Simulation and experimental on the quick-freezing of diced mango by dry ice spray

: In order to improve the quality of quick-frozen diced mango, a cylindrical quick-frozen container with dry ice spray is designed, the temperature field and velocity field of diced mango sprayed by dry ice in quick-freezing tank are simulated by COMSOL Multiphysics. The effects of different inlet velocities (0.15, 0.20, 0.25, 0.30, 0.35 and 0.40m/s), on the quick-freezing process of diced mango are studied. The results show that with the increase of the inlet velocity of dry ice, the time for diced mango to meet the requirements of quick freezing is continuously shortened, and the outlet solid fraction fluctuates within a certain range. When the inlet velocity is 0.25m/s, the inlet radius is 15mm and the size of diced mango is 10mm, the quick-freezing effect is the best. By the experimental verification, the average errors of surface temperature and core temperature of diced mango to meet the requirements of quick freezing are 3.9% and 3.8% respectively. The results lay a foundation for the popularization and application of dry ice spray quick frozen diced mango.


Introduction
Mango is a world-famous tropical fruit, known as the "king of tropical fruits".Mature mango is rich in nutrition, rich in protein, minerals, vitamins, carotenoids and other nutrients [1] .However, mangoes contain a lot of water and sugar, which are perishable after picking and have a relatively short storage life [2] .In order to extend the shelf life of mango and maintain its original quality attributes, quick freezing is the most commonly used method at present.A spray rapid freezing device using liquid N2 or CO2 to directly spray and freeze appears [3] .Cheng [4,5] compared and analyzed the application of numerical simulation technology in food from different aspects, providing a reference for the application of this technology in food freezing.Tan [6] used high-pressure CO2 technology to quickly freeze the agaricus bisporus and found that the pressure relief time would affect the quality of the agaricus bisporus.Li [7] have done a lot of work in spray cooling and simulation experiments, providing theoretical basis for further research.Many foreign scholars [8,9] studied the liquid nitrogen spray fluidization quick freezing system and its freezing performance, and concluded that the main disadvantage of liquid nitrogen quick freezing is the high operating cost.
The natural working medium, dry ice, namely solid carbon dioxide, has a boiling point of -78.5℃ and has a huge latent heat of sublimation, which can take away a large amount of heat in a very short period of time, thus meeting the requirements of quick freezing of food.In this paper, diced mango were sprayed with dry ice for quick freezing, and a quick freezing tank for diced mango was designed.The temperature field and velocity field of the process of quick freezing diced mango in the quick freezing tank by dry ice spraying were simulated by COMSOL Multiphysics.The simulation results of dry ice spray quick freezing mango were analyzed and compared, and the experimental verification was carried out to obtain the best structure and thermal parameters.It provides a theoretical basis for further research on dry ice quick-frozen mango.

Physical model
The size of quick freezing tank is 260mm×430mm (diameter × high), with 4 material trays inside, each of which has a diameter of 200mm, a thickness of 2mm and a spacing of 80mm.The left side of the quick freezing tank is provided with four dry ice inlets and the right side is provided with one carbon dioxide gas outlet (as shown in Fig 1).The inlet radius of dry ice is set to 10, 12, 15, 18 and 20mm respectively, and the outlet radius is set to 30mm.The size of diced mango is set as the cube with the edge length of 5mm, 10mm and 15mm, and the spacing of each diced mango is 10mm.The parameters and characteristics of materials in the model are shown in Table 1.

Calculation method
Assuming that the fluid is incompressible, the physical property of the fluid is constant, there is no internal heat source, and the heat dissipation due to viscous dissipation is negligible, the heat exchange process conforms to the third boundary condition [10,11] ; The diced mango sprayed by dry ice particles and the material tray are forced convection heat exchange.
The heat transfer part of the model is based on the energy conservation equation Model fluid heat transfer part: t The phase change reference equation is as follows: The phase change material parameters of the model are shown in Table 2.The formula symbols are explained in Table 4.

Influence of inlet velocity of dry ice
The diced mango is pre-cooled to 273.15K before quick freezing, and the inlet velocity of dry ice in the quick freezing tank is set to 0.15, 0.20, 0.25, 0.30, 0.35, and 0.40m/s, respectively.It can be observed that within 20 minutes, the surface and core temperatures of the quick-frozen diced mango reach -35℃ and -18℃, respectively.The surface and core temperatures required to meet the quick freezing requirements were simulated and calculated using COMSOL software, as shown in Table 3.

Discussion and Analysis
The results indicate that under the condition of an inlet radius of 15mm, increasing the inlet velocity leads to a decrease in the core temperature of diced mango to -18℃ and the surface temperature to -35℃.In addition, the time required for the diced mango to pass through the maximum ice crystal formation zone decreases.The solid fraction at the outlet fluctuates within a certain range.
Excessive freezing rate can cause the diced mango to crack at low temperatures, affecting the quality and appearance of the mango.Lower solid fraction at the outlet corresponds to a lower amount of dry ice inside the quick freezing tank, resulting in a more uniform temperature distribution when the diced mango meets the quick freezing requirements.It also reduces operating costs.Taking into account these factors, it can be concluded that an inlet velocity of 0.25m/s achieves the optimal freezing effect.The simulation results of the temperature field and velocity field are shown in It can be seen from Figure 4 that at the same time, the core temperature of the second layer of diced mango is relatively high, and the core temperature of the fourth layer of diced mango is relatively low, and the quick freezing effect of diced mango in the middle area of each layer is better than that of both sides.The reason is that after the dry ice is injected into the quick freezing tank, there is a core area with uniform velocity in the core of the jet.With the forward movement of the fluid, the core area continues to shrink, and finally the velocity section shows a distribution of large in the middle and gradually decreasing at the edge.After the dry ice reaches the inner wall of the quick freezing tank, it spreads around along the inner wall to form a wall attached jet zone.After the dry ice reaches the wall surface, it will generate disturbance, and the local heat transfer intensity of the impacted wall surface is high, while the other areas are relatively low.The flow and disturbance of each layer of dry ice are different, resulting in different amount of dry ice contacted by each layer of diced mango, so the temperature change is also different.The quick freezing time is 105s, and the core temperature of all diced mango has dropped below -18℃, which meets the requirements of quick freezing.Therefore, an inlet velocity of 0.25m/s is the better choice for the quick freezing model, considering an inlet radius of 15mm and diced mango with an edge length of 10mm.

Dry ice spraying system
The schematic diagram of dry ice spraying system is shown in Fig 5, which is mainly composed of carbon dioxide cylinder, pressure reducing valve, flow regulating valve, flowmeter, dry ice nozzle, quick freezing tank and data acquisition system.To increase the percentage of dry ice particles obtained, the carbon dioxide cylinder is inverted.Open the valve of the carbon dioxide cylinder, the liquid carbon dioxide flows out of the cylinder, flows through the pressure reducing valve, the temperature drops sharply and reaches the gas-solid boundary, forming dry ice particles, which can be explained by the Joule Thomson expansion effect, and then flows through the flow regulating valve and flowmeter to the dry ice nozzle, which is connected to the inlet of the quick freezing tank, and the dry ice particles enter the quick freezing tank through the nozzle, sublimation takes away the heat of the mango [12] , causing it to freeze.The carbon dioxide gas generated is discharged from the outlet of the quick freezing tank.

Conclusion
By the numerical simulation and experiment of dry ice jet quick freezing of diced mango and the comparison with the existing quick freezing methods of diced mango, the following conclusions can be drawn: (1) By setting different inlet velocity, it can be seen that with the increase of inlet velocity, the time for diced mango to meet the requirements of quick freezing is continuously shortened, and the outlet solid fraction fluctuates within a certain range.When the inlet velocity is 0.25m/s and the inlet radius is 15mm, the time to pass through the maximum ice crystal formation zone is shorter, the solid phase fraction at the outlet is the lowest, the dry ice is less accumulated in the quick freezing tank, the utilization rate is higher, the temperature distribution of diced mango is uniform, and the quick freezing quality is better.
(2) By experimental verification, the average errors of the core temperature and surface temperature of diced mango meeting the requirements of quick freezing are 3.8% and 3.9% from the simulation results respectively.The error is caused by the uneven size of the experimental diced mango, the insertion position error of the thermocouple and the interference of the shelf of the material tray with the dry ice turbulence.

Fig 3 .
Fig 3. Simulation results of temperature field and velocity field for t=105s.(a) Surface temperature of diced mango; (b) Core temperature of diced mango; (c) Streamline trend and fluid temperature.

3. 2 .Figure 4 3 BIOFigure 4 .
Figure4shows the change of core temperature of each layer of diced mango when the inlet radius is 15mm, the Fig 3, where Fig 3c depicts the variation trend and temperature distribution of the fluid inside the quick freezing tank.

Fig 5 .
Fig 5. Schematic diagram of dry ice spraying system

2 k
Thermal conductivity of phase change materials, W/(m• K) Q Enthalpy of dry ice, J/kg Qp Internal energy of dry ice, J/kg Qvd Kinetic energy of dry ice,

Table 1 .
Parameters of the selected materials for the model CP (T), Rho (Pa, T), K (T) and eta (T) in the table are all functions of the properties of the selected materials, and there are no specific values. *

Table 3 .
Comparison of calculation data for different inlet velocity

1 ) Time for the surface of diced mango to drop to -35℃/s Time for the core of diced mango to drop to -18℃/s Time to pass through the maximum ice crystal formation zone/s
The entrance radius is 15mm, and the edge length of diced mango is 10mm.