A review of HTGR graphite dust transport research

Nuclear Engineering and Design 360 (2020) 110477

Contents lists available at ScienceDirect

Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes

A review of HTGR graphite dust transport research a

a,b,⁎

Qi Sun , Wei Peng

c

, Suyuan Yu , Kaiyuan Wang

T

c

a

Institute of Nuclear and New Energy Technology, Advanced Nuclear Energy Technology Cooperation Innovation Center, Key Laboratory of Advanced Nuclear Engineering and Safety, Ministry of Education, Tsinghua University, Beijing 100084, China Tsinghua University-Zhang Jiagang Joint Institute for Hydrogen Energy and Lithium-Ion Battery Technology, Tsinghua University, Beijing 100084, China c Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of the Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Graphite dust HTGR Production Deposition Resuspension Coagulation

Graphite dust is the important contents of source term for safety analysis of high temperature gas-cooled reactors (HTGR). The spherical fuel element circulation in a pebble bed reactor causes many interactions between the fuel elements and other graphite components that inevitably leads to graphite dust production. Micron size graphite particles then move with the helium gas and deposit on various surfaces and in flow dead zones in the primary loop, which complicates equipment maintenance and repair and affects the heat transfer. In addition, the graphite dust is quite porous, so some radioactive fission products will adhere to the dust, which leads to radioactive fission products being distributed on the surfaces of the primary loop. Graphite dust carrying radioactive fission products can also leak into the environment during break accidents leading to radioactive pollution of the environment. Thus, studies are needed for the graphite dust transport in HTGRs. This paper reviews the research on the generation, distribution, radioactivity, deposition, resuspension and coagulation of graphite dust in a pebble bed high temperature reactor. The results show that most of the graphite dust is produced by mechanical wear, while chemical reactions can become an important source during an ingress accident. The graphite dust particles generally have sizes on the order of microns and carry radioactive substances. The graphite dust flows along with the helium in the primary loop and adheres to equipment surfaces. Local turbulent diffusion and large temperature gradients cause the graphite dust to deposit on the surfaces, while gravitational settling has a dominant effect in dead-end zones. In case of accidents or other transients, the dust deposited on the surfaces can become resuspended which will sharply increase the dust concentration, leading to uncertainties about the subsequent operating characteristics. In addition, coagulation and growth of the graphite dust particles due to thermophoresis and electric field forces is also a matter of concern.

1. Introduction The pebble bed high temperature gas cooled reactor (HTGR) is a generation IV reactor concept which uses graphite-moderated nuclear fuel pebbles and helium cooling (Wu and Zhang, 2004; Burchell and Snead, 2007). The reactor has inherent safety features due to its large graphite core and low power density in a modular, efficient design that can be used for various applications including suppling process heat for producing hydrogen via the thermochemical sulfur-iodine cycle (Jiang et al., 2019; Zhang et al., 2018; Sun et al., 2019a). A 200 MWe high temperature gas-cooled reactor using a pebble bed design (HTR-PM) is under construction in Shandong Province in China for commercial operation. The HTR-PM design and major components are shown in Fig. 1. Unlike the prismatic block reactor designs, the pebble bed reactor (PBR) uses 60 mm diameter spherical pebbles made of pyrolytic ⁎

graphite as the fuel elements. Each fuel element contains approximately 12,000 microscopic tristructural-isotropic (TRISO) coated fuel particles 0.92 mm in diameter. The TRISO particles are scattered in a graphite matrix 50 mm in diameter with this UO2 kernel then surrounded by a TRISO coating as shown in Fig. 2. The pebble bed reactor uses continuous power refueling to improve the operating efficiency. The pebbles are periodically cycled out of the reactor with the fuel burnup then detected outside the reactor to determine whether the elements are returned to the pebble bed or discharged with new fuel elements added to the core as necessary (Sun et al., 2014) (Fig. 3.). However, the fuel element cycle may cause pieces of the outer graphite shell to detach from the fuel element surface as dust due to mechanical wear and chemical corrosion. The graphite dust is then the main fission product carrier due to its large sorption capability and the presence of much more graphite dust than any other metal dust. For the

Corresponding author at: Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China. E-mail address: [email protected] (W. Peng).

https://doi.org/10.1016/j.nucengdes.2019.110477 Received 23 October 2019; Received in revised form 8 December 2019; Accepted 11 December 2019 0029-5493/ © 2019 Elsevier B.V. All rights reserved.

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

Fig. 1. HTR-PM reactor module design (Sun et al., 2018e).

Fig. 2. Fuel pebble model (Kadak, 2005).

2

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

Fig. 3. Mechanical wear and damage of fuel elements (Verfondern, 2007).

life cycle of the graphite dust, dust is produced first in the reactor core region, charge pipe region or discharge pipe region. Then, the graphite dust entrained by helium departs from the core and flows through the hot gas duct, heat exchanger and helium circulator in turn. Micron size graphite particles may deposit on various equipment surfaces and in flow dead zones in the primary loop. The graphite dust from the reactor core also brings radioactive fission products which may lead to additional issues and affect the safety and stable operation of the reactor (Moormann, 2008a). Specifically, deposited radioactive graphite dust may complicate system inspection, maintenance and repair and also reduce the heat transfer rate in the heat exchangers (Lind et al., 2010). Undeposited particles may flow back to the reactor core to complete the circulation or be collected by helium purification system. A helium purification system purifies a bypass stream from the primary coolant system by reducing the quantity of radioactive graphite dust and other chemical impurities in the helium (Yao et al., 2002). This system can reduce the radioactivity in the primary helium circuit, however, reactor measurements show that some radioactive graphite dust driven by the helium deposits on facility surfaces after passing through the primary loop which limits the system purifying ability. In addition, deposited graphite dust can resuspend and leak out of the pressure vessel in depressurization accidents caused by the break of pipeline (Zheng et al., 2018) which will pollute the environment with radioactive particles. Therefore, studies are needed of the mobility and activities of graphite dust particles in the primary loop for safe and stable operation of pebble bed reactor high temperature gas-cooled reactors. The main graphite dust transport characters in HTGRs are dust generation, dust motion (deposition, resuspension and coagulation), and the radioactivity bound with the dust. This paper reviews studies on graphite dust transport in PBR, including dust generation, morphology, radioactivity, deposition, resuspension and coagulation. This paper is limited to experimental and numerical simulations of graphite dust transport and does not focus on the wider study of gas–solid twophase flows or dust due to other particles. This paper reviews the existing research on graphite dust transport in HTGRs and identifies various challenges for further research.

reactor, most of the graphite dust is produced by mechanical wear and chemical corrosion as summarized by Luo et al. (2017). The graphite dust is produced not only from pure graphite materials, but also from graphite binder that has stronger adsorption. 1) Mechanical wear from moving graphite components The pebble bed reactor operating characteristics will cause wear on the spherical fuel elements in the charge and discharge pipes, the graphite reflector, and other fuel elements that will produce graphite dust. The location of the graphite dust production due to the mechanical wear can be divided into the reactor core region, charge pipe region and discharge pipe region based on the initial wear location. 2) Mechanical wear from the graphite component expansion In the reactor core, the large graphite bricks experience slight relative displacements of the upper and lower graphite components due to the uneven heat distribution during startup and shutdown. The displacement between the graphite bricks results in wear of the graphite materials and dust production. Similarly, variation of the shape and size of the graphite components due to long-term neutron irradiation also produces a small amount of graphite dust. 3) Chemical peeling and decomposition Oxidized gases or other gases infiltrating into the helium coolant in the primary loop may react with the graphite fuel elements, which may produce graphite dust. Fuel element specimens from the PBR show that the outer graphite coating on some element surfaces showed peeling due to air ingress as shown in Fig. 4. The delaminated graphite layer is 0.1–0.3 mm thick, which produces some graphite dust. In addition, other chemical processes such as hydrocarbon decomposition due to oil contamination and decarbonization of the carbon alloys can also produce graphite dust. 4) Other factors The pebble bed reactor core has high local helium velocities which can erode the graphite and produce dust. The internal graphite components may also be subjected to impact loads (such as due to earthquakes) which will also wear the graphite materials and create graphite dust. Fuel element failures due to mechanical, chemical and irradiation effects can also all lead to graphite dust production.

2. Graphite dust production

2.2. Graphite dust measurements in a reactor

2.1. Dust production mechanism

2.2.1. Dust production The 46 MWt AVR reactor, a prototype pebble bed reactor, was constructed in 1960, grid connected in 1967 and shut down in 1988. During the course of these 21 years of operation, AVR demonstrated the feasibility and safe operation of the HTR concept using spherical fuel elements and accumulated a large amount of operating data, including experiments on the core physics, plant behavior, passive safety systems and HTR safety issues with the primary coolant extraction bypass (Kriiger and Wimmers, 1987; Ziermann, 1990; Gottaut and Krüger,

Nuclear graphite is used as the moderator and structure material in HTGRs, the property of nuclear graphite have been studied and showed its reliability in reactor (Contescu et al., 2012; Snead et al., 2008; Contescu et al., 2014; Eapen et al., 2014; Latifi et al., 2020). However, contact with the fuel elements and wear of the graphite components results in graphite dust during normal reactor operation. This section focuses on the graphite dust production mechanisms. For a pebble bed 3

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

Table 1 Comparison of the AVR and THTR-300 conditions. Name

AVR

THTR-300

Average inlet temperature Average outlet temperature Pebbles in the reactor core Pebble circulation rate Reactor height Reactor radius Dust produced

250 °C 950 °C 100,000 300–500 per day 2.8 m 1.5 m 10 kg per year

250 °C 750 °C 657,000 3561 per day 6m 2.8 m 16 kg per year

1990). Fig. 5 shows a schematic of the AVR design and several experiments which focused on the nuclide activity and dust behavior (Gottaut and Krüger, 1990). The dust inventory in the AVR was estimated to be approximately 60 kg by the end of 1988 which means an average annual dust production of approximately 3 kg. The dust accumulation increased to 100–200 kg total when the reactor was disassembled with a corresponding production rate of 10 kg per year (Bäumer et al., 1990a). Moormann (2008a) estimated that the dust was produced by abrasion in amounts of about 5 kg per year and unexpected air ingress of 100 m3 into the primary loop in 1971 which induced peeling of the outer fuel element layers which probably increased the dust accumulation by about 8 kg. In addition, an oil ingress accident (0.12 m3) can lead to cracking of the graphite which produced about 75 kg of radioactive dust (IRPHE/AVR, 2005). Several water and oil ingress accidents in the AVR prohibited accurate estimates of the dust generation sources. Another well-known larger demonstration pebble bed reactor, THTR-300, was a thorium high-temperature nuclear reactor rated at 300 MWe. This plant started operating in 1983, was synchronized with the grid in 1985, began full power operation in 1987 and was shut down 1989 (Bäumer et al., 1990b). The dust production was approximately 16 kg per full power year, with 6 kg estimated to come from the reactor core (Cogliati et al., 2011). The operating conditions and dust production from these two reactors are shown in Table 1. The dust production rate in the THTR-300 was lower than that in the AVR. The THTR-300 circulation rate was 8.9 times greater with 6.57 times as many reactor core pebbles as in the AVR, but the THTR-300 dust production was only 1.6 times that in the AVR. Two possible reasons for the dust production rate differences are that the main dust in the AVR was not produced by mechanical wear of the fuel elements but by the oil or water ingress accidents. In addition, the AVR had more coolant impurities and a higher outlet temperature which lead to more dust production due to chemical peeling and decomposition than in the THTR-300 (Verfondern, 2007).

Fig. 4. Chemical peeling of fuel elements (Nieder, 1990).

2.2.2. Dust concentration The graphite dust generated was then driven by the helium flow in

Fig. 5. AVR facilities and dust related experiments (Moormann, 2008b). Fig. 6. Measured dust concentration in the AVR coolant (Decken et al., 1990). 4

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

wear is mainly due to wear among the fuel elements while cycling in the reactor core, wear of the fuel elements with the graphite reflector and wear of the fuel elements on the stainless steel tube during charging and discharging. 2.3.1. Wear model The Archard first-order approximate wear model is widely used to estimate the amount of dust produced by abrasive wear (Archard, 1953). The surface curvature leads to a slightly larger contact area than for a flat surface which results in some differences from the model predictions; however, the differences are generally negligible due to the very small size of the fuel elements (Bhushan, 2000). Rostamian et al. (2012) reorganized the wear model to calculate the produced dust mass as

m = kFL

(1)

ρK ad H

(2)

Fig. 7. Dust concentrations during AVR transients (Wawrzik et al., 1988).

k= the pebble reactors. The dust concentration was measured using quartz paper filters which allowed retention of dust particles down to 0.3 μm diameter with 50% efficiency from the AVR bypass flow shown in Fig. 5. The dust concentration in the coolant at different periods is shown in Fig. 6 which shows that the steady-state dust concentrations were 1–2 μg/m3, with some concentration peaks several orders of magnitude higher during transient operating conditions such as at T1, T2 and T3. The average dust concentration in the AVR over the final operating years was about 5 μg/m3 (Wawrzik et al., 1988). Conservative estimates using the data for the transient peaks suggests that 0.5–2% of the coolant-borne dust was deposited per recirculation loop (Verfondern, 1997). Dust concentration experiments measured by the AVR dust filter during blower transients are shown in Fig. 7. When the blower frequency was increased to 3000 min−1 within 1 min, the dust concentration in the coolant increased by 50 to 100 times that of the steady conditions. When the blower speed was increased from 1500 to 4000 min−1, the dust concentration increased 200 to 400 fold to a maximum concentration of 2 mg/m3. After the blower speed was held constant again, the dust concentration required several hours to recover to a steady level due to deposition which indicates that most of the dust particles are very fine (Moormann, 2008b). An experimental sampling loop was installed at the entrance of the helium purification system in the primary loop of HTR-10 to study the dust characteristics. The dust concentration in the primary loop of HTR10 was 1.97 ~ 5.57 μg/m3, which is very close to the average dust concentration with an average pore size of 80 μm (Xie et al., 2017).

where m (g) is wear mass loss, F (N) is the contact normal force, L (m) is the slide distance, ρ (g/m3) is the material density, H (Pa) is the material hardness, Kad is the dimensionless wear coefficient and k (g/ N·m) is the experimentally measured wear coefficient. The wear model reflects the effects of the normal force, friction length, and material properties on the abrasion and also includes indirect effects from the friction coefficient, temperature and abrasive history. For the HTGR conditions, the extreme atmosphere affects the graphite pebble wear properties. Gas adsorption from the environment on the newly created surfaces after wear may also affect the wear. In addition, the fuel element manufacturing conditions and neutron radiation can also damage the graphite matrix and produce graphite dust. Various laboratories have experimentally studied the graphite pebble wear to quantize the effects of these factors. Some published wear coefficient data is listed in Table 2. Table 2 lists measured wear coefficients for graphite dust from various references that vary by three orders-of-magnitude due to different pretreatments, contact methods, experimental conditions, and measurement methods. Some effects of these factors even appear to be completely contradictory, such as for temperature and atmosphere. Such greatly dispersed graphite wear coefficient data and sensitivity to temperature and gas composition makes it difficult to obtain quantitative rules for graphite wear at high temperature and pressure helium conditions in the HTGR. 2.3.2. General atomics tests Stansfield (1969) constructed an apparatus to simulate reactor atmospheric conditions to study the effects of temperature, loading, and sliding on the wear with various graphite materials. Loads of 2 and 8 kg were used to produce nominal contact pressures while rubbing plates with an oscillating motion with a stroke of 0.32 cm. The tests used several graphite grades such as PGX, ATJ, and MHLM at 25, 400, and 800 °C to measure the wear properties. The results showed that the wear at 25 °C was about ten times that at 800 °C. The volume of

2.3. Dust production estimate Section 2.1 describes graphite dust production mechanisms where mechanical wear is believed to be the main source of the dust during normal operation (Turner, 2008). The dust production has been further studied in simulations and experiments. The dust production due to Table 2 Graphite wear coefficients (Cogliati et al. 2011). Reference

Material

Loading (N)

Temperature (°C)

Conditions

Wear coefficient g/(N·m)

Stansfield (1969) Stansfield (1969) Lancaster and Pritchard (1980) Sheng et al. (2003) Sheng et al. (2003) Luo et al. (2004) Luo et al. (2005a) Luo et al. (2005a) Rostamian et al. (2013) Hiruta et al. (2013)

ATJ graphite ATJ graphite Morganite series graphite KG11graphite KG11graphite IG-11 graphite IG-11 graphite-stainless IG-11 graphite-stainless IG-11 graphite IG-11 graphite

78.4 78.4 22 31 31 30 30 30 – 20

25 400, 800 200 room room room room 200, 300, 400 room 200, 400, 750

Helium Helium Wet air Air, Surface contact Air, Line contact Air, upper Helium Helium Air Helium

≈2.2 × 10−6 ≈1.97 × 10−7, 1.56 × 10−6 ≈2 × 10−5 7.32 × 10−9 3.29 × 10−8 4.7 × 10−7 1.9 × 10−7 ≈4.1 × 10−7, 6.5 × 10−7, 7.8 × 10−7 ≈4.42 × 10−9~8.45 × 10−8 ≈1.4 × 10−5, 9.6 × 106, 4.9 × 10−6

5

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

Fig. 9. Experimental wear test bed with spinning pebbles with particle sizers (Troy et al., 2015b).

Fig. 8. Tribometer picture (left) and schematic (right) to study pebble contact wear (Rostamian et al., 2013).

to measure the particle sizes with a Scanning Electron Microscope (SEM) used to observe the graphite dust morphology. The mass loss results showed that the graphite pebble rotationally driven by a milling machine lost more mass than a fixed pebble. In addition, increasing the loading or spin rate created more particles with larger surface areas and lead to higher wear mass. The wear per unit time ranged from 0.003 to 0.07 g/min, however, these results cannot be easily compared to previous results which were reported in units of mass loss per length for spinning abrasion. The results also suggested that longer fuel cycles can reduce the dust production due to surface smoothing.

graphite worn away was directly proportional to the load for approximately the same sliding distance. In addition, they found that the wear coefficient decreased with increasing sliding distance and that the graphite wear coefficient measured in air at 25 °C may be representative of that observed in helium at 800 °C. 2.3.3. Idaho National Laboratory The Idaho National Laboratory conducted many studies to estimate the graphite dust production in a pebble bed high temperature reactor including numerical simulations, tribometer experiments and improved nonlinear wear models (Rostamian et al., 2012; Rostamian et al., 2013; Hiruta et al., 2013; Cogliati and Ougouag, 2008). The numerical simulations used the finite element method based on ABAQUS to calculate the load force for wear between fuel elements considering pebblepebble forces with friction at the contact points and rotation of the center pebble. The wear production was estimated using a damage model and published wear coefficients with the predictions compared with the graphite dust data of AVR and THTR-300. A custom-designed tribometer was used for tests for a PBR at higher temperatures and pressures in a helium environment in the apparatus shown in Fig. 8. The results showed that the wear mass in a helium environment was less than that in an air environment due to the smoothing of the graphite surface by the helium adsorption. At temperatures higher than room temperature, the wear coefficient generally increased due to increased graphite embrittlement while at higher pressures, gas adsorption effects were inferred to reduce the wear mass. In addition, they proposed an analytical model based nonlinear dimensionless wear coefficient to improve the linear Archard wear model. They considered the effect of roughness height on the wear and concluded that the wear mass saturated at long sliding distances due to the graphite dust being produced primarily in the valleys between roughness elements which increased the surface smoothness which reduced the wear coefficient.

2.3.5. Tsinghua University A standard SRV tester was used to study the friction properties of IG11 graphite (Luo et al., 2004, 2005a,b, 2010; Sheng et al., 2003). Many experiment measurements provided dust production rate data for various sliding distances, friction speeds, loads, atmospheric conditions, temperatures and surface roughnesses. The results showed that the wear rate (wear mass loss per unit slide distance) between graphite and graphite significantly increased with increasing load, while the wear rate between graphite and stainless steel remained relatively constant for various loads. The main wear mechanism at room temperature was abrasive wear, at 200 °C was fatigue wear and at 400 °C was adhesive wear with the wear rates increasing slowly with temperature. Dust production rate measurements in the HTR-10 design were used to analyze the wear dust production in HTR-10 due to charging and discharging of the reactor core. Luo et al. (2017) estimated the amount of graphite dust by combining published data with numerical simulations using DEM (Discrete Element Method) and showed that 100 μg graphite dust was produced during a single fuel element cycle which was an acceptable rate. In addition, He et al. (2018) conducted HTR-PM nuclear graphite wear tests on the ART-I chewing machine that provided rolling and sliding contact using complete or hemispherical pebbles in a helium environment. Unlike in other studies, additional smaller stainless steel pebbles were added into the chamber to increase the random movement of the graphite pebbles to simulate rolling wear. The results illustrated that helium gas significantly increased the graphite dust production. The graphite weight loss increased linearly with increasing load and speed and rolling contact produced more wear than sliding. The fuel element wear due to collisions during fuel handling in the transport pipes has also been studied (Shen et al., 2015; Wang et al., 2014; Wu et al., 2018a; Sun et al., 2019c). The experimental system for the HTR-10 fuel handling system shown in Fig. 10 was built to study the wear properties of graphite pebbles in the lifting pipeline. Then, the pneumatic lifting of the graphite pebbles was studied with various

2.3.4. University of Missouri The University of Missouri also experimentally studied the graphite dust production mechanism including the effects of the dust size distribution, dust morphology and dust production rate (Troy et al., 2012, 2015a,b). They designed an apparatus to apply rotational/spinning abrasive loading on graphite hemispheres that generated graphite particles in a way that was close to the actual wear mode of graphite elements in pellet beds as shown in Fig. 9. An Aerodynamic Particle Sizer™ (APS) and a Scanning Mobility Particle Sizer (SMPS) were used 6

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

Fig. 10. Experimental platform for measuring the wear in the graphite pebble lifting system (Shen et al., 2015).

particles from wear experiments using a SEM with some pictures shown in Fig. 13. All the graphite particles have jagged edges with no consistent shapes in the various tests. The tests showed various dust particle shapes from the graphite samples that suggest completely different production methods. The MLRF1 (a nuclear-grade graphite) particles are more likely to coagulate and grow in all directions, while the GM101 (a nonnuclear-grade graphite) particles are more likely to coagulate in one direction leading to a long slender particle. However, due to the limited number of samples and the many factors affecting the experiment, the SEM shape and size measurements could not be used to easily distinguish the abrasion particles. Rather than using wear methods, Shen et al. (2016) observed the particle morphology produced by impacts of a pneumatic lift with typical images shown in Fig. 14. The dust particles have irregular lamellar shapes and fine debris easily attaches to the larger particles.

atmospheres of air, nitrogen and helium with speeds from 3 to 11 m/s. The results showed that interactions between the graphite pebble and the stainless steel walls increased with increasing pebble lifting speed in the same atmosphere with a linear relationship between the graphite pebble wear rate and the lifting speed. The graphite pebble wear rate in the helium atmosphere was much higher than in the air or nitrogen atmospheres due to frequent oscillation. Shen et al. (2015) used Raman spectroscopy to show that both the filler particles and the binder affected the dust generation. Sun et al. (2019c) used a macroscopic particle model to simulate graphite pebble motion in a lifting pipeline. They found that the graphite pebble appeared a spiral upward trajectory due to pneumatic conveying and developed a wear model to predict graphite dust production in a HTGR lifting pipeline. Wu et al. (2018a) studied the friction and wear of graphite pebble by analyzing the impact and wear processes in the HTGR lifting pipeline using the finite element method with experiments to explore the influence of sliding speed, applied load, surface roughness and atmosphere on the friction and wear behavior to understand the friction and wear mechanisms. They found that the graphite wear rate increased with increasing surface roughness and load and that helium caused higher wear rates than air due to the atmosphere affecting the lubrication layer generated at the contact area.

3.2. Dust size distribution 3.2.1. Dust in reactors A typical size distribution of fine dust particles collected from the VAMPYR-I experiment in the AVR is presented in Fig. 11 which is independent of the sampling location. The diameter distribution indicates an average number-weighted dust particle diameter of about 0.76 μm and an average mass-weighted diameter of 2.34 μm at the end of the AVR life which may be attributed to the crushing of large dust particles by the rotation device (Gottaut and Krüger, 1990). Later measurements were conducted in the DEACO1A experiment by Fachinger et al. (2008) 20 years after the AVR shutdown. The dust was collected by scratching the inner surface of the AVR pipes with a number-weighted average dust particle size of 0.55 μm and a mass-weighted average size of 2.79 μm. Such fine particles are difficult to remove by only the flow shear stress due to the strong adhesive bond and the system requires a long time to achieve a stable concentration as shown in Fig. 7. However, during the early AVR operation before the oil ingress accident, preliminary measurements indicated dust sizes of about 5 μm. At high pressures and high temperatures with hypoxia, the oil might been pyrolyzed to form various intermediate products with some products condensing to form spherical particles with diameters between 20 and 40 nm. As a result, the dust particles at the end of the AVR life were

3. Graphite dust characteristics 3.1. Dust shape The dust particles collected from AVR had irregular, non-spherical shapes with most particles being jagged with porous surfaces as shown in Fig. 11. Larger diameter particles may have formed with strong agglomeration forces so that the particles were difficult to separate. Hiruta et al. (2013) observed graphite dust shapes in SEM images at various temperatures with a wide variety of diameters and flake types. Most of the graphite particles showed scale-like surface structures helps produced flakes as seen in Fig. 12. Higher temperatures lead to the larger flakes. They deduced that the flakes adhered to the graphite pebble surfaces due to the larger area-to-weight ratio but that the wear coefficient would slow at temperatures higher than 200 °C up to 750 °C. Troy et al. (2012) and Troy et al. (2015a) analyzed graphite 7

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

Fig. 11. Dust particles collected in AVR (Verfondern, 2007).

very fine. Thus, the dominate dust particles size of less than 1 μm may have been produced by the oil ingress (Moormann, 2008b). Dust from THTR taken from the humidity sensor chambers had a number-weighted average size of 0.60 μm and a mass-weighted average size of 6.85 μm (Oetjen, 1989). In the HTR-10 dust filter experiment, the radioactive dust on the four pore filter elements was collected using liquid ethanol with ultrasonic vibrations (Xie et al., 2015a,b). The dust particle size distribution was measured in suspension using an optical microscope. Fig. 15 shows that most of the particles on the 1#2 filter (second filter at the first sampling experiment) element which was close to AVR data before the oil ingress had diameters between 5 and 10 μm, but some tiny particles may have been omitted due to filter performance (Xie et al., 2017). Obviously, there are significant differences between the relative particle size distributions for the various reactor samples as shown in Fig. 15. The AVR particle size distribution is concentrated at sub-micron sizes, while the HTR-10 particles had a larger size distribution of 1 to 50 μm. The THTR-300 particles had a boarder size distribution.

contact in a helium atmosphere. The size distributions measured from SEM images showed that the rolling contact generated larger particles than the sliding contact. Shen et al. (2016) measured the size distributions of graphite particles produced by a pneumatic lift using both image analyses and a laser diffraction particle size analyzer. The results showed that the number-weighted average particle size was around 2.38 μm and the volume-weighted average size was 14.62 μm. These two sizes were larger than the AVR and THTR results. A large part of the volume-weighted distribution was due to graphite dust particles with diameters ranging from 10 to 40 μm. 3.3. Dust radioactivity Although there is still some uncertainty about the radionuclides on the graphite dust in the primary loop, the deposited graphite dust is known to increase the deposition of key radionuclides such as Cs and Sr which interact strongly with the graphite. The graphite dust is known to absorb more radionuclides than the intact graphite structure. The AVR results showed that Cs-137 on the dust reached 0.1–100 GBq/kg while the I-131 on the dust reached 3.5 GBq/kg in the AVR primary loop. Therefore, the design of modern high temperature gas-cooled reactors cannot ignore the radioactivity loading on the graphite dust (Moormann et al., 2001). Skyrme (1985) showed theoretically that the effect of fission gases on the suspended particles is very important even at low dust concentrations, especially for small particles (sub-micron).

3.2.2. Dust diameter measurements in wear experiments Luo et al. (2005b) measured the sizes of graphite dust particles produced by sliding wear using the projected particle area in helium. The equivalent diameters of most of the graphite dust particles produced by the sliding wear were 1 ~ 3 μm with a lognormal distribution. Abrasive wear experiments between two graphite pebbles conducted by Troy et al. (2015b) used SEM, an Aerodynamic Particle Sizer™ and a Scanning Mobility Particle Sizer to measure the particle diameters. The particle diameters were from 0.18 μm to 20 μm with a lognormal distribution with only a few particles having micron sizes. In addition, the porosity of the graphite dust generated by abrasion was as high as 68% so the particle surface area was 1000 times greater than that of graphite hemispheres which significantly increases the surface area for adsorbing radioactive substances. He et al. (2018) measured the particle size distributions of particles generated by rolling contact and sliding

3.3.1. Radioactivity source Radioactive nuclides released from the UO2 core can become bound to the graphite dust particles including both fission products and activated products. The radioactive nuclides from the graphite dust captured by the helium purification circuit filter in the HTR-10 identified using a γ spectrometer are shown in Fig. 16. 1) Fission products The primary sources of fission products in the primary helium gas

Fig. 12. SEM images of graphite particles from wear tests at (a) 200 °C, (b) 400 °C and (c) 750 °C (Hiruta et al., 2013). 8

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

Fig. 13. SEM micrographs of some typical dust particles collected after abrasion (a) GM-101 (top) graphite samples (b) MLRF1 graphite samples (bottom).

and are strongly adsorbed by graphite. 2) Activation products Activation products are radioactive substances that have been activated by the neutron flux and circulate with the coolant in the primary loop (Verfondern et al., 2012). Some of these particles are captured by the helium purification system with some deposited on the primary loop surfaces, but their radioactivity decays until the total decay rate eventually balances with the production of new radioactive activation products (Kissane, 2009). The activation products mainly come from coolant helium and the graphite matrix materials. The helium can be activated to produce tritium by 3He(n,p)3H and radioactive graphite matrix materials can be produced from 14C activation reactions such as13C(n,γ)14C, 14N(n,p)14C and 17O(n,α)14C where the activation reaction 13C(n,γ)14C is most significant. Other solid activation products including Cr-51, Mn-54, Fe-59, Co-57, Co-58, Co-60, Se-75, and Hg 203 were measured by Xie et al. (2017).

loop are uranium contamination of the fuel pellets and damaged coating layers caused by manufacturing defects, cladding layer wear and neutron irradiation. Fission products can penetrate an intact coated layer in helium by diffusion, especially at high temperatures. Moormann (2009) analyzed the source and factors which affect the metallic fission product release rate from the AVR measurement data. Some typical radioactive nuclides were Sr-89, Sr-90, Ag-110 m, I-131, Cs-134, and Cs-137 on dust from AVR (Gottaut and Krüger, 1990). In addition, the radioactive nuclides Ba-140, La-140, Eu-152 and Hf-181 have been observed in the primary loop of HTR-10 (Xie et al., 2017; Peng et al., 2018). In general, metallic fission product nuclides have relatively high diffusion coefficients in pyrolytic carbon graphite and long half-lives, so they easily accumulate in the primary loop and need to be processed. The experiments also showed that the radioisotopes of Sr and Ba have a great affinity to graphite. And most do not diffuse through the graphite layer even at high temperature of 1400℃. However, most of the Ag-110 m diffuses through the fuel pebble coating at temperatures over 800℃ and is then deposited at low temperatures. The radioactive isotopes of iodine are generally very volatile and are the main nuclides causing internal irradiation in reactors. They can form stable compounds with some metal fragments in the fuel pebble core

3.3.2. Radioactive nuclide fractions Graphite dust particles transported in the flow loop or deposited on the surfaces can adsorb some radionuclides. Bäumer and Barnert (1990) made conservative estimates of the bound radionuclides in graphite

Fig. 14. SEM images of graphite dust produced by impacts with a pneumatic lift (Shen et al., 2016). 9

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

showed that the graphite dust on the fuel pebble surface had much lower radioactivity than the graphite dust from other parts of the primary loop. The high reactor core temperature makes the radioactive nuclides bound by the graphite dust more volatile with the radioactivity gradually decreasing with time. The lower temperatures in the steam generator will result in more radioactivity on the graphite dust in the steam generator. Therefore, the radioactivity of materials bound by the graphite dust should be highest in the steam generator. The graphite dust monitoring during operation of the AVR reactor showed that the graphite dust radioactivity per unit mass in the steam generator was more than 100 times that of the graphite dust on the fuel elements and more than 5 times that of the graphite dust in the cold helium region (Verfondern et al., 2012). Thus, the bound radioactivity on the graphite dust in the steam generator will accumulate and increase until the graphite dust in the steam generator will reach the most radioactivity from radioactive nuclides after a long period of operation.

Fig. 15. Number weighted size distributions of dust particles from AVR, HTR10 and THTR-300.

4. Graphite dust transport 4.1. Dust motion

dust. They estimated that the bound radionuclide shares in the graphite dust deposited on the inner surface of the primary loop are around 5% for Cs, 20% for Sr, Rb, and Ag, 1% for I. Hanson et al. (1980) showed that more than 80% of the Cs and Sr deposits on the primary loop surface of the Peach Bottom reactor were related to graphite dust adhering to the primary loop surface caused by oil ingress accidents. Komen (2007) comprehensively studied the interactions between fission products and wall surfaces. A series of number balance equations for the volumetric concentration of fission products including the bulk gas stream, laminar sublayer, and wall surface are implemented in adsorption model to calculate the evolution of fission products and adsorption in HTGR conditions. Stempniewicz and Goede (2016) studied the sorption of fission products including I-131, Cs-134, and Cs137 on dust particles based on the AVR data and obtained correlations of the sorption coefficient, which can be used in computer codes to compute the sorption rates of different fission products on surfaces. The sorption coefficient depends on temperature and decreases with the increase of temperature. The radioactive fractions bound by the graphite dust depend on the location of the graphite dust in the reactor. The AVR reactor results

The graphite dust will be entrained in the helium and flow in the primary loop as a multispectral aerosol. For the typical conditions of the primary loop of HTGRs, the helium flow is turbulent with many eddies and anisotropic drag forces on the particles. In addition, the heat exchangers such as the steam generator and the intermediate heat exchanger have large temperature gradients that create large thermophoretic forces. Therefore, the graphite dust motion in the primary HTGR loop is strongly affected by the turbulence and temperature gradients. Gravitational settling also has an important effect in deadend zones, such as reactor vessel lower head. During the graphite dust particle transport, the particles may deposit on the surfaces due to turbulent diffusion or gravitational settling and adhesive attraction near the wall. The dust particles will coagulate into larger particles in some high concentration regions. In addition, the deposited graphite dust may be resuspended by the helium flow, especially during transients, until the dust deposition and resuspension rates form a dynamic equilibrium. Thus, the graphite dust particle dynamics in HTGRs is a gas–solid two-phase flow problem including particle deposition, coagulation and resuspension (Humrickhouse, 2011). This section focuses on existing research on the mechanisms specifically governing the

Fig. 16. γ spectra of the radioactive nuclides from HTR-10 (Xie et al., 2017). 10

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

graphite dust particle dynamics rather than classical multiphase flow descriptions.

theories, models and experimental results for turbulent particle deposition and developed an empirical piecewise formula for the dimensionless deposition rate as a function of the Schmidt number and the dimensionless relaxation time. They attributed the scattering of the experimental data to the different particle-gas density ratios in different experiments. Fan and Ahmadi (1993) proposed another semi-empirical formula to predict the dimensionless particle deposition velocity as a function of the particle-gas density ratio, surface roughness, gravitational direction and Reynolds number.

4.2. Dust deposition The graphite dust dynamics mechanisms include inertial impaction, gravitational settling, Brownian diffusion, turbulent diffusion and thermophoresis. The graphite dust deposition is not only related to the particle properties but also the flow patterns as well as the surface characteristics. In a HTGR, the inertial impaction mainly occurs inside the filter or on local equipment surface such as forward-facing step (Lustfeld et al., 2014). However, due to the complex structure layout, there are a lot of flow dead zones which cause dust gravitational settling and accumulate deposition layer. In addition, most areas of the primary loop are in turbulent regime, and there are large temperature gradients in the heat exchange components. Therefore, gravity, turbulence and thermophoretic effects are then the dominant factors affecting the graphite dust deposition. The effect of gravity on particle deposition is dominant in dead-end zones and its mechanism is relatively clear, so this paper focuses on the effects of turbulent deposition and thermophoretic deposition.

+ Vdep

⎜

dp+

(3)

where the dimensionless relaxation time, τ and the dimensionless deposition velocity, Vdep+ can be defined as (Wood, 1981).

Vth+ = −

Cρp dp2 u∗2

Vd+ep =

18ρg v 2

(4)

J u∗N

(5)

+ Vdep

⎟

(6) +

4.2.2. Thermophoretic deposition Thermophoretic deposition means that small particles are driven in the direction opposite to the temperature gradient by molecular collisions (Mehravaran, 2013). The HTGR primary loop has high temperature helium flowing along a cooler wall such as in the steam generator which will create thermophoresis which may dominate the particle deposition. The thermophorectic velocity is expressed based on the balance between the thermal force and the drag:

+

τp+ =

+2 + L1 )

where is dimensionless particle diameter, k is the dimensionless average height of the surface roughness, g+ is dimensionless gravitational acceleration and L1+=3.08/(Sd+) where S is the particle-gas density ratio. For horizontal pipelines g+ = 0 while for vertical pipelines in the direction of gravity, g+=νg/u*3.

4.2.1. Turbulent deposition A large number of experiments concerning particle deposition in turbulent convection have shown that the aerosol particle deposition velocity, Vd, on a tube wall depends on the particle relaxation time (Friedlander and Johnston, 1957; Wells and Chamberlain, 1967; Schwendiman and Postma, 1965; Sehmel, 1968; Liu and Agarwal, 1974). The dimensionless deposition velocity can be related to the dimensionless relaxation time as + Vdep = f (τ +)

1/(1 + τ 2 ⎧ + 2 τ + g+L1+ ⎤ ⎡ ⎛0.64k+ + dp ⎞ + ⎪ ⎜ ⎟ + + 2 2 0.01085(1 + τ L1 ) ⎥ ⎪ 0.084Sc −2/3 + 1 ⎢ ⎝ ⎠ ⎥ 2⎢ τ+2g+L1+ ⎪ + 3.42 ⎥ ⎢ = 0.01085(1 + τ+2L1+) ⎨ ⎦ ⎣ ⎪ + 2 0.037 ×[1 + 8e−(τ − 10) /32] ⎪ 2 g+ ⎞ 1 − τ + L1+ ⎛1 + ⎪ 0.037 ⎠ ⎝ ⎩ < 0.14

Kth ν ∇T u∗T

(7)

Vth+

where is the particle dimensionless thermophoretic velocity, T (K) is the local gas temperature, ∇T is the temperature gradient in the radial direction in the heat transfer tube and Kth is the thermophoretic coefficient which depends on the Knudsen number and has been given in many expressions based on different theories and methods (Brock, 1962; Derjaguin and Yalamov, 1965; Dehbi, 2009). The widely used Brock-Talbot formula for graphite particles in HTGRs is (Talbot et al., 1980).

where u* (m/s) is friction velocity, ρp (kg/m3) and ρg (kg/m3) are the density of particle and gas respectively, v (m2/s) is kinematic viscosity of gas, C is the Cunningham slip correction coefficient which is related to the Knudsen number (Fernandes and Loyalka 1996) and discussed in HTGR conditions by Sun et al. (2018c). J (m−2 s−1) is the particle deposition rate per unit area and N (m−3) is the particle concentration. Then, the relation between the deposition velocity and the relaxation time can be used to divide the particle deposition into three regime as the diffusional deposition, diffusion-impact and inertiamoderated regimes as shown in Fig. 17. In the diffusional zone (τ+ less than 1), the particles are very fine and the particle diffusion is mainly driven by Brownian motion and eddy diffusion. In the diffusion impact region (1 < τ+ < 1 0), the particles move to the wall through the viscous boundary layer and then deposit on the wall due to turbulent core and the transition eddy layer. The coherent structure near the wall also plays an important role affecting the particle deposition. In the inertia-moderated regime (τ+ < 1 0), the particles are relatively large and the particle inertia plays a decisive role in the particle transport with the inertia causing the particles to impact the wall. There are many empirical models for predicting turbulent particle deposition in simple ducts with the model proposed by Papavergos and Hedley (1984) and that of Fan and Ahmadi (1993) being widely used. The accuracy and robustness of these models have been verified in various studies (He and Ahmadi, 1998; Chen and Ahmadi, 1997; Zhang and Ahmadi, 2000). Papavergos and Hedley (1984) reviewed the

Kth =

(k g / kp) + Ct Kn 2Cs Cc ⎞ ⎛ ⎜ ⎟ (1 + 3Cm Kn) ⎝ 1 + 2(k g / kp) + 2Ct Kn ⎠

(8)

where Cs is the thermal slip coefficient, Cc is Cunningham–Millikan–Davies correction factor, Ct is the jump coefficient, Cm is the accommodation coefficient, kg and kp are the gas and particle thermal conductivities and Kn is the Knudsen number which is defined as the ratio of the molecular mean free path length to a representative length scale. The key step in calculating the thermophoretic velocity is to calculate the gas temperature gradient in the radial direction. Laminar flow with a constant wall temperature has an analytical solution to describe the temperature distribution but turbulent flow only has some theoretical expressions for specific tube flows (Nishio et al., 1974; Romay et al., 1998). For turbulent flow with constant wall temperature, various heat transfer correlations can be used to calculate the particle deposition velocity for various thermophoretic conditions. However, turbulent flows with variable wall temperatures need experiments and numerical simulations to predict the gas temperature gradient in the radial direction to predict the thermophoretic deposition velocity (Tu et al., 2018; Yeoh and Tu, 2019). Then, the deposition coefficient governed by the turbulent diffusion and thermophoretic migration can 11

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

Fig. 17. Experimental data for fully developed turbulent deposition (Young and Leeming, 1997).

connects the reactor core to the steam generator. The heat transfer between the hot and cold helium produces a large temperature gradient. Luo et al. (2006a) used particle dynamics theory to estimate graphite dust deposition in the hot gas duct of the HTR-10 for turbulent diffusion and thermophoretic migration. They found that the graphite dust deposition fraction was very low in the hot gas duct and that the thermophoretic effect dominated due to the high helium velocity in the hot gas duct. Peng et al. (2013b) used computational fluid dynamics to calculate the temperature distribution near the hot gas duct wall. The predicted temperature gradient was then used to calculate the thermophoretic and turbulent deposition rates for different particle sizes and conditions. The results showed that thermophoretic deposition is only significant for small particle diameters and that the turbulence deposition rate increased with increasing operating power. In HTGRs, the steam generator is also an important heat transfer device with a spiral coil structure. The high temperature helium of the primary loop transfers heat to the water in the secondary loop in the steam generator with the water vaporizing and then driving the steam turbine to generate electricity. Peng et al. (2013c) and Peng et al. (2016) simplified the steam generator structure as countercurrent and concurrent heat exchanger tube bundles. Then the water phase change inside the tube bundle and the temperature distribution outside the tube bundle were simulated using an evaporation model. The predicted temperature distributions were then used to predict the turbulent and thermophoretic deposition rates. The results showed that the deposition rates in the steam generator were similar but somewhat higher than those in the hot gas duct. Sun et al. (2018b) analyzed a two-dimensional single coil steam generator with a Reynolds stress model to predict the turbulent flow and temperature distribution and then used the Lagrange method to track the particles to model the graphite dust deposition for various particle sizes and conditions. The trajectories illustrated the interactions between the particles and the walls as shown in Fig. 18 which showed that inertial impact dominated the deposition characteristics for large particles, while small particles migrated towards the wall mainly due to turbulent eddies and thermophoresis. Wei et al. (2018) used large eddy simulations to calculate the turbulent eddies in a multi-coil steam generator and then applied a critical capture velocity condition and a restitution coefficient to determine whether a particle

be expressed by (Chen et al., 2012).

j+ =

Vth+ V+

1 − exp ⎛− Vd+ ⎞ ⎝ th ⎠

(9)

Gutti and Loyalka (2009) developed a numerical method to solve the coupled equations for the particle continuity and energy equations including the thermophoresis effect and verified the accuracy of the predicted thermophoretic deposition efficiency for short tubes. They found that the particle deposition is sensitive to mesh size, so a very fine mesh is needed near the surface for accurate results. Boddu et al. (2011) compared experimental data using a spark generator and a thermophoretic deposition cell with computational fluid dynamics models to predict the particle deposition rate in a thermophoretic deposition cell. The numerical predictions agreed well with the experiment results. Tao et al. (2018) designed an experimental system to measure graphite particle migration in high temperature gradients simulating the HTGR conditions. Their thermophoretic deposition rates were similar to previous results for various Reynolds numbers and inlet temperatures and indicated that the thermophoretic deposition of irregular graphite particles may be smaller than the predicted result using theoretical formula based on hypothesis for spherical particles. Fischer et al. (2018) installed a high-temperature test facility to study the deposition of graphite dust in a helium by thermophoresis. A wide range of phenomena including dust agglomeration, separation, deposition and remobilization can be explained in this experiment. 4.2.3. Deposition research in HTGR systems The graphite dust deposition has been extensively studied in important equipment such as the hot gas ducts, steam generator tubes and the HTGR pebble bed core. In heat equipment, the large thermophoresis force moves particles towards the wall so that they are deposited on the wall which increases the thermal resistance and complicates maintenance. The pebble bed core is the main source of the graphite dust with the highest amount of dust. The dust deposition in the pebble bed is important in evaluating the amount of graphite dust released to the primary loop. The early research focused on the hot gas duct of the HTGR which 12

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

Fig. 18. Typical types of particle motion in a steam generator (Sun et al., 2018b).

method to study the graphite particle energy loss during the impact process to determine restitution coefficient. The effects of particle shape, adhesion, damping and plastic deformation are incorporated and the numerical method is validated by experiments (Fang et al., 2020b). Wei et al. (2019) further analyzed the effect of the steam generator tube bundle geometry on the deposition rate. They found that the impact rate decreased as the transverse spacing between tubes increased and first increased and then decreased as the longitudinal spacing increased. Sun et al. (2019b) measured the adhesion force between particles and a steel wall using an atomic force microscope to determine the critical capture velocity and predict the deposition rate in the intermediate heat exchanger inlet channel. Guo et al. (2019) used a helium experimental system to study the deposition distribution of graphite dust carried by high temperature helium in a modeled steam generator and estimated the dust deposition rate in a single heat exchanger unit about 222.6 g. The pebble bed core is a complex, moving structure. Although the fuel pebble motion due to gravity and the helium flow and the heat transfer from the graphite pebble itself are important issues (Liu et al., 2013; Rycroft et al., 2012; Shams et al., 2014; Wu et al., 2018b), this paper only focuses on the motion of the graphite dust among the pebbles. Dehbi (2008) developed a numerical method to accurately predict the particle laden turbulent flow. Simon (2009) then used this method in an Eulerian CFD-RANS method with an RSM turbulence model to predict the air flow past single spheres and linear arrays of eight spheres with various spaces. Dehbi and Martin (2011) focused on particle flows around linear arrays of spheres using a Reynolds stress model and a continuous random walk with particle diffusion due to the fluctuating velocity components. The numerical deposition fraction was verified within the scatter of the data by a single sphere experiment. The results showed very low particle deposition efficiencies for very low inertia particles while for high inertia particles, the shielding effect resulted in much higher make deposition rates on the first sphere than on the following spheres. Barth et al. (2014) experimentally studied graphite particle deposition in an adiabatic scaled pebble bed structure. They used positron emission tomography to measure the multilayer particle deposition with time resolved 3D PET-CT overlays. The results showed particle deposition on the front side of the pebble having an average mass of about 4 mg corresponding to the primary graphite dust concentration. The inertia resulted in more particle deposition on the front sides of the pebbles with an approximately exponential decay along the axial direction. Jayaraju et al. (2015) and Jayaraju et al. (2016) studied the fluid flow and particle deposition in face centered cubic arrays and random stacking pebble beds using the standard k-ε model with

Fig. 19. Deposition patterns on the pebble surfaces of the random pebble-bed (Jayaraju et al., 2015).

deposited or rebounded from the wall (Kim and Dunn, 2007). Their result indicated that the sticking assumptions overestimated the particle deposition rate in the steam generator. Fang et al. (2019) and Fang et al. (2020a) proposed a numerical method based on finite element 13

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

Fig. 20. Dust transport and deposition data (Stempniewicz et al., 2012).

layer from forming on the heat exchanger surfaces due to the high flow speed with the dust instead accumulating as a thick layer around the control rods due to the low helium velocities there. In addition, their results indicated that a filter in the fuel handling system could effectively remove the dust.

enhanced wall functions and a continuous random walk model. The particle deposition patterns were classified into distinct regions as shown in Fig. 19. For compactly stack pebbles, inertial impact was the main factor affecting the particle deposition so the deposition rate increased with increasing particle diameter. In addition, the helium flow accelerates around the pebbles which removed some particles which were then deposited on the bottoms of the pebbles. Chen et al. (2017) and Sun et al. (2018a) modeled the pebble bed as an ideal stack structure with either a body-centered or face-centered cubic structure. They analyzed the effects of particle diameter, number of stack layers, helium inlet velocity and surface temperature on the graphite dust deposition. Unlike in a steam generator, the large thermophoretic force reduced the deposition efficiency. In addition, the rebound effect significantly reduced the deposition of realistic dust particles for highspeed helium flow conditions. Stoker et al. (2010) used the 1D Dust and Activity Migration and Distribution code for an entire reactor which included migration, transport and deposition models to predict the radionuclide distribution in the primary loop of the PBMR. Stempniewicz et al. (2012) used the SPECTRA code (Stempniewicz, 2019) to analyze the dust and fission products in the primary loop of the next generation pebble bed shown in Fig. 20. They took into account the dust production, diffusion, thermophoresis deposition, resuspension and coagulation by adding various aerosol models to infer the spatial deposition distribution and layer thicknesses during the 60 years lifetime (Stempniewicz, 2009). The predictions showed that around 86% of the dust deposited in the reactor vessel with the rest of the dust mostly deposited in the heat exchanger. Particle resuspension normally prevents a thick deposition

4.3. Dust resuspension After the graphite dust deposits on the wall of the primary loop, the deposited graphite dust particles may detach from the wall and again be carried by the helium which is called resuspension. Resuspension significantly increases the dust concentration in the primary loop as shown in Fig. 7. The graphite dust resuspension characteristics need to be studied to assess the radiation release and environmental effects from the reactor during a loss of coolant accident and to determine the graphite dust concentrations during transient operations. 4.3.1. Resuspension mechanism Ziskind et al. (1995) generalized a theoretical model for monolayer particle resuspension and classified the models as force-balance and energy-accumulation approaches. The force-balance method predicts the particle resuspension by the balance of the instantaneous forces or moments on the particles, while the energy-accumulation method considers the energy accumulation effect to determine when the accumulated vibrational energy of the particles exceeds the potential energy of the adhesion force on the wall to predict resuspension. In recent years, the dynamic PDF method has been used to simulate the entire particle resuspension process (Henry et al., 2014). All of the 14

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

regions of a steam generator. The results indicated that particles with diameters less than 1 μm were not easily removed by the helium, while the resuspension of larger particles exhibited differences in different sections due to the anisotropic friction velocity. Zhang et al. (2017b) applied the Rock'n’Roll model to analyze the effects of the adhesion distribution, particle diameter and time on the graphite dust resuspension characteristics. They predicted short-term and long-term effects during resuspension with the resuspension rate increasing rapidly in the short term and then decreasing down to a stable rate in the long term (Wen et al., 1989). Increasing the wall roughness which increases the standard deviation of the adhesion distribution then reduces the slope of the resuspension fraction versus friction velocity curve. Larger diameter particles were more easily resuspended with lower threshold friction velocities. Friess and Yadigaroglu (2002) extended the monolayer approaches to model multilayer particle resuspension to predict more realistic multilayer particle deposition rates in some recirculation zones. Zhang (2011) and Zhang et al. (2013) used the Friess and Yadigaroglu hypothesis to derive a multilayer resuspension expression using the monolayer Rock’n’Roll model. The model was verified against the classic resuspension experiments from Reek et al. (1988) and Costelo et al. (1999). Paci et al. (2005) implemented the multi-layer resuspension model by Fromentin (1989) in the ECART thermal hydraulics code (Fromentin, 1989; Parozzi et al., 1997). The flow calculations were verified using computational fluid dynamics model results while the aerosol characteristics were verified against experimental data from the Small Tank for Aerosol Removal and Dust experiment. They thought that the quantity of mobilized dust in a loss of vacuum accident in ITER in a realistic plant should be lower than the values seen in experiments. Barth et al. (2015) reviewed the monolayer and multilayer resuspension models used in the European research projects THINS and ARCHERT. Stempniewicz et al. (2018) reviewed existing multi-layer resuspension models and developed a new model called KSMB based on a moment balance method. The predictions of the various resuspension models were compared with classic resuspension experiments. They concluded that multilayer resuspension predictions are very uncertain due to uncertainties in the multilayer deposit structures that result in significant differences among the adhesion resuspension rates that are even more important than the selection of the resuspension model. Zhang et al. (2017a) used a multilayer resuspension model to study the effect of various physical properties on the resuspension characteristics. Their results indicated that a shelter effect from underlying particles on all the layers but the first layer with short-term and long-term effects on the resuspension rates. As with monolayer resuspension, particles with large diameters and higher friction velocities more easily detached from the wall and resuspended. In addition, the resuspension fraction decreased with increasing temperature while increasing helium pressures led to the resuspension of more graphite dust particles.

resuspension models are based on the forces between the particles and the fluid such as the drag force and the lift force, as well as particle and wall forces such as adhesion given by various analytical formations (Henry and Minier, 2014; Zhou et al., 2019). The force-balance method is intuitive and easy to implement the coupling with computational fluid dynamics or discrete element method. The improved models are continuously proposed, where Vainshtein model (Vainshtein et al., 1997) and NRG4 model (Komen, 2007) with the results verified by experiments (Stempniewicz and Komen, 2010) are used frequently in the particle resuspension research in HTGRs. The energy-accumulation method reflects the change of system energy in the resuspension process and explains the experiment phenomenon that particles are not instantaneously detached from the substrate, but need time to accumulate some speed (Wang et al., 2012). The most classic Rock'n'Roll model (Reeks and Hall, 2001) is still used to study graphite dust resuspension in HTGRs. From the perspective of force, the effect of irregular graphite dust on drag coefficient is significant to affect particle resuspension and motion. Sun et al. (2018d) studied the drag coefficient of irregular graphite dust particles in HTGRs and investigated the contribution of particle shape, Reynolds number, flow angle on the drag coefficient using a computational fluid dynamics method. The adhesion between the particle and the surface is another key factor that determines the resuspension rate. Some researchers (Mokgalapa et al., 2014; Zhang et al., 2015; Mokgalapa et al., 2017) have used the atomic force microscope (AFM) to measure the adhesion between graphite or silver particles and substrates at different atmospheres and temperature processing. Due to rough particle morphology and unpredictable substrate profile, it is difficult to express the adhesion distribution of graphite particle accurately. From the perspective of resuspension model, Vainshtein et al. (1997) derived the resuspension rate defined as the fraction of deposited particles resuspended per second using the JKR adhesion model (Johnson et al., 1971) and the elastic deformation hypothesis based on the potential well method proposed by Reeks et al. (1988). Stempniewicz et al. (2008) implemented the Vainshtein model in the SPECTRA thermal–hydraulic code with predictions compared with the analytical solutions by Komen (2006). The Rock'n'Roll model (Reeks and Hall, 2001) was proposed to improve the RRH model by including the tangential drag on the particles instead of the normal lift with a moment vibration equation instead of a force vibration equation. This has become the most widely used model and is expressed as:

(F − 〈F 〉)2 ⎞ 1 ⎡ ⎛ FaN − 〈F 〉 ⎞ ⎤ Rm = nθ exp ⎜⎛− aN 2 ⎟/ ⎢1 + erf ⎜ ⎟⎥ 2 2 〈f 〉 ⎝ ⎠ 2⎣ ⎝ 2 〈f 〉 ) ⎠ ⎦ nθ =

1 2π

(10)

2

〈f ̇ 〉 〈f 2 〉

(11)

where FaN is the normal adhesive force, F is the total aerodynamic force including the drag and lift forces, f are f ̇ are the fluctuating components of the aerodynamic force and its time derivative. Jühe et al. (2012) developed the dust code STAR (primary loop) which incorporates correlations for deposition, surface interactions, the quasistatic Rock’n Roll resuspension model and dust transport coupled with the DIREKT thermo-fluid code (Struth et al., 1999) and the COCOSYS reactor building code (Allelein et al., 2008) for the HTR-Module-200 Reactor. They analyzed the amount of dust escaping out of the primary loop during a design basis accident to be 6.3–12 g and during a beyond design basis accident to be 2.0–3.9 kg. In addition, the crucial adhesion distribution and aerodynamic force fluctuation were improved in Biasi et al. (2001) and Kissane et al. (2011). Both models showed that the resuspension process can be divided into short-term and long-term effects. Peng et al. (2014) used the modified Rock'n'Roll model by Biasi et al. (2001) to estimate the graphite dust resuspension in various

4.3.2. Resuspension experiments Wawrzik et al. (1988) planned to carry out dust resuspension experiment in the primary loop of AVR during startup and accident conditions, however, due to the risk and difficulty of accident conditions, only startup experiment is completed and investigated. Therefore, the experimental design only allowed measurements of the variation of the instantaneous graphite dust concentration in the primary loop with the results shown in Fig. 7. The experimental AVR results showed that the graphite dust deposited on the wall of the primary loop had strong mobility and was easily resuspended and re-entrained by the helium flow due to fluctuations of the shear force with varying flow conditions. Work at the Jülich Research Center showed that the graphite dust concentration in the reactor primary loop during startup was on the same order-of-magnitude as during helium circulator start-up at 1000–2000 μg /Nm3 with the estimated total leakage of graphite dust from the AVR primary loop during a LOCA of around 1.73 g 15

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

estimate graphite dust release during a LOCA. 4.4. Dust coagulation Besides dust deposition and resuspension, graphite dust particles will also coagulate. Coagulation means that particles will collide and then stick to each other to form new bigger particles. Coagulation will reduce the particle number concentration and increase the particle size, which alter the particle size distribution which in turn affects the particle dynamics (Wang et al., 2019a,b). Thus, coagulation must be evaluated to understand the dust particle dynamics in high temperature gas-cooled reactors. Although there are many studies focusing on particle deposition and resuspension, only a few studies have considered coagulation of the graphite dust particles. Luo et al. (2006b) used the discrete-sectional method to simulate the time evolution of the particle size distribution undergoing Brownian coagulation in the helium flow of HTR-10. The predictions showed that the graphite dust particle coagulation may not be serious due to the limited residence time. Chen (2012) calculated the various particle dynamics characteristics including coagulation in the primary loop of the HTGR. Palsmeier and Loyalka (2013) numerically investigated the electrostatic charge effects on graphite dust coagulation using the direct simulation Monte Carlo method. They found that charge effects can be significant for practical conditions. Then, Simones and Loyalka (2015) experimentally investigated the evolution of the particle size and charge distributions during coagulation and compared their measurements with direct simulation Monte Carlo results. Fig. 23 compared the measured size and charge distributions for spark-generated silver nanoparticles at coagulation chamber sampling port #4 with the DSMC results. Results for both silver and carbon aerosols show that coagulation occurs faster than predicted by the DSMC method. Wang et al. (2019c) focused on graphite dust coagulation in large temperature gradients and numerically investigated the thermophoretic effects on aerosol coagulation in HTGRs. They compared the Brownian coagulation and thermophoretic coagulation rates for various HTGR conditions. Their results indicate that the thermophoretic effects can locally dominate the Brownian coagulation in the HTGR and should be considered when modeling aerosol evolution.

Fig. 21. AVR dust deposition samples (Fachinger et al., 2008).

(Verfondern et al., 2012). However, experiments by Fachinger et al. (2008) showed that crusted graphite deposits with strong surface cohesion on a pipe in the AVR could only be removed by strong mechanical effort as shown in Fig. 21. Thus, few particles would be separated from pipe surfaces and resuspended by velocity fluctuations. They concluded that previous estimates would overestimate the graphite dust emissions during a LOCA. Kazuhiro et al. (1992) used blow down tests to simulate the resuspension of graphite dust during depressurization of an HTGR. They focused on the correlation between the resuspension fraction and the shear ratio which was described as the ratio of the wall shear stress during blow down to the normal condition. The results gave a linear regression coefficient of the resuspension fraction to the shear ratio of 0.64 with resuspension still occurring for conditions with shear ratios less than 1 which indicates that the simple force balance concept is not sufficient to model the resuspension of dust for all kinds of depressurization conditions. Barth et al. (2014) conducted resuspension experiments for particle deposition in a stacked pebble bed which showed that most particles on the front sides of single pebbles were removed. The remaining dust seemed to be distributed in the spaces in the pebble bed which may correspond to single particles adhering to the surfaces or in recirculation areas. The results showed that the dust particles in the pebble bed were more easily resuspended than in classical resuspension experiments, which may be due to the multilayer structures without studying higher friction speeds because of the limited power of the fan. Peng et al. (2013a) built a test system to simulate the particle behavior during a LOCA in a HTGR that is shown in Fig. 22. The graphite dust resuspension rate was measured for various inertia pressures. The results indicated that higher initial pressures led to higher resuspension fractions. The resuspension fractions measured in the experimental section were consistent with the predictions of the Biasi resuspension model. Peng et al. (2017) also conducted a theoretical analysis model and experiment design of graphite dust emission measurement to

5. Summary The present review introduced the design features of the high temperature gas-cooled reactor and focused on several graphite dust issues in pebble bed reactor to understand the graphite dust behavior characteristics in the primary loop to improve engineering designs. This review includes various studies of the graphite dust dynamics including particle production, particle characteristics, and particle motion which show that: 1) There are lots of sources of the graphite dust particles with some uncertainty about the effects of these sources. The existing research shows that graphite particles are generated by mechanical wear from collisions between moving graphite pebbles and component expansion, chemical peeling and decomposition. The wear due to collisions between graphite fuel pebbles is considered as an important source of the graphite dust. Classical Archard models showed that wear mass is proportional to loading, slide distance and wear coefficient, where the wear coefficient is independent of the loading and slide distance. However, recent experiments have showed that loading and longer slide distances will smooth the graphite surface and reduce the wear coefficient. In addition, various atmospheres will also affect the wear coefficient due to the adsorption of different gases changing graphite property. 2) Graphite wear tests and reactor operation samples showed that the graphite particles in HTGRs were sub-micron particles with sizes depending on the graphite and wear types. Reactor measurements showed low concentrations for normal operation conditions. However, 16

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

Fig. 22. Experimental system to investigate the particle behavior during a LOCA (Peng et al., 2013a).

of-magnitude in a short time. The resuspension depends on the deposition thickness, the aerodynamic force of the helium on the particle, the adhesion force to the wall, and the thermophoretic force caused by the temperature gradient. Resuspension has both short-term and longterm effects and increases with increasing friction velocity. In general, deposited particles are immediately resuspended once a critical friction velocity is exceeded, while larger particles tending to detach at lower velocities. In addition, the resuspension fraction decreases with increasing temperature and decreasing helium pressure. 5) Various mechanisms affect the coagulation of graphite dust particles in HTGRs, such as Brownian motion, gravitational settling, electrostatic forces and thermophoresis. These effects can significantly alter the aerosol coagulation evolution for various situations. Some challenges requiring further study are:

the dust generation mechanism and the particle size distribution will change for changing operating conditions or accidents (such as ingress accidents). The dust morphology in HTGRs had no obvious trends but with large porosities, which greatly increases the specific surface area for adsorbed radioactive elements as has been observed with increasing adsorption of Cs, Sr, I and 3H. 3) Dust particles are carried away from the reactor core by the helium and deposits in other parts of the HTGR. The flow field in the primary loop is typically turbulent with large temperature gradients in the core and heat exchanger. Therefore, the graphite dust deposition is mainly affected by turbulent diffusion and the thermophoretic force. For small particles, the thermophoretic force has a greater effect, while for large particles, turbulent diffusion is more important. In addition, gravitational settling has an important effect in dead-end zones. The reactor vessel and heat exchanger are the main places with particle deposition. 4) During startup or accident conditions, the particle resuspension increases the dust concentration in the primary loop by several orders-

1) The large differences between the results of wear experiments and reactor data indicate that further research is still needed to investigate the effects of chemicals on the graphite dust production for

Fig. 23. Comparison of the measured size and charge distributions for spark-generated silver nanoparticles at coagulation chamber sampling port #4 (t = 183.3 s) with predictions of the DSMC method (Simones and Loyalka, 2015). 17

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

2)

3)

4)

5)

high temperature and accident conditions. Temperature changes affect the graphite roughness and brittleness, but there is still uncertainty about their effects on graphite wear. The mechanisms of various atmospheres changing graphite wear need to be studied further. Although fairly consistent results have been seen in reactors, the mechanisms describing the interactions between radioactive fission products and graphite dust are not well known and prediction models obtained from the existing research need to be improved. There is still great uncertainty about the applicability of widely used theoretical particle deposition models for graphite dust in the HTGR due to their irregular shapes and large porosities which need more verification. Both numerical and experiment methods should be used to visualize deposition distributions and the crucial effects of the turbulent boundary layer and the particle transport. The resuspension behavior is strongly dependent on the distribution of the adhesion force between the aspherical particles and the wall roughness which needs further study. The graphite particle resuspension in the HTGR primary loop is also affected by the particleto-wall sintering effects which means that some graphite deposits in the HTGR could only be removed by strong mechanical efforts. The existing resuspension models ignore the sintering effect and may overestimate the resuspension weight fraction. In addition, the complex facility surfaces are another challenge which may not be properly modeled by classical resuspension models. None of the previous studies have considered sufficient effects together to give a clear picture of the role of each coagulation mechanism. This needs to be included in future research on graphite dust coagulation. In addition, more research is needed to understand the effect of coagulation and reactions on the dust size and shape.

successful operation for a future energy techlonogy /Association of German Engineersa(VDI), The Society for Energy Technologies. VDI-Verl, Dusseldorf. Bäumer, R., Barnert, H., Baust, E., Bergerfurth, A., Bonnenberg, H., Bülling, H., Burger, S., von der Decken, C.-B., Delle, W., Gerwin, H., Hackstein, K.-G., Hantke, H.-J., Hohn, H., Ivens, G., Kirch, N., Kirjushin, A.I., Kröger, W., Krüger, K., Kuzavkov, N.G., Lange, G., Marnet, C., Nickel, H., Pohl, P., Scherer, W., Schöning, J., Schulten, R., Singh, J., Steinwarz, W., Theymann, W., Wahlen, E., Wawrzik, U., Weisbrodt, I., Werner, H., Wimmers, M., Ziermann, E., 1990a. AVR: Experimental High Temperature Reactor; 21 Years of Sucessful Operation for a Future Energy Technology. The Society for Energy Technologies, Association of German Engineers (VDI). Bhushan, B., 2000. Modern Tribology Handbook. CRC Press, Boca Raton, FL, USA (Chapter 7.5). Bäumer, R., Kalinowski, I., Röhler, E., Schöning, J., Wachholz, W., 1990b. Construction and operating experience with the 300-MW THTR nuclear power plant. Nucl. Eng. Des. 121 (2), 155–166. Biasi, L., Reyes de los, A., Reeks, M.W., Santi, G.F., 2001. Use of a simple model for the interpretation of experimental data on particle resuspension in turbulent lows. J. Aerosol. Sci. 32, 1175–1200. Boddu, S., Gutti, V., Meyer, R., Ghosh, T., Tompson, R., Loyalka, S., 2011. Carbon nanoparticle generation, collection, and characterization using a spark generator and a thermophoretic deposition cell. Nucl. Technol. 173 (3), 318–326. Brock, J.R., 1962. On the theory of thermal forces acting on aerosol particles. J. Colloid. Interf. Sci. 17 (8), 768–780. Burchell, T., Snead, L., 2007. The effect of neutron irradiation damage on the properties of grade NBG-10 graphite. J. Nucl. Mater. 371 (1–3), 18–27. Chen, Q., Ahmadi, G., 1997. Deposition of particles in a turbulent pipe flow. J. Aerosol. Sci. 28, 789–796. Chen, T., Wang, J., Peng, W., Sun, X., 2017. Numerical Simulation of Graphite Dust Deposition in Pebble Bed Reactor Core of HTGR. Proceedings of the 25th International Conference on Nuclear Engineering. Chen, Z., Xie, F., Zheng, Y., Shi, L., Li, F., 2012. Development of modeling transport of graphite dust in HTGR during normal operation condition. Proceedings of the 20th International Conference on Nuclear Engineering. Cogliati, J.J., Ougouag, A.M., Ortensi, J., 2011. Survey of dust production in pebble bed reactor cores. Nucl. Eng. Des. 241 (6), 2364–2369. Cogliati, J.J., Ougouag, A.M., 2008. Pebble bed reactor dust production model. 4th International Topical Meeting on High Temperature Reactor Technology. Contescu, C., Guldan, T., Wang, P., Burchell, T., 2012. The effect of microstructure on air oxidation resistance of nuclear graphite. Carbon 50 (9), 3354–3366. Contescu, C., Mee, R., Wang, P., Romanova, A., Burchell, T., 2014. Oxidation of PCEA nuclear graphite by low water concentrations in helium. J. Nucl. Mater. 453 (1–3), 225–232. Costelo, A.R., Capitao, J.A., Santi G.D., 1999. International Standard Problem 40- Aerosol Deposition and Resuspension, Final Comparison Report, OECD NEA/CSNI/R (99) 4. Dehbi, A., 2008. Turbulent particle dispersion in arbitrary wall-bounded geometries: A coupled CFD-Langevin-equation based approach. Int. J. Multiphas. Flow. 34 (9), 819–828. Dehbi, A., 2009. A stochastic Langevin model of turbulent particle dispersion in the presence of thermophoresis. Int. J. Multiphas. Flow. 35 (3), 219–226. Dehbi, A., Martin, S., 2011. CFD simulation of particle deposition on an array of spheres using an Euler/Lagrange approach. Nucl. Eng. Des. 241 (8), 3121–3129. Derjaguin, B.V., Yalamov, Y., 1965. Theory of thermophoresis of large aerosol particles. J. Colloid. Interf. Sci. 20 (6), 555–570. Eapen, J., Krishna, R., Burchell, T., Murty, K., 2014. Early damage mechanisms in nuclear grade graphite under irradiation. Mater. Res. Lett 2 (1), 43–50. Fachinger, J., Barnert, H., Kummer, A., Caspary, G., Seubert, M., Koster, A., Makumbe, M., Naicker, L., 2008. Examination of dust in AVR pipe components. Proceedings of the 4th International Topical Meeting on High Temperature Reactor Technology. 1, 591-602. Fan, F.G., Ahmadi, G., 1993. A sublayer model for turbulent deposition of particles in vertical ducts with smooth and rough surfaces. J. Aerosol. Sci. 24, 45–64. Fang, Z., Wang, H., Zhang, Y., Wei, M., Wu, X., Sun, L., 2019. A finite element method (FEM) study on adhesive particle-wall normal collision. J. Aerosol. Sci. 134, 80–94. Fang, Z., Zhang, Y., Wei, M., Zhao, S., Sun, L., Wu, X., 2020a. The critical sticking velocity of non-spherical graphite particles: A numerical study and validation. Nucl. Eng. Design 359, 110453. https://doi.org/10.1016/j.nucengdes.2019.110453. Fang, Z., Zhang, Y., Wei, M., Zhao, S., Wu, X., Sun, L., 2020b. A numerical study on adhesive collision between a micro-sized particle and a wall. Powder Technol. 360, 769–779. Fernandes, A., Loyalka, S.K., 1996. Modeling of thermophoretic deposition of aerosols in nuclear reactor containments. Nucl. Technol. 116, 270. Fischer, F., Andris, A., Lippmann, W., Hurtado, A., 2018. Particle deposition by thermophoresis under high-temperature conditions in a helium flow. J. Nucl. Eng. Radiat. Sci. 4 (4), 041020. Friedlander, S.K., Johnston, H.F., 1957. Deposition of suspended particles from turbulent gas stream. Ind. Engng. Chem. 49, 1151–1156. Friess, H., Yadigaroglu, G., 2002. Modelling of the resuspension of particle clusters from multilayer aerosol deposits with variable porosity. J. Aerosol. Sci. 33, 883–906. Fromentin, A., 1989. Particle resuspension from a multi-layer deposit by turbulent flow. Paul Scherrer Institut report no. 38, W¨urelingen. LACE Report TR-083. Gottaut, H., Krüger, K., 1990. Results of experiments of the AVR reactor. Nucl. Eng. Des. 121, 143–153. Guo, L., Liang, D., Wang, X., Deng, S., Zhou, D., Zhang, Y., Yu, L., 2019. Graphite dust deposition in high temperature gas cooled reactor. China Powder Sci. Technol. 25 (2). Gutti, V.R., Loyalka, S.K., 2009. Thermophoretic deposition in a cylindrical tube: computations and comparison with experiments. Nucl. Technol. 166 (2), 121–133.

Moreover, it is needed to note that most of the previous studies, especially the experimental studies, were carried out under the normal temperature and pressure conditions, while the actual conditions of HTGRs are high temperatures and pressures, especially for the very high temperature gas cooled reactor (VHTR), the maximum temperature is more than 950 ℃. The high temperature and high pressure environments would have a great influence on graphite dust generation and its motion behavior. Therefore, issues related to graphite dust in the VHTR environment need further investigations. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This project was supported by the National Natural Science Foundation of China (NSFC), No. 51676112, the National Key R&D Program of China (Grant No. 2018YFB1900500), the National S&T Major Project of China (Grant No. ZX069). We also thank Prof. David Christopher for editing the English. References Allelein, H.-J., Arndt, S., Klein-Heßling, W., Schwarz, S., Spengler, C., Weber, G., 2008. COCOSYS: Status of development and validation of the German containment code system. Nucl. Eng. Des. 238, 872–889. Archard, J., 1953. Contact and rubbing of flat surfaces. J. Appl. Phys. 24 (8), 981–988. Barth, T., Kulenkampff, J., Bras, S., Gründig, M., Lippmann-Pipke, J., Hampel, U., 2014. Positron emission tomography in pebble beds. Part 2: Graphite particle deposition and resuspension. Nucl. Eng. Des. 267, 227–237. Barth, T., Lecrivain, G., Jayaraju, S., Hampel, U., 2015. Particle deposition and resuspension in gas-cooled reactors-Activity overview of the two European research projects THINS and ARCHER. Nucl. Eng. Des. 290, 127–134. Bäumer, R., Barnert, H., 1990. AVR-Experimental High-Temperature Reactor; 21 years of

18

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

HTRs: status and further needs, extracted from German safety analyses. Nucl. Technol. 135, 183–193. Moormann, R. 2008a. A safety re-evaluation of the AVR pebble bed reactor operation and its consequences for future HTR concepts. Fourth International Topical Meeting on High Temperature Reactor Technology. IAEA, IAEA Safety Reports series, no. 54. Moormann, R. 2008b. Fission product transport and source terms in HTRs: experience from AVR pebble bed reactor. Sci Technol Nucl Ins. Article ID 597491. Moormann, R., 2009. AVR prototype pebble bed reactor: a safety re-evaluation of its operation and consequences for future reactors. Kerntechnik 74 (1–2), 8–21. Nieder, V.R., 1990. Schlußfolgerungen für die htr-chemie aus 21 jahren betrieb des avrreaktors. Chemie im Kraftwerk. Nishio, G., Kitani, S., Takahashi, K., 1974. Thermophoretic deposition of aerosol particles in a heat-exchanger pipe. Ind. Engng. Chem. Process Des. Develop. 13, 408–415. Oetjen, H.F., 1989. Arbeitsprotokoll zu Behandlung der Proben und Bestimmung von Kornspektren an den THTR-Staubproben. Research Center Jülich. Paci, S., Forgione, N., Parozzi, F., Porfiri, M., 2005. Bases for dust mobilization modelling in the light of STARDUST experiments. Nucl. Eng. Des. 235 (10–12), 1129–1138. Palsmeier, J.F., Loyalka, S.K., 2013. Evolution of charged aerosols: role of charge on coagulation. Nucl. Technol. 184, 78–95. Papavergos, P.G., Hedley, A.B., 1984. Particle deposition behaviour from turbulent flows. Chem. Eng. Res. Des. 62, 275–295. Parozzi, F., Salina, E., Fontana, R., Ambrosini, W., Paci S., 1997. ECART USER MANUAL Part 2: Code Structure and Theory. ENEL Nuclear Energy Division Report, Milan. Peng, W., Chen, T., Sun, Q., Wang, J., Yu, S., 2017. Preliminary experiment design of graphite dust emission measurement under accident conditions for HTGR. Nucl. Eng. Des. 316, 218–227. Peng, W., Sun, Q., Xie, F., Jiang, Y., 2018. Simulations of the dust behavior in the sampling and dust filters in the primary loop of HTR-10. Nucl. Eng. Des. 340, 112–121. Peng, W., Zhang, T., Sun, X., Yu, S., 2016. Thermophoretic and turbulent deposition of graphite dust in HTGR steam generators. Nucl. Eng. Des. 300, 610–619. Peng, W., Zhang, T., Yu, S., Zhen, Y., 2013a. Graphite dust resuspension in a depressurization accident of HTR. Nucl. Eng. Des. 265, 785–790. Peng, W., Zhang, T., Zhen, Y., Yu, S., 2014. Graphite dust resuspension in an HTR-10 steam generator. Particuology 17, 149–157. Peng, W., Zhen, Y.N., Yang, X., Ye, P., 2013b. Analysis of graphite dust deposition in hot gas duct of HTGR. Atom. Energy Sci. Technol. 47 (5), 816–821. Peng, W., Zhen, Y., Yang, X., Yu, S., 2013c. Graphite dust deposition in the HTR-10 steam generator. Particuology 11 (5), 533–539. Reeks, M.W., Hall, D., 2001. Kinetic models for particle resuspension in turbulent flows: theory and measurement. Aerosol Sci. 32, 1–31. Reeks, M.W., Reed, J., Hall, D., 1988. On the resuspension of small particles by a turbulent flow. J. Phys. D: Appl. Phys. 21, 574–589. Romay, F.J., Takagaki, S.S., Pui, D.Y.H., Liu, B.Y.H., 1998. Thermophoretic deposition of aerosol particles in turbulent pipe flow. J. Aerosol. Sci. 29, 943–959. Rostamian, M., Johnson, G., Hiruta, M., Potirniche, G.P., Ougouag, A.M., Cogliati, J.J., Tokuhiro, A., 2013. Computational and experimental prediction of dust production in pebble bed reactors. Part I. Nucl. Eng. Des. 263, 500–508. Rostamian, M., Potirniche, G.P., Cogliati, J.J., Ougouag, A., Tokuhiro, A., 2012. Computational prediction of dust production in pebble bed reactors. Nucl. Eng. Des. 243, 33–40. Rycroft, C.H., Lind, T., Güntay, S., Dehbi, A., 2012. Granular flow in pebble bed reactors: dust generation and scaling. International Congress on Advances in National Power Plants, Chicago, Illinois. Schwendiman, L.C., Postma, A.K., 1965. Turbulent deposition in sampling lines. Tech. Inf. Div. Rep, TID-7628. Sehmel, G.A., 1968. Aerosol deposition from turbulent airstreams in vertical conduits. Batelle northwest Lab, Richland, Washington, USA. Shams, A., Roelofs, F., Komen, E., Baglietto, E., 2014. Large eddy simulation of a randomly stacked nuclear pebble bed. Comput. Fluids. 96, 302–321. Shen, K., Peng, W., Liu, B., Kang, F., Yang, X., Li, W., Yu, S., 2016. Characterization of graphite dust produced by pneumatic lift. Nucl. Eng. Des. 305, 104–109. Shen, K., Su, J., Zhou, H., Peng, W., Liu, B., Yu, S., 2015. Abrasion behavior of graphite pebble in lifting pipe of pebble-bed HTR. Nucl. Eng. Des. 293, 395–402. Sheng, X., Yu, S., Luo, X., He, S., 2003. Wear behavior of graphite studies in an air conditioned environment. Nucl. Eng. Des. 223, 109–115. Simon, M., 2009. Particles deposition on an array of spheres using a hybrid Euler/ Lagrange CFD method. Fluids mechanics. Simones, M.P., Loyalka, S.K., 2015. Measurements of charged aerosol coagulation. Nucl. Technol. 189, 45–62. Skyrme, G., 1985. Attachment of gaseous fission products to aerosols. In: Specialists Meeting on Fission Product Release and Transport in Gas-Cooled Reactors, Berkeley, UK, 22-25 Oct, IWGGCR-13. Snead, L., Burchell, T., Katoh, Y., 2008. Swelling of nuclear graphite and high quality carbon fiber composite under very high irradiation temperature. J. Nucl. Mater. 381 (1–2), 55–61. Stansfield, O.M., 1969. Friction and wear of graphite in dry helium at 25, 400, and 800°C. Nucl. Appl. 6, 313–320. Stempniewicz, M. M., 2019. SPECTRA Computer Code Manuals. https://www.nrg.eu/ fileadmin/nrg/Documenten/Spectra-Vol1.pdf. Stempniewicz, M.M., Komen, E.M., de With, A., 2008. Model of particle resuspension in turbulent flows. Nucl. Eng. Des. 238 (11), 2943–2959. Stempniewicz, M., Chen, Z., Zheng, Y., Komen, E., 2018. Resuspension models for monolayer and multilayer deposits of graphite dust. Ann. Nucl. Energy 120, 186–197. Stempniewicz, M., Komen, E., 2010. Comparison of several resuspension models against measured data. Nucl. Eng. Des. 240 (6), 1657–1670. Stempniewicz, M.M., 2009. SPECTRA-Sophisticated Plant evaluation code for thermal-

Hanson, D, Baldwin, N, Strong, D., 1980. Fission product behaviour in the Peach Bottom and Fort St. Vrain HTGRs. In: Specialists meeting on coolant chemistry, plate-out and decontamination in gas-cooled reactors, Juelich, Germany, 2-4 Dec, IAEA IWGGCR-2. He, C., Ahmadi, G., 1998. Particle deposition with thermophoresis in laminar and turbulent duct flow. Aerosol. Sci. Tech. 29, 525–546. He, X., Shi, L., Li, H., Tan, J., Zhang, B., Fok, A., Sun, L., 2018. Experimental study to estimate the surface wear of nuclear graphite in HTR-PM. Ann. Nucl. Energy. 116, 296–302. Henry, C., Minier, J.P., 2014. Progress in particle resuspension from rough surfaces by turbulent flows. Prog. Energy Combu. 45, 1–53. Henry, C., Minier, J.P., Mohaupt, M., Profeta, C., Pozorski, J., Taniere, A., 2014. A stochastic approach for the simulation of collisions between colloidal particles at large time steps. Int. J. Multiphase Flow. 61, 94–107. Hiruta, M., Johnson, G., Rostamian, M., Potirniche, G.P., Ougouag, A.M., Bertino, M., Franzel, L., Tokuhiro, A., 2013. Computational and experimental prediction of dust production in pebble bed reactors. Part II. Nucl. Eng. Des. 263, 509–514. Humrickhouse, P. W., 2011. HTGR Dust safety issues and needs for research and development. INL/EXT-11-21097, Idaho National Laboratory. IRPHE/AVR: Collection of AVR documents by AEN/NEA,” CD-ROM NEA-1739/01, 2005. Jayaraju, S., Roelofs, F., Komen, E., Dehbi, A., 2016. RANS modeling of fluid flow and dust deposition in nuclear pebble-beds. Nucl. Eng. Des. 308, 222–237. Jayaraju, S., Shams A., Roelofs, F., 2015. Heat and dust transport in a pebble bed HTR. Paper presented at the 16th International Topical Meeting on Nuclear Reactor Thermal Hydraulics. Jiang, S., Tu, J., Yang, X., Gui, N., 2019. A review of pebble flow study for pebble bed high temperature gas-cooled reactor. Exp. Comput. Multiphase Flow 1 (3), 159–176. Johnson, K.L., Kendall, K., Roberts, A.D., 1971. Surface Energy and the Contact of Elastic Solids. Proc. Royal Soc. A: Math. Phys. Eng. Sci. 324 (1558), 301–313. https://doi. org/10.1098/rspa.1971.0141. JÜhe S., Struth S., SchlÖgl B., h.-J., A. 2012. Simulation of dust behavior in HTR with pebble bed fuel. Kadak, A.C., 2005. A future for nuclear energy: Pebble bed reactors. Int. J. Crit. Infrastruct. 1, 330–345. Kazuhiro, S., Takeshi, N., Yoshiaki, M., 1992. Experimental study of dust behavior during depressurization. J. Nucl. Sci. Technol. 29 (10), 1018–1025. Kim, O.V., Dunn, P.F., 2007. A microsphere-surface impact model for implementation in computational fluid dynamics. J. Aerosol. Sci. 38, 532–549. Kissane, M., 2009. A review of radionuclide behaviour in the primary system of a veryhigh-temperature reactor. Nucl. Eng. Des. 239 (12), 3076–3091. Kissane, M.P., Zhang, F., Reeks, M.W., 2011. Dust in HTRs: Its nature and improving prediction of its resuspension. Nucl. Eng. Des. 251, 301–305. Komen, E.M.J., 2006. PBMR resuspension analyses, Main Coolant Lines. NRG report 21544 NRG-PPT. Komen, E.M.J., 2007. Dispersion of fission products and dust in direct cycle HTRs, NRG report 21346/06.60264C, Revision 2, Petten. Kriiger K., Wimmers M., 1987. Test program of the AVR experiment. Nuclear Power Plant Jiihch, AVR Report. Lancaster, J.K., Pritchard, J.R., 1980. On the dusting wear regime of graphite sliding against carbon. J. Phys. D: Appl. Phys. 13, 1551–1564. Latifi, M.S., Colangelo, G., Starace, G., 2020... A CFD study on the effect of size of fuel sphere on PBR core. Exp. Comput. Multiphase Flow. 2 (2), 109–114. Lind, T., Güntay, S., Dehbi, A., Liao, Y., Rycroft, C.H., 2010. PSI project on HTR dust generation and transport. In: Proceedings of HTR, p. 2010. Liu, B., Agarwal, J.K., 1974. Experimental observation of aerosol deposition in turbulent flow. J Aerosol. Sci. 8, 351–356. Liu, Guodong, Zhang, Yining, Lu, Huilin, You, Ersheng, Li, Xiang, 2013. Numerical simulation of particle flow motion in a two-dimensional modular pebble-bed reactor with discrete element method. Sci. Technol. Nucl. Install. 2013, 1–12. https://doi. org/10.1155/2013/458190. Luo, X., Hua, H., Yu, S., 2006b. Coagulating evolution of graphite dust in 20 helium flow of 10 MW high-temperature gas-cooled reactor. Atom. Energy Sci. Technol. 40, 311–315. Luo, X., Li, X., Yu, S., 2010. Nuclear graphite friction properties and the influence of friction properties on the pebble bed. Nucl. Eng. Des. 240 (10), 2674–2681. Luo, X., Wang, X., Shi, L., Yu, X., Yu, S., 2017. Nuclear graphite wear properties and estimation of graphite dust production in HTR-10. Nucl. Eng. Des. 315, 35–41. Luo, X., Yu, S., Sheng, X., He, S., 2005a. Temperature effects on IG-11 graphite wear performance. Nucl. Eng. Des. 235, 2261–2274. Luo, X., Yu, S., Tang, H., 2006a. Deposition of graphite dust in heat gas duct in HTR-10. Nucl. Power Eng. 27 (4), 90–92. Luo, X., Yu, S., Zhang, Z., He, S., 2005b. Estimation of graphite dust quantity and size distribution of graphite particle in HTR-10. Nucl. Power Eng. 26 (2), 203–208. Luo, X., Zhang, L., Yu, S., 2004. The wear properties of nuclear grade graphite IG-11 under different loads. Int. J. Nucl. Energy Sci. Technol. 1 (1), 33–43. Lustfeld, M., Qu, T., Lippmann, W., Hurtado, A., Göhler, D., 2014. Experimental study of graphite particle deposition upstream of a forward-facing step. Nucl. Eng. Des. 271, 552–559. Mehravaran, M., 2013. Thermophoretic transport and deposition of sub-micron particles suspended in gas flows. Michigan State University. Mokgalapa, N.M., Ghosh, T.K., Tompson, R.V., Loyalka, S.K., 2017. Adhesion Force between a Silver Particle and Haynes 230: Role of Surface Conditions. Nucl. Technol. 194 (3), 353–368. Mokgalapa, N.M., Ghosh, T.K., Loyalka, S.K., 2014. Graphite particle adhesion to Hastelloy X: measurements of the adhesive force with an Atomic Force Microscope. Nucl. Technol. 186 (1), 45–59. Moormann, R., Schenk, W., Verfondern, K., 2001. Source term estimation for small sized

19

Nuclear Engineering and Design 360 (2020) 110477

Q. Sun, et al.

coagulation in high-temperature gas-cooled reactors. Particuology. https://doi.org/ 10.1016/j.partic.2019.09.001. Wang, S., Zhao, B., Zhou, B., 2012. An experimental study on short-time particle resuspension from inner surfaces of straight ventilation ducts. Build. Environ. 53, 119–127. Wang, X., Zhang, H., Nie, J., Li, H., Liu, J., He, A. 2014. Experimental study of fuel element motion in HTR-PM conveying pipelines. Proceedings of the HTR 2014. Wawrzik, U., Biedermann, P., Oetjen, H.F., 1988. Staub im AVR-Reaktor. Verhalten bei transienten Stri-mungsbedingungen, Jahrestagung Kerntechnik, Travemiinde. Wei, M., Zhang, Y., Luo, X., Li, X., Wu, X., Zhang, Z., 2018. Graphite dust deposition on HTGR steam generator: Effects of particle-wall and particle-vortex interactions. Nucl. Eng. Des. 330, 217–224. Wei, M., Zhang, Y., Wu, X., Sun, L., 2019. A parametric study of graphite dust deposition on high-temperature gas-cooled reactor (HTGR) steam generator tube bundles. Ann. Nucl. Energy 123, 135–144. Wells, A.C., Chamberlain, A.C., 1967. Transfer of small particles to vertical surfaces. Br. J. Appl. Phys. 18, 1793–1799. Wen, H.Y., Kasper, G., Udischas, R., 1989. Short and long-term particle release from surfaces under the influence of gas flow. J. Aerosol. Sci. 20, 923–926. Wood, N.B., 1981. A simple method for the calculation of turbulent deposition to smooth and rough surfaces. J. Aerosol. Sci. 12, 275–290. Wu, H., Gui, N., Yang, X., Tu, J., Jiang, S., 2018b. A smoothed void fraction method for CFD-DEM simulation of packed pebble beds with particle thermal radiation. Int. J. Heat. Mass. Tran. 118, 275–288. Wu, B., Li, Y., Zhao, H.-S., Liu, S., Liu, B., Wang, J.-H., 2018a. Wear behavior of graphitic matrix of fuel elements used in pebble-bed high-temperature gas-cooled reactors against steel. Nucl. Eng. Des. 328, 353–358. Wu, Z., Zhang, Z., 2004. The advanced nuclear energy system and high temperature gascooled reactor. Tsinghua University Press, Beijing. Xie, F., Cao, J., Chen, Z., Dong, Y., 2015a. The design and study of the radioactive graphite dust experimental system in the primary loop of the HTR-10. Atom. Energy Sci. Technol. 49 (4), 744–749 (in Chinese). Xie, F., Cao, J., Feng, X., Liu, X., Tong, J., Wang, H., Dong, Y., Zhang, Z., Loyalka, S., 2017. Experimental research on the radioactive dust in the primary loop of HTR-10. Nucl. Eng. Des. 324, 372–378. Xie, F., Cao, J., Tong, J., Wei, L., Liu, X., Dong, Y., Yu, S., 2015b. The research progress on the radioactive graphite dust in HTR-10. Proceedings of the 23th International Conference on Nuclear Engineering. Yao, M., Wang, R., Liu, Z., He, X., Li, J., 2002. The helium purification system of the HTR10. Nucl. Eng. Des. 218 (1–3), 163–167. Yeoh, G., Tu, J., 2019. Computational techniques for multiphase flows. ButterworthHeinemann. Young, J., Leeming, A., 1997. A theory of particle deposition in turbulent pipe flow. J. Fluid Mech. 340, 129–159. Zhang, F., 2011. The modelling of particle resuspension in a turbulent boundary layer. Newcastle University. Zhang, F., Reeks, M., Kissane, M., Perkins, R., 2013. Resuspension of small particles from multilayer deposits in turbulent boundary layers. J. Aerosol Sci. 66, 31–61. Zhang, H., Ahmadi, G., 2000. Aerosol particle transport and deposition in vertical and horizontal turbulent duct flow. J. Fluid Mech. 406, 55–80. Zhang, P., Wang, L., Chen, S., Xu, J., 2018. Progress of nuclear hydrogen production through the iodine-sulfur process in China. Renew. Sus. Energy Rev. 81, 1802–1812. Zhang, T., Peng, W., Shen, K., Yu, S., 2015. AFM Measurements of adhesive forces between carbonaceous particles and the substrates. Nucl. Eng. Des. 293, 87–96. Zhang, T., Yu, S., Peng, W., Sun, Q., Jiang, Y., Shi, Q., 2017a. Resuspension of multilayer graphite dust particles in a high temperature gas-cooled reactor. Nucl. Eng. Des. 322, 497–503. Zhang, T., Yu, S., Sun, Q., Peng, W., Wang, J., 2017b. Study on the resuspension of graphite dust based on the Rock’n’Roll model. Prog. Nucl. Energy 98, 313–320. Zheng, Y., Stempniewicz, M.M., Chen, Z., Shi, L., 2018. Study on the DLOFC and PLOFC accidents of the 200 MWe pebble-bed modular high temperature gas-cooled reactor with TINTE and SPECTRA codes. Ann. Nucl. Energy 120, 763–777. Zhou, T., Li, Z., Li, B., Qin, X., Zhu, L., Shi, S., 2019. Study on the method of nuclear power operation and analysis of movement and deposition of accident particles. Scientia Sinica Physica, Mechanica Astronomica (in Chinese). Ziermann, E., 1990. Review of 21 years of power operation at the AVR experimental nuclear power station in Jiilich. Nucl. Eng. Des. 121, 135–142. Ziskind, G., Fichman, M., Gutnger, C., 1995. Resuspension of particulate from surfaces to turbulent flows review and analysis. J. Aerosol. Sci. 26 (4), 613–644.

hydraulic response assessment, Version 3.53, September 2009, Volume 1-Program Description; Volume 2-User’s Guide; Volume 3-Subroutine Description; Volume 4Verification, NRG report K5024/09.97567, Arnhem. Stempniewicz, M.M., Goede, P., 2016. Recommended coefficients for sorption of iodine, silver, and cesium on graphite dust particles. Nucl. Eng. Des. 306, 69–76. Stempniewicz, M.M., Winters, L., Caspersson, S.A., 2012. Analysis of dust and fission products in a pebble bed NGNP. Nucl. Eng. Des. 251, 433–442. Stoker, C.C., Olivier, L.D., Stassen, E., Reitsma, F., van der Merwe, J.J., 2010. PBMR radionuclide source term analysis validation based on AVR operating experience. Nucl. Eng. Des. 240, 2466–2484. Struth, S., Stöcker, B., Hurtado, A., 1999. Component exposure in hypothetical accidents with very fast depressurization in a HTR module reactor. Nucl. Eng. Des. 297–302. Sun, F., Luo, Y., Gao, Q., 2014. On power refueling management of HTR-PM. Proceedings of the HTR 2014 Weihai, China. Sun, Q, Zhao, G., Peng, W., Yu, S., 2018a. A numerical study of particle deposition through fuel pebble bed in HTGR. Proceedings of the 26th International Conference on Nuclear Engineering. Sun, Q., Chen, T., Peng, W., Wang, J., Yu, S., 2018b. A numerical study of particle deposition in HTGR steam generators. Nucl. Eng. Des. 332, 70–78. Sun, X.M., Chen, Z.P., Sun, J., Liu, Y., Zheng, Y.H., Li, F., Shi, L., 2018e. CFD investigation of bypass flow in HTR-PM. Nucl. Eng. Des. 329, 147–155. Sun, Q., Gao, Q., Zhang, P., Peng, W., Chen, S., Zhao, G., Wang, J., 2019a. Numerical study of heat transfer and sulfuric acid decomposition in the process of hydrogen production. Int. J. Energy Res. 43, 5969–5982. Sun, Q., Hai, X., Wang, K., Peng, W., 2019b. Study of the deposition of graphite dust in the inlet passageway of intermediate heat exchanger in VHTR. Exp. Comput. Multiphase Flow 1 (1), 29–37. Sun, Q., Xie, F., Zhao, G., Peng, W., Wang, J., Yu, S., 2018c. A numerical study on slip correction factor of dust particle in HTGR. Nucl. Eng. Des. 340, 31–39. Sun, Q., Ye, P., Peng, W., Yu, S., Zhou, H., Wang, J., 2019c. Wear of graphite pebbles modeled using a macroscopic particle model in a pneumatic transport lifting pipe. Powder Technol. https://doi.org/10.1016/j.powtec.2019.11.075. Sun, Q., Zhao, G., Peng, W., Wang, J., Jiang, Y., Yu, S., 2018d. Numerical predictions of the drag coefficients of irregular particles in an HTGR. Ann. Nucl. Energy 115, 195–208. Talbot, L., Cheng, R.K., Schefer, R.W., Willis, D.R., 1980. Thermophoresis of particles in a heat boundary layer. J. Fluid Mech. 101, 737–758. Tao, C., Zhao, G., Yu, S., Peng, W., Wang, J., 2018. Experimental study of thermophoretic deposition of HTGR graphite particles in a straight pipe. Prog. Nucl. Energy 107, 136–147. Troy, R.S., Tompson, R.V., Ghosh, T.K., Loyalka, S.K., 2012. Generation of graphite particles by rotational/spinning abrasion and their characterization. Nucl. Technol. 178 (3), 241–257. Troy, R.S., Tompson, R.V., Ghosh, T.K., Loyalka, S.K., 2015a. Particle production by rotational abrasion between graphite spheres. Nucl. Technol. 191 (1), 71–91. Tu, J., Yeoh, G., Liu, C., 2018. Computational fluid dynamics: a practical approach. Butterworth-Heinemann. Turner, R. F., 2008. NGNP and hydrogen production preconceptual design study, Contamination Control. NGNP-NHS-50-CC. Troy, R.S., Tompson, R.V., Ghosh, T.K., Loyalka, S.K., Gallego, N.C., 2015b. Generation of graphite particles by sliding abrasion and their characterization. Nucl. Technol. 189 (3), 241–257. Vainshtein, P., Ziskind, G., Fichman, M., Gutfinger, C., 1997. Kinetic model of particle resuspension by drag force. Phys. Rev. Lett. 78 (3), 551–554. Verfondern K., 2007. European Data on HTR Fuel Characterization. Verfondern, K., 1997. Fuel performance and fission product behaviour in gas-cooled reactor. IAEA-TECDOC-978. Verfondern, K., Xhonneux, A., Jühe, S., 2012. HTR-PM Prediction of Fission Product Release During Accident Conditions. Research Center Jülich. Von, der Decken, C.-B., Wawrzik, U., 1990. Dust and Activity Behavior, in: Association of German Engineers (VDI). AVR-Experimental High-Temperature Reactor, 21 Years of Successful Operation for a Future Energy Technology, VDI-Verlag Dusseldorf. 259275. Wang, K., Yu, S., Peng, W., 2019a. A novel moment method using the log skew normal distribution for particle coagulation. J. Aerosol. Sci. 134, 95–108. Wang, K., Yu, S., Peng, W., 2019b. Extended log-normal method of moments for solving the population balance equation for Brownian coagulation. Aerosol. Sci. Technol. 53 (3), 332–343. Wang, K., Yu, S., Peng, W., 2019c. Evaluation of thermophoretic effects on graphite dust

20