Experimental investigation on heat and mass transfer in a vertical glass bubble absorber with R124-NMP pair

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Experimental investigation on heat and mass transfer in a vertical glass bubble absorber with R124-NMP pair Wei Wang , Shiming Xu , Xi Wu , Mengnan Jiang PII: DOI: Reference:

S0140-7007(19)30541-9 https://doi.org/10.1016/j.ijrefrig.2019.12.024 JIJR 4623

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

17 September 2019 23 November 2019 24 December 2019

Please cite this article as: Wei Wang , Shiming Xu , Xi Wu , Mengnan Jiang , Experimental investigation on heat and mass transfer in a vertical glass bubble absorber with R124-NMP pair, International Journal of Refrigeration (2019), doi: https://doi.org/10.1016/j.ijrefrig.2019.12.024

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Highlights 

Heat and mass transfer of R124-NMP in a vertical glass bubble absorber have been investigated.



The key operation parameters were converted into dimensionless parameters and the effects of them on heat and mass transfer of R124-NMP were investigated.



Correlations for overall and two-phase volumetric mass transfer coefficients were proposed.



Dimensionless absorption height was introduced to express volumetric mass transfer coefficient.

1

Experimental investigation on heat and mass transfer in a vertical glass bubble absorber with R124-NMP pair Wei Wang1, Shiming Xu1*, Xi Wu1, Mengnan Jiang1

1

Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of

Energy and Power, Dalian University of Technology, Dalian 116023, China * Corresponding author E-mail address: [email protected]

Abstract: An experimental study on heat and mass transfer characteristics of R124-NMP in a vertical glass bubble absorber has been conducted under operating conditions of air-cooled absorption system. The key operation parameters, solution volumetric flow rate, temperature and mass fraction at the absorption tube entrance, vapor volumetric flow rate, orifice diameter and absorption pressure, are converted into dimensionless numbers. A sensitive study of the key operation parameters on overall heat and mass transfer coefficients and two-phase mass transfer coefficient has been performed. The overall heat and mass transfer coefficients and two-phase mass transfer coefficient increase as Rev and absorption pressure increase and decrease as orifice diameter increases. The overall heat transfer coefficient increases as Res increases and decreases as solution temperature and mass fraction increase. This trend is reversed for overall mass transfer coefficient. The increase of solution inlet mass fraction can improve the two-phase mass transfer coefficient 2

while the solution inlet temperature affects the two-phase mass transfer coefficient slightly. On the basis of the experimental data, dimensionless empirical correlations for overall and two-phase Sherwood numbers are proposed with error bands of ±10% to calculate the volumetric mass transfer coefficient for R124-NMP bubble absorption process in a vertical bubble absorber. Keywords: R124-NMP mixture, Heat transfer, Mass transfer, Bubble absorber, Dimensionless correlations

Nomenclature Abbreviations ACHRC

Absorption

compression

hybrid

R134a

1, 1, 1, 2-tetrafluoroethane

R22

Chlorodifluoromethane

refrigeration cycle

Re

Reynolds number

AH

Absorption height

Sc

Schmidt number

COP

Coefficient of performance

Sh

Sherwood number

CR

Circulation ratio

VARS

Vapor absorption refrigeration system

DAH

Dimensionless absorption height

VLE

DMAC

N, N-Dimethylacetamide

VF

DMEDEG

Dimethylether diethylene glycol

Nomenclature

DMETEG

Dimethylether tetraethylene glycol

D

DMF

N, N-Dimethylformamide

Dc

Diffusion coefficient (m2 s-1)

Ga

Galileo number

d

Diameter (m)

GAX

Generator absorber heat exchanger

g

Gravitational acceleration (m s-2)

GTBA

Glass tube bubble absorber

H

Height (m)

GC

Gas chromatography

h

Specific enthalpy (kJ kg-1)

ID

Inner diameter of outside tube (m)

HCFCs

Hydrochlorofluorocarbons

Vapor liquid equilibrium Volumetric flow

Inner Diameter of inside tube (m)

NMP

N-Methyl-2-Pyrrolidone

i

Numbers (1, 2, 3…)

R124

1-chloro-l, 2, 2, 2,-tetrafluoroethane

L

Tube length (m)

3

K

Mass transfer coefficient (kg m-3 s-1)

Subscripts

M

Molecular weight (-)

a

Absorber

m

Mass flow rate (kg s-1)

c

Critical

p

Pressure (kPa)

cw

Cooling water

Q

Thermal load (kW)

in

Inlet

q

Volumetric flow Rate (L h-1)

lm

Log mean value

T

Thermodynamic temperature (K)

o

Orifice

t

Temperature (℃)

out

Outlet

U

Heat transfer coefficient (W m-2 K-1)

ov

Overall

x

Mass fraction of refrigerant (-)

r

Reference point

s

Solution

Greek letters



Density (kg m-3)

tp

Two-phase



Difference (-)

v

Vapor



Dynamic viscosity (Pa s)

Superscripts

δ

eq

Wall thickness of inside tube (m)



Equilibrium

Dimensionless (-)

1. Introduction Vapor absorption refrigeration systems (VARS) can be applied not only in residential, industrial and commercial buildings but also in automobiles and ships (Manzela et al., 2010; Horuz, 1999; Tian-Jiao and Hong-Tao, 2019; Liang et al., 2014). VARS can be driven by low grade thermal energies to reduce the consumption of fossil energy. VARS is regarded as a very promising and effective technology to replace of the vapor compression system used commonly in automotive air-conditioning (Aphornratana and Sriveerakul, 2007; Aprile et al., 2015). Absorber is a vital component in VARS where there is a complicated heat and mass transfer process. Its performance will significantly affect the operation characteristics of VARS. Bubble and falling film types are 4

two major kinds of absorption modes in the absorber. Compared with the falling film absorber, the bubble absorber has higher heat transfer coefficient and local absorption rate, better mixing and simple vapor distribution (Kang et al., 2000; Castro et al., 2009; Kang et al., 1998). Under the automobile and ship operation conditions like accelerating or decelerating, tossing up and down, the falling film absorber cannot normally work. However, bubble absorber can normally work because refrigerant vapor is always wrapped in absorption solution during bubble absorption process (Xu et al., 2016a; Xu et al., 2013). Therefore, bubble absorber is intensely recommended to the VARS in automobiles and ships. Up to now, the heat and mass transfer characteristics of bubble absorption process have been investigated by many scholars. Kang et al. (2002a; 2002b) visualized the bubble behavior of NH3-H2O bubble absorption process and investigated the influences of critical parameters on the bubble absorber performance. The correlations of initial bubble diameter, volumetric bubble diameter and mass transfer coefficient using dimensionless parameters were developed. Lee et al. (2003; 2002) made a numerical and experimental analysis on NH3-H2O absorption process in a plate-type bubble absorber to explore the effects of vapor and solution flow rates on the absorber performance. It indicated that the increase of solution flow rate improved the heat transfer but affected on the mass transfer slightly. The numerical results agreed well with the experimental results and were helpful for designing a bubble absorber (Lee et al., 2003). Finally, correlations of Nusselt number and Sherwood number were developed. Cerezo et al. (2009) carried out an experiment on NH3-H2O bubble absorption process in a corrugated plate heat exchanger under typical conditions of absorption chillers. The influences of key operation parameters on the absorber performance were investigated. Subsequently, Cerezo et al. (2010) developed a 5

mathematical model to analyze the effects of the selected operation parameters on the absorber thermal load and mass absorption flux. The results agreed well with the experimental results. Finally, correlations for heat transfer coefficient and pressure drop were presented both with an error band of ±8%. For enhancing the mass transfer under solar cooling operation conditions, Chan et al. (2018) conducted an experimental study on a bubble absorption mode in a plate heat exchanger type absorber employing NH3-LiNO3 as working fluid. The results showed that the absorption flux was from 0.015 to 0.024kg m-2 s-1 and the mass transfer coefficients varied from 0.036 to 0.059m s-1. The heat transfer coefficients varied from 0.9 to 1.8kW m-2 k-1 and from 0.96 to 3.16kW m-2 k-1 for transition and turbulent conditions, respectively. Based on the experimental data, the Nusselt number correlations were proposed for the bubble absorption process with NH3-LiNO3 working pair. However, there are many shortcomings for NH3-H2O working pair applied in refrigeration system of automobile and ship (Wu et al., 2019), such as, toxicity and flammability of NH3, a required rectifier in VARS, a relative higher working pressure under air-cooled condition. Some organic working pairs can be applied in VARS to replace of NH3-H2O mixture to overcome these shortcomings, which had been investigated by many scholars (Fatouh and Murthy, 1995; Arun et al., 1998; Borde et al., 1997; Jelinek et al., 2008; Borde et al., 1993). In the VARS with organic working pairs, bubble absorber has also been paid more attention by many scholars (Sujatha et al., 1997a; Sujatha et al., 1997b; Sujatha et al., 1999; Suresh and Mani, 2010, 2012a, b, 2013). Sujatha et al. (1997a) numerically investigated the heat and mass transfer and performance of co-current vertical tubular bubble absorber using R22-DMF as working pair. A correlation for volumetric mass transfer coefficient was proposed with the error bands of ±10%. The authors selected R22-DMF, R22-DMAC, 6

R22-DMETEG, R22-DMEDEG, and R22-NMP as working pairs to develop a model of absorption process in a vertical bubble absorber. The model can be used to analyze the effects of vapor and solution properties on the volumetric mass transfer coefficient (Sujatha et al., 1997b). A correlation for volumetric mass transfer coefficient was proposed. The authors also conducted experiments on R22-DMF bubble absorption process to investigate the heat and mass transfer and pressure drop (Sujatha et al., 1999). The experimental results compared well with the numerical results (Sujatha et al., 1997a). Suresh and Mani (2010) firstly developed a model by the phenomenological theory to numerically analyze the heat and mass transfer process of R134a-DMF in bubble absorber. The results indicated that the average heat and mass transfer coefficients increased with the increase of vapor mass flow rate, solution inlet temperature and mass fraction, but decreased with the increase of solution pressure. Then the authors investigated the bubble behavior (Suresh and Mani, 2012a) and heat and mass transfer characteristics (Suresh and Mani, 2012b) of R134a-DMF in a glass tube bubble absorber (GTBA) by experiments. A correlation for volumetric mass transfer coefficient for R134a-DMF in the GTBA was proposed with error bands of ±20%. Finally, the authors conducted an experiment on heat and mass transfer characteristics of R134a-DMF in a compact copper tube bubble absorber (Suresh and Mani, 2013). A correlation for volumetric mass transfer coefficient for R134a-DMF bubble absorption was proposed with error bands of ±12%. The R124-DMAC working pair was thought to be more suitable for applying in the VARS driven by vehicle waste heat due to its relatively low condenser pressure, generation temperature, circulation ratio (CR) and high COP under air-cooled condition (Arun et al., 1998; Borde et al., 1997). Although R124 belongs to HCFCs, it mainly exists in the form of solution in the VARS. Even if the solution leaks out of the VARS, R124 vapor separated out from solution is quite limited. With this consideration, the absorption-compression 7

hybrid refrigeration cycle (ACHRC) employing R124-DMAC as working pair was proposed (Xu et al., 2013; Li and Xu, 2013). Xu and Jiang et al. conducted a series of experimental studies on bubble absorption characteristics for R124-DMAC (Xu et al., 2016a; Jiang et al., 2015; Xu et al., 2016b; Jiang et al., 2017a; Jiang et al., 2017b). The flow patterns and AH of R124-DMAC bubble absorption process were captured by a visualization experiment (Xu et al., 2016a). A correlation for AH was proposed (Jiang et al., 2015; Xu et al., 2016b). Meanwhile, the influences of key operation parameters on heat and mass transfer were studied and a correlation for volumetric mass transfer coefficient for GTBA was developed (Jiang et al., 2017a). Finally, a vertical copper bubble absorber was made to investigate local heat and mass transfer characteristics of bubble absorption process (Jiang et al., 2017b). Correlations for heat and mass transfer coefficients for copper bubble absorber were developed. R124-NMP pair is also thought to be a potential working pair for ACHRC. Compared with R124-DMAC pair, R124-NMP has a higher boiling point difference and solubility (Xu et al., 2017) and VARS with R124-NMP pair has a better performance (Borde et al., 1997). Therefore, R124-NMP pair seems more favorable to be used in ACHRC. However, the investigation on heat and mass transfer characteristics of R124-NMP in bubble absorption process has few up to now. This work is different from our previous work (Xu et al., 2016a; Jiang et al., 2017a) . In here, R124-NMP pair is selected as working fluid to investigate the heat and mass transfer in a vertical bubble absorber. The key operation parameters are firstly nondimensionalized, and then the effects of dimensionless parameters on heat and mass transfer and the mass transfer coefficient of two-phase region in R124-NMP bubble absorption process are investigated. Finally, two dimensionless correlations of mass transfer coefficient are proposed for 8

vertical bubble absorber designing. By their vapor-liquid equilibrium (VLE) data of R124-NMP pair (Xu et al., 2017), the thermophysical properties of R124-NMP pair are given in Appendix A. 2. Experimental platform and procedures 2.1 Experimental platform An experimental platform is set to explore the heat and mass transfer characteristics of R124-NMP bubble absorption process in a vertical GTBA. Fig.1 depicts the schematic diagram of experimental platform and the structure of bubble absorber. Details of the experimental platform and primary devices are described in our previous works (Xu et al., 2016a; Jiang et al., 2017a). The specifications of experimental devices and instruments in Fig.1 are listed in Tab.1. Fig.2 shows the practicality photo of experimental platform. 12

2

P

15

T

12

11

VF3

T

9

3 11

1

8

H=0.63m

12

Solution Outlet

12

Cooling Water Inlet

12

ID D

13 11 E-13

14

T

12

10

16 12

Cooling Water Outlet

4

P

do

V-8

5

T

VF1

6

P

12

7

12 VF2 T

ID=0.036m D=0.014m δ=0.003m

Solution Inlet

Solution Inlet Vapor Inlet

(a)

(b)

Fig.1 Schematic diagram of (a) heat and mass transfer experimental platform with vertical GTBA and (b) the structure of the GTBA

9

Fig.2 Practicality photo of heat and mass transfer experimental platform with vertical GTBA 2.2 Experimental procedures The experimental procedures are briefly introduced because the relevant experimental process has been described in our previous works (Xu et al., 2016a; Jiang et al., 2017b). Tab.1 Specifications of experimental devices and instruments Number

Item

Model/Material

Accuracy

Range

Remarks

1

Glass tube bubble absorber

Glass

-

-

Fig. 1(b)

2

Gas chromatography (GC)

HP4890A

≤0.02mV/15min

-

TCD detector

3

Rich solution tank

Stainless steel

-

40L

-

4

Poor solution tank

Stainless steel

-

40L

-

5

Solution pump

MDG-H2 A220

-

1.8L/min 4bar

Magnet gear

6

Heat exchanger

Plate

-

-

-

7

Refrigerant R124 tank

-

-

13L

-

8

High speed camera

VITcam

12micron square/PX

1280*1024PX

LED lights

9

Data acquisition computer

-

-

-

HR2300

10

Pressure reducing valve

Stainless steel

-

-

-

11

Liquid six-way valve [42]

Vaclo, 4-port-2 pos Int vol

1μL

1/16*.75mm

8175C/1000psi

12

Needle valve

Stainless steel

-

-

-

13

Thermostatic water bath

-

-

-

High temperature

10

14

Heating water pump

ORS 25-8

-

1L/s 8m

-

15

Thermostatic water bath

-

-

-

Low temperature

16

Cooling water pump

ORS 25-8

-

1L/s 8m

-

VF1

Solution flow meter

Glass Rota meter LZB-4

±4%FS

1-10L/h

Calibration

VF2

Vapor flow meter

Glass Rota meter LZB-6

±2.5%FS

60-600L/h

Calibration

VF3

Cooling water flow meter

Glass Rota meter LZB-10

±2.5%FS

10-100L/h

Calibration

P ○

Pressure gauge

Vacuum manometer Y-60

±2.5%FS

-0.1- 0.15MPa

Calibration

T ○

Thermocouples

WZP Pt-100

±(0.15+0.002|t|)℃

-50- 200℃

Calibration

The solution pump runs to pump the pre-prepared 40% R124-NMP solution flowing through the plate heat exchanger into GTBA. The cooling water pump runs to pump the cooling water flowing into the GTBA to take the absorption heat away. When the operation conditions meet the experimental requirements, the refrigerant tank valve is opened. The R124 vapor flows through the nozzle to be injected into the bottom of GTBA and bubbles are formed. After the bubbles being absorbed, the rich solution leaves GTBA and flows into the rich solution tank. The solution mass fraction is detected by a liquid six-way valve and GC. The bubble absorption process is recorded by a high speed camera. The AH defined as the length between the nozzle outlet and the bubble disappearance location can be measured directly. The experimental operation parameters are listed in Tab.2. These parameters originate from the thermodynamic calculation results of an air-cooled AVRS with R124-NMP at evaporation temperature of 5℃. Tab.2 Experimental operation parameters and their maximal uncertainty Test parameters

Ranges

Maximal standard uncertainties

Absolute absorption pressure (kPa)

165, 175,

4.1

Solution inlet mass fraction (x)

45%-50%

0.18%

Solution inlet temperature (℃)

36, 41, 46, 54

0.38

Solution volume flow rate (L/h)

4, 6, 8

0.23

11

Vapor volume flow rate (L/h)

140~560

8.81

Nozzle orifice diameter (mm)

1, 2.8

0.12

Initial cooling water temperature (℃)

33

0.27

Cooling water volume flow rate (L/h)

44

1.46

0-630

27.8

Absorption height (AH) (mm)

3. Data Analysis The absorption heat in an absorption process is,

Qa  ms ,in hs ,in  mv,in hv,in  ms ,out hs ,out

(1)

The overall heat transfer coefficient of GTBA can be calculated as,

U ov 

tlm 

Qa  DLtlm

t

s ,in

(2)

 tcw,out    ts ,out  tcw,in 

  ts ,in  tcw,out   Ln     ts ,out  tcw,in    

(3)

Similarly, the overall volumetric mass transfer coefficient of GTBA can be calculated as,

K ov 

xlm

mv ,in

 2   D L  xlm 4 

x 

eq in

eq  xin    xout  xout 

  xineq  xin    Ln  eq   xout  xout    

(4)

(5)

The volumetric mass transfer coefficient in two-phase region can be calculated as, K tp 

mv ,in

 2   D H  xlm 4 

(6)

Where, the characteristic length is AH. In present work, the solution volumetric flow rate, inlet mass fraction and temperature, vapor volumetric flow rate, absorption pressure and orifice diameter are considered as the key operation parameters. For

12

exploring the effects of these operation parameters on heat and mass transfer characteristics of GTAB, they are all nondimensionalized and expressed as follows: Vapor Re number (Rev):

Rev 

4 v qv  d o v

(7)

Re s 

4  s qs  D s

(8)

Solution Re number (Res):

Dimensionless orifice diameter:

do 

do

(9)

D

Dimensionless absorption pressure:

p  p

(10)

pr

Where, Pr expresses the saturated pressure when the refrigerant temperature is 0℃. Dimensionless absorption mass fraction:

x 

xs ,in xseq,in

(11)

eq Where, xs ,in stands for the saturated mass fraction at the same pressure and temperature as the inlet

absorption solution. Dimensionless absorption temperature:

T 

Ts ,in (Ts ,in  T ) Tr2

(12)

Where, Tr is set as 293.15K. The method of the experimental standard uncertainty analysis described by Rabinovich (2006) has been 13

employed. The maximal standard uncertainties of tested variables are listed in Tab.2. The derived standard uncertainties of heat and mass transfer coefficients are drawn in result plots. 4. Experimental results and discussion 4.1 Vapor and solution volumetric flow rate Fig.3 illustrates the effects of vapor Reynolds number and solution volumetric flow rate on overall heat and mass transfer coefficients of GTBA under the given operation conditions. Fig.3 (a) shows that the vapor Rev affects significantly on overall heat transfer coefficient (Uov) of GTBA. At the solution volumetric flow rate of 8L h-1, the Uov rises almost linearly from 210.8W m-2 K-1 to 657W m-2 K-1, increased by about 2 times when the Rev increases from 431.3 to 1232. The reasons are: 1) the increase of Rev means the vapor volumetric flow rate increase, which will cause the regions of churn and slug flow patterns in GTBA enlarging and the disturbance of vapor to solution enhances. The enhancement of disturbance will effect on the thermal boundary layer to improve the overall heat transfer coefficient. 2) The velocity of vapor-liquid two-phase flow in GTBA augments with the increase of Rev, which will make the thickness of thermal boundary layer reduction. That leads to the convective heat transfer thermal resistance on solution side reducing or the convective heat transfer coefficient increasing.

14

100

700

90

600

Ktp

K/kgm-3s-1

Uov/Wm-2K-1

80

500 400 qs=4L/h

300 200 100 400

600

800

1000

70 qs=4L/h

60

qs=6L/h

50

qs=8L/h

qs=6L/h

40

qs=4L/h

qs=8L/h

30

1200

1400

20 400

qs=6L/h

Kov

qs=8L/h 600

800

1000

Rev

Rev

a

b

1200

1400

Fig.3 Effects of vapor Reynolds number and solution volumetric flow rate on: (a) heat transfer coefficient; (b) mass transfer coefficients (p=165kPa, x=45%, ts,in=54℃, tcw=33℃, qcw=44L/h, do=0.0028m) These reasons can also be used to explain why the Uov rises with solution volumetric flow rate increasing. Fig.3 (a) depicts that the Uov rises from 536.5W m-2 K-1 to 657W m-2 K-1, increased by about 22.5% when the Rev is 1232 and solution volumetric flow rate increases from 4L h-1 to 8L h-1. Fig.3 (b) shows that both of the overall volumetric mass transfer coefficient (Kov) and two-phase volumetric mass transfer coefficients (Ktp) augment with the Rev increasing. The effect of the Rev on the Kov is higher than that on the Ktp. When the solution volumetric flow rate is 4L h-1 and the Rev rises from 431.3 to 1232, the Kov rises linearly from 31.31kg m-3 s-1 to 96.62kg m-3 s-1 increased by about 2 times. But the Ktp rises from 63.6kg m-3 s-1 to 96.62kg m-3 s-1, increased only by about 50%. According to the penetration theory (Jiang et al., 2017a; Higbie, 1935), the increase of the Rev will create a large interfacial velocity between vapor and solution, which makes the mass transfer improvement and the mass transfer coefficient enhancement. Moreover, the increase of the Rev also makes the churn and slug flow

15

regions augment and mass transfer rate increase (Xu et al., 2016a; Qi and Xia, 2007; Xia and Wei, 2007). Both of the reasons make the Ktp and Kov increase with Rev rising. From the view of mass transfer rate equations, the increase of Rev means the increase of vapor volumetric flow rate ( mv ,in ), which leads to the enlargement of vapor mass fraction in GTBA or the augment of mass transfer force ( xlm ) between vapor and solution. The Kov is related to the ratio of mv ,in to xlm . With the increase of Rev, the growth rate of mv ,in is always higher than that of xlm , so that the Kov increases linearly with respect to Rev. The Ktp is related to the ratio of mv ,in to the product of the AH and xlm . The AH rises with the increase of Rev (Xu et al., 2016a), therefore, the Ktp is always bigger than Kov when the volumetric flow rate of solution ( ms ,in ) is constant. However, the Ktp will approach to Kov with the increase of Rev. When Rev reaches a critical value, the AH equals to the length of bubble absorption tube and the Ktp is the same as Kov. Actually, the difference between Kov and Ktp can represent the absorption tube utilization. A lower difference between Kov and Ktp indicates higher absorption tube utilization. Fig. 3(b) also shows that the Kov drops with the increase of

ms ,in at the same Rev. When mv ,in is constant and ms ,in rises, the solution average mass fraction in GTBA will drop, which means xlm between vapor and solution increases. According to the Eq. (4), the increase of

xlm will make a decrease of the Kov. The Ktp rises with the increase of ms ,in when Rev is less than 740, but it drops with the increase of ms ,in when Rev is greater than 740. The reason is that xlm increases but the AH decreases with the increase of

ms ,in . However, when Rev is less than 740, the reduction rate of the AH is more than the growth rate of xlm with the increase of ms ,in . Under this operation conditions, the AH plays a dominant role for the Ktp. When Rev is greater than 740, the increase of xlm will play a dominant role on the Ktp because the growth rate of 16

the Ktp is more than that of the AH with the increase of ms ,in . Therefore, there exists an intersection point in three curves. 4.2 Inlet temperature and mass fraction of solution Fig.4(a) and Fig.4(b) illustrate respectively the variations of Uov and K with the dimensionless absorption temperature (ΘT) under the given operation conditions. 140

1400 x=45%

1200

120

1000

Kov

qs=4L/h

K/kgm-3s-1

U /Wm-2K-1 ov

x=50%

qv=280L/h

800

Ktp

600

100

x=50%

Ktp Kov

80 x=45% 60 qs=4L/h

400

40 qv=280L/h

200 1.1

1.15

1.2

T

1.25

1.3

a

20 1.1

1.15

1.2

T

1.25

1.3

b

Fig.4 Effects of dimensionless temperature and solution mass fraction on: (a) overall heat transfer coefficient; (b) mass transfer coefficients (p=165kPa, tcw=33℃, qcw=44L/h, do=0.0028m) Fig.4 (a) shows that the Uov drops rapidly with the ΘT increasing, which indicates that, the variation of ΘT effects on the Uov significantly. With the increase of ΘT from 1.14 to 1.28, the Uov drops quickly from 1200W m-2 K-1 to 360W m-2 K-1 under condition of solution inlet mass fraction of 45%. Moreover, the Uov decreases with the solution inlet mass concentration improving at a fixed ΘT. The variation of Uov with respect to ΘT depends on the ratio of heat exchange load to log mean temperature difference ( tlm ). Fig.5 displays the variations of the heat exchange load and tlm with respect to ΘT. It illustrates that the heat exchange load and tlm of GTBA will augment with the increase of ΘT. But, the growth rate of heat exchange load is 17

lower than that of tlm , which leads to the Uov decreasing. 115

120

lm

110

8

105

6

10

110

x=45%

5

q =4L/h s

q =280L/h v

100

10 Log mean temperature difference Heat exchange load/W

1.15

1.2 T

1.25

0 1.3

100

4 x=50% q =4L/h s

95

2

q =280L/h v

90 1.1

1.15

1.2 T

1.25

Log mean temperature difference t

Heat exchange load/W

Log mean temperature difference Heat exchange load/W

Log mean temperature difference t lm Heat exchange load/W

130

0 1.3

Fig.5 Variations of the heat exchange load and log mean temperature difference with respect to ΘT at different solution inlet mass concentration (p=165kPa, tcw=33℃, qcw=44L/h, do=0.0028m) Different from the influence of ΘT on Uov, the increase of ΘT has a positive influence on the K. Fig.4(b) shows that ΘT rises from 1.14 to 1.28, the Kov increases from 30kgm-3s-1 to 65.4kg m-3 s-1 under the solution inlet mass fraction of 45%. The growth rate of the Ktp is less than that of the Kov. The Kov and Ktp both increase with the increase of ΘT. The reasons are: 1) the partial pressure of refrigerant component in the absorption solution rises with increase of ΘT (Xu et al., 2016a; Xu et al., 2016b), which makes the mass transfer force ( xlm ) drop. 2) The increase of ΘT causes the saturated mass fraction (Jiang et al., 2017a) of absorption solution reducing, which also makes the xlm drop. These two reasons lead to the xlm dropping quickly with the increase of ΘT. The decrease of xlm makes the Kov and Ktp increase and it also makes the AH increase in the GTBA. Eq. (4) and Eq. (6) indicate that the K is inversely proportion to the product of L or H and xlm . When the absorption tube length (L) is used as characteristic length, the Kov rises relatively quickly with the increase of ΘT. When the AH is used as characteristic length, the Ktp rises relatively slowly with the increase of ΘT. The 18

reason is that the AH rises but the xlm drops with the increase of ΘT. The solution inlet mass fraction (xs,in) also has a significant influence on the Uov, Kov and Ktp. When ΘT is 1.14 and xs,in rises from 45% to 50%, the Uov drops from 1200W m-2 K-1 to 1076W m-2 K-1, but the Kov and Ktp increase from 30kg m-3 s-1 to 65kg m-3 s-1 and from 80kg m-3 s-1 to 112.5kg m-3 s-1 respectively. The reason is that the increase of xs,in will lead to mass transfer force between the refrigerant vapor and absorption solution decrease, which makes the Kov and Ktp drop. 4.3 Nozzle orifice diameter Fig.6 illustrates the variations of the Uov and K with respect to Rev for two nozzle orifice diameters under the given operation conditions. It can be obviously seen from the figure that the nozzle orifice diameter affects significantly on the Rev and Uov. The Rev will enlarge sharply when vapor volumetric flow rate ( mv ,in ) keeps constant and the nozzle orifice diameter reduces from 2.8 to 1mm, which leads to the Uov increases. Fig.6 (a) shows that the Uov increases from 419W m-2 K-1 to 679.6W m-2 K-1 when mv ,in keeps 160L h-1 but the nozzle orifice diameter reduces from 2.8 to 1mm. The reason is that the decrease of nozzle orifice diameter leads to the vapor velocity flowing through orifice increasing which makes the Rev rise. That will cause two positive effects upon bubble absorption process in GTBA. One is that the high Rev will create a strong vapor disturbance to extend the length of churn flow pattern in GTBA and to enhance heat and mass transfer rate (Qi and Xia, 2007; Xia and Wei, 2007). The other is that the high Rev will make the vapor column at the nozzle exit be broken easily into numerous tiny bubbles to increase the surface contacted with absorption solution.

19

do=2.8mm

do=1mm 180

2500 400L/h

do=0.0028m

1500

320L/h

400L/h 320L/h

1000

240L/h

140

Ktp

120

Kov

80

qs=4L/h

160L/h

400L/h

240L/h 320L/h

Rev =2415

400L/h

60

160L/h

do=0.001m

100

240L/h 500

do=0.0028m

Kov

do=0.001m

K/kgm-3s-1

Uov/Wm-2K-1

2000

160L/h

Ktp

160

320L/h 240L/h

40

qs=4L/h

160L/h

0 0

1000

2000

3000

4000

20 0

1000

2000

Rev

Rev

a

b

3000

4000

Fig.6 Effects of orifice diameter on: (a) overall heat transfer coefficient; (b) mass transfer coefficients (p=165kPa, x=45%, ts,in=45℃, tcw=33℃, qcw=44L/h) The reduction of nozzle orifice diameter makes the AH significantly reduce, which leads to the height of two-phase flow reducing but the height of single-phase flow increasing in GTBA. The height increase of single-phase flow causes the decrease of the absorption solution outlet temperature (Jiang et al., 2017a) and the increase of cooling water outlet temperature. The log mean temperature difference ( tlm ) and the absorption heat load of GTBA rise. Because the growth rate of the heat load is bigger than that of tlm , the Uov will increase. Fig.6 (b) illustrates the influences of nozzle orifice diameter on overall and two-phase mass transfer coefficients. As mentioned above, the decrease of orifice diameter will cause the reduction of solution outlet temperature and mean log mass fraction difference. Therefore, the Kov increases with the decrease of orifice diameter under the same Rev. When the nozzle orifice diameter is 2.8mm, the Ktp increases slightly with vapor volumetric flow rate rising. When the nozzle orifice diameter is 1.0mm, the Ktp decreases first quickly to reach a lowest point at a specific Rev (Rev=2415) and then increases marginally with the increase of vapor 20

volumetric flow rate. The reason is that the AH plays a dominant role on mass transfer coefficient when Rev < 2415. Because the AH reduces with the decrease of vapor volumetric flow rate, only a very short of AH can be observed when the vapor volumetric flow rate is 160L h-1 so that the two-phase mass transfer coefficient is maximal. With the vapor volumetric flow rate increasing, the AH and mean log mass fraction difference increase simultaneously. And the growth rates of them are higher than that of mass transfer flux, which causes the reduction of the two-phase mass transfer coefficient. When Rev > 2415, the growth rate of mass transfer flux is slightly higher than that of the AH and mean log mass fraction difference, which results in the Ktp increasing slightly. 4.4 Absorption pressure Fig.7 illustrates the overall heat transfer and mass transfer coefficients with respect to Rev under different absorption pressures. It can be seen from the figure that the absorption pressure affects largely on heat and mass transfer coefficients. The overall heat or mass transfer coefficient increases with absorption pressure rising. As shown in Fig.7 (a), the Uov increases from 1269 W m-2 K-1 to 2486W m-2 K-1 at Rev of 1232.3 when the absorption pressure rises from 165kPa to 175kPa. The reason is that a high absorption pressure means a big mass transfer force under other operation parameters unchanged, which leads to a low AH and a large amount of vapor absorption. Because the growth rate of absorption heat load is higher than that of mean log temperature difference, the Uov rises with absorption pressure increasing. With the increase of Rev, the Uov rises, especial for a higher absorption pressure.

21

3500 qs=4L/h

2500 2000

p=165kPa

140

p=175kPa

120

K/kgm-3s-1

Uov/Wm-2K-1

3000

160

p=175kPa p=165kPa

1500

Ktp Kov Ktp Kov

100 80

1000

60

500

40

qs=4L/h

0 462.09 616.13 770.16 924.19 1078.2 1232.3 1386.3

20 462.09 616.13 770.16 924.19 1078.2 1232.3 1386.3

Rev

Rev

a

b

Fig.7 Effects of absorption pressure on: (a) overall heat transfer coefficient; (b) mass transfer coefficients (x=45%, ts,in=45℃, tcw=33℃, qcw=44L/h, do=0.0028m) The increase of absorption pressure also influences on the overall or two-phase mass coefficient. As shown in Fig.7 (b), the overall or two-phase mass transfer coefficient increases from 69.72kg m-3 s-1 to 87kg m-3 s-1 or from 85kg m-3 s-1 to 96kg m-3 s-1 at Rev of 1232.3 when the absorption pressure rises from 165 kPa to 175 kPa. The reason is the same as mentioned above. The increase Rev has a positive effect on the Kov. When Rev rises from 492.89 to 1232.3, the Kov increase from 26.3kg m-3 s-1 to 69.72kg m-3 s-1 or from 33.3kg m-3 s-1 to 87kg m-3 s-1 at the absorption pressures of 165 or 175kPa, respectively. However, the increase of the Rev has a different effect on Ktp at different absorption pressures. The Ktp increases slightly at the pressure of 165 kPa, but it decreases at the pressure of 175 kPa with the increase of Rev. It can be explained as follows. At the absorption pressure of 165ka, the Ktp growth rate isn’t significant with the Rev increasing owing to the simultaneous increase of mass absorption volumetric flux ( mv ,in ), log mean concentration difference ( xlm ) and AH. When the absorption pressure rises from 165 to 175kPa, the AH has a notable decrease (Xu et al., 22

2016a) under the same Rev which causes the solution outlet temperature to drop. That leads to an increase in solution outlet saturated concentration which makes the xlm decrease. Therefore, the Ktp at the absorption pressure of 175kPa is obviously higher than that of 165kPa at the same Rev. As mentioned in section 4.3, the AH plays a dominant role on mass transfer coefficient when the Rev is less than 2415. The AH obviously decreases with the absorption pressure improving and it decreases with the vapor volumetric flow rate decreasing. When the Rev is 492.89 at the absorption pressure of 175kPa, only an extremely tiny AH can be obtained which causes a highest Ktp. With the gradual increase in Rev, the increase in the product of the AH and xlm is higher than that of mass transfer flux, which causes the Ktp to drop. Simultaneously, the dominant role of AH weakens gradually. 4.5 Empirical correlations Through analysis and discussion, an equation of volumetric mass transfer coefficient for the GTBA with R124-NMP pair is proposed as follows:

Sh  a Rebv Recs Scsd Gase dof hw

(13)

Where

Sh 

KD 2  s Dc

(14)

The diffusion coefficient, Dc, can be calculated by employing the empirical correlation from Poling et al. (2001). Solution Schmidt number:

Scs 

s

 s Dc

Galileo number, reflecting the influence of gravity on bubble absorption process, is expressed as: 23

(15)

Gas 

gD3  s2

(16)

s2

Because the variation of AH has a significant influence on volumetric mass transfer coefficients, the dimensionless bubble absorption height (DAH) is introduced in here. DAH defined as the ratio of the AH to the absorption tube length can be expressed as:

H  H

(17)

L

DAH is introduced to express Sherwood number to reflect the influences of operation parameters on volumetric mass transfer coefficients. The coefficients in Eq. (13) were calculated by regression of all experimental data using MTALAB software. For two-phase region volumetric mass transfer coefficient, the empirical correlation of Sherwood number, Shtp, is,

Shtp  1.02 104 Re1.19 Res 0.14 Scs0.55Gas0.89do1.07H 1.08 v

(16)

For overall volumetric mass transfer coefficient, the empirical correlation of Sherwood number, Shov, is,

Shov  4.56 102 Re1.23 Res 0.16 Scs0.84Gas0.65do1.06H 0.13 v

(17)

The available ranges of correlations are:

Rev : 431.3~3795.3 Scs : 423~681

Re s : 70~396 Gas : 6.74×107~1.03×108

d o : 0.07~0.2 H : 0.12~1.0

Fig.8 depicts the deviation range between experimental and correlational Sh number. It can be seen that the margin of error between experimental and correlational Sh number are within ±10%. The average deviations are 3.31% and 3.53% for two-phase and overall Sh numbers, respectively. It indicates that the two empirical correlations can predict all the experimental data of mass transfer coefficient with ±10% error 24

bands. Therefore, the dimensionless correlations can be employed to calculate the mass transfer coefficient for designing the vertical bubble absorber with organic working fluids.

3

x 10

Correlated Sh numbers

2.5 2

4

Shtp +10%

Shov

-10%

1.5 1 0.5 0 0

0.5

1 1.5 2 Experimental Sh numbers

2.5

3 x 10

4

Fig.8 Comparison of the experimental Sh number with correlated Sh number 5. Conclusions This paper presents the experimental heat and mass transfer results on bubble absorption process of R124-NMP in a vertical tube under the operation conditions of interest for VARS. The key operation parameters are all nondimensionalized and the influences of the key operation parameters on the heat and mass transfer coefficients are investigated. Dimensionless correlations of two-phase and overall Sh number for R124-NMP in a vertical bubble absorber are developed. The following conclusions are drawn from the present experimental studies: 1.

The overall heat transfer coefficient increases with increasing vapor Reynolds number, solution

Reynolds number and absorption pressure and decreases with increasing orifice diameter, solution inlet temperature and mass fraction. Varying the key absorption parameters makes the heat load and log mean 25

temperature difference change in the same direction. The variation rate of heat load is always higher than that of log mean temperature difference. 2.

The overall mass transfer coefficient rises with increase of vapor Reynolds number, absorption

pressure, solution inlet mass fraction and temperature, but it drops with increase of solution Reynolds number and orifice diameter. 3.

The increase of absorption pressure and solution inlet mass fraction and decreasing orifice diameter

can improve the two-phase mass transfer coefficient while the solution inlet temperature affects the two-phase mass transfer coefficient slightly. 4.

The two-phase mass transfer coefficient increases with the increase of vapor Reynolds number.

There exists a transition vapor Reynolds number which is 740. The two-phase mass transfer coefficient increases with the solution volumetric flow rate increasing when the Re v is less than 740 and decreases with the solution volumetric flow rate increasing when the Rev is greater than 740. 5.

The present study has developed experimental correlations for two-phase and overall Sh number to

calculate mass transfer coefficient of R124-NMP in a vertical bubble absorber. Both correlations can precisely predict all the experimental data of mass transfer coefficient within ±10% error bands. Two-phase Sh number:

Shtp  1.02 104 Re1.19 Res 0.14 Scs0.55Gas0.89do1.07H 1.08 v Overall Sh number:

Shov  4.56 102 Re1.23 Res 0.16 Scs0.84Gas0.65do1.06H 0.13 v Acknowledgements This work is financially supported by National Natural Science Foundation of China (Grant numbers 26

51376032, 51776029, 51606024).

Appendix A Saturation pressure of R124-NMP pair The VLE data of R124-NMP were measured and correlated using five-parameter Non-Random Two Liquid (NRTL) model in our previous work (Xu et al., 2017). The p-T-x relationship can be expressed by Antoine-type equation (Wang et al., 2010). 4 1000 Bi  i  log p    Ai  x T  43.15  i 0 

(A.1)

Base on the VLE data, the parameters, Ai and Bi, in Eq. (A.1) can be obtained by a least-squares method. The values of them are listed in Tab. A1. The maximum and average relative deviations between measured and correlated pressures for R124-NMP are 3.58% and 1.34%, respectively. Tab. A1 Values of parameters in Eq. (A.1) i

0

1

2

3

4

A

7.30

-12.76

37.16

-47.33

22.19

B

-1.83

4.94

-12.77

15.98

-7.34

Enthalpy of R124-NMP pair The five-parameter NRTL model is employed to predict the excess enthalpy characteristic of R124-NMP mixture. For binary solution, the NRTL model is expressed as, 2     G21 12G12  ln  (1  y )  21    2   y  (1  y )G21   (1  y )  yG12   2

(A.2)

𝐺12 and 𝐺21 are defined as:

G12  exp  12 12 

(A.3)

G21  exp  12 21 

(A.4)

27

Where, α12 is the non-randomness parameter of the NRTL model. The binary interaction parameters, 𝜏12 and 𝜏21 , are defined as,

1 2    1 l1n T( ) R/ T

(A.5)

 2 1    2  l2n T( ) R/ T

(A.6)

In Eqs. (A.2) to (A.6), λ1, λ2, φ1, φ2 and α12 are the five parameters in the NRTL model; γ is the activity coefficient of the refrigerant, y is the mole fraction of R124 in solution, R stands for the general gas constant. The five parameters of R124-NMP pair in the NRTL model are shown in Tab. A2 (Xu et al., 2017). Tab. A2 Five parameters of NRTL model for R124-NMP mixture Parameters

λ1

μ1

λ2

μ2

α12

Values

242408

-46295.3

-166747

30875.3

-0.0515

The excess molar Gibbs energy of the mixture, GE, is a function of the molar concentration and the activity coefficient. It can be expressed as,

G E  RT  y ln( ) 

(A.7)

The excess enthalpy of the mixture (Schmidt et al.), HE, can be derived from Eq. (A.7) and it was given as,

  G E T    H    1 T     p, y E

(A.8)

The molecular weight of R124-NMP binary solution, Ms, can be expressed as,

M s  135.8  0.7 x  1.37  0.37 x 

(A.9)

Therefore, the specific excess enthalpy, hE, can be calculated from the NRTL model and Eqs. (A.7), (A.8) and (A.9). Then hE can be expressed as,

hE  H E M s

(A.10)

28

The specific enthalpies of the refrigerant and absorbent, R124 and NMP, in the liquid phase can be expressed as,

 7 4 . 1 8  6 8h  i 1

hr e f 2 0 0

 2 i7 3 . 1 5 ) 

T (

r e f i

 hab t  2 0 0 4 . 1 8 6c p80 T ( 

(A.11)

 ( 2  2 7 3 . 1 5 (A.12) ) 

1 2 7 3 . 1cp51 )T 2

Where, the subscripts ref and abt represent refrigerant and absorbent, respectively. The regression parameters, hrefi, are listed in Tab. A3 and the coefficients, cp0 and cp1, are 0.3732 and 0.000234 respectively (Borde et al., 1997). The enthalpies of the pure components, R124 and NMP, were both assumed to be 200kJ kg-1 at 0℃. Tab. A3 Regression parameters for Eq. (A.11) Parameters

href1

href2

href3

href4

href5

href6

href7

R124

0.2508

0.3478E-3

0.1010E-5

0.3425E-8

0

0

0.6996E-14

Therefore, the enthalpy of R124-NMP solution at R124 mass fraction, x, and temperature, T, can be calculated as follows:

hs  xhref  1  x  habt  h E

(A.13)

Density of R124-NMP pair The densities of the pure components, R124 and NMP, can be expressed by a polynomial equation. 3

    iT i

(A.14)

i 0

The regression parameters ρi (i=0, 1, 2, 3) for R124 and NMP are listed in Tab.A4 (Borde et al., 1997). Tab. A4 Regression parameters for Eq. (A.14) Parameters

ρ0

ρ1

ρ2

ρ3

R124

1.4660

-0.3394E-2

-0.16063E-5

-0.2004E-6

NMP

1.0387

-0.3891E-3

-0.46746E-5

0

The density of R124-NMP solution can be calculated as,

29

s  1  x ref  1  x  abt 

(A.15)

Dynamic viscosity of R124-NMP pair The dynamic viscosity of pure components, R124 and NMP, can be expressed by a polynomial equation.

Ln(  )  0 

1 T  2

(A.16)

The regression parameters μi (i=0, 1, 2) for R124 and NMP are listed in Tab.A5 (Borde et al., 1997). Tab. A5 Regression parameters for Eq. (A.16) Parameters

μ0

μ1

μ2

R124

-8.9301

5094.9

357.4

NMP

-1.3984

202.08

-196.3

The dynamic viscosity of R124-NMP solution can be calculated as, 13 13 3 s  ( xref  (1  x)abt )

(A.17)

Diffusion coefficient Dc The diffusion coefficient, Dc, can be calculated by employing the empirical correlation from (Poling et al., 2001).

Dc 

1.38 1023  T 6  0.35 109  s

(A.18)

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

30

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