ENERGY CONSERVATION THROUGH CONTROL OF GREENHOUSE HUMIDITY.

II. PROMOTION OF FILMWISE CONDENSATION

P. L. Silveston1 and R. R. Hudgins

Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario NIL 3G1

Received 19 February 1979

Silveston, P. L. and R. R. Hudgins.Promotion of filmwise condensation.

1980. Energy conservation through control of greenhouse humidity. II.Can. Agric. Eng. 22: 133-135.

Heat transfer and condensate film thickness calculations for a greenhouse shell formed from two layers of plastic filmindicate that about a 5% energy saving could be achieved by promoting film condensation during most of the heatingseason. However, the use of a commercially available promoter is not justified by this saving. Laboratory tests of othermaterials containing surface active agents show that many are capable of promoting film condensation and at least onelow cost material exhibited good retention on a plastic surface.

INTRODUCTION

Part I of this paper (Silveston et al.1980) concluded that heat savings up to20% could be realized by eliminatingcondensation in a 400-m3 greenhousecovered with a double layer of plasticfilm. It was also demonstrated throughcost calculations based on a quasisteady-state analysis of heat flow andhumidity levels near sunset that the use ofmechanical dehumidification was not

attractive for this purpose even thoughcondensation heat losses could be re

duced by 75%.An alternative to mechanical de

humidification is to increase the resis

tance to heat flow by forming acondensate layer on the innermost surfaceof the greenhouse skin. The concept issimilar to that examined by Walker andWalton (1968) where the condensatereduces the thermal transmittance ofpolyethylene film, thereby loweringradiation heat losses. It is well-known

that filmwise condensation providesgreater heat transfer resistance thandropwise condensation. The dropwisemode is usually encountered ingreenhouses.

The object of this paper is to determinethe energy savings expected by creatingfilmwise condensation. A comparison isthen carried out to see whether the use ofcommercial or other wetting agentsrequired to promote filmwise condensation can be economically justified.

PHYSICS OF CONDENSATION

Vapors form drops of condensation ifthe attractive forces between the liquidmolecules and atoms of the solid surface

are less than those existing amongmolecules of the liquid. The contact angle

'To whom correspondence should be addressed.

is a measure of the difference between

these forces. When the contact angle iszero, spreading of a liquid occurs andvapors condense as a film. Plottingcontact angles for a surface versus surfacetension of liquids permits an estimation ofthe critical surface tension; that is, thesurface tension for which spreading onthe surface occurs. At this point,condensation switches from dropwise tofilm. If the surface tension of a

condensate, however, is greater than thecritical surface tension characterizing thesurface, condensation as drops takesplace. Merte (1973) lists values of 31 and39 mN/m for polyethylene and polyvinylchloride. The surface tension of water in

air at less than 5°C is 75 mN/m or greater;thus, dropwise condensation of water willoccur on both plastics. Dropwise condensation was observed for polyethylene inour laboratory (Waterloo Research Institute 1976).

The mechanism of dropwise condensation remains incompletely understooddespite many years of intensive study. Arecent review by Merte (1973) suggeststhat condensation occurs both on the

drops and on the bare surface arounddrops. Liquid on the bare surface is drawninto the neighboring drop as fast as itforms on the surface, so the "film" isnegligible in thickness. As drop densityon the surface increases, coalescence toform fewer, larger drops is observed.

Difference between the rates of heat

transfer for the two condensation

mechanisms arise first of all from the

liquid which forms on the surface in filmcondensation. This film acts as a heat

transfer resistance by raising the temperature of the surface in contact with moist

air. A further cause of the difference isthat drop condensation — where waterforms a multitude of pools on the surface— substantially increases the available

CANADIAN AGRICULTURAL ENGINEERING, VOL. 22, NO. 2, DECEMBER 1980

surface for heat transfer and condensa

tion. The increase in surface compensatesfor the higher temperatures on the dropsurfaces with respect to temperatures onthe glass or plastic surfaces.

REDUCTION IN HEAT TRANSFER

WITH FILM CONDENSATION .

Although thousandfold differences inheat fluxes between film and dropwisecondensation have been observed for purevapors (McCabe and Smith 1967), thedifference for condensation from humid

air does not seem to have been measured.

It is known that the heat flux is controlled

by the rates of heat conduction and vapordiffusion through the air film next to thesurface as well as by the rate ofconduction through the condensate filmon the surface.

To calculate the heat flux for film

condensation, a film of uniform thicknesswas assumed. This simplifies a complexreal system because film thickness variesdepending on slope of the surface, andchanges, of course, from top to bottom asdrainage occurs. Varying film thicknessimplies varying temperatures and heatfluxes. Calculation of the condensate film

thickness is discussed in the Appendix.For dropwise condensation, we have

made use of laboratory observations ofdrop formation on plastic surfaces. It canbe seen, for example, from the right-handportion of Fig. 1 that where dropwisecondensation occurs, the condensatedrops take up about 50% of the localsurface. Closer examination of the dropsshows that they are approximatelyhemispherical. This means that thesurface for heat transfer is 50% greaterthan that for film condensation. Conden

sation and convective heat transfer takes

place on the drops as well as on the baresurface. To simplify calculation, weassume that the drop surfaces are at a

133

uniform temperature different from thatof the plastic skin. The drop surfacetemperature is calculated by treating thedrop as a cylinder whose base is 1 mm2,about the mean surface area of the dropsshown in Fig. 1, and whose volumeequals that of the hemispherical drop.

Equations used to estimate the energysavings are given in the Appendix anddiscussed there. Successive approximation was used to solve the system ofequations for two conditions: an earlyevening condition of 70°F and 90%relative humidity (RH) and nighttimecondition where the RH has dropped to65%. An ambient winter night temperature of —18°C with a cloud-covered skywas assumed.

Savings of 6 and 5% of the total heatloss were calculated for the two cases.

Using the lower of these figures, thesavings can be calculated on the samebasis used to evaluate mechanical de-

humidification in part I (Silveston et al.1980). They amount to $22/yr for themodel greenhouse of part I if natural gasis used and rise to $35/yr if No. 2 fuel oilat 16.4g/L is the fuel.

A wetting agent (Sun Clear) iscommercially available to promote filmcondensation. The recommended dosageis 1.5 mL/m2 of floor surface. Weestimate from our laboratory test onwetting agents that the inner shell wouldhave to be treated at least monthly. Forthis frequency, the cost of wetting agentwould run to $46/yr at the advertised costof 2.6g/mL. If weekly spraying isneeded, the cost becomes $185/yr,

clearly unattractive. The former, optimistic figure suggests that the useof a wettingagent bears further investigation. Reduction of heat loss is not the only benefitprovided by film condensation. It shouldsignificantly reduce "rain" experiencedin plastic houses and thus workerdiscomfort and the incidence of leaf

diseases such as botrytis.

TEST ON FILM

CONDENSATION PROMOTERSThe Sun Clear wetting agent is

expensive, considering that wettingagents are produced in vast quantities foruse in detergents and other cleansingmixtures. To explore qualitatively whatother readily available materials might beused to promote film condensation, aseries of tests were run in our laboratory(Waterloo Research Institute, 1976). Avariety of glass-cleaning agents based on(1) sulfonated alkyl benzene and sulfonated alcohols, (2) stearic and palmiticacid salts, and (3) sodium salts ofethyoxylated fatty alcohols were tested byobserving whether a 5-10% solution ofthe dry cleaning agent in water promotedfilm condensation when sprayed on thesurface.

All cleaning agents that contained atleast 20% by weight of a surface activeagent caused film condensation. Figure 1shows film condensation on one-half of a

test surface treated with a laboratorydetergent which contained 20% ABS,25% polyphosphate with the remainderinorganic salts. However, the retention ofthe agent on the surface differed

Figure 1. Water vapor condensing dropwise on an untreated surface (right) and filmwise on asurface treated with a glassware detergent (left).

substantially between formulations. Onlytreatment with an agent containingethoxylated fatty alcohols continued togive film condensation after severalwashings of the surface with distilledwater. Washing was used to represent asequence of alternating condensation,drainage and surface drying events. Thisagent, unlike others tested, showed noresidue when the water carrier evaporated. Its cost is a fraction of the cost of

Sun Clear.

Although the scope of these experiments and the number of wetting agentswas limited, the results do suggest thatlow-cost wetting agents can be developed, which will make promotion offilm condensation economical.

CONCLUSIONS

Promoting film condensation appearscapable of reducing the heating demandfor a plastic house by about 5%. The costof currently available agents for causingfilm condensation, however, does notjustify their use. An exploratory laboratory study of commonly available detergents shows that most are capable ofpromoting film condensation. A detergent based on ethoxylated fatty alcoholsappears to be best suited and costs afraction of the cost of one commercial

film condensation agent. Thus, cheaperagents are possible, and, when developed, promotion of film condensationcould become economically feasible.

ACKNOWLEDGMENTThe work reported was performed under a

contract from the Ontario Ministry ofAgriculture and Food as part of their EnergyManagement Program.

REFERENCESFULFORD, G. D. 1964. Flow of liquids in

thin films. In T. B. Drew et al., eds.Advances in chemical engineering.Academic Press, New York;

McCABE, W. L. and J. C. SMITH. 1967.Unit operations of chemical engineering.McGraw-Hill, New York.

MERTE, H., Jr. 1973. Condensation heattransfer. In T. F. Irvine and J. P. Hernett,

eds. Advances in heat transfer. Academic

Press, New York.SILVESTON, P. L., W. D. COSTIGANE, H.

TIESSEN, and R. R. HUDGINS. 1980.Energy conservation through control ofgreenhouse humidity. I. Condensation heatlosses. Can. Agric. Eng. 22: 125-132.

THRELKELD, J. L. 1980. Thermal environmental engineering, 2nd ed. Prentice-Hall,Englewood Cliffs, N.J.

134 CANADIAN AGRICULTURAL ENGINEERING, VOL. 22, NO. 2, DECEMBER 1980

WALKER, J. N. and D. J. COTTER. 1968.

Trans. ASAE(Amer. Soc. Agric. Eng.) I 1:263-266.

WATERLOO RESEARCH INSTITUTE.

1976. Reduction of fuel usage in commercial greenhouses. Waterloo Research Institute. (Report available from the Office ofEnergy Management, Ont. Min. of Agric.and Food, Toronto. Ont.)

APPENDIX

Film Thickness and Reduction in Heat

Flux

In film condensation, a continuouswater film covers the surface and

condensation occurs on the water film.

Drainage from tilted or vertical surfacesmaintains a constant film thickness once

steady state is established. A model forestimating film thickness, according toFulford (1964), is:

^ gsin 6 J (Al)

The parameters for this equation aredefined in the notation. This model

assumes laminar flow and non-rippledfilm surfaces as well as uniform conden

sation. Flow will be laminar for earlyevening condensation rates of 12 kg/h forthe model greenhouse of part I with a wallperimeter of 61 m. The presence ofsurface active agents to promote filmcondensation suggests that the surfacesshould be free from rippling (Fulford1964).

For the peaked roof design assumed inpart I, the mean film thickness calculatedwas 0.04 mm. The effect of surface active

agents on thickness is not known. On theone hand they will increase viscosity, buton the other they increase slip on thesurface, thus promoting drainage andgiving thinner films. A further complication is that plastic greenhouses havecylindrical shells so that 0 in Eq. Alchanges continuously from 0 to 90°. Thismeans that condensate films thicken at the

top of the shell where heat loss is highest.

Although our estimate of thickness mustbe viewed as uncertain, our calculationsshow that in the range of 0.01-0.1 mm,thickness has only a small effect on heatloss.

With the assumptions of 50% averagecoverage of the surface in dropwisecondensation and hemispherical drops of1 mm2base area, the following equationsapply (Silveston et al. 1980):

c„(A-V iu_

2C„•(*-*„,) + o^(t\-t\,)

k*('*,-'*,) +^8ap(?4Bl,-'ll,) <A2)

= h%(tth-tE) + a^t(t\h-t\to) (A3)

1 (A-**) =^-((f-/B,,) (A4)Cp 2y„

Variables and parameters are defined inthe notation. Values assigned to theparameters are given there as well. Forfilm condensation, the second term on theL.H.S. of Eq. A2 drops out and:

•r-(*-V-r-<''-'-.> (A5)

replaces Eq. A4. With the exception ofEq. A4, the terms on either the L.H.S. orR.H.S. represent the heat flux in W/m2transported through the greenhouse shell.Resistance of the plastic film has beenneglected as have the increased surfacefor radiant heat transfer with dropwisecondensation.

Film and dropwise condensation heatfluxes were calculated for the double-film

plastic house for 65 and 90% RH, anambient temperature of —18°C and a stillair condition with total cloud cover. The

model equations are implicit and weresolved for t(, rgi,, fBi2 by successiveapproximations. Mylar films opaque toinfrared radiation were assumed.

NOTATION

C,, = Specific heat of dry air (:kJ/kg • K).

1.00

CANADIAN AGRICULTURAL ENGINEERING, VOL. 22, NO. 2, DECEMBER 1980

»i

t^gap

h,

hE

*.,

*w

k*

Q

h

h

foi

h

'sky

V

X

y

e

Inside view factor for grey bodyradiation (= 0.58).Outside view factor (= 1.0).Grey body view factor for the airgap(= 32.58 W/m2 • K4).Gravitational acceleration (=9.8 m/s2).Enthalpy of humid air at tx andrelative humidity in greenhouse(J/kg).Inside heat transfer coefficient

= 5.62 + 0.36 v (W/m2 • K).Outside heat transfer coefficient

(in still air =9.1 J/s • m2 • K).Enthalpy of saturated air (RH =100%) at ff (J/kg).As above but at fgn.Thermal conductivity of glass(= 1.05 W/m • K).Thermal conductivity of water(= 0.611 W/m • K).Apparent conductivity of gap air(= 0.104 W/m • k).Volumetric flow rate per lengthof wetted perimeter (m3/s • m).Temperature in greenhouse (=294 K).Temperature at surface of condensate film or drop (K).Temperature of the inner mylarfilm (K).Temperature of the outer mylarfilm (K).Ambient (outside) air temperature (= 255 K).Temperature of cloud surface(= 244 K).Inside air velocity in greenhouse(= 0.5 m/s).Air gap (= 2.5 x 10'2 m).Thickness of condensate film

(m).Condensate film thickness (= 5x 10-4m).Angle of inclination to thehorizontal (degrees).Kinematic viscosity of water ( =2(10-6)m2/s).Stefan-Boltzmann Constant ( =5.67 (10-*) W/m2 • K4)..

135