Stavrakakis et al. investigated the capability of three Reynolds Averaged Navier-Stokes models to simulate natural ventilation in buildings. Papakonstantinou et al. presented a mathematical model for turbulent flow and accordingly developed a 3- D numerical code to compute velocity and temperature fields in buildings. A novel gas-liquid mass transfer CFD model was developed by Li et al. to simulate the absorption of CO2 in a microporous microchannel reactor. Yuan et al. visualized the air paths and thermal leakages near a complex geometry using a transient thermal model with buoyancy-driven convection, conduction and thermal radiation heat transfer and flow field near a vehicle structure . In the context of agriculture, researchers have extensively employed CFD analysis for study of ventilation, air flow, and microclimate in indoor systems. Zhang et al. developed a CFD simulation to assess single-phase turbulent air stream in an indoor plant factory system and achieved the highest level of flow uniformity with two perforated tubes. Karadimou and Markatos developed a transient two-phase model to study particle distribution in the indoor environment using Large Eddy Simulation method. Baek et al. used CFD analysis to study various combinations of air conditioners and fans to improve growth rate in a plant factory . More recently, Niam et al. performed numerical investigation and determined the optimum position of air conditioners in a small vertical plant factory is over the top. In addition, a variety of mathematical techniques are proposed to provide sub-model for investigating photosynthesis. According to Boulard et al., tall canopies can induce a stronger cooling of the interior air by using a CFD model to study the water vapor, temperature, and CO2 distribution in a Venlo-type semi-closed glass greenhouse. Despite the fact that photosynthesis plays an integral role in distribution of species and uniformity along cultivation trays, rolling grow trays this issue has not been well addressed. Although numerous research works have been done to investigate the turbulent flow in enclosures and buildings, this study is the first to numerically investigate the transport phenomena considering the product generation and reactant consumption through photosynthesis and plants transpiration with CFD simulations for IVFS-based studies.

Furthermore, a newly proposed objective uniformity parameter is defined to quantify velocity uniformity for individual cultivation trays. Moreover, numerical simulations are performed to simulate and optimize fluid flow and heat transfer in an IVFS for eight distinct placements of flow inlets and outlets in this study. Accordingly, the effects of each case on uniformity, relative humidity, temperature, and carbon dioxide concentration are discussed in detail. Finally, an overall efficiency parameter is defined to provide a holistic comparison of all parameters and their uniformity of each case.In this study, three-dimensional modeling of conjugated fluid flow and heat transfer is performed to simulate the turbulent flow inside a culture room having four towers for hydroponic lettuce growth. Assuming that the four towers are symmetric, a quarter of the room with four cultivation trays is selected as the computational domain, as illustrated in Fig. 1a. Symmetry boundaries are set at the middle of the length and width of the room. The effect of LED lights on heat transfer is considered through constant heat flux boundary conditions at the bottom surface of each tray as shown in Fig. 1b. Lastly, the species transfer due to photosynthesis are occurring only in the exchange zone, which is illustrated in Fig. 1c. To study the impact of air inlet/exit locations on characteristics of air flow, four square areas, denoted as A, B, C, and D in Fig. 1a, are considered to be inlet, exit, or wall. To perform a systematic study, Table 1 presents the location of inlet and exit for all eight cases studied. With the aim of comparing all of the proposed designs, case AB is selected to be the baseline. A fluid stream with horizontal speed ranging from 0.3 to 0.5 m s−1 can escalate the species exchange between the flow and plant leaves resulting in enhancement of photosynthesis. In indoor farming systems, the flow velocity can be controlled well using ventilation fans for more efficient plant growth.

However, heterogeneous distribution of feeding air over plant trays can cause undesirable non-uniformity in crop production, which should be avoided. Therefore, it is important to study the effect of inlet-outlet location and flow rate on the flow patterns throughout the culture room. Herein, the most favorable condition is defined as the condition at which the flow velocity above all trays is equal to the optimum speed Uo, which is set to be 0.4 m s−1. The objective uniformity, OU, defined in Eq. is used to assess the overall flow conditions. The OU for all eight cases as a function of mass flow rate are summarized in Fig. 5. Since the inlet/exit area and air density remain the same, the mass flow rate is directly proportional to flow velocity. In addition, the target flow velocity over the plants is set to be 0.4 m s−1. Therefore, a general trend of OU first increases and then decreases when increasing the overall mass flow rate. Depending on the design, the peak of OU occurs at different mass flow rate for each case. Another general trend can be observed that the peak of OU occurs at a lower mass flow rate if the inlet is located at the top due to buoyancy force. This can be clearly demonstrated by cases AB and BA or AD and DA . Therefore, there exists a different optimal inlet/exit design for each mass flow rate condition. As can be seen from Fig. 5, the maximum OU at flow rates of 0.2, 0.3, 0.4 and 0.5 kg s−1 is observed for configurations AD, BC, BA, and DA, respectively. Therefore, this simulation model can identify optimal flow configuration at a specific mass flow rate condition. Since OU quantifies the deviation of average velocity of each tray from the designed velocity, a higher OU value indicates that the crops will have better and more uniform photosynthesis. It can be observed from Fig. 5 that the maximum OU obtained for all conditions is case BC at a flow rate of 0.3 kg s−1. To develop a better understanding, the two-dimensional velocity and vorticity distributions in the x-y plane along the middle of the z-direction for all eight cases at a mass flow rate of 0.3 kg s−1 are plotted in Figs. 6 and 7.

As can be observed from Figs. 6 to 7, the OU is highest for case BC due to its uniform velocity and vorticity distributions between trays. This can be attributed to the position of inlet/exit location with respect to the tray orientation. For case BC, the inlet flow is parallel to the longitudinal direction of the tray and the exit is along the transverse direction . This design allows the flow to travel through the long side of the tray uninterrupted and then form a helical flow orientation near the end of the tray. This spiral formation of flow induces a more uniform and regular flow in the room. This also explains why case AD has very high OU. Similar spiral formation can also be observed when the inlet flow is parallel to the transverse direction of the tray and the exit is along the longitudinal direction , like case DA. However, since the inlet flow is along the short side of the tray, the benefit is not as great and requires much higher inlet mass flow rate. On the other hand, for cases where the inlet and exit are located on the same wall, such as AB or CD, the air flow only has strong mixing effect along the inlet/exit direction which, in turn, reduces the overall flow uniformity. Besides the velocity distribution, horticulture trays the effect of temperature is also a critical parameter for determining convective flow. Fig. 8 shows the two-dimensional temperature distributions in the x-y plane along the middle of the z-direction for all eight cases at a mass flow rate of 0.3 kg s−1. In our analysis, the temperature of the inlet flow is lower than that of the exit flow due to the heat generated from the LED light. For case BC, the inlet is located near the bottom and the exit is near the top. Due to the density difference, the exit warm stream tends to flow up. This allows the flow to reach the topmost tray more easily and, therefore, achieves more uniform temperature distribution among all trays. Combining the inlet flow along the long side of the tray, the helical flow effect, and the buoyancy, case BC is able to reach the maximum OU of 91.7%. Fig. 9 summarized the velocity and temperature contours for case BC at an inlet mass flow rate of 0.3 kg s−1. The velocity pro- files in Fig. 9a clearly show the spiral effect above each cultivation tray and the local velocity is close to the optimal speed of 0.4 m s−1. In addition, the temperature shows an increasing trend from bottom to top as the flow helically passing through the crops and moving towards the outlet.The distributions of temperature and gas species, such as water vapor and CO2, play an integral role in photosynthesis which, in turn, influences the quality of plant and its growth. Therefore, maintaining these critical parameters in a reasonable range to ensure reliable and efficient production is essential to environmental control of an IVFS. Evaluating the distribution of these parameters can also provide the effectiveness of inlet/exit location. It should be noted that the parameter OU provides an overall assessment of the air flow velocity over planting trays. An optimal design is to achieve desired local temperature and species distribution while maintaining high OU values in an IVFS. In the following discussion, the four cases with highest values of OU at their corresponding mass flow rates are studied and compared to the baseline case AB.Since CO2 is a reactant of photosynthesis, increasing CO2 concentration usually leads to enhancement of crop production. Reports show that increasing the CO2 concentration from the atmospheric average of 400 ppm to 1500 ppm can increase the yield by as much as 30%. In this IVFS analysis, the CO2 level of the inlet mass flow rate is increased by a CO2 generator to be 1000 ppm . Since the consumption rate of CO2 through the exchange zones is fixed, higher overall average CO2 concentration through the system is desirable. Fig. 10 shows the comparison of the average CO2 concentration between the highest OU cases and the baseline case AB at different inlet mass flow rate. A few general trends of CO2 concentration can be observed from Fig. 10. First, the CO2 concentration increases with inlet flow rate due to increasing supply of CO2 molecules. In addition, tray 1 has the highest CO2 concentration because most of the cold fresh inlet air dwells near the bottom of the IVFS due to the buoyancy effect. In contrast, tray 3 has the lowest CO2 concentration because the fresh inlet air has the highest flow resistance to reach tray 3due to the combination of sharp turns and buoyancy effect. This is particularly true at low inlet flow rates and when the inlet is located on the top, which lead to low flow circulation as cold inlet air flows downward directly. As a result, BC, BA, and DA at 0.3, 0.4, and 0.5 kg s−1, respectively, have relatively high CO2 concentrations. Even though the baseline case AB at 0.5 kg s−1 has the highest CO2 concentration, its OU is too low to be considered a good design. Temperature is also a critical parameter to control and monitor because it directly affects both relative humidity and plant growth. The temperature distribution in the system depends on the inlet/exit location, inlet mass flow rate, and amount of heat. Since the inlet temperature and heat flux conditions are fixed, the exit temperature increases with decreasing inlet mass flow rate. Fig. 11 shows a comparison of the average temperatures of the higher OU cases and the baseline case AB at different inlet mass Fig. 12. Comparison of the average RH over each tray between the best OU cases and the baseline case at each inlet mass flow rate condition. flow rates.