Effects of the Turbulent-to-Laminar Transition in Monolithic Reactors

ARTICLE pubs.acs.org/IECR

Effects of the Turbulent-to-Laminar Transition in Monolithic Reactors for Automotive Pollution Control Henrik Str€om,*,†,‡ Srdjan Sasic,§ and Bengt Andersson†,‡ †

Competence Centre for Catalysis, ‡Department of Chemical Reaction Engineering, and §Department of Applied Mechanics, Chalmers University of Technology, G€oteborg, SE-412 96, Sweden ABSTRACT: In the current work a detailed study is performed of the turbulent-to-laminar transition at the inlet of an automotive monolithic reactor. The effects of the transition on the conversion of gaseous species and on the deposition of particulate matter are investigated using numerical simulations. Two main effects of the turbulence on the conversion in the monolith have been identified: slow fluctuations due to turbulent eddies that are too large to enter the channels and rapid fluctuations due to smaller turbulent eddies that penetrate the channels. It is also shown that inertial particles may deposit inside the monolith channels, providing a likely explanation of the experimentally observed spatial deposition profiles of elements that chemically deactivate automotive catalysts.

’ INTRODUCTION Monolithic honeycomb reactors are the standard substrate for automotive catalysts of today. In diesel emission control, both oxidation and reduction catalysts, as well as NOx traps and particulate filters, are typically manufactured from ceramic monolithic substrates. These reactors are also used in other related emission control applications, e.g., gasoline applications and stationary applications. The popular ceramic monolithic reactor typically consists of many small parallel channels of square cross section, as illustrated in Figure 1. The active catalytic material is deposited on the walls inside the channels, and the device is operated within the laminar flow regime. The pollutants, which can be either gaseous or solid particles, must therefore diffuse to the wall inside the channels before the reactions can occur. Since the flow upstream and downstream the monolith is turbulent, there is a transition from turbulent to laminar flow in the first section of the monolith, along with the development of the laminar flow profile. These inlet effects are generally considered to be critical to the modeling of the reactor performance, but at the same time too complex to deal with, so they are usually neglected.1,2 It is often suggested that turbulent inlet effects enhance the performance of the monolithic reactor,3-6 since the heat transfer and mass transfer are significantly enhanced by deviations from a laminar flow profile. Consequently, it has also been shown that the first half of a monolithic reactor has more favorable conditions for pollutant conversion than the second half .7 Taking this into consideration, segmented monolith designs have been suggested, in which the monolith is cut into several smaller sections.8,9 The repeated inlet effects have been shown to enhance the performance of such systems. It has however not been investigated to what extent these effects are due to the developing laminar flow profile or to the turbulent-to-laminar transition. We also believe that the turbulence in front of the catalyst may be involved in augmenting the deposition of soot and ash particles toward the front of an automotive monolithic reactor during vehicle operation. In order to illustrate this phenomenon, r 2011 American Chemical Society

we acquired a used automotive catalyst and had it photographed from the front and the back, as shown in Figure 2. We also took close-up pictures of four channel entries and exits using scanning electron microscopy (SEM). As shown in Figure 3, the difference in the appearance of the front and back of an aged automotive catalyst is very distinct. This form of particulate matter deposition may be both an advantage (due to an increased removal of soot from the exhaust) or a disadvantage (since it might contribute to the aging of the catalyst). Jobson et al. and Angelides et al. observed experimentally a more pronounced chemical deactivation toward the front of aged automotive catalysts.10,11 So did Ekstr€om, who also suggested that contaminants are transported to the entrance region due to (turbulent) flow effects.3 Rokosz et al. found strong concentration gradients of phosphate contaminants from the front to the back in aged catalysts.12 Elements that originate from the lubricating oil (e.g., phosphorus and zinc) or from the engine and exhaust system construction material (e.g., iron, copper, nickel, and chromium)11 are necessarily transported to the catalyst via the exhaust gas flow. One could therefore speculate that any gradients in their axial distribution could be linked to flow effects and possibly the turbulent-to-laminar transition. In an energy-dispersive X-ray spectroscopy (EDX) measurement on the aged catalyst depicted in Figures 2 and 3, we also found an axial gradient of the iron content, as shown in Figure 4. This result is characteristic for contaminant deposition11 in the sense that the elementary content is highest near the inlet section and then drops significantly in the first part of the channel, but that it remains nonzero throughout the entire monolith brick. In summary, the investigation and understanding of the turbulent inlet effects are thus related to both the optimization of the performance of an automotive catalyst and to its aging control and robustness. Received: November 12, 2010 Accepted: January 27, 2011 Revised: January 17, 2011 Published: February 23, 2011 3194

dx.doi.org/10.1021/ie102291t | Ind. Eng. Chem. Res. 2011, 50, 3194–3205

Industrial & Engineering Chemistry Research

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Figure 1. Typical monolithic reactor (catalyst) for automotive pollution control. The ceramic cylindrical brick contains thousands of parallel channels of square cross section. The walls inside the channels are catalytically active for the conversion of pollutants into less harmful substances.

It is the purpose of this work to investigate the effects of the turbulent-to-laminar transition on pollutant conversion and particle deposition by means of numerical simulations. The investigation is done by solving for the actual flow field using a large eddy simulation (LES) and by estimating the conversion of a number of common pollutants under the assumption that the conversion is mass transfer limited (i.e., that the ratio of the wall concentration to the average radial concentration of a reactant species is less than 0.03).13 Although the effects of soot particle dispersion in a diffuser upstream a monolithic reactor have been investigated before,14,15 this is—to our knowledge—the first attempt of an in-depth study of turbulent-to-laminar transition effects at the inlet of a monolithic reactor. In the current work, we assume that the monolith is placed in an exhaust pipe of the same diameter. In other words, we neglect any additional large-scale turbulent structures upstream the reactor arising from the typical enlargement of the exhaust pipe to fit a monolith of larger diameter. These structures have been the focus of earlier studies,14-16 and the influence of this assumption is discussed in detail later in this paper. In the section Mathematical Formulation, we present the mathematical formulation of the problem. First, we give the equations for the different types of species that we are going to investigate. We then give the equations for the gas flow field, introduce the computational domain, and discuss the inlet boundary conditions. In order to quantitatively relate the outlet concentration signals from the numerical simulations to the turbulent characteristics of the system, we will make use of two methods of signal analysis: spectral estimation and the analysis employing wavelets. We then present the results of the current work and provide a thorough discussion under Results and Discussion. The paper ends with a summary of the conclusions.

Figure 2. Front (above) and back (below) of an aged commercial automotive catalyst. The channel entries look considerably different from the inlet view; some of them are blocked and the open inlet area of each channel has been reduced. It is speculated that an increased deposition of particulate matter due to turbulent effects in the first part of the catalyst is a conceivable reason.

transfer phenomena in automotive exhaust applications. The species are described as follows: 1. Species A is a gaseous component with a diffusivity equal to that of carbon monoxide (CO) at 300 C (DA = 6.91 10-5 m2 s-1). 2. Species B is a passive scalar with a diffusivity equal to the Brownian diffusivity of 150 nm diameter diesel soot particles at 300 C (DB = 7.53 10-10 m2 s-1). 3. Species C is Lagrangian point particles representing 1 μm diameter diesel soot particles (Fp = 1000 kg m-3). For species A and B, the motion will be almost entirely determined by diffusion.17,18 Therefore, their deposition efficiency may be obtained by solving a species transport equation:19 ∂yi þ ur 3 yi ¼ Di r2 yi ∂t

’ MATHEMATICAL FORMULATION Species. We investigate the conversion/deposition of three

different types of species, labeled A, B, and C. Together, these species span the entire scale of interest when it comes to mass

ð1Þ

with i = A or B. Here, yi is the mass fraction of species i, u is the velocity field of the gas phase, and Di is the diffusivity of species i. 3195

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Figure 3. Close-up scanning electron microscope (SEM) pictures of the inlet (left) and outlet (right) sides of the aged commercial automotive catalyst depicted in Figure 2.

The boundary condition at all walls is that the mass fraction is equal to zero. For species C, inertial mechanisms will dominate the particle motion.17,18 The deposition efficiency is therefore determined by tracking a large number of point particles for which the particle equation of motion is taken as dup 18μ ¼ ðu - up Þ Fp dp Cc dt

ð2Þ

where up is the particle velocity, μ and u are the viscosity and the velocity of the continuous phase, and Fp and dp are the particle density and diameter. Cc is the Cunningham correction factor20 that takes into account the decrease in momentum transfer due to rarefaction effects. The particles are assumed to deposit upon contact with the wall. Gas Phase Flow Field. The gas phase is solved for using a large eddy simulation (LES) technique with the subgrid scales modeled using the dynamic Smagorinsky-Lilly subgrid model.21,22 The particular implementation used in the current work is that of Kim.23 The filtered incompressible Navier-Stokes equations for the resolved field are ∂ui ¼0 ∂xi ∂ui ∂ðui uj Þ 1 ∂p ∂ ∂ui þ ¼þ ½ν þ νt F ∂xi ∂xj ∂t ∂xj ∂xj

ð3Þ ! ð4Þ

The overbars in eqs 3 and 4 denote filtered variables; u is the velocity and p is the pressure. F is the continuous phase density, and ν is the kinetic viscosity. The subgrid scale turbulent viscosity is νt. The exhaust gas physical properties are approximated to those of air at 300 C. The computational domain is illustrated in Figure 5. The channel hydraulic diameter, D, is 2 mm and the length, L, is 60 mm. The length is chosen so that the laminar flow profile is fully developed at the channel outlet.24 The wall thickness, w, is 0.15 mm. With this choice of computational domain, the monolith channel dimensions resemble those of a low cell density diesel oxidation catalyst or a typical substrate used for diesel particulate filters (although without any plugged channel entries). The mean velocity over the channel inlet is 10 m s-1.

Figure 4. Axial profile of the elementary iron (Fe) content on the washcoat of the aged commercial automotive catalyst depicted in Figure 2, obtained using energy-dispersive X-ray spectroscopy (EDX).

The boundary conditions are constant (atmospheric) pressure at the channel outlets, a specified velocity at the inlet, and symmetry on all planes in the longitudinal direction. The noslip boundary condition is used at all walls. The near-wall mesh spacing is fine enough to allow the flow to be resolved without the use of wall functions. In addition, the dynamic subgrid-scale model used for the subgrid turbulence has the correct asymptotic behavior in the near-wall region, so no ad hoc function (e.g., dampening) is needed.21 To be able to investigate the effects on the deposition of particles due to a layer of already deposited particles (cf. the inlets in Figure 3), a second computational domain is generated in which the frontal walls of the monolith are extended. A cylinder of diameter 3w was placed around each frontal wall, creating a rounded extension of the frontal walls and thus a decrease in the open frontal area. The appearance of this second geometry, referred to as geometry II in the present work, is illustrated in Figure 6. Inlet Boundary Conditions. The inlet boundary conditions are synthesized according to the method proposed by Smirnov et al.25 Since this method creates velocity fluctuations that satisfy continuity but not necessarily the Navier-Stokes equations, the inlet boundary has to be placed a certain distance upstream the region of interest (i.e., the real channel inlet). In the current work, the inlet boundary is placed 20 mm upstream the monolith (cf. l in Figure 5). 3196



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Figure 5. Outline of the computational domain. The domain contains 3 3 whole channels, 12 half channels and 4 quarter channels. All results presented in the present work are taken from the channel in the middle. The mesh contains almost 4 million hexahedral cells and is refined near the inner walls.

Figure 6. Original geometry I (top) and geometry II with rounded extensions on the frontal walls (bottom). Geometry II represents a monolith where a significant buildup of deposits at the inlet has already occurred (cf. Figure 3).

Table 1. Conditions Upstream the Monolith in the Numerical Simulationsa parameter

The flow upstream an automotive monolithic reactor is typically fully turbulent. The values for the input parameters to the inlet velocity boundary condition (the turbulent kinetic energy, k, and the turbulent dissipation rate, ε) are therefore taken from the core of a fully developed turbulent duct flow. These can be estimated from26 k¼

3 ð0:16umean Re-1=8 Þ2 2

ð5Þ

and ε ¼ 2:3471

3=2

k Dpipe

a

ð6Þ

Here, umean is the mean velocity of the turbulent flow upstream the monolith, Dpipe is the diameter of the pipe upstream the monolith, and Re is the Reynolds number based on umean and Dpipe. An exhaust pipe diameter and a mean gas flow velocity are therefore needed to obtain the inlet values of k and ε. The upstream conditions used in the current work are listed in Table 1. Also included in the table are the corresponding size (l ) and lifetime (τ) of the energy-containing turbulent eddies and of the Kolmogorov eddies (l K and τK). Since the particle response time for species C is only 2.6 μs, it is to be expected that the particle motion is affected by all the scales of turbulent motion of the continuous phase. It should be noted here that the quantitative results from the current work most probably will be influenced by the choice of turbulent inlet conditions, and that the actual turbulence characteristics in a real application are a complex function of the geometry and operating conditions. Most notably, the presence of large-scale structures generated by an upstream diffuser (not taken into account in the current work) could cause clustering of inertial particles.15 A detailed discussion about the influence of the values of k and ε chosen in the current work is therefore presented after the results.

variable

value

pipe diameter

Dpipe

10 cm

mean velocity pipe Reynolds number

umean Re

50 m s-1 105 800

turbulent kinetic energy

k

5.32 m2 s-2

turbulent dissipation rate

ε

288 m2 s-3

turbulent length scale

l

6.7 mm

turbulent time scale

τ

5.5 ms

Kolmogorov length scale

lK

0.14 mm

Kolmogorov time scale

τK

0.41 ms

It is assumed that this flow is fully developed turbulent pipe flow.

The mesh cell size is 0.2 mm or smaller, which means that each energy-containing eddy is resolved with at least 33 cells per diameter and that the Kolmogorov eddies are approximately 30% smaller than the largest cells. Another way to quantify the resolution of a large eddy simulation is to monitor the subgrid turbulent-to-laminar viscosity ratio (νt/ν). In the simulations presented here, this viscosity ratio is on average the order of 10-3 and at its highest is around 2.3. The turbulent flow field is thus very well resolved. However, since the particles respond to all the different scales of turbulence, a subgrid-scale model is still included to account for the effects of the unresolved on the resolved scales. The grid resolution at the domain inlet is fine enough to allow the synthesized inlet turbulence to be resolved. In this way, we secure that the resolved inlet turbulence is not dissipated before the flow reaches the monolith inlet. Signal Analysis. One of the aims with the numerical simulations is to obtain signals of the outlet concentration of species A and B. We will analyze these signals in order to quantitatively relate them to the turbulence in the system. We will therefore briefly discuss here two methods for signal processing that we will use in this work: spectral estimation and wavelet analysis. Spectral Estimation. Spectral analysis is a technique by which the distribution of the power of a signal over frequency may be 3197



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obtained. We will use here the method proposed by Welch, where the variance of the estimation is reduced by calculating the power spectra as an average of several subspectra.27 The number of subspectra is chosen to obtain a satisfactory trade-off between frequency resolution and variance. Therefore, the signal treated is divided into time segments and an estimate of the power spectrum of each segment is obtained. The averaged power spectrum becomes N

∑

1 Pi ð f Þ Pxx ð f Þ ¼ N i ¼ 1 xx

ð7Þ

where N is the number of segments and Pixx( f ) is the power spectral estimate of each segment. An important feature of the spectral analysis is that the energy of the signal is conserved in the frequency domain. Hence, summation of the power spectra over the range of interest yields the total energy of the signal in a given frequency range. Wavelets. The introduction of wavelets originates from the interest of dealing with possible time-varying properties of signals. Wavelet transform techniques are nowadays extensively used in many fields of research: in signal processing and denoising,28 in fractal analysis,29 in fluid mechanics for the identification of coherent structures in turbulent flows,30 in image coding,31 etc. The wavelet transform can be regarded as a mathematical “microscope”32 that is able to examine different parts of the time series by adjusting the focus of the “microscope”. As this method has not been widely used within the field of automotive catalysis, we will devote additional attention to its background. The continuous wavelet transformation is defined33 as the inner product of the analyzed signal f(t) and the timeshifted and scaled version of a wavelet function ψ: Z 1 t-b dt ð8Þ CWf ða, bÞ ¼ Æ f , ψa, b æ ¼ 1=2 f ðtÞψ a |a| ψ (the asterisk implies a complex conjugate value) in eq 8 is called the mother wavelet, and a and b are the dilation (scaling) and translation (location) parameters, respectively. The factor 1/|a|1/2 is a normalization factor. The transform allows for localization both in the time domain (via translations of the wavelet) and in the frequency domain (via dilatations of the wavelet). An important feature of the signal representation plane is that the uncertainties in the determination of time and frequency are not constant over the plane, but their product is. This means that the uncertainties (say Δti and Δfi), which localize a certain event in the time-frequency plane, cannot be made arbitrarily small at the same time. Toward high frequencies the time resolution improves at the expense of the frequency determination, whereas toward low frequencies the situation is the opposite. To reduce computational cost, while maintaining the same degree of output information, the dilatation parameter (a) and the location parameter (b) in eq 8 are discretized. The procedure leads to a discrete wavelet transform, and by choosing the special case when the discretizations are proportional to each other (a = m am 0 ; b = nb0a0 ), the following expression is obtained: DWf ðm, nÞ ¼ Æ f , ψm, n æ Z 1 f ðtÞψða-m ¼ 0 t - nb0 Þ dt |a0 |1=2

ð9Þ

Table 2. Conversion/Deposition Efficiencies from Theoretical Predictions (eq 11) and Averaged Results from the LES species A B C

correlation (eq 11) (%)

numerical simulations (%)

81

75

0.22 0.036

0.050 5.1

Daubechies has shown that, for a0 = 2 and b0 = 1, an orthonormal family of functions (the condition imposed with the aim of minimizing the number of wavelet coefficients) may be constructed and that such a representation provides a multiresolution framework for analysis of phenomena present in a time series.34 In practice, the discrete wavelet transform is a pair of digital filters, which decompose a signal into a low-frequency component a1 (called the approximation) and a high-frequency part d1 (called the detail). In the next step, the approximation a1 is used as an input, and by performing this operation recursively up to a level k, a hierarchical representation of the signal is obtained: k

f ðtÞ ¼

∑ di þ ak i¼1

ð10Þ

The detail di contains frequency information in the band [ fs/2jþ1,fs/2j], where fs is the sampling frequency and j is an integer. Finally, the original signal can be reconstructed from wavelet coefficients by the inverse wavelet transform without losing information.33

’ RESULTS AND DISCUSSION Theoretical Predictions. First, we establish the expected deposition efficiency of the three species in the case where the flow is fully laminar throughout the channel. The deposition efficiency E of a diffusing species in a square monolithic channel may be estimated from 4ðShÞDi L ð11Þ E ¼ 1 - exp - 2 D umean

Here, we make use of the notation as defined previously, and employ the Sherwood correlation from Hawthorn for a square duct:35 D 0:45 Sh ¼ 2:98 1 þ 0:095ðReÞðScÞ ð12Þ L where Sc is the Schmidt number, defined as Sc = ν/Di. In the case of a standard monolith with straight channels, the only mechanism transporting particles toward the walls is molecular diffusion. It is therefore possible to use the above analysis to determine the laminar trapping efficiency of all three species. Before we discuss in detail the results of the numerical simulations, we wish to compare the overall conversion/deposition efficiencies to the theoretical predictions for laminar flow. The comparison between mean conversion/deposition efficiencies from the LES and the theoretical expression (eq 11) is shown in Table 2. For species A and B, the theoretical predictions are fair but tend to overestimate the conversion efficiency. This is expected, since the Hawthorn correlation (eq 12) is empirically adjusted to account for wall roughness, which is not present in 3198



Figure 7. Outlet concentration signal of species A from the middle channel in geometry I.

the current simulations. We thus use it here only to provide a reasonable approximation of the expected efficiencies. For species C, the majority of the trapped particles deposit on the frontal walls of the monolith because of their inertia (this is discussed in more detail in a later section of the paper). Since this mechanism for deposition is not taken into account in the theoretical model, it is not captured and the prediction from (eq 11) substantially underestimates the trapping efficiency. Numerical Simulations. Species A and B. The large eddy simulations are performed both with and without turbulent velocity fluctuations at the inlet of the computational domain. In this way it becomes possible to separate the effects of the development of the laminar velocity profile from those of the turbulent fluctuations. The time-averaged outlet concentrations for species A and B with turbulent effects taken into account are identical to those without turbulence taken into account. This result therefore does not suggest that turbulent inlet effects have a significant impact on the time-averaged outlet concentration of gaseous pollutants or the overall deposition efficiency of intermediate-sized particulate matter. However, it turns out that turbulence does have an effect on the observed transient behavior. Figure 7 shows a part of the mixed-cup outlet concentration signal of species A from the middle channel in geometry I. Similar results are found for species B, with the exception that almost all species B passes through the monolith without depositing (cf. Table 2). The turbulent fluctuations cause variations in the mass-flow rate through the channel and, therefore, also variations in the retention time for the fluid elements inside the channel. These variations in retention time translate into variations in the conversion of pollutants. We propose that the fluctuations observed in the outlet concentration of species A could be explained by a combination of two mechanisms. These mechanisms are depicted schematically in Figure 8. We suggest here that a part of the fluctuations can be attributed to the effects of the large energy-containing eddies in front of the monolith. Since these eddies are of a scale l that is larger than the channel diameter D, they will act to transiently divert the flow into the channel in changing directions as shown in the top half of Figure 8. The other part of the fluctuations would then be occurring on a time scale shorter than the lifetime of the largest turbulent eddies in front of the monolith. We therefore suggest that their cause can be traced to the turbulent eddies of a size

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Figure 8. Two conceivable mechanisms for turbulent inlet effects in monolithic reactors. (top) A large turbulent eddy affects the inlet conditions to the channel on a time scale related to the lifetime of the eddies of this size. (bottom) A smaller turbulent eddy penetrates the channel and affects the heat, mass, and momentum transfer characteristics of the flow in the channel on a time scale related to the lifetime of the eddies of this size.

small enough to allow them to penetrate the monolith channels (cf. bottom half of Figure 8). A snapshot of the velocity field obtained by the simulations and supporting the ideas about the mechanisms illustrated in Figure 8 is shown in Figure 9. In order to test the hypothesis presented here, we decompose and analyze the signal of the timevarying outlet concentration of species A, first in the frequency domain and then also in the time-frequency domain. Signal Analysis. The power spectral density diagram obtained with the Welch method is shown in Figure 10 in both linear scale and logarithmic scale. In the linear scale, it is straightforward to discern two distinct peaks: one at approximately 200 Hz (corresponding to τ) and one at approximately 800 Hz (corresponding to 1.2 ms). In the logarithmic scale, it is also evident that there is a group of smaller peaks around 2000 Hz. Since τK corresponds to approximately 2400 Hz, the power spectral density diagram supports the mechanisms proposed in Figure 8. That the peaks in the power spectral density appear in the interval 200-2400 Hz means that the events governing the fluctuations of the outlet concentration of species A are happening on the same time scales as the turbulent fluctuations present in the system. Moreover, that the main peak corresponds to 1.2 ms indicates either that the dominating frequency is an effect of the spatial scales of sizes smaller than the hydraulic channel diameter, or that it originates from an interaction among different scales during the transition to laminar flow. The scale imposed by the channel size itself corresponds to approximately 400 Hz. To obtain a more comprehensive overview of the time resolution of the energy distribution among the frequencies, a wavelet analysis is carried out. Since we know from the spectral analysis at what frequencies the phenomena of interest occur, we choose nine levels of details in order to obtain the appropriate frequency bands. The wavelet used is the Daubechies wavelet number 5. Figure 11 shows the signal and the five details that correspond to the frequency range of interest (see Table 3). In Figure 12, the same signal is shown with a detail coefficient plot. In this plot, a darker color represents a higher energy, and it is thus possible to obtain information about the distribution of energy among the nine levels (details) as a function of time. Below level 5 (see Table 3) there is no significant energy at all times. The energetic events on the two highest levels correspond 3199



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Figure 9. Snapshot of velocity vectors from the simulations that support the idea of the mechanisms suggested in Figure 8. (left) Large-scale motion upstream the catalyst changes the flow direction into the channels with time. (right) Inspection of the velocity vectors in a plane perpendicular to the main flow direction 5 mm into the middle channel reveals flow rotation that is not present in the laminar case.

Figure 10. Power spectral density of the signal (outlet concentration of species A from geometry I) in linear scale (left) and logarithmic scale (right).

to the largest turbulent scales, and the intermediate range (levels 6 and 7, cf. Table 3) seems to contain the most energy in a timeaveraged perspective. All of this is in agreement with the observations from the power spectral density curve. Species C. If 1 μm particles (species C) are transported through a monolith channel where there are no turbulent effects, the deposition should be virtually nonexistent as shown by the laminar prediction in Table 2. The most interesting aspect of the turbulent inlet effects on the motion and deposition of large particles would therefore be if there existed a marked increase in the deposition, especially in the front part of the channel (cf. Figure 3). The results from the large eddy simulations show that the deposition of larger particles inside the channels is indeed small. In fact, no particles are trapped inside the channel further than a few millimeters from the inlet, and only a small fraction of the particles is trapped inside the channels at all. This supports the idea that the limited number of 1 μm particles that reach the wall inside the channel do so with the aid of turbulence. Of the total number of 1 μm particles venturing toward the middle channel, approximately 5% are trapped at the monolith front. The deposition on the frontal wall is not entirely a turbulent effect, though, as this type of inertial impaction also occurs in the laminar flow regime. Johnson and Kittelson estimated the 50% cut size for impaction on the front of a diesel oxidation catalyst (the 50% cut size is the particle size for which 50% deposition of the incoming particles is obtained).17 They

did this for a wall thickness of 0.15 mm, a gas velocity of 58 m s-1, and an open frontal area of 69% of the total cross-sectional area of the monolith. They found that, under these conditions, 50% of the particles of diameter 0.5 μm that approach the monolith in the volume swept by the frontal channel walls would deposit there. In the current problem formulation, their estimation would correspond to a trapping efficiency of 6.7% for 0.5 μm particles. This is indeed similar to the actual results for the trapping efficiency of the 1 μm particles investigated here. We thus conclude that the deposition of particles on the frontal walls is a process mostly governed by the particle inertia (i.e., size), the wall thickness, and the upstream velocity. It is not likely that this process is very much influenced by turbulence. It is however probable that turbulence is the mechanism responsible for the mildly augmented deposition in the near-inlet section inside the channels. Geometry II. In geometry I, less than 1% of the particles end up a few millimeters into the channel. However, when the deposition of species C is investigated for geometry II, the situation is different. The total trapping of particles is about 40% higher in geometry II, and the spatial distribution of the trapped particles has changed so that the additionally trapped particles are found inside the channel. Moreover, these particles are now not only found a few millimeters from the channel inlet, but also throughout the entire channel in the axial direction. The deposition of species C in geometry II is shown in Figure 13. 3200



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Table 3. Exact Frequency Intervals for the Nine Levels of the Wavelet Analysis level

Figure 11. Signal (s) and details (di) 9 through 5. The details correspond to the frequency bands given in Table 3. On the y-axis is the signal level [%] and on the x-axis is time [number of time steps].

In order to establish the explicit influence of the turbulent-tolaminar transition effects, we have also performed a simulation of the deposition of species C in geometry II without any turbulent fluctuations. There are two main observations to be made from the comparison of the results obtained with and without turbulence. The first one is that the total deposition of particles is 24% higher in the absence of turbulent fluctuations. This increase in the deposition is most pronounced on the extended frontal walls. The second observation is that the distribution of the particles that deposit inside the channel is different, as shown in Figure 14. In the absence of turbulence, the particles end up on the frontal walls and inside the channel at a certain distance behind the bulges of the frontal walls. However, when there are turbulent fluctuations present in the flow that enters the channel, the distribution of particles along the axial direction of the channel is much more even (cf. Figure 13). In geometry II, the open frontal area of the monolith has been reduced by 28% compared to geometry I, which causes the increase in deposition on the frontal walls in the laminar case. In addition, the fluid elements closest to the bulges at the inlet contain no particles, as these have already deposited on the front. Any additional deposition thus has to come from the fluid that still contains particles, when the former is brought close to the wall as the geometry expands. This explains the minima just after the inlet seen in Figures 13 and 14. When the approaching flow is turbulent, a part of the particles contained in the fluid passing closest to the frontal walls will be ejected by the turbulence before the particles arrive at the wall to deposit. Since the turbulent fluctuations normal to the monolith walls are more dampened compared to the ones in the parallel directions, the probability that particles are re-entrained into the

frequency interval [Hz]

9

98-195

8 7

195-391 391-781

6

781-1562

5

1562-3125

4

3125-6250

3

6 250-12 500

2

12 500-25 000

1

25 000-50 000

fluid elements heading toward the frontal walls in the strictly wall-normal direction is lower. As a result, the enhanced deposition on the extended frontal walls is not as pronounced as in the laminar case. Note that this also means that there must be an increase in the concentration of particles in the near-wall region at the channel inlet when there are turbulent fluctuations present. Furthermore, when a large turbulent eddy upstream the monolith changes the overall direction of the flow into the channels, the bulges on the frontal walls will assist in creating a recirculation flow on the low-speed side and a jet of particle-laden gas on the high-speed side. These high-speed streaks will continuously change direction as dictated by the upstream turbulence. Since the secondary flow pattern observed in turbulent flow in square ducts is enhanced by axial acceleration,36 one may also expect increased radial mixing in the first part of the channel compared to geometry I. In addition, the turbulent fluctuations in the axial direction will smear out the deposition along the channel compared to the laminar case over time. The deposition in geometry II is thus shifted further into the channel because of the more complex flow situation around the bulges. In a relatively short monolith, such as the one currently investigated, the particles can therefore be found throughout the entire channel in the axial direction. It should be stressed at this point that the particles found inside the channel represent only a fraction of the total number of particles that enter the channel. From these results, we conclude that the deposition of inertial particles is a process that has a built-in mechanism for changing the spatial distribution of the deposited particles. In the beginning of a monolithic reactor’s lifetime, inertial particles deposit either on the front or in the very first section of the channel. Most of the particles pass through the catalyst, however. After a significant buildup of deposits has been formed around the channel inlets, the deposition of particles is shifted further downstream in the axial direction of the channel. However, because of the turbulence, the deposition on the frontal walls does not escalate as would otherwise be expected for a laminar flow situation. Another effect of the turbulent-to-laminar transition is to even out the axial distribution of the deposits inside the monolith channels. These results can therefore help explain not only why the front of the catalyst is most sensitive to deactivation by depositing particles (e.g., ash), but also why the chemical components of the solid deposits are usually found throughout the whole channel length when investigating aged catalysts3 (cf., e.g., Figure 4). Computational Setup in Relation to the Real Application. By performing comprehensive numerical simulations, we have been able to obtain an insight into these complex phenomena 3201



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Figure 12. Signal (top) and detail coefficients (bottom) from wavelet analysis. The levels correspond to the frequency bands given in Table 3. On the y-axis is the signal level [%] (top) or the level number (bottom) and on the x-axis is time [number of time steps].

Figure 13. Histogram of the deposition of species C in the axial direction in the middle channel for geometry II.

that has not been available before. In this section, we will discuss the main assumptions in the current work and their relation to the results. The gravitational acceleration was neglected in the tracking of the 1 μm particles, as gravitational settling is not a significant deposition mechanism for particles of this size and that are comparably light.17 Gravity otherwise reduces the turbulent dispersion effect by moving particles from one turbulent eddy

to another (the so-called “crossing trajectory” effect).37 The herein presented results therefore do not necessarily hold for particles much larger or heavier than the ones presently investigated. However, such particles are not normally present in diesel or gasoline exhaust gases. It should also be noted that Brownian motion was neglected for the large particles (species C). Although an insignificant transport mechanism in the core flow, Brownian motion could have an effect in the near-wall region and thus affect deposition.38 The calculated deposition of species C inside the channels could therefore be underestimated. Another effect that could possibly affect deposition is thermophoresis, which during cold start will transport particles from the hot exhaust gas to the colder surfaces of the catalyst walls.17 In automotive applications, the typical monolithic reactor has an outer diameter that is larger than the exhaust pipe diameter. The exhaust pipe therefore expands via a diffuser before the monolith. A particular design depends on the aftertreatment system components, the manufacturer, and space limitations onboard the vehicle. The dispersion of inertial diesel soot particles in an axisymmetric diffuser was investigated in great detail by Sbrizzai et al.14 The large particles considered in the current work (species C) are still small enough to respond to all scales of fluid motion, i.e., both the instabilities caused by the diffuser and the turbulent fluctuations from upstream the diffuser. Consequently, Sbrizzai et al. also showed that such particles 3202



Figure 14. Histogram of the deposition of species C in the axial direction in the middle channel for geometry II in the absence of turbulent fluctuations.

are quickly dispersed by the combined action of small and large flow structures.15 We can thus conclude that it is reasonable to use a uniform particle distribution at the inlet in the numerical simulations in the current work. If there is a diffuser before the catalyst in a nonsymmetrical system, flow maldistribution may result. Typical side effects of the flow maldistribution include radial variations in the channel velocity, temperature, and concentration fields.39 It is to be expected that such radial variations may exist also with regard to the turbulent characteristics upstream the monolith. The values of k and ε used at the inlet in this work are, according to our experience, similar to what is obtained in front of the monolith if a two-equation turbulence model (e.g., a k-ε variant) and the equivalent continuum approach are used to represent the monolith.40 The quality of such predictions of turbulent quantities is however questionable. We therefore note that Sbrizzai et al. observed that the upstream turbulent fluctuations before the diffuser have been preserved and are thus able to influence the particle dispersion after the instabilities caused by the expansion had decayed.15 It thus seems reasonable to assume that the fully developed turbulence from the exhaust pipe upstream the monolithic reactor is governing the turbulent effects also at the monolith inlet. We believe that using values of k and ε that produce turbulent eddies of a size a few times larger than the monolith channels is realistic for the current investigation. Implications for Future Work. In Figure 15, the channelaveraged Sherwood numbers from the present work (calculated backward from eq 11), with and without turbulence at the inlet, are compared to the predictions from a number of often-used correlations within automotive catalysis. These are the semiempirical correlation of Hawthorn35 (discussed earlier), the theoretical (local) correlation of Tronconi and Forzatti,41 and the experimental correlation of Uberoi and Pereira.42 Also plotted in Figure 15 is the limiting value of the Sherwood number for fully developed flow in a square duct. It has been speculated before that the correlation of Uberoi and Pereira predicts higher Sherwood numbers because of turbulence effects.4,43 The current work agrees well with the correlation of Tronconi and Forzatti when there are no turbulent fluctuations present, and the data points form a vertical string of points at the present value of L/D(Re)(Sc) when turbulence is present. However, these apparent fluctuations in the Sherwood number are mainly an effect of that the axial velocity (and thus the retention time) in

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Figure 15. Comparison of Sherwood number (Sh) correlations commonly used for monolithic reactors as a function of the dimensionless monolith length (L/D(Re)(Sc)). The Sherwood number for fully developed flow in a square duct is compared to the mean Sherwood numbers deducted from the correlations of Hawthorn,35 Tronconi and Forzatti,41 and Uberoi and Pereira.42 The large number of data points (corresponding to the large number of snapshots in time) from the current work with turbulence taken into account form a vertical line at L/D(Re)(Sc) ≈ 0.09.

the monolith channel fluctuates about its mean. As pointed out previously, the time-averaged value of the conversion when turbulent fluctuations are taken into account is the same as the value predicted without turbulence taken into account. The results from the present work therefore do not suggest that turbulence in itself has a significant time-averaged effect on the mass transfer to the monolith walls, at least not under the conditions of this study. When experimental investigations yield higher mass transfer coefficients than what is expected from theory, turbulence is often mentioned as a probable cause. However, a number of other factors are also known to cause deviations from theory. Such factors include that the development of the laminar boundary layer may be delayed by wall roughness, which typically increases the sensitivity to the term (Re)(Sc)D/L in the correlation.35,42 Furthermore, since the monolith substrate is in reality porous, it is to be expected that the wall-normal turbulent fluctuations are more enhanced in reality than in the available theoretical models (including the current work). Lastly, the channel geometry is also affected by the washcoat (e.g., a square channel has in fact rounded corners and washcoat thickness in the axial direction may be nonuniform), which changes the limiting value of the Sherwood number. In further studies of the influence of turbulence on the mass transfer in monolithic reactors, the effects of the walls being rough and slightly permeable should be taken into account. For the case of diesel particulate filters, turbulence is likely to have less influence since, in such reactors, there is already a convective transport to the walls. Turbulent fluctuations may then be expected to affect the positions of particle deposition only more locally, in a similar fashion to the Brownian motion.44

’ CONCLUSIONS The effects of the turbulent-to-laminar transition in an automotive monolithic reactor have been investigated using numerical 3203


Industrial & Engineering Chemistry Research simulations. The turbulent inlet effects are large enough to have a significant impact on the transient channel outlet concentrations of reactants during mass transfer controlled operation. It is found that the turbulence has two major effects on the outlet concentration of a reacting gaseous species from the monolith channels. First, there is a slow variation due to the large energycontaining turbulent eddies of sizes larger than the channel hydraulic diameter. These variations affect the velocity profile at the inlet of the monolith channel in time. Then there are rapid fluctuations inside the channel due to the inflow of turbulent eddies of sizes similar to or smaller than the channel hydraulic diameter. The turbulent-to-laminar transition effects also explain the chemical deactivation of automotive catalysts by presenting a mechanism by which particles are transported first to the near-inlet section of the monolith channels, and then—when a significant buildup of deposits has formed at the inlet—are spread out more evenly over the entire channel in the axial direction.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work has been performed within the Competence Centre for Catalysis, which is financially supported by Chalmers University of Technology, the Swedish Energy Agency, and the member companies: AB Volvo, Volvo Car Corporation, Scania CV AB, GM Powertrain Sweden AB, Haldor Topsoe A/S, and The Swedish Space Corporation. Thanks to Linda Hellstr€om for helping out with the graphics. ’ REFERENCES (1) Karvounis, E.; Assanis, D. N. The effect of inlet flow distribution on catalytic conversion efficiency. Int. J. Heat Mass Transfer 1993, 36, 1495. (2) Groppi, G.; Tronconi, E.; Forzatti, P. Mathematical Models of Catalytic Combustors. Catal. Rev. 1999, 41, 227. (3) Ekstr€om, F. Catalytic Converters for Automotive Exhaust Applications. Flow Dynamics, Mass Transfer and Optimization. Ph.D. thesis, Chalmers University of Technology, G€oteborg, Sweden, 2005. (4) Holmgren, A.; Andersson, B. Mass transfer in monolith catalysts— CO oxidation experiments and simulations. Chem. Eng. Sci. 1998, 53, 2285. (5) More, H.; Mmbaga, J.; Hayes, R. E.; Votsmeier, M.; Checkel, M. D. Heat and mass transfer limitations in pre-turbocharger catalysts. Top. Catal. 2007, 42-43, 429. (6) Winkler, A.; Ferri, D.; Aguirre, M. The influence of chemical and thermal aging on the catalytic activity of a monolithic diesel oxidation catalyst. Appl. Catal., B 2009, 93, 177. (7) Boersma, M. A. M.; Tielen, W. H. M.; van der Baan, H. S. Experimental and theoretical study of the simultaneous development of the velocity and concentration profiles in the entrance region of a monolithic convertor. ACS Symp. Ser. 1978, 65, 72. (8) Barresi, A. A.; Mazzarino, I.; Vanni, M.; Baldi, G. Catalytic afterburners with not fully developed flow: modelling and experimental performances. Chem. Eng. J. 1993, 52, 79. (9) Wendland, D. W. The segmented oxidizing monolith catalytic converter—theory and performance. J. Heat Transfer 1980, 102, 194. (10) Jobson, E.; H€ogberg, E.; Weber, K. H.; Smedler, G.; Lundgren, S.; Romare, A.; Wirmark, G. Spatially resolved effects of deactivation on field-aged automotive catalysts. SAE Tech. Pap. Ser. 1991, No. 910173. (11) Angelides, T. N.; Koutlemani, M. M.; Sklavounos, S. A.; Lioutas, CH. B.; Voulgaropoulos, A.; Papadakis, V. G.; Emons, H.

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Causes of deactivation and an effort to regenerate a commercial spent three-way catalyst. Stud. Surf. Sci. Catal. 1998, 116, 155. (12) Rokosz, M. J.; Chen, A. E.; Lowe-Ma, C. K.; Kucherov, A. V.; Benson, D.; Paputa Peck, M. C.; McCabe, R. W. Characterization of phosphorous-poisoned automotive exhaust catalysts. Appl. Catal., B 2001, 33, 205. (13) Hayes, R. E.; Kolaczkowski, S. T. Mass and heat transfer effects in catalytic monolith reactors. Chem. Eng. Sci. 1994, 49, 3587. (14) Sbrizzai, F.; Verzicco, R.; Pidria, M. F.; Soldati, A. Mechanisms for selective radial dispersion of microparticles in the transitional region of a confined turbulent round jet. Int. J. Multiphase Flow 2004, 30, 1389. (15) Sbrizzai, F.; Verzicco, R.; Soldati, A. Turbulent flow and dispersion of inertial particles in a confined jet issued by a long cylindrical pipe. Flow, Turbul. Combust. 2009, 82, 1. (16) Akselvoll, K.; Moin, P. Large-eddy simulation of turbulent confined coannular jets. J. Fluid Mech. 1996, 315, 387. (17) Johnson, J. E.; Kittelson, D. B. Deposition, diffusion and adsorption in the diesel oxidation catalyst. Appl. Catal., B 1996, 10, 117. (18) Str€om, H.; Andersson, B. Simulations of trapping of diesel and gasoline particulate matter in flow-through devices. Top. Catal. 2009, 52, 13. (19) Str€om, H.; Sasic, S.; Andersson, B. Design of automotive flowthrough catalysts with optimized soot trapping capability. Chem. Eng. J. 2010, 165, 934. (20) Davies, C. N. Definitive equations for the fluid resistance of spheres. Proc. Phys. Soc. 1945, 57, 259. (21) Germano, M.; Piomelli, U.; Moin, P.; Cabot, W. H. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 1991, 3, 1760. (22) Lilly, D. K. A proposed modification of the Germano subgridscale closure method. Phys. Fluids A 1992, 4, 633. (23) Kim, S.-E. Large Eddy Simulation Using an Unstructured Mesh Based Finite-Volume Solver. 34th AIAA Fluid Dynamics Conference and Exhibit; The American Institute of Aeronautics and Astronautics, Inc. (AIAA): Reston, Virginia, 2004; p 2548. (24) Langhaar, H. L. Steady Flow in the Transition Length of a Straight Tube. Trans. Am. Soc. Mech. Eng. 1942, 64, A55. (25) Smirnov, A.; Shi, S.; Celik, I. Random Flow Generation Technique for Large Eddy Simulations and Particle-Dynamics Modeling. J. Fluids Eng. 2001, 123, 359. (26) Wilcox, D. C. Turbulence Modeling for CFD; DCW Industries: La Ca~ nada, CA, 1998. (27) Welch, P. D. The use of fast Fourier transform for the estimation of power spectra: a method based on the averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 1967, AU-15, 70. (28) Johnstone, I. M.; Silverman, B. W. Wavelet threshold estimators for data with correlated noise. J. R. Stat. Soc. B 1997, 59, 319. (29) Argoul, F.; Arneodo, G.; Grasseau, G.; Gagne, Y.; Hopfinger, E. J.; Frish, U. Wavelet analysis of turbulence reveals the multifractal nature of the Richardson cascade. Nature 1989, 338, 51. (30) Farge, M. Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 1992, 24, 395. (31) Antonini, M.; Barlaud, M.; Mathieu, P.; Daubechies, I. Image coding using wavelet transform. IEEE Trans. Image Process. 1992, 1, 205. (32) Drahos, J.; Ruzicka, M. Problems of time series analysis in characterization of multiphase flows. Proceedings of the 5th International Conference on Multiphase Flow (ICMF '04'), Yokohama, Japan [CD-ROM]; 2004; Paper No. K04. (33) Mallat, S. A Wavelet Tour of Signal Processing; Academic Press: London, 1999. (34) Daubechies, I. Ten Lectures on Wavelets; Society for Industrial and Applied Mathematics (SIAM): Philadelphia, 1992. (35) Hawthorn, R. D. Afterburner catalysts—effects of heat and mass transfer between gas and catalyst surface. AIChE Symp. Ser. 1974, 137, 428. (36) Speziale, C. G. On turbulent secondary flows in pipes of noncircular cross-section. Int. J. Eng. Sci. 1982, 20, 863. (37) Csanady, G. T. Turbulent Diffusion of Heavy Particles in the Atmosphere. J. Atmos. Sci. 1963, 20, 201. (38) McLaughlin, J. B. Aerosol particle deposition in numerically simulated channel flow. Phys. Fluids A 1989, 1, 1211. 3204



ARTICLE

(39) Bella, G.; Rocco, V.; Maggiore, M. A Study of Inlet Flow Distortion Effects on Automotive Catalytic Converters. J. Eng. Gas Turbines Power 1991, 113, 419. (40) Benjamin, S. F.; Roberts, C. A. Modelling warm-up of an automotive catalyst substrate using the equivalent continuum approach. Int. J. Veh. Des. 1999, 22, 253. (41) Tronconi, E.; Forzatti, P. Adequacy of Lumped Parameter Models for SCR Reactors with Monolith Structure. AIChE J. 1992, 38, 201. (42) Uberoi, M.; Pereira, C. J. External Mass Transfer Coefficients for Monolith Catalysts. Ind. Eng. Chem. Res. 1996, 35, 113. (43) Tronconi, E.; Beretta, A. The role of inter- and intra-phase mass transfer in the SCR-DeNOx reaction over catalysts of different shapes. Catal. Today 1999, 52, 249. (44) Sbrizzai, F.; Faraldi, P.; Soldati, A. Appraisal of three-dimensional numerical simulation for sub-micron particle deposition in a micro-porous ceramic filter. Chem. Eng. Sci. 2005, 60, 6551.

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Effects of the Turbulent-to-Laminar Transition in Monolithic Reactors

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