An analytical model for the temperature distribution of a spray column, three-phase direct contact heat exchanger is developed. So far there were only numerical models available for this process; however to understand the dynamic behaviour of these systems, characteristic models are required. In this work, using cell model configuration and irrotational potential flow approximation characteristic models has been developed for the relative velocity and the drag coefficient of the evaporation swarm of drops in an immiscible liquid, using a convective heat transfer coefficient of those drops included the drop interaction effect, which derived by authors already. Moreover, one-dimensional energy equation was formulated involving the direct contact heat transfer coefficient, the holdup ratio, the drop radius, the relative velocity, and the physical phases properties. In addition, time-dependent drops sizes were taken into account as a function of vaporization ratio inside the drops, while a constant holdup ratio along the column was assumed. Furthermore, the model correlated well against experimental data. 1. Introduction A direct contact heat exchanger is a highly effective device for transferring heat between two immiscible fluids while they are flowing co-currently or countercurrently inside a column. The main feature of the direct contact heat exchanger is that it permits a confident contact between a hot fluid and a cold fluid. However, a number of different methods have been used to define the type of direct contact heat exchanger, including layer type, where the hot fluid is stagnant while the cold fluid flows on top, and a spray type, where one of two fluids is injected into the other. Generally, there are two types of spray column, depending on which injection technique is being used: an integrated type and a split type. In the former, the cold fluid is dispersed from the bottom of the column into a hot fluid, whereas in the second one, the hot fluid is pumped in countercurrently with the flowing cold fluid [1]. A direct contact heat exchanger has several advantages over surface heat exchangers [2], such as eliminating metallic heat transfer surface between fluids which are prone to corrosion and fouling, as well as increasing the heat transfer resistance. It can be operated at very low temperature differences or heat transfer driving forces and allows lower mass flow rates of transferring fluids, convenient separation of the fluids, and a high heat transfer coefficient (about 20–100 times than single phase or surface type heat exchanger) [3].
References
[1]
L. Tadrist, P. Seguin, R. Santini, J. Pantaloni, and A. Bricard, “Experimental and numerical study of direct contact heat exchangers,” International Journal of Heat and Mass Transfer, vol. 28, no. 6, pp. 1215–1227, 1985.
[2]
M. Song, A. Steiff, and P. M. Weinspach, “Direct-contact heat transfer with change of phase: a population balance model,” Chemical Engineering Science, vol. 54, no. 17, pp. 3861–3871, 1999.
[3]
Z. Peng, W. Yiping, G. Cuili, and W. Kun, “Heat transfer in gas-liquid-liquid three-phase direct-contact exchanger,” Chemical Engineering Journal, vol. 84, no. 3, pp. 381–388, 2001.
[4]
F. Dammel and H. Beer, “Heat transfer from a continuous liquid to an evaporating drop: a numerical analysis,” International Journal of Thermal Sciences, vol. 42, no. 7, pp. 677–686, 2003.
[5]
S. Sideman and Y. Gat, “Direct contact heat transfer with change of phase: spray column studies of a three—phase heat exchanger,” AIChE Journal, vol. 12, no. 2, pp. 296–303, 1966.
[6]
R. Letan and E. Kehat, “The mechanism of heat transfer in spray column heat exchanger,” AIChE Journal, vol. 14, no. 3, pp. 398–405, 1968.
[7]
S. B. Plass, H. R. Jacobs, and R. F. Boehm, “Operational characteristics of spray column type direct contact preheater,” AIChE Symposium Series—Heat Transfer, vol. 75, no. 189, pp. 227–234, 1979.
[8]
T. Coban and R. Boehm, “Performance of a three-phase, spray-column, direct-contact heat exchanger,” Journal of Heat Transfer, vol. 111, no. 1, pp. 166–172, 1989.
[9]
H. R. Jacobs and M. Golafshani, “Heuristic evaluation of the governing mode of heat transfer in a liquid-liquid spray column,” Journal of Heat Transfer, vol. 111, no. 3, pp. 773–779, 1989.
[10]
R. A. Brickman and R. F. Boehm, “Maximizing three-phase direct-contact heat exchanger output,” Numerical Heat Transfer A, vol. 26, no. 3, pp. 287–299, 1994.
[11]
Y. H. Kang, N. J. Kim, B. K. Hur, and C. B. Kim, “A numerical study on heat transfer characteristics in a spray column direct contact heat exchanger,” KSME International Journal, vol. 16, no. 3, pp. 344–353, 2002.
[12]
H. B. Mahood, “Theoretical modelling of three-phase direct contact spray column heat exchanger,” AMPhil-PhD Transfer Report, University of Surrey, 2012.
[13]
J. Isenberg and S. Sideman, “Direct contact heat transfer with change of phase: bubble condensation in immiscible liquids,” International Journal of Heat and Mass Transfer, vol. 13, no. 6, pp. 997–1011, 1970.
[14]
D. Moalem, S. Sideman, A. Orell, and G. Hetsroni, “Direct contact heat transfer with change of phase: condensation of a bubble train,” International Journal of Heat and Mass Transfer, vol. 16, no. 12, pp. 2305–2319, 1973.
[15]
D. Moalem-Maron, M. Sokolov, and S. Sideman, “A closed periodic condensation-evaporation cycle of an immiscible, gravity driven bubble,” International Journal of Heat and Mass Transfer, vol. 23, no. 11, pp. 1417–1424, 1980.
[16]
L. M. Milne-Thomson, Theoretical Hydrodynamics, Macmilan, London, UK, 5th edition, 1972.
[17]
X. Cai and G. B. Wallis, “A more general cell model for added mass in two-phase flow,” Chemical Engineering Science, vol. 49, no. 10, pp. 1631–1638, 1994.
[18]
H. Lamb, Hydrodynamics, Cambridge University Press, 6th edition, 1932.
[19]
A. A. Kendoush, “Theory of convective drop evaporation in direct contact with an immiscible liquid,” Desalination, vol. 169, no. 1, pp. 33–41, 2004.
[20]
G. Marrucci, “Rising velocity of a swarm of spherical bubbles,” Industrial and Engineering Chemistry Fundamentals, vol. 4, no. 2, pp. 224–225, 1965.
[21]
A. A. Kendoush, “Hydrodynamic model for bubbles in a swarm,” Chemical Engineering Science, vol. 56, no. 1, pp. 235–238, 2001.
[22]
M. Worner, “A compact introduction to the numerical modelling of multiphase flow,” Forschungszentrum Karlrsruhe, Wissenschaftliche Berichte FZKA 6932, 2003.
[23]
D. D. Joseph, “Potential flow of viscous fluids: historical notes,” International Journal of Multiphase Flow, vol. 32, no. 3, pp. 285–310, 2006.
[24]
H. B. Mahood, A. Sharif, S. A. Hossini, and R. Thorpe, “Hydrodynamics of two-phase bubbles condensation in an immiscible liquid media,” In press.
[25]
F. Concha, “Settling velocities of particulate systems,” Kona Powder and Particle Journal, vol. 27, pp. 18–37, 2009.
[26]
R. K. Wanchoo and G. K. Raina, “Motion of a two—phase bubble through a quiescent liquid,” The Canadian Journal of Chemical Engineering, vol. 65, no. 5, pp. 716–722, 1987.
[27]
R. Olander, S. Oshmyansku, K. Nichols, and D. Werner, “Final phase testing and evaluation of the 500kWe direct contact pilot plant at East Mesa,” U.S.D.O.E. Report DOE/SF/11700-T1, Arvada, Colo, USA, 1983.
[28]
M. Golafshani, Stability of a direct contact heat exchanger [Ph.D. thesis], University of Utah, 1984.
[29]
S. Sideman and G. Hirsch, “Direct contact heat transfer with change of phase: condensation of a single vapour bubbles in an immiscible liquid medium: preliminary sui,” AIChE Journal, vol. 11, no. 6, pp. 1019–1025, 1965.
