Aerosol Retention in the Vicinity of a Breach in a Tube Bundle: An Experimental Investigation

Abstract

This article summarizes the main results of a bench-scale program focused on experimentally assessing the aerosol retention near the tube breach in a tube bundle. The major variables investigated were particle nature (polydispersed TiO ₂ agglomerates vs. solid, monodisperse SiO ₂ spheres) and Re _D (0.8−2.7· 10 ⁵ ). In addition, comparisons to other data sets provided insights into the particle aerodynamic size effect on retention efficiency. Results showed that particle nature substantially affects aerosol retention in the tube bundle: mass retention efficiency was low for TiO ₂ agglomerates (less than 30%) whereas it was much higher for SiO ₂ particles (around 85%). Retention efficiency is also affected by Re _D : its sensitivity was found to follow a log-normal behavior with a maximum retention attained at Re _D near 1· 10 ⁵ . This evolution with Re _D was similar for both types of compounds. Particle size also influences retention efficiency: the bigger the TiO₂ agglomerates the lower retention efficiency (no data were available for SiO ₂ ). Among all these variables, particle nature was noted to have a prime importance for in-bundle retention, whereas Re _D and particle aerodynamic size, although also affect retention efficiency, did not play such a key role. In light of the results, the presence of retention-inhibiting mechanisms such as fragmentation, resuspension or bouncing has been discussed. The data recorded will enhance the overall understanding of the governing mechanisms involved and will serve as a database against which compare model predictions. Nevertheless, further experimental data would be desirable to set up a sound database.

NOMENCLATURE

Cin,Cout	=	mass concentration at the inlet and outlet of the bundle
D	=	tube diameter
d	=	particle diameter
dae	=	aerodynamic median diameter
Ma = Vtheo/(γ · Rg· T)0.5	=	Mach number
mout	=	aerosol particle mass measured at the outlet of the bundle
mret	=	aerosol particle mass retained at the tube bundle
m7x7%	=	fraction of mass bundle retained in the central square of 7× 7 tubes
n.a.	=	not available
p	=	pitch of tube bundle, i.e., distance between in center lines of adjacent tubes
Pb	=	pressure at the bundle
Pin	=	pressure upstream the breach
r	=	correlation coefficient of the fitting defined as (1-Sum of Squared Errors/Sum of Squared Totals)0.5
ReD. = ρ · v· D/μ	=	tube Reynolds number
Rep = Vtheo· dp/ν	=	particle Reynolds number
T	=	temperature of the flow
v	=	particle velocity
vnormal	=	normal impaction velocity
Vtheo = 4Φ /(ρ π D2)	=	theoretical flow velocity
Greek	=
μ	=	dynamic viscosity
ρ	=	gas density
δ #	=	estimated uncertainty associated with variable #
Δ #	=	differential or increment of variable #
Δ p	=	gas pressure jump at the tube breach
Φ	=	inlet gas mass flow rate at the broken tube
Ψ	=	particle nature parameter for Equation (6)
Subscripts	=
asint	=	asymptotic value
crit	=	critical
max	=	maximum
min	=	minimum
p	=	particle
rebound	=	rebound
ref	=	reference
Superscripts	=
Inlet	=	upstream the broken tube
outlet	=	downstream the bundle

I. INTRODUCTION

Aerosol retention in a bundle of tubes arises in numerous engineering applications from filtering technology to coating industry (Hinds 1982). It attracts especial attention in the case of heat exchangers and power plants. The steam generator of a power plant (SG) is a complex structure housing various components and around 4000 U-inverted tubes used to produce the steam that eventually expands through the turbine of a Rankine cycle. During the plant operation a variety of phenomena (i.e., stress corrosion cracking, erosion-corrosion, high-cycle fatigue, etc.) may degrade the boundary between the primary and the secondary side of the SG resulting in a tube rupture (Hwang et al. 2008). This problem is especially critical in nuclear power plants. Under the very unlikely circumstances of a reactor core melting in a pressurized water reactor, such a failure might lead to leaks of radioactive aerosol to the environment. This scenario, generally called Steam Generator Tube Rupture (SGTR), is of an outstanding importance in nuclear safety (Herranz et al. 2008; Da Silva et al. 2007; US NRC 1996; US NRC 1990). Given the large surface area available, during the accident radioactive particles could be partially retained as they pass through the surface of the multiple tubes within the secondary side of the steam generator. The extent of aerosol trapping is heavily dependent on the conditions in the secondary side during the accident. In the most critical conditions, the tube breach would be over the water level or the water of the SG would have evaporated totally and particles would enter a “dry” secondary side carried by a high-velocity gas flow. In this case, it is expected that the tube surfaces in the region between the tube breach and the upper support plate (hereafter called “break stage”), play a key role in the retention process. Therefore, the characterization of the aerosol retention across a tube bundle is of major importance to assess decontamination capability of the SG during SGTR sequences (Herranz et al. 2008; Herranz et al. 2007).

This article summarizes the main results of a bench-scale program focused on experimentally assessing the aerosol retention near the tube breach in a tube bundle. The major variables investigated in this program were the particle nature and Re_D. Particle nature influence was analyzed by comparing retention efficiency of different types of aerosols (polydispersed TiO₂ agglomerates vs. solid, monodisperse SiO₂ spheres). The Re_D influence on retention was assessed between 0.8–2.7 · 10⁵ by varying the inlet gas mass flow rate for each type of aerosol studied. In addition, comparisons to other data sets provided insights into the particle size effect on retention efficiency. The observations gathered provided relevant qualitative and quantitative insights into the filtering capability of a tube bundle and the governing mechanisms. Additionally, key aspects deserving further research in the near-term are highlighted.

II. BACKGROUND

Previous articles that discuss aerosol retention in tubes are briefly reviewed below.

There exists several experimental studies on particle retention on single tubes (Douglas and Illias 1988; Ilias and Douglas 1989; Wessel et al. 1988; Wong et al. 1953; Ranz et al. 1952; Zhu et al.2000) as well as on dynamic adhesion of particles impacting on single tubes (Wang and John 1988; Pau 1982; Aylor et al. 1985). Douglas and Ilias (1988) obtained some experimental data for Re_D < 7200 by exposing a tube inside a wind tunnel to an aerosol stream and collecting the mass retained on it afterwards. His sparse and scattered data showed that retention efficiency roughly correlates with Stk number for Stk ≤ 0.1. Ranz et al. (1952) and Wong et al. (1953) performed similar experimental studies for Re_D < 450 and Stk > 0.1. Their results constitute a more consistent database of around 135 experimental data. Their data showed that, under the conditions studied, retention efficiency increases with Stk number.

Regarding particle adhesion, Pau (1982) and Aylor et al. (1985) showed that particle rebound when colliding against a tube surface is a function of its kinetic energy. In the case of the particles studied, the sticking probability was measured to be near unity for kinetic energies below 10^–12 J and dropped to < 0.01 when kinetic energy was raised by one order of magnitude.

There are few investigations dealing with the particle retention across a bundle of tubes. In the bundle configuration, the retention of a tube differs to the one obtained in the single tube configuration since the “proximity effects” of adjacent tubes might influence deposition (Konstandopoulos et al. 1993). In this case, the presence of neighbor tubes, modifies the flow field in the tube analyzed resulting in a different aerosol retention efficiency and thus in a non-uniform deposition across the tubes of the bundle. Tsiang et al. (1982), McLaughlin et al. (1986), and Ingham et al. (1989) dealt with arrays of fibers in cross-flow for low Re numbers (which is out of the range of interest of the present research).

The unique available experimental research on particle retention efficiency of the tube bundle in the Re_D range under study is the EU-SGTR program (Auvinen et al. 2005; Güntay et al. 2004; Herranz et al. 2006). Herranz et al. (2006) showed that, for particles ranging an inlet d_ae between 4–7 μ m, the mass fraction retained in the tube bundle of the break stage (η) was less than 30% and it was found to be inversely proportional to the square of the inlet gas mass flow rate (Φ) between 75 and 250 kg/h. They also showed that the influence of the breach type (i.e., guillotine or fish-mouth), its orientation and location within the bundle had a secondary importance with respect to the mass flow rate one.

III. EXPERIMENTAL SET-UP

A. Facility Description

The experimental campaign was carried out in the PECA rig of the Ciemat Laboratory for Analysis of Safety Systems (LASS). Basically, the rig consisted of a gas supply system, an aerosol generation device, a tube bundle and a measurement system (i.e., sampling and instrumentation). Figure 1 shows a sketch of the facility, the break tested, and a top view of the tube bundle within the 8.3 m³ vessel where it stood.

FIG. 1 Scheme of the PECA facility for the aerosol retention experiments and guillotine break tested.

The bundle (330 × 300 mm) was a mock-up of the break stage of the secondary side of a steam generator. The tubes are 1.5 m high and 19.05 mm in diameter with a pitch to diameter ratio in the bundle of p/D = 1.4. They are arranged in a squared assembly of 11 × 11 (121 tubes). Such a configuration was based on CFD simulations (López del Prá et al. 2007; Quarini 1999), which indicated that tubes beyond the fifth row from the breach should not affect substantially aerosol deposition. In other words, the size of the bundle is considered large enough to reproduce most of momentum dissipation of the incoming gas jet when moving through the system. The breach is of guillotine type (axi-symmetric type), with an open area equivalent to one tube diameter. The breach height was H = 0.24· D and it was placed in the central tube at 0.24 m from the base. The flow was injected into the broken tube through the base. Since the top end of the tube was closed, the flow was forced to exit through the breach and to expand across the bundle. Materials and dimensions of tubes (except for tube height) and support plates were identical to those used in a real SG (Güntay et al. 2004). The whole structure was housed in a methacrylate frame and ended up with an upper plate simulating the separation between the break stage and the rest of the SG.

A fluidized bed generator (FBG) was used to produce the aerosol. It permitted the injection of up to 25kg/h N₂-seed-flow at high pressure. A Venturi cone placed at the exit of the FBG partially de-agglomerated the particles reducing the injected aerosol d_ae. Characterization of particles incoming and outgoing the bundle was done by online measurements devices based on different fundamentals: optical particle counter (OPC), aerodynamic particle sizer (APS®), electrical low pressure impactor (ELPI®) as well as by integral gravimetric systems: cascade impactors (low pressure Dekati Ldt., Sierra and Mark III Andersen Inc.), membrane filters. This instrumentation characterized the aerosol size distribution and concentration upstream the broken tube and at the bundle exit via iso-kinetic samples. The aerosol deposits on tube surfaces were also collected and weighed to characterize the deposition pattern in each tube of the bundle. The collection was performed by means of U-rings, set around the base of each tube before the test, and wet paper.

B. Test Matrix and Test Procedure

The specific objective of the experiments was to assess the influence of the type of particles used in the aerosol (i.e., particle nature) on the retention efficiency of the tube bundle in the Re_D range studied.

The design of the experimental matrix was based on the analysis of the expected boundary conditions during the rupture of a tube in a SG and the LASS capabilities and limitations. The non-dimensional numbers characterizing the experiments are Re_D = 10⁴–10⁶, Stk = 10^–2–10, Ma = 0.03–0.9, Re_p ²/Stk = 10²–10³. The program focused on achieving aerodynamic scenarios as close as possible to the actual one. The potential effect of thermal or steam concentration gradients were not taken into account in the experimental matrix. This made it feasible to use air as carrier gas during the tests.

A total of thirteen different tests were performed. Table 1 shows the experimental matrix used. The matrix was focused on two main variables: the type of particle used in the aerosol and Re_D from 0.8· 10⁵ to 2.7· 10⁵.

TABLE 1 Test matrix

	ReD[10^5]					Particle nature
Test number	0.8	1.06	1.59	2.16	2.70	TiO2 (Deg)	TiO2 (Nph)	SiO2
1		X				X
2					X	X
3		X					X
4				X			X
5			X				X
6		X						X
7			X					X
8				X				X
9		X						X
10			X					X
11					X			X
12			X			X
13	X							X

TABLE 2 Experimental results and boundary conditions

Test number	1	2	3	4	5	6	7	8	9	10	11	12	13
Particle nature	TiO2 (Deg)	TiO2 (Deg)	TiO2 (Nph)	TiO2 (Nph)	TiO2 (Nph)	SiO2	SiO2	SiO2	SiO2	SiO2	SiO2	TiO2 (Deg)	SiO2
ReD [10^5]	1.00	2.40	1.06	1.80	1.33	1.29	1.58	1.96	1.43	1.78	2.53	1.55	0.87
δ ReD/ReD (%) ^a	19	2	17	37	13	3	2	16	3	7	19	2	4
Δ p (bar)	0.2	1.4	0.1	1.2	0.2	0.6	0.2	0.5	0.1	0.5	0.8	0.5	<0.1
Cin (mg/Nm3)	n.a.	n.a.	n.a.	744.7	1506.2	n.a.	42.1	344.2	426.1	266.5	201.4	n.a.	947.0
Cout (mg/Nm3)	304.9	85.8	1564.2	561.5	981.8	30.5	12.8	42.4	46.2	22.5	10.9	178.0	151.6
Inlet dae (μ m)	2.5	2.5	1.5	2.8	2.6	2	2.1	1.3	1.6	2.0	1.7	3.2	1.3
Inlet GSD	2.5	2.4	2.3	2.5	2.4	2.1	2.4	1.5	2.1	2.2	2.3	2.6	2.2
Outlet dae (μ m)	1.7	0.6	2	0.5	1.2	0.9	0.9	1	n.a.	n.a.	1.2	0.7	1.2
mret (g)	5.30	1.29	17.46	10.26	9.22	2.39	0.86	28.27	69.72	30.11	8.93	2.82	32.45
δ mret (g)	1	1	1.75	1.03	1	1	1	2.83	7.70	3.01	1	1	3.25
mout (g)	13.98	8.23	92.68	64.98	49.15	1.62	0.94	5.34	4.32	2.29	2.10	17.34	7.50
m7x7% (%)	46.6	32.1	61.1	57.6	70.9	53.6	73.9	46.9	51.3	48.0	51.5	59.2	59.1
δ mout (g)	4.49	5.32	49.87	37.64	23.53	1.21	1.40	2.64	2.79	1.34	1.17	8.01	4.38
η (%)	27.48	13.53	15.85	13.64	15.79	59.47	48.03	84.11	94.16	92.94	80.93	14.00	81.24
δ η/η (%)	27	87	46	50	41	34	98	8	4	4	11	50	11

Presently, there is an important lack of knowledge regarding the morphology and composition of a prototypical particle in the hypothetical case of a severe accident in a nuclear power plant. Even though the PHEBUS-FP (Arreghini et al. 2000) project has produced particles consisting roughly of 33% structural and nuclear fuel material, 33% control rod material and 33% fission products (Kissane 2008), these particles were not representative of those that might be encountered during a severe accident SGTR sequence. In case of this type of sequence, the chemical composition of a prototypical particle is unknown. As a consequence, the particle types to be used in the experiments were chosen so that they bracketed to some extent two extreme conditions: highly agglomerated and porous particles (TiO₂) and compact ones (SiO₂). Three different types of aerosols were used: TiO₂(Deg) (Degussa 2005), TiO₂(Nph) (Nanophase 2002), and SiO₂ (Nagase 2006). TiO₂ aerosols were generated from nano-seeds agglomeration in the FBG, producing a polydispersed aerosol size distribution. SiO₂ aerosol was generated from 1-micron solid spheres producing a monodispersed aerosol size distribution. This size was expected to be representative of the particles playing a role in a SGTR sequence (Kissane 2008; Arreghini et al. 2000).

The aerodynamic mass median diameter of the aerosol produced by the FBG ranged from 0.7 to 3 μ m for TiO₂ particles whereas it was measured to be 1.4 μ m for the SiO₂ particles. Figure 2 shows scanning electron microscopy (SEM) views of TiO₂ (Deg) and TiO₂ (Nph) and SiO₂ particles. As expected, TiO₂ particles were porous, fractal-like agglomerates. Thus, uncertainties related to the aerosol shape and density affected the characterization of this kind of particles. SEM analysis indicated that, even though the compound used was TiO₂ in Deg and Nph powder, agglomerates show qualitative microscopic differences. Deg agglomerates showed a smaller pore characteristic length than the one of Nph agglomerates and they also seemed to be more loosely packed than the Nph ones. These differences may rise from the fact that the manufacturers used different generation processes to obtain the primary TiO₂ seeds. One of the objectives of using these compounds was to study if the differences in microscopic particle properties illustrated in Figure 2 result in different global retention behavior.

FIG. 2 SEM images. Left: TiO₂ (Nph) agglomerate, Right: SiO₂ particle.

The tests were designed to last approximately 50 min. Room temperature and atmospheric pressure was kept in the bundle during the tests. Once the desired aerodynamic conditions were reached and stabilized, the aerosol injection and the inlet and outlet on-line measurements were started. Then, the integral gravimetric measurements were executed. Once the gravimetric measurements finished, the aerosol injection was shut down and the test was considered ended. Twenty four hours after each test, the bundle shroud was removed and the U-rings were slid along each tube without dismounting it. This way the mass retained was collected avoiding the fall of the deposits. After that, the tubes were washed with wet paper to collect any remaining aerosol deposits. Finally, the samples were weighed.

C. Calibration Campaign and Uncertainty Analysis

Previous to the aerosol retention experiments, a calibration campaign was carried out to properly characterize the actual response of the on-line instrumentation: OPC, APS, and ELPI (Velasco et al 2007). Since the three on-line devices rely on different physical measurement principles to estimate particle size (light scattering, time of flight, charge counting, respectively), and they were calibrated by manufacturers against latex particles, it was of outstanding importance to asses their differences in the estimation of the actual aerosol size distributions.

During the campaign these devices were used to measure in different configurations with different types of aerosols under the conditions used in the aerosol retention experiments. Results showed that different devices measuring the same aerosol sample provide partially different particle size distributions. Figure 3 shows the particle size distribution measured simultaneously for a TiO₂ (Deg) aerosol for APS and ELPI. Comparison has been based on the fraction of particle counted in each bin per unit of diameter logarithm. Both qualitative and quantitative differences can be observed. The figure reveals that relatively big uncertainties would affect the description of the aerosol size distributions for particle aerodynamic diameters smaller than 0.9 μ m, whereas both devices estimated a similar distribution for particle aerodynamic diameters bigger than 0.9 μ m.

FIG. 3 Estimated uncertainty associated to TiO₂ (Deg) aerosol size distribution from APS and ELPI measurements.

The differences in the measurements found in the calibration campaign were considered and quantified for the device uncertainty estimation of the aerosol retention experiments. On the other hand, uncertainty in the measurement of mass retention efficiency was quantified by error propagation calculus from the measured quantities, following ISO guidelines (ISO 1995). These uncertainties were also properly taken into account in the analysis of the results of the research program.

IV. RESULTS AND DISCUSSION

A. General Observations

Table 2 summarizes the major results of the experiments in terms of in-bundle mass retention efficiency (η (%)).

As noted, a mass fraction lower than 30% was retained in the tube bundle for TiO₂ agglomerates, whereas it was notably higher (around 85%) for SiO₂ particles. This difference indicates that particle nature influences retention. T-06 and T-07 experiments reached one order of magnitude lower aerosol concentration than other tests of the campaign, so that the resulting uncertainty was too high for them to be considered. Hence, they were disregarded in the overall experiments discussion.

The deposition of particles in the bundle was uneven both radially and axially. The deposits' surface density of aerosol mass decreased with radial distance from the breach. On the closest tubes thick and dense deposits were built up, whereas deposits looked more spread farther away from the closest tubes. From the fourth tube row on, deposits' surface density became very small.

Particle nature was observed to affect the deposition pattern. To illustrate this statement, the bundle can be split in two regions: the neighbor tubes and the rest of the bundle. Figure 4 shows two pictures of the aerosol deposit distribution over the tubes surrounding the broken one for TiO₂ (Nph) and SiO₂ tests. In the case of TiO₂ tests, hill-shaped deposits were built-up (in some cases they underwent sloughing when they reached a critical size). Even though overall retention efficiency does not seem to depend on the manufacturer of TiO₂ material, it was observed to affect deposition pattern. TiO₂(Nph) hill-shaped deposits were more firmly bound to tubes than TiO₂(Deg) ones, which fell off easily and left a clean area on the tube surface. Very often, the hill-shaped deposits were found on the base of the tubes at the end of the experiments. By illuminating the bundle during the experiments using a laser extinction method, TiO₂(Deg) deposits were observed to get resuspended from the base after falling, whereas TiO₂(Nph) remained on the base. This indicate that TiO₂(Nph) particles are stickier and harder to remove from surfaces than the TiO₂(Deg) ones and that the deposits of the Deggusa powder are lighter and/or more loosely packed than the Nanophase ones.

FIG. 4 Deposits found. Left: TiO₂ (Nph) experiment, Right: SiO₂ experiment.

In the case of SiO₂ tests, deposits were found to be significantly different from TiO₂ ones. No hill-shaped deposits were found on the tubes in SiO₂ tests. Instead, an extensive clean region was found around a central small deposit of noticeable surface density but negligible thickness. The main aerosol deposits appeared downstream the clean areas and/or further away from the breach. Eventually some tiny deposits appear also at the base of the tubes.

Regarding the region further than the first neighbor tubes, Figure 5 presents the deposited mass on tubes for two different tests (1/4 of the bundle is shown). Deposition profiles were notably different, TiO₂ (Nph) (a) resulted in a deposition pattern with a sharp decrease where the neighbor tubes to the broken one have an important contribution to the total mass (2F deposit was found at the base), while SiO₂ ones (b) showed a milder decrease of the tube deposition with the distance to the break. This result is quantified in Table 2, where the fraction of mass retained in the 49 central tubes (i.e., 7 × 7 which means 40% of the 121 tubes) is presented. As shown, TiO₂ (Nph) retains higher amount of mass in the central tubes than the other types of powder, whereas TiO₂ (Deg) is the aerosol type that less fraction of the total mass retains in the central tubes. This might be due to the sloughing tendency of TiO₂ (Deg) powder when hill-shape deposits are formed close to the breach. SiO₂ aerosol shows higher fraction of the total mass retained in the central tubes than TiO₂ (Deg) but lower fraction than TiO₂ (Nph).

FIG. 5 Mass deposition profiles on the tubes near the broken one for different aerosol type tests. Left up: SiO₂. Right down: TiO₂ (Nph).

Two factors with opposite effects might contribute to this pattern. On one hand SiO₂ deposits showed clean regions on the tubes close to the breach which reduce the total fraction of mass retained on the closest tubes. On the other, SiO₂ particles probably have higher particle density than TiO₂ agglomerates, which are porous fractal-like particles. This fact contributes to increase the total fraction of mass retained in the central region. Regardless of deposition profiles, on-tube surface retention amounted to more than 80% of the total mass depleted; most of the remaining 20% was located on the base and it was eventually observed to come from total or partial detachments of tube deposits (sloughing).

This study provides insights into the effects of air flow on distributions of the aerosol deposits found (Velasco et al. 2008; López del Prá et al. 2008; Velasco et al. 2007; López del Prá et al. 2007; Sanchez-Velasco et al. 2006; Herranz et al. 2005) permitted to get insights into the distribution of the aerosol deposits found. The gas exiting the breach approached the adjacent tubes at high velocity and it lost much of its momentum in the perpendicular direction to the tube axis. The Coanda effect enhances the adhesion of the gas to tube surface when the jet impinges on the neighbor tubes to the broken one, so that the vertical component of the gas trajectory is reinforced. The combined action of both processes would have resulted in the final jet trajectory observed through the tubes deposits (Figure 4 (left)) as well as in the axial extension of the deposits in the wake of the tubes over the jet center trajectory line.

The jet generated from the breach impinges on the neighbor tubes at high velocity and it smashes particles against the tubes generating the hill-shaped deposits and/or the “spots” of noticeable surface density and negligible thickness. These “spots” would be related to compressed aerosol deposits that remained on tube at the center of the jet impinging region (i.e., in the stagnation zone) where the jet pressure on the tube surface is maximum. Around the stagnation zone, a wall-jet region appears where the flow diverges, re-accelerates and spreads around the tube surface. This region is covered by deposits of relatively high surface density indicating that the wall-jet region is very effective in depleting aerosol particles.

Figure 4 (left), shows the deposits found in tube facing the breach. In the upper part of the figure, it can be noticed a region where the wall-jet detaches from the surface and deposits disappear. This region is characterized by an enhancement of the surface roughness of the deposits that might be related to the transition of the wall-jet or inception of the tube wake and the subsequent increase of turbulence intensity and friction velocity in the area found in CFD simulations (Herranz et al. 2005).

In addition, Velasco et al. (2008) pointed that a gas vortex developed in the gap between the broken tube and the adjacent ones (Figure 4 (left)). These results support the above interpretation on aerosol deposition. The deposits found on the broken tube over the breach would have been mainly driven by the eddy and/or recirculation region effect.

The clean slot-type regions at both sides of the hill-shaped deposits (Figure 4 (left)) are located right where the jet touches the wall surface tangentially and the shear stress over the surface is maximum. Namely, the jet has a sweep effect on that region of the tube surface.

In the case of SiO₂ tests, the clean areas are considerably extended and cover practically the whole jet impinging region indicating that, at the flow conditions investigated, SiO₂ particles do not remain on the surface after impacting. Aerosol deposits appear downstream the jet impingement, in the wall-jet region where the flow surrounds the tube at lower velocity and disappears in the separation line where flow stream detaches and the tube wake incepts.

B. Influence of Matrix Variables

The experimental data obtained during the aerosol retention experiments were discussed in terms of mass retention efficiency of the bundle. This efficiency was studied and analyzed as a function of three primary variables: particle nature (agglomerates vs. solid spheres), Re_D and d_ae. Data from other programs carried out under similar conditions have been included to show a more complete picture of the scenario under analysis.

Figure 6 shows the bundle retention efficiency versus Re_D for the aerosol retention experiments. For comparison purposes, data from Herranz et al. (2006), which were based on TiO₂ (Nph) agglomerates, were also included (denoted as EU-SGTR). The figure shows that efficiency was strongly dependent on particle nature: SiO₂ particles were efficiently removed from the gas flow (retention efficiency ≥80%), whereas TiO₂ particles underwent substantially less net deposition (retention efficiency < 30%). In absolute terms, efficiency variation (η_max−η_min) was similar for both types of particles (around 15% in retention efficiency units). However, in relative terms the variation was different. SiO₂ variation represented hardly 16% of the mean efficiency value whereas TiO₂ variation represented around 50% of the mean efficiency value. In other words, TiO₂ particles were more sensitive to Re_D than SiO₂.

FIG. 6 Mass retention efficiency as a function of the Re_D.

In order to focus the analysis just on the Re_D effect, a “non-dimensional” efficiency has been defined for each particle type as:

where η_ref is a reference efficiency taken to be the asymptotic value of efficiency when Re_D tends to very high values for each type of particles, and Δ η_max is the maximum efficiency difference (i.e., η_max−η_ref). Figure 7 shows that behavior is similar regardless particle type: it increases up to a maximum value with Re_D (roughly located at Re_D = 1.06· 10⁵) and, then, it decreases monotonically.

FIG. 7 Nondimensional mass retention efficiency as a function of the Re_D.

Literature dealing with particle retention on tubes (Wessel et al. 1988; Ilias et al. 1989) usually correlates particle retention efficiency with Re_p. Thus, the dependence of on Re_D is somehow expected since Re_D is directly related with Re_p, through the formula: Re_D = D/d· Re_p. In the problem studied, Re_D is not only an indicator of turbulence in the aerosol flow but also a dimensionless expression of the gas mass flow rate expanding through the tube bundle. Thus, Re_D number encapsulates the gas flow regime characteristics, which are of outstanding importance for aerosol phenomena that could play a key role in the scenario, like turbulent deposition, inertial impaction, resuspension, etc. All that gas motion information is not within the non-dimensional Stk number. Therefore, the dependence of the non-dimensional mass retention efficiency with Re_D should be understood as an indicator of the importance of phenomena mentioned above in the scenario.

The evolution of the nondimensional mass retention efficiency with Re_D can be well correlated by a log-normal function,

where the parameters a₁, a₂, a₃ are known as the location, scale and the shape parameters, respectively. The parameter a₄ is a multiplicative factor and ψ is a parameter depending of the particle nature of the aerosol. The values proposed for this fitting are: a₁ = 71755, a₂ = 1, a₃ = 106666, a₄ = 3200000 and ψ ≅ 0 for TiO₂ or ψ = 77 for SiO₂. Thus, the TiO₂ and SiO₂ retention efficiency evolutions with the Re_D follow a lognormal behavior. Equation (2) obtaining r = 0.63 for TiO₂ and r = 0.71 for SiO₂, respectively (Figure 6):

The lognormal behavior of retention efficiency with Re_D is consistent with the reported decreasing trend by Herranz et al. (2006) as η ∝ Φ^–2 for Φ > 100 kg/h for TiO₂ particles (Equation (3), Figure 6):

In short, particle nature and Re_D affect the aerosol retention efficiency in the bundle. Nonetheless, whereas particle nature (i.e., agglomerates vs. solid spheres) practically determines the quantitative range of retention efficiency, the Re_D does not play such a key role. Then, retention efficiency of both particle types could be approximately described by the same equation, where ψ parameter sets the “baseline value” of retention efficiency and encapsulates most of particle nature influence. In other words, ψ will be presumably a function of particle properties like density, shape, size, charge, elasticity and/or fracture toughness. According to Equation (2), the relative importance of the two terms on the right side depends on the type of particles: ψ largely dominates for SiO₂ particles, whereas it does not represent an important contribution for TiO₂ agglomerates. The analysis of the aerosol particle charge measured at the outlet of the bundle with ELPI raises particle charge as a major candidate influencing ψ.

Figure 8 shows the bundle retention efficiency versus the inlet d_ae for the present aerosol retention experiments and EU-SGTR data presented in Figure 6. The vertical bars represent the experimental uncertainty in the retention efficiency of each experiment. The horizontal bars represent the GSD value of the inlet aerosol distribution measured in each experiment. Three main groups of data can be noticed in the figure. The first one consists of the present aerosol retention experiments performed with polydispersed TiO₂ agglomerates whose inlet d_ae ranged from 1.5 to 3.5 μ m. The second one is formed by the EU-SGTR experiments which were performed with polydispersed TiO₂ (Nph) agglomerates with inlet d_ae between 5 and 7.5 μ m. The third group is formed by the present aerosol retention experiments performed with monodispersed SiO₂ solid spheres of 1 μ m nominal diameter (d_ae around 1.4 μ m). The dispersion found in the inlet d_ae for SiO₂ tests fell within the uncertainty associated to the measurement of inlet aerodynamic median diameter. TiO₂ and SiO₂ data groups from the present aerosol retention experiments had similar inlet d_ae range whereas EU-SGTR data group had a different inlet d_ae range, with a bigger particle size. The d_ae range similarity between the TiO₂ and SiO₂ groups, again highlights that the source of such a difference in the retention efficiency is other than particle size: particle nature.

FIG. 8 Mass retention efficiency as a function inlet d_ae.

By comparing the TiO₂ data in the two size groups (i.e., 1.5–3.5 and 5–7.5), it may be noted that the bigger the agglomerate, the lower the retention. This could be related to the fact that large agglomerates are more loosely packed and, as a consequence, they are more easily fragmented. This tendency cannot be applied to SiO₂ particles since data are reduced to a narrow size interval that falls within uncertainty in the particle size measurement.

In short, particle nature has a prime importance for in-bundle retention. Re_D and particle aerodynamic size also affect retention efficiency, but their influence cannot be considered as important as the particle nature one. The relative effect of Re_D and particle aerodynamic size on retention efficiency results to be of similar importance.

C. Phenomena Involved

The presented aerosol retention experiments are of an integral nature. Measurements provide information on the net effect of a set of phenomena that are active in the scenario, but they do not allow quantitatively assessing the impact of each individual phenomenon. Nonetheless, from the integral data recorded some specifics can be discussed.

Herranz et al. (2007) indicated that according to their estimates inertial impaction and turbulent deposition should be the most effective retention mechanisms in the scenarios under study. Both phenomena depend on variables such as particle diameter, tube diameter and gas velocity. Such dependencies may be expressed in terms of nondimensional numbers like Stk, Sc, and Re_D. By taking Stk as a reference, two deposition regimes could be defined in the scenario (Fuchs 1964): one dominated by turbulent deposition (Stk ≤ 0.1) and another one governed by inertial impaction (Stk > 0.1).

In light of the results, inertial impaction would be responsible for the hill-shaped deposit on the adjacent tubes to the broken one (big particles striking the surface just in front of the breach) since the gas exiting the breach approached the adjacent tubes at high velocity. Turbulent deposition could also have removed effectively particles from the gas by turbulent diffusion and/or eddy deposition in the regions of high turbulent intensity, particularly on the tubes surface downstream the jet impingement, in the tube wakes and in the recirculating regions over the breach. All in all, these processes would enhance collection efficiency as particle velocity and, hence, Re_D increases. This would justify the increasing tendency of with Re_D below Re_D = 1.06 · 10⁵.

As previously discussed, in case of TiO₂ agglomerates, retention efficiency was found to decrease when inlet d_ae increased. This tendency is opposite to what it is expected from inertial impaction and/or turbulent deposition processes that increase their collection efficiency with d_ae, with particle velocity and, in general terms, with Stk (Herranz et al. 2007). This suggests that other phenomena inhibiting net deposition like particle fragmentation, bouncing, resuspension, and/or erosion could play a role in the scenario.

Fragmentation was found to be one of these mechanisms. Fragmentation of agglomerates across the tube bank can be mainly driven by the high shear stresses in the flow and/or by particle-surface collision. These processes would break up agglomerates into smaller particles, which would be less efficiently collected on tube surfaces (Fuchs 1964). As big agglomerates would be more likely fragmented than small ones by the previous named driving causes, their retention efficiency would consequently be lower. Namely, size of particles approaching tube surface would have been likely smaller than the measured one upstream the breach in the case of aggregates; this effect should have been more noticeable for large agglomerates.

As the jet moves across the tube bundle, aerosol size distribution shifts towards small sizes. In most of TiO₂ experiments outlet size distributions showed a higher mass fraction at the smallest size bins, which highlights the splitting of bigger particles (Figure 9). This observation was already noted by Herranz et al. (2006) in the EU-SGTR tests.

FIG. 9 Inlet/outlet aerosol size distribution for T-02.

In the surroundings of the breach, pressure gradients, shear stress and particle kinetic energy reach maximum values. As a consequence flow-particle and particle-tube interactions are strong and agglomerate fragmentation would be enhanced in this region. Figure 10 shows the d_ae inlet/outlet ratio for present aerosol retention experiments and EU-SGTR experiments as a function of the jet pressure jump at the breach:

Even though the low r value indicates that other mechanisms than pressure jump must likely affect particle fragmentation, the data suggest a rough correlation between the fragmentation of the particles and the flow expansion at the breach (Equation [4]). Note that, as pressure gradient and Re_D follow a linear relationship, the figure also illustrates a correlation between fragmentation and particle kinetic energy. These observations are consistent with those made by Brandt et al. (1987) and by Froeschke et al. (2003).

FIG. 10 Inlet/outlet d_ae vs pressure jump at the breach for TiO₂ agglomerates.

Fragmentation was not observed for SiO₂ particles. Again, this difference highlights the importance of particle nature on retention efficiency, but also it points other factors may also inhibit the deposition of SiO₂ particles. Bouncing and/or resuspension of deposited particles in the tube bundle are highly likely phenomena under velocities and turbulent intensities that existed during the tests.

The Ma numbers reached during the experiments (from less than 0.3 up to 0.9) resulted in high particle velocity that may exceed a critical value over which particles are observed to rebound. Wang and John (1988) and Aylor and Ferrandino (1985) experimentally showed that the sticking probability dropped from 1 to less than 0.1 when the particle velocity is increased by a factor of 3 over the critical one. This behavior has been theoretically supported by Rosner et al. (1995) and by Konstandopoulos (2006), who proposed an exponential and a potential law, respectively, for such decay in the sticking probability. In short, this would mean that over a critical Re_D, the higher Re_D the lower retention efficiency.

High gas velocities resulted in high on-tube wall shear stress fields and turbulence levels that according to Blackwelder and Haritonidis (1983) could have been capable of fostering local instabilities (i.e., turbulent burst or sweeping eddies) in the boundary layers developed over tube surfaces. Both phenomena enhance drag and lift forces acting on the deposited particles that may eventually detach particles from the substrate underneath. Then, it should be expected that once drag and lift forces overcome adhesion forces, particle resuspension may start; that is, once a certain Re_D threshold is reached, resuspension would also support the trend stated above from the bouncing analysis: the higher Re_D the lower retention efficiency.

Therefore, even though as said above the integral nature of the experiments did not allow specific measurements of resuspension and/or bouncing, there is evidence consistent with the fact that these phenomena, or at least one of them, could play a role in the scenarios under investigation. A validation of this statement should be experimentally pursued.

V. CONCLUSIONS AND FINAL REMARKS

A bench-scale experimental program has been carried out to investigate the retention capability of a tube bundle when the particle laden jet expands through it from a tube breach. The influence of particle nature in the bundle retention has been studied using the Re_D as parameter. Two different types of polydispersed TiO₂ agglomerates as well as monodispersed SiO₂ solid spheres were used as aerosols. By characterizing aerosol mass size distribution entering and leaving the bundle and the on-tube retained mass, the mass retention efficiency of the bundle was obtained for each type of aerosol.

This research demonstrates that even under conditions that are least likely to lead to deposition in a tube bundle (i.e., high Re_D and weakly bonded aggregates), significant particle deposition occurs on the external surfaces of tubes that are in close vicinity a tube breach. Retention is mainly caused by inertial impaction and turbulent deposition. Nevertheless, the potential retention efficiency of the tube bundle gets reduced due to the action of other phenomena which inhibit deposition, like fragmentation. Additionally, the results highlighted other significant specifics:

• Particle nature substantially affects aerosol retention and it determines the order of magnitude of the retention in the tube bundle. Mass retention was found to be low for TiO₂ agglomerates (less than 30%) whereas it was much higher for SiO₂ solid spheres (around 85%).

• Radial and axial deposits distribution in the bundle was shown to be different depending on the type of aerosol. Mass surface-density distribution in the closest tubes to the break showed different pattern even for the same compound used (TiO₂) obtained from different manufacturers.

• Inlet Re_D influences the retention efficiency of the tube bundle. However, the magnitude of its influence is particle nature dependent.

• The retention efficiency sensitivity to Re_D follows a lognormal behavior. The maximum retention is attained near Re_D = 1.06· 10⁵. This evolution with Re_D was similar for both types of compounds.

• Particle size also influences retention efficiency: the bigger the TiO₂ agglomerates the lower retention efficiency (no data were available for SiO₂).

• The effect of Re_D and particle aerodynamic diameter on retention efficiency can be considered secondary with respect to particle nature that practically determines the quantitative range of retention efficiency. The relative effect of the former two variables results to be of similar importance.

• The influence of particle nature on the retention efficiency evolution with Re_D can be accomplished by an “offset” or “particle nature parameter.” Results show that this parameter can be high enough to influence drastically retention efficiency.

Observations show that large TiO₂ agglomerates (d_ae ^inlet≈ 7 μ m) are deposited less efficiently than small ones (d_ae ^inlet≈ 2 μ m). This is because the large particles undergo fragmentation due to processes such as flow shear and impaction, leading to small secondary particles that are less likely to be collected.

Finally, experimental evidence suggests that inhibiting retention phenomena such as resuspension, erosion and/or bouncing might be present in the scenario become determinant when Re_D surpasses a certain level. Future research programs should focus specifically on characterizing the influence of these phenomena on the retention efficiency.

The authors wish to thank the Spanish Nuclear Safety Council for the financial support of this research and the Paul Scherrer Institut (Switzerland) scientist of ARTIST project for the fruitful technical discussions.

Notes

^a δ # represents the uncertainty associated to a variable # and estimated following the procedure of ISO Norm (1995).