The influence of liquid-side mass transfer on heat transfer and selectivity during surface and nucleate boiling of liquid mixtures in a falling film

103

The Influence of Liquid-side Mass Transfer on Heat Transfer and Selectivity During Surface and Nucleate Boiling of Liquid Mix&es in g Falling Film uber den Einfluss des fliissigseitigen Stofftransportes und die Selektivitit bei der Oberfltichenverdampfung von Fliissigkeitsgemischen U. GROPP* Institutfiir (F.R.G.) (Received

auf den Wtieiibergang und beim Blasensieden

and E. U. SCHLDNDER 7hermische Mfahrenstechnik, October

Universittit Karlsruhe, Postfach 6380,750O

Karlsruhel

18, 1985)

Abstract Experimental studies using a falling film apparatus and a theoretical analysis of heat and mass transfer for mixtures lead to the following results. During nucleate boiling the separation effect, that is, the selectivity, and the heat transfer are influenced to a great extent by liquid-side mass transfer resistances. The selectivity diminishes significantly with increasing heat flux. The heat transfer coefficients far boiling mixtures can be much lower than for pure substances. For the calculations liquidside mass transfer resistances were assumed to be the only reason for the reduction of both the selectivity and the heat transfer coefficients. No further physical explanations were needed. During surface boiling the reduction of the heat transfer coefficients is negligible for practical applications. The selectivity is mainly controlled by the thermodynamic equilibrium. The liquid-side mass transfer coefficients are of the same order of magnitude as found in physical absorption and absorption with chemical reactions, i.e. (2-S) X 10e4 m s-r.

Kurzfassung Die experimentellen Untersuchungen mit einer Rieselfilmapparatur und die theoretischen Untersuchungen fiihrten zu folgenden Ergebnissen. Im Bereich des Blasensiedens werden die Trennwirkung, d.h. die Selektivitlt, und der Wlrmeiibergang von fliissig. . seitigen Stofftransportwiderstlnden beeinflusst. Die Selektivrtat nimmt mit steigender Warmestromdichte erheblich ab. Die WBrmeiibergangskoeffizienten fiir siedende Gemische kijnnen ebenfalls erheblich niedriger sein, als die fiir die reinen Stoffe. Bei der Berechnung der SelektivitCt und des WIrmeiibergangs beim Gemischsieden wurde angenommen, dass fhissigseitige Stofftransportwiderst5nde die einzige Ursache der Verschlechterung sind. Weitere physikalische Erkkirungen wurden nicht bcn6tigt. Bei der Oberfllchenverdampfung ist die Verschlechterung des Wtimeiibergangs nicht von praktischer Bedeutung. Die Selektivitlt wird vom thermodynamischen Gleichgewicht bestimmt. Die fltissigseitigen Stofftransportkoeffizienten liegen in der gleichen Grbssenordnung wie bei der Absorption und der chemischen Wgsche, nimlich bei(2-5) X lo4 m s-l.

Synopse Beim Blasensieden von Gem&hen ist der W&meiibergang oft erheblich schlechter als beim Sieden der zugehorigen reinen Stoffe. Eine mijgriche Erkkimng daft2 ist die durch Stofftrnsportwiderstli;nde in der jltissigen Phase verursachte Verschiebung des thermodynumischen Gleichgewichtes an der PhasengrenzjL?che

*Now at DEGUSSA

02%2701/86/$3.50

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Chem Eng. Process., 20 (1986) 103-l

und die damit verbundene Vem-ngerung des zur W&metibertragung verfigbaren Temperaturgef#lles. Bei der Verdampfung von bin&en Rll-R113 Gemischen am Rieselfilm konnte diese Hypothese experimentell durch Messung der Dampf- und Fliissigkeitszusammensetzung unterstiitzt werden. Die Wtirmtibergangskoeffizienten (Y beim Gemischsieden kiinnen in einfacher Weise mit Gl. (11) berechnet werden, deren Herleitung allein auf dieser Annahme griindet. Zur Bestimmung des aid- Wertes werden die Wriimtibergangskoeffizienten cx, und CQ fir die reinen Stoffe (Gl. (8)) 14

0 ELsetier Sequoia/Printed

in The Netherlands

104

beniitigt. Die Siedetemperatur i-3 zum jeweiligen FEiissigkeitsmolenbruch x1 und zum jeweils herrschenden Systemdruck p wird aus dem Siedegleichgewicht bestimmt. Die zugehiirige Phasengrenztemperatur TPh erhilt man mit GE. (5) aus den Phasengrenzmolenbtichen x ,_ Ph bzw. y,? Ph wieder mit dem Siedegleichgewicht (Abb. 2). Die Verdampfungsgeschwindigkeit uQ wird dabei mit der an der Heizfltiche iibertragenen Wtiimestromdich te 4 berechnet (Gl. (6)). Der fiir die Berechnung bentitigte Stoffiibergangskoeffizient & ist in der Grtissenordnung von (I-3)X10F4 m s I, wie er such bei der Absorption und der chemischcn Wtischegefilndcn wird (Abb. 8 ---26). Dabei ist der Zahlenwert PC;jeweils unabh&q& von der an der IleizfiZche aufgeprcigten Wtirmestromdichte, den Anstrtimbedingungen, dem Systemdmck und der Gemischzusammensetzung, such bei Gem&hen mit stark nichtidealen Siedegleichgewichterl. Das Rechenverfahren l&t sich mit ertrriglichem Rechenaufwand such auf Gemische mit mehr als zwei Komponenten anwenden. Rechnet man mit einem einzigen bin&en Stoffiibergangskoeffizienten fir fir alle in einem Cemisch mit n-Komponentcn enthaltenen Stoffpaare, so erhtilt man zur Bestimmung der Phasengrenztemperatur T,, n -- I unabhringig l&bare Gleichungen analog GI. (5). Es miissen allerdings die Siedegleichgewichte fiir die n-Stoff-Gemische bekannt sein. Aus den Konzentrationsmessungen bei der Oberjl&henverdampfung (ohne Blasenbildungj wurden ehenfalls Stofftibergangskoeffizienten & im Bereich (2 5) X low4 m SC’ ermittelt. Eine Verschlechtenrng des W&metibergangs heim Cemischsieden war hier jedoch wegen der geringen VerdampfungsstrSme nicht zu beobachten. Es zeigte sich, dass sich das gekoppelte W&me- und Stofftiansportproblem bei der Rieselfilmverdampfung mit den gleichen Antitzen fiir die Hydrodynamic des lamirlaren und turbulenten Rieselfilmes beschreiben l&St wie hei der Kondensation und der Absorption. Introduction Evaporation from a falling film may occur either as surface boiling at low heat fluxes or as nucleate boiling at higher heat fluxes. For the study of surjticc boiling of mixtures, the liquid-side mass transfer resistances on heat transfer and the separation effect are generally neglected [ 1 ~-31. In condensation, some authors assume the liquid film to be totally mixed, thus neglecting mass transfer resistances in the liquid phase [4, 51. To calculate condensation rates and concentration profiles in the vapour phase. Krishna et al. [6] assume infinitely high liquid-side resistances, as do S&Kinder et al. in recent publications [7.8]. In physical absorption and absorption with chemical reactions, however, the velocity of the whole process is determined by the mass transfer resistances in the liquid, with the liquid-side mass transfer coefficients on being in the range (I- 5) X 10e4 m s-l [9]. Similar values for /3~ were recently found for falling film evaporation of binary mixtures [IO]. In summary, there seem to be contradictory assumptions as to the influence of liquid-side mass transfer resistances in similar processes differing only in the direction of mass flow through the vapour---liyuid interface.

For nucleate boiling, it is well known that the boiling heat transfer coefficients for mixtures can be significantly lower than those for the pure components. This decrease of the heat transfer coefficients has been studied extensively [7]. One physical explanation is the rise in the local boiling tempcraturc due to the preferential evaporation of the more volatile component. Thus. this component has to be transported to the interface against mzass transfer resistances. This explanation was presented for the first time by van Wijk. Vos and van Stralen [ 1 11. To calculate the bubble growth rates in superheated [ 17. 131 used the same binary mixtures van Stralen relationships for the mass transfer in the liquid phase as did S&hinder 1141 to calculate the heat lransl‘er coefficients. During pool boiling of mixtures. the rising vapour is always in equilibrium with the entire boiling liquid because rectification of the bubbles is possible after their departure from the heating surface. Because the bubbles pass through only a thin liquid film during falling jilrn boiling, equilibrium should not be achieved. By measuring the vapour and liquid compositions while varying the heat flux 4. the film Reynolds number and the mole fraction x1, this explanation for the reduction of the heat transfer coefficients may be verified. Theory The following considerations concern snr$zce boiling. With the assumptions described below. they basically and apply to nucleate boiling as well. The temperature concentration profiles which arc formed during surface boiling in a falling film ale shown schematically in Fig. I The binary liquid mixture flows downwards along a vertical wall and is evaporated partially due to the heat flux i. The more volatile component 1 is depleted at the vapour -hquid Interface and must be transported from the bulk of the liquid film by diffusion and convection. The mole fractions of the vapour _I’~Ph and the liquid xl, Ph and the temperature 7& at the interface are connected by the thermodynamic equilibrium. If the vapour is withdrawn perpendicular- to the film. there is no possibility of a concentration profile forming in the vapour phase under steady state conditions. Therefore the measured mole fraction J’, is identical to the mole fractiony,, Ph at the interface. To calculate the flux of the more volatile component ri, towards the interface. the following equation can be used 11-51.

‘,

Fig. 1. Temperature evaporation.

and concentration

profiles

film

105

axI iii, = pQsQ+ fix,

Many investigations [7] in the regime of nucleate boiling show that the a-values can be much lower than so-called [ 161 ‘ideal’ heat transfer coefficients

as

where fi is the total flux of both components r-l = Ii1 +tiz

(2)

Integrating fir = ?+I,

Ph

(3) the mass transfer

coefficient (4)

hQ/s

film theory

[ 1 S] leads to the following

relationship

:

Y’*Ph-X1

KP =

(5)

Y1,Ph-X1,Ph

?i VQ =

4

=-

-

PQ

PQ

(6)

Ah,

to the rate of mass transfer in the liquid, characterized by Pa. Equation (5) involves two limiting cases. In the case of very low velocities of evaporation, i.e. vQ < flQ, the mole fraction at the interface is equal to the mole fraction in the bulk of the liquid film: x1, Ph = x1 and KQ = 1. The evaporation process is controlled exclusively by thermodynamic equilibrium. The corresponding temperature at the interface is equal to the saturation temperature rpr, = T&x1, p), as shown in Fig. 2. Of WapOratiOn, i.e. vQ % flQ, lead Very high VelOCitieS to yl, ph = x1 and KQ = 0. The liquid evaporates like an azeotropic mixture, that is, it does not change its composition along the falling film. The temperature at the interface is equal to the dewpoint temperature Tph= TTfXI, Ph For evaporation of mixtures the heat transfer coefficient cr is usually defined with the heat flux and the difference between the temperature of the heating surface Tw and the saturation temperature Tafxr, p):

4

a-

(7)

Tw - T&XI, P+

-Ts,,-23.3

0

0.2

Fig. 2. Vapour-liquid

‘.’ 0.6

0.8 1 x1 * Yl

equilibrium

of the Rl l- .R113 mixture.

1 -xr __012

-’ )

where or and 0~~are the heat transfer coefficients of the pure components. This relationship globally takes into account the dependence of the physical properties of the mixture on the composition x1. Owing to the depletion of the more volatile component at the interface, the actual temperature difference Tw - TPr.,(xI, Pu, p) is lower than the difference Tw- ~a{xr,p> Defining an actual heat transfer coefficient Ly*=

The concentration ratio KQ is determined by the ratio of the velocity of the liquid towards the interface,

z+ i

eqn. (1) with

and introducing Pa =

o&J=

~~

4 (9)

Tw - TPh+ 1. Ph>P+

means that CY*is always greater than cr. The assumption that the heat transfer coefficient decrease (a < oidj is only caused by the reduction of the temperature difference available for heat transfer leads to the statement a* = crre

(10)

The combination of eqns. (7)-(lo), eliminating the wall temperature Tw, provides the following relationship for the heat transfer coefficient (Y: %d

(Y=

01) 1 + (%d/G)(TPh

-

Ts)

which was first developed by Schltinder 1141. For the limiting case of KQ = 1 (thermodynamic equilibrium), TPh is equal to Ts and so o( = Olid. For KQ + 0, Tph becomes equal to T, and (Yreaches its lowest value.

Experimental

equipment

The equipment is shown schematically in Fig. 3. The RI l-R1 13 mixture was fed from the reservoir 1 by means of a gear pump 2 into a heat exchanger 4, in which it was preheated approximately to the saturation temperature. The flow rate was controlled by means of a bypass valve 9. The medium then passed through a porous sinter metal filter serving as the feed distributer, flowed downwards through an electrically heated tube 5 and was partially evaporated. The unvaporized liquid flowed through an intermediate cooler 6 and then back into the reservoir. The vapour was removed from the vapour chamber perpendicular to the heating surface and totally recondensed in three condensers 7. The condensate also flowed back into the feed reser-voir. To obtain another liquid composition at the test section a part of the condensate was fed to the condensate vessel 8. The samples required for the tests were taken at the points K. A refractometer with a closed cell was available for carrying out the analyses. The compositions could be determined to an accuracy of 0.2% by mole fraction. The temperatures at the points T were measured with thermocouples (NiCr-Ni).

106

P,.lZ Q

~

5

/

I

0 0

I

9000 6000

2

, _I.-_j-10' 2

5

Fig. 5. Mass transfer

Pa = -q/In

Fig. 3. Experimental equipment: 1, reservoir; 2, gear pump; 3, flow meters; 4, heat exchanger; 5, test section; 6, intermediate cooler; 7, condenser; 8, condensate vessel; 9, bypass line; 10, three-way stopcock; 11, syphon; 12, weighing scale; 13, electrical heating; K, sample points:P, pressure indicator;T, thermocouples.

Experimental

procedure

for surface boiling

The tests were carried out at about p = 1 bar while varying the heat flux (i, the film Reynolds number Re and the liquid molt fraction x1 in the following ranges: Cj= 4500,

6000,

9000

x1 = 0.28,

0.48,

0.62

w m-2

60 5 Re 5 1000 After reaching a steady state, the concentrations of the liquid x1 and the vapoury,. the wall temperature rw and pressure p were measured. The heating surface is divided into three sections. For the analyses only the measured values of the middle section were used. The upper and the lower section were heated to prevent the effects of axial heat conduction from the middle section.

Results and discussion

coefficients

j

i

/

102

2

5

&

103

& for surface boiling.

KP

(12)

are plotted against the film Reynolds number Ke with the heat flux (i as parameter. The mole fraction x1 Ph can be calculated by means of the vapour-liquid equiiibrium of the Rll RI13 mixture [17, IX]. It is obvious that there are only minor deviations from Kg = I, so that evaporation is controlled by thermodynamic equilibrium. Starting from KQ * 0.96 at Re z 1000 and 4 = 4500 W rr?, KP decreases with decreasing Reynolds numbers and increasing heat fluxes 4. The lowest value measured in the regime of surface boiling is Kg zz 0.85 at Re 3 120 and (i = 9000 W m -‘. ‘The mass transfer coefficients fip increase with increasing Reynolds number and are independent of the heat flux 4 and, like Kg, are independent of the liquid composition within the scattering of the measured values. As expected, the &,-values are of the same order of magnitude 3s found in physical absorption and absorption with chemical reaction, i.e. PQ s (2-S) X 1 0e4 m s-~‘. In Fig. 6 the CV-and a*-VdlUeS are plotted against Re for4 = 6000 W rn-~’ andx, = 0.48. The ‘ideal’heat transfer coefficients aid are determined with the measured values of 01, and a2 for the pure components Ri 1 and RI 13 (eqn. (8)). Because of the minor deviations flom KQ = 1 during surface boiling, there is no significant effect of the mass transfer resistances on heat transfer. The (Yidvalues predict the measured a-values quite well. The curves plotted in Figs. 4-6 are calculated by solution of the differential equations for the temperature and concentration fields as described in detail in

for surface boiling 1500

In Fig. 4 the Kp-values determined with the measured mole fractions y, and x1 (eqn. (5)) and in Fig. 5 the mass transfer coefficients

I

I

a

I

I

I

~,=0~8

I

i

I

I

w m2K 1000

1 .o

Kl

0.9 500

0.8 0.7

0.6 m10'

cl 2

5

102

Fig. 4. Kp-values for surface boiling.

2

5 Re

103

Pig. 6, Heat transfer

coefficients

~1,CY*and aid for surface boiling.

107 ref. 17, without any fitting to the measured values. For the calculations a model for the turbulent transport properties was used. It was developed by Blangetti [19] for heat transfer in falling film condensation assuming a laminar layer at the vapour-liquid interface due to the surface tension. The calculated and measured values agree well, the largest deviations being at low Reynolds numbers in the transition regime between laminar and turbulent film flow. These results show that the coupled heat and mass transfer during evaporation of mixtures, condensation and absorption [ 181 in a falling film can be calculated with the same relationships as for the hydrodynamics of falling films.

Experimental

procedure

for nucleate boiling

During nucleate boiZing the heat flux 4, the film Reynolds number Re and the Rl 1 mole fraction x1 were varied as follows: (5 = 90 000, O
70 000,

50 000,

30 000,

16 000 W m--2

1

Re = 400,

800

The tests were carried out in the direction of decreaswere made in ing heat fluxes (i: and the measurements the same way as described for surface boiling.

Experimental boiling

results and discussion

for nucleate

In Fig. 7 the Kp-values determined with the measured mole fractions of the vapour, yr, and of the liquid, x1 (eqn. (S)), are plotted against the heat flux 4 for x1 = 0.55 and for two Reynolds numbers Re = 400 and 800. As expected, the deviation from Kp = 1, that is, from evaporation exclusively controlled by thermodynamic equilibrium, is considerable. The lowest value is KQ E 0.55 at 4 = 90 000 W m-‘. Within the scattering of the measured values, KQ is independent of the Rll mole fraction. During nucleate boiling no influence of the Reynolds number was observed. Depending on the magnitude of the heat flux, one part of the total heat supplied is used for bubble formation at the heating surface, while the other part is

0.6

0

20

40

Fig. 7. Kg-values WB).

60.

q,JypO d

for surface boiling

(SB)

and

nucleate

boiling

transported by convection to the liquid surface and is used for evaporation by surface boiling [20, 2 I]. Therefore, the measured vapour mole fraction is a result of mixing the vapour from the bubbles and from the surface. Furthermore, after their departure from the heating surface, the bubbles have to pass through a thin liquid film whose thickness is of the same order of magnitude as the bubble diameter. Assuming the limiting case, that the vapour in a bubble just formed has the same composition as the surrounding liquid, the bubble would be saturated to a degree of about 45% after penetrating through the film [17]. Only a distance of about four bubble diameters is required for the bubble to achieve equilibrium. Because of these effects only qualitative conclusions can be drawn from the measured Kp-values shown in Fig. 7. The bubble formation during nucleate boiling is influenced to a great extent by liquid-side mass transfer The selectivity during falling film boiling resistance. diminishes more and more with increasing evaporation rate. It follows, furthermore, that the liquid-side mass transfer coefficients fie required for the calculation of the heat transfer coefficients OL(eqn. (7)) have to be fitted to the measured o-values. Because of the proportionate evaporation at the surface and the rectification of the vapour bubbles, the &-values determined with the measured Kn-values cannot be related detinitely to the process of bubble formation. In Figs. 8 and 9 the heat transfer coefficients Q: determined by eqn. (7) are plotted against the Rl 1 mole fraction x1 for Re = 400 and 800, respectively. The heat flux 4 has been chosen as the parameter. As expected, the a-values are smaller than the aid-function (eqn. (8)) which is nearly the linear connection between the e-values of the pure components. The reduction of the heat transfer coefficients increases with increasing heat flux. During surface boiling (4 = 6000 W m-‘) no reduction was observed because of the small deviations from KP = 1. During nucleate boiling the Reynolds number is of minor importance. The curves plotted in these Figures are calculated as described below.

Estimation formation

of the KQ-values during bubble

The heat transfer coefficients o during nucleate boiling of mixtures can be calculated by eqn. (11) if the temperature TPh is known. TPh can be determined if the value of KP for bubble formation is known. This value of KQ can be estimated using experimental data for the bubble departure diameters and formation frequencies. The departure diameter ddep and the bubble frequencyf are about 1 mm and 100 s-l, respectively. Thus the vapour velocity is about i?, = 0.1 m SC’ [22 1. For the Rl l-R1 13 mixture with the liquid density PQ g 1400 kg me3 and vapour density pv 2 6 kg mA3, these values lead to a time-averaged liquid velocity UQ towards the interface of about 4.3 X lop4 m s-l. The bubble diameter is proportional to the square root of the time [23] :

108 (13)

ltbcc 4

w

Thus, the proportionality ueft)a

LOO0

a dK

(14)

lIti

3000

is valid

and vp(tdep)= const./&= 2.2 X lop4 m S-I at the departure time tdeP = 1if. Analogous to transient heat transfer, the Fourier number Fo for transient mass transfer in the liquid phase is defined as Fo = 6,rjd,,*

(19

where & is the binary diffusion coefficient, with 6~ z 3.1 X 10P9 m2 s-l for RI 1 -RI 13. d, is the bubble diameter at time t. LJsing eqn. (13) it follows that Fo = 3 X 10e5 = constant during bubble formation. The liquid-side mass transfer coefficient f3p at t = t&p is obtained as Sh hv fip = -ddep = 3.1 X 10m4 m s-l

1000

0

0.2

0.4

06

x,

0.6

1

Fig. 8. Heat transfer coefficients 01 for nucleate boiling of RI lR113 mixtures; film Reynolds number Re = 400. LOO0

(16) a

where the Sherwood

number

d!L mZK

1 1 - Sh = 1’ x Fo

= 103

is also independent PQ a

3000

(17)

of time. since (18)

liti

as well as vQ (eqn. (14)). Thus, the ratio “Q -

= ~
Ky=exp

and the KQ-value is

= 0.47

-z i

formation

I

0

I

!

!

0.2

0.L

0.6

!

I

0.8 x,

1

Fig. 9. Heat transfer coefficients a for nucleate boiling of RllR113 mixtures;film Reynolds number Re = 800.

!

With increasing heat flux the vapour velocity vy and the liquid velocity ve increase. Because of the decreasing Kn-values, the temperature TPh at the vapour-liquid interface increases and so the heat transfer coefficients 01 are reduced (eqn. (1 l)), as observed in numerous measurements.

w=O.lZmls

5000

a w

mZK 4000

Calculation comparison boiling

of heat transfer coefficients and with measured values for nucleate

The heat transfer coefficients cy for the Rll -R113 mixture which was studied experimentally in this work [ 171, and for ten other binary and two ternary mixtures, were calculated as described above with the eqns. (S), (6) and (11) and the corresponding vapour--liquid equilibria 1241. The liquid-side mass transfer coefficient &, which is required for the calculations, was fitted to the measured heat transfer coefficients Q. The experimental results and the calculated curves are plotted in Figs. H-25 against the mole fraction of the more volatile component. In Figs. 26 and 27 only

0

0.2

0.4

Fig. 10. Heat transfer R113 mixtures

06

0.6

XI

coef!icients

I

01 for pool

[ 18 ] ; w = flow velocity.

boiling

of Rll-

109 a

a

w

p= I

mzK

I

--8,=0.99.10-'rd.

W

bar

2iT

,.3.10-Lml*

---B,=

1woo

22000

p. 1 bar

20000 12000

16000 16000

6000

lLOO0

-I

12000

8

LOO0

10000 8000

n_

woo

0

4000

0.2

0.L

0.6

Fig. 14. Heat transfer tures [31].

coefficients

LYfor i-propanol-water

mix-

01 for i-propanol-water

mix-

2000 0

0.2

0.4

11. Heat transfer

Fii.

0.6

0.8 x,

1

coefficients

01for methanol-water

mixtures

[261.

-_B,=o.so~lo-~ -.-._

Ink p =0.99 bar

~=1,3.!O-‘m,.

12oJO

8000

4000

0 0

0

0.2

0.4

Fig. 12. Heat transfer [271.

0.6

0.6 y,

coefficients

-.-.-B~.14-Lm,s‘itledfor 1

0.L

Fig. 15. Heat transfer tures [ 161.

01

p

0.2

0.6

0.6

XI

1

coefficients

1 01for methanol-water

mixtures

A

.o

aid

0.8 0.6

0

0.2

0.L

0.6

0.6.,

1

Fig. 13. Heat transfer

coefficients (Yfor ethanol-water mixtures: O, Shakir, from ref. 28, (i = 200 kW mw2; o, ref. 26, 0, ref. 27, o, ref. 29, 4 = 232.6 kW mA2; n, ref. 30, (i = 250 kW m?; p = 1 bar.

the calculated curves are plotted. As shown in the Figs. 11-13 the greatest problem in comparing measured and predicted heat transfer coefficients is the fact that to some extent different authors measure different reduc-

0

0.2

0.L

Fig. 16. Heat transfer 1311.

0.6

0.8

X1 1

coefficients

a for acetone-water

mixtures

110

12000 a w m2K 8000

2000 0

0.2

Fig. 17. Heat tures [16].

04

transfer

0.6

0.8 x,

coefficients

0.2

0

1

01for acetone-n-butanol

mix-

OL

Fig. 20. Heat transfer tures [16].

10000

0.6

0.8

x,

1

coefficients

OLfor benzene-toluene

mix-

coefficients

o( for benzen+toluene

mix-

01 for benzene-toluene

mix-

01 for acetone-methanol

mix-

10000

a

a

w

W

mZK

;;;riT

6000

6000

LOO0

2000 0 0

02

0.L

Fig. 18. Heat transfer

0.6

0.8

x,

coefficients

1 QIfor acetone-n-butanol

mix-

Fig. 21. Heat transfer twes [16].

tures [16].

8000

12000 a

a W

AL m2K

TX 6000

8000

5000

6000 LOO0

3000 2000

0

0.2

Fig. 22. Heat tures [31]. Fig. 19. Heat transfer tures [ 271.

coefficients

(I for acetone-n-butanol

0.L

transfer

0.6

0.8

x,

1

coefficients

mix-

tions of the heat transfer coefficients for the same mixture with nearly equal a-values for the corresponding Despite this discrepancy the following pure components. conclusions can be drawn from a comparison of the measured and calculated values. For all mixtures studied in this work the heat transfer coefficients a: could be predicted assuming the liquidside mass transfer resistances to be the only reason for the reduction of heat transfer during boiling of mixtures. No further physical explanation was needed. All other influences during nucleate boiling, such as work of

7000 a L m2K 5000 It000 3000 0

02

OL

Fig. 23. Heat transfer tures 126 I.

06

oa.,

coefficients

1

111

10000

a

7% 6000

_

A’

0

0.2

Oh

0.6

Fig. 24. Heat transfer tures [16].

0.8 x, 1

coefficients

aid

01 for methanol-benzene

mix-

0.8 0.6

pi

I

10000

2 bar

-

6,;

1.3.104mlr

0.1

I

0.2

a

w

IGK

0

6000 11)

LOO0

Xl

_

(21

Fig. 27. Heat transfer coefficients IYfor acetone(l)-methanol(2)water(3) mixtures [26]. Q = 100 kW rn-‘, & = 1.3 X 10-4ms-1.

2000 0 0.2

0 Pig.

25.

Heat

04

transfer

0.6

0.8 x, 1

coefficients

~2 for

R23-R13

mixtures

1321.

1

a

CLid

0.6 0.6 0.A

0.2 0.

0 (1)

12)

Fig. 26. Heat transfer coefficients CYfor methanol(l)-ethanol(2)water(3) mixtures [26]. 4 = 100 kW II-?, flQ = 1.3 X 10-4ms-1.

bubble formation [25], bubble departure diameter and bubble formation frequency, seem to be of minor importance. All of them depend strongly on the composition of the mixture. However, the liquid-phase mass transfer coefficients &_ which were fitted to the measured a-values are shown to be independent of the composition in all cases; even for mixtures with physical properties varying drastically with composition as well as for mixtures with non-ideal vapour-liquid equilibria. Furthermore, the liquid-phase mass transfer coefticients 0~ are found to be independent of the film Reynolds number, the heat flux and the system pressure. In nearly all cases the fitted values of fiQ are in the range (I-3) X lop4 m s-l. The value & = 1.3 X lop4 m s-r follows from fitting to our own measured o-values for falling film evaporation of Rl 1-R113. For prediction of the heat transfer coefficients cr for multicomponent mixtures, the Stefan-Maxwell equations [15] instead of eqn. (1) have to be solved. For the binary mixtures good results for the heat transfer coefticients are achieved using the same mass transfer coefficient, for example /3a = 1.3 X lop4 m s-l, in the calculations for all mixtures. This good agreement between the measured and calculated values can also be expected for multicomponent mixtures using the same &-value for all pairs. In this case the Stefan-Maxwell equations can be reduced ton - 1 independent equations for Iz components like eqn. (5). For the two ternary mixtures the heat transfer coefficients (Y calculated in this way (Figs. 24 and 25) are about 2.5% lower than the values measured by Preusser

[261.

112

Summary

6 P

The effect of liquid-side mass transfer resistances on heat transfer and selectivity during partial evaporation of the binary refrigerant mixture Rl 1 --R113 in a falling filnl apparatus was investigated by varying the heat flux, the film Reynolds number and the liquid composition. During surface hailing the reduction of the heat transfer coefficients is negligible fol- technical applications, because of the minor deviations from evaporation which controlled by thermodynamic equilibrium. are mainly Nevertheless, the liquid-side mass transfer coefficients; which can be determined hy the measured vapour and liquid mole fractions, are of the same order of magnitude as in physical absorption and absorption with chemical reactions, i.e. 0~ = (2-S) X 10P4 m s ‘. The coupled heat and mass transfer during falling film evaporation of mixtures, condensation and absorption [ 17, 191 can be calculated with the same relationships as for the hydrodynamics of falling films. During nuclmte builing the selectivity diminishes significantly and heat transfer is influenced to a great extent by liquid-side mass transfer resistances. There is considerable deviation from evaporation controlled exclusively by thermodynamic equilibrium. The heat transfer coefficients (Y for the Rl I-RI 13 mixture as well as for ten other binary and two ternary mixtures could be calculated assuming the mass transfer resistances to be the only reason for the reduction of the heat transfer coefficient 01 during boiling of mixtures. No other physical explanations were needed. The calculation method is easily extendable to multicomponent mixtures, if the corresponding vapour4iquid equilibria are available.

binary diffusion coefficient, molar density, kmol me3

Subscripts 1 2 b dep id Q Ph S T ;

R. A. W. Shock, Evaporation of binary mixtures in upward annular flow, lilt. J. Multiphase Flow, 2 (1976) 411-433. The performance of 2 K. Honda. A. Matsuda and T. Munakata, externally hcatcd or cooled wetted-wall columns for distillation in both the laminar regime of vapor flaw under reduced pressure and in the turbulent regime of vapor flow at atmosphcrlc pressure, Ir,f. C/zew;. E?rlg., 24 (1984) 321 -329. Tung. J. F. Davis, R. S. W. Mah, F’raclionating 3 Hsien-Hsin with condensation and evaporation in wetted-wall columns. I

4

5

Acknowledgement 7 8

Nomenclature

9

Z Sh

bubble diameter at time t latent heat of vaporization, kJ kmol-’ bubble formation frequency, s-l Fourier number concentration ratio molar flux, kmol tr? SC’ pressure. bar heat flux, W me2 thickness of concentration boundary layer. m Sherwood number

t

time,

T ” v

temperature, K velocity, m s-l time average velocity, liquid mole fraction vapour mole fraction

db Ah, f Fo K ri P

X

Y

10

11

12

s

m s-l

13

14

heat transfer coefficient, mass transfer coefficient,

W m 2 K-’ m s-l

more volatile component less volatile component bubble departure ideal liquid interface saturation dew point vapour wall

References

6

The authors thank the ‘Deutsche Forschungsgemeinschaft’ for financial support of this work.

m2 s-l

AI&E J., 30 (1984) 328-m338. K. Stephan, W~rmeiibertragung mit PhasrnCnderung in vcrfahrenstechnichen Prozcssen, (7zern:Ing.-Tech., JO (1978) 100-107. B. C. Price and R. 1. Bell, Design of binary vapor condensers using the Colhurn-- Dre\r, equations. AIChE Symp. Se’.. 70 (1974) 163.---171. R. Krishna, C. B. Pan&al, D. R. W&h and I. Coward, An Ackermann-Colburn and Dre~v type analysis for condensation of multicomponent misturcs, Lett. Heat Mass l?a~7S.terlr. 3 (1976) 163-172. VDI-Warrnentlas. VDI-Vcrlag, Diisseldorf. 4th edn., 1984, Section Jh 7. D. Fullarton and E. U. Schliinder, h’8herungsweise Beatinmung dcr AustauschEiche bei der Kondensation van GasDarnIlfgellli~chen, C/zwz. f&p. Process., IB (1 984) 283 -292. 0. Nagel, H. Hegner and H. Kiirten, Kriterien fiir die Auswahl und die -luslegung van C;as-Fliissigkcitsrcaktoren. C%cm.Irrg:Te&., so (1978) 934-944. U. Gropp, G. Schnabel and I,:. II. Schliinder, . van Stralen, Heat transfer to hoihng binary mixtures. Clww. Ew. Sci., 5 (1956) 68-80. S. J. D. van Stralen, W. M. Sluyter and R. Cole, Bubble growth rates in nucleate boiling of aqueous binary systems at subatmosphelic p~~wu~rs, lnt. .I. fIrat Mass Trmrs,t~r. 19 (1976) 931-941, W. K. van Wijk and S. J. D. van Straien, Masnnalc WPrmestromdichte und Wachstu~nsgeschwir~di~k~it van Darnpfhlasen in siedenden Zwcistoffgernischen, (li?er,r.-lnfi.-Tech.. 37(1965)509-517. 1,. IJ. Schliindrr, iiher den Wirmetihcrgang hci der Hlasenverdampfung van Gemischen. Vt- I/[,rfahrenstechnih~, 16 (1982) 692-698.

113 15 R. 8. Bird, W. E. Steward and E. M. Lightfoot, Transport Phenomena, Wiley, New York, 1960. 16 M. KBrner, Beitrag zum Wgimeiibergang bei der Blasenverdampfung bin&r Gemische, Dissertation, RWTH Aachen, 1967. bei der Oberflachen17 U. Gropp, Warme- und Stofftibergang verdampfung und beim Blasensieden eines bin&en Ka’ltemittelgemisches am Rieselfilm, Dissertation, Universitiit Karlsruhe, 1985. von Rll/R113 Gemischen an einem 18 J. Fink, Verdampfung querangestrdmten waagerechten Zylinder, Dissertation, Universittit Clausthal, 1982. bei der Kondensation 19 F. Blangetti, Lokaler WLmetibergang mit tiberlagerter Konvektion im vertikalen Rohr, Dissertation, Universitiit Karlsruhe, 1979. an eine an einer Heizwand 20 J. Piening, Der Wgrmetibergang wachsenden Dampfhlase, Dissertation, TU Berlin, 197 1. 21 C. J. Rallis and H. H. Jawurek, Latent heat transport in saturated nucleate boiling, Int. J. Heat Mass Transfer, 20 (1964) 1051-1068. 22 J. Schmadl, Wsrmeiibergang beim Blasensieden binlrer Stoffgemische unter hohem Druck, Dissertation, Universitat Karlsruhe, 1982. Physikalische Grundlagen der Verfahrens23 P. Grassmann, technik, Salle + Sauerllnder, Frankfurt-on-Main, 1983. 24 J. Gmehling, U. Onken and W. Arlt, Vapor-Liquid Equilibrium Data Coilech’on, DECHEMA Data Series, DECHEMA, Frankfurt-on-Main, 1977-. 25 M. Stephan and M. Klirner, Berechnung des Warmetibergangs verdampfender binZrer Fliissigkeitsgemische, Chem-hzng.Tech., 41 (1969) 4099484. 26 P. Preusser, Warmetibergang bcim Verdampfen bin&r und terntier Fltissigkeitsgemische, Dissertntz’on, Ruhr-Universitat, Bochum, 1978. 21 L. N. Grigorev and A. G. Usmanov, Heat transfer during boiling of binary mixtures, Sov. Phys.-Tech. Phys., 3 (1958) 297-305. 28 J. R. Theme and R. A. W. Shock, Boiling of multicomponent mixtures, Adv. Heat Mass Transfer, 16 (1984) 60-153. 29 L. N. Grigorev, I. Kh. Khairullin and A. G. Usmanov, An experlmental study of the critical heat flux in the boiling of binary mixtures,Znt. Chem. Eng., 8 (1968) 39-42. und 30 V. Valent and N. Afgan, Dynamik des Blasenwachstums Warmetibergangs beim Sieden bintier Gemische von Athylalkohol-Wasser, Wirme- Stoffiibertrag., 6 (1979) 235-240. 31 0. Happel, Witrmeiibergang bei der Verdampfung biniirer Gemische im Gebiet des Blasen- und Ubergangssiedens, Dissertation, Ruhr-Universitlt, Bochum, 1975. bei der Blasen32 P. Wassilev, Beitrag zum WBrmetibergang Dissertation, verdampfung binlrer Kaltemittelgemische, Technische Universita‘t, Dresden, 1978. 33 R. Plank, Handbuch der Kiltetechnik, Band 4, Kiiltemittel, Springer-Verlag, Berlin, Gottingen, Heidelberg, 1960.

Appendix

TABLE A-l. Antoine

constants

Component

A

B

D

Water Methanol Ethanol i-Propanol Acetone n-Butanol Benzene Toluene R23 R13

8.19621 8.20587 8.23710 9.00323 7.24204 7.96290 7.00477 7.07577 7.31195 7.01263

1730.63 1582.271 1592.864 2010.330 1210.595 1558.190 1196.760 1342.310 741.34624 690.60706

233.426 239.726 226.184 252.636 229.664 196.881 219.161 219.187 254.19076 253.85205

TABLE A-2. Wilson parameters

for binary mixtures

Mixture

-412

A21

(1)-W

(kcal kmol-‘)

(kcal kmol-‘)

Methanol-water Ethanol-water i-Propanol-water Acetone-water Acetone-n-butanol Benzene-toluene Acetone-methanol Methanol-benzene

-105.9234 222.7734 505.1942 344.3346 -127.9322 794.4068 -124.9332 1.621.2357

648.0054 1000.8756 1311.9637 1428.2133 513.5023 -550.8902 551.4545 202.0307

TABLE A-3. Wilson parameters

for ternary

mixtures

Aij (kcal kmol-r)

Acetone(l)Methanol(2)Water(3)

Methanol(l)Ethanol(2)) Water(3)

A12

-765.421 1827.665 -360.904 2011.217 1334.536 626.972

-240.152 -41.027 447.171 637.320 651.139 904.717

A13 A23 -421 A31 A32

TABLE A-4. Molar volumes $ Water Acetone Methanol Ethanol

18.07 74.05 40.73 58.68

X lop3

(m3 kmol-‘) i-Propanol Benzene Toluene ndutanol

76.92 89.41 106.85 91.97

VapourPliquid equilibria The vapour-liquid transfer calculations equation log&*=/l

-

equilibria required for the heat were calculated using the Antoine

B -~ T+D

for the vapour pressures pi* (in mbar) of the pure components (T in “C) and the Wilson equations for the activity coefficients ri

lnyi=

-In

i=

j=l

1, . . ..n (A-2)

with L Aii = % Oi

exp _ A!! (

RT i

(A-3)

114 and

(A-4) The corresponding constants are listed in Tables A-l -A-4. The activity coefficients for the R23SR13 mixture were calculated with the van Laar equations

2

A2x2 -

lny,=A,

tA

1x1

+AzX2

(A-5)

The vapour--liquid equilibrium of the Rl 1--R113 mixtures was calculated with the Riedel equations [33] (p in atm) log pl* = 10.4466 + 0.1753 log pz* = 9.6842 +0.1171

1995.8 -- ---/-

- 1.7697 X lo--’ T

x 1o--4 T2 2099 - ~~~~ T

(A-7) 1.3505 x 10-2 T

X10-4T2

(A-8 )

1

and with the Margules equations

(A-6) withA1=1.35S67andA2=1.07408forp=2bar.

In y1 = (1 - r12)(0.2131 Iny,=n,~[0.0174

[17]

-- 0.3914~~)

+0.3914(1

x,)]

(A-9) (A-10)