Jordan Clark
Airflow Modeling Final Report
7 Dec 2009
INTRODUCTION
In this project, the parameters governing efficient control of the indoor environment in an indoor plant
growth facility were analyzed using computational fluid dynamics. In order to do this, a section of the indoor
agricultural facility was modeled in Airpak with associated thermodynamic, aerodynamic, and hygric parameters
included. Six trials were executed with variation of relevant supply parameters for each trial. The final solution was
a system of ventilation that provides near ideal conditions to plants within an indoor plant growth facility. The
following paragraphs explain how the model was created and verified.
PROBLEM DESCRIPTION
.5m
1m
.5m
Geometry/Components
The CFD analyses were conducted for a typical
section of a hypothetical facility that housed three levels
of plants. Eight levels were originally analyzed but it was
soon realized that computation time for this size would be
too great. The typical section analyzed was 1m thick (into
the page in Figure 1). A section view through one layer is
shown in Figure 1. The pattern was repeated for
subsequent layers.
Repeat
LIGHTS ATTACHED TO
BALLAST ABOVE
3”
21”
PLANTS
BALLAST
Lights were model as a two-dimensional heat
7”
source. Plants were modeled as rectangular prismatic flow
resistances. The ballast was modeled as a hollow block.
Fig. 1 Schematic of Vertical Section of One Layer of Model
Supply air inlets for each level of plants were placed on
the right wall of the model and their size and direction
were varied during the analysis. A return vent for the entire model was placed horizontally in the upper left corner.
Its dimensions were 1m X 0.5m . The right wall was modeled as commercial aluminum to simulate ducts. The left,
front and back walls were modeled as symmetry walls. The floor and ceiling were left as default surfaces.
Sources
Both the plants and the lights dissipate energy in the facility and their effects were quantified and included.
[ Note: When determining the energy balance for ultra-efficient lights used by NASA researcher to grow potatoes in
space, it was not easily understood how the plant maintained an equilibrium with its surroundings, and for this
reason, lights of readily available efficiencies, with no allowance for pulsation of lights in on-off cycles were used.]
The irradiation needed to sustain typical plants is given as 400micromoles of photons of photosynthetically active
radiation” per square meter per second. (Barta, et. al., 1992) Accordingly, the rate at which energy falls on the
plants is given as
400e-6 mol photons * 6.022e23photons * 6.626068e-34 m2 kg * 3e8m 1
= 70kgm2 =
2
m * s
1 mol
680e-9m
s
s photon
s3m2
70W/m2
calculated using Ephoton=hc/, where h is planck's constant, c is the speed of light in m/s, and is the average
wavelength of the light, taken to be 680nm, as documented in Barta, et. Al (1992)
It was assumed that the lights had an electrical conversion efficiency of 22%, implying that total electrical power
to the lights was 320W. 250W of this power was assumed to be dissipated as heat, and was included as a heat
source. 70W, as detailed, was assumed absorbed by plants in the form of radiation.
Jordan Clark
Airflow Modeling Final Report
7 Dec 2009
It is assumed that of the energy irradiated on the plant, 100% of the photosynthetically active radiation is
absorbed, and 100% of the long wave radiation and any radiation not accounted for in the 400mol is reflected. Of
the portion absorbed, it is assumed that 50% is dissipated by convection and 50% by evapotranspiration. This
means that the resistances used to model the plants contain an energy source of 35W/m2. The other 35W/m2 is used
to evaporate water from the plant’s surface, according to the following:
35J * kg water evaporated = 1.55e-5 kg/s/m2 = 1.344 kg/day/m2 (similar values given in Casanova, 2009)
s m2
2250e3 J
The 1.55e-5 kg/s/m2 moisture source is also included in the resistances.
The flow resistances themselves are defined according to available literature. According to Boulard (2002), the
pressure drop across the plant canopy is conventionally modeled as a source in the momentum equations according
to the following equation:
dP/dx = LCDv2
where
L = leaf area density (m2/m3), given as 8 by Boulard (2002)
CD=empirically determined drag coefficient, given as 0.32 by Molina-Aiz, et. al. (2006)
v= velocity
= air density
In contrast, Airpak uses
P =Cvincident2 across the length of the flow resistance input, where C is user-defined and v is the incident velocity
(at the outside of the resistance)
Therefore, assuming constant velocity equal to .5m/s through the plant (this is the desired situation), for one meter of
plant canopy, using the equation from the literature,
P= (LCDx) v 2 = (8*0.32*1*1.2) .52 =.768N/m2 across 1m plants for average v of .5m/s
Since vincident is not known and is determined by a non-linear equation, an iterative process was used to find a value
for c in the Airpak equation that would result in a pressure drop of .768N/m2 across 1 m of plants with a velocity at
the middle resistance of .5 m/s. A resistance of the appropriate size was put into a separate model in Airpak and c
was varied until the desired pressure drop was produced. It was determined that a c value of 5 produced a pressure
drop of 0.766N/m2, this value was used.
METHODS
Several parameters are coupled in the energy and mass balances of the plants. For this reason, the parametric
analysis was conducted varying more than one parameter at one time. The relevant parameters for this model were
supply T, RH, v, and mass flow rate. Seven trials were run, with qualitative judgments made at the end of each trial.
The parameters in question were then tweaked for the next trial in a way that was predicted to move nearer to ideal
conditions throughout the facility. The ideal conditions were taken from the Plant Growth Chamber Handbook, and
are as follows:
Jordan Clark
Airflow Modeling Final Report
7 Dec 2009
V around the plants: 0.2-0.5 m/s
T around plants: 70-75 degrees F
RH around plants: ideal 70%
Mass flow rate: as low as possible to conserve fan power
Trials are given in the following table:
TRIAL
Tsupply RHsupply
1
2
3
4
5
6
7
60 F
60 F
60F
60F
60F
SAME
SAME
30%
40%
70%
100%
100%
q supply
(degrees v supply m supply m supply m supply
above
(m/s)
1 (kg/s)
2 (kg/s)
3 (kg/s)
horiz.)
Changes Made After
0
30
30
30
30
0.5
0.5
1, 2, 3
2,8,6
3,12,6
0.009375 0.009375 0.009375 point vents upward toward lights, increase RH
0.009375 0.009375 0.009375 increase V, most at top, least at bottom; increase RH
0.004688 0.009375 0.014063 quadrupled v2, doubled others, increased RH
0.009375 0.0375 0.028125 lower all T's, increase v in bottom 2 inlets
0.014063 0.05625 0.028125 run more iterations and check
refine mesh to check
Table 1. Description of Trials
Mesh
The mesh was a source of infinite frustration but ultimately was decided upon, and the mesh used was deemed
sufficient to model the situation in question. Initially a coarse mesh was used, and solutions diverged fairly quickly.
The minimum number of elements along an object face and maximum sizes along cardinal directions were altered,
and a believable solution was approached. However, it was noticed that temperatures at monitoring points were
oscillating over fairly large ranges of values (5-10 degrees F). The “initial height” option in the meshing pramaters
was then selected for the source objects (See Figure 2a), and made very small. The max size ratio was also altered
and made small as well. It was observed that the amplitude of the oscillations was directly proportional to the initial
height chosen. Ultimately, an initial height of 0.1 in and max sixe ratio of 1.5 were chosen and the oscillations were
not noticeable. An initial height of 0.05 in was tried to see its effect on its results and no change in results was
observed, implying mesh-independence. The final trial had
roughly 50,000 cells.
Source (Lights)
Figure 2a Meshing Near Sources: Notice Small
Size of Cells Along Large Temperature Gradient
Figure 2b Mesh of Entire Model
Jordan Clark
Airflow Modeling Final Report
7 Dec 2009
Relaxation
It was observed that the solution would not converge without considerable relaxation, regardless of mesh size. A
relaxation factor of 0.05 was used for the energy equation, and 0.1 was used for species. A solution was reached for
this condition. Both the mesh considerations and the relaxation needed were most likely due to the large
temperature gradients at the surface of the heat sources. The temperature changed from around 200°F at the light
surface to around 70°F, 2 inches away.
QUALITY CONTROL
Quality control was accomplished via several methods. First, mesh
independence was verified as previously mentioned. Iterationindependence was verified by letting the model run for 40,000
iterations during the 6th trial. Less than 1% change in temperature
was observed at each of 6 monitoring points between 2000 iterations
and 40,000 iterations, implying 2000 iterations was sufficient to
determine the steady state conditions.
Lastly, an energy balance, and a mass balance for both air and water
were conducted as follows:
Mass Balance, Air:
msupply(kgair/sec) =mexhaust
Figure 3 shows convergence near 2000
iterations. Subsequent iterations up to
40000 showed little change.
The following tabulated results show conservation of mass:
Flow (kg/s)
Supply 1
0.0113498
Supply 2
0.0449341
Supply 3
0.0224671
Return
-0.0788181
TOTAL
-6.71E-05
Error Fraction 0.00085205
Location
Mass Balance, Water:
[Wsup (kg H20/kgair)*m(kgair/sec)] + SSH2O(kg/s) =Wexmair
S= 1.55e-5kg/s as mentioned previously
The following tabulated data show that there was a near 10% error in the overall species balance. Considering RH
levels were lower than needed for proper plant growth, and moisture could be easily added to the system, these
results were taken as sufficient.
Jordan Clark
Airflow Modeling Final Report
7 Dec 2009
Location Mass Ratio (kg/kg) Air Flow (kg/s) Water Mass Flow (kg/s)
Supply 1
0.011593
0.0113498
0.000131578
Supply 2
0.011592473
0.0449341
0.000520897
Supply 3
0.0115161
0.0224671
0.000258733
Return
0.011012122
-0.0788181
-0.000867955
Res. 1
1.50E-05
Res. 2
1.50E-05
Res. 3
1.50E-05
TOTAL
8.83E-05
Error Fraction
0.101680944
Energy Balance:
hsup (kj /kg)*msup(kgair/sec) + Slights(kW) +Splants(kW) =hexmex
Slights=250W per light
Splants=35W per plant
The following results show that energy was conserved to a reasonable degree of accuracy.
Location
Supply 1
Supply 2
Supply 3
Return
Res. 1
Res. 2
Res. 3
Light 1
Light 2
Light 3
TOTAL
Error Fraction
h (kJ/kg) Air Flow (kg/s) Heat Flow (W) Alternate Calculation
46.414
46.4865
45.9804
55.02078
0.0113498
0.0449341
0.0224671
-0.0788181
526.7896172
2088.82904
1033.046245
-4336.63334
35
35
35
250
250
250
167.0315616
0.038516413
RESULTS
Results for each trial are shown in the following table and graphs, organized by relevant environmental variable. As
can be seen, a situation that was near ideal for plant growth was created. Level “1” refers to the bottom level of
plants, “2” to the middle, and “3” to the top level.
Jordan Clark
Trial Level
1
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
3
3
4
4
4
4
4
4
5
5
5
5
5
5
1 LOW
1 HIGH
2 LOW
2 HIGH
3 LOW
3 HIGH
1 LOW
1 HIGH
2 LOW
2 HIGH
3 LOW
3 HIGH
1 LOW
1 HIGH
2 LOW
2 HIGH
3 LOW
3 HIGH
1 LOW
1 HIGH
2 LOW
2 HIGH
3 LOW
3 HIGH
1 LOW
1 HIGH
2 LOW
2 HIGH
3 LOW
3 HIGH
Airflow Modeling Final Report
T (F)
68
75
82
90
93
98
67
73
77
86
82
89
73
80
80
90
77
82
75
78
75
78
73
76
75
77
74
78
74
76
7 Dec 2009
RH (%) V (m/s)
12
0
24 0.02
9
0
16
0.1
9
0
12 0.15
20
0
30 0.02
6
0
60
0.1
10
0
20 0.15
10 0.05
35
0.1
10 0.05
20 0.015
20 0.05
25
0.2
55
0.2
65 0.35
55
0.1
65
0.3
65
0.1
70 0.45
55 0.15
65
0.3
55
0.1
65
0.4
55 0.05
65
0.4
Figures 4a,b,c,d show how environmental variables varied during the course of the analysis and arrived finally at
values that are near ideal for plant growth.
Jordan Clark
Airflow Modeling Final Report
7 Dec 2009
CONCLUSIONS
Further improvements could be made to improve the design and refine the accuracy of the model. First, supply
velocities that were necessary to create the conditions needed would produce a ventilation rate of roughly 60ACH,
which is too large to be supplied efficiently. Secondly, relative humidity levels near 100% are difficult to achieve,
and therefore a solution with supply RH near 70% should be determined in future research. An accurate mass
balance for water would need to be achieved if the results were to have the validity desired. Overall, the analysis
showed that large fans would be needed to produced the perfectly mixed condition desired, and a proper indoor
environment is acheivable through proper input conditions.
Works Cited:
Barta, D., Tibbits, T., Bula, R., & Morrow, R. (1992) Evaluation of light emitting diode
characteristics for a space-based plant irradiation source. Advances in space research ,
141-149.
Casanova, Manuel et a. (2009) Methods to estimate lettuce evapotranspiration in greenhouse
conditions in the central zone of Chile. Chilean Journal of Agricultural Research, 69 (1), 60-70
Boulard, Kittas, Roy and Wang (2002) Convective and Ventilation Transfers in Greenhouses, Part
2: Determination of the Distributed Greenhouse Climate . Biosystems Engineering, 83 (1),
129-147
Molina-Aiz, Valera, Alvarez, and Madueno (2006) A Wind Tunnel Study of Airflow through Horticultural Crops:
Determination of the Drag Coefficient. Biosystems Engineering, 93, (4), 447-457
Langhans, R., & Tibbits, T. (1997) Plant Growth Chamber Handbook. Iowa State University.