Development of a fixed bed solar dryer : experimental study and CFD simulation

Facing the challenges to develop more efficient solar dryers, this work used the Computational fluid dynamics (CFD) to test different configurations of lateral air feeding in a fixed bed solar dryer. Through the simulations, it was found the best configuration of air inlet that provided a better fluid-particle contact. It was made a fixed bed solar dryer, which was tested using soybeans seeds and Moringa oleifera LAM leaves to evaluate the drying rate using two bed configurations: fully opened and partially opened inlets. The CFD results indicated that the air flow rate was more pronounced at the bed top, near the exhaust fan. This can explain the poor drying near the bottom for the experiments performed with all lateral inlets opened. According to the simulation results, the air velocity profile was more homogeneous when the air was fed only near the bottom. So, the use of a partially opened configuration led to a more homogenous solar drying, with a drying rate about 300% higher than the one using the fully opened inlets.


Introduction
In 2017, the annual average solar radiation at the southeast of Brazil was about 4.95 kWh·m -2 (INPE, 2017), which demonstrates the high potential of solar energy application as solar drying, both in domestic and industrial sectors. In addition, this region has an intensive grain harvest and generates a large amount of crop residues, which eventually need to be dried. An example is the soybean seeds (SS) production, which requires the seeds to be adequately dried to ensure appropriate water content for commerce and increase their post-harvest conservation potential, maintaining their physical proprieties (Souza et al., 2015a, Souza et al., 2015b. Another important dried product commercialized as nutrient supplement is the Moringa oleifera Lam. (MOL), also called drumstick tree or horseradish tree. This plant is indigenous to northwestern India (Perumal & Klaus, 2003;Olabode et al., 2015) and is common in Southeast Brazil. The MOL is classified as a multifunctional plant, as it has become increasingly widespread in animal and human food; it is also used in the cosmetic and pharmaceutical industries; for the production of oil, soap, fertilizers and biopesticides; as an additive for clarifiers; surfactants (Andrade et al., 2020) and for sewage and water treatments Regarding the solar drying using fixed beds, Mardiyani et al. (2019) developed a convective ecofriendly fixed-bed solar dryer working with one air inlet and using five trays with 7 cm of packed material. The drying of red pepper required about 5-6 days to dry the first tray, 8-9 days for the second tray, and 9-10 days for the third tray, until 12% (w.b.) of moisture was achieved. Therefore, the drying process took some days, which shows the necessity to better investigate the phenomena that take place in the fixed-bed dryer using solar energy.
According to Tegenaw et al. (2019), the CFD technique is a promising design and modeling tool that can provide important information in cases where experimentation is limited, reducing costly experimental trials. The computational simulations are successfully used to predict air velocity profiles, temperature, and moisture within the dryer, allowing to examine and interpret the different operating conditions without an extensive set of experimental tests.
The CFD technique has been contributing to the design of new equipment and the optimization of existing dryers, which ensures a better final product, under suitable processing and storage conditions. Krawczyk & Badyda (2011) proposed a model based on the heat and mass-transfer phenomena in a drying process. The authors considered the application of boundary conditions on the material surface and the physical boundary between the air and the solid phase (dry material) and calculated the dryness and humidity as a function of dryer position. Tegenaw et al. (2019) used a CFD model to predict the airflow patterns and transient heat transfer within a truncated pyramid-shaped solar dryer. The simulations revealed higher values of air velocity (about 0.5 m·s −1 ) near the exhaust fan. The spatial Research, Society and Development, v. 9, n. 3, e123932667, 2020(CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i3.2667 6 temperature distribution was uniform after 30 min of solar exposure, reaching a maximum temperature of 60°C. Béttega et al. (2011) performed mathematical simulations of radial heat transfer in packed beds using pseudo-homogeneous modeling. Béttega et al. (2013) studied the heat transfer inside a packed bed of glass beads with heat source located on the wall of the equipment from a 2D model. Different profiles were evaluated for the voidage distribution along the radial direction of the bed and its effect on the behavior in the whole device. From this approach, the authors determined the temperature distribution at the outlet for different fluid velocities, using physical parameters of the phases present in the system. Comparing the CFD results with experimental data and other models from the literature, the capacity of the model and the numerical procedure adopted to represent the phenomenon were verified.
In the present study, a sustainable solar dryer was designed for drying different agricultural materials, such as SS and MOL leaves, with low cost and high efficiency. For this, new different configurations of a fixed bed were evaluated by CFD simulations. It was studied the effect of different settings of airflow inlets over the air velocity profile along the fixed bed, to find a condition that improves the particle-fluid contact and also the heat and mass transfers. Then, two configurations were tested experimentally to capture the influence of the climatic conditions over the drying processes. The mathematical model and initial condition used for the CFD simulations are detailed in the next section, as well as the experimental procedure used in the drying experiments. The experimental results were analyzed, and the discussion was supported by the simulation results and literature works.

Mathematical modeling
A porous media model can be used for a wide variety of problems, single-phase or multiphase systems, including flow through packed beds, filters, and perforated plates. In this study, when this model was used, a cell zone was defined where it was applied, and the pressure drop in the flow was determined through its inputs, being described by the momentum equation in the porous media. Heat transfer through the medium might also be represented, with or without the assumption of thermal equilibrium between the solid and the fluid, modeled by the energy equation in a porous media. The porous media model incorporated a flow resistance determined empirically in a region of the system defined as porous. In essence, this model added a dissipation term to the momentum equation. Consequently, some hypotheses were assumed in the model, and its Research, Society and Development, v. 9, n. 3, e123932667, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i3.2667 7 limitations might be recognized (Béttega et al., 2011), such as a 2D transient axis-symmetric model, where the porous media momentum resistance and heat source terms are calculated separately on each phase; the assumption of isotropic porosity and an initial air velocity at the entrance of 0.98 m·s −1 at 338.15 K. Since the block generated by the porous medium that was physically present was not represented in the model, the ANSYS Fluent 17.2 Standard reported a surface velocity inside the porous medium, to ensure the continuity of the velocity vectors through the interface of the porous medium. A more representative alternative in which the mean interstitial velocity was calculated inside the porous medium was chosen, and in this way, the voidage was included in the differential terms of the transport equations.
The set of conservative and constitutive equations for the fluid in a porous media, as presented in Table 1, were solved by the finite-volume method. Assuming isotropic voidage and a single-phase system, the continuity and momentum equations could be described by Eqs.
(H) Constitutive equation for the inertial resistance of porous media: Research, Society and Development, v. 9, n. 3, e123932667, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i3.2667 8 The inputs of the resistance coefficients were assumed to be based on well-established empirical correlations, which have been usually based on surface velocity. Thereby, the inputs of resistance coefficients were automatically converted to those that were compatible with this formulation. Consequently, the homogeneous porous medium was modeled by adding a source term Si, as shown in Eq. (3), in the continuity and momentum equations (Béttega et al., 2013).
In a turbulent flow, the fixed bed was modeled using both the permeability and inertial loss coefficient. For this, Ergun's equation could be used, as shown in Eq. (4) (Ergun, 1952).
The permeability () and the inertial loss coefficient (C2) in each component may be identified by Eqs. (5) and (6), where is the voidage; Dp is the particle diameter (m); and ϕ is the particle sphericity, obtained experimentally.
The mathematical model for heat transfer simulation adopted by ANSYS Fluent 17.2 used the energy equation, i.e., Eq. (7), with some modifications in the conductive transport of heat and in the transient terms, specifically for the case of the porous media. The morphological proprieties of SSs and MOL leaves, such as the mean diameter of Sauter, apparent density, and sphericity, need to measured experimentally to calculate the packed bed properties: voidage, permeability, and the inertial resistance factor.

Experimental Apparatus
The fixed-bed solar dryer developed in this work is presented in the Figure 1. The equipment consists of a black fixed bed (A) (absorber body) located inside a solar furnace cabin, which consists of a metal support (B) covered by a glass box (C) to create a greenhouse effect. A radiator (D) was painted black and inserted between the metal support and the fixed bed to increase the metallic surface area that absorbs the solar radiation and transfers heat to the air. Two side plates covered by a reflective film (F) were added to increase solar radiation uptake. Behind the metallic support, a thermal insulation (G) was design to avoid thermal losses. The fixed-bed geometry was a rectangular vessel with an exhaust fan at the exit (E) to promote the air suction through the several lateral inlets (Figure 1b

Particle Characterization
To calculate the porous media properties, all particles were submitted for characterization, with all analyses in triplicates. The mean volumetric diameter for SSs was calculated by 3D measurements taken with a pachymeter. Therefore, their volume was determined by assuming an ellipsoidal form, using a sample of 30 particles. These particles were then weighed, and the apparent density was calculated by the weight-to-volume ratio of the sample.
Regarding the MOL particles, fresh samples were collected daily since the leaves rapidly lose their freshness. The weight, thickness, and a projected area of 20 samples (with 15 leaves each) were measured and recorded to estimate the apparent density. Therefore, the volume was the product between the projected area and thickness. The voidage was calculated considering the particles weight packed in the fixed bed.

Simulation Conditions
Some CFD simulations were performed to analyze the influence of different inlets arrangements over the air velocity profile through the packed bed. The airflow inlets at different assemblies are showed in Figure   The conditions adopted in CFD studies are described in Table 2. The fluid consisted of air at 60 ºC (maximum temperature found experimentally), while the particles were considered as a porous zone. The values for the viscous and inertial resistances of the porous media were calculated by Eqs. (6) and (7), which were derived from Ergun's equation, in Table 1 (Ergun, 1952). Research, Society and Development, v. 9, n. 3, e123932667, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i3.2667 Table 2 also shows the conditions simulated in this work, all them for packed beds with an initial static bed height of 0.57 m. Simulations 1 to 4 were realized for the SS in order to evaluate the influence of different air inlet settings on the fluid paths inside the fixed bed, for outlets air velocities of 0.5, 1, and 2 m·s −1 . Thus, a fixed bed filled with SS (Case 1) were simulated for all arrangements in Figure 2. Afterward, some simulations were performed for the FO bed and PO bed, using Moringa oleifera leaves (Case 2). Simulations 5 and 6 were done for a packed bed of MOL leaves, operating with the FO and PO air inlet configurations, at an outlet air velocity of 2 m·s −1 .  The solar dryer experiments consisted of packing the particles inside the bed until a static bed height of 0.57 m was achieved, which led to an amount of 6.2 kg of SSs and 1.41 kg of MOL (Figure 3a). After that, the equipment was exposed to solar radiation, and the exhaust fan was turned on (Figure 3b).  whereby w w is the water weight and p w is the weight of the dried particle. Therefore, Eq. (10) establishes the moisture ratio (MR) removed at instant (i); it is also used to describe the kinetics of drying at the packed bed. Research, Society and Development, v. 9, n. 3, e123932667, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i3.2667

13
The experimental packed bed drying using solar energy with MOL (Case 2) was performed using the FO and PO inlet configurations, and the MRs along the experiments were calculated for a final drying time of 6 h. A dynamic equilibrium moisture was used, obtained by experimental drying tests in an infrared humidity analyzer, at 40 and 60 ºC.

Particles Characterization
Table 2 also shows the characterization of particulate materials used in this work. The mean diameters were 0.006 m and 0.015 m, with apparent densities of 1289 ± 100 kg·m −3 and 546 ± 113 kg·m −3 for SS and MOL, respectively. The soybeans were close to a spherical form (ϕ = 0.9), while the MOL had small sphericity, about 0.435. These lead to a very compacted bed for soybeans, with voidage ε = 0.370 and an extra porous bed for MOL (ε = 0.679), since small particles sphericity leads to a packing with a higher void fraction.
The viscous and inertial resistances of SSs and MOL-packed beds were calculated using the particulate proprieties. It can be seen in Table 2 that small viscous and inertial resistances were found for the MO leaves due to their lower sphericity and higher voidage.

Simulated air velocity profiles
Case 1: The effect of different air inlet settings: To clarify the influence of different air inlet settings on the fluid dynamics inside the fixed bed, some CFD simulations were performed using SS, chosen due their higher sphericity, which brings them closer to a perfect sphere. In addition, soybeans do not suffer much shrinkage when subjected to the drying process. Figure 4 presents the air velocity contours flowing through the porous bed for all air inlets studied in this work. With increments of outlet air velocity from 0.5 m·s −1 to 1.0 m·s −1 and 2.0 m·s −1 , there was a proportional response in the bed: the velocities of the air that runs through the bed increases, for all bed configurations. Moreover, the air inlets near the exhaust fan showed a higher air velocity than near the bottom, as the packed-bed offers a head loss that increases with the length of the porous medium from the airflow source.
Regarding the different airflow inlets arrangements, the AAI and PO configurations provided more homogeneity of air distribution inside the packed bed, while for the FO configuration, the air was collected only at the top of the bed, due to its proximity to the exhaust fan outlet. Considering the UAI configuration, the axial air distribution through the bed was heterogeneous, which is not desirable since near the closed inlets, there was no effective contact between air and particles, which could lead to partial drying. The simulations for the PO configuration showed greater air velocities along all axial directions and a better homogeneity; this resulted in higher drying rates during drying. Case 2 -Packed beds operating with MOL particles: CFD simulations were performed to obtain air velocity contours for an MOL-packed bed (FO and PO configurations), which presents a high voidage due to the low sphericity of particles. It can be observed from Figure 5 that a better distribution of airflow took place in the PO configuration because the preferred paths were prevented since the upper entrances were closed. Therefore, the ascendant air had increased velocities even at lower bed heights, providing a more homogenous air distribution and higher particle-fluid velocities. This can improve the heat and mass-transfer coefficients and promote a more efficient drying.

Solar drying tests
Case 1 -Drying of soybean seeds: Experimental drying tests of SSs in PO packed-bed configuration were conducted on sunny days. The environment relative humidity was between 31% and 44% for the experiment with 3 h, while a range of 46%-55% was observed for the test with 4 h. Regarding the air inside the packed bed, the bottom presented lower temperatures than the bed top. This can be explained because the cold air was denser than the hot air, causing a temperature gradient in the air between the glass cover and the fixed bed. As the air velocities were pronounced near the exhaust fan, warm air gets inside, promoting the quick drying of the particles at the top.
According to Silva et al. (20018), in conventional fixed beds there is also a gradient of moisture and temperature through the fixed bed, once the particles near the heated air supply usually dry faster than those farthest away. In this study, the particles near the entrances in the top dried faster than those near the bottom.     Figure 10b, which Research, Society and Development, v. 9, n. 3, e123932667, 2020(CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i3.2667 19 shows the solar radiation changes and the wind velocity during the experiments. Hence, the increases of solar radiation levels coincided with elevations in temperature, especially at the top and bottom; moreover, they were inversely proportional to the increase in wind speed, since the heat losses by convection had decreased the temperature of the solar dryer. were also verified to have a more pronounced drying, since they were closer to the outlet.
After four hours of drying, shrinkage of the leaves was noticed, about 20%, due to the high temperatures recorded during the day. Thus, the static bed height was reduced, and sampling in the axial positions of 0.27 and 0.34 m was not possible.
To better understand the influence of the air inlets arrangements on the MOL drying, an experiment using PO fixed-bed configuration was also performed. Figures 10d and 10e present the temperatures and the climate conditions against the time, respectively. The solar radiation (632 ± 124 W·m −2 ) had a greater influence on the bed temperature than the external temperature mainly at the beginning of the drying. The temperature peak (60 °C) occurred at the bed top after 1.5 h of drying in the period of low wind speed (1.5 m·s −1 ) and high solar radiation (678 W·m −2 ). The opposite occurred between three and four hours of drying, when an increase of wind speed reduced the bed temperature.
The MR as a function of time can be seen in Figure 10f, for the PO bed. A greater decline in the moisture was noticed for all axial positions, including near the bottom, mainly in the first two hours. The most accentuated drying (MR = 0.2) occurred at 0.20 and 0.27 m, near the third airflow inlet, as this entrance had a superior air velocity due to its proximity to the exhaust fan. This agrees with air velocity contours produced by CFD simulations ( Figure 6). However, the particles near the bottom still had a smaller drying efficiency, with a final MR of 0.52. Since these particles were behind the first inlet, there was no significant air velocity in this position, as predicted by CFD simulations.
As regards the drying rate (in percentage points per hour, pp·h −1 ), Figure 11 demonstrates that the PO bed was more efficient than the FO bed configuration, as the PO bed removed about 6 to 9 pp·h −1 of moisture, while the FO bed removed less than 2 pp·h −1 in axial positions until 0.27 m and a maximum of 5 pp·h −1 at the top. This means an increment of about 300% in the drying rate for the PO bed, mainly around the bottom. In addition, the final MR along the bed was similar and almost constant after two hours of drying, showing a sharp decrease in the drying heterogeneity.   Drying rate (pp·h-1 )

Bed Height [cm]
PO Bed FO bed  dried SSs in a conventional fixed bed, heated by electrical resistance, with an air inlet at the bottom and found a maximum drying rate of 2.35 pp·h −1 , working with an air velocity of 1 m·s −1 and 45 °C. Comparing these results with the present solar dryer, the FO bed configuration achieved similar results of drying rate (2-5 pp·h −1 ), while the PO bed could remove about 6 to 9 pp·h −1 of moisture. Moreover, the conventional fixed bed also showed a strong heterogeneity of the final product, as found in the FO configuration. Therefore, the modifications proposed in this study by CFD simulations could be useful to improve the drying rate by closing the upper entrances, which drastically modified the air fluid dynamics in the porous media and consequently the convective coefficients of heat and mass transfers.

Conclusions
In this work, the CFD technique was used to develop new configurations of fixed-bed dryers using solar energy. Regardless of material, the results showed that the fixed bed working with all inlets open (FO bed) achieved similar drying rates compared with conventional fixed-bed dryers , and a relatively homogeneous dried product was obtained, with the air stream heated by a natural and free energy source.
The CFD simulations also demonstrated some possible changes in the air inlet configurations and showed that closing the upper inlets modified the airflow path through the porous media. Therefore, the PO bed configuration had a more homogeneous air velocity profile in the axial direction, leading to a more homogeneous dry product. Comparing the solar drying experiments of MOL leaves, the PO configuration conducted a more homogenous solar drying, with a drying rate about 300% higher than the one using the FO configuration, due to the closure of upper inlets. Moreover, temperatures of about 40 and 60°C were achieved, which are appropriate for the drying of temperature-sensitive materials.
The fixed-bed dryers are recommended for agricultural products, which usually present poor flowability due their high angle of repose, low density, and high moisture content. Therefore, this new equipment can be an interesting alternative for drying in small facilities and farms and can be scaled up to increase its capacity.