Heat Transfer in Condensation and Boiling

7/26/2019 Heat Transfer in Condensation and Boiling

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ISSN 00405795, Theoretical Foundations of Chemical Engineering, 2012, Vol. 46, No. 4, pp. 359367. Pleiades Publishing, Ltd., 2012.Original Russian Text N.A. Voinov, O.P. Zhukova, A.N. Nikolaev, 2012, published in Teoreticheskie Osnovy Khimicheskoi Tekhnologii, 2012, Vol. 46, No. 4, pp. 432440.

359

INTRODUCTION

Tubular film evaporators are used in the desalina

tion of seawater, suspension concentrations, and sewage treatment. However, relationships for calculatingheat transfer in these apparatuses are insufficientlyperfect, which, when designing plants, leads to unreasonably high dimensions and metal consumption. Theproblem of creating a stable film flow and avoiding theformation of dry spots or film breakdown on the surface of evaporator tubes, which causes a decrease incapacity, is also not solved. The main heat transferprocesses in an evaporator are boiling and film condensation. The combination of a large number of factors that affect these processes makes the generaliza

tion of procedures for calculating apparatuses ratherdifficult. The objective of this study is to investigateheat transfer in condensation and boiling in a tubular

evaporator with smooth and rough surfaces undergravity flow of a water film and derive relationships forcalculating the heattransfer coefficient.

COMPUTATIONAL RELATIONSHIPS

Characteristic relationships for calculating theheattransfer coefficient in a turbulent film in boilingare given in Table 1.

A comparison of heattransfer coefficients calculated by equations given in Table 1 shows their sub

Heat Transfer in Condensation and Boiling

in a Tubular Film Evaporator

N. A. Voinov, O. P. Zhukova, and A. N. Nikolaev

Siberian State Technological University, pr. Mira 82, Krasnoyarsk, 660049 Russia

email: [email protected]

Received August 16, 2011

AbstractThe results of a study of heat transfer in condensation and boiling in a tubular evaporator withsmooth and rough surfaces under the gravity flow of a water film are presented. Relationships are derived forcalculating a heattransfer coefficient, and the effect of helical roughness on heat transfer is revealed.

DOI: 10.1134/S0040579512030104

Table 1. Equations for calculating the heattransfer coefficient in liquid film in boiling

No. Parameters Computational formula Source

1

Re = (285) 103,

m= 0.191.06,

n= 0.330.5

[18]

2 Re > 2000 [9]

3 2000 < Re < 7000 [10]

4

At q = (820) 103W/m2,C = 164, n= 0.264, m= 0.685.

At q> 15 103W/m2,C = 2.6, n = 0.203, m= 0.322.

[11]

5 Re < 10000 [12]

6 = 34 kg/(m s) [13]

7 Re > 1900 [14]

( Re Pr ) ;m n

f=Nu

( ) ( )

1 321 3

Pr

1 Pr 0.4 Pr 5 Pr 5 ln 1 5 Pr 2.5 ln

1 11 Pr

g

=

+ + + ++

0.32 0.435438q= Nu

Re

mn q

Ct

= = satNu

2 0.58 0.58 0.34* 1.1 10 Re Pr wK

= Nu

0.63 0.2213500 t q

=

0.15 0.13 0.0750.064 Re Re Pr u

=Nu


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VOINOV et al.

stantial disagreement (Fig. 1). The observed scatter invalues can be explained by different experimental pro

cedures and narrow ranges of physical and designparameters. As a rule, the cooling of the upper layers ofa falling film during evaporation from its surface is nottaken into account at low heat fluxes. The regimes ofheat transfer that are caused by heat duty are not takeninto account. Known data on the effect of helicalroughness on heat transfer are scarce, which requiresadditional studies.

In the turbulent flow of a condensate film, equations for calculating heat transfer are usually expressed

in terms of dimensionless numbers (Table 2) as =f(Recond, Res, Pr, Cr, Ga, K).

An analysis of the relationships given in Table 2 hasshown (Fig. 2) that they adequately describe the process only in the ranges in which they are derived. Thisis explained by the complexity of heat and mass transfer, in which the nonuniformity of temperature andmass fields; the variable composition of a gassteammixture; and, accordingly, the variations in the physical properties of steam and condensate are observed.

In the case of high steam flow rates (movingsteam), the influence of shear stresses at the interface

10

3

101

b103, W/(m2)

20 Re

6

45

7 1

3

8

2

Fig. 1.Heattransfer coefficient in boiling in a water filmthat falls along the hydraulically smooth surface of a tubeas a function of the Reynolds number of the liquid. Thelines represent calculation at d= 30 mm, l= 1.7 m, andPr = 3.5 by equations from the following studies: (1) [10],(2) [1], (3) [2], (4) [9], (5) [4], (6) [8], (7) [7], and (8) [5].

Table 2. Relationships for calculating the heattransfer coefficient in steam film condensation on the inner surfaces of vertical

tubesNo. Range of application Heattransfer coefficient Source

1 Recond> 100 [18]

2 Recond> 180 [19]

3 Recond> 100 [6]

4 PrKGa > 1015 [20]

5 Recond> 400 [8]

6 Res > 25000 [17]

7 [21]

8 [16]

1 3

1 3

0. 16 P r Re

Re 100 63 Pr =

+

cond

cond

*Nu

1 2 0.250.23 Pr

=N u Ga

( ) ( ) ( ) )(1 3 0.2 0.8 0.60.925 Re 1 0.03 4 Re 0.00075 4 Re Pr = + +cond condcond*Nu0.25

0.943(Pr )=Nu KGa

( ) ( ) 4 30.5

( ) 89 0.024 Pr 2300r l t t z = + sat c

1 320

=

.6 s ss

dNu 0.28Re K P r

l

0.5 0,50.8 0.43

1 2Re Pr 1 1 1C x x

= + + +

cond condcond

s cond

Nu

1 31 0. 13

( )w

u

g

= + s

cond

10

5

3000200010000

cond103, W/(m2)

Recond

1

4

23

Fig. 2.Dependence of the heattransfer coefficient in thecondensation of pure steam on the Reynolds number for acondensate at d= 20 mm and l= 2 m. Experimental pointsare obtained at K = 12. The lines are as follows: (1) [20],(2) [18], (3) [6], and (4) [8].


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THEORETICAL FOUNDATIONS OF CHEMICAL ENGINEERING Vol. 46 No. 4 2012

HEAT TRANSFER IN CONDENSATION AND BOILING 361

causes an increase in the velocity and a decrease in the

thickness of a condensate film, as well as the formationof waves on its surface, which, depending on the flowregime, has an enhancing effect on heat transfer.These phenomena are also not reflected in knownstudies into condensation.

Under the conditions of the downward motion of acondensate film, with allowance for friction at thephase boundary, it is proposed to determine a heattransfer coefficient for moving steam from Eq. (8)(Table 2). However, in a descending cocurrent flow,three regimes of the interaction of a gas with a liquid

with different intensities of heat transfer are observed[15], the boundaries of which depend on both theinner diameter of a channel and the Reynolds numberof the gas. For a turbulent film flow and the prevailinginfluence of steam, formula (7) (see Table 2) is proposed in [21], according to which there is a considerable influence of the condensate film on heat transfer

and the effect of shear stresses, the determination of which is experimentally complicated, is evaluated through steam contents x1andx2.

Equation (6) (see Table 2), proposed in [17], whichis recommended to be used at Res > 25000, where

cond which is in agreement with the data [15]obtained in the case of the heating of a water film in adescending cocurrent flow in the transition flow

region, is of interest. In addition, dimensionlessparameter K, which takes into account the influence ofthe interphase transition is introduced into the equation. However, Eq. (6) (see Table 2) does not include theparameter Recond; therefore, it can only be valid in astudied range of condensable steam flow rates.

In the case of the condensation of an airsteammixture, additional resistance to steam transport tothe condensation surface is produced due to the formation of a boundary layer that consists of noncon

cond

0.8Re ,

s

0.6Re ,

densable gas molecules, which leads to a considerable

decrease in the heattransfer coefficient [25]. In thiscase, the value of the heattransfer coefficient dependson the intensity of interrelated heat and mass transferprocesses both in a gassteam mixture and in a condensate film. By now, a large number of studies intonumerical description of such systems have been performed using different approaches and assumptions;however, the models are not yet perfect for practicaluse [2631]. The authors point out that the thermalresistance of the gassteam boundary layer is high atlow values of the Reynolds number Recond and theresistance decreases with its increase. The overallheattransfer coefficient in condensation decreasesalong the length of the tube, which is explained by adecrease in the fraction of steam and an increase in themass fraction of noncondensable gases at the interface. As for the enhancement of the condensation process, it is pointed out that stirring leads to the intensification of condensation of a gassteam mixture. Toenhance heat transfer in steam condensation, variousprofiled surfaces of tubes are used [3234], whichmakes it possible to reduce the thermal resistance ofthe condensate film due to a decrease in its thickness.However, the use of profiled surfaces is insufficientlyeffective to decrease diffusive resistance in the condensation of an airsteam mixture, which requiressearching for a new method for enhancing heat trans

fer. In this study, the removal of noncondensable gas isensured by generating circulation vortices over the surface of the condensate film, which form when steamflows over streamlined bodies made in the form of a

wire helix installed with a gap to the heat transfer surface. Figure 3 presents a scheme of the flow and temperature distributions in the evaporator tube.

Tubes made of copper with a diameter of 201mmand a length of l= 2 m along the inner surface of whicha condensate film falls and along the outer surface of

() (b) (c)

Gair Gwat Gcond Gg Gas Gair Gwat Gcond Gg Gas

W

W

W

W

tf tc

tctf

tastas

S

S2

Dc

h

h2

1

2

3

4

Fig. 3.Scheme of the distribution of heat transfer media and temperature in the evaporator tube: (a) general view of tube 1withturbulators2and 3and turbulencepromoting insert 4, (b) surface without turbulators, and (c) surface with helical roughness anda turbulencepromoting insert.


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VOINOV et al.

which a water film falls were studied. To enhancesteam condensation, turbulencepromoting insert 4(Fig. 3) made of wire 2.5 mm in diameter with steps ofs = 5, 10, and 25 mm was installed inside heatexchange tubes. Regular artificial helical roughness(Fig. 3a) made of wire with diameters of h= 0.25, 0.5,and 1.5 mm at a roughness parameter ofs/h= 67 wasinstalled on the tube surface; in some cases, an M20metric thread was produced on the outer surface of thetube.

Water supplied to the steam generator was predegassed by boiling. The residual concentration of

oxygen in water was 2 mg/L. The physical propertiesof water and steam were calculated using the averagetemperature at the inlet and outlet of the working section of the tube. Temperature was measured usingTSM9418 resistance thermometers. Temperaturedata were output on secondary Termodat35TSO/GVS devices and entered in the computerdatabase using Termonet 1.01 software. The heat flux

was q= 50250 kW/m2, and the flow rate of the liquid varied from 0.2 to 2 m3/h.

The heattransfer coefficient was determined fromthe equation

= 1/[(1/Kexp) (1/f) (w/w)]. (1)

The experimental values of the heattransfer coefficient Kexpwere calculated by

Kexp= Q/(Ft). (2)

The heattransfer coefficient from the water film inheating at a heat flux of q< 50 kW/m2was determinedfrom the relationship [15]

Nu*= 0.004 Re0.39 Pr0.78. (3)

At q 50 kW/m2, the correction of f was performed using experimental data presented in Fig. 4.

The thickness of a falling water film was calculatedby the relationship [15]

(4)

CONDENSATION OF STEAM

AND AN AIRSTEAM MIXTUREDepending on the flow rate of steam, three charac

teristic regimes of interaction of a gas with a condensate are observed in condensation: weakinteraction,transient, and annular dispersed regimes (Fig. 5),

where the Reynolds number of steam was calculatedusing the average flow velocity of an airsteam mixture supplied to the tube.

The dashed line in Fig. 5 represents the data of [15]for a descending cocurrent flow in the heating of a

water film. The mismatch between the boundaries ofregime transition for steamcondensate and air

water systems is explained by different densities ofsteam and air, since, due to the lower density of steamcompared to air, a larger flow rate of steam is requiredto achieve the necessary value of shear stress at theinterface.

The region of weak interaction is Res20 000 forthe studied diameter of the channel. In this range ofthe Reynolds numbers for steam, the heattransfercoefficient in condensation hardly depends on shearstresses at the interface. In the region of weak interactions, the value of the heattransfer coefficient in condensation is most affected by the flow rate of the condensate and the phase transition criterion K (Fig. 6),and the value of the heattransfer coefficient for puresteam can be calculated by the relationship

(5)

The flux of condensable steam depends to thegreatest extent on pressure in the condensation zoneand decreases with its decrease (Fig. 7).

To estimate the value of a heattransfer coefficientin the condensation of pure steam in the transientregime (Fig. 5), the following equation is derived:

(6)

7 120.135 Re . =

( )condNu 1.87 1.16 0.78

* 2.2 10 Re Pr .K

=

( )cond sNu 1.81.16 0.94 0.78

* Re Re Pr ,C K=

10

8

20015010050

f103,W/(m2K)

q103, W/m2

6

4

2300

Fig. 4.Heattransfer coefficient in heating of a water filmthat falls along the smooth surface of a tube as a functionof the heat flux at l= 2 m, d= 20 mm, Ref= 9000, and Pr =3.5.

4

3

3020105

cond103,W/(m2K)

Res103

12

2

5678

40 50

Weak

interactions

Transient

regime

Annular

dispersed regime

Fig. 5.Dependence of heattransfer coefficient in condensation of pure steam on Resat d= 20 mm, l = 2 m, andt= 50C. Experimental points are as follows: Recond=(1) 3000 and (2) 2000. Dashed line represents data for theairwater system in heating [15].


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where the constant changes depending on the diameter of the used tube of the evaporator [35].

The effect of shear stresses on the intensity of heattransfer due to a change in the hydrodynamics of theflow of a condensate film is evaluated by the dimension

less parameter A similar dependence in thetransient regime was obtained in [15] in studying heattransfer in heating for an airwater system.

The maximum increase in the value of the heattransfer coefficient in the transition region is twofold,

both in the condensation of pure steam and the condensation of an airsteam mixture. From this, we caninfer that an increase in the velocity of the airsteammixture in a tube does not lead to a decrease in diffusive resistance at the interface and only affects a condensate film.

In the annular dispersed flow regime, a decrease inheat transfer is observed, which is caused by the influence of drop entrainment on the turbulence of steam[15]. As was found, in the condensation of an airsteam mixture, a decrease in the heattransfer coeffi

cient with an increase in the fraction of air in steam isobserved (Fig. 8) according to the relationship

cond2/cond1= 0.97exp(3.8E), (7)

where cond1 is the heattransfer coefficient for puresteam andcond2is the heattransfer coefficient for theairsteam mixture.

According to the data in Fig. 8, the presence of aturbulizing insert in a tube enhances the film condensation of an airsteam mixture by a factor of 2.3.

A helix with an optimum roughness parameter ofs2/h2 = 47 makes it possible to ensure the maximumvalue of a heattransfer coefficient due to the genera

tion of circulation vortices in the entire interturn spaceof the turbulencepromoting insert, which removesthe noncondensable gas from the interface and stir anairsteam mixture, equalizing the profiles of the gastemperature and partial pressure over the condensatefilm. Circulation vortices do not form at a roughnessparameter of s2/h23, which leads to a decrease inheat transfer.

An analysis of experimental data presented inFigs. 8 and 9 shows that the installation of a turbulencepromoting insert ensures the intensification ofcondensation for both a steamliquid mixture andpure steam.

This can be explained by the effect of vortices

formed by helix coils on the equalization of temperature profile. The enhancing effect of vortices on thecondensation of an airsteam mixture begins tomanifest itself at the Reynolds number of a gassteam mixture that flows over a streamlined bodyRe = uh2/s 10

3, whereas the generation of vorticesoccurs at Re > 5 according to [25].

The application of helical roughness to the surfacealong which the condensate film falls leads to theintensification of condensation by a factor of 2 (Fig. 9,

s

0.94Re .

10

5

200010000

cond103,W/(m2K)

Recond

12

15

20

3000 4000

3456

Fig. 6.Dependence of heattransfer coefficient in condensation of pure steam on Reynolds number for a condensateat d = 20 mm, q= 80200 kW/m2, andl= 2 m. Experimental points 13 (atmospheric pressure) are as follows:K = (1) 8, (2) 12, and (3) 20. Experimental points 46 areas follows: (4) 80% vacuum and K = 20, (5) 60% vacuumand K = 12, and (6) 20% vacuum and K = 9. The solidlines represent calculation by Eq. (5).

0.020.20

W/F, kg/(s m2)

Pab, atm

123

0.4 0.6

0.06

0.10

0.14

0.18

Fig. 7.Mass flux of condensed steam as a function of absolute pressure at d= 20 mm, q= 80200 kW/m2, l = 2 m,and Recond= 16009000. The experimental points are asfollows: K = (1) 20, (2) 12, and (3) 9.

10

5

0.050

cond103,W/(m2K))

E

12

15

0.10

34

Fig. 8.Dependence of heattransfer coefficient in condensation on fraction of air in steam Eat Recond= 2500, Res 20 000, t = 4060C, Dc = 11 mm, and h = 2.5 mm.Experimental points are as follows: s/h= (1) 6.6, (2) 3.3,and (3) 16.6; (4) h= 0.


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VOINOV et al.

point 2), whereas enhancement does not exceed a factor of 1.65 in the heating of a falling water film [33].Thus, in the case of steam condensation, it can beassumed that helical roughness stirs not only liquidlayers, but also the steam phase in the cavities of

roughness [36].

HEAT TRANSFER IN BOILINGIN A FALLING LIQUID FILM

In the organization of boiling in a liquid film, twomechanisms of steam formation on its surface wererevealed: surface evaporation due to the difference inmoisture contents at the interface and in the core of anairsteam mixture that surrounds the film and the for

mation of steam bubbles on the heat transfer wall ofthe tube.

Under the conditions of surface evaporation andnegligible heat duties (t< 25) (Fig. 10, points 14),partial condensation of steam bubbles in the filmoccurs due to the cooling of a liquid as a result of theevaporation effect, which leads to an increase in theheattransfer coefficient in the film. When the film

falls along the smooth surface of a tube, we have bt1.0; when there is helical roughness, we have bt0.55. The lesser effect of ton heat transfer when thefilm falls along helical roughness (compared to asmooth filmforming surface) is caused by steam stirring in the cavities of roughness.

The amount of evaporated moisture from the surface of the water film can be determined using the

value of a mass transfer coefficient as follows [33]:

for the surface of a tube without a turbulator,

(8)

for the surface of a tube with helical roughness,

(9)

At t25, intense steam formation on the wallof the tube leads to the rejection of air from the interface and the termination of moisture evaporation fromthe surface, which stabilizes b, which becomes independent of a temperature difference. The installationof a jacket coaxial to the tube and the supply of steamto the produced gap, in order to moisten air, lead to theelimination of surface evaporation and the stabilization of a film flow at small values of t(Fig. 10, points57).

At q50kW/m2, the effect of the heat flux on theintensity of heat transfer in a falling water film for bothsmooth and rough surfaces was bq

0.7. The effect of

the Reynolds number of the film was b Re0.1

(Figs. 11, 12), whereas, during heating [33], we have

heat since heat transfer mainly occurs bythermal conduction in heating and by convection in

boiling.

A relationship for calculating the heattransfercoefficient in a water film that falls along the smoothsurface of a tube in the absence of surface evaporationat q= 50300 kW/m2has the form

(10)

The value of the heattransfer coefficient increaseswith an increase in the height of the hill of helicalroughness, whereas the intensity of heat transferdecreases in heating at h> 0.25 mm (Fig. 13). All otherconditions being equal, the maximum enhancementof heat transfer compared with a smooth surface in

boiling was no more than a factor of 1.7.

The presence of a metric thread on the surface ofthe tube when a water film falls along this surface does

f sSc0.15 0.33 0.85

0.32 Re ( );X D d =

f sSc0.5 0.33 0.850.02 Re ( ).X D d =

f

0.39Re ,

bf

sat

Nu

0.75

0.11.85 Re .

q

t

= =

10

200010000

cond103,W/(m2K)

Recond

12

30

3000 4000

40

20

Fig. 9. Heattransfer coefficient in condensation of airsteam mixture as a function of Reynolds number for a condensate at d= 20 mm, q= 80200 kW/m2, l = 2 m, K =12, E= 0.05, Res20 000, and s/h= 6.7. Experimentalpoints are as follows: (1) with turbulencepromoting insertand (2) with helical roughness on the inner surface of atube at h = 0.5 mm. Dashed line represents condensationon surface without turbulators.

4

15105

b103,W/(m2K)

t, C

1

2

12

20 25

16

8 34

5

6

70

Fig. 10.Dependence of heattransfer coefficient in boilingof water film on temperature at d = 20 mm and Ref =15000. Experimental points 14for tube without turbulators are as follows: q = (1) 75, (2) 150, and (3) 250 kW/m2;(4) rough surface of a tube at h= 1.5 mm,s/h= 6.0, andq = 250 kW/m2. Experimental points 57 are same aspoints 1, 3, and 4, but with moistening in air surroundingthe film.


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not promote the intensification of heat transfer both inboiling and in heating, which is due to the absence ofliquid stirring in the cavities of roughness as a result ofa nonoptimum roughness parameter of s/h= 1. It canalso be stated that the hills of roughness formed by thecoils of a metric thread are not evaporation centers.

CONCLUSIONS

In this study, the effect of helical roughness on heattransfer is revealed. The use of regular helical roughness on a surface along which a condensate film fallsleads to the intensification of condensation by a factorof two. The maximum enhancement of heat transfer ascompared with a smooth surface in boiling underother conditions being equal is not more than a factorof 1.7. Relationships for calculating the value of aheattransfer coefficient are derived.

NOTATION

thermal diffusivity, m2/s;

cspecific heat, J/(kg K);Ddiffusion coefficient for steam in air, m2/s;

ddiameter of the tube, m;

air fraction in steam;

Fsurface area of the tube, m2;

Gflow rate, m3/s;

gacceleration due to gravity, m/s2;

hheight of the hill of roughness (diameter ofwire), m;

Kheattransfer coefficient, W/(m2K);

llength of the channel (tube), m;

Qheat flow rate, W;

qheat flux, W/m2;rspecific heat of steam formation, kJ/kg;

sdistance between the coils of roughness, m;

ttemperature, ;tlogarithmic average temperature difference,

;average flow velocity, m/s;

Wflow rate of the condensate, m3/s;xdifference in moisture contents at the liquid

temperature and gas temperature, kg/kg;heattransfer coefficient, W/(m2K);mass transfer coefficient in the gas phase, m/s;mass flow rate of the liquid per unit length,

kg/(m s);thickness of the film or wall, m;dimensionless thickness of the film;= (2/g)0.33reduced thickness of the film, m;thermal conductivity, W/(m K);kinematic viscosity, m2/s;GaGalileo number;

GrGrashof number;

K = r/ctphase transformation criterion;

v

5

15000100005000

b103,W/(m2K)

Ref

1

2

15

20

10

34

0

Fig. 11.Dependence of heattransfer coefficient in boilingon Reynolds number of film at d = 20 mm, q =250 kW/m2, and s/h = 67. Experimental points are asfollows: (1) M20 thread, (2) helical roughness at h =0.25 mm, (3) h= 0.5 mm, and (4) h = 1.5 mm. Dashed linerepresents smooth surface of tube.

5

2001000

b103

,W/(m2

K)

q103, W/m2

1

2

15

20

10 3

4

300

Fig. 12.Heattransfer coefficient in boiling as a function ofheat flux at d = 20 mm, t= 27, Ref = 15000, ands/h=

67. Experimental points 1 and 2 are as follows:(1) smooth surface of a tube and (2) surface with helicalroughness at h= 1.5 mm. Lines 3 and 4 are as follows:(3) data [14] and (4) data [12].

5

1.00.50

103,W/(m2K)

h, mm

1

2

10

34

1.5

Fig. 13.Dependence of the heattransfer coefficient on theheight of hill when water film falls along a surface withhelical roughness at s/h= 68, Pr = 45, l= 1.9 m, andRef = 10 00012000. Experimental points 13 areobtained in heating: (1) [33], (2) [37], and (3) [38]. Experimental points 4are obtained in boiling.


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Nu = /Nusselt number;

Nu* = /modified Nusselt number;

Pr = /aPrandtl number;

Re = 4W/dReynolds number for the condensate film;

Re = 4/Reynolds number for the liquidfilm;

Re = ud/Reynolds number for steam.

SUBSCRIPTS AND SUPERSCRIPTS

airair;

asairsteam mixture;

bboiling;

ccondensate;

condcondensation;

expexperimental;

ffilm;

gnoncondensable gas;

ssteam;satsaturation;

wwall;

watwater.

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Heat Transfer in Condensation and Boiling