Furthermore, employment of light emitting diodes as light sources can initiate and sustain photosynthesis reactions and the optical wavelength, light intensity, and radiation intervals can further enhance growth quality. Recently, many studies have been carried out to investigate how environmental parameters, such as closed-loop control, ultrasound, and electro-degradation, affect hydroponic cultivation of leafy vegetables in these systems. One of the most influential factors affecting growth in IVFS is to maintain a uniform air flow at an optimal air current speed over plants canopy surfaces. Poor flow uniformity or variation in air velocity over culture beds destabilizes crop production rates. It has been found that inducing a horizontal air speed of 0.3–0.5 m s−1 boosts photosynthesis through more efficiently exchanging species between the stomatal cavities in plants and the flow of air. Lee et al. studied the effects of air temperature and flow rate on the occurrence of lettuce leaf tip burn in a closed plant factory system. Furthermore, it was observed that the relative humidity of the air flow can significantly influence calcium transportation in lisian thus cultivars . According to Vanhassel et al., higher levels of relative humidity can significantly decrease the occurrence of tip burn. Therefore, it is vital to maintain relative humidity in the desired range to ensure even distribution of calcium in lettuce leaves. Over the past few years, researchers have been trying to develop techniques for improving uniformity over cultivation zones. Regardless of the recent progress, the control and automation systems of IVFS bring additional costs,seedling grow rack which makes systematic experimental investigation and optimization a challenge. Computational fluid dynamics has been utilized as a reliable tool to numerically simulate complex physical phenomena. Markatos et al. developed a CFD procedure to study velocity and temperature distribution in enclosures using buoyancy-induced physics. 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 micro-porous micro-channel 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, 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.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.In our model, a tetrahedral grid type is used to discretize the entire computational domain. To ensure that the numerical results are independent of grid dimensions, five grid numbers ranging from 196,951 to 1,164,624 are used to study the baseline Case AB at a mass flow rate of 1 kg s−1. Fig. 2 summarizes the average temperature and pressure difference for the five grid numbers. Balancing between the accuracy of the simulation results and computational cost, the grid number of 697,537 is employed throughout the rest of the study.

The simulation domain consists of rectangular prisms as cultivation tray, the exchange zone in which the photosynthesis processes occur, and the rest of the open volume. To validate our numerical code, we performed simulation of conjugated heat transfer and turbulent flow passing over one rectangular prism in a duct. The exact dimensions and input conditions of this test case can be found in the study of Nakagawa et al.. The induced flow involves periodic vortex shedding that can be problematic for numerical analysis. The results of the numerical simulations are compared with the experimental measurements done by Lyn et al., Franke and Rodi , and Durao et al. [46]. Fig. 3 shows the average axial velocity distribution and our simulation results agree well with the experimental data both before and after the rectangular prisms. To further validate the reliability of heat transfer calculation, the simulated local Nusselt number along the upper wall of the square prism are compared with the experimental data measured by Nakagawa et al. in Fig. 4. When x/H is between 1and 2, the wake flow is extremely unsteady and adverse flow can be observed in Fig. 3. Therefore, it is extremely difficult to accurately predict the convective heat transfer in this region. Nevertheless,indoor growing racks the simulation results show good agreement with the experimental data, especially in the wake region . Further, the calculation of species transport in this work is simulated using species exchange sub-model, which has been validated extensively in the literature.In this study, three dimensional simulations of conjugated turbulent flow and heat transfer are carried out to study the concept of the IVFS. The exchange zone above each tray is designed to represent the volume where the photosynthesis reaction takes place including carbon dioxide consumption along with water transpiration and oxygen production. In addition, the room is assumed to be insulated by wooden walls with known thickness and thermal properties for modeling heat exchange with the outdoor ambient air. In this study, we analyze the effect of eight distinctive inlet outlet placements on flow uniformity over the lettuce canopy, temperature and relative humidity distribution in the room, and the power required for air circulation.One of the most critical factors affecting crop growth rate is the air flow velocity over plants. 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.