condensation heat and mass transfer … heat and mass transfer from steam/air mixtures to a retort...

CONDENSATION HEAT AND MASS TRANSFER FROM STEAM/AIRMIXTURES TO A RETORT POUCH LAMINATE

W.S. Kisaalita1, K.V. Lo1, L.M. Staley1, and M.A. Hing2

'Department ofBio-Resource Engineering, 2Department ofFood Science, University ofBritishColumbia, Vancouver, B.C. V6T1W5

Received 3 July 1984, accepted 11 June 1985

Kisaalita, W.S., K.V. Lo, L.M. Staley, and M.A. Tung. 1985. Condensation heatand mass transferfrom steam/airmixturesto a retort pouch laminate. Can. Agric. Eng. 27: 137-145.

Asystem employing astainless steel condensing block was designed and fabricated for measuring heat flux during filmcondensation ofsteam/air mixtures onaretort pouch laminate surface. Theblock was incorporated inachamber that couldaccommodate steam/air mixtures up to 50% air, by volume. The effects of the Reynolds number (Re\ and the bulktemperature (Th) onthe heat and mass transfer inthe vapor-liquid condensate region were investigated, foraconfigurationofhorizontal medium flow, withcondensation taking placeontheunderside. Thesensiblefraction of theheattransferred tothe vapor-liquid condensate interface was negligibly small. The data were well correlated bytheequation

Sh = 205.7 /fc-0746 (Sc) 0526.

The quantitativedisparity observedbetweenother investigators and this work was attributed to enhancement of heat andmass transfer due to disturbances on the condensate film surface. Generally an increase in Th was found to result inincreased heat and mass transfer coefficients and for a given Tb the heat and mass transfer coefficients could beapproximated by linear functions ofair content (xa). The overall heat transfer coefficient (H) could be approximated bylogarithmic functions ofthe surface temperature (TJand the temperature difference (AT) between the pouch surface andthe steam/air medium.

CONDENSATE LAYER

INTRODUCTION

The retort pouch is a multi-layer polymer-foil pouch used in lieu of the metal canor glass jar for shelf-stable, refrigeratedand frozen foods. This packaging technique is one of the significant innovationsof the past two decades in the food andpharmaceutical industries. Pflug (1964)and Pflug and Borrero (1967) recognizedthree potential heating media for thermalprocessing of retort pouched food products, namely: pure steam, water/air andsteam/air cooks. Despite the advantagessteam/air systems offer over the alternativetechniques, commercialization of the process is slow. This reluctance can be partlyattributed to the meagre fundamentalinformation available regardingheat transfer in the air content range of interest tofood processors. The experimental investigation reported in this paper wasprompted by the indicated paucity of data.

In additionto the physio-thermal properties of the processed product, other factors that are important to the rate of heattransfer from a steam/air medium into aprocessed product are air content, mediumflow, bulk temperature and packageorientation. This work was undertaken to investigate the heat transfer from steam/airmixtures to the undersideof a retort pouchlaminate with horizontal steam/air flow.This configuration was chosen, among anumberofotherconfigurations thatpertainto the problem, since it was found to beleast studied from both the analytical andthe numerical view-point.

—TT

CANADIANAGRICULTURAL ENGINEERING, VOL. 27, NO. 2, FALL1985

STEAM-AIR

BULK

RETORT POUCH

LAMINA TE

Figure 1. Steam/air condensation mechanism.

•TTvvb

-TTab

137

ADHESIVE"RETORT POUCHLAMINATE

cj: K

BLOCK—

(—rrr.1 lLl

PREVIOUS WORK

The presence of small quantities of airin condensing steam has a profound influence on heat transfer. Reference to Fig. 1shows a cold product surface in contactwith the steam/air medium. Condensation

occurs on the cold surface and the air iscarried with the vapor to, and accumulatesat, the liquid-vapor interface. The partialpressure of air at the interface increasesabove that in the bulk of the mixture, producing a driving force for air diffusionaway from the surface. This diffusion isexactly counterbalanced by the diffusionof the steam/air mixture towards the interface. Since the total pressure remains constant, the partial pressure of vapor at theinterface is lower than that in the bulkmixture which provides the driving forcefor vapor diffusion towards the interface.The temperature variation in the region ofthe interface is as illustrated in Fig. 1.

138

3X6 35 0

II

TTTTIl i l J

I

254

73 66

99 06

Figure 2. Condensing block and surface.

One of the earliest quantitative study ofthis phenomena was undertaken byOthmer (1929). He concluded that an airmass fraction as low as 0.5% caused morethan a 50% reduction in the heat transferrate. This conclusion has been confirmedrecently by Minkowycz and Sparrow(1966) and Sparrow et al. (1967) for stagnant and flowing steam/air mixtures for airmass fractions ranging between 0.05 and0.1. Their results indicated that higher heattransfer rates are associated with higherbulk temperaturesand flow. In an effort toobtain heat transfer data at higher air contents, relevant to food processing, anumber of investigators (Blaisdell 1963;Pflug 1964; Yamano 1967; Adams andPeterson 1982; Peterson and Adams 1982;Ramaswamy 1983) haveemployedlumpedcapacity techniques to evaluate theoverallheat transfer coefficient at different aircontents of steam/air media. The wide

—0

variations in the reported "heat transfercoefficients" is not surprising, given thediverse experimental conditions and configurations employed. Also, none of thesestudies focused on the heat transfer mechanism at the condensation surface. Almostall the above-mentioned studies have

reported increased heat transfer rates as aresult of higher medium flow. Unfortunately, the data are presented in such aform that comparison with well-established heat and mass transfer correlations

is impossible.For the horizontal medium flow config

uration with condensation on the underside, little has been found in the literature.The only study found was conducted byGestermann and Griffith (1967), understagnant conditions, who wereable to conclude that heat transfer depended on gravity and surface tension only.

The subject of this study was therefore

CANADIAN AGRICULTURAL ENGINEERING, VOL. 27, NO. 2, FALL 1985

COOLANT

OUTLET

Figure 3. Section of the tubular condensation chamberwith the condensing block in situ.

dxy _ _ dx* _dy dy'Xv~l **'

Therefore

dy

(3)

where

(4)

namh = (nvb - nvi)

nam =nai - nab

in (nai/nab)

(7)

(8)

to investigate the influence of larger aircontents and horizontal steam/air flow

velocityon heat transfer rates in the regionof the liquid-vapor interface, assuming acondensation mechanism as illustrated inFig. 1, with condensationoccurring on theunderside of a retort pouch test surface.

THEORETICAL ANALYSIS

Referring to Fig. 1, the molar flux of air(Ja) passing through a plane parallel toand at a distance y from the interface isgiven by (Collier 1981):

Eliminating J between Eqs. 4 and 1 gives, and

'--»-$[z+']

A /•JCa +D-C'^dy (1)

In a similar manner the molar flux of vapor is given by:

yv = /-jcv + d-cdy'

(2)

but

(5)

Integrating the above equation betweenthe interface (y = 0) and the edge of thediffusion layer (;y = 8) gives,

y--Trto[H£] (6)

Equation 6 can be written in terms of massconcentration flux (yv) as,

*- Kp-|n [f^S]or


K = 2 (9)

The heat transfer is also affected by theoccurrence of mass transfer. The totalheat flux at a distance y from the interfaceis made up of two components, namely asensible heat transfer (conductive) component and a sensible heat transport (con-vective) component as follows:

^ =xg +yvcp(r-ri). (10)

Integrating from y = 0 to y = 8T and usingh = X/8t gives:

139

STEAM-AIR

STEAM

*= —

where

•[h'(T-Tl)] = h,'(T-Tl), (11)

n = (yv-Cp/«.

Therefore, h and h' are the sensible heattransfer coefficients with and withoutmass transfer, respectively. The correction in Eq. 11, that accounts for the effect of mass transfer was reported byAckermann (1937) and Colburn and Drew(1937) to be insignificant. Colburn andHougen (1934) proposed a heat transfermodel made up of two components,namely the sensible heat transfer throughthe air-vapor layer to the interface and thelatent heat released due to condensation ofthe vapor reaching the interface as:

% = <?fg + <7c

=I^P'(nb-nvi) +/*'-(rb-ri). (13)

For any flow regime (laminar, transitionand turbulent) and geometry (tube or flatplate), a suitable correlation can be usedto evaluate h', and K can be evaluated bymaking use of Reynold Colburn analogy

140

COOLANT

£ —XISCANNER

<=>VENT

CONDENSATION CHAMBER

CONTROLLER

ROTAMETER

AIR

Figure 4. A flowsheet of the experimental unit.

between heat and mass transfer as fol

lows;

K pCp IScl (14)

It has, however, been observed that actual heat and mass transfer coefficients are

higher than those predicted by the correlations (Collier 1981), mainly as a resultof unstable falling liquid films. As a resultof this disturbance waves develop andgrow on the interface at all Reynolds numbers. A summary of studies regardingmethods for estimating this enhancementhas been compiled by Collier (1981). Thesimplest of these was proposed by Wallis(1969) and was based on the expectedanalogy between heat and mass transferand the increase found in friction factors

(Hewitt and Hall-Taylor 1970). It involves multiplying h! by the ratio (fjfg)\the ratio can be estimated by

flf% =1+300 (5) (15)

Hewitt and Hall-Taylor (1970) have proposed the expression for (h/d) for fully

developed flow in a tube as:

5 = 43.5fo-°-8Sc-,/3a

(16)

Equations 16 and 15 can be employed tocorrect h' for the observed enhancement.

In this study the corrected b! has beendesignated by hi'.

MATERIALS AND METHODS

Experimental ApparatusThe experimental apparatus used in this

work consisted of a condensing block (Fig.2) for the measurement of the surface temperature (7W) and total heat flux qv Thepurpose of fins was to increase the surfacearea in contact with the cooling medium atthe cold end. The flanged block was fabricated out of stainless steel (AINS 316;25.4 mm in diameter and 38.1 mm deep).Four 1.6-mm-diameter holes were drilled

on the same dimensional plane, perpendicular and up to the center. A copper-constantan thermocouple was soldered atthe bottom of each hole. The condensation

surface, a retort pouch material (12 u,mPolyester/12 |xm Aluminium/70 jxmPoly-


0.060

0.055

0.016

AIR MOLE FRACTION.

Figure 5. Mass transfer coefficient vs. air mole fraction.

olefin, was glued on the condensor blockby a small amount of high conductivityadhesive (3M EC-1711). As shown in Fig.3, the block was inserted in a tubular condensation chamber (0.1541m diameterand 1.02 m long) 0.75 m from the steam/air inlet end of the chamber. The con

densation block was insulated by Teflon,the thickness of which was such that radial

heat loss was found negligible. A flowsheet showing the full experimental apparatus is presented in Fig. 4.

Experimental ProcedureThe desired steam/air mixture was gen

erated by controlling the temperature andpressure inside the retort (Fig. 4) using aTaylorFiilscopeRecording Controller. Theamount of air entering the system was controlled and metered through a variableflowmeter and was then mixed with the

steam before entering the retort through aspreader to impart homogeneity. Thehomogeneous mixture was then introduced into the condensation chamberthrough a venting manifold located at thetop of the retort. The pressures and temperatures in the chamber and the retort

were monitored separately as there werechanges in mixture air content between theretort and the condensation chamber due to

the loss of condensed steam, in some casesincreases up to 0.1 air mole fraction wereobserved. The chamber and the rest of the

system circuitry were insulated with one-inch-thick fibreglass to minimize this loss.

The experiments were carried out tomeasure Tw and qx through the condensation block which was done at five

temperature levels (105, 110, 115, 121 and125°C) often used for thermal processingin the food industry. Air content was varied between 0.1 and 0.5 by volume and airflow into the system ranged between 4.72x 10~3 to 14.5 x 10~3 m3/sec. Theexperimental design consisted of a total of41 runs. Each run consisted of six experiments with varying cooling water flow-rates (36.5,45.6,52.7,78.5 and 78.7 mL/sec) past the fined end of the block, set by acalibrated valve. By varying the coolingwater flow it was possible to vary the heatflux through the block. After setting thetemperature and pressure controller at thedesired values and allowing the system toachieve steady state, thermocouple tem


perature readings were recorded at 2-minintervals and averaged by means of a KayeRamp II Scanner/Processor system. Afterthe cooling water flow-rate was changed tothe next desired value, the system wasallowed to stabilize and the thermocouplereading was recorded. The procedure wasrepeated until all desired flow-rates wereobtained.

Calculations

The air mole fraction was calculated

using Dalton's Law of Partial Pressures:

xa = 1--nvb/n

and the accuracy of pressure measurements was ± 0.0345 bars (± 0.5 psi),resulting into a 4.5% uncertainty in xa.

At steady-state conditions, with negligible heat loss through the Teflon blockinsulation, uni-dimensional heat conduction through the block was assumed asit was not a source of significant error (q ^1% qt). Therefore, qt was calculated byFourier's law of heat conduction as fol

lows:

<7t = -Kx'dT/dy (17)

where dTldy is the thermal gradient alongthe block and was established by regression analysis of the thermocouple temperature measurements with respect todistance. The coefficient of correlation for

all the data was equal to or better than0.99. Tw was obtained by extrapolation.

Theproperties IIv, p, i\, A., C and hfgfor steam were obtained from tabulations

by Schmidt (1979) and the properties p,Cp, r\ and A. for air were taken fromNational Bureau of Standards tables (1955)and air was treated as a perfect gas. Thethermal conductivities of the mixtures

were calculated using the equation ofLindsay and Bromley (1950). Typicallyerrors in the calculated values do not

exceed 1-3%. Values of p and Cp for themixtures were calculated by standardadditive procedures. D was calculated byGilliland's correlation found in Sherwood

and Rigford (1952). The mixture viscosities were calculated using the approximation by Wilke (1950), for whichaverage deviations between calculated andexperimental values have been reported tobe 1.9%.

Since the conditions at the liquid-vaporinterface were unknown, it was assumedthat T{ corresponded to the saturation temperature equivalent to the partial pressureof the vapor at the interface. With theknowledge of Tw, Th and qx an iterativeprocedure was employed to estimate T{ (7W< Tx < Th) such that Eq. 13 was satisfied.The evaluation of A was based on Hansen's

141

0.0466

0.04453000 10000

REYNOLDS NUMBER.

Figure 6. Mass transfer coefficient vs. Reynolds number for a steam/air temperature of 105°C andair mole fraction of 0.3.

equation recommended by Knudsen inPerry and Chilton (1973).

RESULTS AND DISCUSSION

The sensible heat transfer rate throughthe diffusion layer has been found to be avery small component of the total heattransfer totheinterface. The fraction qfg/qtranges between 0.996 for the lowestxaand0.950 for the highest xa. Therefore, thediscussion of the influence of the processparameters on h" has been considered ofsmall significance.

Reynolds Number and Bulk Temperature Effects

Empirical relationships were sought toshow the dependence of K on Tb and xa.The data obtained have been plotted (Kagainst jca for constant 7b), and plots of thistype are shown in Fig. 5. For a given Tb, Kcan be approximated by a linear functionofjca. However, for the plotof rb = 105°C,a number of points, which correspond tohigher/&? in the region of 8 400-12 700 lieoff the plot. This confirms the well-knownassociation of high mass transfer coefficients (K) with high Reynolds numbers

(Re). Plotting the values of K against/te forjca = 0.3 and Tb = 105 further confirmsthe influence of Re on K as shown in Fig.6. A relationship between K and xa thatdoes not take Re into account has been

found inadequate.

Mass Transfer Data Corrections

The Chilton-Colburn (1934) masstransfer analogy which agrees well withexperimental data is:

RebC V(Re) = Jd (18)

Figure 7 shows a plot of Jd against Re,and these results are in qualitative agreement with the experimental results ofGilliland and Sherwood (1934) and Linton and Sherwood (1950). However, theirexperiments were conducted in vertical socalled wetted-wall towers. All their data

are empirically correlated by the following equation:

Sh = 0.023 Re° 83 Sc0-44 = C Rem(Sc)n. (19)

By taking the logarithm of both sides ofEq. 19 and performing a multiple regression analysis using a Triangular Regres

sion Package (Le and Tenisci 1978), theparameters C, m and n were estimated forthe data in this study. And they were foundto be equal to 205.7, 0.0746 and 0.0526with standard deviations (roots of variances) of 1.0, 0.0021 and 0.0113, respectively. The correlation coefficient wasfound to be equal to 0.9769.

For condensation on the underside of ahorizontal surface, Gerstmann and Griffith(1957) observed enhancement of heat andmass transfer coefficients and attributed

this to the disturbances they observed onthe condensate film surface as waves.However, the results of other investigators(Stern and Volta 1968; Onda et al. 1970;Deo and Webb 1983) have confirmed theabsence of waves during condensation ofvapor in presence of non-condensables forconfigurations where the condensate isflowing on a vertical surface. Their resultswere in close agreement with the film theory predictions using correlations of heatand mass transfer coefficients which did

not take into account any enhancement.Therefore, given the horizontal configuration employed in this work, the cause ofthe quantitative disparity between thisstudy and those that employed the verticalconfiguration (Gilliland and Sherwood1934; Linton and Sherwood 1950) has beenattributed to the disturbances on the con

densate film surface.

The applicability of the proposed correlation in this study has some disadvantages that the influence of xa is impliedindirectly through the dimensionlessparameters that are xa dependent.

Bulk Temperature and AT Effects on theLumped Heat Transfer Coefficient

There are various methods employed toestimate the sterilizing capacity of heatprocesses (Stumbo 1973). These evaluations are based on heat penetration measurements at a location or locations of

interest in a packaged food product.Pflug et al. (1965) indicated that the rate

of conduction heating of a food product ina container is a function of the geometry ofthe container, the physio-thermal properties of the food, the heat transfer characteristics of the container and the heatingmedium. They further indicated that in asystem for processing food where the overall heat transfer coefficient (H) is largeenough such that the Biot number (Bi) isgreater than 10, the heating rate of theproduct becomes independent of//, and isa fraction of the thermal properties of thefood and the container dimensions. This

implies that for situations where Bi»10, the internal resistance to heat penetration is much greater than the external resis-

142 CANADIAN AGRICULTURAL ENGINEERING, VOL. 27, NO. 2, FALL 1985

0.1

0.011000

10000

o

E

|ZUJ

O

UJ

OO

ocUJ 1000u.COz<

<ui

<a:UJ>o

100

10

LegendA Experimental Data.

Model.

I I I I I I I •

10000

REYNOLDS NUMBER.

LegendA Tb=105 deg.C.

X Tb=1l0 deg.C.

O Tb=115 deg.C.

Tb=121 deg.C.

Tb=125 deg.C.

Model

—T—

20

i i i

100000

TEMPERATURE DIFFERENCE (deg.C).


Figure 7. Jd vs.Reynolds number.

Figure 8.Overall

heat transfer

coefficient vs.

block surfacetemperature.

tance and, therefore, the surface temperature (rw) of the food can be assumedto be equal to the heating medium temperature (Tb). For situations whereBi«10, the internal resistance to heat penetrations would be considerably smaller thanthe surface resistance such that the lumpedparameter approach can be used todescribe the heating of the food product. Inthis case there would be an appreciabletemperature difference (AT) between thefood product surface and the heatingmedium at the beginning of the process,which would reduce gradually as the foodproduct average temperature approachesthe process target temperature.

The effects of steam/air Tb, Tw and ATon the heat penetration rate are desirablefor thermal process evaluation. By lumping up the thermal resistances (refer toFigs. 1 and 2) due to the retort pouchmaterial, the condensate and the gas layerinto a combined thermal resistance (\/H),relationships between //, AT and 7W weresought. As shown in Figs. 8 and 9, H canbe approximated by logarithmic functionsof 7W and AT, in the region considered, ofthe forms:

H , «2TW (20)

P2A7H = ft* (21)

where a,, a2, (3, and 02 are parameters.The data shown in Fig. 8 were pooledtogether to estimate the values of 0, and p2and they were found equal to 5200.2 and-0.06356 with standard deviations of

105.1 and 0.0010, respectively. The estimates of a, and a2 are shown in Table I.

However, it should be emphasized thatthese data can only be useful for situationswhere Bi» 10, for cases with Bi« 10,Tw rises suddenly so that AT is very smallfor the largest part of the process period.

CONCLUSIONS

A systematic experimental investigation has been carried out to study the influence of process parameters (Tb, xaand Re)on the heat transfer in the vapor-liquidregion during film condensation on theunderside of a horizontal surface. The

results suggest the following:(i) The fraction of the sensible heat

transferred to the interface is a very smallcomponent of the total heat transferredmaking h" an insignificant variable.

(ii) An increase in jca results in adecrease of both h" and K and an increase

in Tb and Re results in an increase in bothh" and K and the heat and mass transfer

parameters are well correlated by an equation of the form Sh = C Rem(Sc)n.

(iii) Heat and mass transfer correla-

143

10000

o

E

|ZUJ

oLLULUJ

OO

rrUJu.COz<

<UJ

<ccUJ>o

1000-

100

Tb=105 deg.C.

Tb=110 deg.C.

Tb=115 deg.C.

Tb=121 deg.C.

Tb=125 deg.C.

Models

SURFACE TEMPERATURE (deg.C).110

Figure 9. Overall heat transfer coefficient vs. temperature difference (AT) between the blocksurface and the bulk steam/air mixtures.

TABLE 1. ESTIMATED PARAMETERS, o^ AND <x2

Temp.

(°C) (W/m2 C)<*2

(1/C°)

SDtof SDof

a2

105

110

115

121

125

1.2686

4.0383

6.9137

4.1374

5.3205

0.0813

0.0648

0.0564

0.0589

0.0545

0.1157

0.4896

0.7155

0.6526

1.0895

0.0010

0.0013

0.0011

0.0016

0.0020

tSD is the standard deviation.

tions which do not take into account anyenhancement due to disturbances on the

condensate film surface should not be used

in predicting heat and mass transfer coefficients.

(iv) For a given steam/air temperature,the lumped heat transfer coefficient can bedetermined empirically from exponentialfunctions of Tb or AT.

ACKNOWLEDGMENTS

The authors are indebted to Dr. E.G.

Hauptman, Professor of the Department ofMechanical Engineering, University of BritishColumbia, for his numerous helpful suggestions and wish to acknowledge the financialsupport provided by Agriculture Canada.

NOMENCLATURE

c = total molar concentration

(mol/mol)C = constant

Cp = specific heat capacity(J/(kg-K))QL

d = pipe diameter (m)D = molar diffusion coefficient

(m2/sec)

h = interfacial friction factors

u = friction factor based on air

alone

H = overall heat transfer coefficient

(W/(m2-K))QLh, h', h" = sensible heat transfer

coefficient (W/(m2-K))QL

K = latent heat of vaporization(J/kg)

J drift flux of bulk fluid towardsinterface (m/sec)

K mass transfer coefficient

(m/sec)m = constant

n = constant

ava^ac = heat flux (W/m2)v = linear velocity (m/sec)T temperature (K)x = mole fraction

v distance measured from areference point (m)

Dimensionless Groups

Bi = hy/K, Biot number

Nu = hdlK Nusselt number

Pr = t\C l\, Prandtl numberRe = pva/i] , Reynolds numberSc = Ti/pD, Schmidt number

Sh = Kd/D, Sherwood number

Greek symbols

<*, 0 parameters5 thickness of diffusion layer

(m)

P density (kg/m3)* designates functionn pressure (bars)X thermal conductivity

(W/(m-K))T) viscosity (kg/m.s)

Subscripts

a = air

b bulk

i = interface

sa = steam/air

ss = stainless steel

m = log meanv = vapor

w = wall

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