Keywords

1 Introduction

The phenomenon of aerosol particle resuspension is the deposited particles on the surface are resuspended under the action of disturbance [1]. Resuspension may occur in many scenarios, such as pesticide resuspension from soil, biological particle resuspension, outdoor industrial product resuspension, indoor dust resuspension, etc. [1]. During the severe accident of the nuclear power plant, the resuspension of the aerosol particles deposited in the containment would occur due to some disturbance, resulting in the increase of radioactive aerosols released into the environment [2, 3]. Therefore, aerosol resuspension should be considered for the radiological consequence assessment. Accurate aerosol resuspension prediction model plays a vital role.

Since the beginning of last century, research about resuspension has been carried out. University of Kansas and other organizations carried out resuspension experiments on glass surfaces with relatively large particles [4], whose mean diameters ranged from 18 to 34 microns. In 1998, the Joint Research Centre of the European Commission conducted STORM (Simplified Test Of Resuspension Mechanism) experiment, the SR11 condition of it is in accordance with the ISP-40 standard [5]. Then Reeks and Hall [6] used alumina particles, graphite particles and polished stainless steel flat plate performed resuspension experiment. Oak Ridge National Laboratory (ORNL) conducted the ART (Aerosol Resuspension Tests) experiment with micron-sized particles and horizontal tube [7]. From 2003 to 2007, the experiment of resuspension after hydrogen deflagration was carried out in the THAI (Thermal-hydraulics, Hydrogen, Aerosol, and Iodine) experimental facility, however, there is a discrepancy between the experimental measured aerosol particle diameter distribution and the fast deposition velocity after resuspension [8, 9]. Overall, most resuspension experiments could provide parameters affecting aerosol resuspension such as particle size distribution and density, disturbing airflow velocity and physical properties, and corresponding resuspension fraction, etc., but lack of refined measurement about the deposition surface and aerosol particle, which may not be sufficient to support verification of complicated model [10]. Considering the aerosol characteristics and thermal hydraulic conditions during nuclear reactor severe accidents and data availability, the STORM experiment and the ART experiment are screened out as validation experiments for model applicability analysis.

With the development of resuspension experimental research and the cognition of resuspension mechanism, research on resuspension models has also been carried out. Particle resuspension models are generally divided into two categories: models based on force balance and models based on energy conservation [11]. Resuspension models based on energy conservation include RRH [12], VZFG [13], and Rock’n’Roll [6] models, which assumes that the particle vibrate and accumulate energy until it has enough energy to overcome the adhesion from the surface, and resuspend. Resuspension models based on force balance consider that resuspension occurs when the aerodynamic disturbing force is greater than the hindering force [14], including Wichner [15], Michael [10], ECART [16] models, etc., which differ in their consideration for the forces acting on the particle.

With the effect of resuspension on radiological assessment is recognized, aerosol resuspension models are gradually applied to the severe accident analysis codes and particle tracking code, such as ASTEC code [17], ECART code [18], Melcor2.2 code [15] and a 2D lagrangian particle tracking code–CAESAR code [19], all of which apply the models based on the force balance theory. While the resuspension behavior is closely related to the particle characteristics, deposited surface characteristics and disturbed airflow characteristics. Therefore, it is essential to study and evaluate the applicability of this type of aerosol particle resuspension model under severe accident in nuclear power plant.

In this paper, three typical aerosol resuspension models considering force balance, named Wichner model, Michael model and ECART model, are investigated. Considering the aerosol characteristics and thermal hydraulic conditions during nuclear reactor severe accidents, the simulation for STORM and ART experiments with the three models is carried out. Finally, by comparing and analyzing the prediction results and experimental results, the applicability of these models is evaluated. The research in this paper can support the subsequent codes improvements.

2 Models for Resuspension

Michael and Wichner resuspension models believe that when the criterion of aerodynamic disturbing force is greater than the hindering force is met, the particle will resuspend, regardless of time [10, 15]. ECART model considers the particle resuspension rate is an exponential function of the resultant force on particles [16].

Michael model proposes that aerodynamic disturbing force is composed of lift and drag forces [10], both acting at the center of the particle. Only the hindering effect of adhesive force on resuspension is considered. There are two contact points between the particle and deposited surface, the distance between two contact points is ‘A’. The adhesive force \(F_{A}\) (N) between the deposited surface and particles is determined by the ratio of the particle diameter \(d_{p}\) (μm) to the surface roughness \(\varepsilon\) (μm).

$$ F_{R} = \frac{1}{2}F_{L} + \frac{r}{A}F_{D} $$
(1)
$$ \left\langle {F_{L} } \right\rangle \approx 20.9\rho \nu^{2} \left( {\frac{{ru^{ * } }}{\nu }} \right)^{2.31} $$
(2)
$$ \left\langle {F_{D} } \right\rangle \approx 32\rho \nu^{2} \left( {\frac{{ru^{ * } }}{\nu }} \right)^{2} $$
(3)
$$ u^{ * } = \sqrt {{{\tau_{w} } \mathord{\left/ {\vphantom {{\tau_{w} } \rho }} \right. \kern-0pt} \rho }} $$
(4)
$$ \tau_{w} = \frac{1}{2}f\rho U^{2} $$
(5)
$$ F_{A} = 5.0 \times 10^{ - 10} {{d_{p} } \mathord{\left/ {\vphantom {{d_{p} } \varepsilon }} \right. \kern-0pt} \varepsilon } $$
(6)

where \(F_{R}\) is the aerodynamic disturbing force (N), \(F_{L}\) is lift force (N), \(F_{D}\) is drag force (N), and r is particle radius (m). The average lift force is related to gas kinematic viscosity \(\nu\) (m2/s), gas density \(\rho\) (kg/m3), friction velocity \(u^{ * }\) (m/s). Friction velocity equals to square root of the ratio of turbulent shear stress to air density, which characterizes the turbulent shear stress property and has a velocity dimension. \(\tau_{w}\) is wall shear stress (N/m2), f is the friction factor, and \(U\) is gas velocity (m/s).

Wichner model [15] suggests that the aerodynamic disturbing force acting on particles is related to gas density, aerosol particle radius, friction velocity and the aerodynamic disturbing force coefficient \(\alpha\). The assumption about hindering force is the same as in the Michael model.

$$ F_{R} = \alpha \pi \rho \left( {ru^{ * } } \right)^{2} $$
(7)

ECART force balance model considers [16] that hindering force mainly includes gravity of aerosol particle \(F_{G}\) (N), cohesive force \(F_{C}\) (N) and adhesive force \(F_{A}\) (N), the aerodynamic disturbing force is composed of drag force \(F_{D}\) (N) and burst force \(F_{B}\) (N) which are generated by disturbing air flow.

$$ N(r) = \left\{ \begin{gathered} 0.4037 \cdot \left[ {F(r)} \right]^{0.6003} 0 < F(r) \le 3.065 \cdot 10^{{{ - }4}} \mu N \hfill \\ 90.28 \cdot \left[ {F(r)} \right]^{1.269} F(r) \ge 3.065 \cdot 10^{{{ - }4}} \mu N \hfill \\ \end{gathered} \right. $$
(8)
$$ F_{G} = \frac{{4\pi r^{3} }}{3}\rho_{p} g $$
(9)
$$ F_{C} = 2Hr\gamma $$
(10)
$$ F_{A} = 0.2 \cdot (F_{g} \gamma^{3} + F_{c} ) $$
(11)
$$ F_{D} = \tau_{w} \pi r^{2} \chi^{{{\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{$3$}}}} $$
(12)
$$ F_{B} = 4.21\rho_{g} \chi \nu^{2} \left( {\frac{{2r\rho_{g} u^{*} }}{\nu }} \right)^{2.31} $$
(13)

where, \(N(r)\) refers to resuspension rate (1/s), \(F(r)\) refers to resultant force acts on the particle (μN), \(\rho_{p}\) refers to density of aerosol particle (kg/m3), g refers to acceleration of gravity (m2/s), H refers to empirical coefficient related to the number of deposition layers, \(\gamma\) refers to collision shape factor, \(\chi\) is the aerodynamic shape factor.

3 Evaluation for Resuspension Models Application

3.1 Verification Experiments

In the process of the resuspension experiments, the aerosol particles are deposited firstly, then the airflow passing through the deposited area is supplied to resuspend the particles. Considering the aerosol conditions, thermal hydraulic conditions during nuclear reactor severe accidents and data availability, the STORM SR11 experiment [5] and the ART 05 experiment [7] are screened out as validation experiments. The particle diameters of the experiments conform to log-normal distribution, and the particle diameter ranges from a few tenths of a micron to a few microns, which is consistent with the size of most aerosol particles in the containment under severe accidents. And the experimental disturbing airflow velocity scope is broad, in the range of 11.9 m/s to 127 m/s. The key aerosol and thermal hydraulic parameters are shown in Table 1 [5, 7, 20, 21], where GMD is geometric mean diameter of aerosol particle and GSD refers to geometric mean deviation.

Table 1. Aerosol and thermal hydraulic conditions.
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3.2 Comparison with Experiments

In these force balance models, the parameters such as the gas velocity, density and viscosity, particles size distribution can all be determined from the experimental measurement. Apart from these factors, the distance between two contact points of particle and deposited surface ‘A’ in Michael model, the coefficient of aerodynamic disturbing force ‘\(\alpha\)’ in Wichner model, the empirical coefficient related to the number of deposition layers ‘H’ will also affect the models’ prediction results. However, experimental measurements do not provide the accurate values. Therefore, different values are adopted in the simulations to conduct sensitivity analysis.

Table 2. The ratio of models’ prediction and STORM SR11 experimental resuspension fraction
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Table 2 shows the comparison between the Wichner model’s predictions and STORM SR11 experiment measurements [5]. The prediction results agree well with experimental results when ‘\(\alpha\)’ values 5. Comparing the model’s prediction results when ‘\(\alpha\)’ takes different values, the resuspension fraction is positive proportional to ‘\(\alpha\)’. The greater the disturbing force coefficient, the greater the aerodynamic disturbing force, particles are more prone to resuspension.

Comparison between Michael force balance model’s predictions and measurements for STORM SR11 experiment [5] is shown in Table 2. The prediction when ‘A’ takes different values is conducted to analyze the effect. The model considers the aerodynamic disturbing force equal to the sum of 0.5 times the lift force and r/A times the drag force, the larger the A, the smaller the r/A, the smaller the aerodynamic disturbing force, and the harder it is for the particles to resuspend. Overall, the prediction results satisfy experimental results better when ‘A’ values 2.

In ECART force balance model, the empirical coefficient about the number of deposition layers (‘H’) is related to the experimental conditions. Meanwhile, the prediction for STORM SR11 experiment [5] is taken when ‘H’ values 1E−6, 1E−5, 5E−5 to analyze the effect. As shown in Table 2, under the same friction velocity, the aerosol resuspension fraction predicted by the model decreases with the increase of ‘H’. The prediction result fits well with the experimental measurement when ‘H’ takes 5E−5, overall. The deviation is obvious only when the friction velocity is 5.4 m/s and 6.1 m/s, which are 13.79% and 9.21%.

However, both Wichner, Michael and ECART model underestimate resuspension under low velocity disturbing airflow when the models accurately predict the resuspension under higher velocity airflow. The force driving aerosol resuspension are related to the physical properties of the disturbing airflow, the diameter of aerosol particles, and the friction velocity. When the friction velocity is low, the force to drive the resuspension calculated by these models is not enough to overcome the adhesive force. This may be related to the heterogeneity of the deposited surface in experiments. The adhesive force acting on the deposited particles is related to their state on the surface, and there exists fraction particles subjected to smaller adhesive force that can be resuspended at lower disturbing airflow velocities, as shown in Fig. 1. These three models adopt relationships can characterize the adhesive force of most particles with key parameters such as particle size and surface roughness, and ignores the adhesive force difference caused by the heterogeneity.

Fig. 1.
figure 1

Schematic diagram of particle deposition on the surface

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These changes of the disturbing gas velocity and resuspension fraction with time under STROM SR11 [5] condition demonstrates most particle resuspension will complete in a very short time after the disturbing gas velocity changes in STORM SR11 experiment. Wichner and Michael force balance model are steady state model, its resuspension fraction predicted is independent of time and could reflect the rapid change of resuspension with disturbing gas velocity. However, ECART model considers the influence of time, which needs to estimate the action time of the force and consider their change with time. When obtaining resuspension fraction with ECART model, the rapid increase in resuspension fraction when the disturbing gas velocity disturbing changes suddenly could not be accurately predicted.

Figures 2, 3 and 4 shows the comparison between the measurements of ART 05 experiment [20, 21] and the prediction of Wichner, Michael and ECART force balance model respectively. The disturbing airflow’s friction velocity of the ART 05 experiment ranges from 0.7 m/s to 2.9 m/s. Michael and Wichner models could not capture the resuspension of aerosols when the friction velocity is 0.7 m/s and could predict resuspension under higher velocity airflow, which is similar to the simulation of the STORM experiment. ECART model obviously overestimates the resuspension of the ART 05 experiment when the friction velocity is over 0.7 m/s. It’s probably because the model considers that the force driving the aerosol resuspension includes the burst force, which is greater than the force that hinders the aerosol resuspension under this condition. For the simulation of the ART experiment, simulation deviation of Wichner model is minimal when ‘\(\alpha\)’ values 5, while the Michael model fit the experiment best when ‘A’ is 4. The resuspension fraction predicted by ECART model shows a drop trend with the increase of ‘H’ and this change is not obvious.

Fig. 2.
figure 2

Comparison between ART 05 experiment and predictions of Wichner model

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Fig. 3.
figure 3

Comparison between ART 05 experiment and predictions of Michael model

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Fig. 4.
figure 4

Comparison between ART 05 experiment and predictions of ECART model

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3.3 Discussion

Above all, it comes to summarize the comparison between these typical force balance models’ simulations and selected experiments. When the coefficients take appropriate values, Wichner and Michael model are in better agreement with the experimental results.

The main difference between Wichner and Michael models is assumption about force acting on particle [10, 15]. Wichner model considers particle only contacts the deposition surface through a single point and determines whether the particles are resuspended by comparing the aerodynamic disturbing force and adhesive force in the vertical direction, as shown in Fig. 5. Michael model considers the particle is in contact with deposition surface at two points, and takes into account the forces on the particles in vertical and horizontal directions, as shown in Fig. 6.

Fig. 5.
figure 5

Assumption about force acting on particle of Wichner model

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Fig. 6.
figure 6

Assumption about force acting on particle of Michael model

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From the force assumption of the model, Michael model actually determines whether the particle could resuspend by comparing the torques. The resuspension judgment criteria of the Michael model is shown in Eq. (14), which can be expressed in the form of Eq. (15),

$$ F_{R} = \frac{1}{2}F_{L} + \frac{r}{A}F_{D} { > }F_{A} $$
(14)
$$ F_{R} \cdot A = \frac{1}{2}AF_{L} + rF_{D} { > }F_{A} \cdot A $$
(15)

where \(0.5A\), \(r\), \(A\) are the torque arms of lift, drag, and adhesive force respectively. The force assumption is valid only when the particle diameter is greater than ‘A’. However, according to the prediction results of Michael model, it fits well with the STORM SR11 experiment when ‘A’ values 2 μm, while the GMD of aerosol particles in this experiment is 0.434 μm, and diameter of most particles is less than 2 μm. Similarly, the particles’ GMD in ART 05 experiment is 1.68 μm, which is smaller than the value of ‘A’ (4 μm) when the fit is best. Overall, by comparing and analyzing the prediction results and experiment measurements, and considering the valid condition of models, Wichner force balance model is recommended for predicting aerosol resuspension behavior during nuclear reactor severe accidents.

4 Conclusions

By comparing the experiment measurements with the predictions of the models, the applicability of Wichner, Michael and ECART force balance model to predict the resuspension phenomenon is evaluated and sensitivity analysis about the aerodynamic disturbing force coefficient, the distance between the two contact points of particle and deposited surface and empirical coefficient related to the number of deposition layers are conducted. The conclusions obtained in this paper are as follows.

When the aerodynamic disturbing force coefficient values 5, Wichner model agrees with the STORM SR11 and ART 05 experimental results, the predicted resuspension fraction is positive proportional to the coefficient. Michael model could predict STORM SR11 and ART experiments well when the distance between the two contact points values 2 μm and 4 μm separately, which is larger than most experimental particle diameters. And the assumption about force acting on particle of Michael model is not valid in the circumstance, the distance is negatively correlated with the predicted resuspension fraction. ECART model could not accurately predicted the rapid increase in resuspension fraction when the disturbing gas velocity disturbing changes suddenly of STORM SR11 experiment and overestimates the resuspension of the ART 05 experiment at friction velocity greater than 0.7 m/s when different values of the empirical coefficient related to the number of deposition layers are adopted. Wichner force balance model is recommended for predicting aerosol resuspension behavior during nuclear reactor severe accidents.