Two aeronautical radiation anomalies in Inner Mongolia Autonomous Region were selected as the test area to carry out the test flight. The survey line flight was 51.4 km,

**Fig. 4.** Aeromagnetic (left) and airborne radiometer (right) measurement results

**Table 3.** Comparison and statistics of measurement results

the average flight altitude was 49.7 m, the average flight speed was 27.57 km/h, and the data sampling rate was 1 Hz.

According to the projection coordinates, K, u, th contents and TC of the navigation and positioning data of UAV aerial measurement in the abnormal area, the minimum curvature method is used to grid the data, and the UAV aerial measurement TC isograms and K, u, th contents isograms are obtained. Among them, the hf-09 TC contour map is shown in Fig. 5 (a). In this abnormal area, the high value of u content is mainly distributed in the northeast and southwest, with 5 × 10–6 and 10 × 10–6 delineate the abnormal area for the boundary value (see Fig. 5 (b)).

**Fig. 5.** (a) Tc contour map of UAV airborne radio (HF-09) (b) U abnormal range delineated (HF-09).

Pilotless aircraft aviation γ The energy spectrum measurement results are compared with the ground measurement results, as shown in Table 4:

**Table 4.** Data statistics of the same range measured by line 8040 UAV and ground

## **4 Conclusions**

## **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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## **Research on the Radioactive Waste Discharge Permit Regulation**

Li Huang, Ting Liu(B) , Yun Fan, Meng Chang, and Yiman Dong

Nuclear and Radiation Safety Center, MEE, Beijing, China<EMAIL_ADDRESS>
**Abstract.** For the release of radioactive waste, the regulatory body must establish or approve operational limits and conditions relating to public exposure, including approved discharge limits. The parties concerned must ensure that the release of radioactive waste and radioactive substances into the environment is managed in accordance with the instrument of ratification. Discharge authorization procedures, including the establishment of emission authorizations and emission allowances, the establishment and use of dose constraints, emission characteristics, and the circumstances of exposure used in the establishment of emission allowances, etc., According to the legal requirements of our country, at present, all units in the nuclear industry that produce and discharge radioactive waste gases and liquids into the Environment shall rely on the examination and approval of prior environmental impact reports or environmental impact assessment documents, the permit mode of total discharge control for the examination and approval of the designed nuclide discharge of radioactive waste gas and liquid. At present, China's radioactive contamination emissions are not included in the management of emission permits, nuclear and radiation-related key industries and units are not included in the "Fixed Source Emission Permits Classified Management Directory" management. Whether it is feasible to carry out the pollution discharge permit system in the nuclear and radiation industry of our country, in the theoretical system, there are already relevant laws and regulations of our country to guarantee or can guarantee, however, there are still some problems in the actual operation, such as insufficient research on radiation environmental quality objectives,further work is needed to promote the full implementation of the discharge permit system in the nuclear industry.

**Keywords:** Radioactive Waste · Discharge · Limit Value · Control Value · Permit · License

## **1 Introduction**

The discharge of radioactive waste must be regulated and restricted by the state. Article 41 of my country's "Radioactive Pollution Prevention and Control Law" stipulates that units that generate radioactive waste gas and waste liquid discharge into the environment radioactive waste gas and waste liquid that meet the national standards for the prevention and control of radioactive pollution, shall report to the environmental protection administrative director who has examined and approved the environmental impact assessment documents. The department applies for the discharge of radionuclides and regularly reports the discharge measurement results.

In January, China issued regulations on the management of pollution permits, 2021 that enterprises, institutions and other producers and operators under the management of pollution permits should apply for pollution permits in accordance with the regulations, no pollutants shall be discharged. According to the factors such as the amount of pollutants produced, the amount of pollutants discharged and the degree of impact on the environment, etc., the discharge units shall be subject to the classified management of discharge permits. However, the nuclear and radiation industries are not explicitly included in the current "Classified management list of emission permits for fixed sources of pollution", and there are no specific requirements for emission permits in China's current Local ordinance regulations, therefore, the industry has not implemented a licensing system.

## **2 Relevant Regulations of Chinese Standards**

#### **2.1 GB18871 "Basic Standard for Protection Against Ionizing Radiation and for the Safety of Radiation Source"**

Article 8.6.2 stipulates that radioactive waste liquid shall not be discharged into ordinary sewers, unless it is confirmed by the review and management department that it is lowlevel waste liquid that meets the following conditions, it can be directly discharged into ordinary sewers with a flow rate greater than 10 times the discharge amount, and Each discharge should be recorded:

a) The total activity emitted per month does not exceed 10 ALImin (ALImin is the smaller of the ingestion and inhalation ALI values corresponding to occupational exposure, and the specific value can be obtained according to the provisions of B1.3.4 and B1.3.5);

b) The activity of each discharge shall not exceed 1 ALImin and shall be flushed with not less than 3 times the amount of water discharged after each discharge.

### **2.2 GB6249 "Environmental Radiation Protection Regulations for Nuclear Power Plants"**

Article 6 "Dose constraint value and emission control value in operating state" stipulates that the effective dose to any individual in the public caused by the radioactive substances released to the environment from all nuclear power reactors at any site must be less than the dose constraint value of 0.25 mSv per year.

The operating organization of the nuclear power plant shall formulate the dose management target values for airborne radioactive effluent and liquid radioactive effluent respectively according to the dose constraint value approved by the audit and management department. The nuclear power plant must implement the control of the total annual emission of radioactive effluents for each reactor. For a reactor with a thermal power of 3000 MW, the control value is as follows (Tables 1 and 2).

**Table 1.** Control values of airborne radioactive effluents

**Table 2.** Control values for liquid radioactive effluents

## **3 Radioactive Waste Discharge Permits in China**

At present, the discharge of radioactive pollutants in my country has not been included in the management of pollutant discharge permits for the time being, and relevant key industries and units have not been included in the "List of Fixed Pollution Source Pollutant Discharge Permit Classification Management" management.

According to the requirements of the Pollution Discharge Law, at present, all units in my country that generate and discharge radioactive waste gas and waste liquid into the environment implement a permit system based on construction permits, safety permits, mining permits, etc., with pre-environmental impact reports or environmental impact assessment documents. Based on the approval of radioactive waste gas and waste liquid, the total emission control permit mode is approved for the design of radioactive waste gas and waste liquid emission.

When submitting an environmental impact report to the ecological environment department, the unit producing radioactive waste gas and liquid should also submit an application for the estimated discharge of radioactive waste gas and waste liquid, including determining the characteristics and activities of the radionuclides to be discharged and possible discharges where and how, and the exposure doses to key populations of the public that may be caused by the planned discharge. According to the discharge situation of other facilities in the area where the emission unit is located, the ecological environment department will allocate a certain emission share to the unit according to the public dose limit standard. The approved emission limits for nuclear power plants and research reactors must be included in the operating limits and conditions. The nuclear technology utilization unit generally adopt emission and clean decontamination models that conform to national standards, while uranium mines adopt emission limits for corresponding nuclides based on environmental standards, and associated mines currently do not have relevant standards, the corresponding limits of national sewage discharge standards can be used.

A nuclear power plant unit is a million kilowatt-class pressurized water reactor nuclear power unit. According to the approval of the original Ministry of Environmental Protection "Approval of the Environmental Impact Report of a Nuclear Power Plant (Operation Stage)" and other documents, as well as the monitoring of the effluent of the nuclear power plant, the annual emission control value and actual value of the radioactive effluent of the unit in a certain year as follows (Table 3):

**Table 3.** Annual emission control value and actual value of radioactive effluents from 1/2 unit of a nuclear power plant

The annual emissions of Airborne Carbon 14 and liquid tritium were higher than the annual control value, and the emissions of other airborne and liquid radioactive effluents were far lower than the annual control value. The annual maximum individual effective dose of effluents released to the public was 4.52 \* 10–7 Sv, and the residents receiving the maximum individual dose were adults within 1–2 km north-northeast (NNE) of the plant site, about 0.18% of the dose-limiting value of 0.25 mSv/a.

For radioactive contamination, the monthly and quarterly monitoring results of the water samples near the outfall comply with the first-class Standard in Table 4 of the comprehensive wastewater discharge standard (GB8978-1996), and there is no obvious change compared with the outfall. Monthly monitoring and analysis items include dissolved oxygen, residual chlorine, conductivity, Ph value, hexavalent chromium, total chromium, orthophosphate, hydrazine. Quarterly monitoring items include Boron, iron, anions, sulphates, lithium, sodium, nickel and oils.

**Table 4.** Annual emission control value and actual value of radioactive effluents from 3/4 unit of a nuclear power plant

### **3.1 Nuclear Technology Utilization Units**

My country's nuclear technology utilization units basically have very few waste gas emissions, and the amount is also very small. The main radioactive pollutants in the management of pollutant discharge licenses are mainly concentrated in waste liquids, and in various industries, waste liquid discharges are mainly medical-related units. Although there are many types of radionuclides used in medical institutions, most of them are of low toxicity and short half-life. However, in the investigation and research on the application status of nuclear medicine projects in Guangdong Province, it was found that the total β of the wastewater at the outlet of the decay pool of the hospital with a large amount of iodine-131 was greater than the "Water Pollutant Discharge Standard for Medical Institutions" (GB18466-2005) the specified emission limits.

#### **3.2 Associated Minerals**

At present, my country has no associated radioactive mine radiation environmental safety standard guidelines and associated mine development and utilization project effluent discharge limit. From the actual discharge situation, the discharge concentration of wastewater may be higher than the relevant limit in the "Integrated Wastewater Discharge Standard" (GB8978-1996), and the radon concentration in some places will also be higher than the limit, but the resulting dose is basically low The public individual effective dose limit for the development and utilization of mineral resources is 1 mSv/a.

#### **3.3 Situation Analysis**

After investigation, various local provinces in my country have carried out relevant explorations in the implementation of the radioactive pollutant discharge permit system. Article 18 of the "Administrative Measures for the Prevention and Control of Radioactive Pollution in Sichuan Province" promulgated by Sichuan Province in 1999 stipulates: "Any unit that discharges radioactive waste water and waste gas into the environment must be monitored by a statutory monitoring agency; It is prohibited to discharge radioactive waste water and waste gas into the environment without a pollution discharge permit or beyond the regulations of the pollution discharge permit." But this method has been abolished at present, and there is no such relatedness in the newly issued Regulations on the Prevention and Control of Radiation Pollution in Sichuan Province in 2016. Regulation. At present, radioactive pollutant discharge permits have also been set up in the ecological environment examination and approval of Shandong and other provinces, but there has been zero application status.

Whether it is feasible to implement a pollutant discharge permit system in my country's nuclear and radiation industry, in terms of theoretical system, there are relevant laws and regulations in my country to guarantee or can be guaranteed, but in terms of practical operation, there are problems such as insufficient research on radiation environmental quality objectives.

The ultimate purpose of the implementation of the pollutant discharge permit system is to reduce the discharge of pollutants, thereby improving the quality of the environment. However, in the nuclear and radiation industry, there is a lack of relevant standards and research on how to link the allowable amount of radioactive pollutant discharge with environmental quality goals.

According to the pollution discharge permit management regulations, three modes of management are stipulated according to factors such as pollutant generation, discharge, and degree of impact on the environment, which are divided into key management, simplified management and registration management. The corresponding degree of environmental impact is divided into three categories. In the nuclear and radiation industry, it is generally based on the natural background, and the 1mSv equivalent dose limit for humans is used to control the effluent discharge of relevant units, but when it comes to the degree of environmental impact It is difficult to define the size of the industry and the impact on the ecological environment, which is also a problem that affects the determination of which mode of supervision the relevant industry should be.

## **4 Conclusions**

In general, the conditions for implementing a pollutant discharge permit system in accordance with the requirements of the pollutant discharge permit regulations in my country's nuclear and radiation industries are not yet mature. However, in the medical and associated mining industries where management is relatively weak at present, a pilot registration management model can be considered, and It is possible to explore more scientific and reasonable emission standards and management models based on practice, laying the foundation for the comprehensive implementation of the emission permit system in the nuclear and radiation industry. At the same time, it is recommended to establish a radiation environment quality index system, improve the standard system, and strengthen the building of monitoring capabilities and professional supervision teams. Carry out research on the relationship between the discharge of radioactive pollutants and environmental quality objectives, to provide sufficient theoretical basis for the implementation of key management, simplified management, and registration management of pollutant discharge permits, and to achieve the goal of improving environmental quality and ensuring the health of personnel with pollutant discharge permits.

## **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Preparation and Shielding Performance of Gamma Ray Shielding Composite Materials Based on 3D Printing Technology**

Yulong Li, Chengxin Li(B) , Danfeng Jiang, Feng Liu, Xiajie Liu, and Li Li

China Nuclear Power Technology Research Institute, Shenzhen, Guangdong, China<EMAIL_ADDRESS>
**Abstract.** Excessive gamma-rays will be emitted when a nuclear power plant is under the refueling overhaul, leading to a certain number of hotspots. To meet the shielding requirements of these hotspots of complex components, a nylontungsten shielding composite material was developed by laser selective sintering 3D printing technology. The effects to shielding performance of 3D printing shielding materials were emphatically studied for two preparation processes (including mechanical mixing method and coating method) of 3D printing composite powders. Experimental results show that the nylon-tungsten shielding composite material with tungsten content of 70–85% was obtained by 3D printing technology, which realizes the manufacture of mold-free customized and bonded shielding materials. The shielding material prepared by 3D printing technology by coating method is better than that by mechanical mixing method in shielding performance. When the mass ratio of tungsten powders is 80%, the linear attenuation coefficient can reach 0.32, which is the best formula of the composite material and can be used for shielding of complex components. All these results lay a theoretical foundation for the engineering application of 3D printing shielding materials.

**Keywords:** 3D printing · Shielding materials · Performance study

## **1 Introduction**

During the operation of a PWR nuclear power plant, many radiation hotspots may appear on different operating pipelines and equipments in the control area. Therefore, it is necessary to adopt certain radiation shielding measures to reduce the external dose for working staff near the radiation hotspots.

At present, it is common to use sheet lead or lead apron for radiation shielding in the domestic nuclear power plants [1, 2], but there are many problems for this shielding way. Sheet lead is messy and difficult to clean. Sheet lead and lead apron are soft, which is easy to cause deformation and affect the stability of radiation protection. This shielding method does not meet the seismic performance requirements of nuclear power plants, and hinders the operation and maintenance of instruments and valves. In addition, most of the wrapped shielding sheet lead and lead apron need to be removed when the refueling overhaul is finished for the nuclear power plant. Repeating installations and removals not only consumes a lot of sheet lead and lead apron, but also causes high dose on the working staff. According to the management requirements of the control area of nuclear power plants, it is necessary to develop a new shielding composite material which is customized and completely fitting with the component, and innovate the traditional shielding mode of nuclear power plants.

At present, research on the new type of shielding materials has aroused more and more attention. Shin et al. [3] developed a BN/high-density polyethylene composite material with good neutron shielding performance; A kind of rubber-based flexible shielding materials has been developed by British ITW Company for radiation shielding in nuclear industry and the nondestructive testing field, which has been applied in the Size-well B nuclear power plant in Britain; Fu Ming et al. [4] developed a flexible shielding material with styrene butadiene rubber (SBR) for matrix; Zhuo Mingchuan et al. prepared PA6 tungsten shielding composites with different densities by melt extrusion method [5]; Ahmed et al. Studied the gamma-ray shielding characteristics of tungsten-silicone rubber composites, which can be used as manufacturing materials for protective clothing such as gloves and jackets [6]; Samantha et al. used 3D printing technology to prepare resinbased neutron and gamma-ray shielding materials, of which the content of functional filler Bi can reach 40% or the content of 10B can reach 60% [7].

It is complex and diverse for equipment structure at radiation hotspots in nuclear power plants. Radiation protection composite materials based on polymer materials are generally produced by injection molding or compression molding. There are many disadvantages for preparing shielding materials with complex structures by traditional manufacturing method, such as a long manufacturing cycle, high mold cost, low mold utilization rate and easy to cause lead pollution. Therefore, it is necessary to develop a new gamma-ray shielding composite material based on advanced manufacturing technology, in order to meet the requirements of customized coated shielding materials for complex equipments in nuclear power plants.

3D printing technology is an additive manufacturing technology, which was born in 1980s. With this technology, rapid and free molding can be realized, and polymer materials with complex structure can be manufactured conveniently, quickly and at low cost. In this paper, a new type of nylon-tungsten shielding composite materials is prepared by 3D printing technology, in which thermoplastic nylon is used as matrix material, and tungsten is used as functional filler. Through the research of powder mixing process and shielding performance, the best material formula is obtained, and the shielding protection problem of complex components in nuclear power site is solved effectively.

### **2 3D Printing Radiation Protection Material Design**

3D printing is a new type of additive manufacturing technologies compared with the current traditional manufacturing technologies (such as turning, milling, planning, grinding, etc.). This technology is a rapid manufacturing technology by which materials can be fusioned in one-time. Based on digital model files, it uses powdery metal or plastic and other bindable materials to construct three-dimensional objects by printing layer by layer and superimposing different shapes [8]. Compared with traditional manufacturing process, 3D printing has some advantages as followed: (1) Rapid free forming without mold; (2) Short manufacturing cycle and low cost; (3) near net shape and even net shape of complex structure; (4) Full digitalization; (5) multi-materials arbitrary composite manufacturing.

At present, the most widely used radiation protection materials are those containing the elements with high atomic numbers such as lead and tungsten. Lead is toxic and has a "Pb weak absorption zone" for rays with energy between 40–88 keV, which is easy to produce secondary bremsstrahlung radiation. In addition, lead has poor structural strength and is not resistant to high temperature. It is commonly used as lead containers, movable screens, lead bricks, etc. Tungsten has high density and atomic number. As an ideal shielding material, it has many advantages, such as good ray shielding effect and no secondary electron radiation produced [9]. It is an environmentally friendly radiation protection material with the strong ability of ray protection. However, tungsten has the characteristics of high melting temperature, high strength, poor plasticity and toughness, so it is difficult to process it into parts with complex shapes. Nylon is one of the engineering materials with the characteristics of excellent mechanical properties, low cost, easy processing and widely used, especially commonly used as one kind of 3D printing materials. It is a practical and effective way to solve the above problems by using nylon powders as substrate and the filler of tungsten powders to prepare nylon-tungsten composite products with complex shapes, which is based on 3D printing technology. Nylon-tungsten composites belong to the environmentally friendly materials. It is particularly important that the parts with complex shapes, which are difficult to be formed with pure tungsten, can be easily produced by using 3D printing technology with nylontungsten composites. Based on the above analysis, a new nylon-tungsten gamma-ray shielding composite was prepared by using 3D printing technology with thermoplastic nylon as the matrix and tungsten powders as the functional filler, which can meet the customized shielding requirements of the complex components in the control area of nuclear power plant.

## **3 Materials and Method**

#### **3.1 Raw Materials and Forming Process**

The median particle size of tungsten particles with 99.99% pure is 15–20 μm, while the median particle size of nylon powders is 50–55 μm.

Composite materials are composed of polymer materials and metal materials. 3D printing technology that can both print nonmetallic materials and metal materials mainly includes fused deposition modeling (FDM), stereo lithography apparatus (SLA) and selective laser sintering (SLS). Table 1 shows the comparison of three process types of 3D printing technology. Compared with SLA and FDM, SLS has the following advantages: (1) SLS process is applicable to a wide range of materials, and the powder laying process adopted by SLS process is more suitable for mixed materials printing with great different density such as nylon powder and tungsten powder, which can ensure the dispersion and distribution of tungsten powder particles in nylon matrix; (2) SLS process is better than SLA and FDM process in forming precision and forming speed; (3) The SLS printing environment is generally a sealed space with inert gases such as argon as the protective gas. There is no risk of toxic and harmful substances being released during the printing process; (4) SLS does not need supporting materials, and is more suitable for the preparation of complex structural parts. Comprehensively considering material applicability, precision, forming efficiency and other factors, SLS printing process is chosen as the best one of the 3D printing process of shielding composite materials.

**Table 1.** Comparison of Process Types

Figure 1 shows the molding principle of the SLS process of shielding composite materials. When the laser acts on the mixed powder of nylon and tungsten, the mixed powder absorbs heat, and its temperature gradually increases. When the temperature reaches the melting temperature (*TR*) of nylon powder, the nylon powder changes from a solid state at room temperature to a liquid viscous flow state. As the temperature increases, the viscosity of the melt decreases, but its fluidity increases. It is easy to contact with the surrounding particles of tungsten powders. After cooling, the melt nylon powder solidifies and binds together. The particles of tungsten powders are uniformly dispersed in the nylon matrix without any change. The parts of the shielding material which are molded by laser selective sintering, mainly bond tungsten powder particles together through the adhesion of nylon. The adhesion value is determined by the cohesion and adhesion force of liquid nylon. Cohesion force refers to the force between the molecules of nylon binder itself, that is, the strength of nylon. Adhesion force is the force between the particles of nylon and tungsten powders, that is, the force of nylon adhering to the surface of tungsten powders.

**Fig. 1.** SLS Forming Principle of Shielding Composites Material

Figure 2 shows the process flow of the shielding material prepared by 3D printing. The specific preparation process is as follows: Firstly, a certain quality of nylon powder and tungsten powder are mixed according to the design ratio by the mixing process; Secondly, the fully mixed nylon and tungsten powders were put into the laser selective sintering 3D printing equipment. After preheating the mixture and parameter settings, including laser power, scanning speed, scanning spacing and scanning mode, researchers input the model size of the printing part, and start printing; Finally, the sample was taken out for post-treatment. The powder adhered to the sample surface was removed, and then the sample was polished to make its surface bright, as shown in Fig. 3. During the preparation of 3D printing composite shielding materials, the batching design, mixing process and SLS sintering process are the most important factors, which affect the shielding performance, mechanical properties and forming accuracy of the shielding material.

**Fig. 2.** 3D Printing Shielding Material Preparation Process

**Fig. 3.** 3D Printing Nylon-Tungsten Composite Shielding Material

### **3.2 Test and Analysis**

The gamma shielding performance test of radiation protection composite materials was conducted with 137Cs (0.662 meV). The radiation decay rate of the sample was tested by standard device of γ-ray radiation amount (protection level) and dosimeter, according to GBZT 147-2002.

## **4 Results and Discussion**

### **4.1 Composite Powder Mixing Process**

At present, there are two main methods for preparing composite powders suitable for SLS printing, including the mechanical mixing method and the film coating method.

## **4.1.1 Mechanical Mixing Method**

Mechanical mixing method is to mix polymer powders and filler powders mechanically in the mixer for three-dimensional movement, high speed kneading machine and other mixing equipments. The tungsten powder and nylon powder with a certain mass ratio were put into the double-motion mixer and mixed for 30 min. The surface appearance of the composite powder is shown in Fig. 4 (a). The mechanical mixing method is simple in process, low in equipment requirements, and economical. However, when the particle size of filler powders is very small (for example, less than 10 microns), or when the proportion of the filler powders (for example, metal powders) is much larger than that of polymer, it is difficult to disperse inorganic filler particles evenly in the polymer matrix by mechanical mixing method. The powder particles are easy to segregate during transportation and SLS powder laying, which leads to the existence of non-uniform distribution of filler particle aggregates in SLS formed parts, resulting in the decrease of capability of the products.

## **4.1.2 Film Covering Method**

The coating method is to coat the polymer material on the outer surface of the filler powders to form a kind of composite powders with a polymer coating. The steps of preparing the shielding composite material powder by the film coating method are as follows: putting nylon powders, tungsten powders, coupling agent, leveling assistant into a stainless steel reaction kettle in a certain proportion, sealing and injecting nitrogen for protection, slowly heating up to about 150 °C, so that nylon powders are completely dissolved in solvent, then cooling the kettle to room temperature at a certain rate under vigorous stirring, and solid-liquid separation is carried out to obtain precipitated coated composite powders. After vacuum drying, crushing and sieving the obtained aggregates, the composite material containing nylon coated tungsten powders with suitable particle size distribution can be obtained. The surface appearance of the powder is shown in Fig. 4(b). In the coated powder, the filler and polymer matrix are mixed evenly without the segregation phenomenon in the process of transportation and powder spreading.

a) Preparation of powder by mechanical mixing

b) Preparation of powder by film coating

**Fig. 4.** Nylon-tungsten composite powder

According to the characteristics of the two composite powder mixing processes, nylon can be coated on the surface of tungsten powders uniformly by coating method. 602 Y. Li et al.

The particle size of the nylon is significantly reduced during melting, coating on the surface of tungsten powder particles to achieve adhesion effect, so that the dispersion of tungsten powders in nylon matrix is more uniform.

#### **4.2 Shielding Performance Research**

#### **4.2.1 Theoretical Shielding Efficiency of Composites**

In the study of γ-ray shielding materials, the shielding performance of the materials was simulated in advance, which facilitated formulation design and adjustment. WPA1, WPA2, WPA3, WPA4, WPA5 and WPA6 were defined as different proportions of tungsten and nylon. The material proportions are listed in Table 2. The simulation of 90% (mass ratio) of tungsten powder ratio was not carried out because the sample could not be formed in the machine.

**Table 2.** Proportions of shielding composite materials

The linear attenuation coefficient model of the shielding composites was established. The theoretical shielding coefficients of the composites were calculated by MCNP (Monte Carlo N Particle Transport Code) program. MCNP is a general software package developed by Los Alamos National Laboratory (LANL) based on Monte Carlo method for computing neutrons, photons, electrons or coupled neutrons, photons, electrons transport problems in complex three-dimensional geometry. It can greatly save research funds and time by simulating shielding performance of materials with MCNP. The calculation model is shown in Fig. 5. The source is a unidirectional point source, which is 1m away from the detection point and 0.46 m away from the material surface. The material size is 20 cm (length) × 20 cm (width) × 1 cm (thickness). The attenuation of the material to 137Cs source was simulated, and the source energy was 0.662 meV. The radiation intensity before and after the material was recorded by F1 card. The linear attenuation coefficient μ of the composite material was obtained according to the formula (2).

All the test results were converted into linear attenuation coefficients in order to compare the test results of different formulations. The attenuation rate and linear attenuation coefficient were calculated as follows:

When gamma-rays pass through the shielding material, they will not be completely absorbed, but attenuated (intensity decreases). The attenuation relationship is shown in

**Fig. 5.** Calculation model of linear attenuation coefficients of composite materials

Eq. (1):

$$R\_{\chi} = R\_0 e^{-\mu x} \tag{l}$$

where Rx is the dose rate after passing through a certain thickness x of shielding material; R0 is the dose rate before shielding;

X is the thickness of the shielding material;

and μ is the linear attenuation coefficient of the shielding material.

Formula (1) is converted to the following Eq. (2):

$$\mu = -\frac{-Ln\left(\frac{R\_\chi}{R\_0}\right)}{\chi} \tag{2}$$

The simulation values of linear attenuation coefficients of the shielding composites with different formulas were calculated by formula (2), which are shown in Fig. 6. The γ-ray shielding performance of composites increases exponentially with the increase of tungsten powder content. When the proportion of tungsten powders is low (*<*70%), the theoretical linear attenuation coefficient of the composite is low. Thus the ingredients with tungsten powder ratio between 70 and 85% were selected for 3D printing experiment.

#### **4.2.2 Effect of Powder Ratio on Shielding Performance of Composites**

According to the simulation results of linear attenuation coefficients of composite materials in Fig. 6 and combined with the powder mixing process of composite materials, the sample preparation and testing schemes of different formulas are set in Table 3. The linear attenuation coefficients of the samples with different formulas are obtained through shielding performance tests and conversion results by formula (2).

The shielding effect of the samples with different contents of tungsten powders was tested. The results are shown in Fig. 7: (1) The shielding performance of the composite is obviously improved when the mass fraction of tungsten powders increases from 70% to 80%. When the mass fraction of tungsten powders increases from 80% to 85%, the

**Fig. 6.** Analog value of linear attenuation coefficients of composites without formula

**Table 3.** Test values of attenuation coefficients of samples with different formulations

shielding performance of the composite decreases. When the mass fraction of tungsten powders increases from 70% to 80%, the laser selective sintering of composites is in good condition, and there is no obvious defect in the samples. When the mass fraction of tungsten powders increases from 80% to 85%, due to the nylon content of the composite material is only 15%, cracks and warping occur in some areas of the sample during laser selective sintering, resulting in the final measured shielding performance of the composite material being lower than that of the composite material with the mass fraction of tungsten powders of 80%. (2) For mechanical mixing process, the linear attenuation coefficient of tungsten powders with 80% mass fraction is obviously lower than that of coated tungsten powders with 80% mass fraction. (3) The linear attenuation coefficient of the sample coated with film is lower than the simulation value of Monte Carlo under any tungsten powder mass ratio, which shows that there is still much room for improvement in the 3D printing process, and the uniform dispersion of tungsten powders in the matrix needs further improvement. When using the film covered mixing process, the best formula is that the mass fraction of tungsten powders and nylon matrix are 80% and 20% respectively.

**Fig. 7.** Comparison of shielding capability of 3D printing shielding materials with different formulas

The main factor affecting the shielding performance of the shielding composite is the content of tungsten powders in the composite, followed by the dispersion of tungsten powders in the matrix. According to the above results, the higher the content of tungsten powders, the better the shielding performance of qualified samples. Under the condition of same mass fraction, the more uniform the dispersion of tungsten powders in matrix, the better the shielding performance of the material. The mixing process of composite powders has a great influence on the dispersion of tungsten powders in matrix.

#### **4.2.3 Effect of Powder Mixing Process on Shielding Performance of Composite Materials**

In order to further explore the reasons for the difference of shielding performance of samples under the two mixing process conditions, SEM-scan of 3D printing products of mechanical mixing and coated mixing was carried out, as shown in Fig. 8. It can be found that the macroscopic fracture surface of mechanical mixture presents obvious lines, showing typical characteristics of brittle fracture, while the microscopic fracture presents agglomeration of tungsten powders and only nylon powders in some areas (as shown in the box area in Fig. 5 (e)); In contrast, the surface of macroscopic fracture is smooth and the distribution of tungsten powder in the matrix is uniform in microstructure This also verified the results of the shielding performance experiment, and the 3D printing shielding composite products under the condition of mulching and mixing technology showed better shielding performance. The composite powder prepared by coating method has good sintering capability, high bonding strength and high forming precision, and the shielding composite powder is well coated, and almost no exposed tungsten powder is found.

The essential attribute of 3D printing radiation protection composite materials lies in its shielding performance, which is mainly reflected in the mass fraction and dispersion state of tungsten particles in the composite material. Excellent powder mixing and manufacturing process can ensure the uniform dispersion of tungsten powders in the matrix under high mass fraction and ensure the shielding performance.

**Fig. 8.** Fracture scan photo

## **5 Conclusions**

In this paper, a nylon-tungsten gamma-ray shielding composite material was developed by using laser selective sintering 3D printing technology, and two kinds of 3D printing composite powders were prepared by mechanical mixing method and coating method, respectively. The performance of the shielding materials was studied, and the conclusions are as follows:

3D printing shielding composite materials can effectively solve the radiation protection problem of complex components in the control area of nuclear power plants. This study lays a theoretical foundation for the engineering application of 3D printing shielding composite materials.

## **References**

608 Y. Li et al.

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Dynamic Response Analysis of Floating Nuclear Power Plant Containment Under Marine Environment**

Jialin Cui1,2, Lijuan Li3, Meng Zhang1(B) , Hongbing Liu1,2, and Xianqiang Qu1,2

1 Yantai Research Institute and Graduate School, Harbin Engineering University, Yantai, China<EMAIL_ADDRESS>
2 College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China 3 Nuclear Power Institute of China, Chengdu, China

**Abstract.** Floating nuclear containment is in a harsher environment than conventional onshore nuclear containment. In view of the Marine environment under the condition of floating nuclear power plant containment structure safety, combined water dynamics and structural mechanics, considering the containment response under random movement of hull in the Marine environment, the influence of the containment structure load calculation, thus checking containment when working in pile structure safety, provide theoretical basis for the safe operation of floating nuclear power plants. In this paper, taking a floating nuclear power plant as an example, ANSYS 2021R1, Workbench, Fluent and other software of finite element analysis are used to conduct fatigue simulation of floating nuclear power plant. The time course curve of the 6-dof motion of the ship's center of gravity is obtained, then, a remote displacement method is adopted to transfer the hull motion to the containment vessel to realize the numerical simulation of the containment vessel movement with the hull, thus to solve maximum normal stress and strain, the maximum load component of containment bearing under the action of Marine environmental load is obtained. The results show that the maximum stress and strain of the vessel increase obviously in the moving state compared with the static state of the vessel, which indicates that the random motion response of the vessel must be considered in the structural safety analysis of the floating nuclear power plant containment.

**Keywords:** floating nuclear power plant · Ocean circulation · containment · structural loads · Random motion response

## **1 Introduction**

With the continuous adjustment and optimization of China's energy structure and the continuous promotion of the strategy of becoming a maritime power, traditional fossil energy and emerging energy such as wind, wave and solar energy are increasingly difficult to meet the energy needs brought about by China's coastal oil and gas resources and island development. Therefore, as a clean, efficient and flexible location of offshore nuclear power generation technology, the national government pays more and more attention to it.Marine floating nuclear power station is a mobile floating offshore platform equipped with nuclear reactor and power generation system. It is the organic combination of mobile small nuclear power station technology with ship and ocean engineering technology. In floating nuclear power plants, a sealed steel containment structure is usually installed around the reactor and other auxiliary power generation structures to protect the normal operation of the reactor and the external environment. Compared with the traditional onshore nuclear power plant containment, the environment and load borne by the small steel containment (including support) of floating nuclear power plant at sea are very different, especially the complexity of the Marine environment leads to more complex load borne by the containment (including support). Therefore, in order to ensure the safe operation of floating nuclear power plants and protect the surrounding personnel and the external environment from nuclear radiation damage, it is urgent to carry out researches on mechanical analysis and safety evaluation technology of steel containment of floating nuclear power plants in marine environment.

The floating nuclear power plant containment vessel is not only subjected to huge vertical and horizontal loads, but also inevitably subjected to wind load, wave load and current load. Therefore, it is particularly important to analyze the dynamic response of the floating nuclear power plant containment vessel in the Marine environment. Reissner [1] studied the vibration characteristics of rigid circular foundation plate under vertical load, and proposed and verified the feasibility of elastic half-space theory in vibration research of foundation and foundation. Choprah [2] proposed the dynamic substructure method, which made numerical calculation effectively applied in this field. Lysmer et al. [3] proposed lumped parameter method, which laid the foundation for structural dynamic response analysis. Gazetas [4] and Mrakis et al. [5] proposed the calculation and analysis method of pile-soil-structure dynamic interaction, and provided empirical expressions of stiffness coefficients and damping coefficients. Fan Min et al. [6] conducted nonlinear seismic response analysis and research, and the results showed that the soil-pile-structure interaction system would affect the dynamic characteristics of the structure, resulting in the extension of the natural vibration period and the increase of damping of the system. Wang et al. [7] used hydrodynamic model to simulate the evolution of wind, wave and tide under 32 typhoon events in Bohai Bay from 1985 to 2014, and used two-dimensional Gumbel Logistic model to establish the joint distribution of wave and storm surge in Bohai Sea. De Waal and Van Gelder [8] established the joint distribution of extreme wave height and period through Copula function. Michele et al. [9] used two-dimensional Copula function to analyze the frequency of effective wave height, storm duration, storm direction and storm interval of ocean storms, and established the joint probability distribution between pairs. Xu et al. [10] established the two-dimensional joint distribution of storm surge height and effective wave height. Dong Sheng et al. [11] established the joint distribution of the annual maximum wave height and the corresponding wind speed of a jacket platform for 24 years based on Archimedean Copula function, combined with the response of the offshore platform, and found that considering the joint effect, the response of the offshore platform could be reduced in the same return period. Chen Minglu et al. [12] conducted hydrodynamic analysis and wave load prediction for semi-submersible offshore platforms. Zhou Sulian et al. [13] studied the mooring system design of deep-water semi-submersible platform.

Due to the complex wind, wave and current environment under the action of Marine environment of floating nuclear power plant containment, the research on dynamic response characteristics of floating nuclear power plant containment is insufficient and almost no reports have been reported. Therefore, it is of great significance to carry out dynamic response analysis of floating nuclear power plant containment under Marine environment conditions, and to explore the variability and ultimate load effect of shortterm time history analysis, so as to understand dynamic response characteristics of floating nuclear power plant containment under Marine environment.

The main work of this paper is to establish a hydrodynamic analysis model, using Ansys Workbench HD software module for frequency domain analysis of the platform and obtain the hydrodynamic parameters of the platform. The anchor chain model was added to the platform model to control the six degrees of freedom movement of the platform under the action of wave and flow. The HR module of Ansys Workbench software was used to conduct time-domain analysis of the platform to obtain the timehistory curve of the platform motion response. The structural dynamic response analysis of the containment vessel of floating nuclear power plant under the action of wind load, wave load and current load is carried out, which provides important reference for the safe operation of floating nuclear power plant.

### **2 Theoretical Basis of Potential Flow**

#### **2.1 Small Scale Member**

The stress of offshore floating structures in waves is studied. The stress of offshore structures is the most important topic in the field of offshore engineering, in which the wave force of piles is the basis of the stress of offshore structures. The method proposed by Morison et al. in 1950 is used to calculate wave force for small components, that is, structures whose diameter is smaller than the wavelength of the incident wave. Morison equation is basically an empirical formula, which takes wave particle velocity, acceleration and cylinder diameter as parameters to calculate the wave force in each depth of water, and then obtains the wave force along the length of the column.

Morrison et al. believed that the horizontal wave force acting on any height of the cylinder included two components:

$$f\_H = f\_D + f\_I \tag{1}$$

Its magnitude is in the same mode as the drag force exerted on the column by unidirectional steady water flow, that is, it is proportional to the square of the horizontal velocity of the wave water point and the projection area of the unit column height perpendicular to the wave direction. The difference is that the wave water points oscillate periodically, and the horizontal velocity is positive and negative, so the drag force on the cylinder is also positive and negative:

$$f\_D = \frac{1}{2} C\_D \rho A u\_\chi |u\_\chi| \tag{2}$$

$$
\rho\_I f\_l = \rho V\_0 \frac{du\_\chi}{dt} + C\_m \rho V\_0 \frac{du\_\chi}{dt} = C\_M \rho V\_0 \frac{du\_\chi}{dt} \tag{3}
$$

In the engineering design of floating buildings and piled offshore platforms, one of the main problems to be solved is to determine the movement, stress and deformation of these structures under the action of external forces such as wave and wind. We can regard these structures as a dynamic system, the wave action is called the input of the system, and the movement, stress and deformation of the structure are called the output of the system.

Remember this transformation as:

$$\mathbf{y}(t) = \mathbf{K}[\mathbf{x}(t)] \tag{4}$$

For different systems and different inputs, the operator K may have different forms. According to the different operators, dynamic systems can be divided into linear systems and nonlinear systems. An operator is a linear system if it has the following properties, and its operator is denoted by L.

a. Superposition property

$$L[\mathbf{x}\_1(t) + \mathbf{x}\_2(t)] = L[\mathbf{x}\_1(t)] + L[\mathbf{x}\_2(t)] = \mathbf{y}\_1(t) + \mathbf{y}\_2(t) \tag{5}$$

b. The constant α can be removed from the operator

$$L[\alpha \mathbf{x}(t)] = \alpha L[\mathbf{x}(t)] = \alpha \mathbf{y}(t) \tag{6}$$

therefore:

$$L\left[\sum\_{i} \alpha\_{i} \chi\_{i}(t)\right] = \sum\_{i} \alpha\_{i} \chi\_{i}(t) \tag{7}$$

It's called the principle of linear superposition, which means that the response of a linear system to inputs is equal to the sum of the responses of the inputs acting independently.

The following operations are linear transformations:

$$\mathbf{y}(t) = \frac{\mathbf{d}}{\mathbf{d}t}\mathbf{x}(t), \ y(t) = \int\_0^T \mathbf{x}(t)\mathbf{d}t, \ \mathbf{y}(t) = \boldsymbol{\varphi}(t)\mathbf{x}(t) \tag{8}$$

In Formula (1-179), ϕ(*t*) is A non-random function. The above types are linear secondary operations. If a certain function is added, they are called linear non-secondary operations, such as:

$$\mathbf{y}(t) = \frac{\mathbf{d}}{\mathbf{d}t}\mathbf{x}(t) + \boldsymbol{\varphi}(t) \tag{9}$$

Systems whose operators do not conform to the above conditions are called nonlinear systems. Linear systems are often encountered in practical work, and some nonlinear systems can be linearized within a certain range.

#### **2.2 Large Scale Member**

Ship hydrodynamic problems can be solved by frequency domain method. The frequency-domain method is based on the assumption that the wave-ship interaction has lasted for quite a long time, the initial disturbance of the incident wave and the transient influence of the initial rocking of the ship have disappeared, and the fluid motion in the field has reached a steady state. In this case, if the incident wave is harmonic, then the ship's motion is also harmonic (the encounter frequency must be the changing frequency), and the steady-state solution can be obtained in the frequency domain.

Due to the action of waves, the ship has six degrees of freedom besides constant speed forward motion. Assuming that the motion of the six degrees of freedom is small, the ship's center of gravity G point can be at. The three linear displacements (swing, roll, and heave) and the three angular displacements (roll, pitch, and yaw) around the G point in the O-XYZ coordinate system are represented. In the stable state, its displacement vector will be regarded as the harmonic quantity with the encounter frequency field as the changing frequency:

$$\{\eta(t)\} = \{\eta\}e^{i\alpha t} = (\eta\_1 \ \eta\_2 \ \eta\_3 \ \eta\_4 \ \eta\_5 \ \eta\_6)^T e^{i\alpha t} \tag{10}$$

According to rigid body dynamics, the ship motion equation with the center of gravity G as the center of moment can be expressed as:

$$\{M\} \left| \ddot{\eta}(t) \right\rangle = \{F(t)\} = \{F\} e^{i\omega t} \tag{11}$$

For the convenience of calculation, the fluid loads acting on the hull are divided into two parts: hydrostatic loads due to changes in the position of the ship's relative hydrostatic equilibrium and hydrodynamic loads dependent on wave and ship motion. Hydrostatic load comes from the contribution of hydrostatic pressure change caused by ship movement, which can be directly given by ship statics as follows:

$$\left\{ F^{S}(t) \right\} = -[C] \{ \eta(t) \} \tag{12}$$

Among them, only 5 items of hydrostatic coefficient *Cij*, *i*, *j* = 1, 2, ··· , 6 are not zero, they are:

$$\begin{cases} C\_{33} = \rho g A \\ C\_{35} = C\_{53} = -\rho g S\_{\text{y}} \\ C\_{44} = \rho g \forall h\_{\text{x}} \\ C\_{55} = \rho g \forall h\_{\text{y}} \end{cases} \tag{13}$$

In Formula (13), *A* and *Sy* are the waterplane area of the ship and the static moment to the Y-axis, ∀ is the drainage volume of the ship, *hx* and *hy* are the transverse and longitudinal metacentric heights of the ship respectively. According to the different dimensions of the mathematical model used to solve the flow field, it can be divided into three dimensional method and two dimensional method (slice method).

The above equation shows that the free surface condition under low speed has the same form as that under zero speed.

614 J. Cui et al.

If zero velocity radiation potential φ0 *j* and φ*U j* additional velocity potential φ*U j* are defined, let them satisfy continuity equation [*L*] of the fixed solution, bottom condition [*D*], distant radiation condition [*R*], free surface condition and object surface condition [*S*] defined by the following formula:

$$\begin{cases} \frac{\partial}{\partial n} \phi\_j^0 = n\_j, (j = 1, 2, ..., 6) \text{ It's on plane S} \\ \frac{\partial}{\partial n} \phi\_j^U = m\_j, (j = 1, 2, ..., 6) \text{ It's on plane S} \end{cases} \tag{14}$$

For the above fixed solution problem, the disturbance potential φ*j* and its gradient ∇φ*j*(*j* = 1 ∼ 7) can be determined by using appropriate numerical solution method. Introducing differential operator:

$$\frac{d}{dt} \equiv \frac{\partial}{\partial t} - U \frac{\partial}{\partial \mathbf{x}} = \mathbf{i}\boldsymbol{\omega} - U \frac{\partial}{\partial \mathbf{x}}\tag{15}$$

According to the linearized Bernoulli equation, the hydrodynamic pressure after deducting the change of hydrostatic pressure is as follows:

$$p(\mathbf{x}, \mathbf{y}, z, t) = -\rho \frac{d}{dt} \left[ \phi\_T(\mathbf{x}, \mathbf{y}, z) e^{i\omega t} \right] \tag{16}$$

## **3 Wave Load and Structural Response in Frequency Domain**

#### **3.1 Wave Load in Frequency Domain**

A floating nuclear power plant with a total length of 229.8 m and a total weight of 83,200 tons is taken as the numerical simulation object, and the model is modeled by the APDL module in Ansys 2021R1. The finite element model of hull structure is constructed by Shell181 and BEAM188 elements. The mesh size of the bottom and supporting part of the containment is 0.1 m, the mesh size of the upper part of the containment is 0.2 m, and the mesh size of the rest of the containment is 0.8 m. The total number of the whole ship elements is about 1.56 million. The finite element model of the built floating nuclear power plant and containment vessel is shown in the figure below (Figs. 1 and 2).

**Fig. 1.** Overall finite element model of floating nuclear power plant structure

In general, the hydrodynamic response of large floating body structure is a linear system. Therefore, when calculating the hydrodynamic response of the containment vessel of floating nuclear power plant under random waves, regular waves can be used

**Fig. 2.** Finite element model of floating nuclear power plant containment

to calculate first, and the calculated response can be divided by wave amplitude. In this way, the RAO of the floating nuclear power plant containment vessel can be obtained, which preliminarily reflects the hydrodynamic performance of the containment vessel, and then the HD module in Ansys Workbench is used for frequency domain analysis. As the floating nuclear power plant in this paper is symmetric about X-axis and Y-axis, the dynamic response caused by waves within the range of 0º–180º to the containment vessel of floating nuclear power plant is mainly analyzed. A wave direction is set every 15º, which is divided into 13 wave directions in total. The schematic diagram of wave incidence Angle is shown in the figure below (Fig. 3).

**Fig. 3.** Diagram of wave incidence Angle

The wave load calculation and structure analysis in this paper are based on linear theory. Under this condition, if the wave is a stationary random process, so is the alternating stress obtained by transformation. According to random process theory, the power spectral density of the above two stationary random processes has the following relationship:

$$G\_{\rm XY}(\omega) = \left| T(\omega) \right|^2 G\_{\rm NN}(\omega) \tag{17}$$

For A linear system composed of ships and waves, the stress response follows the characteristics of the linear system, and the synthetic stress can be written as σ = σ*C* + *i*σ*S* . In actual calculation, it is necessary to process the loads generated by regular waves of unit amplitude with different frequencies according to the real and imaginary parts respectively to obtain the corresponding response σ*c* and σ*s*, and then synthesize it into σ*A*(ω*e*). Thus, the transfer function of stress can be written as:

$$H\_{\sigma}(\omega\_{\mathfrak{e}}) = \sigma\_{A}(\omega\_{\mathfrak{e}}) \tag{18}$$

P-m spectrum can be written as the expression of different parameters. If it is expressed by the two parameters of meaningful wave height Hs and mean zero-crossing period *Tz*, the expression of wave spectrum can be written as follows:

$$G\_{\eta\eta}(\omega) = \frac{H\_S^2}{4\pi} (\frac{2\pi}{T\_Z})^2 \omega^{-5} \exp(-\frac{1}{\pi} (\frac{2\pi}{T\_Z})^4 \omega^{-4}) \tag{19}$$

In the analysis, the actual response frequency should be the encounter frequency A, and its relationship with wave frequency A is as follows:

$$
\omega e = \omega (1 + \frac{2\omega U}{g} \cos \theta) \tag{20}
$$

Therefore, the response spectrum of stress can be expressed as:

$$|G\_{\chi\chi}(\omega\_{\varepsilon}) = |H\_{\sigma}(\omega\_{\varepsilon})|^{2} G\_{\eta\eta}(\omega\_{\varepsilon}) \tag{21}$$

#### **3.2 Structural Response Calculation of Wave Load**

In the pre-processing of AQWA, the mass information and moment of inertia information of the hull structure need to be obtained through the whole ship finite element analysis. The incident wave direction interval is 15°, the number of wet surface units of the hydrodynamic model is 20403, and the total number of units is 38559, as shown in the figure below (Fig. 4).

**Fig. 4.** Hydrodynamic model

The calculated frequencies of waves in the frequency domain were 0.01592 Hz– 0.27 Hz, and 48 calculated frequency points were interpolated at equal intervals, totaling 50 calculated frequency points.

In AQWA calculating unit amplitude structural response under the action of amplitude, according to the main control parameters (RY), namely the total longitudinal bending moment, derived the relationship between the frequency and phase, and then according to the wave height (2 m), wave Angle of incidence, frequency and phase extraction wet surface wave pressure and the ship's hull acceleration, and loads it into structural response of the hull computation, as shown in the figure below (Figs. 5 and 6):

**Fig. 5.** Stress cloud of containment at wave frequency 0.06139 Hz

**Fig. 6.** Stress cloud of containment at wave frequency 0.06688 Hz

## **4 Wind Load and Structural Response**

#### **4.1 Wind Load**

The wind load rapid loading plug-in currently in use is based on API 4F specification: "Drilling and Workover Structure Specification", 2008 edition. Typical structural analysis is derrick, fan pile leg and jacket platform. The API Wind load Quick loading plugin is limited to API 4F specification profiles and methods and is not intended for general use. Other wind codes (like ASCE 7-05/7-10) are not included in this plugin.

This plug-in has the following advantages:

The total wind force on the structure is estimated by the vector sum of the wind force acting on individual components and accessories, as shown in the following formula:

$$F\_{\rm m} = 0.00338 \times K\_l \times V\_{\varepsilon}^2 \times C\_s \times A \tag{22}$$

$$F\_I = G\_f \times K\_{sh} \times \Sigma F\_m \tag{23}$$

In Eqs. (3-1) and (3-2):

Fm – The force of the wind perpendicular to the vertical axis of a single member, or to the surface of the wind wall, or to the projected area of the appendage.

Ki – a factor of the inclination Angle ϕ between the longitudinal axis of a single member and the wind.

Vz – Local wind speed at altitude Z.

Cs – shape coefficient.

A – The projected area of A single member is equal to the length of the member multiplied by its projected width with respect to the normal wind component.

Gf – Gust effect factor, used to explain spatial coherence.

Ksh – the conversion factor for the total shielding of a member or accessory and the variation of airflow around the end of the member or accessory.

Ft – the vector sum of wind forces acting on each individual member or accessory throughout the drilling structure.

## **4.2 Structural Response Calculation of Wind Load**

In this paper, the wind-loading plug-in in ANSYS Workbench is used. Firstly, the structural model of floating nuclear power plant is fixed rigidly and released inertia, and then constant Wind load is carried out on the Wind receiving surface of floating nuclear power plant (Wind speed 50.7 = 98.56 knot, Wind direction: 13, 0° to 180° with wind direction set at 15° intervals), at the same time, then export the result file, and perform post-processing in classic ANSYS.

The wind speed is 50.7 m/s, and the maximum equivalent stress of the containment is 8.15 MPa. The maximum stress occurs at the junction between the upper support and the bulkhead, as shown in the figure below (Figs. 7, 8 and 9).

**Fig. 7.** Ship - wide stress cloud **Fig. 8.** Containment stress cloud map

**Fig. 9.** Maximum stress and position of containment under wind load

## **5 Flow Load and Structural Response**

#### **5.1 Current Loading**

Ocean currents can be caused by many factors, such as local stationary currents caused by ocean circulation, tidal currents caused by periodic changes in the gravitational pull of the sun and moon on the Earth, differences in the density of ocean water, and the action of wind. It should be pointed out that the speed of wind on the sea surface is about 3% of the speed at 10 m above the sea surface. Tidal currents have an important influence on the flow field in some restricted waters. Tidal currents in restricted waters generally have a speed of 2–3 m/s and a maximum of 10 m/s.

For floating bodies, the flow of the ocean surface is of greatest concern to us. However, for the mooring system at sea, the distribution of water flow along the water depth is also our concern. For the designers, the maximum limit flow encountered during the operation of floating body is the most important factor affecting the design, so the actual measurement and monitoring of water flow velocity is essential. Since the velocity and direction of the water flow change slowly, we can approximately consider the water flow to be steady.

The action of water flow on floating body can be divided into the following two parts:

(1) Viscosity effect. Viscosity resistance due to frictional effects, and differential pressure resistance. For blunt body, the friction resistance can be ignored, and the pressure difference resistance is mainly.

(2) Influence of potential flow. The lift effect caused by the ring volume and the drag effect caused by the free surface effect are small in comparison.

Using flow force coefficient to estimate the flow load on the surface ship floating body:

The flow force/moment can be calculated by the following formula, in which the flow force coefficients are usually determined by model test methods.

$$\begin{aligned} X\_c &= \frac{1}{2} \rho \nu\_c^2 C\_{X\_c}(\alpha\_c) A\_{TS} \\ Y\_c &= \frac{1}{2} \rho \nu\_c^2 C\_{Y\_c}(\alpha\_c) A\_{LS} \\ N\_c &= \frac{1}{2} \rho \nu\_c^2 C\_{N\_c}(\alpha\_c) A\_{LS} L \end{aligned} \tag{24}$$

Similar to the wind load calculation of ship type floating body, the key to the flow load of ship type floating body is how to obtain the flow load coefficient, which is mainly obtained by model test.

For the calculation of flow load of large oil tankers, OCIMF based on model test data gives flow force coefficient curves of two different bow forms, full load and ballast, which have good reference value and are widely used in engineering design and analysis of mooring ships.

Remery and Van Oortmerssen carried out an experimental study in the MARIN Tank to test the flow loads on tanker models of different profiles and sizes. Since ships are mostly slender bodies, the axial flow load is mainly caused by frictional resistance. If the axial flow velocity is small, this resistance is difficult to measure, and it is not accurate to predict the axial resistance of real ships from model tests, because the scale effect is very obvious.

The axial flow load is important for anchored vessels. The force can be estimated based on the frictional resistance of the plate. The following formula is recommended by ITTC:

$$X\_c = \frac{0.075}{\left(\log\_{10}(R\_N - 2)\right)} \cdot \frac{1}{2} \rho V\_\text{c}^2 \cos \alpha\_c \cdot |\cos \alpha\_c| \cdot S \tag{25}$$

$$\text{Re} = \frac{|\cos \alpha\_c| V\_c \cdot L}{\upsilon} \tag{26}$$

For tanker, it is generally not a problem to estimate the transverse force and yawing moment of the real ship. For the transverse flow of ocean current in an oil tanker, the ship can be regarded as a blunt body. Because the bilge radius of the hull is relatively small, it can be considered that the flow separation situation in the model and the real ship is consistent, and the transverse force and the bow rolling moment can be considered independent of the Reynolds number.

In MARIN pool, the lateral force and bow rolling moment are expanded into Fourier series through experiments.

$$C\_{Y\_c}(\alpha\_c) = \sum\_{l}^{n} b\_n \cdot \sin(n \cdot \alpha\_c) \tag{27}$$

$$C\_{N\_c}(\alpha\_c) = \sum\_{l}^{n} c\_{l^\*} \cdot \sin(n \cdot \alpha\_c) \tag{28}$$

The above formula can be applied in deep water, but for shallow water, the lateral force and bow torque coefficients need to be multiplied by a correction factor. In practice, the free surface effect is small for deep water with flow rates of 3kn.

#### **5.2 Structural Response Calculation of Flow Load**

In this paper, Workbench Fluent and classical ANSYS 2021R1 are used to realize flow field analysis and structural response calculation. The viscous flow model, namely K-Omega (2EQN) SST model, is selected for flow field analysis. A THREE-DIMENSIONAL flow field model is established in Workbench DM module, and the flow field size is 500 × 600 × 27.6 (m), as shown in the figure below (Fig. 10):

**Fig. 10.** 3d model of flow field

The mesh of fluid domain is divided in Workbench mesh module. The mesh size of near-field fluid domain is 1.5 m, and that of far-field fluid domain is 3.5 m. The flow field and structural stress (75° flow direction as an example) corresponding to flow velocity of 0.83 m/s are shown as follows (Fig. 11):

At a flow rate of 0.83 m/s and a flow direction of 75°, the maximum equivalent stress of the containment fourth strength is 1.15 MPa. The maximum stress occurs at the arc transition of the equipment base inside the containment vessel, as shown below (Fig. 12).

**Fig. 11.** Calculation results of 75° flow direction

**Fig. 12.** Maximum stress position

## **6 Conclusions**

622 J. Cui et al.

## **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Research on Process Diagnosis of Severe Accidents Based on Deep Learning and Probabilistic Safety Analysis**

Zheng Liu1(B) and Hao Wang2

1 CNNC Key Laboratory on Severe Accident in Nuclear Power Safety, CNPE, Beijing, China<EMAIL_ADDRESS>
2 Department of Engineering Physics, Tsinghua University, Beijing, China

**Abstract.** Severe accident process diagnosis provides data basis for severe accident prognosis, positive and negative effect evaluation of Severe Accident Management Guidelines (SAMGs), especially to quickly diagnose Plant Damage State (PDS) for operators in the main control room or personnel in the Technical Support Center (TSC) based on historic data of the limited number of instruments during the operation transition from Emergency Operation Procedures (EOPs) to SAMGs. This diagnosis methodology is based on tens of thousands of simulations of severe accidents using the integrated analysis program MAAP. The simulation process is organized in reference to Level 1 Probabilistic Safety Analysis (L1 PSA) and EOPs. According to L1 PSA, the initial event of accidents and scenarios from the initial event to core damage are presented in Event Trees (ET), which include operator actions following up EOPs. During simulation, the time uncertainty of operations in scenarios is considered. Besides the big data collection of simulations, a deep learning algorithm, Convolutional Neural Network (CNN), has been used in this severe accident diagnosis methodology, to diagnose the type of severe accident initiation event, the breach size, breach location, and occurrence time of the initial event of LOCA, and action time by operators following up EOPs intending to take Nuclear Power Plant (NPP) back to safety state. These algorithms train classification and regression models with ET-based numerical simulations, such as the classification model of sequence number, break location, and regression model of the break size and occurrence time of initial event MBLOCA. Then these trained models take advantage of historic data from instruments in NPP to generate a diagnosis conclusion, which is automatically written into an input deck file of MAAP. This input deck originated from previous traceback efforts and provides a numerical analysis basis for predicting the follow-up process of a severe accident, which is conducive to severe accident management. Results of this paper show a theoretical possibility that under limited available instruments, this traceback and diagnosis method can automatically and quickly diagnose PDS when operation transit from EOPs to SAMGs and provide numerical analysis basis for severe accident process prognosis.

**Keywords:** Process Diagnose · Process Traceback · EOP · SAMG · Deep Learning · PSA · ET · MAAP

## **1 Introduction**

The application of the concept of defense in depth is the primary means of preventing accidents in a nuclear power plant and mitigating the consequences of accidents if they do occur [1]. If an accident occurs at a nuclear power plant, to restore safety, two types of accident management guidance documents are typically used: EOP for preventing fuel rod degradation, and SAMG for mitigating significant fuel rod degradation when a severe accident is imminent [2]. And the relationship between different components of an Accident Management Programme (AMP) is illustrated in Fig. 1. Preventive accident management EOPs integrate actions and measures needed to prevent or delay severe damage to the reactor core. Mitigatory accident management SAMGs refers to those actions or measures which become necessary if the preventive measures fail and severe core damage occurs or is likely to occur [3].

**Fig. 1.** Relationship between EOPs and SAMGs

Severe accident management guidelines should be comprehensively Verified and Validated [4] (V&V). Implementing and enhancing the existing SAMG program in NPPs is an important post-Fukushima activity [5]. Expert judgment, simulators, field training, tabletop exercises, emergency drill, and exercise and analysis are current practices related to SAMG V&V. Moreover, informing SAMG and actions through analytical simulation is a practical and commendable practice [5].

While numerical simulation is scenario/event based from initiating event to core damage, and even to fission product release to the off-site environment. There is a great challenge that SAMGs take an integrated, symptom-and-knowledge-based approach [5], and that means, SAMGs contain actions to be taken that are based on the values of directly measurable plant parameters [6].

SAMEX, a decision support system, is developed for use in severe accident management following an incident at a nuclear power plant [6]. Risk-informed severe accident risk database management module (RI-SARD), which is a risk-informed accident diagnosis and prognosis module of SAMEX [7], examines (a) a symptom-based diagnosis of a plant damage state (PDS) sequence in a risk-informing way and (b) a PDS sequencebased prognosis of key plant parameter behavior, through a prepared database, SARDB, which stores the data of integrated severe accident analysis code results like MAAP and MELCOR for hundreds of high-frequency scenarios from the plant damage state event tree of a Level 2 PSA. RI-SARD predicts a series of potential severe accident sequences that match the user-specified symptom criteria, and then prioritizes and adds more symptoms to screen down scenarios for prognosis analysis.

The accident process diagnosis and prognosis method, with fast-running severe accident codes and scenario selection, used in SAMEX, fills the gap between symptom-based analysis and event-based analysis. But with the given symptom of key parameters of NPPs, a small set of initiating events and sequences may lead to a similar plant damage state, and this method is not precisely focused on one scenario, which means multiple parallel sub-section simulations should be conducted to provide information for users to select.

Numerically reproducing symptom-based scenarios and selecting a small set of accident sequences to be simulated is practical in accident process diagnosis for SAMG implementation and assessment. Ideally, the selection of scenarios to be simulated should be made from the results of both Level 1 and Level 2 PSA [5], whereas only Level 2 PSA result is used in SAMEX.

The main purpose of this paper is to: 1) a concept of risk-and-knowledge informed diagnosis and prognosis of plant damage state during the entrance of SAMG, tracing back process progression from initiating event to core damage; 2) a feasible way to select only one scenario from the result of Level 1 PSA, especially ET, for numerically decision support for SAMG implementation and assessment, with an application of advanced algorithms, deep learning, in Artificial Intelligence (AI).

## **2 AI Application in Accident Diagnosis of NPPs**

Since the 1980s, with the field of artificial intelligence evolved, kinds of artificial intelligence methodologies are implemented for accident diagnosis in NPPs.

Jaques Reifman [8] provides a comprehensive survey of computer-based diagnostic systems using artificial intelligence techniques that have been proposed for the nuclear industry up to 1997. Two computing tools: expert systems or Artificial Neural Networks (ANNs), are used for artificial intelligence-based systems for process diagnostics. Hybrids of them and a combination of these technologies with numerical quantitative simulation programs have also been proposed.

The early diagnostic approaches were based on expert systems, and then ANNs before the 21st century, which follows chronologically the popularity of these artificial intelligence technologies.

Kinds of diagnosis systems were developed based on an expert system. REACTOR, an expert system for diagnosis and treatment of nuclear reactor accidents, was developed at the beginning of the 1980s in the U.S.A [9]. DISKET, which is based on knowledge engineering in the field of expert systems, has been developed to identify the cause and the type of abnormal transient of a nuclear power plant in the middle of the 1980s in Japan [10]. ADAM, an accident diagnostic, analysis, and management system application for severe accident simulation and management in the 2000s in the U.S.A [11]. Even in the past few years, a decision support system called SEVERA was developed in Europe [12], aimed at supporting the decision-making team during an accident or a training exercise, using decision modeling software DEXi, which is based on if-then rules.

The ANNs method application for diagnosis in NPPs is data-driven with model training and is mainly trained with simulation data of NPPs. Diagnosis result is highly dependent on the quality of simulation results. At the early stage, numerical simulation is not quite competent for accident progression. No systemic application was built based on ANNs, only in some specific domains, ANNs were applied as a methodology basis.

But nowadays, integrated simulation code, MAAP or MELCOR, is advanced involved in the past few decades. And several diagnosis systems were developed. ADAS, using neural networks, was developed in the 2000s in Korea for accident diagnosis and support operator decision-making [13]. A severe accident diagnosis and response support system was developed in China, which uses three diagnostic methods including BP neural network method, SDG expert diagnosis, and artificial diagnosis [14].

Moreover, some other machine learning methods emerged and are applied for accident diagnosis in NPPS. A cascaded support vector regression (CSVR) model is used to predict accident scenarios, accident locations, and accident information [15]. An approach for diagnosis of multiple failures based on dynamic Bayesian networks (DBNs) is proposed to support emergency response in case of an incident [16].

Nowadays, the most popular AI technology is Deep Learning, which is a subset of machine learning and essentially a neural network with three or more layers. Related algorithms in this domain include Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN), Auto Encoder (AE), Generative Adversarial Network (GAN), etc. These algorisms greatly improve the ability to solve practical issues, such as image recognition, speech recognition, auto driving, language translation, etc. And inspires new prosperity of AI applications.

Although numerical simulation is applied to generate accident data, those AI methods mentioned above do require not a very large dataset to train the model, hundreds or even thousands of simulations may be enough. As a drawback, the diagnosis capability may be limited.

## **3 Traceback Accident Progression Methodology During Transition from EOP to SAMG**

Following the occurrence of initiating event, EOPs are step-by-step procedures for operators in the main control room to put the NPPs into a safe state. Prevention efforts, including safety system function and human performance, with success or failure execution, direct to different branches of the progression path, which are static sets of ETs of L1 PSA. Key procedures in EOPs are simplified as header events of ETs, for example, depressurizing the primary system. This path with the uncertainty of time may produce tens of thousands of scenarios.

According to different SAMG entrance conditions, for example, core exit temperature exceeds 650 °C, TSC is formed to mitigate accident progression from large nuclide release. Plant damage state assessments are required when operation transitions from EOPs to SAMG.

With fast-running simulation code, qualitatively PDS and SAMG action assessment is conducive for accident management. But the obstacle gap between symptom-based SAMG and event-based numerical analysis needs to be filled first.

This paper promotes a traceback method for TSC, which can automatically generate an input deck of simulation code, based on chronological parameter data from initiating event occurrence time to time when SAMG entrance condition is realized. And this method is data-driven, using the good performance of deep learning algorithms to diagnose header events and their time to define a relatively reasonable scenario that confines symptoms on assessment time. It's their advantage to diagnose from big datasets for DL algorithms, while with a little number of datasets, they may diagnose with poor capability.

#### **3.1 Traceback Methodology**

The main steps are described as follows:

1) Analysis of event trees and header events selection

First, a review of event trees from publicly available Level 1 PSA is performed to select the main header events for every sequence path which causes core damage.

2) Sequences simulation and database generation

With the previously identified header events delineated for each sequence, using a simulation tool, and with the occurring time uncertainty branch, a database is produced with a large amount of CPU calculation work. The branching method will be explained in the following section. Selection of key parameters as the figure of merits is performed for simulation output.

3) Traceback model training for scenario confinement

Using DL algorithms, classification and regression models are trained with formerly generated scenarios database. This may last for weeks. Different kinds of DL algorithms are tried to be used, and hyperparameters are tuned with effort.

4) PDS diagnose with simulation and real-time instruments indicator

Put chronological real-time instrument data into DL-trained models to diagnose confined scenarios, and then generate an input deck of the simulation tool, ranging from initiating event occurrence time to the time when core exit temperature exceeds 650 °C. This defined scenario is a base scenario for the following accident simulation.

5) Prognosis and SAMG action assessment

Put SAMG action into input deck of base scenario, and following simulation code execution, which runs fast ahead of real-time, will prognosis the following accident progression with/without SAMG action.

#### **3.2 Header Event Branches**

According to step 2, header event branching is conducted in dealing with scenario uncertainties.

The third issue described in the report of OECD/NEA [5] is the treatment of simulation uncertainty for assessing SAM actions using an analytical tool. The best-estimate approach is recommended for analytical simulation because a conservative approach may not be of much help and sometimes could even lead to a wrong decision.

Despite code uncertainties, representation uncertainties, numerical inadequacies, user effects, computer/compiler effects, and plant data uncertainties for the analysis of an individual event, branching time is one important uncertainty for sequence definition. Lots of evaluation effort has been done for computer code uncertainty.

While some safety systems function automatically, there is still uncertainty between simulation and real-time accident progression. In addition, automatic safety systems may fail and manual work with delayed time may still be needed to define accident scenarios.

Besides, manual actions following up EOPs may delay branching time for diagnosis time, preparation time, and execution time.

**Fig. 2.** Event tree branches

Kinds of breaching time for both safety systems and manual actions are simulated for scenarios, as shown in Fig. 2. For one sequence of ETs, header event 1 action should be done at time t1 as action condition is fulfilled in simulation, three branches deviated t1 time, which are 10 min after t1, 20 min after t1 and 30 min after t1. The safety system or manual actions at header event 2 is similar to header event 1, and three branches are formed with different delay times. And another three branches for t2 action are formed for a scenario with t1–2 action in 20 min. So, the permutation of delayed action time for header events makes a very large number of scenarios for one sequence of ETs.

## **4 Case Study – Medium Break LOCA (MBLOCA) in a Pressurized Water Reactor (PWR)**

This section presents an example application of the above-referred traceback methodology to define a suitable input deck of accident progression scenario from initiating event to core exit temperature exceeding 650 °C in no more than one day, which is the basic scenario for SAMG actions implementation assessment.

The initiating event of this case study is the middle break loss of coolant accident in a pressurized water reactor. According to L1 PSA, two ETs are analyzed which differ in the position of break, one break is on one hot leg, and the other one is on one cold leg. Only hog leg ETs is analyzed in this case study.

#### **4.1 Event Tree Analysis and Header Events Selection**

The event tree of MBLOCA with a break on the hot leg is depicted in Fig. 3. There are a total of 21 sequences in this ET, 4 sequences result in bringing back to safety status (OK), and the remaining 17 sequences lead to core damage (CD), which cause different plant damage state.

Among these 17 sequences, some of them may not need to be distinguished due to their header events. For example, sequences 7, 8, and 9 are like sequences 11, 12, and 13 respectively. The difference between them is human error in safety actions or the mechanical inherent failure of these safety systems. So, 13 sequences causing CD are screened for the next steps.

Not all of the header events in Fig. 3 are used for each sequence. For example, only E01, H01, and E02 are used for scenario 2. And head events needed for each sequence are analyzed for each sequence.

**Fig. 3.** MBLOCA Event Trees

#### **4.2 Event Tree Scenarios Simulation with Branches**

Modular Accident Analysis Program (MAAP) is used as a numerical analysis tool for scenario simulation.

For every one of the screened 13 sequences, 10 different initiating event occurrence times, 10 break sizes, 2 break locations (near/not pressurizer), and 10 branching times for each header event are analyzed and simulated. The branching point is managed in the above-referred method. All these simulation results generate a database of knowledge on accident progression. Some parameters chosen as figure-of-merits (FOMs) are listed in Table 1.

**Table 1.** FOMs of simulation

#### **4.3 DL Models Training**

1D-CNN (one-dimension convolutional neural network) algorithm is used for this modeling task. The knowledge database formally generated is used as training and testing data for classification and regression models.

The classification models include the sequence number of ETs, and break location near or not near the pressurizer.

And regression models include initiating event occurrence time, break size, and branching time for every header event in every sequence.

The result of the training models is listed in Table 2.

Due to the large scale of scenarios, weeks of training time may be needed for this task.

**Table 2.** Result for sequence 2 of ETs in MBLOCA

#### **4.4 Trace Back Accident Progression**

Accident data from the simulator or MAAP is generated for testing 1D-CNN trained models. In the case of real implementation, parameters of instrument indicators are used for gathering chronological data of accident progression.

The task in this section is to automatically generate a defined input deck of MAAP, which relatively accurately depicts the chronological progression from initiating event to core exit temperature exceeding 650 °C. And the methodology is to input chronological data to 1D-CNN trained models and get classification and regression data for each model. These tracked back model data are written to an input deck of MAAP.

Based on this section, a basic scenario for testing accident data is confined to an input deck of MAAP.

#### **4.5 Application of Basic Scenario for SAMG Assessment**

With the above-referred tasks, TSC can diagnose plant damage state using an input deck of basic scenarios. For the prognosis of an accident, TSC personnel put related action commands for SAMG actions into this basic input deck, with the calculation result of MAAP, the negative or positive effect of these actions can be foreseeable with fast running code. And the simulation result is used for decision support of TSC.

## **5 Conclusions**

Numerical analysis is a practical tool for SAMG assessment. But the gap between symposium-based SAMG actions and event/scenario-based numerical simulation is the first obstacle to on-time decision support. Although methods of using L2 PSA are provided, the drawback of several screened scenarios are not focused and may generate controversial calculation results.

Event trees of L1 PSA are used for scenarios database generation, and header events selection is performed to generate the skeleton of scenarios.

Uncertainty of scenarios is considered in this traceback method, with different time branching points for each header event of scenarios, and confidence is gained for the following decision-making support.

The method described in this paper is good at automatically generating an input deck for a basic scenario ranging from initiating event to core exit temperature exceeding 650 °C. And the track back result fills the gap between symposium-based SAMG actions and event-based simulations. The prognosis for SAMG assessment can be realized based on this methodology.

## **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Study on Calculation Method of Corrosion Product Source Term in Lead-Bismuth Fast Reactor Coolant System**

Haixia Wan(B)

China Institute of Atomic Energy, Beijing, China<EMAIL_ADDRESS>
**Abstract.** In the coolant system of lead-bismuth fast reactor, the corrosion products produce great occupational radiation dose to the workers, especially in the process of maintenance and repair of nuclear facilities. Therefore, it is very important to accurately calculate the corrosion product source term caused by the reaction between coolant and structural materials. The generation, migration, decay and deposition of corrosion products are described by the corrosion characteristics of lead-bismuth alloy on stainless steel in coolant loop, and the mathematical equilibrium equation is established. The equation is used to calculate the corrosion product source term of the coolant loop in the 20MWth lead-bismuth fast reactor and the variation laws of the corrosion product with time are obtained. The results show that the radioactivity of the corrosion products mainly comes from nuclides such as 51Cr, 54Mn, 58Co and 60Co, and the short-lived nuclides such as 51Cr and 58Co decay gradually after shutdown, long-lived nuclides such as 54Mn and 60Co are the main sources of radioactivity.

**Keywords:** Corrosion Product · Coolant · Lead-Bismuth Alloy · Stainless Steel · Activity

## **1 Introduction**

Lead-bismuth fast reactor is one of the six main types of the fourth generation reactor, which has the characteristics of safety, economy, continuity and nuclear nonproliferation. However, the corrosion ability of lead-bismuth alloy cannot be neglected, and the corrosion products caused by it should not be underestimated. Studies have shown that more than 90% of occupational exposure is caused by corrosion products deposited on the pipe wall from the coolant, which continue to decay and emit gamma rays in the pipe wall or coolant, in particular, some long-life nuclides in the shutdown for a period of time will still cause radiation damage to equipment maintenance workers. Therefore, it is important to study the generation and migration of corrosion products in the alkali metal coolant loop, predict the change and distribution of corrosion products for the radiation shielding design of lead-bismuth fast reactor, the inspection and maintenance of the reactor, and the accident analysis.

In view of the important influence of corrosion products on radiation protection, a great deal of research has been carried out at home and abroad, Such as the PWR-GALE program developed in the United States, the PACTOLE program in France, the Nuclear Power Institute, the Suzhou Thermal Engineering Institute, Tsinghua University, the North China Electric Power University Shanghai Jiao Tong University, and Harbin Engineering University. The above calculation program or method, the principle used is basically the same, but the simplification and assumptions used, as well as the specific treatment methods are not the same. The point reactor model is often used in the calculation, which does not take into account the influence of uneven distribution of neutron flux rate and coolant flow time, so its calculation precision is not high. In addition, the existing source item calculation program has some limitations; the calculation system and equipment are also specific, not universal. At present, the study on source term of corrosion products in water-cooled reactor is mainly focused in China, but there is no systematic study on source term of corrosion products for lead-bismuth coolant.

Based on the characteristics of lead-bismuth reactor coolant loop, the corrosion mechanism of lead-bismuth alloy and the corrosion rate of lead-bismuth alloy, the process of corrosion products generation, decay, migration and deposition in the loop are simulated in this paper; the mathematical equilibrium equation is established. The source term of corrosion products of lead-bismuth coolant was calculated by calculating the fast neutron reaction cross section of the reactor. This study provides reference data for related research in China.

## **2 Corrosion Source**

#### **2.1 Impurities in the Coolant**

The impurities in the coolant mainly come from the raw materials and the impurities introduced in the operation. The lead-bismuth alloy was synthesized from lead and bismuth in the ratio of 44.5% and 55.5%, the impurities are mainly non-metallic impurities such as oxygen, carbon, and metallic impurities such as calcium. The pipelines and equipment of the reactor loop are processed, welded and cleaned in the process of manufacture, installation and maintenance, this process inevitably leaves behind some dirt, grease, gasoline, metal chips, welding slag, surface oxides and moisture, which is another major cause of contamination and impurities in the coolant system.

### **2.2 The Structural Material of the Coolant Channel**

Lead and bismuth coolants have the characteristics of high melting point, high boiling point, chemical property inactivity and "Negative" cavitation reactivity. Lead and bismuth are chemically inert with fuels, low alloy steel, water and air. The structural material commonly used in contact with lead-bismuth alloys is stainless steel.

By analyzing the main components and impurities in stainless steel, the possible activation reaction types were determined. Finally, the radionuclide types of various corrosion products, the corresponding reaction types and the main sources of structural materials were counted; the results are shown in Table 1. The common active corrosion products in the main circuit are radionuclide as 24Na, 51Cr, 56Mn, 59Fe, 58Co and 60Co, and their initial nuclides are mainly Fe, Cr, Ni, Mn and Co in the structural materials.

**Table 1.** Source of Corrosion Products

## **3 Method of Establishment**

#### **3.1 Coolant Migration Process**

When calculating the source term of corrosion products in the main loop, there are two general conditions. One is that the materials in contact with the coolant in the main circuit are first corroded and dissolved in the coolant; the other is that the material in the core is first activated by radiation, and then corroded down to dissolve in the coolant. As the coolant flows, some of the activated corrosion products in the main circuit will be deposited on the equipment or pipelines in the main circuit, most of which will be cleaned by the purification system, and some will remain in the main circuit coolant. The generation and migration of corrosion product source term in the main loop can be divided into six processes as follows:

#### **3.2 Computational Model**

In the coolant loop, the amount of the target radionuclide of the structural material decreases gradually with neutron irradiation.

$$\frac{dN\_1}{dt} = -\overline{\sigma}\_1 \overline{\phi}\_1 N\_1$$

638 H. Wan

$$\frac{dN\_2}{dt} = \overline{\sigma}\_1 \overline{\phi}\_1 N\_1 - \lambda\_2 N\_2$$

In the formula, N1 is the nuclear density of the target nucleus in the structural material; t is the time;N2 is the nuclear density of the irradiated radionuclide; σ1 is the average neutron activation cross section of the target nucleus; φ1 is the average neutron flux rate of irradiation; λ2 is the decay constant of the irradiated radionuclide.

The increase in radionuclide in the primary circuit due to corrosion of the reactor activated materials at constant reactor power can be calculated as follows:

$$\begin{split} R\_{cl} &= \sum\_{l} \left( \sum\_{j} \frac{f\_{nl} \cdot C\_{0j} \cdot S\_{j} \cdot N\_{A}}{A\_{l}} \right) \\ &= \sum\_{l} \left( \sum\_{j} \frac{f\_{nll} \cdot f\_{sllj} \cdot C\_{0j} \cdot S\_{j} \cdot N\_{A}}{A\_{l}} \cdot \chi\_{l} \right) \\ &= \sum\_{l} \left[ \sum\_{j} \frac{f\_{nll} \cdot f\_{slj} \cdot C\_{0j} \cdot S\_{j} \cdot N\_{A}}{A\_{l}} \cdot \frac{-\overline{\phi} \cdot \overline{\sigma}\_{I}}{\lambda\_{i}} \cdot \left(1 - e^{-\lambda\_{i}t} \right) \right] \\ &= \frac{N\_{A} \cdot \overline{\phi}}{A\_{i} \cdot \lambda\_{i}} \cdot \left(1 - e^{-\lambda\_{j} \cdot t} \right) \sum\_{l} \left[ \overline{\sigma}\_{Il} \cdot \left(\sum\_{j} f\_{mll} \cdot f\_{slj} \cdot C\_{0j} \cdot S\_{j} \right) \right] \end{split}$$

In the formula, *f* ai is the quality share of the radionuclide in the material; *C*oj is the material corrosion rate of module j; *S*j is the corrosion area of module j; NA is the Amado Avogadro constant; Ai is the atomic weight of radionuclide I; *f* sILj is the mass share of the nuclide chemical element in the material composition of module j; *f* nIl is the natural abundance of the target nucleus; λi is the decay constant of radionuclide i.

When the reactor power is constant, the total nucleon number of the activated corrosion products in the coolant changes with time according to the following equation:

$$\begin{split} \frac{d\boldsymbol{n}\_{\rm{vl}}}{dt} &= \boldsymbol{R}\_{\rm{cl}} - \boldsymbol{\lambda}\_{\boldsymbol{i}} \cdot \boldsymbol{n}\_{\rm{vl}} \\ &= \frac{\boldsymbol{N}\_{\rm{A}} \cdot \overline{\boldsymbol{\phi}}}{\boldsymbol{A}\_{\boldsymbol{i}} \cdot \boldsymbol{\lambda}\_{\boldsymbol{l}}} (1 - e^{-\boldsymbol{\lambda}\_{\boldsymbol{i}} \cdot \boldsymbol{t}}) \sum\_{l} \left[ \overline{\boldsymbol{\sigma}\_{\rm{ll}}} \left( \sum\_{j} f\_{\rm{vl}l} f\_{\rm{slf}j} \boldsymbol{C}\_{0} \boldsymbol{S}\_{j} \right) \right] - \boldsymbol{\lambda}\_{\boldsymbol{i}} \cdot \boldsymbol{n}\_{\rm{vl}} \\ &= \frac{\boldsymbol{N}\_{\rm{A}} \cdot \overline{\boldsymbol{\Phi}}}{\boldsymbol{A}\_{\boldsymbol{i}} \cdot \boldsymbol{\lambda}\_{\boldsymbol{l}}} \sum\_{l} \left[ \overline{\boldsymbol{\sigma}\_{\rm{ll}}} \left( \sum\_{j} f\_{\rm{nll}l} f\_{\rm{sfl}j} \boldsymbol{C}\_{0} \boldsymbol{S}\_{j} \right) \right] \\ &= \frac{d \boldsymbol{n}\_{\rm{wl}}}{dt} = \boldsymbol{R}\_{\rm{cl}} (1 - e^{-\boldsymbol{\lambda}\_{\boldsymbol{l}} \boldsymbol{t}}) - \boldsymbol{\lambda}\_{\boldsymbol{l}} \cdot \boldsymbol{n}\_{\rm{wl}} \end{split}$$

If *t* ≤ *t*1, the analytical solution of the equation is:

$$\mathbf{n}\_{\mathbb{W}l}(\mathbf{t}) = \frac{\mathcal{R}\_{\mathcal{C}l}}{\lambda\_l} - \frac{\mathcal{R}\_{\mathcal{C}l}\lambda\_l t + \mathcal{R}\_{\mathcal{C}l}}{\lambda\_l}e^{-\lambda\_1 t}$$

if *t* > *t*1, The power of the reactor has changed, the average neutron flux rate of the reactor has changed, The solution of the equation is:

$$\begin{split} \mathbf{n}\_{\rm wt}(\mathbf{t}) &= \frac{\mathcal{R}\_{c12}}{\lambda\_{l}} \Big[ 1 - \mathbf{e}^{\lambda\_{l}(t\_{1}-t)} \Big] - \mathcal{R}\_{cc2}(t - t\_{1}) \mathbf{e}^{-\lambda\_{l}t} \\ &+ \frac{\mathcal{R}\_{c1}}{\lambda\_{l}} \Big[ \mathbf{e}^{\lambda\_{l}(t\_{1}-t)} - \mathbf{e}^{-\lambda\_{l}t} \Big] - \mathcal{R}\_{c1}t\_{1} \mathbf{e}^{-\lambda\_{l}t} \end{split}$$

#### **3.3 Example Description**

The type of this example is a compact pool structure, as shown in Fig. 1; the main parameters are shown in Table 2. Under normal operating conditions, the circulation flow of lead-bismuth medium in the first circuit is as follows: Lead and Bismuth are heated from bottom to top by the core in the internal components of the reactor, and then enter the upper steam generator of the collector chamber through openings in the upper part of the containment vessel, After the heat transfer is completed from the top to the bottom of the primary side of the steam generator and the secondary side, the secondary side outlet is reintegrated into the lower collecting cavity of the side shield, and the inner opening of the side shield returns to the upper collecting cavity from the bottom to the top, Then flow down the annular passage between the side shield and the main vessel and enter the main pump inlet, under the pumping of the main pump, the annular passage between the lower shield and the lower head of the main vessel enters the lower collecting cavity of the core along the flow distribution mechanism, and finally returns to the core.

**Fig. 1.** Schematic Diagram of Pool-type Structure of Lead-bismuth Fast Reactor

**Table 2.** Main Parameters

#### **3.4 Calculation Results and Comparative Analysis**

The fast neutron average reaction cross sections for various reactions were calculated using the MCNP code, as shown in Table 3. The radioactivity of the corrosion products in the model coolant is calculated using the formula in Sect. 3.2, and a comparison with the results of the same type of reactor is shown in Table 4.

**Table 4.** Results and Comparison of Radioactive Activity of Corrosion Products

As can be seen from Table 4, the total activity of corrosion products in the leadbismuth coolant circuit is 1.97E+15Bq. Among them, 51Cr, 54Mn, 58Co and 60Co have the largest proportion, but 51Cr and 58Co are short-lived nuclides, which can decay rapidly after shut down for a period of time, and 54Mn and 60Co have longer lifetime, which are the main contributors to the total activity.

Compared with ClEAR-1, the model has same life, but different power, temperature, flow, and structural materials. These factors cause the total amount of corrosion products to be more than ClEAR-1.

## **4 Conclusions**

The sediment source term of corrosion products is the main source of occupational irradiation, and it is also the key and difficult point in the source term analysis of nuclear facilities. Based on the characteristics of lead-bismuth coolant system, the release, migration, decay and deposition of corrosion products in the coolant loop are fully considered, a method for calculating the source term of corrosion products in lead-bismuth coolant loop is developed, The method is used to simulate the coolant loop of lead-bismuth fast reactor, and the source term of corrosion products is calculated. The results show that the source terms of the corrosion products are mainly composed of 51Cr, 54Mn, 56Mn, 58Co, 60Co and 59Fe, among which the long-lived nuclides 60Co and 54Mn are the main contributors to the radioactive activity. The analytical methods and conclusions of this paper can provide theoretical support for relevant domestic research.

### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

#### **Research on** *-***I Control Strategy During Rapid Power Reduction**

Desheng Meng(B) , Rong Duan, and Zhijun Li

China Nuclear Power Technology Research Institute, Shenzhen, Guangdong, China<EMAIL_ADDRESS>{duanrong<EMAIL_ADDRESS>
**Abstract.** Cold source for the cooling system is provided by CRF pump in nuclear power plant. During failure of CRF pump, a rapid core power reduction to a lower power level is needed, which poses a challenge to -I control of the core. Based on the requirements of operating technical specifications, the influence of various factors concerned the -I control strategy such as cycle burn-up, low power level and power reduction methods is researched for the rapid power reduction process in a certain balance cycle. Meanwhile, sensitivity analysis is carried out on the action of the control banks for different phases during the rapid power reduction process. Based on the analysis of the main influencing factors, proposal on the rapid power reduction strategy related to the reduced power level, power reduction method and different characteristic burn-up is put forward. The match of the cooling capacity of the CRF pump and the reduced core power is realized, thus ensure the safety and economy performance of reactor core.

**Keywords:** -I · Power Reduction · Control Strategy · Operation Diagram · CRF Pump

## **1 Introduction**

Two circulating water pumps (CRF pumps) are equipped in the three loops of the nuclear power plant in order to provide cooling water and thus to realize the heat removal [1]. During a cold source failure or CRF pump failure, a rapid core power reduction to a lower power level is demanded based on the available CRF pump cooling capacity. During the power reduction process and the stay of the low-power platform, the core axial power distribution is disturbed, and the axial power deviation of the core (-I) is relatively hard to control, which is likely to cause a reactor trip. Consequently, it is vital to study the -I control strategy in order to achieve a compromise between the CRF pump cooling capacity and -I control. It is also of importance for core safety and plant economics.

In the process of rapid power reduction, many problems appear in -I control. The power reduction methods in nuclear power plants can be divided into two types: boronization and rod insertion. As for the method of boronization, the power distribution is less perturbed. However, due to the limitation of the boronization speed, the power change rated is relatively low, which is difficult to satisfy the rapid reduce power requirements at some time. Meanwhile, when using the boronization method to reduce power, -I is likely to continue increasing. As the power difference is so large until exceeding the right boundary the operation diagram. It will cause a reactor trip. The safety and economy performance of the unit are infected. As far as the way of rod insertion is concerned, the power reduction process can be realized within a short period of time by a rapid introduction of negative reactivity. Nevertheless, the rod insertion method disturbs largely the core power distribution. Meanwhile, The GN rods must be fully extracted out of the core within a certain period of time after the operating technical specifications which strictly restricts on rod insertion time. During the GN rod withdrawal, it is likely for -I to exceed the right boundary. In addition, during the rapid power reduction, the core -I is also significantly related to the core burnup and the magnitude of the power reduction, that's why the core control strategy research is challenging.

In this paper, the SCIENCE program is utilized to simulate the variation of -I in the process of rapid power reduction. The control strategy of -I, which involves fuel burnup, low-power platform, and power-reduction methods, is optimized with the help of SOPHORA program. At the same time, the control rod action sensitivity analysis is also completed in this paper. Suggestions for -I control strategy in the process of rapid power reduction are given.

## **2 Research Background of Rapid Power Reduction**

Researchers have carried out a lot of explorations and researches on the problem of -I control strategy of the rapid power reduction process. Among them, qualitative analysis has been given from the perspective of core characteristic including burn up, burnable absorber, control rod position, fuel type and moderator temperature in a large number of literatures [2–10]. At the same time, power reduction types, such as power reduction to hot shutdown, daily power reduction or augmentation, extended low power operation (namely ELPO), stretch out operation, are also described qualitatively [5]. Nevertheless, literature related to rapid power reduction is relatively scarce, especially the quantitative analysis. The difficulty of -I control is mentioned [9] in a case that the reactor realize a reduction of power rapidly by a speed of 50 MW/min due to cooling source failure. Therefore, the power is forced to reduce to below 30% FP in order to prevents load rejection action due to the uncontrollable -I. On the basis of previous research, quantitative and in-depth research on the impact of different factors in the process of rapid power reduction is meaningful to the -I control and to the matching between the low-power platform and the cooling capacity of the cold source pump, thus ensuring the safety and economy performance of the reactor operation.

## **3 Research Methods**

In order to ensure the safe operation of reactor, the operating diagram limitations on -I must be met. In addition, operation technical specifications are also mandatory considering the operation factors. Under the condition of meeting these limitations, SCIENCE and SOPHORA programs are utilized to study the influence of difference factors, such as burnup, low-power platform, power reduction method and control rod action on -I control in the process of rapid power reduction.

#### **3.1 Operation Technical Specifications**

As one of the main bases for the operator to control the reactor, the operation diagram shows the relationship between the allowable value of -I and the relative reactor power. During the rapid power reduction process, the operator must ensure that -I satisfies the operation diagram. In addition, the -I performance also needs to meet the operation technical specification in which the operation diagram is defined. Related operating technical specifications are listed: when P-Iref is determined and the power of the core is reduced from high power to 50% or less, control rod insertion time is limited to 12 h in any 24 h period in region I and -I is limited at region I. In the case of a capacity of a quick return to high power levels, the control rod insertion limitation time can be extended to 24 h. When all the power compensation rods(GN rod) are completely drawn out, -I is able to leave the area I after 6 h of stable operation.

#### **3.2 SCIENCE and SOPHORA Software**

SCIENCE graphical software package, which invoked by the Copilote graphical user interface is used in this paper for calculations. SMART programs is used for 3D homogenized cores calculation. SOPHORA program is utilized for -I control strategy optimization.

#### **3.3 Overall Control Strategy**

Under the condition of meeting the demands of operation technical specifications, two periods related to rapid power reduction, which is the period of rapid power reduction and the low power platform is respectively considered in order to evaluate various influencing factors in this article.

Concerned the strategy of rapid power reduction period, the control of -I is achieved in two ways. One is to insert the GN rod according to the G9 curve, while the power decrease at a speed of 10MW/min until reaching the low power platform. The other is to increase the boron concentration of the core firstly, at the same time, the power decrease at a rate of 3 MW/min until 80%FP. Then, GN rods is inserted in order to reduce the power at a relatively high speed of 10 MW/min. As for the strategy of low power platform, the core is boronized in order to withdraw all GN rods while R rod is used to control -I in order to meet the requirements of operating technical specifications in Sect. 3.1 (the time limitation for rod insertion).

In order to study the -I control strategy of reducing power to different low-power platforms at different fuel burnup points, a certain 18-month refueling cycle was selected for research at 150 (BLX), 6000, 11000 (-I most negative burnup point), 14000 (MOL), 16000 (80%EOL), 18000MWd/tU and EOL. Low power platform of 50%, 60%, 65%, 70%, 80% FP are studied and the -I control strategy is carried out in case of reactor cold source failure.

## **4 Optimization Results**

The -I control strategy optimization results of rapid power reduction is researched by mainly focusing on three factors: fuel burnup, reached low power level platform, and the power reduction method. The comprehensive impact evaluation of the three factors is also studied. Then, this paper introduces the sensitivity analysis of the control rod action in the process of rapid power reduction, and gives the -I control strategy conclusion of the rapid power reduction process.

## **4.1 Influence of Fuel Burnup**

During the reactor normal operation, the temperature of the lower part of the core is lower than that of the upper part. Due to the negative feedback of temperature, the core -I is generally negative. Along with the deepening of burnup, the burnup in the lower part of the core is gradually larger than that of the upper part, therefore, -I tends to increase due to the influence of the burnup effect. In this research, after the GN rods are extracted, a larger -I is unfavorable for core control. Worse, the xenon oscillation effect manifest more negative effects at EOL than BOL.

In order to study the influence of the fuel burnup effect, the GN rod is inserted to reduce the power to 50% PN during the rapid power reduction period and the -I variation is compared at BLX, MOL and EOL. R rod is used to control -I only at the low power platform. The variations of -I are shown in Fig. 1:

**Fig. 1.** Burnup influence for -I control

It can be seen from Fig. 1 that -I exceeds zone I when the GN insertion time is limited to 12h for all three burnup points. Therefore, we can draw that for the whole cycle, it's likely to exceed zone I when the power is reduced to 50%FP rapidly. We also note that -I will not exceed the right boundary at operation diagram at BLX; Nevertheless, at MOL and 80% EOL burnup, the xenon oscillates more violently and -I tends to be bigger, thus it exceeds the right boundary. -I control is influenced significantly by fuel burnup.

#### **4.2 Impact of Low-Power Platforms**

In addition to fuel burnup, the low power level reached by the core after a rapid power reduction also has a considerable impact on -I control. When the core power is reduced from 100% to 80% FP or more, -I is easy to control due to the small variations in power. Additionally, if the core power is reduced to 30% FP or even less, although power distribution go worse, -I may still be controllable thanks to the lower power levels. However, as the power is reduced to 30%–80% FP, -I is the most difficult to control.

**Fig. 2.** Low-power platform influence for -I control

As shown in Fig. 2, when the power is reduced to a low-power platform which is greater than 50% PN, the greater is the power reduction, the greater is the -I oscillation caused by the xenon oscillation. When the power is decreased to the 80% FP, -I varies slightly within zone I. While the power is reduced to 60% or 80% FP, -I exceeds zone I. Therefore the low-power platform also affects largely the -I control.

#### **4.3 Influence of Boronization and Rod Insertion**

It can be obtained from Sect. 3.3. That two methods can be used for rapid power reduction: one is direct rod insertion and the other is boronization to 80%FP and then rod insertion. The power drops rapidly in the upper part of the core because of the rod insertion, and thus -I becomes more negative. The boronization power reduction method disturbs less to the core -I than rod insertion method, and it leads to a more positive -I. In order to compare the effects of two power reduction methods on -I control, the core -I elevation of the two cases is compared.

It can be seen from Fig. 3 that the -I performance is slightly improved by adopting the method of boronizing and then inserting the rod. At the same time, studies have shown that if boronization itself is used to reduce power to 50% PN, not only the power change rate is limited, but -I is easy to exceeds the right boundary. The -I oscillation can be slightly reduced by using the rapid power reduction strategy of boronization and then insertion the control rod.

**Fig. 3.** Boronization and rod insertion influence for -I control

#### **4.4 Comprehensive Feasibility Analysis of Fuel Burnup, Low Power Platform and Boronization**

It can be drawn from Sect. 4.1–4.3 that fuel burnup, low power platform and power reduction method have major influence on -I control. A comprehensive analysis contains the -I control strategy optimization at different fuel burnups to different low-power platforms and by using different methods. We also note that the criteria of feasibility for rapid power reduction strategy is that -I does not exceed the operation diagram.

The power reduction analysis is based on two assumptions to facilitate the calculation. The first is that, at a higher fuel burnup, if the core power can be reduced to a certain power level without exceeding the right boundary, the core power can also be reduced to that level without exceeding the right boundary at a relatively lower burnup. The other is that, if the direct insertion of control rod method is feasible to reduce the power without exceeding the right boundary, the power reduction method of boronization and then rod insertion will also be feasible. These two assumptions correspond to the conclusions in Sects. 4.1 and 4.3, respectively. On the basis of these two assumptions, the conclusion of whether -I is controllable can be obtained for different fuel burnups (the unit of fuel burnup is %EOL), with different power reduction method (use direct rod insertion, boronization without stay at 80%FP and rod insertion, and finally boronization with stay at 80%FP and rod insertion) to different power platform including 80%, 70%, 65%, 60% and 50% FP. The result is shown in Fig. 4:

From Fig. 4, the boundary between controllable and uncontrollable power is obtained. When the fuel burn-up is less than about 50% EOL (about 11GWd/tU), -I does not exceed the operation diagram if the power is reduced rapidly to 50%. However, as the

**Fig. 4.** Combined influence of burn-up, low power platform and power reduction method for the feasibility of rapid power reduction

fuel burn-up increases, in order to prevent -I from exceeding the operation diagram, the power reduction magnitude should be gradually reduced. When the fuel burn-up is high enough, a direct rod insertion to reduce the power may cause the -I exceeding the right boundary. In this case, the power can be reduced by boronization followed by rod insertion, and a stay of 80%FP may be necessary to avoid -I oscillation. The matching of cooling capacity and core power can be achieved with help of the strategy.

### **5 Sensitivity Analysis of Control Rod Motion**

To limit -I oscillations during rapid power reduction, the R-rod action can be manually optimized. In addition, after reaching the low power platform, the GN rod is supposed to be raised in 12h, the GN rod action is flexible in time and in speed. Therefore, it is also of importance to carry out the analysis of the influence of the control rod action on -I during the rapid power reduction and the low-power platform.

Considering the power reduction method of direct insertion of control rod, according to the time and logical sequence, the sensitivity analysis of control rod action can be divided into: R rod action in power reduction process, GN rod action at low-power platform and R rod action low-power platform. The sensitivity analysis is simulated at a burnup of 80%EOL.

#### **5.1 Sensitivity Analysis of R Rod Action During Power Reduction Process**