1
Heat Transfer Research, 2004, Vol. 35, Nos. 3
4
of Natural
Convection a Horticultural Greenhouse Heated from Below (bY Using CFD)
Numerieal Simulation
in
&
TADJ NeCrrtle University Center of Béchar Institute of Exact Sciences, BP 417 08000 Béchar, Algeria.
[email protected].
The analysis of the possibility of determining climate under a greenhouse confionts us with a very complex system composed at least of three components (culture, substrate or soil, and air) and of exChange of energy, steam, and COe between them. The recent advance of greenhouse surfaces in the Mediterranean basin puts in the forefront the protlem of air-conditioning whose solution will improve production at least as far as the quality is concerned. This work is concerned with numerical simulation'of natural convection in a laminar regime in closed greenhouses (tunnel greenhouse and single span greenhouse) of length 25 m, width 6 m, and height 3.5 m, intended for planting vegetation for the table with soil heated by a flux of 100 W. The walls of a single span greenhouse are adiabatic, the roof is maintained at a temperature of 280 K in both greenhouses. For all the walls of the two greenhouses and the soil in them the conditions of adhesion hold: u = v = w = 0 m/sec. The model suggested repre' sents the equation of motion associated with an energy equation; it is solved by means of a Computational Fluid Dynamic software (CFD2000) based on the PISO algorittrm. The results are represented in the form of streamlines, isotherms, and velocity profiles. The results obtained allow one to characterize the general flow of air in a greenhouse. It is also shown ttrat for the bonditions of flux application to soil (heating by rneans of a buried tube), the circulation of air is characterized by two recirculation cells rotating in the opposite directions. Therefore, this study will permit one to improve thermal designs of greenhouses and positioning of air-conditioning systems. **rF
342
rssNl064-2285 @2004 Begell House, Inc.
INTRODUCTION the neighThe natural convection generated by transfer of heat (and of mass) in and experiborhood of heated surfaces has been thoroughly studied both theoretically since the appearance of mentally. The interest in this problem is indeed considerable, phenomena that fog, perspiration, freezing and drying of cultures are all those natural cause transfers of heat (and of mass) by natural conveçtion, conAs concerns greenhouses, the majority of the studies available in the literature and ventilation [9' 14' sider the problems of the greenhouse heating fl, 4, and 191 and 161 and also the problem of perspiration [6, 8, and l3]' It is difficult to *oa"t a greenhouse because of the presence of different surfaces, several disciplines notably plants, in between its walls [19]; moreover, it involves aspects shows the such as agronomy, heat transfer, etc, The diversity of the problem extent of investigation and the complexity of its theoretical study' on the hyHowever, the physical (thermal) modeling of greenhouses is based here greenhouse' The first pothesis of the perfect homogeneity of the temperature inside a greenhouse have detailed studies based on static modeling of the thermal balance in a simulation of the been made in the 1960's. Then, many dynamic models permitting
thermal behavior of a greenhouse appeared V ' 9l' From a review of a pertinent literature one can see that equations of energy balpossibilities of ance are written for each constituent of the greenhouse' The proposed balances calculating precisely the intermediate flux intervening in these energizing permit one to globally optimize the climate of lreenhouses by quantitative prediction of exchanges between the inside and the outside, but they do not inform us on the greenhouse [9]. details of internal exchanges of temperature, humidity, and Co2 in a The study of these internal fields requires development of operational characteristics and simulation of heat and mass transfer inside a greenhouse. The equations that govern the phenomenon of natural convection arc the differential equations whose exact integration is difficult, or even impossible because they are get nonlinear. Once again, it is necessary to have recourse to numerical rnethods to solutions which approximate the transient problems and can be used in practice. With development of microcomputing, the numeric methods became indispensable for analytical and experirnental methods. Researchers were able to solve a lot of problems that were previously very complex and required laborious calculations by classical methods. The numerical simulation allows one to circumvent the complexities of problems employing an approximate solution of the equations of mathematical models under the conditions inaccessible for the classical techniques. Natural convection within a greenhouse was studied numerically and experimentally by Nara [20]. The author used a model of a greenhouse with a heating floor. The numerical results are in good agreement with experimental data. In the same statment, Lamrani [17] canied out a study in two parts. The first part is devoted to modeling of natural convection in a stationary turbulent regime in a greenhouse without vegetation, while the second part is devoted to characterization of flows using a 303
model of a greenhouse (scale). Results obtained in the first part (É-e model of turbulence is in good agreement with the experimentally obtained results). Lately, several teams were interested in ventilation in the case of natural convection, notably Boulard et al. [lJ; they treated this phenomenon both theoretically and experimentally, In the theoretical approach with the use the CFD2000 software, they simulated flows of air in a greenhouse with one or two openings in the roof. Experiments were then run to validate the theoretical models. The objectivc of this article is to numerically determine thermal transient connective transfer in a greenhouse without vegetation and with heating from below.
STATE OF THE ART Mathematical Formulation of the Problem. The domain of the study is represented schematically by Figs. I and 2. To construct some sufficiently detailed and precise models, sometirnes it is necessary to take into account a certain number of simplifying hypotheses: o The flow velocity is low, the external flow is laminar. r The physical properties of the air confined inside the greenhouse are supposed to be constant except for density (its variation with temperature is given by the Boussinesq approximation), where p is the density at the reference temperature T6. o The fluid is transparent.
Physical Model, Our physical model iS rèpresented by both (tunnel and single span) greenhouses; they are shown respectively in Figs. I and 2, their dimensions are 25 x 6 x 3.5 m for the tunnel greenhouse and 25 x 6 x 3,25 m for the single-span greenhouse.
Equations of Transfer. The equations that govern the natural-convection transfer inside the greenhouse subject to the simplifying hypotheses are:
Fig. 1. Single-span
greenhouse.
Fig. 2. Tunnel greenhouse. 304
heat
Continuiry equation âo
ôx
(1)
ù.* ÈL =o *.ây àz
Momentum equation
*.
*# "* "$* *
=
+*. {#.#.#J
**= ;#."[#.#.#J.*' $n"** "#* g*"s*" #.-#
=
(2)
-P(r-r'
-i#*"t*.#.#J
I
(3)
(4)
Energy equation
#*"#."#.-#=#[#.#.#J
(s)
COMPUTER MODEL
tool which has emerged from cFD. Computational fluid dynamics is a simulation the design tool' It is widely used to snrdy the development stage and is now a robust which involve fluid flow' heat and rnass behavior of all kinds of transport processes distribu-
simulations are spatial and temporal transfer [1a]. Typical outputs from CFD temperature, and concentration' The oritions of flow speed and direction, PIessure, aerosPace' and nuclear industries' gins of cFD are found in the chemical, automotive' apapplied to food Processing' A more fecent and in recent years cFD has also been where it is used for modeling plication for CFD is its use in horticulàrd '"'eutch used to greenhouses' Such models can then be the internal climate of glasshouses and conand on extemal weather conditions study the dependence of Ur" internal clilrate
trol strategies. CFDisconsideredasanalternativestudytool'Whenusedcorrectly'itcanprovide processes inside the glasshouse and accurate and detailed simulations of the transport information on the glasshouse cliprovide the horticultural industry ïeith a plausible measurements [21]' mate and reduce the need for extensive and expensive simulating systems in about cFD. CFD is the tool and science of analyzing heat and mass transfer and which a fluid flow is of central interest and in which over conventional experimental studchemical reaction may take place. Its advantages for the study of the sysies are substantial reductions in time and cost, accessibility 305
Table I Characteristics of the greenhouses Tunnel greenhouse
greenhouse
Width
6m
Length
25m
Length
Height
3.5 m
Ridge height Gûtter height Side wall temperature
3.25 m
Roof temperature Heat flux from soil
280 K
Air
293 K
Roof temperature Heat flux from soil
Air
temperature
Width
280 K r00 w 293 K
temperature
6m 25m 2.5 m Adiabatic 100
w
Table 2 Numerical parameters Numerical parameters
Body fitted
3D
Mesh size
(3000)
Mesh size
(3000)
x 15 x l0 (single-span greenhouse) 20 x 15 x 10 (tunnel greenhouse) 20
Laminar model
Incompressible and unsteady flow
''
Heat transfer
Initial
Boussinesq approximation
280 K
temperature
tems where experiments are not possible, and ease of performing a large range of parametric studies for optimization. The Principles of CFD. If a CFD simulation is carried out, the space in which the simulation will take place, e.g., the greenhouse plus its environment, must de defïned. This space will be the computational domain divided into small cells, control volumes, in each of which a value for the sirnulated variables is calculated (e.g., air speed and direction, temperature, and gas concentration). Conservation principles are applied to each of these control volumes (e.g., mass in = mass out * mass accumulated/lost, energy in = energy out energy accumulated/lost) [21J.
t
RESULTS AND DISCUSSION In this study, the tracing of streamlines, isotherns, as well as different profiles will be presented for tunnel and single-span greenhouses heated by soil (imposed flux). The streamlines and isotherms for single-span greenhousss are presented in Figs, 3-6 and 7, respectively. Every figure shows the evolution of these traeings for different times. Initially, Fig. 3, one attends the appearance of the first coûtours of streamlines situated on all the sides of the greenhouse. One also notices a first formation of 306
Fig. 3. Streamlines and isotherms in 10
sec.
'ers isotherms stratified displaying the beginning of heat diffusion. The isotherms , nearly parallel, and this representation is characteristic of the thermal transfer minated by conduction. With time, the flow is characterized by two main cells ning in opposite directions. The isotherms deform and move toward all the spaces .the greenhouse, but always at the level of soil their stratification persists. Figures 9-12, 15, 16, 18-20, 22-24, 26, and 27 represent the evolution of the air rperature inside a single-span greenhouse during the time. Figure 9 shows the evolution of the horizontal profile of the temperature to the t-height (1.75 rn) of the greenhouse up to 100 sec, the temperature varies between ,.75 K and 281.5 K. It is maximal in the neighborhood of the walls and minimal a distance of 1.5 m and 4.5 m; closer to the center of the greenhouse (i.e., 3 m width) the temperature reaches a value of 283 K. Figure l0 represents the eyolution of temperah,rre along the greenhouse and to the l-height for 100 sec. The temperature is variable for a zone of length from 0 m to m and is almost constant from 14 m to 25 m. 307
Fig. 4. Streamlines and isotherms in 30
sec.
teml
Similarly, the temperature along the greenhouse at the level of soil and to the center of the greenhouse to the l00th second in Fig. I I varies in an interval of length from 0 m to 10 m and is almost constant from 10 rn to 25 m, where the temperature is 284.95 K. The temperature profile along the greenhouse over the whole width of 6 m and at the mid-height (1.75 m) is shown in Fig. 12; one can note that the distribution of the temperahJre on the two surfaces in the plan (yz) it is not the same; and thereafter one can justiff that a three-dimensional study is important. Figures 13 and 14 represent, respectively, the profile of velocity w along the greenhouse, over the entfue width of 6 m to the mid-height (1,75 m) and the profile of velocity v along the greenhouse, over the entire width of 6 m to the mid-height (1.75 m); by the 100th sec the change in sign is due to the air flow in the greenhouse determined by two curls turning in two opposite directions. Figure 16 gives the temperature profile over the entire width of the greenhouse and to the mid-height by the 30th sec; one sees well that there is a change in the 30E
isb 1 leve
K,
I
'l mid
t two 1
prel
I tain one
can enc
Fig, 5. Streamlines and isotherms in 60
sec.
in the neighborhood of the walls, but in the central part, where the width between 2 m and 4 m, the temperature is low, it is always at about 280 K. The distribution of the temperature along the greenhouse to a width of 3 m at the :vel of soil by the 30th sec in Fig. 18 takes values between 280J71 K and 280.776 , the variation is very weak, so that one can assume it constant. 'The evolution of the velocity v along the greenhouse over the entire width to the rid-height by the 30th sec is shown in Fig. 17, where there are two types of flow. Figure 8 represents the velocity fields for different times, where one can see well vo directions of air flow inside the greenhouse. The profiles of velocity and temperature for one time of 300 sec (i.e., 5 min) are rsented in Figs. 27, 28 and 22-26, respectively. 'It should be noted here that the optimum temperature of the ambient air was atined; it promotes a good growth of plants and lies between 15oC and 20oC. 'TVhen te continues to heat the greenhouse, the temperature increases further, where one rn find zones where the temperature passes the optimum temperature and this influtces negatively the crops from the viewpoint of yield and quality. rmperature
309
Fig, 6. Streamlines and isotherms in 60
sec.
In what follows, we discuss the case of a tunnel greenhouse heated from below by a flux (imposed flux). Generally, what has been said for the single-span greenhouse remains valid for the tunnel greenhouse, except that the temperature inside the single-span greenhouse is distributed better than in the tunnel greenhouse. Streamlines and isotherms for tunnel greenhouses are Presented in Figs. 29-33 respectively. Every figure shows the evolution of these tracings for different times. Figures 3742, 47-56, and 58 represent the evolution of the air temperature inside a tunnel greenhouse in time. The evolution of the velocity along the greenhouse to the mid-height by the 30th sec is shown in Figs, 35-38, where there are two types of flow. Figure 34 represents the velocity fields for different times, where one can see well
pr
two types of air flow inside the greenhouse.
p(
310
gI fa m p( ht at
Fig. ?. Isotherms and sbeamlines in 300 sec'
to the mid-height by the 100th The evolution of the velocity along the greenhouse sec is shown in Figs. 4346' of 300 sec (i'e" 5 min) are The profiles of ielocity and temperature for one time presented in Figs. 59-62 and 53-58, respectively' except geometry (tunnel According to tbe results obtained for ttre same conditions that a single-span shape better greenhouse, single-span greenhouse), one can conclude except that the cost refavors the flow of air, this shupe is therefore more convenient mains relatively higher because of its glass cover' not good at the As concerns tfrJ heating by soil (geothermal), some results are inside the greenpoint where the distribution of the temperature is not homogeneous going to see the overheated zones house; with increase in the time of heating we are of soil or the optimal temat the level of soil that can pass the optimal temperature growth of roots' perature of root medium between 18oC and 20oc which favor the
3ll
L--.r
r./'..F.-".
l;!r ii i; .: :. II ,1 i i r t il i r - t,z t 1.
i !
r."-
.l
; \ l. r' h - / , :-,-t :--' '-J
VelocitY
Fig. 8, Variations of velocity fields in time.
q,
= o {,
o E
o F
Fig, 9. Temperature profile along the greenhouse, to a width of 3 m at the level of soil (100 sec).
312
æ2, 2A2AS
o
æ28
5
w.n E ê
Ê
m27 2t2.65
Fig. 10. Temperature profile along the greenhouse, to a width of 3 m to the mid-height (1.75 m)
-
100 sec.
Lenglh
Fig. 11. Temperature profÏle along the greenhouse, over the entire width of 6 m 100 sec' to the mid-height (1.75m)
-
{t
)
o {,
o. E
ru
Fig. 12. Temperature profïle the entire width of ttre greenhouse, and to the mid100 sec. height (1.75 m)
-
313
0.6
o4 o.2
Ëo o
9 I
-o.z -0'4 -0.6 -0.E
Fig. 13. Profile of the velocity u along ttre grééntrour", ôË-iiil entire îvidth of 6 m to the mid-height (1.75 m) 100 sec.
-
0.04
0.@
o
.9
o
I
I
-0.0?
-0.04 rttl
tro?sJ0
Fig. 14.
0iÉtonca
hofile of the velocity w along the greenhouse, over the entire width of
6m to the mid-height
(1.75 m)
-
100 sec.
o
L
:'
Eæ+ o E
o
F
æ3
282 Vrtidth
Fig. 15. Temperature profile over the entire width of the greenhouse at the level
of soil
-
100 sec.
3t4
2æ 281,5
ù l 0
2Il1
il,
o ffi. E a,
F
ffi 279.â tt
34
idth
Fig. 16. Temperature profile over the entire width of the greenhouse, and to the mid-height (1.75 m)
30
-
sec.
02
o o
g
0
*
-42 -04
Fig. 17. Profile of the velocity u along the greenhouse, over the entire width of 30 sec. 6 m to the mid-height (1.75 m)
-
!)
5 2û.774
(' ()
ê Ë
t-o
2æ.
05
1015æ
29
Lenglh
Fig. 18, Temperature profile along the greenhouse, to a width of 3 m at 30 sec. level of soil
-
315
the
2U
281 il, f' s)
282
-o
æ1
o. E
2æ J
width
Fig. 19. Temperature profile over the entire width of the level of soil 30 sec.
greenhouse, at the
-
€,
5 It L
c,
o. E C)
F
Fig. 20. Temperature profile along the greenhouse, to a width of 3 m to mid-height (1.25 m) 30 sec.
the
-
g
o
3 I
=
Fig. 21. Profile of the velocity w along the greenhouse, to a width of 3 m the mid-heighr (1,75 m)
-
30
sec.
3t6
ro
à *in 4
5
Fig,2l,Temperatureprofileovertheentirewidthofthegreenhouse,atthe 3fi) sec' level of soil
-
æ2
791
o 3
o
o
o
æ0
E
IU
F
?89
Fig.23.Temperatureprofilealongthegreenhouse,toawidthof3rnatthe 300 sec' level of soil
-
Fig.Z4.Temperatureprofileovertheentirewidthofthegreenhouse,andtothe 300 sec, for .r = 0 m'
*ù-t"igttt (f.?5 m) -
3t7
289.5
ru
â .)
?88'5
or
cr E (, F
?w
\ 287.5
23455
wîdth
Fig. 25. Temperature profile over the entire width of the greenhouse, and to the mid-height (1.75 m) 300 sec, for x = 25 m.
-
l
o a L
o
g
{,
F
Fig. 26. Temperature profile over the entire width of the greenhouse, at level of soil 300 sec, for.r = 0.
the
-
Fig. ?i7. Profile of the velocity w along the greenhouse, to a width of 3 m to the mid-height (1.75 m) 300 sec.
-
3r8
0.4
()
o
>o q) I
-n')
r0 Len
t5 gth
Fig, 28. Profile of the velocity y along the greenhouse, to a width of 3 m to the mid-height (1.75 rn) 300 sec.
-
.!.
-.:- -.i
Fig. 29. Isotherms and velocity field 3r9
in l0 sec.
/ï
{j*J
Fig. 30. Streamlines and isotherms in 30
320
sec.
i
Fig. 31. Srcamlines and isotherms
32r
in 60 sec'
Ë=iii';
#%i Fig. 32, Steamlines and isotherms in 100 322
sec.
y
'l)
Ë:;'+i
Fig. 33. Isotherms and velocity field in 300
il 3'8iT l.fiffi
sec.
F 9:îii fl-E:3i;
i' - '- ;1
".-
r:8:lii ;-; -.- ' -'
| .,,":tli'",. ..'r' t 't'..-\ll r rrl, -,i.if !.i.-
l,
i,r'
r..'-'-t,il.ii,.!\*--',r.
:
i 1
i
[:.;:+:âffiF-]Ël:i Velocity field at 30s
l.Ë.lËï
Velocity field at l00s
, .-
..;
Velocity field at 300s
Fig. 34. Variation of velocity field in time,
323
g2
ol a
o
I
0
7
-ol
I
-û2
1015æ?5 Lenglh
Fig. 35. Profile of the velocity w along the greenhouse, over the entire width of 6 m to the mid-height (1.75 m) 30 sec.
-
0.6
c4 0.2
o
-0'? -o.4
Fig. 36. Profile of the veloeity y along the greenhouse, over the entire width of 6 m to the mid-height (1.75 m) 30 sec.
-
o t
2&,
C)
(t,
o E
Pm1
l0ls?f
Lenglh
Fig. 37. Temperature profile along the greenhouse, to a width of 3 m at level of soil 30 sec.
-
the
m m4 q, l
o !
M
6)
o E
o
l-
?&2 28ûl
Fig.3S.Temperatureprofilealongthegreenhouse,toawidthof3mtothe mid-height (1.75 m)
o>
30
-
sec'
282
3 It L tl,
è c
rbm1
?14
Length
greenhouse, and at the Fig. 39. Temperature profile over the entire width of the level of soil- 30 sec, for x = 25 m'
æ2
l
E f
R
zet
E
ru
F
?gI5
\
I
I Lenglh
greenhouse, and to the Fig. 40. Temperature profile over the entire width of the 30 sec' for a = 25 m' mid-height (1.75 m)
-
282
281.5
{,
t o
281
{,
o
E
o
F
\
æ.5
Length
Fig. 41. Temperature profile over the entire width of the greænhouse, and to the 30 sec, for x = 0 m. mid-height (1.75 m)
-
æ6 285
n4
o f
o (,
8t
cL
E
o
æ2
F
281
ffi Length
Fig.
profile over the entire \ilidth of the greenhouse, and at the 30 sec, for x = 0 m.
42, Temperature
level of
soil-
()
o
3 I
3
Fig. 43. Profile of the velocity w along the greenhouse, to a width of ,3 m to 100 sec. the mid-height (1.?5 m)
-
326
02 o.l
*\
= 9
-ol
E I
-0.?
Length
the
Fig. 44. Profile of the velocify y along the greenhouse, to a \tridth of 3 m to the mid-height (1.75 m) 100 sec.
-
I
o
t I
=
he
Fig. 45, Profile of the velocity w along the greenhouse, over the entire width of 100 sec. 6 m to the mid-height (1.75 rn)
-
h
