Introduction

Dust safety limits have been demonstrated as the main issues during the operation of ITER. Dusts are produced inside the vacuum vessel (VV) due to the plasma interactions with the plasma facing wall and the divertor [1, 2], which are generally activated by neutron and also tritiated due to the tritium movement in the VV. Note that the dusts will be transported to the vacuum vessel pressure suppression system (VVPSS) and the draining system in case of the design basis accidents (DBAs), which potentially release the in-vessel source term such as tritiated dust to the environment.

The ITER safety approach developed for the radioactive dust is usually based on the DBAs such as LOCA (Loss of Coolant Accidents) and LOVA (Loss of Vacuum Accidents). Regarding the air or steam ingress in such conditions, the air ingress into VV may form a flammable mixture, while the interactions of hot dusts and steam can cause significant hydrogen generation rates, leading to the dust and hydrogen explosions, which could threaten the integrity of VV, and thus present safety crisis to the public [3,4,5]. Notably, the licensing process of ITER have defined the safety limits as 1 kg and 1000 kg for mobilizable tritium and dust (size < 150 μm) respectively [2, 6]. To determine the accident evolution process and analyze the migration of radioactive source terms, simulation and experimental studies have been commonly applied to reproduce the dust resuspension scenarios subjected to the DBAs and beyond design basis accidents (BDBAs). STARDUST and STARDUST-Upgrade are the representative facilities, commissioned to reproduce the thermal hydraulic conditions comparable to the low pressurization rate (300 Pa/s) LOVA event in ITER [7,8,9,10,11,12], thereby the consequences of dust resuspension induced by LOVA events have been demonstrated. Since the limitations to the experimental facility conditions [13], it is not possible to simulate LOCA scenarios, and therefore the dust resuspension scenarios induced by LOCA is significant to be demonstrated. Note that the scaled experimental facilities simplify the configurations of ITER, and simulation is generally applied to characterize the actual dust resuspension behaviors supplementing with experimental results.

To simulate the dust resuspension events due to LOCAs or LOVAs in ITER, some thermal hydraulics simulation codes were used. ASTEC code (Accident Source Term Evaluation Code), jointly developed by IRSN and GRS, was initially designed to model the entire accident sequence for pressurized light water reactors and being gradually adapted to represent other designs such as ITER fusion facility [14]. Aerosol resuspension models have been demonstrated in ASTEC within the fusion framework, and preliminary analysis of physical and chemical phenomena involved in ITER such as thermal hydraulics and dust resuspension behaviors are already implemented and applicable [15, 16]. In general, the CPA module is activated to simulate thermal-hydraulics behaviors in containment, and the SOPHAEROS module provides modelling features specifically addressing the physical states and phenomena of aerosol resuspension [17, 18].

Helium-cooled blanket is consistently employed to the fusion reactors since the late 1960s, and the helium coolant is contained in the blanket modules and diameter tubes with operating pressure at 5–10 MPa [19, 20]. As multiple breaks appear in blanket during LOCA, VV will be pressurized due to the ingress of helium [21], which mainly resuspends the deposited dust in divertor. Characterization of thermal hydraulics and dust resuspension behaviors in such accidental condition is required to support the R&D program in dust control.

Thus, ASTEC simulation of dust resuspension induced by in-vessel LOCA with the consideration of keeping the same pressure rate as the LOCA scenario of China’s ITER TBM was performed, and the results obtained by the DustSAFER (Dust Safety Experimental Facility for Fusion Reactor) were compared. The following issues were mainly addressed: (1) the characteristics of thermal–hydraulic parameters with regard to the dust resuspension behaviors induced by in-vessel LOCA; (2) the improvement of the dust resuspension model; and (3) the analysis of relations between the thermal hydraulic parameters and dust resuspension rates. The observations can contribute to the implementation of dust resuspension model applicable to LOCA in ASTEC, and provide the understanding of migration behaviors of radioactive dust to the environment in case of DBA.

Dust Resuspension Experiment

China Helium Coolant Ceramic Breeder (CN HCCB TBM) has been approved by ITER organization, and will be tested in ITER to verify corresponding DEMO blanket requirements [22, 23]. To comply with the CN ITER TBM conceptual design and support the ITER licensing process, in-vessel LOCA within the framework was analyzed. Regarding the in-vessel LOCA condition, 8 MPa helium gas was injected into the vacuum chamber of DustSAFER.

Dust Characteristics

The dust resuspension experiment of DustSAFER was conducted in Hefei Institutes of Physical Science (HFIPS), Chinese Academy of Sciences. The tungsten dust was selected, which is similar to that existing inside the VV of ITER. The dust sample had the typical dimensions and some other properties of the powders used in the representative dust resuspension experiments [10, 12]. Dust physical properties of two different tungsten dust distributions are shown in Table 1, where ρ is particle mean density, kg/m3; λ is particle mean thermal conductivity, J/(m K); R_min is particle minimum radius, m; R_max is particle maximum radius, m; R_g is geometrical mean radius of first distribution; and stdv_g is standard deviation of first distribution. Figure 1 shows the dust particle size distribution.

Table 1 Dust physical properties
Full size table
Fig. 1
figure 1

Dust particle size distribution

Full size image

Determination of the Dust Resuspension Fraction of the Experiment

The variation of the mass ratio of deposited dust during the resuspension experiment is defined by the dust resuspension rates, and its equation is as follows [24]:

$$\Lambda = \frac{{M_{1} - M_{2} }}{{M_{1} }} \times 100\%$$
(1)

where Λ is the dust resuspension rates (%), M1 is the initial mass of deposited dust (g), M2 is the deposited dust mass of ending moment (g).

Experimental Apparatus and Protocol

The scaled facility is mainly composed of a stainless-steel cylindrical tank (VV tank), a vacuum pump and helium tanks. The vacuum chamber is with the volume of 0.181 m3, and the diameter of 0.501 m. A tray (40 mm × 50 mm) containing dust was placed on the equatorial port level inside the VV tank. One pressure sensor was set to measure the pressure of vacuum chamber during the DBA sequence, while the others were set at the compressed helium tank to monitor the 8 MPa helium pressure of the pipes at the beginning of the LOCA sequence. The initial pressure of VV tank was controlled by the vacuum pump, and the solenoid valve was closed when the pressure inside VV tank was nearly vacuum condition. Moreover, the pressure of the helium tanks, and the pipes between the solenoid valve and helium tanks were adjusted to 8 MPa as a helium source of the in-vessel LOCA. Figure 2 is a schematic diagram of the DustSAFER system, and Table 2 is the text matrix of the experiment.

Fig. 2
figure 2

Schematic diagram of the Dust SAFER system. 1: the vacuum chamber (VV tank); 2: the helium tanks; 3: electromagnetic flowmeter; 4: solenoid valve; 5: vacuum pump; 6: helium inlet (equatorial port); 7: compressed helium tank; 8: absolute pressure sensor; 9: the pressure sensors of the compressed helium tank; 10: the pipes

Full size image
Table 2 Typical dust resuspension experiments selected for ASTEC simulation
Full size table

The dust resuspension experiment considers different dust particle sizes, initial helium volume, and positions of the break inlet and the dust tray. Note that the mean dust resuspension fraction is obtained by three runs for each condition. Here two typical conditions are selected to perform the ASTEC simulation to develop the method for dust resuspension calculation of in-vessel LOCA, as shown in Table 2.

ASTEC Models and Simulations

Dust Resuspension Models

Force-balance (FB) model and Rock’n’roll (RnR) model are available for characterizing the resuspension behaviors of deposited dust in ASTEC code. Since the dust resuspension models with default coefficients are mainly validated in atmospheric conditions and LOVA, such as in STORM and STARDUST [15, 25], the empirical default coefficients may not be applicable to LOCA. Thus, it is necessary to optimize empirical coefficients based on the experimental data obtained from DustSAFER.

Force-Balance Model

The FB model assumes that the resuspension is determined by a balance between aerodynamic and adhesive forces, which is a quasi-static model [18]. The resuspension force FRes is correlated with aerodynamic lift force and adhesive force, which is shown in Eq. 2.

$$\left\{ {\begin{array}{*{20}l} {F_{Res} = F_{d} + F_{b} - \left( {F_{C} + f \times \gamma \times F_{C} } \right)} \hfill & {for} \hfill & {wall/ceiling\;surfaces} \hfill \\ {F_{Res} = F_{d} + F_{b} - \left( {F_{g} + F_{C} + f \times \gamma \times \left\{ {F_{g} + F_{C} } \right\}} \right)} \hfill & {for} \hfill & {horizontal\;bottom\;surfaces} \hfill \\ \end{array} } \right.$$
(2)

where Fd is aerodynamic drag force (N), Fb is burst force (N), FC is cohesive force (N), f is frictional coefficient, γ is coagulation form factor, and Fg is gravitational force (N).

For resuspension force FRes > 0, the FB model resuspension rate is defined as Eq. 3.

$$\Lambda_{E} = E_{1} \times \left[ {10^{6} \times F_{Res} } \right]^{{E_{2} }}$$
(3)

where ΛE is resuspension rate (1/s); E1 and E2 are constants of the resuspension rate model, and FRes is resuspension force (N).

For FB model, the default Reynolds number and the empirical coefficients in Table 3 can be modified based on the experimental data.where v is carrier-gas kinematic viscosity (m2/s), ρf is carrier-gas density (kg/m3), r is particle radius (m), \(V_{fr}^{w}\) is wall friction fluid velocity (m/s), χ is particle dynamic form factor, Hc is coefficient dependent on material and system properties (N/m), and γ is coagulation form factor.

Table 3 Empirical coefficients of FB model
Full size table

Rock’n’Roll Model

Since the kinetics of the aerosol resuspension cannot perform well by the FB approach in ISP 40 [26], RnR model was implemented in ASTEC. RnR model is a dynamic model based on energy transfer between turbulent gas flow and deposited aerosols for an isolated particle [27]. The particle in RnR model is supposed to have two points of contact with surface, and it rotates around the pivot point under the fluctuations of the aerodynamic forces. For RnR model, the empirical coefficients cannot be modified in ASTEC input deck, and the dust resuspension rate is affected by the default Reynolds number setting. The resuspension rate Λ (1/s) of particles subjected to adhesion force (fa) is defined as Eq. 4.

$$\Lambda \left( {f_{a} } \right) = {\text{MIN}}\left[ {n_{\theta } ;n_{\theta } \times \frac{{\exp \left( {\frac{{ - \left( {f_{a} - \overline{{F_{R} }} } \right)^{2} }}{{2 \times \sigma_{R}^{2} }}} \right)}}{{\frac{1}{2}\left( {1 + {\text{erf}}\left( {\frac{{f_{a} - \overline{{F_{R} }} }}{{\sqrt 2 \times \sigma_{R} }}} \right)} \right)}}} \right]$$
(4)

where nθ is the frequency characteristic of the forced oscillations of the particle, FR is the average component, and σR is the variance of the temporal distribution (supposed Gaussian) of the aerodynamic forces.

Simulation Scenarios

CPA (Containment Part of ASTEC) module is usually employed to simulate the thermal-hydraulics behaviors in containment, which can describe the pressure and temperature build-up, distributions and heat transfer to the wall. SOPHAEROS module can simulate aerosols transport and deposition during a severe accident, and presents some physical models to describe aerosol deposition, resuspension and agglomeration mechanisms. The CPA calculation is with an imposed time step of 0.001 s, and the outputs, such as wall temperature, carrier-gas temperature, pressure and mass flow rates, will be considered as input parameters for dust resuspension calculation. Note that CPA module cannot initialize the helium gas, and thus, the helium mass injection is imposed with an application of the ‘SOURCE’ boundary condition. Moreover, to comply with the physical properties and aerosol state transformation of tungsten dust in the SOPHAEROS module, the dust calculation is consisted of aerosol injection (deposition) phase and aerosol resuspension phase, and the time step is set at 1.0 s.

The modules of ASTEC are lumped-parameter models, and the compartments of the considered power plant, test facility or other building types can either be combined to become a control volume (zone) in CPA, or can be divided into several zones to cover flow peculiarities simply. The DustSAFER system is nodalized as 11 zones with connected atmospheric junctions and valves. Zones (Zones A3–A11) are used to model the vacuum chamber (d = 0.501 m, V = 0.181 m3), which are connected with the atmospheric junctions (D1-D12), and the deposited dust is imposed in Zone A7. Note that Zone A1 is to model the helium tanks (d = 7 cm, V = 0.001 m3) and the pipes (d = 2 cm, V = 0.00116 m3) with 8 MPa helium and Zone A2 is to model the pipes (d = 1.4 cm, V = 0.000477 m3) with vacuum condition, to avoid the possible overflow of ASTEC. The CONN B is the inlet (d = 2 mm, L = 0.214 m) of helium into the vacuum chamber. Moreover, Zone A9 is the region that the pressure sensor positioned in the experiment, and the break inlet is with a height of 0.2505 m. The thermodynamic behavior of walls is controlled by the heat structure, and the thermodynamic state of zones is defined by the specified temperature and pressure. The nodalization scheme for DustSAFER system is shown in Fig. 3, and note that Fig. 3 is out of scale to the model geometry parameters.

Fig. 3
figure 3

Nodalization scheme of the DustSAFER system

Full size image

Results and Discussion

Thermal–Hydraulic Characteristics

The evolution characteristics of thermal–hydraulic parameters in each zone are necessary for dust resuspension analysis, especially the carrier-gas temperature, pressure, and velocity (or mass flow rates). Moreover, it significantly determines aerosol transport, aerosol dynamics and aerosol deposition mechanism during the DBA sequence.

Figure 4 shows the pressurization results of VV induced by in-vessel LOCA and the mass flow rate of the break. Note that the pressure tendency of Zone A9 is well predicted of ASTEC simulation, which is similar to that of the experimental pressure monitoring zone. Moreover, it shows that VV is pressurized to nearly 116 kPa and 93 kPa for the ASTEC simulation and experiment, respectively, both of which satisfy the ITER design limit of 200 kPa [28]. Since non-equilibrium zone model is employed to describe the thermodynamic behaviors, and the calculation follows the ideal gas law, when an ingress of 8 MPa helium gas into VV during an extremely short time, the gas temperature exhibits a sharp increase and the adiabatic wall setting cannot work instantly, which results an overestimation of the equilibrium pressure at the end of the transients in the vacuum chamber of ASTEC simulation.

Fig. 4
figure 4

Thermal–hydraulic characteristics of VV for in-vessel LOCA

Full size image

Choked flow is a fluid dynamic condition associated with the Venturi effect, which is a limiting condition when the mass flow rates will not increase with a decrease in the downstream pressure [29]. Since an enormous pressure difference between the pipe and the containment, choked flow is expected to occur at the break. However, the model is oversimplified to implement in the lumped parameter code, and thus, the gas flow profile tackled by ASTEC is different from the actual one, and the choked flow cannot be captured in ASTEC simulation. Figure 4b indicates the mass flow rate at the break.

Gas flow velocity has remarkable effects on aerosol resuspension. Figure 5 shows the gas flow velocity and mass flow rates of the dust zone (Zone A7). It is found that a dramatic increase in velocity occurs during the initial period due to the 8 MPa helium ingresses into the vacuum chamber rapidly, also, overestimation of the helium velocity is calculated due to the absence of chocked flow simulation, and then velocity in the connections D4 and D9 decreases since the pressure gradually approaches equilibrium in the vacuum chamber, while one in D6 and D7 varies dramatically. Moreover, it can be noted that the increasing trend of mass flow rates of D4 and D9 is not consistent with the velocity during the initial period, and the mass flow rates of D6 and D7 change substantially with dynamic variations during the latter period during the latter period (3–5 s) of LOCA sequence.

Fig. 5
figure 5

Flow characteristics of the dust zone (Zone A7)

Full size image

Improvement of Dust Resuspension Model

RnR model is calculated with Biasi correlations [30], and it has been validated with experiments, such as STORM [25], Braaten [31], ORNL [32], Hall [33] and STARDUST [15], however, the experiments were developed with ambient pressure or LOVA condition, which is extremely different from the scenario 8 MPa helium ingress into VV. Also, it has been found that the modification of default Reynolds number to RnR model does not work on dust resuspension calculation induced by in-vessel LOCA, since the empirical coefficients related to the RnR model cannot be modified in ASTEC, and thus, the empirical coefficients of FB model would be considered to modify based on the experimental results.

Carrier-gas flow is characterized by Reynolds number, which affects the occurrence of dust resuspension. Figure 6 shows the Reynolds number and friction velocity of the dust zone, and it can be noted that the calculated Reynolds number varies from 0 to 450. Note that the dust resuspension is associated with the condition of flow turbulence close to the wall, and the Reynolds number is employed to evaluate the flow turbulence condition. The default Reynolds number of occurring dust resuspension event is 2300, whereas it should be modified according to the experimental conditions and the calculated values of ASTEC. Dust resuspension fraction has been calculated with application of different Reynolds number, which is to determine the appropriate Reynolds number of the test, and the dust resuspended fraction is with minor variations ranging from 200 to 450. Considering the dust resuspended mass and timing of ASTEC simulation and experiment, the default Reynolds number is adjusted to 400.

Fig. 6
figure 6

Characteristics of the dust zone (Zone A7)

Full size image

The drag and lift forces are significantly associated with turbulent fluid flow, and it has been found that modifications of the lift-force coefficients can achieve a well-predicted result of dust resuspension fraction, while other empirical coefficients cannot work remarkably on the results. Note that lift force is associated with turbulent bursts, and modifications to the model constants Ab, Bb of burst force can adjust the dust resuspended fraction comparable to the experimental results. Thus, it is necessary to obtain the empirical correlations of Ab, Bb and the dust resuspension fraction (Λ) via modifying Ab and Bb for multiple debugging. Figure 7 is the fitting results of Ab, Bb and Λ, and the empirical correlation is obtained in Eq. 5, where D50 is the mean particle size.

$$f(A_{b} ,B_{b} ) = \left\{ \begin{gathered} 130.6 + 0.0423A_{b} - 164.7B_{b} - 2.327 \times 10^{ - 5} A_{b}^{2} + 0.04501A_{b} B_{b} + 0.1637y^{2} \;(D_{50} = 1.66\;\mu m) \hfill \\ 104.7 + 0.05312A_{b} - 122.4B_{b} - 2.39 \times 10^{ - 5} A_{b}^{2} + 0.03713A_{b} B_{b} - 10.83y^{2} \;(D_{50} = 3.511\;\mu m) \hfill \\ \end{gathered} \right.$$
(5)
Fig. 7
figure 7

Empirical correlations of Ab, Bb and Λ

Full size image

To determine appropriate Ab, Bb for the in-vessel LOCA experiment, optimization algorithm is employed to obtain a set of (Ab, Bb) based on the experimental results. The mean dust resuspension fraction is measured to be 22.0 and 40.0 for the mean dust size of 1.66 μm and 3.511 μm in the experiment, respectively. Therefore, the set of equations is built to satisfy that the function of f(Ab, Bb) approaches the experimental results simultaneously to obtain the Ab and Bb. Note that the values of Hall [34] are considered as the default setting (the initial values) for Ab and Bb in ASTEC, and Ab = 4.21 ± 0.32, Bb = 2.31 ± 0.02. The obtained value is shown below:

$$A_{b} = 1589.8479,\;B_{b} = 1.2151$$
(6)

The improved dust resuspension model is employed to calculate the dust resuspension fraction. It is also found in the study that the long-term resuspension would be related to the duration of turbulent bursts, and the rapid resuspension follows an increase in mass flow rates. Since the dust particle size affects the aerodynamic forces (the drag and lift forces) [35], the dust resuspension rates will increase with a larger particle size. Figure 8 shows the calculated dust resuspension fraction of the tungsten dust.

Fig. 8
figure 8

Dust resuspension fraction of tungsten dust

Full size image

It is found that the default burst force coefficients could not work properly in this LOCA condition, since the default values of Ab and Bb are obtained at the atmospheric conditions, the test condition of which is significantly different from in-vessel LOCA, and the modified coefficients are capable of better predicting the dust resuspension characteristics, as shown in Table 4.

Table 4 Comparison of the dust resuspension fraction
Full size table

Conclusions

This paper presents the dust resuspension characteristics induced by in-vessel LOCA. The evolution of pressurization behaviors, carrier gas flow peculiarities were analyzed with ASTEC in DustSAFER facility, and the dust resuspension model was improved based on the experimental data. The findings can be significant to radioactive aerosol source term analysis of fusion reactors. The main conclusions are summarized as follows:

  1. (1)

    The default dust resuspension models of ASTEC code cannot work properly on dust resuspension for the LOCA condition, since the empirical coefficients are mainly obtained by series of experiments in atmospheric and vacuum conditions.

  2. (2)

    The empirical coefficients of FB model are modified accordingly to better predict the dust resuspension characteristics. The tuned value of Ab and Bb is 1589.85 and 1.22, respectively.

  3. (3)

    The long-term resuspension would be associated to the duration of turbulent bursts, and the dust resuspension rates will follow an increase in mass flow rates. Since the particle size is related to the aerodynamic forces, it can significantly affect the dust resuspension.

Note that the modified strategy for the FB model is based on the situation that only parameters in the ASTEC input deck can be tuned. More simulations will be conducted to investigate the adaptability of the modified FB model to different scenarios.