Stolk, A. L.

Waszenaar, R. H.

English

Purdue E-Pubs

Purdue UniversityPurdue e-PubsInternational Refrigeration and Air ConditioningConference School of Mechanical Engineering1986Heat and Mass Transfer Phenomena in anAbsorber with Drop-Wise Falling Film onHorizontal TubesA. L. StolkR. H. WaszenaarFollow this and additional works at: http://docs.lib.purdue.edu/iraccThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.htmlStolk, A. L. and Waszenaar, R. H., "Heat and Mass Transfer Phenomena in an Absorber with Drop-Wise Falling Film on HorizontalTubes" (1986). International Refrigeration and Air Conditioning Conference. Paper 31.http://docs.lib.purdue.edu/iracc/31HEAT AND MASS TRANSFER PHENOMENA IN AN ABSORBER WITH DROP WISE FALLING FILM ON HORIZONTAL TUBES A.L. Stolk and R. Wassenaar Laboratory for Refrigeration and Indoor Climate Technology Delft University of Technology (The Netherlands) I . ABSORBER DESIGNS In thermal absorption cycles, as used for refrigeration machines, heat pumps and heat transformers, the absorber is a crucial component in optimizing the c.o.P. of the system. The combination of heat and mass transfer leads to complicated phenomena occurring in these absorbers. The search for optimally working apparatus resulted into a number of designs. In the design three important points have to be considered: a. The interface surface between vapour and absorbent has to be as large as possible. b. The boundary layer of the absorbent has to be refreshed continuously. c. The absorption heat is to be withdrawn at nearly the same place as it is developed. To meet the first demand one of the phases has to be dispersed into the other one. The first choice to be made is whether the vapour or the liquid will form the continu-ous phase. Solid absorbers are not regarded in this paper. If the liquid is in the continuous phase the vapour is dispersed into bubbles, feeded at-the bottom of a bubble column or a vertical tube. In the other case the liquid is sprayed into the vapour or forms a falling film in a packed column, on vertical tubes or on horizontal tubes. Also a helical tube is being appli<.ated. Some types of absorbers are given schematically in figure 1 . ..-. Spray absorber Bubble absorber Filmabsorber Tube bubble absorber Fig. I - Different types of absorber design for thermal sorption systems. The spray absorber has the disadvantage that the drops cannot release the absorp-tion heat during their travel through the vapour space. So, the third design demand is not fulfilled. The falling film absorber is much better in this respect if the film is formed over cooled tubes, because the absorption heat is being withdrawn directly through the thin liquid film. Due to the fact that relative low mass flows mostly are involved the film will often be laminar or, at a maximum show a wavy flow. The helical cooling tube will give a certain amount of mixing of the boundary layer with the bulk of the liquid film. However, an interesting study of Uddholm /1/ shows that under certain circumstances the film on a smooth vertical tube can become wavy, which gives a much better mass transfer than on smooth laminar films. Another problem with falling film absorbers is that complete wetting of the heat and mass exchanger surface is very difficult. This is happening especially in viscous liquids. The vertical tube bubble absorber, as described by Keizer /2/ and Infante Ferreira /3/, has the advantage that along, the slugs a complete and stable liquid film is formed inside the tube, but the fact that the liquid-gas column causes an extra pressure loss makes this type not suitable for low pressure working fluids. Iedema /4/ proposed a drop wise falling film on horizontal tubes for absorbers. Experiments showed that a rather good wetting can be obtained when the design is op-timal and that a good amount of mixing occurs, enhancing heat and mass transfer and L I.F, - I. I. R. - Commissions Bl, B2, El , E2, Purdue (U.S.A.) - 1986 250 reta1n1ng the advantage of a low pressure drop. This design is very suitable for low pressure media and viscous absorbents. ® t;l ... l-Pt;T- Ttillll.\ltUII t• 1M. Tullt..!o ® ~IIHJ-U~l- lllol&l.I.I~ TIT1411~;'o1111.1UTI 'WITM ~IU~hh - -t.•lllll\ Fig. 2.- Horizontal tube absorber for drop wise falling film. Wassenaar and Van der Lans did fundamental research on this topic by means of models and experiments. A schematic drawing of this type of absorber is given in figure 2. 2. EXPERIMENTAL COND I !IONS In the absorber a mixture of LiBr/ZnBr2/cH30H, at mole fraction LiBr:ZnBrz ~ 2:1, flows around the tubes, absorbing CH30H vapour and releasing the heat of absorption to the cooling water, flowing inside the tubes. The mentioned mixture is rather vis-cous in the region of the mass-fraction; methanol w - 0,29 - 0,35 kg/kg and the tem-perature range is 8 - 30- 60°C. The viscosity range in this case is n ~ 38~9- 10,1 cP, compared with water: 0,8 - 0,5 cP. The density is: p ~ 1790 - 1610 kg/mJ. The heat and mass transfer has been studied in an absorber consisting of one vertical row of 10 horizontal copper tubes with a diameter of 12 mm outside and of 10 mm inside, and a length of 300 mm. The vertical pitch was 27 mm. The absorber was placed under a glass cap to allow flow observations. The measured data were: inlet and outlet temperatures and mass flows of the mixture, vapour and cooling water, vapour pre~sure and the inlet and outlet density of the mixture. These densities have been measured very accurately by a vibrating U-tube meter (reproducibility -,01 kg/m3). From these properties the mass fractions of the methanol have been deri-ved. A number of thermocouples were placed in the absorber to measure the mixture and cooling water temperatures in the flow direction and along the tubes. The operating conditions of the absorber were: w 0,29 - 0,35 kg/kg ~ 30 - 6ooc Re puo/n- 0,1 - 0,7 Pr v/a ~ 60 - 220 Le ~ D/a ~ 0,0013 - 0,0054 On those place~ where thermocouples disturbed the flow, sometimes jets were observed. Apart from these spots the liquid feed was droplet wise at all flow rates within the operation conditions. 3. DESCRIPTION OF DROPLET FLOW At the bottom of a tube at regular distances, d ~ 2TI /;s(, determined by the Tailor instability /5/, /6/, spots are situated from which pg droplets fall. The flow rate influences the fall frequency of these droplets. 251 The volume of the droplets is V ~ k (~) 1 • 5 where according to /7/ k ~ 14 ~ pg , :t • Close up observatLons have been made by aid of a high speed camera at 1000 frames per second. A description resulting from these observations is given in figure 3. Fig. 3 - Hydrodynamics of a drop wise falling film on a relative time scale of 0-100. Distances and velocities in mm. In this case the flow rate was per unit rv ~ 3,3 mm2/s, the mass fraction methanol w- 0,36 kg/kg and the temperature: v - 30 - 50°C. The time interval between the consecutive drops, 0,44 sj has been put at 100 in the figure. From t s- 0,12 to t~O a primary volume of 40 mm falls at v ~ 0,3 m/s at the top o~ the tube. Between t"'O and t- 0.06 the volume spreads out over an area: A~ 250 mm-; 37% of the area be-longing to the droplet site. At that time the volume has 'disappeared' into the film, but still a liquid column is present between the tubes, that breaks up at t ~ 0,07, falling at t- 0,1 as a secundary volume of 10 mm3 at v ~ 0,83 m/s on the tube, ini-tiating a concentric ripple in the film. This ripple decayed at t- 0,13 at a radius of r - 3 =· Data, obtained from these flow. Film thickness and mean function of time and position wise flow with o ~ U ~] g s~n e t ':1 observations are used in a hydrodynamic velocity from this model are plotted in and compared with results of stationary - r andu 5 6 . t u ~Lo--~--~~~./~L~,-+---.~,--~--~~--~- YL,- .s model of the figure 4 as a uniform sheet 0 1 2. 3 .;.. s Fig. 4 - Relative film thickness Y and mean velocity U along the tube (top to bottom) 0: classical Nusselt result> for smooth continuous feed; 1: time averaged results for droplet feed; 2: results at t- .007; 3: results at t- .037; 4: results at t- . 109; 5. results at t- .367. 252 From the plot it becomes clear that the time averaged film thickness and the velocity are considerably lower than in the case of stationary l~quid feed. It can be conclu-ded also that the thin film is being swallowed by the pool in which the droplet spreads out. It is presumed that the phenomena taking place here, are comparable to those in the wavy flow of inclined thin film, although the flow phenomena are not as vigorous as in the wavy flow of inclined films /8, 9/. 4. HEAT AND MASS TRANSFER MODEL The film thickness and the velocity on the tube are varying in time and in axial and tangential direction. A heat and mass transfer model, which takes the hydrodyna-mics fully into account, would be too complex. Therefore, we base our model on stati-onary smooth flow and try to summarize the hydrodynamics in empirically determined fitting parameters. The Fourier number is almost immediately after the entrance of the droplet in the film, rather high, Fo >> .15. So, the entrance effects are negligible for the heat transfer. The mass diffusion coefficient is about 500 times smaller than the heat diffu-sion coefficient, which means that even at the bottom of the tube the concentration boundary layer only is 10 to 20~ of the filmthickness. Our model has been based on the finite difference formulation of the conserva-tion equations /4/. The film i's split up into elements in the flow direction. For the conservation of mass in one element is found: mw + dm ~ (m + dm)(w + dm) ~ mw + wdm + Wdw For the conservation of energy is written: em. + dm) Ch + dh) - rllh "" mdh + hdm ~ drilh v - d~ (I) . -(2) These equations are solved by means of the von Klirman-Pohlhausen met:hod·: a (y) and w(y} are approximated by polynomials. The coefficients of the polynomials are found from the boundary conditions: e (y) and w(y) ~ b (I - Z) 2 + b (I - Z) + b) I li 2 o The velocity and the thickness of the smooth film are: u ~ 3 u {Z- _l(y)z}· u "' rv 0 2 0 , 0 The boundary conditions are: • r_:_Q_ftu~~-~~!11= A~~~ aw(ew- ec); e ~ e w I) w From the enthalpy equation at y "' 0 a2 e -~ 0 ay2 ae ae u~ + v-ax ay • l_~_£_i~~E~~f~s~~~~E~~~-~~E~~~l= There is a thermodynamic equilib~ium. -w -w * e "' e (w , p) a2 e ~ ~ follows because u (3) (4) (5) (6) (7) 0 and v 0 (8) (9) The inte~face conditions differ a little from those found by other authors. Since at the interface contrary to the bulk, the net mass flow is not zero, a drift flow has to be taken into accou~t /10/. dm ~ -p o aw + dmw _,_ dm - pD aw ay - T=w ay_ (lOa) 253 ;\, 1i ~ ...£Q._ dW (h\1 - h ) ay (1-w) ay p • !_:_f(l- 0wli££Eder_£~-!~~-~~~~-~E~£Ei£2_£~~2~~E!_l~!~l= w ~ wb aw "' 0 ay (lOb) (II) (12) Because of the simplicity of the model, discrepancies with experiments will exist. This asks for the use of fitting parameters, preferably based on good experi-ments. The model has two outcomes, heat production and absorbed mass flow, so two parameters are to be used. The mentioned swallowing-up of the thin film by the spreading out droplet is supposed to cause an enhanced mass transfer. Also· already has been stated that the mean film thickness is lower than in the case of smooth stationary flow. The follow-ing equation can be written: kT/n k 0 0 I ,45.10- 14 (~)1/3 g (13) (14) The model is now e\laluated by the experiments mentioned before. The results of this work will be presented at the meeting. S!JMMARY A concise overview is given of different types of absorbers for thermal absorption cycles, leading to the conclusion that for viscous mixtures a dropletwise falling film over horizontal tubes might be a good design. Investigations on heat and mass transfer for such an absorber are described. A simplified computer model is develo-ped, which is to be used with two empirical correlation parameters. Some model out-comes from experimental results are given. The model is a design tool for this type of absorbers. 254 a D dm dqiN" d,. g h hv ~p m p u v p NO~ENCLATURE - thermal diffusion coefficient - mass diffusion coefficient ~ vapour mass fl01:0 into an element - heat flo1:0 into the tube wall per element - tube wall thickness - gravitational acceleration - mixture enthalpy - vapour enthalpy - partional methanol enthalpy in the mixture - mixture mass flow - vapour pressure - film mean velocity - co-ordinate perpendicular to the flow direction - heat transfer coefficient - surface tension volume flow per wetted length - film thickness - dynamic viscosity temperature - heat condictivuty kinematic ciscosity - density REFERENCES [m2/s) [m2/s] [ kg/s] [w I [m I [m/s 2) [ kJ/kg) [ kJ/kg] [ kJ/kgl [ kg/sl [ Pa I [m/sl [m I [ W/m2/KI [N/m) [m2/sl [m I [ kg/m/sl [K I [ W/m/KI [ m2/s~ [ kg/m I 1. H. Uddholm. A model for the design of a falling film absorber in an absorption heat pump.Workshop on heat transformation and storage, Ispra, October 1985. 2. C. Keizer. Absorption refrigeration machines. Thesis Delft University_ of Technolo-gy, 1982. 3. C.A. Infante Ferreira. Vertical tubular absorbers for ammonia-salt absorption refrigeration. Thesis Delft University of Technology, 1985. 4. P. !edema. The absorption heat pump with lithiumbromide-zincbromide-methanol. Thesis Delft University of Technology, 1984. 5. K. Taghavi-Tafreshi, V.K. Dhir. Tailor instabilities in boiling, melting and con-densation or evaporation. Int. J.of Heat and Mass Transfer, Vol. 23, 1980, pp. 1433-1445. 6. J. Berghmans. Stabilityof the vapour filmboiling from horizontal cylinders. Int.J. of Multiphase Flow, Vol. 2, 1975, pp. 319-336. 7. D. Yung, J.J. Lorentz, E.N. Gassic. Vapour-liquid interaction and entrainment in falling film evaporators. J. of Heat Transfer, Vol. 2, 1980, pp. 20-25. 8. N. Brauner, D.M. Maron. Characteristics of inclined thin films, waviness and the associated mass transfer. Int. J. of Heat and Mass Transfer, Vol. 25, 1982, pp. 99-110. 9. N. Brauner, D.M. Maron. Modeling of wavy flow in inclined thin films. Chem.Eng. Science, Vol. 83, 1983, pp. 775-788. 10. R.B. Bird, W.E. Stewart, E.N. Lightfoot. Transport phenomena. J. Wiley, New York, 1960, 7th ed., par. 19.1. LES PHENOMENES DU TRANSFER DE CHALEUR ET DE MASSE D'UN ABSORBEUR A PELLICULE DESCENDANT EN GOUTELETTES SUR DES TUBES HORIZONTAUX. RESUME: Une vue concise est presentee pour des types differents des cycles thermique~ a absorption, ce qui, p~ovoquant des melanges visqueux une pellicule descendant en goutelettes sur des tubes horizontaux, pourrait etre une bonne solution. On a ecrit des recherches sur le transfer de chaleur et de masse pour un tel absorbeur. On a developpe un modele pour ordinateur homologue a utiliser avec 2 parametres de corre-lations empiriques. Des modeles etablis a partir de recherches experimentales sont indiques. Le modele est con~u pour ce type d'absorbeur. 255 THE PHENOMENONS OF HEAT AND MASS TRANSFER OF AN ABSORBER WHICH CHARACTERISTIC IS A FILM SLIDING DOWN IN LITTLE DROPS ON HORIZONTAL TUBES SUMMARY A concise view is presented for different types of absorption thermical cycles. The latter being the cause of viscous mixtures, a film, sliding down in little drops on hori~ontal tubes, could be a right solution. Studies have been written on the heat and mass transfer for such absorber. A model has been developed for computers authorize·d to be used with two parameters of empirical correlation. Models established from experimental researches are indicated. This model is conceived for this type of absorber. 256 

Heat and Mass Transfer Phenomena in an Absorber with Drop-Wise Falling Film on Horizontal Tubes

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Heat and Mass Transfer Phenomena in an Absorber with Drop-Wise Falling Film on Horizontal Tubes

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