temperature profiles of streams in lengthwise of the absorber Fig. 7. Mass flowrates of liquid solution film and gas along the length of the absorber Fig. 8. Ammonia concentration profiles of gas, liquid solution film, and interface along the length of absorber Fig. 9. Share of absorption of different portions of the absorber’s pipes Fig. 10. Rate of absorption of ammonia and water at the interface Fig. 11. Driving forces of heat and mass transfer between gas and liquid solution film Fig. 12. Heat and mass transfer coefficients at the interface of gas and liquid solution film Fig. 13. Reynolds and Prandtl of gas and liquid film along the length of absorber

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Table 1. Measurement uncertainties. Percentages refer to the read values. Quantity

Meter

Range

Uncertainty

Pt100 Pt100 magnetic flow meter Calculated T thermocouple capacitive P probe Coriolis flow meter Coriolis flow meter

50÷80 °C 5÷15 °C 0.4÷1.0 m3/h 3÷4 kW 40÷80 °C 15÷25 bar 40÷50 kg/h 600÷800 kg/m3

±0.10 °C ±0.15 °C 1.00% < 5% ±0.4 °C 0.5÷1.1% 0.01% 0.6÷1.0%

Table 2. Inlet conditions of the experimental tests and model Test 1 2 3 4 5 6 7 8 9

T[ ] 71.97 70.04 70.00 70.00 72.00 73.96 75.93 79.89 79.98

(point 1) P[Kpa] 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00

[

T[ ] 58.96 55.79 59.36 59.43 59.49 59.57 56.33 59.16 59.79

]

488.0 488.0 488.0 488.0 488.0 488.0 488.0 488.0 488.0

(point 3) P[Kpa] [ ] 19.95 14.22 18.86 12.40 18.95 13.03 18.31 12.42 19.53 12.98 20.04 12.83 19.99 11.55 19.72 8.64 22.86 13.43

X[-] 0.9987 0.9989 0.9984 0.9982 0.9985 0.9986 0.999 0.999 0.999

(point 4) P[Kpa] [ ] 19.95 32.54 18.86 34.01 18.95 31.36 18.31 31.35 19.53 33.14 20.04 35.36 19.99 31.96 19.72 33.12 22.86 30.81

T[ ] 72.60 69.81 70.04 70.18 72.14 73.86 76.17 79.22 80.54

X[-] 0.4611 0.4844 0.4680 0.4580 0.4648 0.4702 0.4754 0.4832 0.4682

Table 3. Outlet Conditions of the experimental tests and the error of the model Outlet experimental data Test

(point 2) T[ ]

(point 5)

79.92 76.67 77.23 77.09 79.16 81.05 81.47 83.49 86.24

73.43 71.08 70.83 70.78 73.13 75.03 76.28 79.35 80.76

(point 2)

X[-]

T[ ] [

1 2 3 4 5 6 7 8 9

Error of the model

]

46.76 46.38 44.39 43.77 46.10 48.13 43.49 42.09 44.2

0.625 0.622 0.624 0.611 0.615 0.611 0.614 0.590 0.629

[kW] [ ] 0.34 0.58 0.79 1.00 0.96 0.72 -1.08 -1.46 -1.39

4.510 3.769 4.101 4.027 4.064 4.029 3.137 2.042 3.542

T[ ] 0.3811 0.1158 0.1777 0.1311 0.0043 0.2610 0.2064 0.0028 0.2074

(point 5) T[ ] 0.2029 -0.0681 -0.2494 -0.1952 -0.0160 -0.0823 -0.2937 -0.8716 -0.0030

[%] 1.37 1.19 1.13 0.60 0.36 0.75 3.94 5.25 4.32

X[-] 0.0055 0.0048 0.0047 0.0020 0.0015 0.0035 0.0157 0.0189 0.0168

[%] [ ] -0.88 -0.53 -0.33 -0.06 -0.18 -0.38 0.29 0.87 0.01

4.63 1.81 2.31 1.79 -0.06 3.65 3.41 -0.30 2.75

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Table 4. Sensitivity of the model on inlet conditions Deviation from the results of the base case (Test 5) Inlet Changed (point (point 5) Value Parameter 2) T[ ]

T[ ]

[%]

X[-]

[ ]

[%]

59.49+0.4

=

59.89

0.0074

0.0007

0.00

-0.001

0.001

0.10

59.49-0.4

=

59.09

-0.0074

-0.0007

0.00

0.001

-0.001

-0.10

=

72.54

0.0269

0.0027

-0.01

-0.004

0.003

0.37

=

71.74

-0.0269

-0.0027

0.01

0.004

-0.003

-0.38

19.53+0.55% =

19.64

0.0923

0.0433

0.36

0.137

0.123

1.27

19.53-1.1%

=

19.32

-0.1853

-0.0591

-0.78

-0.299

-0.070

-2.66

=

72.1

0.0521

0.0860

-0.15

-0.058

0.083

-0.67

72.00-0.1

=

71.9

-0.0520

-0.0859

0.15

0.058

-0.083

0.67

488.0+1%

=

492.88

-0.0581

-0.0122

0.05

0.017

-0.015

0.18

488.0-1%

=

483.12

0.0590

0.0125

-0.05

-0.018

0.015

-0.18

12.97+8%

=

14.017

-0.035

0.006

-0.04

-0.006

0.007

-0.50

12.97-1.15% =

12.829

0.005

-0.001

0.01

0.001

-0.001

0.07

0.9985+0.2% =

1

-0.034

-0.005

-0.09

0.008

-0.007

-0.48

0.9985-0.5% =

0.9935

0.113

0.018

0.30

-0.026

0.015

1.56

33.14+1.69% =

33.70

0.083

0.046

1.52

-0.059

0.053

1.14

33.14-3%

32.14

-0.150

-0.080

-2.82

0.104

-0.093

-2.14

0.4648+1.0% =

0.4694

-0.211

-0.037

-0.75

0.054

-0.045

-3.04

0.4648-0.42% =

0.4628

0.090

0.016

0.31

-0.023

0.019

1.24

72.14+0.4 72.14-0.4

72.00+0.1

=

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