Study on Sublimation Drying of Carrot and Simulation by Using Cellular Automata
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials
2.2. Experimental Procedure
2.3. Model of Sublimation Drying
- The material itself is isotropic, featuring uniform heat and mass transfer in the frozen region.
- The change in the volume of the material during sublimation is ignored.
- The sublimation interface exists between the dried region and the frozen region, which is continuous and infinitesimal in thickness.
- The concentration of water vapor is in equilibrium with ice at the sublimation interface.
- The porous matrix formed by ice sublimation is rigid in structure, and the matrix is permeable, which enables the vapor flux to circulate.
2.3.1. Governing Equations
2.3.2. The Initial and Boundary Conditions
2.4. Cellular Automata Model
3. Results and Discussion
3.1. Simulation Results
3.2. Comparison of Moisture Content Curve
3.3. Comparison of Temperature Curve
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
constant dependent only upon the structure of the porous medium and giving relative D’Arcy flow permeability | |
constant dependent only upon the structure of the porous medium and giving relative Knudsen flow permeability | |
constant dependent only upon the structure of the porous medium and giving the ratio of bulk diffusivity within the porous medium to the free gas bulk diffusivity | |
specific heat capacity at constant pressure | |
free gas mutual diffusivity in a binary mixture of water vapor and inert gas | |
F | view factor for radiative heat transfer |
geometric shape of the moving interface, a function of time and radial distance | |
convective heat transfer coefficient | |
k | thermal conductivity |
bulk diffusivity constant | |
self-diffusivity constant | |
knudsen diffusivity for inert gas | |
mean Knudsen diffusivity for binary gas mixture | |
knudsen diffusivity for water vapor | |
L | thickness of sample |
M | molecular weight |
N | mass flux |
P | partial pressure in the dried layer |
Q | heat flux |
r | space coordinate of radial distance |
R | radius of sample |
ideal gas constant | |
t | drying time |
T | temperature |
v | velocity of moving interface |
z | space coordinate of distance along the thickness of the sample |
Z | value of z at the moving interface |
Greek letters | |
thermal diffusivity | |
heat of sublimation of ice (J/kg) | |
emissivity of the material surface. | |
porosity of sample | |
viscosity of vapor phase in pores of the dried layer | |
density | |
Stefan–Boltzmann constant | |
Subscripts | |
e | effective |
I | frozen region |
II | dried region |
in | inert gas |
lp | lower heating plate |
r | r direction |
up | upper heating plate |
w | water vapor |
z | z direction |
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Parameters | Value | Unit |
---|---|---|
7.219 × 10−15 | m2 | |
3.85583 × 10−4 | m | |
0.921 | – | |
m2/s | ||
) | m4/N·s | |
m2/s | ||
8.729 × 10−7(T0 + Tint)2.334 | kg/ms3 | |
m2/s | ||
m2/s | ||
m2/s | ||
[18.4858(T1.5/(T + 650))] | kg/ms | |
L | 10 | mm |
R | 40 | mm |
243.15 | K | |
303.15 | K | |
263.15 | K | |
303.15 | K | |
1000 | kg/m3 | |
236 | kg/m3 | |
388 | kg/m3 | |
1616.6 | J/(kg∙K) | |
2590 | J/(kg∙K) | |
1930 | J/(kg∙K) | |
2.68 | W/(m∙K) | |
0.18 | W/(m∙K) | |
680[12.98 × 10−8P + 39.806 × 10−6] | W/(m∙K) | |
0.581 | – | |
18 | g/mol | |
28 | g/mol | |
1.07 | Pa | |
24 | Pa | |
2.7912 × 103 | kJ/kg | |
8.314 | J/(mol∙K) | |
5.67 × 10−8 | W/(m2∙K4) | |
0.85 | – | |
0.75 | – | |
0.795 | – | |
0.00809 | – | |
26 | W/(m2∙K) |
Cell Status | Symbols | Description |
---|---|---|
Plate | P (gray) | For fixed cells, heat exchange occurs only with the bottom layer of the carrot. |
Frozen State | FS (yellow) | The initial state of the carrot cells, with the level of water content indicated by the number of blue dots. |
Dried State | DS (red) | As the moisture content decreases below a certain threshold, the cell transitions into a dried state, and at this point, the number of blue dots in the cell is 0. |
Air | Air (white) | Referring to the air within the drying chamber, heat exchange transpires between the air and the material through radiation and convective mechanisms. |
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Shao, J.; Jiao, F.; Nie, L.; Wang, Y.; Du, Y.; Liu, Z. Study on Sublimation Drying of Carrot and Simulation by Using Cellular Automata. Processes 2023, 11, 2507. https://doi.org/10.3390/pr11082507
Shao J, Jiao F, Nie L, Wang Y, Du Y, Liu Z. Study on Sublimation Drying of Carrot and Simulation by Using Cellular Automata. Processes. 2023; 11(8):2507. https://doi.org/10.3390/pr11082507
Chicago/Turabian StyleShao, Jiayuan, Fan Jiao, Lili Nie, Ying Wang, Yihan Du, and Zhenyu Liu. 2023. "Study on Sublimation Drying of Carrot and Simulation by Using Cellular Automata" Processes 11, no. 8: 2507. https://doi.org/10.3390/pr11082507