Experimental and Numerical Study of a Turbulent Air-Drying Process for an Ellipsoidal Fruit with Volume Changes
Abstract
:1. Introduction
2. Materials and Methods
2.1. Raw Material
2.2. Drying Experiments
2.3. Volume Determination
2.4. Image Capture
2.5. Mathematical Modeling
2.5.1. Mathematical Model for Airflow in the Dryer
2.5.2. Mathematical Model for Fruit in the Dryer
2.5.3. Initial and Boundary Conditions
2.6. Numerical Procedure and Grid Selection
2.7. Energetic Analysis
Energy Consumption and Efficiency
3. Results and Discussions
3.1. Experimental Results
3.1.1. Fruit Characterization and Volume Changes
3.1.2. Drying Rates
3.2. Numerical Simulation
3.2.1. Shrinkage Procedure for the Fruit
3.2.2. Pre-Exponential Factor and Calculation Algorithm
3.2.3. Comparison between Experimental and Calculated Drying Curves
3.3. Energy Consumption Results
4. Conclusions
- Convective drying with air at different temperatures, in the range between 328 K (55 °C) and 358 K (85 °C), shows that the volume changes of P. peruviana are similar. It also shows that the volume loss is highly anisotropic, with the shrinkage occurring essentially in a direction aligned with the minor semi-axis of the ellipsoidal fruit. This anisotropic behavior can be attributable to the particular structural characteristics of the fruit studied, and it is a factor that must be taken into account when studying the convective drying of fruits.
- In the drying process, shrinkage can occur in one or more preferential directions and not symmetrically as is considered in most of the published research. The image capture procedure proposed in this work allowed the incorporation of experimental data into the numerical model that improved the accuracy of the simulations.
- A 3D computational simulation of the conjugate heat and mass transfer in a dryer and its load, which also includes the fluid dynamics of the drying air, constitutes a useful tool for analyzing the process, and provides data that would be very difficult to obtain experimentally, such as the internal temperature in the dried material.
- To improve the accuracy of such a kind of simulations, it is important to consider the shrinkage of the material. Furthermore, it would be advisable to assign more importance to the characteristic mode of deformation during the drying. Until now, this anisotropy has not been included in models. This work shows that the anisotropic shrinkage has a significant impact on the accuracy of a numerical simulation.
- More research can be done along the lines introduced in this work to characterize and calibrate models of anisotropic shrinkage of other materials.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
A | Arrhenius factor [m2 s−1] | Special characters | |
C | Moisture [kg kg−1] (w.b.) | ρ | Density [kg m−3] |
Average moisture in fruit [kg kg−1] (w.b.) | Δ | Difference | |
Cp | Specific heat [J kg−1 K−1] | Γ | Transport general diffusion eq. |
D | Moisture diffusion coeff. [m2 s−1] | α | Thermal diffusivity [m2 s−1] |
d | Load density [kg m−2] | μ | Dynamic viscosity [Pa s] |
Ea | Activation energy [kJ mol−1] | ν | Kinematic viscosity [m2 s−1] |
Et | Total energy consumption [kJ kg−1] | κ | Turbulent kinetic energy [m2 s−2] |
k | Thermal conductivity [W m−1 K−1] | ε | Turb. kinetic energy dissipation [m2 s−3] |
Lc | Characteristic length (0.5 [m]) | φ | General transported variable |
Pr | Prandtl number | ||
R | Ideal gas constant [kJ K−1 mol−1] | ||
RE | Relative error [%] | Subscripts | |
Sc | Schmidt number | a | Air |
Sc | Independent source term (Equation (21)) | exp | Experimental value |
Sp | Dependent source term (Equation (21)) | f | Fruit |
t | Time [s] | fg | Fluid to gas |
T | Temperature [K] | in | Inlet of the dryer |
u | Velocity vector [m s−1] | initial | Initial value |
u | x-component of velocity [m s−1] | out | Out of the dryer |
v | y-component of velocity [m s−1] | T | Temperature |
w | z-component of velocity [m s−1] |
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T (K) | Polynomial Coefficients | ||||||
---|---|---|---|---|---|---|---|
a | b | c | d | e | f | g | |
328 | 1.42 × 10−6 | 1.12 × 10−4 | −3.88 × 10−3 | −1.50 × 10−3 | 3.74 × 10−3 | −3.58 × 10−3 | 1.21 × 10−3 |
338 | 4.20 × 10−5 | −8.32 × 10−4 | 6.63 × 10−3 | −2.24 × 10−2 | 3.67 × 10−2 | −2.91 × 10−2 | 8.93 × 10−3 |
348 | 1.73 × 10−5 | −4.90 × 10−4 | 5.17 × 10−3 | −2.00 × 10−2 | 3.54 × 10−2 | −2.98 × 10−2 | 9.63 × 10−3 |
358 | 1.62 × 10−5 | −1.10 × 10−4 | 1.35 × 10−3 | −5.85 × 10−3 | 1.11 × 10−2 | −9.77 × 10−3 | 3.24 × 10−3 |
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Zambra, C.E.; Puente-Díaz, L.; Ah-Hen, K.; Rosales, C.; Hernandez, D.; Lemus-Mondaca, R. Experimental and Numerical Study of a Turbulent Air-Drying Process for an Ellipsoidal Fruit with Volume Changes. Foods 2022, 11, 1880. https://doi.org/10.3390/foods11131880
Zambra CE, Puente-Díaz L, Ah-Hen K, Rosales C, Hernandez D, Lemus-Mondaca R. Experimental and Numerical Study of a Turbulent Air-Drying Process for an Ellipsoidal Fruit with Volume Changes. Foods. 2022; 11(13):1880. https://doi.org/10.3390/foods11131880
Chicago/Turabian StyleZambra, Carlos E., Luis Puente-Díaz, Kong Ah-Hen, Carlos Rosales, Diógenes Hernandez, and Roberto Lemus-Mondaca. 2022. "Experimental and Numerical Study of a Turbulent Air-Drying Process for an Ellipsoidal Fruit with Volume Changes" Foods 11, no. 13: 1880. https://doi.org/10.3390/foods11131880
APA StyleZambra, C. E., Puente-Díaz, L., Ah-Hen, K., Rosales, C., Hernandez, D., & Lemus-Mondaca, R. (2022). Experimental and Numerical Study of a Turbulent Air-Drying Process for an Ellipsoidal Fruit with Volume Changes. Foods, 11(13), 1880. https://doi.org/10.3390/foods11131880