Abstract
In this study, CFD simulations that incorporate the inherent coupling between the moisture content of the mushroom and hot air flow in the tray dryer were performed. Conservation principles were applied to the fundamental quantities of mass, momentum, and heat. The source terms due to the moisture evaporation, the viscous and inertial resistance, and continuous evaporative cooling were determined through experimental results. Experiments were conducted to study and select the drying kinetics model at the optimum drying conditions and moisture sorption isotherm model at 30, 40, and 50°C temperatures. The best model describing the drying kinetics of mushrooms and moisture sorption isotherm model was chosen based on the lowest RMSE values and the highest value. Midilli et al.’s drying kinetics model and the modified Henderson sorption isotherm model were adopted in CFD modelling. The CFD software ANSYS Fluent was used for the 3D modelling of mushroom drying in a tray dryer. The mass and energy source term equations were added to the ANSYS Fluent software using a user-defined function (UDF). The parameter permeability of medium () and pressure-jump coefficient () appearing in the momentum source term were directly introduced in the Fluent setup as cell zone conditions. The simulation results of the moisture removal and drying temperatures were validated against experimental data. Both results are in good agreement with the experimental data, with values of 0.9906 for moisture contents and 0.926 for drying temperature. Thus, simulation can be an option to study the drying mechanisms and alleviate some drawbacks of doing experiments.
1. Introduction
All food items in our daily life must be preserved in some way. Mushroom is highly nutritious, delicious, and safe to eat, but it is highly perishable because it has a moisture content in the range of 85-95% by weight (wt) when wet and has a very short shelf life [1]. Harvested mushroom can remain in atmospheric condition for up to one day only without rotting [2]. For this reason, processes that suppress product deterioration have become an important issue. The most common methods of preserving food, such as mushrooms and fruits, are long-term preservation methods, such as canning, pickling, drying, and adding chemicals [3, 4]. Drying is the most common method of preserving food and shows promise for preserving moist foods and other agricultural products [5].
Therefore, the drying of food products, such as mushrooms, meat, and fruits, is carried out to preserve their desired nutritional properties for as long as possible, thus facilitating their transport, storage, and handling [6, 7]. Many drying techniques can be used for mushroom drying such as sun drying, vacuum drying, microwave drying, freeze-drying, and tray drying. When tray drying is applied, the moisture content in the mushroom should be removed at some optimum conditions. The drying process depends on the moisture content inside the material, drying temperature, drying medium, and time. Therefore, the drying process should be optimized to save energy and to keep the important nutrients in the drying process, especially for mushroom drying [8, 9]. The experimental processes of drying such as the measurement of temperature distribution, mass flow, and velocity of air in the tray dryer chamber are expensive, difficult, and time-consuming. Even only partial information will be obtained from the experimental result. This is because it requires many installed sensors and must be adjusted in several parts of the dryer other than inlet and outlet measuring sensors. On top of that, most industrial dryers are designed based on expensive pilot-scale experiments [10]. The complexity of the drying process due to the diverse nature of the material being dried hinders the development of a global drying model that can be used for various tray dryer designs under different operating. Since the cost of experimental testing can be substantial, theoretical analyses of these drying systems at the design and modelling stage can reduce the cost largely, while producing a better understanding of the process with detailed analyses [11].
Recently, there have been many pieces of research on the mathematical modelling and experimental studies of the drying characteristics of various vegetables and fruits, such as grapes [12], apples [13], peaches [14], carrots [15], beriberi [16], and potatoes [17]. Some work has been reported to dry mushroom and extend shelf life using various postharvest techniques. However, there are sparse studies in the literature on computer-aided modelling techniques for mushroom drying in tray dryers [3, 18]. Moreover, previous modelling attempts were limited to mathematical modelling and whole-food drying processes.
In the last decade, Arumuganathan et al. [5] developed a model for a fluidized bed dryer for drying milky mushroom by taking into account only the mass transfer during drying. Nevertheless, to my knowledge, there was no computational fluid dynamics (CFD) model for drying mushroom by considering the simultaneous heat and mass transfer during drying. Effective modelling and simulation of the tray dryer system may eliminate or reduce the nonuniformity of drying and increase dryer efficiency. This paper discussed the optimization of drying parameters, CFD modelling, and simulation of a tray dryer system for drying mushroom by using an appropriate modelling approach. CFD simulation is a very useful tool in the optimization of the drying chamber configuration by predicting the airflow distribution and the temperature profile throughout the tray-drying chamber [19, 20]. This is very important for many food industries and research institutes (laboratories) since it reduces the number of experiments saving time and money.
2. Materials and Method
2.1. Materials
The raw materials used in this research was oyster mushroom collected from Menagesha Integrated Organic Farm mushroom harvesting company, Holeta, Addis Ababa, Ethiopia.
2.2. Experimental Methods
2.2.1. Sample Preparation
Freshly harvested oyster mushrooms were washed several times with water to remove dust and impurities. After draining, mushrooms were covered with blotting paper to remove surface moisture. Then, cleaned mushroom having flat shapes were cut into small slices with an average rectangular dimension of using a slicer to increase the moisture removal rate. The slices of mushroom samples were kept in a refrigerator at 4°C to keep the moisture content until used for further processing.
2.2.2. Oyster Mushroom Drying Process Using Tray Dryer
Drying was performed in a hot air-drying medium of a computer-controlled tray dryer (CCTD/SCADA, Edibon, Italy). The dryer mainly consists of four basic units (1) an air compressor, (2) an air velocity regulator, (3) an electrical heater, and (4) a drying chamber (tray). The drying chamber had four trays made up of stainless steel with 270 mm by 240 mm dimensions. The compressor blew air into the heater; the hot air was blown to the tray horizontally; and then the hot air removed the moisture from the sample. The tray dryer used in this study is presented in Figure 1. A known amount of sample in grams () was placed on the tray, and the temperature and air speed were set within the range of 40–80°C and 0.5–5.5 m/s, respectively. Then, the sample weight was continuously recorded and used to estimate the amount of moisture removed during drying as per the following equation: where , , and are the amount of moisture present in a dried sample, the amount of moisture present in a fresh sample, and the amount of moisture removed at some time , respectively.
2.2.3. Determination of Initial Moisture Content and Dry Weight
The fresh mushroom sliced was weighed by using an electronic balance (AD-300-3, USA) and put in an oven (700LT-model no. TD-1315, Cooper Technology, UK) set at 105°C for 24 hrs. About 0.2 kg sample was taken in a tray and weighed again accurately to give the exact weight of the sample. The residual weight after 24 hours was used as the dry weight () of the mushroom. To obtain the initial moisture content (), equation (2) was used. where is the initial weight of the mushroom sample and is the dry weight of the sample.
2.3. Parameter Optimization for Mushroom Drying in a Tray Dryer
The preliminary experiments were conducted with a drying period of eight hours by considering drying temperature (40–80°C), hot drying air speed (1–5.5 m/s), and mass load (50–500 g) as parameters, and the individual effect has been investigated on the moisture content of the final product. Based on the preliminary experimental results, the upper and lower limits for temperature, hot air speed, and mass loading were fixed to obtain the experimental matrix to investigate the interaction effect between these drying parameters on the drying of oyster mushroom listed in Table 1. A design expert was used to optimize the parameters for mushroom drying [21].
Numerical optimization was performed for three parameters (temperature, hot air speed, and mass of mushroom) to minimize moisture in oyster mushroom during tray dryer. The optimum drying parameters obtained from the optimization process were further used to study mushroom drying kinetics and in the CFD model simulation steps. The interaction between the parameters of the drying process is fitted with the following equation: where is the response function (moisture content), are regression coefficients, , , and are the independent parameters, and is the error [22].
2.4. CFD-Based Modelling for Mushroom Drying in Tray Dryer
The CFD model is based on the fundamental conservation equations of mass, momentum, and energy. The source terms (mass during moisture evaporation, momentum due to viscous and inertial resistance of mushroom, and energy due to the continuous cooling evaporation process) were not included in the conservation equations of the CFD software package (ANSYS 2020R1). The source terms for the three quantities were derived and determined from the experiments. All the parameters and physical properties required to build the model were obtained from the literature and direct experimental results of drying experiments.
2.4.1. Source Term Determination
(1) Mass Source Term Determination. The conservation of air mass when the mushroom was drying is given in equation (4) [23–25]. where is the density of the fluid (air), is the velocity vector, and is the mass source term.
The source is the mass added to the continuous phase (drying air) from the second phase (porous medium) due to vaporization moisture from the mushroom slices. can be expressed similarly to Fick’s second law of diffusion as per equation (5) as suggested by Thorpe [23]. where is the density of the mushroom and is the porosity of the sliced mushroom.
(2) External/Bulk Porosity (). The porosity of the slices of mushroom was calculated using the expression given in the following equation: where is the total volume () of the sample holder and (volume of samples) is equal to the volume of a single slice multiplied by the total number of slices.
(3) Momentum Source Determination. Conservation of momentum is described in equation (7) as discussed in [25]. where is the static pressure, is the stress tensor, and and are the gravitational body force and external body force (i.e., it may be from the interaction with the dispersed phase), respectively. also contains other model-dependent source terms, such as porous media and user-defined momentum sources. In the tray dryer case, the hot air flow is horizontal. Then, this momentum source term was determined through the following equation: where is the permeability, is the inertial resistance factor, and is the velocity of air in the horizontal direction. and were determined using Ergun’s equation (9), as suggested by [26–28]. where , , and is the effective diameter of mushroom slices and is the porosity. For spherical particles, in equation (9) is equal to unity.
(4) Effective Diameter () of Mushroom Slices. The shapes of different mushroom species are irregular. To determine the effective diameter of the mushroom slices, liquid water is used in a measuring cylinder filled with an initial volume of 60 ml. After the slices of mushroom were immersed, the resulting volume differences observed between the water volumes with slices and without slices were taken, and the of the sliced mushroom was calculated, exploiting the formula of the sphere volume, as
(5) Energy Source Determination. Energy conservation equation was determined as described in reference [25]. where is the total energy. The first three terms on the left-hand side of the equation represent energy transfer due to conduction, species diffusion, and viscous dissipation, respectively. is the energy source term, which is due to the effect of evaporative cooling. This was determined using the expression in equation (12) as reported in reference [23]: where is the latent heat of vaporization, which was calculated, for the range of temperature 0 to 260°C, from the relation [29]. where is the temperature expressed in . Substituting the expression for obtained from mass source determination and equation (13) into equation (12), the heat source term was determined.
2.4.2. Drying Kinetics Models
A mass of mushrooms of 200 g was dried at six different temperatures (50, 55, 60, 65, 70, and 75°C) with a hot air speed of 3 m/s. The weight percent moisture content () was recorded at 15-minute intervals and used to study the mushroom drying rate. The moisture content remaining in the samples was plotted against time at various temperatures [30, 31]. The dimensionless ratio of moisture content difference () is defined by [32–34]. where Mt, Me, and Mo are the moisture content at a time , the equilibrium moisture content, and the initial moisture content, respectively.
Then, the mushroom drying rate was obtained by the time derivative of .
changes with the moisture content of mushroom slices. So, has been determined from the moisture sorption isotherm model (see section 2.4.3).
In this study, the experimental data were fitted with eight selected well-known thin-layer drying kinetics models listed in Table 2. The model parameters were estimated through a nonlinear regression method using a MATLAB script (MATLAB R2018b). The fitting quality of the experimental data for all selected models was evaluated using the coefficient of determination () and the root means square error (RMSE). The best model describing the drying kinetics of mushrooms (showing the lowest RMSE value and the highest value) was selected to determine the source term.
2.4.3. Moisture Sorption Models
The remaining term to be determined is the equilibrium water content , which can be determined from the water sorption model. Food sorption isotherms describe the thermodynamic relationship between water activity and the equilibrium water content of food at constant temperature and pressure [35]. Seven selected sorption models were tested and the one with the good-of-fit was used in the modelling (Table 3). Water activity () experiments were done to select the sorption model using water activity meters (AQUA LAB: 4TE, Italy), which measure the water activity of mushrooms when the moisture content reached equilibrium at a given temperature. vs. equilibrium moisture content data was generated at temperatures of 30, 40, and 50°C. The goodness-of-fit of the model was determined with a higher value of and lower values of RMSE.
After the model is selected, the water activity of the sample is related to the absolute humidity and relative humidity of the drying medium [23, 29] through the following equation: where is the relative humidity of drying air and is related to the absolute humidity () as where is the saturation vapor pressure of free water, which is a function of the absolute temperature. In this study, was determined using the Antione equation for free water [36] as where is the absolute temperature. Finally, the rate of drying was obtained as a function of absolute humidity, moisture content, temperature, and drying time.
2.5. CFD Modelling
The CFD-based model for drying mushrooms was implemented to capture the moisture and temperature variation of the mushroom during drying. The ANSYS Fluent has a conserved Navier-Stokes equation for the fundamental quantities of the mass, momentum, and energy, whereas the source terms were not included in the conservation equations of CFD software package. These terms were determined and added to the ANSYS Fluent package by developing a user-defined function (UDF) written in C-program using the Code::Blocks software which is compatible with ANSYS Fluent.
2.5.1. Geometry and Meshing
In ANSYS Fluent, the DesignModeler was used to draw the geometry of the tray dryer (fluid domain) and the mushroom slices. The fluid domain was made symmetric to minimize the simulation time, and due to computational cost, the mushroom slices were considered as a large rectangular slice. The dimensions of the tray dryer, tray, and mushroom slices are given in Table 4 from the specification and measurement of actual dimensions at the laboratory.
A tetrahedron meshing method was used in the grid generation because it produced a good mesh with skewness less than 0.95 [25]. To reduce simulation time, a 0.003 m mesh size was used. An additional inflation layer was applied to capture the near-wall flow variables in the boundary layer region. To define the thickness of the first layer, an online calculator was used and found 0.0009 m. expresses the distance from the wall to the center of the first grid cell. The boundary layer was inflated to 24 layers at a growth rate of 1.2. The air inlet, outlet, symmetry surface, walls, and fluid domain were defined after the mesh was generated. The mushroom slices were modelled as porous media.
2.5.2. Setup and Solutions
In the physics setup, double precision for better accuracy was selected. The solver was pressure-based steady state for fluid flow only, and transient simulations after UDF were compiled. The mushroom slice was considered a solid and was created in the materials list; then, it was modeled as a porous media. First, viscous (realizable and shear-stress transport (SST)) turbulent models have been used to solve the flow without source terms. Then, the two turbulence models were compared based on their wall values. The wall is used as guidance in selecting the appropriate grid configuration and corresponding turbulence models in Fluent [37]. Energy was activated in the Fluent physics setup after the steady flow simulation converged. All material properties and boundary conditions are given in Table 5. Convergence criteria for all residuals were set, and standard initialization was used. More than 2000 iterations were made with a fixed 0.01 sec time-step.
2.5.3. UDF: User-Defined Functions
UDFs ( and ) were written in the C-programming language using Code::Blocks and were defined using DEFINE macros provided by ANSYS Fluent. Three general macros are used to develop the UDF for mushroom drying: the macro DEFINE_INIT (name, d) to specify the initial value of the parameters and variables; the macro DEFINE_ADJUST (name update, d) to update the moisture value at every time-step at each element; and the macro DEFINE_SOURCE (name, d) to specify the mass and energy source terms. The coefficients ( and ) of the term were calculated and fed to the porous zone in the cell zone conditions. Source files containing UDFs were compiled into ANSYS Fluent (the detail of UDF is given in supplementary file (available here)). Finally, the simulation results were analyzed using contours, streamlines, graphs, and animations. The simulation procedure was sketched in Figure 2.
2.6. Comparison of Simulation and Experimental Results
The simulation result was validated against the experimental data from the tray dryer. In this study, the simulation results of moisture content and drying temperature on the porous media were compared with the experimental data of the temperature distribution on the porous media and moisture removal rate from the mushroom [38].
3. Results and Discussions
3.1. Optimized Parameters for Oyster Mushroom Drying
Determination of optimal parameter values to dry mushroom using a tray drier in a hot air-drying medium with three parameters (temperature, drying airspeed, and mass loading of slice mushroom) was conducted. To achieve the desired moisture content of 10 wt%, numerical optimization was done and validated with experiments as indicated in Table 6. The optimum drying temperature, drying airspeed, and mass of the sliced mushroom were 59.81°C, 2.96 m/s, and 200 g, respectively, according to the fitted model numerical optimization performed using a design expert. This gave a moisture content of 9.99 wt% at which the major component of mushroom was well deserved, and the mushroom has a longer shelf life [30]. The interaction between the parameters of the drying process in terms of coded factors was given in the following equation:
3.2. Modelling and Source Term Determination
3.2.1. Drying Kinetics and Moisture Sorption Models
(1) Drying Kinetics Model. The drying curves of oyster mushroom ( vs. and vs. ) at different temperatures using a tray dryer are presented in Figures 3(a) and 3(b), respectively. As can be seen in Figure 3(a), the drying rate increased when drying temperatures rose from 50°C to 55°C. At higher temperatures, the moisture loss is quick, especially in the first 150 minutes (from 93 to roughly 30 wt%). According to this, there was a dropping rate period (i.e., moisture removal is fast) from the start to the first 300 minutes, and then a steady rate period (almost all the moisture is removed) was noticed till the end. A similar tendency is demonstrated in the plot of moisture ratio vs. time at each drying temperature (Figure 3(b)), where faster moisture removal is connected to a higher temperature. The models were evaluated as a function of the moisture ratio and drying time. A nonlinear regression method (implemented in MATLAB) was used to fit the calculated data. Drying kinetics model parameters and related goodness of fit are reported in Table 7 along with statistical values of and RMSE.
(a)
(b)
For 60°C, the Midilli et al. drying kinetic model is the best-fit drying kinetics model with and (Table 7). It was described by Midilli et al. as the best-fit drying model for mushrooms [33]. So, Midilli et al.’s model is the selected model for determining the source term for CFD models. The moisture ratio vs. time curve fit for the Midilli et al. model is shown in Figure 4.
(2) Moisture Sorption Isotherm Model. The moisture sorption isotherm model, which correlates and EMC of the mushroom, was evaluated by comparison with the experimental results. The experimental data at 30, 40, and 50°C and the nonlinear regression curve fitting for sorption isotherm models were studied. The constant coefficients and statistical parameters from the nonlinear regression for sorption Isotherm models are presented in Table 8. The best-fitted model is the modified Henderson sorption model with and at 40°C. The regression curve based on the modified Henderson model is shown in Figure 5.
Then, the modified Henderson model is selected to deal with the moisture sorption of oyster mushroom species, where , , and are model parameters with values -0.004215, -37.53, and 1.228, respectively, and is the water activity (), being the relative humidity.
(3) Bulk Porosity () and Effective Diameter () of Mushroom Slices. The external bulk porosity of the sample was found to be 0.388, which is 61% of the tray surface covered by the mushroom slices. The average value of of the mushroom slices was calculated from the difference of volumes of water with mushroom slice and without mushroom and is .
(4) Source Term Expression Determination. By combining the drying kinetics model (Midilli et al. model) and the moisture sorption model (modified Henderson model), equation (20) was obtained. where is the equilibrium moisture content as obtained from the moisture sorption isotherm model defined in the modified Henderson sorption isotherm model.
Equation (20) and the modified Henderson model equation were written in a C-code including the constant values and compiled in ANSYS Fluent. The momentum source term including the permeability and inertial resistance factors (, ) was determined from the Ergun equations [28] and found to be and 12924.6427 m-1, respectively. These factors were inserted in the momentum source term dialog box of ANSYS Fluent.
3.3. Simulation of Mushroom Drying in a Tray Dryer
3.3.1. Geometry and Meshing
The simulation via ANSYS Fluent of moisture removal in the mushroom drying process was performed on an Intel Core i7 computer with 3.25 CPU and 16 GB RAM with 4 parallel processes and double precision calculations for about five hours.
(1) Geometry of the Tray Dryer. The actual tray dryer was converted into a computer-designed geometry using the given dimensions of the real dryer as shown in Figure 6. To reduce the simulation time and memory requirements, half of the dryer was considered in the simulations exploiting its symmetry.
(2) Grid Generation. The symmetrical 3D flow domain was discretized into a fine unstructured computational element (small volumes) by a meshing subprogram of ANSYS software. The generated grid has 1,075,142 elements and 362,144 nodes, with a maximum aspect ratio of 9.98 and a skewness of 0.89, which indicate a good mesh quality, as reported in [39]. The generated computational grid with inflation layer in the near wall is shown in Figures 7(a) and 7(b).
3.3.2. Solution and Simulation Results
(1) Flow Convergence. Y+: wall function approach: the flow of hot air in the dryer was simulated with two turbulence models (realizable and SST). The SST model gave a maximum of 1.22 for wall , whereas the realizable k-Ꜫ model returns a maximum value of 1.53. The SST model resulted in better wall values. Therefore, the SST model has the capability of handling the flows in the near walls. The wall value for the viscous layer would be preferred less than five, better yet near to 1 [37]. In this case, both models gave a good result, and the SST model is converged fast with 2000 iterations and also selected since its value is nearer to one. Providing a suitable inflation mesh for the geometry is strongly tied to the choice of the turbulence model, and so, for a porous media, modelling with the SST turbulence model was preferred. The contour plot of wall values and the residual plot for both SST and realizable are shown in Figures 8(a), 8(b), 9(a), and 9(b).
(a)
(b)
(a)
(b)
The convergence of the numerical simulations (in the absence of the source terms) was checked by the plots of the residual values and the solution imbalance between the inlet and outlet. The residual plots and the iterative values were less than 10-6 for velocities, turbulent kinetic energy, and dissipation rate and less than 10-5 for continuity in both turbulence models, as shown in Figure 9. The mass-flux net difference between the inlet and out was very small () and less than 1%. So, this indicates that the numerical simulation is so converged.
3.4. Results Obtained with the Inclusion of the Source Term and Postprocessing Analysis
3.4.1. Temperature Distribution
From the beginning of the tray dryer till near the sample, the temperature of the drying medium is fixed at the inlet temperature (60°C). After a short while, the hot air reached the porous zone, which is at the room temperature (25°C), and exchanges heat. The hot air can hold more moisture than the moist air, and so, the moisture in the sample is removed and reached at the equilibrium moisture content with a temperature of 57°C on the sample. The porous zone and drying air reach the same temperature within five hours, and the whole fluid domain shows a uniform temperature distribution with the porous zone (Figure 10(a)). At the end of the simulations, the minimum temperature (322 K) was observed at the near wall of the dryer. The temperature distribution on the sample (porous media) is shown in Figure 10(b). The temperature in the porous zone increases from the room temperature of 330 K and then continued at a constant temperature of drying air (60°C).
(a)
(b)
3.4.2. Air Flow Predictions (Velocity Contour)
The drying air velocity distribution in the drying unit has a significant effect on moisture removal from the sample. Figure 11 shows the air velocity magnitude in the symmetry plane. The maximum velocity (17.2 m/s) was observed at the exit of the tray dryer. The velocity profile from the inlet to the whole fluid domain is uniform (equal to 3 m/s), whereas it slows down (1 m/s) near and along the porous zone. It is clearly shown that on the forwards of the porous zone, the slowest airflow has happened. This is due to the viscous and inertial resistance of the porous media (mushroom).
3.4.3. Absolute Humidity Profile
The relative humidity profile (the UDS) contour plot is shown in Figure 12. The minimum absolute humidity of air at the inlet of the dryer was observed to be 12.8%. Then, when it came to the mushroom, it increased to 13.0%, which is the maximum observed. This is due to moisture transfer from the mushroom to the flowing air.
3.4.4. Pressure Contour
The pressure contour of the airflow in the symmetry plane of the dryer is presented in Figure 13. Its distribution is uniform along the dryer except for the outlet section. The gauge static pressure at the exit of the dryer is approximately zero (equal to the pressure assumed in the outlet boundary condition). This is because the fluid velocity at the constriction is greater.
3.4.5. Moisture Removal from the Porous Media (Mushroom Drying)
At the end of the simulation, the mushroom moisture content achieves around 5.7 wt% from the initial moisture content of 93.8 wt%. At the end of the simulation, 88.1% of the moisture content of the mushroom was removed (Figure 14). This shows that the drying of mushroom was fast in the first hour, and then the constant period was observed after two and half hours. The final moisture content (5.7 wt%) observed in the simulation result was the nearest value to the moisture value found in the drying kinetics study at 60°C (5.21 wt%).
3.5. Validation of Simulation Results with the Experimental Value
The validation of the numerical results was done against the drying temperature and the moisture removal from the sample. The comparison of drying moisture content measured in the experiments with the CFD simulation results with drying time, and experimental vs. simulation results of moisture content are shown in Figures 15(a)–15(c). In Figure 15(a), it can reasonably be stated that the experimental result of the moisture content measured was well matched with the volume-averaged simulation result of the moisture content. Besides, the value of 0.9906 is a good indication that both simulation and experimental results were more or less similar to each other as illustrated in Figure 15(c). In a similar fashion, the distribution of drying temperature in the sample found during the experiment and simulation had a similar pattern as demonstrated in Figure 15(b). It is evident that the simulation of mushroom drying explains pretty well. The fitting of simulation and experimental results yielded value of 0.926.
(a)
(b)
(c)
However, a little deviation was observed in the volume average of simulated drying temperature and experimental data as well as in the moisture removal comparison as depicted in the plot (Figure 15(b)). This would be due to the loss of heat while measuring the temperature in the experiment and instrumental errors.
4. Conclusions
The drying model of mushroom drying and related parameters of the drying process were optimized using Design-Expert and found that 60°C drying temperature, 3 m/s air speed, and 200 g mass loading are the optimal values. At these optimum drying conditions, the moisture content of the mushroom sample was reduced from 93.8 to 5.7 wt% using a tray dryer. The drying kinetics analysis shows that Midilli et al.’s kinetic model was the best-fit model for oyster mushroom drying. The modified Henderson sorption’s isotherm model was the best-fit model that relates of mushroom with its water activity. In combination with the kinetics and sorption models and applying the conservation equations of mass, momentum, and energy, a CFD-based model of a tray dryer for mushroom drying was developed. The source terms for the mass and heat were written in C-programs and compiled for the ANSYS Fluent solver. The drying process of mushrooms in a tray dryer was simulated in 3D. The results of the simulation (moisture content and drying temperature on the porous zone) were compared with the experimental results of moisture content and drying temperature, showing a good agreement with values of 0.99 and 0.93, respectively.
Generally, this work revealed that at the optimum drying conditions, CFD-based modelling and simulation are effective tools for describing mushroom or all other fruits drying in a tray dryer involving a continuous transfer of mass, momentum, and heat in a drying fluid flow. This is very important for many food industries and research institutes (laboratories) since it reduces the number of experiments which lowers operating costs and also saves more time. The mushrooms were sliced and taken as flat in this study, but some are spherical. To the best of our knowledge, dealing with simulations of this type has not yet been studied and could be considered in future work. Moreover, the physical parameters of the mushroom (thermal conductivity, density, and heat capacity) are all taken as constant. For instance, these parameters could be assumed as a function of moisture content and temperature to lower the deviation observed in the validation.
Nomenclature
| AH: | Absolute humidity |
| : | Water activity |
| hr., min, s: | Hour, minute, second, respectively |
| : | Time |
| : | Turbulent kinetic energy |
| : | Moisture content |
| : | Moisture ratio |
| : | Moisture content at time t |
| : | Initial moisture content |
| : | Equilibrium moisture content |
| : | Saturation pressure |
| : | Relative humidity |
| : | Absolute temperature |
| UDF/UDS: | User-defined-function/user-defined-scalars |
| : | Weight |
| : | Coefficient of determination |
| : | Effective moisture diffusivity |
| : | Effective diameter |
| : | Density of the fluid |
| : | Velocity vector |
| : | Dynamic viscosity |
| : | Specific heat capacity at constant pressure |
| , , : | Source term for mass, momentum, and energy equation |
| : | Fluid density |
| : | Any variant (velocity, components, and enthalpy) |
| : | Source term of any property variant |
| : | Permeability of the medium |
| : | The pressure-jump coefficient |
| : | Wall functions or wall distance estimation |
| 3D; 2D: | Three dimensional; two dimensional. |
Data Availability
The data used to support the findings of this study are included in the article and supplementary file. Anyone looking for any data can contact the corresponding author or first author upon reasonable request.
Conflicts of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Authors’ Contributions
Talbachew Tadesse Nadew was responsible for the conceptualization, methodology, formal analysis, investigation, writing—original draft preparation, data curation reviewing, and C-coding. Tsegaye Sissay Tedila was responsible for the writing—review and supervision, visualization, and editing. Petros Demissie Tegenaw was responsible for the software, validation, visualization, reviewing, and supervision. All authors have read and agreed to publish this version of the manuscript.
Acknowledgments
The authors would like to thank the Department of Chemical Engineering, College of Food and Chemical Engineering, Wollo University, Kombolcha Institute of Technology, Kombolcha, Ethiopia, and Addis Ababa Science Technology University, Addis Ababa, Ethiopia, for their collaboration during the laboratory work.
Supplementary Materials
UDF is a C-code function that can be dynamically loaded with the ANSYS Fluent solver to enhance moisture transport phenomena. The C-code written on Code:: Blocks include the DEFINE macros, flow variable macros, user-defined scalar and memory macros, and looping macros. The definition of constants and initial values was defined using DEFINE_INIT macros. The mushroom moisture content update at each time step for each computational cell according to the temperature and absolute humidity of intergranular air was defined using DEFINE_ADJUST macros. The mass and energy source term calculation and return to the solver were introduced using DEFINE_SOURCE macros. The solution iteration loop begins with the execution of ADJUST UDFs. Then, ANSYS Fluent solves the governing equations of continuity, momentum, and energy transport in a coupled fashion. (Supplementary Materials)