Jordan Clark Airflow Modeling Final Report 7 Dec 2009

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

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.

Lights were model as a two-dimensional heat source. Plants were modeled as rectangular prismatic flow resistances. The ballast was modeled as a hollow block. 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 = 70W/m2

m2 * s 1 mol 680e-9m s s photon s3m2

calculated using Ephoton=hc/l, where h is planck's constant, c is the speed of light in m/s, and l 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.

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 400mmol 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 = LCDrv2

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

r= air density

In contrast, Airpak uses

DP =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,

DP= (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:

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:

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.

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. Iteration-independence 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:

Smsupply(kgair/sec) =mexhaust

The following tabulated results show conservation of mass:

Mass Balance, Water:

S[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.

Energy Balance:

Shsup (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.

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.

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.

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.