INFLUENCE OF MATERIAL PROPERTIES ON GREENHOUSE CLIMATE

J. A. St of -fers I MAS Postbus 43 6700 AA Wageningen The Netherlands

Abstract

A comprehensive computermodel is created which takes material properties as input and produces the greenhouse climate as output. The approach of a technician, to physical as wel as some physiological aspects o-f protected cultivation leeds automatically to a growthsimulation o-f a "stylized" canopy.

1. Introducti on

Decades o-f glaznost did not hurt the Dutch horticulture, and according to this tradition, the Department " Fysische Techniek", IMAG , Wageningen o-f-fers a Turbo Pascal computerprogram called "Solanum IMAGinatum" to the interested horticulturist, greenhouse constructor, adviser, manager or tradesman.

1.1 ' Wissenschaft-die Kunst, die richtigen Fehler zu machen'(Fucks,1965).

Solanum IMAGinatum, not quite known by Carol us Linnaeus, is a stylized tomato-plant without -fruits, without -flowers and with very simple relations between length, surface area, average diameter etc. The tomato grows in a dutch greenhouse, this means a multispan more or less one dimensional greenhouse covered with one, two or three layers of glass or plastic. An energy saving screen and a shading screen may be installed, the heating system may consist o-f circular or rectangular shaped pipes, the plant grows in rockwool and the soil is covered with a white -foil. The shape o-f the canopy row is rectangular and the leafdistribution is spherical*

The program is divided in two main parts.

1- CONSTR.PAS where the book-keeping (even literally) is done and where after "design and construction" of a particular greenhouse, the light transmissivity is computed and stored (UITREK.DAT). The greenhouse blue-print and the prices of energy, labour, water ,the investment costs, the amortization time and the interest-rate are all stored in a file called PARAM.#.(The asterisk substitutes NED,ENG,FRA,DUI,ITA, dutch abbreviations of five european languages since the communication with the computer can be held in the Dutch, English, French, German

Acta Horticulturae 281,- 1990 Greenhouse Construction, Design 231

or Italian language.) 11- T E E L . P A S In th i s part the s i m u l a t i o n is done, the dutch word "teel" means "grow". It is possible to use the program in -four di-f-ferent ways, automatic supply of invented weather—data (invented without meteorological pretentions) or manual input of we a t h e r - d a t a as well as automatic crop t e m p e r a t u r e control 1 or manual input of data concerning h e a t - and c o 2 - s u p p l y and ventilation. T i m e s t e p s of one hour are put into practice s i n c e the dynamic proces of heat conduction in the soil is solved with an operator method, w h i l e t he less important h e a t s t o r a g e in the gre e n h o u s e itself is tackled by applying temperature d i f f e r e n c e s per hour instead of exact time d e r i v a t e s in the various energy balance equations.

A lot of subroutines in the program can be replaced easily, thus a creative user is not urged to share t he IMAG-opinions and may. construct a fil e with realistic weather conditions.

The program can be seen a s a tool for per s o n s of various disciplines with v a r i o u s questions; c a p a b l e of improvement, open to extension ,amenable to cri t i c i s m and s u s c e p t i b l e to run-time errors.

2. Input variables concerning the g r e e n h o u s e lay-out and market situation.

An e x a m p l e of PAR A M . E N G .

Market G a s p c e Cfl/m A33 : 0.31 C 0 2 _ p r i c e Cfl/kg 3 : 0. 3 2 W a t e r p r i c e Cfl/m'3] : 0.33 Labour Cf 1 / (m^2. a) 3 : 35. 0 V a r i o u s [f 1 / (m' 2. a3 : 4.0 0 Interest E"/, /al s 8.6 0

Materi althi ckness! Materi althi ckness! Materi al t h i c k n e s s !

1 2 3

) 1 ) 2 ) 3

Greenhousecover! Number of layers A * D < Absorbtivity * A * D ( Absorbtivity » A * D ( Absorbtivity * Refrac, index of layer Refrac, index of layer Refrac, index of layer Rho#cp*d [Joule/(K.m'-2) 1 1 Rho#cp*d CJoule/(K.m^2)3 2 Rho*cp*d CJoule/(K.m A2)3 3 Fi 1mcondensation? Y/N C h o o s e kind of gas in cavity! 1 Cho o s e kind of gas in cavity! 2 Thi c k n e s s cavity? Cm! 1 Thic k n e s s cavity? Cm! 2 Slop e of roof 0 _45 Deg Relativ surface of obs t a c l e s parrai 1. to ridge Horizontal part (II) ?

3 0.010 0.005 0 . 0 0 3 1.590 1.560 1. 520 10000 10000 10000 V 1 3 0.015 0.010 28 0.010 0 . 4 0

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Relativ surface of obst. perpend, to ridge : 0.010 Horizontal part <-*->,? •* 0.30 Reflectivity of obstacles parr, to ridge : 0.60 Reflectivity of obstacles perp. to ridge : 0.70 Rho#cp#th i ckness of obstacle C Joul e/ (K.m^2) 3 : 7000 Width of bay. Cm] : 3.20 Size of vent (|l ridge) Cm] : 1.00 Size of vent - (i ridge) Cm] : 0.80 Distance between vents Cm] : 0.80 Height of gutter Cm] : 3.00 Transmissivity (wavelen.>3pm) layer 1 : 0.00 Emissivity topside (wavel. >3|.im) layer 1 : 0.83 Emissivity bottoms.(wavel.>3pm) layer 1 : 0.83 Transmissivity (wavelen.>3pm) layer 2 : 0.70 Emissivity topside (wavel.>3pm) layer 2 : 0.20 Emissivity bottoms, (wavel. >3j.tm) layer 2 : 0.20 Transmissivity (wavelen.>3pm) layer 3 : 0.00 Emissivity topside (wavel.>3^m) layer 3 : 0.83 Emissivity bottoms.(wavel.>3pm) layer 3 s 0.83 Investment cover Cfl/m^2] : 150.0 Amortization time Ca] - : 10

Y/N ? transparant Y/N

Screens! Energy saving screen Energy saving screen A#D? Refractionindex of transp. screen? Transpar. screen with detergent Y/N ? Shading screen Y/N ? Distance screens ? Cm] Perf orationrate of the shading. scr. ? (0 100)"/. Perforationrate of the energ.sav.scr.(0 100)% Height of screen package (opened)? Cm] Width of screen package (opened)? Cm] Reflectivity of the package ? Distance to ground shadingscreen ? Cm] Rho#cp#dCJoule/(K.m~2)] screens. Transmissivity (wavel.>3^m) Emissivity topside (wavel.>3pm) Emissivity bottoms.(wavel.>3pm) Transmissivity (wavel . >3(-im) Emissivity topside (wavel. >3|am) Emissivity bottoms.(wavel.>3pm) Radiative prop. scr.(400nm_700nm) Transmissivity of screen Reflectivity of "topside screen Reflectivity of bottomside screen Costs Investment screens Cfl/m'"2] Amortization time Ca]

screen screen screen screen screen screen

Y Y 0.010 1.700 Y Y 0. 10 50 1

0 . 10 0.20 0.50 2.00

200 0.60 0.30 0.30 0.60 0.30 0.30

0.50 0.45 0.45

6.00 3.0

Overhead heating. Reciprocal pipedistance Distance heatingpipe to ground? Circumference heatingpipe Cm]

Cl/m] Cm]

1.07 2.00 0. 16

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Circular pipe Y/N ? s Y Rho*cp#thickness of the pipe? [ Joui e/ (K. nr~2) ] « 1000 Emissivity o-f the pipe? : 0.90 (Shortwave) reflectivity of the pipe? i 0.20 Costs per m pipe! Investment overhead heatingif1/m3 ? s 3.00 Amortizationtime [a] : 10

Heating system !(not overhead) Circumference heatingpipe Cm3 3 0. ló Circular pipe Y/N ? 3 N Ratio height/width of pipe ? m 2.00 Rho*cp*thickness of the pipe? [Joule/(K.m"2)3 : 1000 Emissivity of the pipe? a 0.90 (Shortwave) reflectivity of the pipe? 3 0.20 Distance pipe to center canopyrow? [m3 3 0.50 Distance pipe to ground ? Cm3 3 0.30 Costs per m pipe! Investment heating system [fl/m3(not overhead) 3 3.00 Amortization time [a3 3 10 Rockwool Thickness rockwool ? [m3 : 0. 10 Width rockwool ? Cm3 3 0.70 Emissivity ? 3 0.80 (Shortwave ) reflectivity 3 0.80 Conductivity rockwool [W/(K.m)3 ? 3 0. 10 Rhotcp [kJoule/(K.m~3)3 3 3000 Number of plants per m"-2 ? 3 4.00 Distance between canopyrows ? Cm3 3 1.60 Costs rockwool. Investment [fl/m/v23 ? 3 3.00 Amortization time [a3 ? 3 1.0

Soil and soil cover! Emissivity of soil cover ? : 0.80 (Shortwave ) reflectivity of cover ? s 0.80 Heatconductivity of soil [W/(K.m>3? s 1.00 Specific heat of soil [Joule/(kg.K)3? s 2000 Density of soil [kg/m^SD? s 2000 Heattransfer soil to soilcover CW/(k.m~23? s 10 Costs soilcover ! Investment [f 1/(1^23 ? s 0.30 Amortizationtime Ea3 ? : 1.0

Additional constructiveparts in screenzone.! Relativ surface of obstales parrallel to ridge : 0.01 Relativ surface of obst. perpendicular to ridges 0.01 Horizontal part (||> ? s 0.50 Horizontal part (J-) ? s 0.50 Reflectivity? s 0.50 Rho*cp*conf ac obstacles [Joule/ (K. m/s2) 3 ? : 2.00

Boi1 er ! Boilerefficiency (<1> t 0.85 Investment [fl/m^23 ? s 29.00

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Amortizationtime Call ? : 29 Greenhouse location Latitude Deg Longitude Deg (e.g. Dublin negativ) Orientation (N>S=0, E>W=90>

52.0 5.7

45.0

Definitions

A simplified Dutch "warenhuis"represented by 19 layers.

TCI 3 .Sky

TC23 Outside air

/ \ / \ T C 3 3 \ / \ / \ / \ / \ /TC83 \ / . \ / \ / \ / \

T C 10 ]

TC12] • • TC 14]

-TC9] Shading screen

-TC11] Energy screen

TC133 • • Overhead heating

TC 15]_ Canopy_ •• •• •• '»•TC173 »« •• »Heating

7 T C 1 9 T Rock wool T C 2 i : T s o I T cover F " ~~

TCI] sky temperature, TC23 outside air temperature, Unknown variables TC3] ...TC21]: temperature of layer 3 to 21. (Even numbered layers : gas.) TC3],TC5],TC7] Greenhouse cover (The influence of rho#cp*dC joul e/(K. m"*2) 3 *dTCeven]/dt is of course neglected, the long wave radiation exchange of the gaslayers is not neglected.) TC22] , TC23] , TC24] vaporpressure CF'a] of layer 8,10,12. (This means 22 unknown variables, 19 energy balance equations, 3 water balance equations.) Q C 4] , Q C 6] , Q C 8],Q C10],Q C12],Q C14],Q C16],Q C18],Q C 20], absorbed long wave radiation of gaslayers CW/m""23. QC3],QC5],QC7],QC9],QC11],0C13],QC15],QC173,QC19],QC21] absorbed short wave radiation (direct+diffuse radiation) CW/m A2]. Short wave radiation pattern: IdCO..4,1..2] downward radiation

IdCO,. . ] outsi de IdCl,. . ] below cover IdC2,. . ] between screens IdC3,. . ] above verhead

heati ng IdC4,. . 3 above the canopy

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IuCO..4,1..23 upward radiation IuCO,..3 outside I u C 1, . . 3 below cover IuC2,..3 between screens IuC3,..3 above overhead •

heati ng IuC4,..3 above the canopy,

I..C..,13 diffuse part, I..C..,23 direct part. (Remark Z QCod3=IdCO,13+IdCO,23-IuCO,13-IuCO,23)

4. Further defiriitions

All fluxes and transfer coefficients are related to the soil surface. Except the internal resistance ri Cs/m3, of the solanum IMAGinatum leave.

The ventilationrates are not presented as air exchange values Cl/h3, nor as velocities Cm/s3 but in terms of heat transfer coefficients CW/(K. nf-2)3 or (sensitive and latent) heatfluxes CW/m A23.

To define the direction of sunradiation (Beta, Teta) a cylindrical coordinate system is useful.(fig )

When interest rate RC'¿/a3 and amortization time A Ca3 are known it is possible to transform investment costs Inv Cfl/(m~23 in money fluxes F Cf 1 / (m"-2. a) 3 . Not for the book-keeper but for for the technician is 1 C%/month3 = 12C/l/a3 , so the money flux is computed accordi ng

F=R.Inv.exp(R.A)/(exp(R.A)-l)

The. programs CONSTR.PAS / TEEL.PAS

It is impracticable to give a listing, more then 100 pages long of a program full of Dutch variable-names, while a diskette is available. It is better to mention the sources from which the information is taken and to mention the thorny assumptions.In all conscience one has to admit that the selection of heat and mass transfer coefficients is more or less a matter of arbritrariness(e.g. Hiller, 1957; Stoffers, 1979 1984; Meijer, 1980; Bot,1983; Von Elsener,1982). One line or one figure in a program can represent a lot of labourius experimental or theoretical research as well as a safe quoting of other peoples assumptions. In this program Dutch prophets are -against the proverb - most honoured.

Heat and masstransfer.

Internal resistance and heat transfer coefficient of the tomato leaf. (Stanghel1 i ni, 1987) Greenhouse ventilation. (Bot, 1983)

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Heat transfer coefficient greenhouse deck outside. (Bot. 1983) Heat transfer coefficient greenhouse deck inside. (Stoffers» 1979. 1984) Heat transfer coefficient heating system. (von Jodlbauer, 1933; Nawrocki, 1985

Stanghe 11 ini, 1983; Stoffers, 1979. 1984) Heat transfer coefficient screen. Heat transfer coefficient soil surface.

(Bailey, 1982; Stoffers, 1984 )

(Hi lier, 1957 ) Solanum IMAGinatum Dry matter and leaf area. (Germing, 1963 ) Canopy height,number of leaves leaf area, leaf dimension. (Van der Varst, 1972) Photosynthesis. (de Wit, 1965; Gaastra, 1959;

Stoffers, 1975 ) (Remark: The results of "Radiation absorption of canopy rows" (1975) were at that time gathered in formulas instead of tables. This was done in the case of overcast sky situations only. Thus saturation effects caused by direct sun radiation are not taken into account. The lay out of the program enables to include saturation effects in a future version. Radiation exchange Lighttransmission. (Stoffers. 1971, 1985 ) Longwave radiation exchange. (Stoffers, 1982, 1984 ). {Remark: Layer 15 -the canopy- and layer 17 -the heating system- cannot be considerd as two successive layers, while the radiaton exchange between canopy and heating pipe is important, especially if an influence of the heating pipe shape (circular or rectangular) is regarded. Therefore (the geometrical part of) the radiation exchange between pipe and canopy is computed separately and then translated in replacing values for emissivity and transmissivity of the respective layers.)

5.1 Heat conduction into the soil, short explanation of the PROCEDURE OPERATOR

The well known equation

lab*d*2T/dx"*2-rho*c*dT/dt" . where lab [W/mKJ represents the conductivity , rho [Jcg/m*3] the density, c [joule/(kg.K) ] the specific heat of the soil , T the temperature at the time t" [s] and depth x [m] , can easily be transformed in a dimensionless form, apart from the temperature:

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rx-0 Tbo

d~2T/dx*2-dT/dt.

When D [m] , the thickness of the relevant soil layer then x-xVD has a value between 0 and 1. t-t"«lab/(rho*c*D*2) is the dimensionless time. If lab-1[W/(mK)], c-2000Ijoule/(kg.K)], rho-2000[kg/m"3] and t"-3600[s] then t-3.6E-5, or if t~-278[h] then t-0.01. The numerical solution of this equation is achievedwith the help of J.Mikusinsi's "Operatorenrechnung" (1957), a method analog to Laplace-transform but much more elegant.The choosen boundary conditions are :

x-0 dT/dx«q(t) (dimensionless heatflux at soil surface)

x-1 (x'-Dtm]) dT/dx-0. The symbols used are s the operator for differentiation (or Laplace operator). the analogon of Dirac's 6(r): hT or e?' e.g. h* (q(t)>- 0 for 0<t<r

q(t-r) for t>r The heatflux q at soil surface versus time is regarded as a stepwise linear function; so during the time span At'-llh], a heatflux changing lineary in time.

In operatorformulation: (t-n.at) q(t)-(l/sa ) (ql- ql.h" + («2-ql) .h^ -(q2-ql) . (q3-q2) or q(t)-(l/SJ) (ql+(q2-ql) .h" + (q3-2q2+ql) -h*^. . (q -2q +q) .h"'*

i>M n n-» |

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The convolution (("faltung") written as a multiplication) of q(t) and the operator s.G(l-x) delivers the solution T(x,t) :

T(*,t)«q(t).s.G(l-x) [2] The operator G(x) is representable as: G(x) -( 1/s) < (1/Uirt) )3f(-l)n [exp( (2n+l-x) ~2/(-4t) ) -

# • exp ( (2n+l+x) "2/ (-4t) ) ] } Since q (t) consists of (operator) terms like (l/s2)q .h04*, the solution consists of terms like q,.hn^.G(l-x)/s, where G(1-x)/s equals ^ ( 1/s2 ) { ( 1/ Kirt) ) 2(-l) n [exp ( (2n+x) '2/ (-4t) ) -

exp((2n+2-x)*2/(- 4t))]>. [3] So the PROCEDURE OPERATOR needs 1) a subroutine (PROCEDURE.DUB ;) where the integral JP exp(-(x~2/4t))dt dt can be computed

J <vt 2) a routine where the soil flux "history" [1] is connected with the different terms of[3] according to [2]. The average temperature (heat storage) of the total soil layer is computable on the same manner by spatial (x) integration of the the terms and can .when compared with the temperature profile, moreover serve as a check. The temperature near to the soil surface Tbo depends on the (well known) soil flux history q2, q3, ....qn and the still unknown soi If lux ql, let's say

Tbo-a + b.ql. At the other hand ql is dependant on the physical circumstances in the greenhouse, namely proportional to some temperaturedifferences

ql-k.(Tbo- w.T21-(l-w).T19). (w is a weightfactor,T19 is the rockwoo1temperature, T21 is the temperature of the reflecting white foil which covers the soilsurface.) So the equation

ql-(k. w(a-T21)/(1-k.b)} + ((1-w) .(a-T19)/(1-k.b)} is valid and shows the two additional parts in the energy balance of layér 19 and layer 21 which are nescessary and sufficient for solving the greenhouse equations. Practical remarks.

When a control-strategy is applied, several simulation cycles may be needed to achieve the desired situation, whereas the values a and b remain their validity.

The soil flux history stored in the file FLUX.DAT contains all the information needed for indépendant computation of soiltemperatures (indépendant of the simulation process) . (A more detailed explanation is given in: "Operator.pas",

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Intern rapport,IMAG,J.A.Stoffers,September 1989.) 6. A listing of DAC15.12 as an example of the result SOLANUM IMAGinatum (Version[1.0] 1-9-1989) DATE OF COMPUTATION 21-8-1989 Time of computation 16:55:57 dacl5.12 ( Month 1 .the 15 day.) Min. number of iterations 12, iterationcondition 0.010 Fantasyrate-1 Unrest-1 See file PARAM.* for param. greenhouse! Automatic (compl.) control layer Storagecoeff. 3 11326[ws/(K.m*2)] 5 11326[ws/(K.m*2)J 7 11326[ws/(K.m"2)] 9 0[ws/(K.m*2)] 11 200[ws/(K.m*2)] 13 9296[ws/(K.m"2)J 15 1204[ws/(K.m"2)] 17 7642[ws/(K.m"2)) 19 131250[ws/(K.m~2)] 21 0[ws/(K.m"2)] Day of year- 15 , time 12 h. Temperature in centigrade. Tsky—1.7, T air- 3.9 Watervap . pres. - 632 Re 1. Humid.- 78% , Windveloc.- 1.6[m/s] Cloudinessdegree-70.0 % Dif. rad. (400-3000nm)-122.4 [w/m"2], Dir. rad. (400-3000nm)- 38.0[w/nT2] DECLINATION- -21.1

[Pa]

TETA - 73.5 BETA -78.9 TETAB -34.6 BETAB - 19.8 Layer Long wave transm. abs. energ. [i 4 1.00 Q[4] 0. 0 6 1.00 Q[6] -0. 0 8 0.80 Q[8] -1. 8 10 0.97 Q[10] -0. 2 12 1.00 Q[12] 0. 0 14 0.80 Q114] -0. 3 16 0.90 Q [ 16 ) 0. 1 18 0.94 Q [ 18] 0. 1 20 1.00 Q[20] 0. 0 Layer Transm. Eps. a Eps .b 3 0.00 0.83 0.83 4 1.00 0.00 0.00 5 0.70 0.20 0.20 6 1.00 0.00 0.00 7 0.00 0.83 0.93 8 0.80 0.20 0.20 9 0.99 0.01 0.01 10 0.97 0.03 0.03

'2]

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11 0.91 0.08 0.08 12 1.00 0.00 0.00 13 0.93 0.07 0.07 14 0.80 0.20 0.20 15 0.71 0.29 0.29 16 0.90 0.10 0.10 17 0.92 0.07 0.07 18 0.94 0.06 0.06 19 0.56 0.35 0.00 20 1.00 0.00 0.00 21 0.00 0.80 2.00 ALFA Heattransfercoeff icient [w/(K 3 5.4 4.4 5 4.4 3.9 7 3.9 4.4 9 0.1 0.1 11 0.3 0.3 13 0.3 0.3 15 3.4 3.4 17 0.2 0.2 19 1.3 0.0 21 1.7 0.0 ALFA_VENT [w/(K.m'2)l Greenhouse: 0.2 Sunscreen:10000.0 Energyscreen:10000.0 WINDOWOPENING [degrees]:

Lee-slde : 0 Weather-side: 0

Heatconsumption : Uppersystem 0.0[Watt/m'2]

0.0[Watt/m*2] So called K-value 3.2[W/(m2.K)] 59.6[w/m*2] 3 Layers, cavities filled with AIR and ARGON. Heatstorage in the greenhouse= 14 [w/m~2] Long wave rad. 3 4 5[Watt/m' 2 Long wave rad. 4 0 0 [Watt/m" 2 Long wave rad. 5 1 1[Watt/m* 2 Long wave rad. 6 -0 0[Watt/m' 2 Long wave rad. 7 -19 5[Watt/m-2 Long wave rad. 8 -1 8[Watt/m-2 Long wave rad. 9 -0 3[Watt/m-2 Long wave rad. 10 -0 2[Watt/m* 2 Long wave rad. 11 -4 5[Watt/m* 2 Long wave rad. 12 0 0[Watt/m' 2 Long wave rad. 13 -4 9[Watt/m* 2 Long wave rad- 14 -0 3[Watt/m* 2 Long wave rad. 15 -6 7[Watt/m-2 Long wave rad. 16 0 1[Watt/m* 2 Long wave rad. 17 -0 2 [Watt/m-2 Long wave rad. 18 0 1[Watt/m' 2 Long wave rad. 19 -4 5[Watt/m-2 Long wave rad. 20 0 0[Watt/m* 2 Long wave rad. 21 2 0[Watt/m* 2 Convection clad.mat.- 16.9[Watt/m"2] Lat. conv.clad.mat.- 0.0[Watt/m*2]

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00 CO2 6.37 H20 0.02

Ventil.- 2.9 [w/m~2l ,Lat. 4.6 [w/m'2] Check: 0.0 % error in energybalance! Temperatures T3 7.0 T4 10.0 T5 12.9 T6 16.1 T7 19.3 T8 22.3 T9 24.2 T10 22.3 T U 26.1 T12 22.3 T13 27.8 T15 23.9 T17 22.7 T19 24.4 T21 21.6 Vapor pressures [Pa] P8 2566 P10 2566 P12 2567

ENERGYSCREEN IS OPEN ! SUNSCREEN IS OPEN ! TOTAL COSTS [fl/(a.m*2)] 75.78 Specified:INV. 69.38 ENERG. 0 Dry matter production 9.93 [kg/(nT2.a)] LAI 0.96 Diametr leave 0.12[m] Canopy density 4.13[l/m] Width canopy 0.5[m] Height canopy 0.7[m] Leaves/plant 15.6 ri-plant 541 [s/m] Evapor. 25.5 [w/m"2] 25.6 Vent.outs. 4.6 4.6 [w/m*2] COND. SURFACE 7 20.9 [w/m"2] Vent Energyscreen 16.7 Lat 25.5 [w/m*2] Vent Shadingscreen 18.0 Lat 25.5 [w/m~2] Dif. light, trans 0.725 0.720 clad. mat.+ constr. parts Dir. light trans.0.743 0.736 clad. mat.+ constr. parts Radiation pattern 400-3000nm Id downward Iu upward Id[0,1]- 122.40 [w/m*2] Iu[0,1]« Id[0,2]-lu[0,2]-Id[1,1] -Iu[l,l]-Id[1,2]-Iu[1,21 -Id[2,1] -Iu[2,1] -Id[2,2]-Iu[2,2]-Id[3,1]-Iu[3,1]-Id[3,2]-Iu[3,2]= Id[4,1]-Iu[4,1]-Id[4,2]-Iu[4,2]-Absorbed Q[3] -Q[5]-Q [7] -Q191-Qt 11 ] -

35.76 38.01 10.36 89.52 5.16 28.38 1.50

88.87 4.97 28.10 1.44

82.00 2.38 24.88 0.64 75.70 1.82

20.94 0.50

[w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m [w/m

2] ' 2 ] 2 ]

• 2 ] 2]

• 2 ] • 2 ] • 2 ] 2 ]

• 2 ] • 2 ] •21

2 ] • 2 ] ' 2 ] '2] • 2 ] 2] 2 ]

Iu[0, ] f / Id[0, ] /\/\/\/\/\/\/\/\/\/\/\/\/\/ lull.

Iu[2,

Iu [3, * Iu [4,

l / •

1 /

/ Id[1, ] -Shading scr. ^ Id[2, ]

—energy scr. .Id[3, ] • i • ,Id[4, ]

C A N O P Y

short wave radiation Q[I] [w/m"2] 1.69 0.85 0.51 0.70 6.69

2H2

Q[13]" 9.55 Q[ 15]» 48.24 Q[17]- 1.17 Q119]— 19.65 Q[21]- 25.26 C02 concentration 1520[mgC02/kgAIR] 1520[mgC02/kgAIR] 1520 tmgC02/kgAIR] 456[mgC02/kgAIR] C02-supply 22.73 Fot. Synth.16.63 Cumulative values Energy costs [fl/m'ZJ Water costs [fl/m"2] C02 costs [fl/m-2] Tot. costs tfl/m'2]

Cum. glob, radiation ENERGY SOIL [W.h/m'2] Tbo 16.3 Tbg 15.0Soil

Q_F0T SYNTH. 5.04

Near the canopy Between screens Above screens Outside [kg/(ha.h)] [kg/(ha.h)]

Time of computation 17:1:44

O.OOOOOOOOOOE+OO 4.4037943262E-06 .1.4148267054E—03 1.7260428256E-02

in [kgC02 max/ha] 210.8 51.4 51.4

flux("=+) -35.5[w/m~2]

7. Acknow1edgements Some prts of the program contain translated BASIC programs, as can be seen from the references where the help of two stagiaires Ing. A.Krechting and Ing.J.W van der Voort was very useful. In particular the collecting of the inputparameters (PARAM.*)was designed by A.Krechting.

REFERENCES

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