Cooling Fan-ventilated Greenhouses: a Modelling Study

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Biosystems Engineering (2003) 84 (3), 315–329 doi:10.1016/S1537-5110(02)00270-2 SE}Structures and Environment

Cooling Fan-ventilated Greenhouses: a Modelling Study D.H. Willits Biological and Agricultural Engineering, North Carolina State University, Raleigh, NC, USA; e-mail: dan [email protected] (Received 18 March 2002; accepted in revised form 20 November 2002)

A model for fan-ventilated greenhouse cooling is presented in which the primary heat transfer surfaces (cover/ structure, canopy and floor) are represented as three parallel planes. Validation of the model was accomplished using data collected over 14 days. Agreement was good, with canopy temperatures overpredicted by only 0
1%, air temperatures in the canopy under-predicted by 0
5%, humidity of the canopy air under-predicted by 1
6% and transpiration rates under-predicted by 1
4%. Simulation runs suggest that when evaporative pad cooling is not used, little advantage is derived from increasing airflow rates beyond about 0
05 m3 m2 s1. When evaporative pad cooling is used, however, both air and canopy temperatures decline with increasing airflow rates up to 0
13 m3 m2 s1, the highest level considered. Increasing canopy size is predicted to be more influential in reducing air temperatures when evaporative pad cooling is used than when it is not, but its effect on canopy temperature is expected to be approximately the same whether or not evaporative pad cooling is used. With no evaporative pad cooling, the evapotranspiration coefficient (i.e., the ratio of energy used for transpiration to incoming solar energy) is predicted to range from 1
75 for an outside temperature of 36
88C and an outside humidity ratios of 3
3 g kg1 to 0
8 for an outside humidity ratio of 29
9 g kg1 at the same temperature. With evaporative pad cooling, the coefficient is predicted to range from 0
6 to 0
8 at the same outside temperature and the same range of outside humidity ratios. # 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Science Ltd

1. Introduction Cooling has always been an important problem for greenhouse operators in warm climates, potentially limiting production and constraining profits. Greenhouse cooling is typically accomplished by ventilation, either mechanically, via exhaust fans, or naturally, via wind and buoyancy. While it is convenient to think of designing cooling systems for a fixed upper temperature limit, above which damage is assumed to occur and below which everything is satisfactory (Fuchs, 1993), there is evidence to suggest that damage occurs at temperatures lower than normally assumed. Peet et al. (1997) found that increasing mean daily temperatures from 258C to 268C reduced tomato fruit weight, number and seed content nearly as much as increasing from 288C to 298C. Similarly, in several cultivars of chrysanthemum the inverse of time-to-flower was shown to decrease linearly with increasing mean daily temperatures above an optimum of approximately 188C (Pearson et al., 1993; 1537-5110/03/$30.00

Willits & Bailey, 2000). These observations suggest that cooling design may be more critical than previously believed considering that even small increases in temperature above the optimum may result in reduced yields. This also suggests that a better understanding of the uniformity of temperature control within the greenhouse is needed if production penalties are to be avoided. Over the years a number of models have been developed to describe fan-ventilated cooling systems (Walker, 1965; Seginer & Livne, 1978; Landsberg et al., 1979; Fuchs, 1993; Seginer, 1994; 1997; Al-Helal & Short, 1999). At least one model (Al-Helal & Short, 1999) considered temperature and humidity gradients in the direction of airflow, but more typically it has been assumed that the axial gradients are either sufficiently linear that the interior conditions can be represented adequately by overall averages or that only maximum temperatures and humidities need to be considered, thereby permitting a focus on the exhaust conditions. Although these simplifications are appropriate 315

# 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Science Ltd

316

D.H. WILLITS

Notation A a,b c E H h h0 k k0 q L m ’ m

Q rs Rs S T t U u uw W W1 W2 w x y y0 z a b G g d e

area, m2 variables, m specific heat, J kg1 K1 evapotranspiration coefficient solar hour angle, rad convective heat transfer coefficient, W m2 K1 convective moisture transfer coefficient, W m2 K1 thermal conductivity, W m1 K1 extinction coefficient heat flux, W m2 length of plant row, m mass per unit floor area, kg m2 floor] mass flow rate of air per unit width of the greenhouse, kg [air] m1 [floor] s1 airflow rate per unit floor area, m3 [air] m2 [floor] s1 stomatal resistance, s m1 bulk resistance of the canopy to transpiration, m2 kW1 shelter factor absolute temperature, K temperature, 8C overall heat transfer coefficient, W m2 K1 air velocity, m s1 wind velocity, m s1 width of greenhouse, m width of a single row of plants, or plant diameter, m width of a double row of plants, m humidity ratio of the air, kg [H2O] kg1 [air], distance in the direction of airflow, m height of the upper edge of canopy measured from the floor, m height of lower edge of canopy measured from the floor, m depth of soil, m absorptivity solar altitude, rad outside radiation, W m2 l/cp, kg [air] K kg1 [H2O] leaf diameter, m emissivity

for some studies (Seginer & Livne, 1978), if information about the axial temperature and humi-dity profiles is required a different approach must be used. This paper presents a cooling model for fanventilated greenhouses designed to predict axial

Z Y y L l r s t t0 f c

evaporative pad efficiency evapotranspiration rate, kg [H2O] m2 [floor] s1 time, s leaf area index, m2 [leaf area] m2 [floor] latent heat of vaporisation of water, J kg1 density, kg m3 Stefan–Boltzman constant, 5.67  108 W m2 K4 transmissivity transmissivity of the regions occupied by plants reflectivity specific transpiration, g [H2O] m2 [leaf] s1

Subscripts a avg c cv ds e ex est f gh i inlet lw nc o old p pm r sw wv x y z

air average over the whole greenhouse canopy cover deep soil section exit greenhouse exhaust estimate floor greenhouse cross section incoming greenhouse inlet longwave non-canopy outside value from the previous time step at constant pressure plant material removed shortwave water vapour shaded unshaded at 08C

Superscripts i n

counter for greenhouse sections number of greenhouse sections

gradients of temperature and humidity in the direction of airflow. Model validation is presented, as are simulations illustrating important considerations for the design of fan-ventilated cooling systems for greenhouses.

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FAN-VENTILATED GREENHOUSES

2. Materials and methods 2.1. Model development The model, written in FORTRAN 90, is largely based upon the work of Seginer and Livne (1978). It calculates (from weather data inputs) the energy to be removed from the plants, ground and cover to predict temperature and humidity gradients in the direction of airflow. The air stream was divided into two parts, one passing through the canopy and removing both sensible and latent energy, and the other contacting only non-canopy surfaces and removing only sensible energy. These streams are assumed to converge at the exhaust fan(s) just prior to exiting the house. The house is assumed to be divided into multiple sections of unit width and length dx. The sensible energy gained by the air moving through the canopy is assumed to be only that from the canopy itself, qc; therefore the differential temperature change of the air, dta,c, as it moves through a section is: dta;c qc ¼ ’ dx mc cp;a;c

ð1Þ

’ c is the mass flow rate of the air per unit width where m of greenhouse in kg [air] m1 s1 and cp;a;c is the specific heat of the air (at constant pressure) passing through the canopy in J kg1 [air] K1. The latent energy gained by the canopy air is lY, thus the differential increase in humidity ratio if the air as it passes through a section is: dwa;c Y ¼ ’c dx m

qf þ qcv dta;nc ¼ ’ nc cp;a;nc dx m

ð4Þ

dwa;nc ¼0 dx

ð5Þ

and

The energy to be removed by the non-canopy air is then qr;nc ¼ qf þ qcv ¼ m’ nc cp;a;nc




hf ðtf  ta;i;nc Þ hcv ðtcv  ta;i;nc Þ þ ’ nc cp;a;nc þ 0
5Dxhcv ’ nc cp;a;nc þ 0
5Dxhf m m



ð6Þ where the total energy removed by the two air streams is qr ¼ qr;c þ qr;nc

ð7Þ

ð2Þ

where l is the latent heat of vaporisation of water in J kg1 [H2O], Y is the transpiration rate from the canopy in kg [H2O] m2 [floor] s1, and wa;c is the humidity ratio of the air passing through the canopy in kg [H2O] kg1 [air]. By assuming that heat and moisture transfer take place at the average temperature or humidity over the section, and approximating the differentials as finite differences, the total energy to be removed by the canopy air stream as it passes through each section qr;c can be approximated as (Seginer & Livne, 1978) qr;c ¼ qc þ lY
’ c cp;a;c ¼m

respectively, in kg [H2O] kg1 [air], and g is a convenient representation of the quantity l=Cp;a;c . Only sensible energy is assumed to be exchanged in the air stream passing the non-canopy surfaces (denoted by the subscript nc); i.e., the floor (denoted by the subscript f ) and the cover plus structure (denoted by the subscript cv). This ignores moisture evaporation and condensation from and to the non-canopy surfaces; however, the error should be small for most high temperature, high radiation loading cooling situations. The additional complication of considering these fluxes at this time did not seem worthwhile given that the validation data for the model (see below) were collected under conditions of no evaporation or condensation and thus the effort could not be validated. Thus

 hc ðtc  ta;i;c Þ gh0c ðwc  wa;i;c Þ þ ð3Þ ’ c cp;a;c þ 0
5Dxhc m ’ c cp;a;c þ 0
5Dxh0c m

where hc and h0c are the convective heat and mass transfer coefficients, respectively, of the canopy in W m2 K1, tc and ta;i;c are the temperatures of the canopy and canopy air at the inlet, respectively, in 8C, wc and wa;i;c are the humidity ratios of the canopy (assumed to be saturated at tc ) and canopy air at the inlet,

2.2. Solution The algorithm used iteratively solved for ta;c , ta;nc and tc for each greenhouse section until two successive calculations of the greenhouse exhaust air temperature (mass average of ta;c and ta;nc ) agreed within 0
0018C. The energy fluxes qc , qf and qcv were determined as functions of outside weather conditions based on energy balances on the three primary elements of the system (cover plus structure, canopy and floor). The three elements were modelled as parallel planes. Only first reflections were considered in the radiation balances below because the canopy and cover of a greenhouse are not particularly reflective, yielding multiple reflection terms that are typically quite small (less than 0
05% of the transmitted energy). An approximate energy balance on the cover for the ith section was written by adding the radiative and convective fluxes from the environment surrounding the cover to the thermal energy stored from the previous time step and equating that to the

318

D.H. WILLITS

radiative and convective fluxes leaving the cover; i.e.,

in the ith section was

ðacv;sw þ acv;sw fc;sw tcv;sw þ acv;sw tc;sw ff ;sw tc;sw tcv;sw ÞGsw

qir;c ¼ ðac;sw þ ac;sw ff ;sw tc;sw Þtcv;sw Gsw

þ ðacv;lw þ acv;lw fc;lw tcv;lw þ acv;lw tc;lw ff ;lw tc;lw tcv;lw ÞGlw  4  4 þ acv;lw ec;lw s Tci þacv;lw tc;lw ef ;lw s Tfi  i 4 þ ðacv;lw fc;lw þ acv;lw tc;lw ff ;lw tc;lw Þecv;lw s Tcv ccv mcv ðticv;old  ticv Þ þ hcv;o tia;o þ hcv;i tia;nc þ Dy  i 4 ¼ 2ecv;lw s Tcv þhcv;o ticv þ hcv;i ticv

þ ð8Þ

where c is specific heat in J kg1 K1, G is incident radiation on a horizontal surface outside the greenhouse in W m2, y is time in s, a; f; t; e are absorptivity, reflectivity, transmissivity and emissivity, respectively, s is the Stefan–Boltzman constant in W m2 K4, T is the absolute temperature in K, and the subscripts sw, lw, o, and old denote shortwave radiation, longwave radiation, outside conditions, and the value from the previous time step, respectively. Incident thermal radiation was calculated as (Swinbank, 1963) h  1
5 i4 Glw ¼ s 0
0552 Ta;o ð9Þ Equation (8) was solved iteratively for ticv using estimates of tia;nc , tic and tif . When ticv converged to within 0
01%, a solution was assumed and the cover temperature loop exited. Using the same convention as for the cover, a sensible energy balance on the floor for the ith section was then written as af ;sw tc;sw tcv;sw Gsw þ af ;lw tc;lw tcv;lw Glw  i 4  4 þ af ;lw tc;lw ecv;lw s Tcv þaf ;lw ec;lw s Tci  4 þ ðaf ;lw fc;lw þ af ;lw tc;lw fcv;lw tc;lw Þef ;lw s Tfi þ hf ta;nc þ

þ ðac;lw þ ac;lw ff ;lw tc;lw Þtcv;lw Glw  i 4 þ ðac;lw þ ac;lw ff ;lw tc;lw Þecv;lw s Tcv  4 þ ðac;lw þ ac;lw fcv;lw tc;lw Þef ;lw s Tfi

cf mf ðtif ;old  tif Þ

Dy  4 kf ðtif  tds Þ ð10Þ ¼ ef ;lw s Tfi þhf tif þ z where kf is the conductivity of the floor material, z is the depth to the point where the soil temperature is constant year round, i.e., the deep soil temperature, tds . Equation (10) was solved iteratively for tif using the previous estimates of tia;nc and tic along with the recently updated estimate of ticv . Again, a solution was assumed, and the floor temperature loop exited, when tif converged to within 0
01%. An estimate of the energy to be removed from the canopy (both sensible and latent) was determined by assuming that the energy to be removed by the air is that radiated to canopy (plus any reduction in thermal energy). The resulting energy transfer to the canopy air

 4 cc mc ðtic;old  tic Þ  2ec;lw s Tci Dy

ð11Þ

With the temperatures of the cover and floor updated for this section based on the solution of Eqns (8) and (10), the sensible energy flux transferred to the noncanopy air was estimated as qir;nc ¼ qif þ qicv;i ¼ hf ðtif  tia;nc Þ þ hcv;i ðticv  tia;nc Þ

ð12Þ

using the previous estimate for tia;nc . This allowed the total energy transferred to both air streams, qir;est , to be estimated using Eqn (7). New values of ta;c and ta;nc for the ith section were determined from tia;c ¼

’ c cp;a;c tia;i;c 0
5hc Dxtic þ m ’ c cp;a;c 0
5hc Dx þ m

ð13Þ

and tia;nc

  ’ nc cp;a;nc tia;i;nc 0
5Dx hcv ticv þ hf tif þ m   ¼ ’ nc cp;a;nc 0
5Dx hcv þ hf þ m

ð14Þ

which were then used to determine new values of qir;c and qir;nc (and therefore qir ) using Eqns (3) and (12). This procedure was repeated in an overall loop until successive values of tic , tia;c and tia;nc agreed within 0
01%. The air temperatures tia;c and tia;nc were modified using successive substitution while tic was modified using a bracketing and bisection technique (Press et al., 1986) based on the difference between qir;est and qir . The average humidity ratio of the canopy air stream through the section was determined by wia;c ¼

’ c wia;i;c 0
5Dxgh0c wic þ lm ’c 0
5Dxgh0c þ lm

ð15Þ

whereas the average humidity ratio of the non-canopy air stream was given by wia;nc ¼ wia;i;nc

ð16Þ

Once convergence of the average temperatures was obtained, the exit conditions for the section are determined, set equal to the entrance conditions of the next section, the section counter incremented and the procedure repeated until the total number of sections had been processed. The conditions of the exhaust air

319

FAN-VENTILATED GREENHOUSES

leaving the greenhouse were then determined as   ’ c wna;e;c ’ nc wna;e;nc þ m m wa;ex ¼ ’t m   ’ c hna;e;c ’ nc hna;e;nc þ m m ha;ex ¼ ’t m ta;ex ¼

ha;ex  wa;ex ðlz þ cp;wv tna;e;c Þ cp;a

ð17Þ

ð18Þ ð19Þ

where the superscript n represents the nth (last) section and subscripts e, ex, z and wv denote the exit of a section, greenhouse exhaust conditions, value at 08C and water vapour, respectively. After processing all of the sections, the calculations were repeated until the resulting exhaust air temperature for the greenhouse agreed with the previous estimate within 0
0018C. The heat transfer coefficient from the canopy was calculated based upon an equation designed to account for both natural and forced convection (Seginer & Livne, 1978): " 0
25 #

u 0
5 tc  ta;c 2L c h ¼ 5
2 ð20Þ þ1
9 S d d 2

where d is leaf diameter in m, L is leaf area index in m [leaf] m2 [floor], S is a shelter factor to adjust for a portion of the canopy that is protected from the air stream and u is the velocity of the air in m s1. The dependence of h on the difference between tc and ta,c requires that it be updated as these temperatures change; i.e., immediately after the determination of qr,est from Eqn (7) and prior to the use of h in Eqn (13). The moisture transfer coefficient, h0 , is assumed to be related to h through the bulk stomatal resistance Rs (Seginer & Livne, 1978) h ð21Þ h0 ¼ 1 þ Rs h

discontinuous canopies. The canopy configuration used was that of the validation greenhouse (described below), consisting of three double rows of plants oriented on a north–south axis, flanked by a single row along either side (Fig. 1). Each double row consisted of two rows of plants separated from each other by a utility aisle and from the other double rows by walking aisles. The amount of floor area A in m2 shaded by the canopy (subscript x) at solar noon (hour angle H = 0 rad) was determined as Ax ¼ ½2W1 þ 3W2 L

ð24Þ

where W1 is the width of a single row in m, W2 is the width of double row in m and L is the length of the rows in m. When the sun was at an hour angle other than zero, the shaded area was represented by Ax ¼ ½2ðW1 þ a  bÞ þ 3ðW2 þ a  bÞ L

ð25Þ

where the variables a and b are given by y a¼ tanðp=2  HÞ y0 b¼ tanðp=2  HÞ

ð25aÞ

where y and y0 are the heights of the upper and lower edges of the canopy, respectively, in m. Line of Symmetry

H

W2

W1

y

where Rs ¼

rs rcp L

ð22Þ

and where rs is the stomatal resistance, and P is the density in kg m3. Heat transfer coefficients from the floor and the cover surfaces were determined from a relationship for heat transfer from a smooth surface (Henderson & Perry, 1982) h ¼ 4
54 þ 3
05u

ð23Þ

The canopy was modelled as a two-dimensional structure using a method outlined by France and Thornley (1984) for calculating the transmissivity of

y'

β a

b

Floor

Fig. 1. Schematic representation of canopy shading of the floor, where H is the hour angle of the sun measured from the vertical in rad, W1 and W2 are the widths of a double row and a single row of plants, respectively, y and y0 are the heights of the upper and lower edges of the canopy, respectively, measured from the floor in m, a and b are dimensions defined above measured in m and b is the solar altitude of the sun measured from the horizontal in rad

320

D.H. WILLITS

The hour angle of the sun was determined using the standard equations describing the position of the sun in the sky (ASHRAE, 1997b). The solar transmissivity of the open areas (subscript y) was determined from the ratio of the open area to the total floor area, or Af  Ax ty;sw ¼ ð26Þ Af Transmissivity through regions occupied by the plants t0sw was determined by (France & Thornley, 1984) Ax ½ksw 0 LAf =Ax

t0sw ¼ ð27Þ e Af where k0 is the extinction coefficient, yielding an effective transmissivity of the canopy to solar radiation of tc;sw ¼ ty;sw þ tsw

ð28Þ

Reflection of solar energy by the canopy was approximated by Ax fc;sw ¼ fpm;sw ð29Þ Af where the subscript pm refers to the plant material. For simplicity, the thermal radiation properties of the canopy were modelled using the same approach; however, an hour angle of p/4 was assumed to account for the diffuse nature of thermal radiation. The amount of air moving through the canopy versus. that contacting only non-canopy surfaces was determined by considering the approximate cross-sectional area of the canopy relative to the cross-sectional area of the greenhouse Agh; i.e., ’c ¼ m

ðy  y0 ÞW ’t m Agh

ð30Þ

’ t is where W is the width of the greenhouse in m and m the total mass flow rate of the air per unit width in kg m1 s1. Equation (30) assumes that the aisles are narrow enough that the air flowing through them has a negligible dilution effect on the canopy air. It also assumes, based on air velocity measurements reported below, that the airflow rates in the different sections were approximately equal. The mass flow rate of air ’ nc through the non-canopy portion of the greenhouse m was taken as the complement of Eqn (30). 2.3. Model validation Data for the validation were taken from a separate study conducted in two 6
7 m by 12
1 m, quonset-style, double-polyethylene covered greenhouses located at the Horticultural Field Laboratory on the NC State University campus in Raleigh, NC (358470 N latitude; 788390 W longitude). The cooling equipment in each

house consisted of two exhaust fans (one two-speed and one single-speed) capable of producing ventilation rates up to 0
087 m3 m2 s1. Also available were evaporative pad cooling systems sized for pad face velocities of 1
27 m s1 at the highest ventilation rate. The floor was graded for drainage and covered with an ethylene propylene diene monomer (EPDM) membrane to eliminate water evaporation from the floor with a landscape cloth placed on top. Details are available in Seginer et al. (2000) and a brief summary is presented below. 2.3.1. Plants The houses were planted with 208 tomato plants (cv. Trust) 14 June, 1999, distributed in eight rows of 28 plants each. The rows were oriented parallel to the direction of airflow (north to south). The plants were grown in 18
9 l black polyethylene bags filled with 50%, by volume, commercial potting mix and 50% screened pine bark. Fertilisation was automatic with each watering through drip emitters. Waterings were once per day in the early morning. 2.3.2. Data collection Validation data were taken from unshaded cooling treatments consisting of two levels of evaporative pad cooling (full and none) and two levels of ventilation rate (0
041 m3 m2 s1 versus 0
087 m3 m2 s1). Environmental control and data collection were via personal computer connected data-logger front ends. The data were recorded as 10 min averages of 1 min readings. Solar radiation on a horizontal surface at the top of the canopy was measured using an Epply model 8-48 pyranometer mounted at the top of the evaporative pad on the north wall of each house. Outside solar radiation was measured using an identical pyranometer mounted at the top of the north end of one of the houses. Floor temperatures were measured at three locations along the direction of airflow. Lengths of approximately 15 cm of 36 gauge thermocouple wire were glued to the landscape cloth with contact cement. A 25 cm by 25 cm layer of landscape cloth was glued over each thermocouple to minimise radiation error and to make the surface similar to the rest of the floor. Five aspirated dry-bulb/wet-bulb stations were located on either side of the longitudinal axes of each house directly in line with the exhaust fans, one at the air entrance, three spaced equal distances down the length of the house and one at the fan entrance. The heights of the stations in the canopy were adjusted each week so that the uptakes remained in the middle of the canopies. Outside conditions were monitored using an aspirated station located outside each air entrance.

321

FAN-VENTILATED GREENHOUSES

Leaf temperatures were monitored with 0
077 mm diameter thermocouples glued to the underside of leaves in the upper canopy. Eighteen plants were used in each house, one leaf per plant. The plants were spread across the width of the house at three locations down the length of the house (0
15, 0
5 and 0
84 of the distance from the air entrance end). The thermocouples were inspected daily and the data discarded for those thermocouples where contact between the thermocouple and the leaf were lost. Canopy transpiration was estimated using temperature-compensated platform scales to measure the moisture loss of six plants in each house. The plants were supported via lightweight structures made from polyvinyl chloride (PVC) pipe resting on each scale. Leaf areas were estimated by measuring overall lengths and widths of each compound leaf on ten sample plants in each house every 2 weeks. At the end of testing, all leaves were run through the leaf area meter in addition to measuring lengths and widths. Regression equations were developed to estimate leaf area from the length/width measurements and used to determine leaf area indices (based on total greenhouse floor area) as a function of Julian date. Air velocities were measured using a hot-wire anemometer at eight heights starting at 0
3 m and ending at 2
4 m up from the floor. The velocities were measured in each house and in each aisle at three locations, at the air inlet, the middle and at the air exit positions.

2.3.3. Model parameters Based on measurements, air velocities were taken to be 0
15 m s1 near the cover, 0
33 m s1 through the canopy and 0
26 m s1 over the floor for the lower ventilation rate. Those for the higher ventilation rate were 0
53 m s1 near the cover, 0
69 m s1 through the canopy and 0
43 m s1 near the floor. The thermal resistance of the airspace between the double-polyethylene layers was assumed to be 0
09 m2 K W1 (Henderson et al., 1997). Ignoring the conductive resistance of the 0.15 mm thick polyethylene film, the outside cover coefficient hcv,o was approximated as hcv;o ¼

1 1= ð4
54 þ 3
05uw Þ þ 0
09

ð31Þ

where uw is the wind velocity in m s1. Seginer and Livne (1978) used a value of 1
5 for the shelter factor S in Eqn (20); however, a single fixed value was found to be inadequate for both dense and sparse canopies. As a result, S was set equal to 1
0 when the canopy was sparse (L40
5) and 2
0 when the canopy was dense (L52
0), with values in between

determined by S ¼ 0
6667 þ 0
6667L

ð32Þ

The evaporative pad was modelled assuming a constant wet-bulb temperature through the pad with the air temperature entering the house determined as ta;inlet ¼ ta;o  Zðta;o  twb;o Þ

ð33Þ

A constant of 0
80 for the evaporative pad efficiency Z was assumed based on data presented by Koca et al. (1991), analysis of the data collected in the greenhouses used in this study and the assumption that for design purposes the size of the evaporative pad can be altered to keep Z constant with flow rate. Values for some of the other parameters used in the model are presented in Table 1. A total of 14 days (ranging from day 184 to day 223) were modelled in two houses. The days were selected based on weather and cooling treatment and were thus not necessarily consecutive. Only sunny hot days were selected, spread out over the season such that L ranged from 0
52 to 2
04 and plant height ranged from 0
99 to 1
9 m.

2.4. Simulations The model was used to predict the effect of airflow rate, stomatal resistance, leaf area index, outside humidity and evaporative pad cooling on air and canopy temperatures. The weather conditions used were selected from a bright sunny day (day 214) in the validation dataset. Outside solar radiation was set to 955 W m2 and outside air temperature to 36
88C. Outside humidity was varied by changing wet-bulb temperature in five equal steps yielding humidity ratios of 3
3, 8
4, 14
4, 21
4 and 29
9 g kg1. This resulted in relative humidities of 8
6%, 22
8%, 37
0%, 54
3% and 74
9%. Airflow rate was varied between 0
022 and 0
130 m3 m2 s1 in six equal steps with L being varied between 0
5 and 3
0 in five steps. Canopy height y was determined using a regression equation developed from the data taken from the validation study, y ¼ 0
38

0
0552 þ 0
505L W1

ð34Þ

up to a plant height of 2
3 m, the height of the suspension wire. The time of day was set to solar noon and rs was set to 100 s m1. In addition to examining air and canopy temperatures and specific transpiration rates, evapotranspiration coefficients were generated based upon the cooling design equation recommended by EP 406
3, the ASAE design guideline for ventilating and cooling greenhouses

322

D.H. WILLITS

Table 1 Parameter values used Parameter

Symbol

Value

Source

Shortwave absorptivity of cover* Specific heat of cover* Specific heat of floor Specific heat of plant material Leaf diameter Longwave emissivity of cover* Longwave emissivity of floor Thermal conductivity of floor Shortwave extinction coefficient of canopy Mass of the floor Mass of the cover* Mass of the canopy Number of greenhouse sections Shortwave reflectivity of cover* Shortwave reflectivity of floor Longwave reflectivity of floor Shortwave reflectivity of plant material Deep soil temperature Longwave transmissivity of cover* Shortwave transmissivity of cover*

acv,sw ccv cf cpm d ecv,lw ef,lw kf k0 sw mf mcv mc n fcv,sw ff,sw ff,lw fpm,sw tds tcv,lw tcv,sw

0
16 1000 J kg1 K1 450 J kg1 K1 3500 J kg1 K1 0
045 m 0
2 0
9 1
2 W m1 K1 0
59 75 kg m2 10 kg m2 0
7L kg m2 10 0
15 0
25 0
1 0
12 15
5 C 0
62tcv,sw 0
69

Estimated Estimated Estimated Stanghellini (1987) Measured Estimated Estimated Kreith (1965) Stanghellini (1987) Estimated Estimated Stanghellini (1987) } Estimated Measured Stanghellini (1987) Stanghellini (1987) NCDC (2001) Estimated Measured

*Cover properties include the effect of area averaging (radiation) or mass averaging (thermal mass) of the properties of the polyethylene film with the properties of the structural members.

(ASAE, 1999): ð1  EÞtGsw Af ¼ UAcv ðta;avg  to Þ þ rcp;a QAf ðta;ex  ta;i Þ ð35Þ where E is the evapotranspiration coefficient (the ratio of energy used to evaporate water from the canopy to the incoming solar energy), U is the overall heat transfer coefficient in W m2 K1 and Q is the volumetric airflow rate, m3 s1. Values of E less than one yield values of ta,ex greater than ta,i whereas values of E greater than one result in values of ta,ex less than ta,i The ratio of cover to floor area was assumed to be 1
4, U was chosen to be 4
0 W m2 K1 based on EP 406
3 (ASAE, 1999) and ta was calculated as the average of the inlet and exhaust air temperatures.

3. Results and discussion 3.1. Validation Table 2 presents the average outside temperatures, humidities and solar radiation levels, as well as the percentage differences (based on the observed values) between predicted and observed results for the 14 days. Only the period from 0900 to 1500 h EST was considered each day. Negative values of percentage differences represent under-predictions while positive values represent over-predictions. The air conditions in the canopy were well predicted with an average

difference for air temperature of 0
5% and for humidity of 1
6%. The maximum differences were 3
6% for temperature and 9
9% for humidity. Although the average differences for the exit air conditions were larger than for the canopy air, the maximum differences were smaller, suggesting a more consistent prediction of exit air conditions. The temperature of the canopy itself was very well predicted, with an average difference of 0
1% and a maximum of 4
2%. Floor temperature predictions carried the largest error, with an average difference of 8
1% and a maximum difference of 17
9%. Transpiration differences were 1
4% for the average and 9
6% for the maximum. Figures 2–4 present the graphical results for 3 of the 14 days for 1200 h (solar noon) and 1400 h. Solar noon was chosen as the time of day when the floor is maximally exposed to solar radiation while 1400 h represents a time when the canopy is intercepting a significant percentage of the incident energy. Figure 2 presents the results for day 187 in house 1 plotted as a function of relative distance through the house. The evaporative pad was on and the airflow rate was 0
041 m3 m2 s1. The canopy was relatively small (L ¼ 0
57; y ¼ 1
06 m) with the floor largely exposed. Floor temperatures were over-predicted at both solar noon and 1400 h, but the over-predictions were not large (10%). The over-predictions at 1400 h are probably because the model output is the average floor temperature whereas the observed data were measured at

187 188 190 197 200 206 211 214 223

184 197 200 206 212

1 1 1 1 1 1 1 1 1

2 2 2 2 2

0
087 0
087 0
041 0
087 0
041

0
041 0
087 0
087 0
041 0
087 0
087 0
041 0
087 0
087 Yes No Yes Yes Yes

Yes Yes No No No No Yes No Yes

House Day Air flow Evap. no. no. (Q), m3 m2 s1 pad

30
6 29
0 31
9 30
9 36
7

35
2 31
8 33
5 29
0 31
9 30
9 33
8 31
1 32
7

Averages

15
9 14
1 14
8 16
0 12
4

16
9 16
3 15
0 14
1 14
8 16
0 14
6 8
9 14
3 816 807 832 856 841

730 782 805 807 832 856 811 856 785

Outside Outside Outside air temp. shortwave air (ta,o), 8C humidity radiation (Gsw), W m2 (wa,o), g kg1 0
4 0
1 8
2 1
8 3
9 6
1 0
9 9
9 1
6 1
7 3
9 3
1 1
0 1
8 1
9

0
7 2
2 2
7 0
7 3
6 2
0 1
5 0
4 2
1 1
7 2
0 1
1 0
0 2
4 0
5

2
5

2
8 5
6 2
4 3
9 3
1

2
5 2
0 1
2 3
2 0
3 1
4 2
1 2
2 1
9

1
8

2
7 1
7 3
4 2
8 3
6

2
8 3
8 0
7 0
4 1
1 0
4 2
8 0
1 3
1

0
2

3
4 4
2 3
1 0
6 0
2

0
7 3
9 2
7 1
1 2
1 0
1 2
5 2
0 0
8

8
0

7
2 14
2 5
5 2
4 5
9

15
4 10
9 9
4 17
9 8
2 3
6 4
1 3
6 4
1

1
3

9
6 2
2 2
1 1
7 2
2

6
3 7
3 2
5 7
4 0
2 2
3 3
8 4
2 3
4

Exhaust Canopy Floor Transpiration (c), % Air Exhaust Air air temp. temp. temp. in humidity air temp. canopy in canopy (ta,ex), % humidity (tc), % (tf), % (wa,ex), % (ta,c), % (wa,c), %

Differences between predicted and observed

Table 2 Average external environmental conditions and percent differences between predicted and observed results for the period from 0900 to 1500 h EST each day

FAN-VENTILATED GREENHOUSES

323

324

D.H. WILLITS

40

30 Canopy temp

30

25

Air temp 20 0.2

(a)

0.4

0.6

0.8

25

40 Air temp

20

Canopy temp

30

20

15

Air humidity 0.0

1.0

30

50

20

Air humidity 0.0

Temperature, oC

o

Temperature, C

35

Humidity ratio, g kg-1

Floor temp

Floor temp 50

0.2

0.4

0.6

0.8

Humidity ratio, g kg-1

40

1.0

Relative distance

(a)

Relative distance

40

30

Canopy temp 30

25

Air temp Air humidity

20

(b)

0.2

0.4

0.6

25 40

Air temp 20 Canopy temp

30

15

Air humidity 20 0.0

20 0.0

30

50

o

35

Temperature, C

Temperature, oC

50

Floor temp

Humidity ratio, g kg-1

Floor temp

Humidity ratio, g kg -1

60

40

0.8

1.0

(b)

0.2

0.4

0.6

0.8

1.0

Relative distance

Relative distance

Fig. 2. Predicted and observed data for day 187 in house 1 at (a) 1200 h EST and (b) 1400 h EST; circles are air temperature, triangles are canopy temperature, squares are air humidity and diamonds are floor temperature. Observed and predicted transpiration rates c were 0
095 g s1 m2 [leaf] and 0
089 g s1 m2 [leaf], respectively, at 1200 h; 0
086 g s1 m2 [leaf] and 0
082 g s1 m2 [leaf], respectively, at 1400 h. Air temperatures and humidities for relative distances 40
95 are those of the canopy air. Air temperatures and humidities for relative distances >0
95 are those of the exhaust air

specific locations. The rise in air temperature and reduction in air humidity at the exit results from the mixing of the canopy and non-canopy air streams. The data suggest that perhaps some mixing of the two streams occurred prior to the exhaust fan. Canopy temperatures were generally well predicted. Transpiration was under-predicted, but the under-predictions were small (6
3% and 4
7%). Figure 3 presents the results for day 190 in house 1 for an airflow of 0
087 m3 m2 s1 and no evaporative pad. The plants were only slightly larger (L ¼ 0
65; y ¼ 1
06 m) so the floor was still largely exposed. The floor temperature prediction at 1200 h is reasonable, but, again, it is over-predicted at 1400 h. Temperatures of the air flowing through the canopy were predicted to decrease with distance through the

Fig. 3. Predicted and observed data for day 190 in house 1 at (a) 1200 h EST and (b) 1400 h EST; circles are air temperature, triangles are canopy temperature, squares are air humidity and diamonds are floor temperature. Observed and predicted transpiration rates c were 0
145 g s1 m2 [leaf] and 0
141 g s1 m2 [leaf], respectively, at 1200 h; 0
146 g s1 m2 [leaf] and 0
147 g s1 m2 [leaf], respectively, at 1400 h. Air temperatures and humidities for relative distances 40
95 are those of the canopy air. Air temperatures and humidities for relative distances >0
95 are those of the exhaust air

canopy but in reality they increased slightly. The largest discrepancy in air temperature was about 1
18C (3
1% error) just prior to mixing with the non-canopy air but the agreement of the exhaust air temperature was quite good (within 0
48C or 1
1%). Canopy temperatures were also over-predicted, but mainly at mid-house where the difference was approximately 18C (53%). At the relative distance of 0
9, canopy temperature was only over-predicted by 0
28C. Agreement between predicted and observed air temperatures and canopy temperatures was better at 1400 h, with differences less than 0
38C for canopy temperature and less than 18C for air temperature. The observed trend in canopy air humidity was well predicted for both time periods, but the values were under-predicted, except at the exhaust. Transpiration rates were well predicted for both time periods, with a maximum error of 2
7%.

FAN-VENTILATED GREENHOUSES

35

o

Temperature, C

Floor temp 40

30 Canopy temp

30

25

Air temp 20

20

Humidity ratio, g kg-1

50

Air humidity 10

0.0

0.2

(a)

0.4

0.6

0.8

1.0

15

Relative distance 35

Temperature, oC

Floor temp 40

30 Canopy temp

30

25

Air temp 20

20

Humidity ratio, g kg -1

50

325

fan. Without evaporative pad cooling, however, the improvement from splitting the air stream was dramatic for both humidity (9
76% versus 5
63%) and transpiration (9
42% versus 2
32%). Canopy and air temperatures also improved (1
57% versus 1
10% and 1
33% versus 1
11%, respectively), as did exhaust air humidity (0
67% versus 0
01%). Only exhaust air and floor temperatures worsened slightly (1
60% versus 2
31% and 8
73% versus 9
49%). The validation results suggest that the model predicts fan-ventilated cooling well. The largest prediction error for temperature (occasionally >108C) was for the floor, but since floor temperature only indirectly affects the parameters of interest the errors were considered acceptable. The maximum prediction error in either tc or ta,c occurred on day 212, an under-prediction of 1
48C in tc (a difference of only 4
6%) for one time period and one location. Errors for tc and ta,c were generally less than 0
58C and were very often much less, as suggested by the results presented in Table 2. Prediction of exhaust air conditions was very good, with the worst errors being less than 0
58C and 0
8 g kg1.

Air humidity 10 (b)

0.0

0.2

0.4

0.6

0.8

1.0

15

Relative distance

Fig. 4. Predicted and observed data for day 223 in house 1 at (a) 1200 h EST and (b) 1400 h EST; circles are air temperature, triangles are canopy temperature, squares are air humidity and diamonds are floor temperature. Observed and predicted transpiration rates c were 0
052 g s1 m2 [leaf] and 0
048 g s1 m2 [leaf], respectively, at 1200 h; 0
049 g s1 m2 [leaf] and 0
046 g s1 m2 [leaf], respectively, at 1400 h. Air temperatures and humidities for relative distances 40
95 are those of the canopy air. Air temperatures and humidities for relative distances >0
95 are those of the exhaust air

Figure 4 presents the results from day 223 in house 1, when Q was 0
087 m3 m2 s1 and no evaporative pad cooling was used. Leaf area index L was 1
57 and y was 1
65 m. Except for an observed floor temperature of only 318C at 1400 h, all parameters were well modelled. The effectiveness of modelling the airflow as two streams was checked for the 14 days by comparing percent differences with a single air stream (not presented) to those with the split air stream (Table 2). Splitting the air stream provided little improvement for the evaporative pad case, with air temperature predictions improving (1
5% versus –0
05%), canopy temperatures slightly worse (0
15% versus 0
5%) and all other variables remaining about the same. The lack of improvement for the evaporative pad case seems to stem from the fact that some mixing of the air streams appears to happen prior to the entrance to the exhaust

3.2. Simulations 3.2.1. Cooling versus airflow rate Figure 5 presents ta,ex, and tnc for the conditions outlined in Section 2.3.3, both with (dashed lines) and without (solid lines) evaporative pad cooling. The results suggest that when evaporative pad cooling is not used there is little or no benefit to either air or canopy temperature in increasing Q beyond about 0
05 m3 m2 s1. This is very close to the one air change per minute design criteria for cooling used by some (Walker & Duncan, 1973; Walker et al., 1983; ASHRAE, 1997a), provided that the height of the greenhouse is about 3 m. It is interesting to note that for the two most arid conditions, even though ta,ex rises as Q increases above 0
043 m3 m2 s1, tnc is predicted to remain essentially constant. A more detailed look at cooling without an evaporative pad is presented in Fig. 6 where tic (solid lines) and tia;c (broken lines) are plotted as a function of relative distance through the house. Considering the arid case first, tic is shown to be relatively insensitive to Q. Canopy air temperature, on the other hand, changes dramatically both with distance and flow rate, with nearly a 68C difference in tia;c from entrance to exit at the lowest Q. One reason for the difference in response is that as Q increases, the ability of a fixed canopy to cool an increasing air mass diminishes, but it is also true that as tia;c increases, the balance between sensible and latent

D.H. WILLITS

40 36

38

e d c b a

36

e

32

d

28

c

24 0.00

0.02

0.04

0.06

0.08

0.10

0.12

34 32

b

30

a

28 0.0

0.14

0.2

(a)

Airflow rate Q, m3 m-2 s-1

(a)

Temperature, °C

Exhaust air temperature, °C

326

0.4

0.6

0.8

1.0

0.8

1.0

Relative distance

40 36

d

e

c 32

d

b a

c

28

a 0.02

0.04

0.06

0.08

0.10

0.12

0.14

Airflow rate Q, m3 m-2 s-1

Fig. 5. (a) Exhaust air temperature and (b) canopy temperature at the exhaust end as functions of airflow rate. Dashed lines represent evaporative pad cooling and solid lines represent no evaporative pad cooling. Leaf area index was 1
32 m2 m2 and outside air temperature was 36
88C. Curves are identified with letters (a)–(e) representing outside humidity ratios ranging from 3
3 to 29
9 g kg1

energy exchange shifts toward the sensible, increasing tic in the process. The predicted behaviour of tia;c with Q agrees, in part, with that found by Al-Helal and Short (1999) for an outside relative humidity of 10% and a value of ta;o of 458C. They concluded that lower airflow rates would be superior for cooling under arid outside conditions, but canopy temperatures were not considered. At the highest level of outside humidity considered, tic is predicted to be significantly greater than for the arid case, with tia;c less than tic at every point. Here, increasing Q reduced both tia;c and tic . The relationships between temperature and Q and temperature and distance are the result of the fact that the high outside humidity conditions have minimised the effect of transpirational cooling. It is also true that because tia;c and tic are less

39

38

37

b

24 0.00

(b)

e Temperature, °C

Canopy air temperature, °C

40

36

(b)

0.0

0.2

0.4

0.6

Relative distance

Fig. 6. Canopy air temperature (open symbols) and canopy temperature (closed symbols) as functions of relative distance through the house for (a) an outside humidity ratio of 3
3 g kg1 and (b) an outside humidity ratio of 29
9 g kg1, both without evaporative pad cooling. Squares were at an airflow rate of 0
022 m3 m2 s1, triangles at 0
065 m3 m2 s1 and circles at 0
130 m3 m2 s1. Leaf area index was 1
32 m2 m2 and outside air temperature was 36
88C

different initially, increasing Q did not replace significantly lower temperature air with significantly higher temperature air, as was the case for arid outside conditions. The results for evaporative pad cooling (Fig. 5) suggest a different relationship between Q and cooling from that illustrated above. Both ta,ex and tnc are predicted to decrease significantly with increasing Q, although the effect is more pronounced for the less humid conditions. Even for the most humid conditions, temperatures continue to fall as Q is increased; however, less at the pad end of the house than at the exhaust end of the house. This prediction agrees with the observations of Willits (2000) and Seginer et al. (2000), where a similar observation was attributed to the extension of the evaporative cooling effect further down the length of the house as Q increased.

FAN-VENTILATED GREENHOUSES

Exhaust air temperature,°C

3.2.2. Cooling versus leaf area index and stomatal resistance Figure 7 shows ta;ex and tnc as a function of L (canopy size) for the same outside conditions as above for a value of Q of 0
087 m3 m2 s1. Both ta,ex and tnc are predicted to decline with increasing L when evaporative pad cooling is not used. The effect on ta;ex is more pronounced at the more arid outside conditions but the effect on tnc is relatively constant regardless of outside humidity level. On the other hand, when evaporative pad cooling is used, ta;ex is shown to be essentially unaffected by L but the relationship between tnc and L is approximately the same as without evaporative pad cooling. The results suggest that at any L or outside humidity, tnc would be expected to be less with evaporative pad cooling than without. Canopy air temperature at the exhaust end of the house (not shown) was predicted to decline only slightly with

40 36

e

32

d

e d c b a

c 28

b

24

a

20 0. 0

0. 5

1. 0

1.5

2. 0

2. 5

3.0

3. 5

Leaf area index
, m2 m -2

(a)

Canopy temperature,°C

40 e 36

e

d

32

d

c

c b a

b

28

a 24

327

increasing L, about half of that of tnc ; however, the percentage of air passing through the canopy increases with L such that the total amount of cooling provided by the canopy to the air increases. The evaporative cooling effect of the pad appears to be complementary to that of the canopy when humidities are very low; however, at the most humid condition, only a small reduction in tnc is predicted when evaporative pad cooling is added. This suggests that as outside humidity levels increase the two sources of evaporative cooling begin to compete. The effect of diffusion resistance was not very different from that of L (at least at solar noon) and the results are therefore not presented separately. Increasing the stomatal resistance rs from 100 to 200 s m1 increased temperatures essentially the same as reducing L from 1
32 to about 0
7. 3.2.3. Evapotranspiration coefficient Figure 8 presents E as a function of Q for the same outside conditions outlined above, both with and without evaporative pad cooling, for a value of L of 1
32 m2 m2. Airflow rate is predicted to have a relatively small effect on E, much less than outside humidity or the use of evaporative pad cooling. The effect of Q is predicted to be the greatest for nonevaporative pad cooling operating under the most arid outside conditions. With evaporative pad cooling, E ranged from 0
6 to 0
7. Without evaporative pad cooling, E ranged from about 0
85 to about 1
25. This is higher than the upper limit of 1
0 suggested in EP 406
2 (ASAE, 1999) but it agrees qualitatively with the observation of Seginer (1997). The effect of L on E (Fig 9) when evaporative pad cooling was not used was much more significant than the effect of Q on E and even more significant than the effect of outside humidity. Values of E were predicted to range from a low of 0
8 for a value of L of 0
5 at the most humid outside conditions to a value of about 1
75 for a L of 3
0 at the most arid outside condition. Again, this is in contrast to the upper limit for E of 1
0 mentioned in EP 406
2 (ASAE, 1999). When evaporative pad cooling was used, E was predicted to range from 0
6 to 0
75, with practically no dependence on L.

20 0. 0 (b)

0.5

1.0

1.5

2. 0

2. 5

3. 0

3.5

Leaf area index
, m2 m -2

Fig. 7. (a) Exhaust air temperature and (b) canopy air temperature as functions of leaf area index. Dashed lines represent evaporative pad cooling and solid lines represent no evaporative pad cooling. Airflow rate Q was 0
087 m3 m2 s1 and outside air temperature was 36
88C. Curves are identified with letters from (a)–(e) representing outside humidity ratios ranging from 3
3 to 29
9 g kg1

3.3. Longitudinal temperature and humidity profiles Evidence of the need for a greenhouse cooling model to be able to describe non-linear temperature and humidity profiles is presented in Fig. 6, where for the lowest airflow rate and lowest outside humidity ratio the canopy air temperature (and to a lesser extent the canopy temperature) is predicted to be non-linear.

Evapotranspiration coefficient, E

328

D.H. WILLITS

sections. At the centre of the house, values of tc predicted using a single section were 0
58C (1
7%) higher than those predicted using ten sections. Prediction differences were less than 1% when airflow was 50
087 m3 m3 s1. At the highest outside humidity ratio (29
9 g kg1), there were no differences between the predictions generated using one section and those generated using ten sections, suggesting that as evapotranspiration is reduced, longitudinal profiles of temperature and humidity become sufficiently linear that the internal conditions of the greenhouse can be represented by overall averages.

1.8 1.6 1.4 1.2 a b c d e

1.0 0.8 0.6

a b c

0.4 0.00

0.02

0.04

0.06

d e

0.08

0.10

0.12

0.14

Airflow rate Q, m2 m-2 s-1

(a)

Evapotranspiration coefficient, E

4. Conclusions 1.8

a

1.6

b

1.4

c

1.2

d

1.0

e

0.8 0.6

a b c d e

0.4 0.0

(b)

The results suggest that the model presented in this paper represents the fan-ventilated cooling of greenhouses reasonably well. The decision to divide the air stream into two components seems warranted but more data are needed for refinement. Additional work may also be needed to improve the predictions of floor temperature; however, given the non-criticality of floor temperature to the cooling process, the current accuracy may prove to be sufficient. The simulations conducted appear to support the following conclusions:

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Leaf area index
, m 2 m-2

Fig. 8. Evapotranspiration coefficient E as a function of (a) airflow rate, with leaf area index equal to 1
32 m2 m2, and (b) leaf area index, for an airflow rate of 0
087 m3 m2 s1. Dashed lines represent evaporative pad cooling and solid lines represent no evaporative pad cooling. Outside air temperature was 36
88C. Curves are identified with letters (a)–(e) representing outside humidity ratios ranging from 3
3 to 29
9 g kg1

Repeating these calculations using a single section (instead of ten) yielded differences in the predicted values of ta;ex and wa;ex of 1
08C (2
8%) and 0
4 g kg1 (3
8%), respectively, at an airflow rate of 0
022 m3 m2 s1 with the outside humidity ratio equal to 3
3 g kg1. At the center of the house the differences in the predicted values of ta;c and wa;c were 1
78C (5
4%) and 0
8 g kg1 (7
0%), respectively, indicating a much larger deviation from linear within the canopy than without. Canopy temperature differences could not be determined at the exit of the single section, since the model only calculates average values of tc over each section; however, the average over one section was 0
78C (2
2%) lower than that predicted at the exit using ten

(1) Increasing airflow rates beyond about 0
05 m3 m2 s1 is not beneficial when evaporative pad cooling is not used. Air temperatures may actually increase under conditions of low outside humidity; however, canopy temperatures may remain relatively unaffected by airflow rate at any outside humidity conditions. (2) Increasing airflow rates beyond 0
05 m3 m2 s1 is beneficial when evaporative pad cooling is used. Both air and canopy temperatures are predicted to decline as airflow rate is increased up to 0
13 m3 m2 s1, although air temperature declines at a faster rate than canopy temperature. (3) Both air and canopy temperature decrease with increasing canopy size L when evaporative pad cooling is not used. When it is used, however, only canopy temperature decreases. (4) The evapotranspiration coefficient E is relatively insensitive to airflow rate either with or without evaporative pad cooling, and to canopy size L when evaporative pad cooling is used; however, when evaporative pad cooling is not used E is predicted to range from 0
8 to about 1
7, depending upon outside humidity conditions. The latter result suggests that the stated limits for E in EP 406
2 (ASAE, 1999) must be reconsidered.

FAN-VENTILATED GREENHOUSES

Finally, there appears to be justification for including the ability to handle non-linear temperature and humidity profiles in a greenhouse cooling model, especially if high evapotranspiration rates are to be considered (arid outside conditions without evaporative pad cooling) and errors in temperature predictions on the order of 0
58C to 1
78C are likely to be important.

Acknowledgements This work was supported, in part, by Research Grant Awards IS-2538-95R and US-3189-01 from BARD}The United States}Israel Binational Agricultural Research and Development Fund. I am also grateful for the comments and suggestions of Ido Seginer (Technion, Haifa, Israel) and the dedication and hard work of Ron Scott (NCSU).

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