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 Transfer26, 357 G. Grossman and M. T. Health, (1984) .Int. J. Heat Mass Transfer27, 2365 Brauner, N., Moalem-Maron, D., Meyerson, (1989) H., Int. J. Heat Mass Transfer32 1897-1906 Brauner, N., (1991) Int. J. Heat Mass Transfer34 767-784 Bubbly flow: Infante Ferreira, C. A., Keizer, C., Machielsen, C. H. M. (1984) Int. J. Refrigeration6, 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. Refrigeration8 326-334 Elperin, T., Fominykh, A., (1999) Int. J. Heat Mass Transfer42 153-163 Elperin, T., Fominykh, A. (2000) Int. J. Thermal Sciences39 753-761 Droplets V.E. Nakoryakov, N.I. Grigoreva, J. Eng. Phys. 32 (3) (1977) 243–247 I. Morioka, M. Kiyota, A. Ousaka, T. Kobayashi, (1992) JSME Intern. Journ. Ser. II35 58–464 H.H. Lu, T.Ch. Wu, Y.M. Yang, J .R. Maa (1998).Int. Com. Heat Mass Transfer8 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 < Re < 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. Refrigeration30 (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 , values of concentration and temperature in a liquid droplet are determined by the following formulas When (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”