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Coupled heat and mass transfer during nonisothermal absorption by falling droplets

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Coupled heat and mass transfer during nonisothermal absorption by falling droplets ... Slug flow. Infante Ferreira, C. A., (1985) Int. J. Refrigeration 8 326-334 ... – PowerPoint PPT presentation

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Title: Coupled heat and mass transfer during nonisothermal absorption by falling droplets


1
Coupled heat and mass transfer during
nonisothermal absorption by falling
droplets Elperin T. and Fominykh A. Department
of Mechanical Engineering Ben-Gurion University
of the Negev Israel
  • Applications
  • two-phase absorber design and analysis
  • chemical engineering
  • 3. refrigeration engineering and air-conditioning

2
applications
Examples of industrial operations where thermal
effects of absorption are important 1.
absorption of ammonia into water 2. water vapor
absorption by aqueous solutions of LiBr, LiCl and
potassium formate (HCOOK) 3. absorption of carbon
dioxide and hydrogen sulfide into amine
solutions 4. absorption of friendly refrigerants
such as R32, R134a and R124 by dimethyl acetamide
5. absorption of trifluoroethanol and
hexafluoroisopropanol by solvents from the group
of organic heterocycles 6. chlorinating of
organic liquids 7. absorption of SO2 and HCl into
water and aqueous solutions

3
fundamentals
Process is characterized by D - coefficient of
diffusion in a liquid phase a - coefficient of
thermal diffusivity ?- thermal conductivity L -
heat of absorption Xs- gas solubility

Fig. 1 Dependence of Henry constant from
temperature
4
fundamentals
Linear approximation of absorbate
Fig. 2 Equilibrium state of aqueous solution of
LiBr in water
5
fundamentals
6
fundamentals
Fig. 3 Regimes of two-phase flow
7
state of the art
Film flow V. E. Nakoryakov and N. I. Grigorieva,
(1977). J. Eng. Phys. 32, 399 G. Grossman,
(1983) Int. J. Heat Mass Transfer 26, 357 G.
Grossman and M. T. Health, (1984) .Int. J. Heat
Mass Transfer 27, 2365 Brauner, N.,
Moalem-Maron, D., Meyerson, (1989) H., Int. J.
Heat Mass Transfer 32 1897-1906 Brauner, N.,
(1991) Int. J. Heat Mass Transfer 34 767-784
Bubbly flow Infante Ferreira, C. A., Keizer, C.,
Machielsen, C. H. M. (1984) Int. J. Refrigeration
6, 348-357 Merrill, T. L. Perez-Blanco, H.
(1997). Int. J. Heat Mass Transfer, 40,
589-603 Elperin, T., Fominykh, A. (1999). Heat
Mass Transfer, 35, 517-524 Merrill T. L. (2000).
Int. J. Heat Mass Transfer, 43, 3287-3298 Cao,
J., Christensen, R.N. (2001). Int. J. Heat Mass
Transfer, 44, 1411-1423 Elperin, T., Fominykh, A
(2003). Chem Eng. Sci., 58, 3555 - 3564
8
state of the art
Slug flow Infante Ferreira, C. A., (1985) Int.
J. Refrigeration 8 326-334 Elperin, T., Fominykh,
A., (1999) Int. J. Heat Mass Transfer 42
153-163 Elperin, T., Fominykh, A. (2000) Int. J.
Thermal Sciences 39 753-761 Droplets V.E.
Nakoryakov, N.I. Grigoreva, J. Eng. Phys. 32 (3)
(1977) 243247 I. Morioka, M. Kiyota, A. Ousaka,
T. Kobayashi, (1992) JSME Intern. Journ. Ser. II
35 58464 H.H. Lu, T.Ch. Wu, Y.M. Yang, J .R.
Maa (1998).Int. Com. Heat Mass Transfer 8
1115-1126 M. Venegas, M. Izquierdo, P. Rodríguez,
A. Lecuona Int. J. Heat Mass Transfer 47 (2004)
2653-2667
9
state of the art
10
fundamentals
  • Advantages of spray absorbers
  • higher contact surfaces per unit volume and
    higher rates of mass transfer in spray absorbers
    in comparison with conventional falling film
    absorbers
  • 2. intensification of the HMT process and
    miniaturization of equipment

Fig. 4 Schematic view of a spray absorber
11
fundamentals
Fig. 5 Terminal velocity and aspect ratio of
water drops falling in air at 20 oC and 1 bar
12
fundamentals
Fig. 6 Streamlines and vorticity contours inside
a water drop falling in air at Re 100
13
fundamentals
Fig. 7 Velocity of circulations inside water
droplets falling in air with terminal velocity
14
fundamentals
Fig. 8 Shape of water drops falling in air
15
state of the art Nakoryakov (1977)
16
state of the art Nakoryakov (1977)
17
state of the art Lu et al. (1998)
18
state of the art Lu et al. (1998)
19
state of the art Lu et al. (1998)
Fig. 9 Concentration profile development with
time inside a droplet. System LiBr - water vapor
20
state of the art Lu et al. (1998)
Fig. 10 Concentration profile along the ? for Pe
0 and Pe 5000
21
state of the art Lu et al. (1998)
Fig. 11 Influence of thermal effect and internal
circulation on absorption rate
22
state of the art Morioka et al. (1992)
3. Morioka et al.(1992) Hamielec and Johnson
(1962) (Re ? 80)
(11)
where Ai are functions of viscosity ratio in
dispersed and continuous phases. Boundary
conditions Linear absorbate approximation, all
heat of absorption is dissipated in a
droplet. Symmetry of temperature and
concentration fields Morioka (1992) do not use
condition of zero mass flux in a center of a
droplet.
Fig. 12 Steady-state velocity vectors inside a
droplet for Re 1 and Re 10
23
state of the art Morioka et al. (1992)
Fig. 13 Profiles of temperature and
concentration, isotherms and lines of constant
concentration. Re 1 and t/Re 300
24
state of the art Morioka et al. (1992)
Fig. 14 Profiles of temperature and
concentration, isotherms and lines of constant
concentration. Re 10 and t/Re 100
25
state of the art Morioka et al. (1992)
Fig. 15 Profiles of temperature and
concentration, isotherms and lines of constant
concentration. Re 10 and t/Re 200
26
state of the art Morioka et al. (1992)
Fig. 16 Profiles of temperature and
concentration, isotherms and lines of constant
concentration. Re 10 and t/Re 300
27
state of the art Morioka et al. (1992)
Fig. 17 Local absorption rate of absorbate
28
state of the art Morioka et al. (1992)
Fig. 18 Dependence of average temperature of a
droplet vs. time
29
state of the art Venegas et al. (2004)
Venegas et al. (2004) Uribe-Ramirez and
Korchinsky (2000) (10 lt Re lt 250)
(13)
where Bi are functions of viscosity ratio in
dispersed and continuous phases. Calculations
for 60 ?m droplets falling with terminal velocity
0.17 m/s.
Fig. 19 Evolution of ammonia concentration inside
a droplet. Low-pressure absorber, subcooling 14
oC and 19 oC.
30
state of the art Moser and Tsotsas (2000)
Fig. 20 Dependence of evaporating droplet radius
vs time for different initial ammonia
concentrations inside a droplet. Tg0 293K, RH
88
31
state of the art Moser and Tsotsas (2000)
Fig. 21 Normalized droplet temperature vs time
for different initial ammonia concentrations
inside a droplet
32
modelling
T. Elperin, A. Fominykh, Int. J. Refrigeration 30
(2007) 274-281. T. Elperin, A. Fominykh,
Atmosphereic Environment, 39 (2005) 4575-4582
Tangential and radial fluid velocity component at
gas-liquid interface (Pruppacher and Klett
(1997))
(1a)
where coefficient k varies from 0.009 up to 0.044
for different Reynolds numbers
33
modelling
Equation of nonstationary convective diffusion
(2a)
Differential energy balance equation
(3a)
boundary conditions
(4a)
34
modelling
Solution is found by combining the similarity
transformation method with Duhamel's Theorem
(5a)
,
(6a)
(7a)
(8a)
35
modelling
(9a)
(10a)
concentration and temperature in the bulk of
liquid droplet
(11a)
(12a)
36
modelling
When
, values of concentration
and temperature in a liquid droplet are
determined by the following formulas
(13a)
(14a)
(15a)
37
modelling
Fig. 1a Dependence of concentration in the bulk
of a droplet from time
38
modelling
Fig. 2a Dependence of droplet temperature from
time
39
modelling
Fig. 3a Absorption of water vapor by water
solution of LiBr
40
modelling
Fig. 4a Absorption of water vapor by water
solution of LiBr
41
modelling
D'- thermal diffusion coefficient of solution
42
modelling
43
unsolved problems
44
unsolved problems
45
unsolved problems
3. Non sphericity of droplets 4. Inert
admixtures 5. Droplet growth due to gas
absorption
The droplet erodes the stone not by its power,
but by constantly falling
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