Turbulence generation after a monolith in automotive catalytic converters
Introduction
Monolith based catalytic converters were initially developed for the automotive industry to reduce the pollutants present in the exhaust gas, however, due to its many advantages over other reactor types, such as a relatively low pressure drop and high external area, they are now used in other industrial applications (Xu and Moulijn, 1998, Heck et al., 2001, Marín et al., 2005, Tischer and Deutschmann, 2005, Schutt and Abraham, 2004). In recent years, there has been much work on the modeling of monolith reactors, (Sadeghi et al., 2017, Gu and Balakotaiah, 2017, Devatine et al., 2017, Martínez et al., 2016), phenomena inside micro channels Iwaniszyn et al., 2017, Avramenko et al., 2015, Avramenko et al., 2017 and model-based optimization Karamitros and Koltsakis, 2017. Given current computational limitations, numerical models of the converter usually represent the monolith as a homogeneous anisotropic porous medium, through a volume average approach (Bella et al., 1991, Baxendale, 1993, Kumar and Mazumder, 2010, Bertrand et al., 2012, Hayes et al., 2012). This approach often leads to an acceptable agreement with experimental velocity profiles right after the monolith (Hayes et al., 2012, Clarkson et al., 1993, Jeong, 2014), but it fails to represent some phenomena existing in an actual honeycomb structure, especially at the beginning and the end of the monolith (Cornejo et al., 2017). In particular, models utilizing the homogeneous porous medium approach, are unable to predict turbulence-monolith-turbulence interaction adequately. The flow entering the converter has a Reynolds number of the order of 104, it decreases to a magnitude of 102 inside of the monolith channels, and then increases back to 104 after leaving the monolith. Those Reynolds numbers imply flow regime transitions from turbulent to laminar and laminar to turbulent along the converter in a driving cycle. To obtain accurate results in modeling experimental data, decoupled from the effect of the turbulence, researchers carefully control the operating conditions to keep the flow in laminar regime (Holmgren and Andersson, 1998, Shuai and Wang, 2004, Gu and Balakotaiah, 2016, Engelbrecht et al., 2017). If those conditions are not met, the turbulence inside the channels might have a significant impact on the results (Khodadadian et al., 2018). Strom et al. (2011) studied the flow transition entering a monolith and its effect on the deposition of solid particles in the monolith entrance. Ekström and Andersson (2002) reported experimental evidence of the effect of the turbulence at the beginning of the monolith on the pressure drop along the substrate. Cornejo et al. (2017) analyzed the decay of the turbulence once the flow enters into a single channel under typical operating conditions, then proposed a damping of the turbulence for a two-equations eddy viscosity models that includes this behaviour in the continuum approach. Despite many works aimed at understanding the flow behaviour in the first part of the monolith, the laminar to turbulent transition at its last part, where the flow passes from inside the substrate into an open space, has not received much attention in the literature. It should be emphasized that this phenomenon is not appropriately represented by a homogeneous porous medium, because the turbulence generation is a consequence of the presence of the solid substrate. The turbulence after the monolith requires attention because it affects the overall pressure drop of the exhaust gas after-treatment system significantly, which results important for the engine operating efficiency and fuel economy. In addition, in close coupled monoliths, the outflow of the first impacts the performance of the second by changing its inlet conditions.
There are three main phenomena that might generate instability and turbulence in the flow leaving the monolith. These are the turbulence from inside the channels, the turbulence caused by the flow leaving a channel acting as a jet, and the instability from the stream around the last part of the solid walls between channels. The channels of the monolith are often approximately square and the turbulence inside rectangular ducts has been studied by Tosun et al. (1988). They reported a critical Reynolds number close to 1600 and a strong effect of the corners in the generation of turbulence. Xu et al. (2015) observed turbulence in single square jets with Reynolds numbers above 30,000. The flow around the end of a wall between channels is comparable to the flow around rectangular objects, which depends on the width of the object, which in the case of a monolith, is the wall thickness. For flow around rectangular objects, Bruer et al. (2000) reported that for Reynolds numbers above 300, based on the object width, turbulence is generated after the object. Also, between 90 and 300, the flow is unsteady laminar, meanwhile, below Reynolds 90, it is steady. Those studies considered a single jet and the flow around a single rectangular object. A monolith has thousands of channels running in parallel at a short distance from each other, where the flow might interact, increasing the instability and producing turbulence at lower Reynolds numbers. It is also notable that obtaining detailed experimental data inside and close to the monolith channels is non-trivial. Hettel et al. (2013) reported that the inclusion of probes inside a monolith channel might introduce up to 50% of error in the measurements. Hence, numerical experiments are preferable to study this phenomenon at a channel scale.
The objective of this work is the study and description of the velocity fluctuations and flow regimes after the monolith of an automotive catalytic converter. Several geometries in 3D commonly found in the literature were analyzed using large eddy simulation (LES) and Reynolds Average Navier-Stokes (RANS) models in a discrete channel geometry. The results were compared in terms of the average and standard deviation of the velocity, flow regime and turbulence kinetic energy. The main novelty of this work is that we confirmed numerically that at some given values of the Reynolds number, defined using the monolith wall thickness, the flow becomes turbulent. To the best of our knowledge, this problem is not addressed in the literature, and it is needed to design new computational models, that take into account the generation of turbulence after a monolith.
Section snippets
Computational model
The central point of this work is the characterization of a flow leaving a monolith, therefore, we considered the last part of a series of discrete channels followed by an open space as a domain. Although phenomena such as the heat produced by the chemical reactions and the irregularity of the washcoat might also affect the flow regime and distribution in an operating catalytic converter, we considered only isothermal unwashcoated channels. Under these conditions, it is reasonable to assume
Discretization and grid independence
The complete domain was discretized into a fully orthogonal and uniform grid, composed of four million hexaedra with 50 m as characteristic length. The time step was set to obtain a maximum Courant number (CFL) of around 0.5, which is equivalent to time steps of the order of 10−6 s. Both, the characteristic size of the control volumes and the CFL set on the simulations are the result of a systematic study described later in this paper. The discretization schemes and solver settings are
Results and discussion
This section discusses the basic flow features occurring at the monolith outlet and their dependence on the Reynolds number. This work uses two different Reynolds numbers to analyze the flow regime, turbulent or laminar, after the monolith. First, the channel Reynolds number, based in the channel size, and second, the wall Reynolds number, referred to the wall thickness of the substrate. Their mathematical expressions are described in Eqs. (11), (12) respectively.
For both
Conclusions
The flow after an unwashcoated monolith at different conditions was successfully studied by LES with a discrete channel geometry. The results were analyzed in terms of the flow regime and average and standard deviation of the velocity. Flow instability downstream the monolith was observed and it generates turbulence under certain circumstances. It was found that the main source of instability is the flow going around the last part of the substrate and it is focused close to the intersections
Acknowledgements
I. Cornejo acknowledges the receipt of a Becas-Chile (CONICYT) scholarship. Other funding was provided by the Natural Sciences and Engineering Research Council of Canada.
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