Experimental and Computational Characterization of a Modified Sioutas Cascade Impactor for Respirable Radioactive Aerosols

Abstract

Oak Ridge National Laboratory is collecting and characterizing aerosols released when spent nuclear fuel (SNF) rods are fractured in bending. An aerosol collection system was designed and tested to collect respirable sized (<10 μm aerodynamic diameter [AED]) particulates inside a hot cell facility. The setup is a modified version of the commercially available Sioutas cascade impactor, to which additional stages were added to expand the aerosol collection range from 2.5 to ~15 μm AED. To accommodate the additional stages and specific test conditions, the operating flow rate for aerosol collection was reduced, and testing was conducted by using pressure drop measurements, surrogate dust collection, and particle size characterization. The fluid flow distribution within the cascade and its stages was simulated in STAR-CCM+, and the stage-wise pressure drops obtained using the computational fluid dynamics model were then compared to experimental data. Lagrangian particle simulations were also performed, and stage-wise collection statistics were obtained from the simulation for comparison with the experimental data obtained using SNF-surrogate dust particles. The results provide valuable insights into the stage-wise particle collection characteristics of the modified cascade impactor and can also be used to improve the prediction accuracy of the manufacturer-determined analytical correlations.

1. Introduction

Respirable aerosol releases of spent nuclear fuel (SNF) particulates [1] have been studied in the context of a high energy density device and radioactive dispersal device interaction and explosion, looking at targeted attacks on SNF storage casks and the source term of aerosolized radioactive materials that result [2,3]. More recently, Montgomery et al. investigated the source term of aerosolized radioactive material from a fuel rod fractured in quasi-static bending fracture by using a modified Sioutas cascade impactor [4]. The present study focuses on the design and validation of the modified Sioutas cascade impactor used by Montgomery et al. The objectives of this study are threefold: (1) experimentally design and characterize the performance of a modified Sioutas cascade impactor–based aerosol collection capability for radioactive particles, (2) build a computational fluid dynamics (CFD) model of the modified Sioutas cascade impactor in STAR-CCM+ and validate the model with experimental pressure drop tests, and (3) compare particle distribution statistics obtained using a Lagrangian approach in STAR-CCM+ against experimental data collected using sized dust particles. The cascade modifications were conducted outside of the manufacturer specified operating conditions and using additional modifications. Hence the work does not infringe upon the manufacturer prescribed efficiencies.

2. Theory

Several methods exist for aerosol collection, separation, and characterization based on optical, chemical, electrical, or inertial techniques [5]. Unfortunately, most of these methods are unsuitable for use with SNF because it exposes the associated instrumentation to high levels of radiation. The cascade impactor discussed in this study is largely unaffected by radiation. The cascade impactor itself works on the principle of inertial impaction, in which a gas containing the aerosolized particulates is accelerated through an orifice plate toward a collection filter plate placed at a fixed distance below (Figure 1). The collection filter plate forces the air stream to abruptly change direction, and particles within a size range having enough inertia to escape the air stream are deposited onto the filter. Smaller particles follow the air stream and remain suspended in the gas flow, moving on to the next stage of the impactor. The cut-point of each stage of an impaction sampler corresponds to the size of particles collected by the sampler with 50% efficiency [6]. Based on the Stokes number (a function of the orifice diameter and flow rate used), the collection efficiency increases for particles larger than the cut-point and decreases for smaller particles. The particle diameter distribution is generally characterized by a log-normal distribution. Under impaction theory [6], the cut-point can be calculated at different flow rates for a rectangular jet impactor, as shown in Equation (1).

$$d_{50}\sqrt{C_c}=\sqrt{{\displaystyle \frac{9\mu W^{2}L\left({Stk}_{50}\right)}{{\rho }_{p}Q}}}$$

(1)

For the Sioutas cascade impactor purchased for this study, the stated cut-points of the as-received stages are based on Equation (1), where Q is the average flow rate of the jet (LPM), Stk50 is the Stokes number for 50% collection efficiency for impactors, W and L are the width and length of the orifice, respectively, C_c is the Cunningham’s slip correction factor, ρ_p is the particle density (g/cm³ [1000 kg/m³ for AED]), and μ is the dynamic viscosity of the gas (g/cm/s).

Impactor stages are validated by comparing the experimentally and computationally obtained collection efficiency curves to the analytically calculated collection efficiencies. Experimental evaluations of impactor designs are often conducted by sampling aerosols of a known size range and characterizing the sampled aerosols in each stage to determine its cut-point, AED size range, and efficiency. The performance characteristics of the Sioutas Personal Cascade Impactor Sampler (PCIS) [7] were established by the manufacturer at 9 LPM using monodisperse latex particles and polydisperse ammonium sulfate and ammonium aerosols on various filter materials [8,9]. Collection efficiency curves were generated for individual stages by bleeding 0.3 LPM from the original 9 LPM inflow to a scanning mobility particle sizer (SMPS) or DataRAM that measured the aerosol concentration upstream and downstream of the impactor. In addition to the SMPS and DataRAM counting, monodisperse fluorescent aerosols were also used as test aerosols for individual stages. The fluorescent aerosols were dissolved in ethyl acetate to release the fluorescent dye, and the aerosol concentration was in turn estimated from a fluorescence spectrophotometer analysis of the extraction solution [5]. Marple et al. also used monodisperse aerosol samples for calibrating a novel impactor called the Micro-Orifice Uniform Deposit Impactor (MOUDI) with cut-points ranging from 0.056 to 18 µm at 30 LPM [10]. The calibration was done using monodisperse polystyrene latex aerosols generated from a vibrating orifice monodisperse aerosol generator and analyzed using an electrical aerosol detector by diverting the upstream and downstream flows. Although monodisperse aerosols produce the most accurate collection efficiencies, the setup is complicated and expensive, involving specialized aerosol generators to ensure aerosol particle size uniformity [10]. Demokritou et al. discussed the design and calibration of CASPER, a novel four-stage personal cascade impactor [11]. The impactor was characterized using polydisperse glass aerosol particles with a nominal range of 2–20 µm. The collection efficiency curves were determined from the difference in aerosol concentrations in the upstream and downstream collected from an aerodynamic particle sizer and an SMPS [11]. The techniques used for aerosol concentration measurement in the studies discussed thus far are based on laser diffraction. The major advantages of using laser diffraction are the short measuring times and the capability to provide direct measurement outputs, thereby eliminating post-processing requirements [12].

In the absence of specialized particle sizing equipment such as a laser diffraction setup or Time-Of-Flight analyzer, impactor stage cut-points have been obtained from post-collection imaging of the deposited aerosols using techniques such as scanning electron microscopy (SEM) or transmission electron microscopy (TEM). Nöel et al. compared the performance of MOUDI and an Electrical Low-Pressure Impactor using electron microscopy characterization and also listed the different approaches of conducting microscopy-based analysis of the collected aerosol particles and the challenges involved [13]. They used a combination of SEM and TEM in the characterization of sample titanium dioxide nanoparticles collected in the upper and lower stages, respectively. As described, the best approach for obtaining log-normal size distributions from microscopy is to rely on calculations based on the measured circular diameters (i.e., an imaginary circle having the same area as the particle being measured). In a recent study from Dechraska et al., polydisperse dry powders were used to calibrate an Andersen Cascade Impactor (ACI) [14]. A dry powder device was used to deagglomerate the polydisperse sample powder, and the projected diameters of the particles were analyzed using a particle-sizing analysis software to obtain particle size distribution (PSD). The study found good agreement between the microscopically estimated PSD of the collected aerosol particles and the laser diffraction, computational simulations, and analytical cut-points. Dechraska et al. observed that agglomerated polydisperse powders acted as large particles and were collected on the early stages of the impactor.

CFD solvers are also used to analyze the performance of cascade impactors to assess the impactor’s performance and internal transport characteristics of aerosol particles. In numerous studies, the Andersen Cascade Impactor (ACI) was analyzed [14,15,16,17], primarily using the commercial CFD solvers: ANSYS Fluent and STAR-CCM+. The majority of the studies used an iterative procedure to model the flow in segments until an overall convergence was obtained. This avoids the computational cost of simulating the full geometry. The studies can be divided into two buckets: one set of studies only looked at flow modeling, and another set of studies which combined this with particle deposition simulations using a one-way coupled Lagrangian approach with mono-disperse spherical particles. Flow modeling simulations by Dechraksa et al. [14] predicted the nozzle velocities within 8.1% of the manufacturers’ data for all stages at a flow rate of 28.3 L/min. The simulation identified that the addition of the pre-separator could reduce particle resuspension and minimize particle concentration especially on the lower stages. Vinchurkar et al. [15] used the low Reynolds number k-ω turbulence model to model transitional and fully turbulent flows, with sections of the impactor being modeled as laminar flow. The stage cut-points were predicted within ~20% as compared with the manufacturers’ specification. Flynn et al. [16] used a three-equation eddy viscosity model for turbulence modeling and the Discrete Phase Method (DPM) for Lagrangian simulations. The predicted cut-points from the particle simulations matched the manufacturer data for all stages within a relative error of 7%, except for stage 3, where the relative error increased to 16%. The authors observed that the collection efficiency decreased with increasing air flow rates to 60 L/min, because of increased crossflow interactions and recirculation vortices [16]. Versteeg et al. [17] modeled the start-up kinetics of the ACI. The start-up transient simulation predicted a suction wave which started at the exit of the impactor and propagated towards the induction port. The authors observed that steady-state flow conditions were established around 150 milliseconds, which agreed well with theoretical predictions and experimental measurements [17]. While the majority of the pressure drop occurred across each of the stage nozzle plates, the flow distribution throughout the impactor was observed to be complex. Ohsaki et al. [18] used numerical modeling and experimental validation to investigate the particle motions and deposition behavior of the 8-Stage AN-200 cascade impactor. Two coupled Eulerian-Lagrangian approaches were investigated in the study to model both fluid motion and particle transportation: the CFD-DPM using ANSYS Fluent 17.2, and the CFD-Discrete Element Method (DEM) using ANSYS Fluent 17.2 coupled with EDEM 2018. Two sets of particle sizes were modeled: 10 µm and 100 µm, at a fluid flow rate of 28.3 L/min. The authors concluded that the CFD-DEM model is more accurate as it considers particle-particle and particle-wall collisions and applied the CFD-DEM model to study particle transport in a simple-lung geometry [18].

The validation of cascade stages in aerosol samplers often involves comparing collection efficiency curves obtained experimentally, computationally, and analytically. Experimental evaluations typically employ aerosol sampling with known characteristics to assess cut-points, size ranges, and efficiencies for impactor stages. Various studies have established the performance of impactors such as the Sioutas PCIS, MOUDI, CASPER, and ACI using techniques that include SMPS, DataRAM, fluorescence spectrophotometry, SEM, and TEM to characterize aerosol collection and analyze PSDs. Studies highlight the use of CFD solvers to model internal transport and collection efficiencies across impactor stages, allowing detailed analysis of airflow, particle interactions, and deposition behavior. The current study presents the calibration of additional stages added to a Sioutas Cascade Impactor using CFD and experimental analysis that involves polydisperse surrogate powders and SEM analysis.

3. Methods

3.1. Physical Tests with Dust

The commercially available Sioutas cascade impactor has four collection stages with cut-points of 2.5, 1.0, 0.50, and 0.25 µm AED specified at a flow rate of 9 LPM [5]. From Equation (1), the main variables that affect the cut-point are the orifice dimensions and sampling flowrate. The diaphragm pump (Parker Inc., Cleveland, OH, USA, BTX pump) used to supply flow to the impactor was fitted with a potentiometer to allow several flow rates to be studied with the additional stages, but a nominal flowrate of 7 LPM was expected to achieve the desired cut-point distribution for all stages based on Equation (1). The orifice dimensions required to achieve the desired cut-points for the added stages (~15, ~10, and ~8 μm) at 7 LPM were specified by holding the orifice length constant and optimizing the width, as calculated using Equation (1). The first added stage was envisioned as a prefilter to collect the larger airborne particles that make it into the cascade, as is typically observed in most inertial impaction–based cascade impactors [14]. The final cascade configuration (Figure 2) included the three additional custom-machined stages, labeled MA, MB, and MC, and the four commercially purchased stages, labeled PA, PB, PC, and PD, stacked on extended lead screws in the original Sioutas cascade holder. The as-machined orifice dimensions were measured for all seven stages using a Leica S9i light microscope. The results were averaged from five readings. An example of one such measurement (x-z plane) of the orifice width for stage PD at various locations is shown in Figure 3.

Table 1. Measurements for the seven stage impactor using a microscope and compared to the manufacturers’ specifications for the commercially available stages.

Impaction Stage	Orifice Width, mm	Orifice Length, mm	Separation Distance to Orifice Width, s/w	Measured Width, mm ± 0.015 mm	Measured Length, mm ± 0.015 mm
Stage MA	N/A	N/A	N/A	3.87	19.52
Stage MB	N/A	N/A	N/A	2.88	19.19
Stage MC	N/A	N/A	N/A	1.92	19.38
Stage PA	0.90	19.00	2.10	1.02	20.07
Stage PB	0.50	21.00	3.78	0.51	20.07
Stage PC	0.36	19.00	5.25	0.39	20.24
Stage PD	0.14	25.00	13.50	0.26	20.29

lists the measured dimensions of the stages. In Table 1, the separation distance, S, is defined as the distance between the orifice exit and the impaction plate.

Experimental pressure drop measurements were collected at an inlet flowrate of 7 LPM. The diaphragm pump was first turned on and adjusted to achieve the desired steady-state flow rate. Pressure drop tests were conducted using both the fully assembled impactor and partial assemblies. Individual stage pressure drops were calculated by removing a stage and measuring the pressure drop across the remaining stack. The results are provided in

Table 2. Experimental pressure drop values for the seven-stage cascade impactor at 7 LPM.

Impaction Stage	Measured ΔP [Pa]
Stage MA	0
Stage MB	0
Stage MC	30 ± 30
Stage PA	62 ± 30
Stage PB	128 ± 30
Stage PC	220 ± 30
Stage PD	675 ± 30
Overall	1156

. The pressure drop measurements are used in conjunction with the CFD models to verify expected impactor performance with the inclusion of the modified stages.

Aerosol collection testing of the modified cascade impactor (at 7 LPM) was conducted using a surrogate powder to verify the performance with a setup shown in Figure 4. A powder dispenser was used to puff a known powder mixture into an enclosure connected to the cascade system through ¼″ tubing. Silver filters were loaded in the cascade collection plates. After testing, the stages were disassembled, and the collected particles were analyzed using SEM imaging. The image analysis steps adopted for characterizing and counting the particles are discussed elsewhere [4]. All validation tests were conducted using purchased ISO 12103-1 [19] A1 Ultrafine dust mixtures that consisted of several compounds of varying density and particle sizes.

Table 3. Composition and PSD of ultrafine ISO test dust.

Component	Quantity
Silica (fine dust)	69–77%
Aluminum oxide	8–14%
Calcium oxide (mineral)	2.5–5.5%
Potassium oxide (mineral)	2–5%
Sodium oxide (mineral)	1–4%
Iron(III) oxide (hematite)	4–7%
Magnesium oxide	1–2%
Titanium dioxide	0–1%

lists the ISO dust concentrations used for the tests. The densities of the specific mineral oxide composition mentioned in Table 3 was used for the AED conversion in the experimental analysis.

The surrogate dust deposits in the modified cascade were weighed, photographed (Figure 5), imaged using SEM, and analyzed.

SEM images from the experimental evaluation in this study were processed using a combination of MATLAB and IMAGEJ for obtaining PSDs [20,21,22,23,24,25,26]. The SEM images were taken from different sites along the collection media for counting. The counts were then compared, and the dataset with the largest count rate and range was chosen to evaluate each stage. This produced a human-manageable image library and evaluation dataset; the datasets were not averaged for this validation experiment. However, the actual SNF experiments, as opposed to this validation study, will involve summing the counts from multiple locations to obtain a more comprehensive frequency distribution of the particular stage. One issue that limits the applicability of this study is the agglomeration tendency of the ISO dust sample in air, and some regions of the deposits were eliminated from the counting where agglomeration was observed. This was a basis for ruling out certain regions that were imaged for counting. The authors propose that future validation and actual experiments should involve a combination of image analysis and other quantitative analysis techniques such as mass spectrometry to obtain the total isotopic size distribution.

The collection curves for the seven stages are shown in Figure 6. The individual curves were generated using fixed bin sizes between 0 and 30 µm AED. It was assumed while generating these curves that all the particles downstream of the first stage were deposited on stage collection plates with zero intrastage wall losses. This was a good approximation because most of the particle wall losses occurred upstream of the first stage. The cut-points for the seven stages are presented Figure 6. Stages PB, PC, and PD collect most smaller particles between 0.1 and 1.5 µm, and the machined stages collect very few particles in this size range. The MA stage has a wide range of collection, perhaps due to the tipping of aerosol particles into the orifice rather than the effect of inertial impaction. As seen from

Table 4. Experimentally obtained cut-points in AED using ISO-dust.

Stage	d50 (µm)
Stage MA	8.4
Stage MB	6.4
Stage MC	5.1
Stage PA	5.1
Stage PB	3.4
Stage PC	1.1
Stage PD	1.4

, the experimentally obtained particle cut-points are lower than the analytical cut-point values for which the stages were designed. This has two likely causes—First, the concentration of the ISO dust powder used in the experimental studies had a lower mean diameter than what is ideal for the cut-points of the modified cascade. This results in a low flux of larger-sized particles to bin in the higher cut-point stages (e.g., MA, MB, MC), leading to the particle density functions (PDFs) for these stages to be shifted toward the longer tail of smaller particles. Second, the image processing has some limitations when it comes to fully characterizing the particles collected, since only visible particles can be measured and counted. Particles below the surface cannot be characterized.

3.2. Computational Fluid Dynamics Modeling

The flow distribution and particle deposition on the cascade impactors are investigated using the STAR-CCM+ commercial CFD code. STAR-CCM+ (Version 2021.1 Build 16.02.008) from Siemens [27] is an American Society of Mechanical Engineers, Nuclear Quality Assurance (NQA-1)–compliant CFD solver, and it has been extensively benchmarked and applied to multiphase flows, external aerodynamics, reacting flow networks, and treatment of complex geometric shapes. STAR-CCM+ uses a finite-volume formulation to solve a set of conservation equations for mass, momentum, and energy along with models that provide closure to the Reynolds-Averaged Navier-Stokes equations that describe turbulent flow on a finely discretized computational grid. The CFD simulations discussed here are run on high-performance computing resources hosted by Oak Ridge National Laboratory’s (ORNL’s) Nuclear Energy and Fuel Cycle Division.

In this study, the results of only the seven-stage impactor are discussed. However, prior to modeling the seven-stage cascade, the commercially available 4-stage Sioutas cascade was also modeled as a starting point to verify basic functionality of the simulation. This initial simulation used the manufacturer’s recommended inlet flow rate of 9 LPM. The model was then extended to the modified seven-stage impactor. The 3D geometry of the seven-stage cascade impactor and the modeled fluid domain are shown in Figure 7. The solid-fluid interfaces are considered walls. For the model, the long flexible tubing in the experimental setup is replaced by a rigid pipe geometry that is adequately extended to ensure a fully developed flow at the inlet of the cascade impactor over the range of simulated Reynolds numbers.

The stage pressure drop is very sensitive to the orifice dimensions, and the modeled flow geometry is based on stage microscope measurements shown in Table 1 as opposed to the nominal design dimensions. One-half of the cascade sampler was modeled because the single-phase flow distribution is expected to be symmetric about the Y-Z (x = 0) plane. The coupled solver was used to solve for the continuity and momentum equations without solving for the energy equation. Because these tests were conducted at room temperature at low Mach numbers, the energy equation was ignored. Air with constant material properties was used at atmospheric system pressure. The Shear Stress Transport k-ω model with an all y+ wall treatment was selected to model turbulence. Second-order numerics were used for spatial discretization for both the coupled and turbulence solvers. The flow in the domain switches between transitional turbulent flow to laminar flow. Tests with a transition turbulence model showed less than a 2% change in the predicted stage-wise and overall pressure drops and provided a similar flow distribution compared with the one without a transition model (base model). The flow remained turbulent for all inlet conditions. Therefore, it was decided that the base turbulence model was adequate for this study. The flow distribution tests were performed for a steady flow condition. The velocity inlet boundary condition (BC) was used for the inlet boundary, and the outlet BC was used for the outlet boundary. The no-slip BC was used for all walls, and the symmetry BC was used for the symmetry plane. A block structured mesh was generated in STAR-CCM+ with a total mesh count of ~3.87 million. The block structured (hex) mesh strategy was used to minimize computational cost as well as to adequately resolve the regions of interest. Four prism layers were used to capture the boundary layer, with the wall y+ being less than one for most the domain.

Table 5. Mesh setting for the trimmer and surface re-mesher models.

Parameter	Value
Meshing tool	Trimmer
Base size	5.00 × 10−4 m
Surface growth rate	1.30
Number of prism layers	4.00
Prism layer thickness	4.50 × 10−5 m
Stage-1 notch custom size	2.00 × 10−4 m
Stage-2 notch custom size	2.00 × 10−4 m
Stage-3 notch custom size	2.00 × 10−4 m
Stage-4 notch custom size	1.75 × 10−4 m
Stage-5 notch custom size	1.50 × 10−4 m
Stage-6 notch custom size	1.00 × 10−4 m
Stage-7 notch custom size	5.00 × 10−5 m
Total number of cells	3.87 × 106

lists the mesh settings used for all simulations.

The computational domain is shown in Figure 8a, with a close up of the refined mesh in the region of the orifices and the collectors shown in Figure 8b. The mesh was refined in the orifice and collector region, and initial runs showed that the gradients of pressure and velocity were high in that region. Almost all the pressure drops and flow acceleration occurred as the flow entered the orifice. Similarly, the collector region is also important because it has a direct influence on the particle collection dynamics. A mesh refinement study was conducted using the 4-stage impactor model and the highest flow rate (9 LPM), by halving the base mesh size with a refined cell count of 20.7 × 10⁶. The mesh was shown to be converged as the difference in predicted stage-wise pressure drops and overall pressure drops between the two meshes was within 1%.

4. Computational Fluid Dynamics Results and Discussions

In the CFD study, all steady-state simulations were performed using 64 processors of a midsize ORNL compute cluster and a total run time of ~1 day. The solution was deemed converged when residuals (continuity, momentum, and turbulence) dropped by ~3 orders of magnitude versus initial conditions. Additionally, negligible changes were obtained in the selected monitor points: velocity magnitude monitor points in the nozzles, pressure and turbulence intensity at the outlet boundary, and maximum y+ of all the wall surfaces in the domain. The results of the seven-stage cascade impactor for an inlet flow rate of 7 LPM are shown in Figure 9, Figure 10, Figure 11 and Figure 12.

The velocity contour plot in two y-z planes is shown in Figure 9 and the velocity magnitude in the seven orifices about a X-Z mid-plane is shown in Figure 10. Figure 11 shows the corresponding streamline plot with the flow distribution of the entire domain. Three primary observations can be made regarding flow results: (1) the flow accelerates as it enters the orifices, and the majority of the pressure drop also occurs in this region; (2) the velocity magnitudes in the remaining parts of the domain are negligible, and low magnitude recirculation patterns can be seen in various parts of the domain (e.g., the inlet region before stage MA); and (3) the flow through the orifice in stage MA has a sharp gradient in the x-direction (seen in Figure 10) because the flow exiting the inlet pipe section does not pass through a header. Furthermore, the flow exits the orifice with a similar velocity profile because of a short orifice–flow development length. This has implications for the predicted particle depositions, as discussed in the next section. Contours of (static) pressure are shown in Figure 12 at two y-z planes. Significant pressure drop is shown at the entrance of each of the orifices, with the maximum pressure drop observed for stage PD (circled in green in Figure 12). A small rise in pressure is seen at the stagnation point.

A comparison of predicted and measured stages and overall pressure drops are summarized in

Table 6. Comparison of model vs. experimental pressure drop values and model flow parameters for the seven-stage cascade impactor for 7 LPM.

	Simulation				Measured
Impaction Stage	Uavg [m/s]	ReW [-]	ReDh [-]	ΔP [Pa]	ΔP [Pa]	Abs. Relative Error [%]
Stage MA	1.69	418.2	693.5	0	0	-
Stage MB	2.20	404.1	696.0	7	0	-
Stage MC	3.24	398.1	714.5	12	30 ± 30	-
Stage PA	5.58	363.7	714.0	34 ± 1	62 ± 30	45
Stage PB	11.13	362.4	729.0	150 ± 9	128 ± 30	17
Stage PC	14.62	370.6	726.9	258 ± 20	220 ± 30	17
Stage PD	21.79	368.6	727.8	603 ± 68	675 ± 30	11
Overall	-	-	-	1116	1156	3.5

for a flow rate of 7 LPM. In the table, Re_W is the Reynolds number defined with respect to the orifice width, and Re_Dh is the Reynolds number defined with respect to the hydraulic diameter of the orifice. The Reynolds numbers based on D_h only show a modest increase from stage MA to stage PD. The pressure drops were also compared for a 6 LPM flow rate, which was reported elsewhere [4]. For both simulated flow rates, the relative error for stages PB–PD is less than 20%, which is considered acceptable given the measurement and model uncertainties. The reason as to why the as-machined stages: MA, MB and MC have relatively smaller drops in comparison to the purchased stages: PA, PB, PC and PD is because of the relatively larger notch width as the as-machined stages were designed to filter larger-sized particles. Given the sensitivity of the pressure drop to the orifice dimensions, the differences could be due to manufacturing variability. Nonetheless, the overall pressure drop comparison for both flow rates is excellent, and the model can be considered validated. In general, the model predicts a higher pressure drop for a given dynamic head when comparing the manufacturer’s mean velocity, U_mean, with the model’s U_mean, where U_mean is defined as the following:

$$U_{mean}={\displaystyle \frac{\int \rho u\left(x,y,z\right)d{A}_c}{\rho d{A}_c}}$$

(2)

Here, ρ is the (constant) air density, A_c is the cross-sectional area of the orifice, and u is the local velocity magnitude. The model uncertainties are determined by first calculating the discharge coefficient, C_d, for each orifice based on mean orifice dimensions:

$${\mathrm{C}}_d={\displaystyle \frac{\rho U_{avg}^2}{2∆P}}$$

(3)

Here, ρ is air density (1.18415 kg/m³), and ΔP is the stage pressure drop. Assuming the discharge coefficients are the same for small deviations in orifice dimensions, the range of pressure drops are then calculated accounting for the uncertainties in orifice length and orifice width. The model uncertainty is expected to be higher if all uncertainties are accounted for.

Particle Deposition Simulations

The purpose of the present study was to broadly capture a distribution of aerosol-sized particles and determine the mean cut-point for each stage in the cascade. To accomplish this, the Lagrangian modeling approach was used to investigate particle deposition on the collection plates. In the present study, solid uranium dioxide particles with a density of 10,970 kg/m³ are used. Note that all particle diameters cited within the CFD simulations are physical diameters, not to be confused with the AED specified in the cascade cut-points. In the Lagrangian framework, particles are treated as parcels of mass, using applicable conservation laws. Lagrangian models are recommended for particle-laden flows in which the volume fraction of particles is low (less than 10%) compared with the finite-volume cell. In the Lagrangian approach in STAR-CCM+ [27], the equation of conservation of (linear) momentum for a material particle of mass, $m_p$, is given by

$$m_p{\displaystyle \frac{d{v}_p}{dt}}={\mathrm{F}}_s+{\mathrm{F}}_b,$$

(4)

where $v_p$ denotes the instantaneous particle velocity, ${\mathrm{F}}_s$ is the resultant of the surface forces, and ${\mathrm{F}}_b$ is the resultant of the body forces. In the Lagrangian framework, the state evolved on a particle-by-particle basis while the Eulerian fields were frozen. The particle position and particle velocity are obtained by numerically integrating the position/displacement equation with time:

$$m_p{\displaystyle \frac{d{r}_p}{dt}}=v_p,$$

(5)

where $r_p\left(t\right)$ is the instantaneous position vector at time, $t$. In the statistical Lagrangian approach, parcels of particles are tracked. For large particle loadings, to save computational cost, the parcel approach can be used and is the method of choice here. A single integration of the state is applied to all the particles in the parcel, and the interaction term with the Eulerian phase is calculated by multiplying by the number of particles in the parcel. For statistically converged results, it is recommended to have sufficient computational parcels. The surface forces can be broken down into

$${\mathrm{F}}_s={\mathrm{F}}_d+{\mathrm{F}}_p+{\mathrm{F}}_{vm},$$

(6)

where ${\mathrm{F}}_d$ is the drag force, ${\mathrm{F}}_p$ is the pressure gradient force, and ${\mathrm{F}}_{vm}$ is the virtual mass force. The resultant of the surface forces is the momentum that is transferred from the continuous phase to the particle. The body force term can be similarly decomposed into

$${\mathrm{F}}_b={\mathrm{F}}_g+{\mathrm{F}}_u+{\mathrm{F}}_{MRF}+{\mathrm{F}}_{Co},$$

(7)

where ${\mathrm{F}}_g$ is the gravity force, ${\mathrm{F}}_u$ is the user-defined body force term, ${\mathrm{F}}_{MRF}$ is applicable for moving reference frames, and ${\mathrm{F}}_{Co}$ is the Coulomb force. In the current study, ${\mathrm{F}}_g$ is the only applicable body force. There are various submodels for each particle interaction force, and they are described in detail in the Star-CCM+ user manual [27]. The current study uses the following surface force models: virtual mass force, pressure gradient force, Schiller-Naumann drag force, and the Sommerfeld shear lift force model [27].

To complete the Lagrangian model setup, particle injectors and particle-wall interactions must be defined. For the current study, the part injector is used with injector properties described in

Table 7. Part injector parameters.

Parameters	Values
Physical particle diameter distribution	Log-normal distribution with a range of [0.1, 10] µm and a mean of 3 µm (10 µm AED)
Point inclusion probability	0.1
Parcel streams	100
Velocity	Same as fluid velocity

. The part injector uses the injection faces from the meshed part (i.e., the inlet face). The number of injection points in the inlet face is controlled by the point inclusion probability. The total number of injection faces for the current setup is ~300. The number of particles per parcel (i.e., parcel streams) is 100. The particles are injected with the same velocity as the fluid (i.e., zero slip velocity), which is a reasonable assumption given that the particles are essentially driven by the flow. The particle flow rate is controlled by the number of injection points and parcel streams (300 × 100 per timestep). Therefore, although the specified particle flow rate is arbitrary, the total number of injections are set to inject about ~0.5 million particles (~5 ×10³ parcels) in the computational domain. The timing of the injections occur is controlled. The total number of injected particles in the system is selected arbitrarily while accounting for the computational time required to ensure that most particles are caught in the collectors. A few particles escape from the computational domain.

There are four options available in STAR-CCM+ to model particle-wall interactions: rebound, sticky, escape, and composite. In the rebound mode, particles rebound elastically off the wall surface and are solved using user-specified normal and tangential restitution coefficients. The sticky surface BC is the exact opposite, with particles sufficiently close to the wall and sticking to the surface. The escape mode, which was not applied for the current study, allows for the particles to escape from the boundary. The composite mode allows for a user-defined probability of all three modes. In the current study, all collector surfaces are defined as sticky surfaces, and the other wall surfaces are defined as rebound surfaces. A parameter is available in STAR-CCM+ to define the degree to which particles stick; for this study, particles are considered to stick if the coefficient is ≥0.8, with 1.0 defined as completely stuck onto the surface. The locations of the part injector and the sticky boundary surfaces are highlighted in Figure 13.

The solution was obtained in two steps. First, the steady flow distribution for the seven-stage impactor for a flow rate of 7 LPM was obtained. Second, the fluid solver was frozen, and the Lagrangian solver was turned on for a transient solve using the steady flow distribution as the initial condition. A user-specified Courant number, fixed for this problem at 5, is used to determine the local pseudo–timestep for the dual-timestepping scheme used in STAR-CCM+ [27]. This value was deemed adequate because the local convective Courant number was less than 1.0 in most of the flow domain. The timestep duration is set to 1 × 10⁻⁴ s using a second-order implicit scheme, thereby ensuring a 1:1 timestep with the Lagrangian solver if a two-way coupling approach is required. The two-way coupling approach was tested for the current problem and was found to be unnecessary; a near identical particle distribution was observed for all stages, with and without a two-way coupling approach. It is possible that an increased particle concentration would have a greater impact on the flow field, but for the simulated particle concentration, the results indicate that the impaction is flow/gravity-driven, and wall-particle/particle-particle interactions do not significantly influence the solution. For the Lagrangian particle solver, a second-order, implicit, unsteady tracking method was used with the maximum substeps capped at 1 × 10⁴. This ensures that if a small number of parcels do not achieve convergence with the particle solver, then they are not tracked indefinitely. In the current study, all parcels converge for every timestep.

The particle solution was run for a physical timestep of 2 s. Although this might be insufficient to replicate the full implementation of the test method in the hot cell (the event is sampled for ~300 s), the purpose of this study is to broadly capture the distribution of particles and estimate the cut-point for each stage. The simulation ran on 64 processors of a midsize ORNL compute cluster and had a wall time of time ~2 days. Particle injection occurred within the first 100 timesteps (Δt = 1 × 10⁻⁴), after which the injector was shut down. A histogram showing the final PSD in the flow domain is shown in Figure 14. The final particle distribution is expected to follow a log-normal distribution, as defined in the injector, with only a tiny fraction of all injected particles (~0.58%) having exited from the flow domain during the simulation.

A snapshot of the particle distribution at the end of the simulation is shown in Figure 15 and Figure 16. In Figure 15, particles of different sizes are scaled to a fixed pixel size, whereas in Figure 16, particles are scaled 10 times to their actual physical size. After ~2.5 s, ~95% of the total particles were collected in the seven-stages, and particle distributions were analyzed. The distribution of particles on the collection filter within the impinging jet area created by the orifice is very similar to the distributions observed in physical testing. The simulation further identified that many particles are distributed on other areas of the collection plate, but physical testing did not confirm this behavior. Three observations can be made regarding the particle distribution: (1) at a flow rate of 7 LPM, the flow speeds in orifices PB–PD are high enough to force particles to collect in and around the stagnation zone; (2) stages MB and MC do not trap many particles, and further investigation is needed to fully evaluate their performance; and (3) stage MA collects many particles much smaller than its designed (mean) cut-point, primarily driven by the core peaked flow, which forces a high velocity jet near the center, as discussed in the steady-state flow distributions (Figure 9). The AED histogram distributions are shown for stages MA, PA, and PD in Figure 17.

The distribution of particles collected across the seven stages for various ranges of physical particle diameters is shown in

Table 8. Percentage of the injected particles collected across various size groups for the seven stages (7 LPM).

Size Distribution (µm)
Physical, ρ = 10.97 g/cc	AED	MA	MB	MC	PA	PB	PC	PD
0.1–0.25	0.33–0.83	11.8%	0%	0%	0%	0%	35.3%	52.9%
0.25–0.5	0.83–1.66	0.2%	0%	0%	0.1%	0.3%	27.2%	72%
0.5–0.75	1.66–2.48	0.2%	0.1%	0.1%	0.5%	69.2%	29.9%	0%
0.75–1.0	2.48–3.31	0.6%	0.3%	0.1%	4.9%	94.1%	0%	0%
1.0–1.5	3.31–4.97	15.2%	0.9%	3.2%	68.4%	12.3%	0%	0%
1.5–2.0	4.97–6.62	67.3%	2.2%	10.1%	20.4%	0%	0%	0%
2.0–2.5	6.62–8.28	93.6%	2.2%	4%	0.1%	0%	0%	0%
2.5–3.0	8.28–9.93	97.9%	1.7%	0.4%	0%	0%	0%	0%
≥3.0	≥9.93	99.7%	0.3%	0%	0%	0%	0%	0%

. While stages PA–PD show sharp cut-points trapping particles between 0.1 and 1.5 µm, stages MB–MC collect relatively few particles within the expected range, and Stage MA shows a wider range of particle sizes for reasons highlighted earlier. The particle collection statistics are shown in

Table 9. Particle collection statistics for the seven stages (7 LPM).

Parameter	Stage MA	Stage MB	Stage MC	Stage PA	Stage PB	Stage PC	Stage PD
Physical mean (µm)	4.23	2.26	1.78	1.35	0.82	0.52	0.37
Physical median (µm)	3.65	2.03	1.79	1.34	0.82	0.52	0.36
Physical STD (µm)	2.15	0.84	0.31	0.22	0.14	0.05	0.04
AED mean (µm)	14.01	7.49	5.90	4.47	2.72	1.72	1.23
AED median (µm)	12.09	6.72	5.93	4.44	2.72	1.72	1.19
AED STD (µm)	7.12	2.78	1.03	0.73	0.46	0.17	0.13

, and the stage cut-points are quantified. The standard deviation is highest for stage MA indicating of a wider range of particle sizes.

The collection efficiency curves (Figure 17 and Figure 18) are calculated for each stage using the technique discussed in Section 3. A comparison of the stages’ cut-points from the CFD results (d₅₀ from collection curves) with the analytical correlation (Equation (1)) is shown in Figure 19. An absolute mean error of ~19.7% was obtained when comparing CFD with analytical stage d₅₀s. For both methods, the cut-points line up well except for stage MA in the CFD results. This requires further investigation because, unlike the other stages, the predicted particle distribution for stage MA showed considerable variation in particle sizes. The differences between CFD and the analytical correlation for stages PA and PB are within (geometrical) uncertainty bounds. From both methods, it can be concluded that the added stages MA, MB, and MC mostly trap the larger particles, but they could be improved to obtain sharper cut-point distributions similar to those of the purchased stages.

5. Conclusions

This work presented a generic, reproducible modified Sioutas impactor design capable of sampling radioactive (SNF) aerosols across a large range of respirable particle sizes. The modified impactor can capture aerosol particles under ~15 µm within the errors obtained from the validation studies.

The modified impactor was designed based on analytical first-principles correlations. Empirically, the modified impactor was used to sample polydisperse ISO dust particles, and the collection was characterized under an electron microscope to obtain stage-wise distributions and collection efficiencies. Computationally, the flow distribution and Lagrangian particle modeling of the Sioutas cascade impactor was performed using STAR-CCM+ to characterize its performance. The CFD predictions matched the analytical correlations within a mean absolute error of ~19.7%. The cut-points predicted by both the approaches are higher than specified by the manufacturer of the commercially available stages because the measured geometrical dimensions of the stage orifices are generally larger than manufacturer specifications. The cut-point predictions from CFD confirmed that the three additional stages help collect larger respirable particles, with the commercially available stages used to collect smaller aerosols. Stage MA trapped most large particles but also undesirably trapped some smaller particles as a result of the jet developed at its orifice. Stages MB and MC seem to under-sample within their designed size ranges. This phenomenon requires further investigation through experimental particle size characterization studies using monodisperse particles of specific cut-off ranges.

Future work will look into addressing the disagreement between the experimental and CFD results by using monodisperse dust for experiments and charged particle simulations (to model agglomerations) for CFD. The post-processing difficulties of the verification experiments related to identifying layered particles will be addressed by using advanced image processing techniques while also looking at the DEM model to improve CFD predictions.