https://orcid.org/0009-0007-2523-1576
Figures
Abstract
Aiming at the independent research and development of a simulated high-level waste liquid spray calcination transformation treatment test device, a three-dimensional multi-physical field model of spray calcination was established by means of finite element analysis method. In this paper, the simulated high-level waste liquid is a mixed solution of nitrate solution and sucrose. The main chemical components of nitrate dissolution are HNO3 and NaNO3. The process of evaporation and calcination of high-level waste liquid to form oxides is also called the pretreatment of high-level waste liquid or the conversion of high-level waste liquid. In this experiment, the atomized droplets sprayed at high speed are evaporated, dried and calcined in turn in the calciner to obtain the calcined product. The distribution law of temperature flow field and chemical reaction state and results inside the test device were revealed by simulation calculation. The results show that under the condition of multi-physical field coupling, the chemical reaction temperature has an effect on the yield of the product. The temperature is positively correlated with the product concentration, and the effect of temperature on the yield of NO2 is greater than that of Na2O. At the same time, in this chemical reaction, the concentration of reactants (NaNO3 and HNO3) had a positive correlation with the concentration of main products (NO2 and Na2O). However, the rate of increase in the concentration of the main products (NO2 and Na2O) decreased with the increase of the concentration of the reactants (NaNO3 and HNO3).
Citation: CHENG Y, LI K, JIA X, YE G (2024) Multi-physical field simulation calculation and analysis of simulated high-level waste liquid spray calcination. PLoS ONE 19(8): e0308145. https://doi.org/10.1371/journal.pone.0308145
Editor: Niravkumar Joshi, Federal University of ABC, BRAZIL
Received: May 8, 2024; Accepted: July 17, 2024; Published: August 9, 2024
Copyright: © 2024 CHENG et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the manuscript and its Supporting Information files.
Funding: This study was supported by Fundamental Research Funds for the Central Universities form of a grant awarded to YC (JD2423). The specific roles of this author are articulated in the ‘author contributions’ section. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
1. Introduction
The high-level waste liquid produced after spent fuel treatment [1, 2] still contains more than 99% of fission products and minor actinides in spent fuel [3]. High-level liquid waste has the characteristics of complex composition, strong radioactivity, strong corrosion and strong toxicity [4], and its treatment and disposal has always been one of the key and difficult problems in the nuclear industry. At present, the widely recognized and relatively mature technology in the world is the glass solidification technology of high-level liquid waste [3, 5–7]. China Institute of Atomic Energy has made relevant research and development on the two-step cold crucible glass curing technology [8, 9]. The transformation technology of high-level waste liquid described in this paper is the first step of the two-step cold crucible glass curing technology. Specifically, it refers to the evaporation and calcination of high-level waste liquid under high temperature conditions, and finally the formation of solid calcinations products [10].
At present, there are many methods of independent pretreatment of high-level liquid waste calcination process, such as tank calcination method, rotary furnace calcination method, fluidized bed calcination method, microwave calcination method and spray calcination method [11]. The spray calcination equipment has the advantages of simple structure, convenient operation and maintenance, and high calcination efficiency (the high-level waste liquid can be directly dried into powder, and the drying process is rapid). Based on the spray calcination method, American researchers have developed a spray-type high-level waste liquid transformation experimental device for waste liquid transformation treatment [12]. Under the background of the international verification of this process flow, based on the spray calcination method, this paper independently developed a simulated high-level liquid waste spray calcination transformation treatment test device for simulated high-level liquid waste transformation treatment experimental research, which provides a good research platform for this treatment technology.
Over the years, domestic and foreign scholars have carried out a large number of experiments and numerical simulations on spray drying technology. Bass Ler [13] proposed the spray drying method to prepare milk powder. Wu and Liu [14] used the strong oscillating flow field generated by the pulse combustor to spray dry the sodium chloride solution, and used the computational fluid dynamics method to simulate the momentum, heat and mass transfer processes of the gas phase and the particle phase, and discussed the influence of the airflow pulsation frequency on the drying process. Oluwafemi et al. [15] deeply explored the local characteristics of evaporation rate at the interface between droplet and air by means of single droplet drying (SDD), and successfully obtained the distribution information of temperature and evaporation rate inside droplet. Roman et al. [16] deeply analyzed the correlation between the evaporation rate of atomized droplets and the temperature and velocity of airflow through fluorescence optical diagnostic technology. In addition, numerical simulation software (CFD) has shown great ability in describing the evaporation process of droplet group, which has been applied to the study of wastewater evaporation by researchers, and remarkable progress has been made [17, 18]. The problem of traditional simulation is that the heat transfer calculation is calculated for a single flow field, and the coupling of chemical reaction is not considered. Therefore, this paper considers the coupling effect of flow heat transfer and chemical reaction simulation.
2. Numerical calculation method and calculation model
2. 1 Flow field model
The ’turbulence, k-ε’ model is suitable for fully turbulent, medium to high pressure range and high viscosity fluid models. This model is a turbulence model. The ’turbulence, k-ε’ model is widely used in industry because of its wide applicability, economy and reasonable accuracy. For most applications, the k-ε model can provide stable and reliable simulation results. In engineering calculation, the calculation amount of this model is moderate, and the calculation accuracy and convergence are reasonable. After the above analysis, the ’turbulence, k-ε’ model is selected.
The ’turbulent, k-ε’ model is used to simulate the fluid motion inside the test device. In addition, considering that the flow rate of the liquid inside the test device is relatively low and the pressure change is relatively small, it is regarded as an incompressible Newtonian fluid. Because the overall fluid flow process inside the device is the flow provided by the negative pressure at the outlet, the influence of gravity can be ignored. The mathematical model is described as follows:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
In the formula: u is the fluid velocity; p is the fluid pressure, Pa; Iis the unit matrix; K is the expansion of stress term; F is the volume force vector; k is turbulent kinetic energy; ε is the turbulent dissipation rate; μT is turbulent viscosity; Pk is the expansion of the generating term; σk, σε, Cμ, Cε1 and Cε2 are all empirical constants. ▽ is Hamiltonian operator; u = (ux, uy, uz), ux, uy, uz are the x, y, z axis components of the three-dimensional space vector u.
2. 2 Thermal model
The ’solid + fluid heat transfer model’ is used to simulate heat transfer through conduction, convection and radiation in solids and fluids. During the spray calcination process, the heat exchange between the droplet (fluid) and the hot surface (solid) involves two main mechanisms: heat conduction and heat convection. This is consistent with the heat transfer mechanism described by the solid + fluid heat transfer model. Thermal conduction occurs inside the solid or between solids, while thermal convection occurs between the solid surface and the contact fluid. Therefore, the ’solid + fluid heat transfer model’ is adopted.
The wall of the calciner body of the equipment provides a high-temperature heat source. There is heat exchange between the calciner, the product hopper and the filter, and there is heat exchange between the injected feed liquid and the test device. Because there are both solid and fluid in the whole model domain, the ’solid + fluid heat transfer’ model is used to simulate the heat transfer process. The transient mathematical model is described as:
(8)
(9)
In the formula: Cp is the constant pressure heat capacity, J/(kg·K); q is the heat flux, W/m2; k is the thermal conductivity, W/(m·K); Q is the heat source term; Qted is thermoelastic damping; T is temperature, K.
2. 3 Reaction model
The transport of dilute substances (tds) is used to calculate the concentration field of dilute solutes in solvents. The transport and reaction of substances dissolved in gas, liquid or solid can be processed using this interface. The spray calcination model in this paper can simulate the concentration of reactants and products at different temperatures through the dilute material transfer module.
The transfer and reaction in the reaction channel are described by the mass conservation given by the steady-state convection-diffusion equation:
(10)
In the formula: Di denotes the diffusion coefficient, m2/s; ci is the substance concentration, mol/m3; u is the velocity vector, m/s. Ri (mol/(m3·s)) is equivalent to the reaction rate expression of the substance.
3. Multi-physical field coupling calculation model of spray calcination
3. 1 Three-dimensional model
The model described in this paper is a high-level waste liquid spray calcination transformation treatment test device, which is mainly composed of a feeding system, a spray calcination system, an exhaust gas filtration system and a product collection system. The process diagram is shown in Fig 1. Firstly, the waste liquid is sprayed into the furnace chamber from the top of the calcination chamber in the form of droplets by the atomization device. The droplets are evaporated, dried and calcined vertically through the calcination chamber. At the same time, the intermittent vibration of the vibrator installed on the outside of the furnace can reduce the deposition and scaling of the material on the surface of the furnace. The calcined product falls into the hopper for storage or direct glass curing. The steam produced in the calcination process is filtered by the tail gas filter. The filtered tail gas enters the tail gas purification treatment system for washing, absorption and other operations, and finally discharges to the atmosphere after meeting the emission standards. In order to stop the filter blockage and reduce the filtration pressure difference, the tail gas filter needs to have a hot air reverse blowing function to blow the calcined product attached to the filter back to the product receiving hopper.
The simulation object of this part is the main part of the spray calciner. According to the design size of the industrial model, a multi-physical field coupling calculation area including the spray calcination system, the product hopper and the exhaust gas filtration system is established, as shown in Fig 2. The tetrahedral element is used to mesh the geometric model of the whole fluid calculation domain, and the grid independence analysis is carried out. The total number of grid vertices is 7407, the number of grids is 21050, and the average unit mass is 0.6244. The grid quality is good, and the grid division of the multi-physical field coupling calculation area is shown in Fig 3.
3. 2 Boundary condition setting
In the simulation, the ’turbulent, k-ε’ model is used to simulate the internal flow field, and the spray point is used as the ’inlet’ boundary condition. The inlet normal inflow velocity is 3m/s, the turbulence intensity is specified as medium (0.5), and there is no slip on the inner wall. The filter outlet is used as the ’outlet’ boundary condition. The filter outlet is provided with negative pressure by the fan during the actual operation, and the boundary condition of the outlet is negative pressure -2000 Pa.
In the simulation, the ’solid + fluid heat transfer’ model is used to simulate the internal thermal field. All domains are defined as ’fluid’, and the initial temperature of the internal environment of the equipment is set to 293.15 K. Using the ’inflow’ boundary condition, the nozzle injection temperature is set to 293.15 K; using the ’heat source’ boundary condition, the calciner, product hopper and filter area are set as generalized sources; using the ’temperature 1’ boundary condition, the calcination furnace area is set to 400–800°C; using the ’temperature 2’ boundary condition, the temperature of the product hopper and filter area is set to 200°C.
In the simulation, the ’dilute matter transfer’ model is used to simulate the internal chemical reaction, and the simulated chemical reaction equations are shown in (11) and (12). The initial concentration of HNO3 and NaNO3 in the calcination furnace and product hopper was set as 48mol/m3. Using the ’inflow’ boundary condition, the concentration of C12H22O11 was set to 1mol/m3. Using the ’reaction’ boundary condition, the reaction rate Ri is defined to be related to the reaction temperature. Using the ’distribution condition’ boundary condition, the distribution coefficients of NO2, CO2 and H2O are set to be 1, the region is the interface between the filter inlet and the product hopper, and the distribution coefficients of the remaining substances are 0.
3. 3 Calculation conditions
According to the actual operation of the test device, the calculation conditions are set. Temperature is one of the important factors affecting the chemical reaction rate and product yield. In the simulation, the influence of calcination furnace temperature on chemical reaction is studied. The temperature variable is set to 400–800°C. The effects of the concentration of reactants (NaNO3 and HNO3) on the concentration of main products (NO2 and Na2O) were investigated. The concentrations of reactants (NaNO3 and HNO3) were set to 12mol/m3, 24mol/m3, 36mol/m3, 48mol/m3 and 60mol/m3, respectively. The boundary conditions are shown in Table 1.
4. Numerical calculation results experimental verification
The simulated high-level waste liquid spray calcination transformation treatment test device is shown in Fig 4. The central control multi-function display screen can display the numerical results of heating temperature measurement. The specific value of temperature changing with time is shown in Table 2. Through experimental verification, the error between the temperature test results and the calculation results is less than 10%, indicating the accuracy of the numerical calculation results.
5. Analysis of numerical results
5. 1 Analysis of flow field temperature field
The flow field and temperature field were analyzed by taking the calculation condition of ’sucrose concentration of 1mol/m3, NaNO3 and HNO3 concentration of 48mol/m3, calcination furnace temperature of 800°C as an example.
Fig 5 is the internal flow chart of the simulation model. The velocity cloud diagram clearly reflects the velocity distribution and spray shape of the liquid injected from the nozzle at the maximum speed of 3m/s. The inlet velocity is the largest, and as the injection distance increases, the velocity gradually decreases, which is consistent with the theoretical expectation.
Fig 6 is the temperature cloud diagram of the simulation model. It can be seen that the temperature of the calcination furnace area is 800°C, the temperature of the product hopper and the filter area is 200°C, and the heat transfer occurs in the contact area between the calcination furnace and the product hopper. Through the contact area cloud diagram of the calciner and the product hopper, it can be seen that as the distance between the contact surface and the heat source (calciner) increases, the temperature gradually decreases, and the heat transfer properties are consistent with the theoretical expectations, which indirectly proves the accuracy of the simulation results.
5. 2 Analysis of chemical reaction results
The results of the chemical reaction inside the equipment were analyzed. According to the simulation results, it was found that the product reached the bottom of the calciner at about 40s of the chemical reaction. At this time point, the effect of calcination on the chemical reaction is over, so the product concentration at 40s is more accurate, which can truly reflect the effect of calcination furnace temperature on the chemical reaction. The calculation conditions are as follow: the concentration of sucrose is 1mol/m3, the concentration of NaNO3 and HNO3 is 48mol/m3. The calcination furnace temperature variable is set to 400–800°C, and the concentrations of NO2 and Na2O at 400°C, 500°C, 600°C, 700°C and 800°C for 40s are recorded, as shown in Figs 7 and 8. The temperature has an effect on the yield of the product. With the increase of temperature, the concentration of NO2 and Na2O increases. It can be found from the specific values that the concentration of NO2 increased by 0.5 mol/m3 and the concentration of Na2O increased by 0.12 mol/m3 at the same time when the temperature rise was also 400°C, indicating that in this chemical reaction, the effect of temperature on the yield of NO2 was greater than that of Na2O.
The effects of the concentration of reactants (NaNO3 and HNO3) on the concentration of main products (NO2 and Na2O) were investigated by simulation. The calculation conditions are as follow: The sucrose concentration is 1 mol/m3, and the calcination furnace temperature is set to 800°C. The concentration of reactants was set as a variable, and the effects of NaNO3 and HNO3 concentrations of 12 mol/m3, 24 mol/m3, 36 mol/m3, 48 mol/m3 and 60 mol/m3 on the concentration of NO2 and Na2O at 40s were investigated. The simulation results are shown in Figs 9 and 10. The concentration of reactants (NaNO3 and HNO3) has an effect on the concentration of the product. As the concentration of reactants (NaNO3 and HNO3) increases, the concentration of NO2 and Na2O increases. Taking NO2 as an example, it can be found that the concentration of reactants (NaNO3 and HNO3) increased from 12 mol/m3 to 24 mol/m3, and the concentration of NO2 increased by 7.1 mol/m3. The concentration of reactants (NaNO3 and HNO3) increased from 48 mol/m3 to 60 mol/m3, and the concentration of NO2 increased by 0.5 mol/m3. Similarly, the product Na2O can also draw the same conclusion. Therefore, the higher the concentration of reactants (NaNO3 and HNO3), the lower the rate of increase in the concentration of the main products (NO2 and Na2O).
The calculation condition is ’sucrose concentration is 1mol/m3, NaNO3 and HNO3 concentration is 48mol/m3, calcining furnace temperature is 800°C. Taking the cloud map of NO2 concentration changing with time (as shown in Fig 11) as an example, the chemical reaction process in internal spray calcination is shown. Through the cloud map, it can be seen that with the change of time, NO2 is generated in the calciner, flows down the calciner into the product hopper, and then diffuses into the filter. It is consistent with the streamline diagram and the actual experiment. The accuracy of the experimental results is proved.
6. Conclusion and foresight
In view of the independent research and development of a simulated high-level liquid waste spray calcination and transformation treatment test device, a multi-physical field coupling calculation model for spray calcination was established. The specific conclusions and prospects are as follows:
- In this chemical reaction, temperature is an important factor. Temperature has an effect on the yield of the product. With the increase of temperature, the concentration of NO2 and Na2O increases continuously, and the effect of temperature on the yield of NO2 is greater than that of Na2O.
- In this chemical reaction, the concentration of reactants (NaNO3 and HNO3) has an effect on the concentration of the product. With the increase of the concentration of reactants (NaNO3 and HNO3), the concentration of NO2 and Na2O increases. At the same time, the higher the concentration of reactants (NaNO3 and HNO3), the lower the rate of increase in the concentration of main products (NO2 and Na2O).
- The current calculation model lacks the tracking of spray particles and cannot track the trajectory of spray particles. In addition, the spray cone angle is currently achieved through the simplification of the nozzle structure, which is not real enough and can be further improved in the model in the future.
Supporting information
S1 Raw data. The numerical calculation of the original data contains all the data points that make up the statistical chart.
https://doi.org/10.1371/journal.pone.0308145.s001
(DOCX)
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