Title: Coupled heat and mass transfer during nonisothermal absorption by falling droplets
1Coupled 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
2applications
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
3fundamentals
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
4fundamentals
Linear approximation of absorbate
Fig. 2 Equilibrium state of aqueous solution of
LiBr in water
5fundamentals
6fundamentals
Fig. 3 Regimes of two-phase flow
7state 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
8state 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
9state of the art
10fundamentals
- 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
11fundamentals
Fig. 5 Terminal velocity and aspect ratio of
water drops falling in air at 20 oC and 1 bar
12fundamentals
Fig. 6 Streamlines and vorticity contours inside
a water drop falling in air at Re 100
13fundamentals
Fig. 7 Velocity of circulations inside water
droplets falling in air with terminal velocity
14fundamentals
Fig. 8 Shape of water drops falling in air
15state of the art Nakoryakov (1977)
16state of the art Nakoryakov (1977)
17state of the art Lu et al. (1998)
18state of the art Lu et al. (1998)
19state of the art Lu et al. (1998)
Fig. 9 Concentration profile development with
time inside a droplet. System LiBr - water vapor
20state of the art Lu et al. (1998)
Fig. 10 Concentration profile along the ? for Pe
0 and Pe 5000
21state of the art Lu et al. (1998)
Fig. 11 Influence of thermal effect and internal
circulation on absorption rate
22state 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
23state 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
24state 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
25state 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
26state 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
27state of the art Morioka et al. (1992)
Fig. 17 Local absorption rate of absorbate
28state of the art Morioka et al. (1992)
Fig. 18 Dependence of average temperature of a
droplet vs. time
29state 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.
30state 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
31state of the art Moser and Tsotsas (2000)
Fig. 21 Normalized droplet temperature vs time
for different initial ammonia concentrations
inside a droplet
32modelling
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
33modelling
Equation of nonstationary convective diffusion
(2a)
Differential energy balance equation
(3a)
boundary conditions
(4a)
34modelling
Solution is found by combining the similarity
transformation method with Duhamel's Theorem
(5a)
,
(6a)
(7a)
(8a)
35modelling
(9a)
(10a)
concentration and temperature in the bulk of
liquid droplet
(11a)
(12a)
36modelling
When
, values of concentration
and temperature in a liquid droplet are
determined by the following formulas
(13a)
(14a)
(15a)
37modelling
Fig. 1a Dependence of concentration in the bulk
of a droplet from time
38modelling
Fig. 2a Dependence of droplet temperature from
time
39modelling
Fig. 3a Absorption of water vapor by water
solution of LiBr
40modelling
Fig. 4a Absorption of water vapor by water
solution of LiBr
41modelling
D'- thermal diffusion coefficient of solution
42modelling
43unsolved problems
44unsolved problems
45unsolved 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