Multi-scale simulation of automotive catalytic converters

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Cansu Ozhan

To cite this version:

Cansu Ozhan. Multi-scale simulation of automotive catalytic converters. Fluid mechanics [physics.class-ph]. Université Pierre et Marie Curie - Paris VI, 2014. English. �NNT : 2014PA066484�. �tel-01232031�

TH`ESE DE DOCTORAT

DE L’UNIVERSIT´E PIERRE ET MARIE CURIE (UPMC - PARIS VI)

Sp´ecialit´e

G´ENIE DES PROC´ED´ES - M´ECANIQUE DES FLUIDES (Ecole doctorale SMAER 391)

Pr´esent´ee par

Cansu OZHAN

pour obtenir le grade de

DOCTEUR DE L’UNIVERSIT´E PIERRE ET MARIE CURIE

Sujet de la th`ese

Multi-scale simulation of automotive catalytic

converters

Soutenue `a l’UPMC le 21 novembre 2014 devant le jury compos´e de :

Stephen BENJAMIN Coventry University Rapporteur Carlo VISCONTI Politecnico di Milano Rapporteur

St´ephane ZALESKI UPMC Examinateur

Christophe DUJARDIN Universit´e de Lille Examinateur

Patrick DA COSTA UPMC Directeur de th`ese

Remerciements

Cette th`ese fut bien ´evidemment une grande aventure scientifique, mais elle fut surtout une aventure humaine. La suite de ce manuscrit va d´ecrire la partie scientifique, j’aimerais donc ici profiter de ces quelques lignes pour parler de la partie humaine, celle qui restera grav´ee dans mon esprit.

Je voudrais tout d’abord adresser mes sinc`eres remerciements `a mon directeur de th`ese, Patrick Da Costa de m’avoir donn´e l’opportunit´e de faire ce travail. Ton objectif est tou-jours de faire avancer tes th´esards et de nous pr´eparer pour le monde professionnel. Merci chef!

Un grand merci `a mon encadrant durant cette th`ese, Daniel Fuster, pour l’aide pr´ecieuse que tu m’a apport´e, pour ta patience et pour ta disponibilit´e. Tu a su, gr`ace `

a ta rigueur scientifique et `a tes critiques constructives am´eliorer la qualit´e de ce travail. Je suis vraiment consciente de la chance exceptionnelle que j’ai eue d’avoir travaill´e avec toi!

Mes remerciements `a Stephen Benjamin et `a Carlo Visconti d’avoir accept´e d’ˆetre rap-porteurs de mon manuscrit de th`ese et pour leurs pr´ecieuses remarques. Je tiens ´egalement `

a remercier St´ephane Zaleski et Christophe Dujardin d’avoir accept´e de participer `a mon jury.

Tout mes remerciements `a Jean-Fran¸cois Krawczynski, pour le soutien moral du d´ebut jusqu’`a la fin de ma th`ese. Tu ´etais plus qu’un encadrant mais un vrai ami non seulement avec qui je passe des bons moments, mais aussi sur qui je peux toujours compter.

Je remercie ´egalement tous les doctorants et les coll´egues de l’Institut pour la bonne ambiance. La liste est tr`es longue, je ne vais que citer quelques uns. Je remercie mes coll`egues: Julien, Zhen, Gouns´eti, Raja, Marcello et Luca avec qui j’ai partag´e des mo-ments tr`es agr´eables! Mes ch`eres amies Valentina et Simona, vous ˆetes g´eniales et un grand merci pour tout les moments pass´es `a s’´ecouter, se r´econforter, parfois pleurer, mais souvent `a rire. Et sans oublier Acacio et Alexis, merci `a tous, c’est que des bons souvenirs avec vous!

Merci `a Antonyo et `a son groupe de musique “Melting Bastards” pour votre belle surprise et performance, vous avez vraiment color´e mon pˆot de soutenance de th`ese!

aux moments o`u j’en avais vraiment besoin, me redonner la force de continuer.

Enfin, mes sinc`eres remerciements `a mes tr`es ch`ers parents. Votre confiance, votre ten-dresse, votre soutien et votre amour que vous me portez font ce que je suis aujourd’hui. C’est `a vous que je d´edie ce m´emoire - Son olarak, en i¸cten te¸sekk¨urlerim sevgili aileme. Sizin g¨uveniniz, ¸sevkatiniz, deste˘giniz ve bana olan sevginiz beni bug¨unlere getirdi. Dok-tora tezimi size adiyorum.

Abstract

The increasing use of passenger vehicles over the past decades has caused an increase in harmful exhaust gas emissions which give rise to environmental and health problems. This problematic has led governments to establish very stringent emission limits. The emis-sion restrictions require more performant after-treatment systems. Among many other solutions, analysing and optimising the flow impact on the conversion efficiency is an im-portant step towards the solution of the complex engineering problem. Detailed velocity, temperature and concentration distributions are very difficult to measure experimentally. Numerical simulations can provide additional information to understand the interaction of flow distribution and conversion efficiency. The simulation of these systems is com-putationally very expensive due to complex physical and chemical phenomena occurring simultaneously throughout the system. To overcome this cost, one can resort to some simplified physical and chemical models together with specific numerical techniques to simulate the system with a reduced computational time. In this dissertation, we develop a general approach to model and simulate the automotive catalytic converter system in-cluding all the physical and chemical processes.

The present approach combines sub-grid models and numerical multi-resolution tech-niques in order to correctly capture the flow characteristics inside an automotive catalytic converter. While Adaptive Mesh Refinement (AMR) techniques are optimised in order to minimise the computational effort in the divergent and convergent regions, a sub-grid model is developed to describe the flow inside the catalytic substrate placed between the convergent and divergent regions. The performance of the sub-grid model is validated against the experimental results obtained by Benjamin et al. (2002). The effective cou-pling of AMR techniques and the sub-grid model allows to capture the flow features with significantly reduced computational time. The impact of pulsating flow on the conversion efficiency within a single monolith channel is investigated numerically. AMR techniques are shown to capture the small boundary layers near the wall at the solid-fluid interface. Based on the numerical results, we propose a simplified transport model that captures the effects of flow, diffusion and catalytic wall reactions. The simplified transport model can be directly applied as a sub-grid model for the complete description of all the physical and chemical processes taking place inside the system. The developed physical, chemical and numerical modelling approaches make the three-dimensional simulations possible with a reasonable computational time still capturing the main physics of the problem.

Contents

1 Introduction 25

1.1 A brief historical background . . . 26

1.2 Development of automotive catalysts . . . 28

1.2.1 Diesel Particulate Filter (DPF) . . . 28

1.2.2 Diesel Oxidation Catalyst (DOC) . . . 29

1.2.3 NOx aftertreatment systems . . . 29

1.2.3.1 Lean NOx Trap (LNT) . . . 30

1.2.3.2 Urea Selective Catalytic Reduction (Urea-SCR) . . . 30

1.2.4 Three-Way Catalyst (TWC) . . . 31

1.2.5 Latest developments in autocatalysts and other emission control systems . . . 32

1.3 Factors affecting system’s efficiency . . . 32

1.3.1 Air/Fuel ratio . . . 34

1.3.2 Cold start emission . . . 34

1.3.3 Substrate technology . . . 35

1.3.4 Flow uniformity at the catalyst inlet . . . 36

1.4 Description of the physical and chemical problem . . . 37

1.4.1 Flow features . . . 37

1.4.2 Transport and reaction mechanisms inside a monolith substrate channel . . . 40

1.4.2.1 Reaction mechanisms . . . 40

1.4.2.2 Mass transfer . . . 42

1.4.2.3 Heat transfer . . . 43

1.5 Modelling and simulation approaches . . . 44

1.6 Objective and structure of the present study . . . 50

2 Modelling and numerical approaches 53 2.1 Governing equations . . . 53

2.2 Modelling approaches . . . 54

2.2.1 Sub-grid pressure jump model . . . 54

2.2.2 Sub-grid reaction model . . . 56

2.3 Numerical techniques . . . 57

2.3.1 The Gerris flow solver . . . 58

2.3.1.1 Temporal discretisation scheme . . . 59

2.3.1.3 Dynamic adaptive discretisation scheme . . . 61

3 AMR optimisation strategies 63 3.1 AMR techniques . . . 63

3.1.1 Error indicators . . . 64

3.1.2 Error estimators . . . 65

3.1.2.1 Hessian error estimator based on the h-refinement algorithm 65 3.1.2.2 Residual based error estimator . . . 66

3.2 Error measurement methodologies . . . 67

3.3 Grid optimisation strategies for turbulent flows . . . 68

3.3.1 Lamb-Oseen Vortex . . . 70

3.3.2 Growth of random noise perturbations in a shear layer . . . 75

3.3.3 Energy decay in isotropic homogeneous turbulence . . . 78

3.4 Grid optimisation strategies for reactive flows . . . 82

3.4.1 Regular boundary layer for a scalar quantity . . . 82

3.4.2 Regular boundary layer for a scalar quantity with the oscillatory temporal term . . . 89

3.5 Conclusion . . . 90

4 Flow simulation in the automotive catalytic converter 93 4.1 Solid implementation . . . 93

4.1.1 Solid implementation for the substrate geometry . . . 94

4.1.2 Solid implementation for the outer geometry . . . 95

4.2 Sub-grid pressure drop model . . . 95

4.2.1 Axisymmetric 2D flow simulation . . . 98

4.2.2 Comparison of Axisymmetric and 3D simulations . . . 103

4.3 Simulation of a catalytic converter system . . . 105

4.4 Conclusion . . . 107

5 Flow-reaction coupling effects in a single monolith substrate channel 109 5.1 Steady state transport models for wall reactions . . . 110

5.1.1 Transport model for the kinetic regime . . . 111

5.1.2 Transport model for the mass transfer regime . . . 113

5.1.3 Comparison of the transport models with Direct Numerical Simu-lations . . . 115

5.1.4 Sub-grid reaction model verification . . . 118

5.2 Pulsating flow effects on the conversion process . . . 120

5.2.1 Pulsating effects on the flow profile . . . 121

5.2.2 Pulsation effects on mass transfer . . . 124

5.2.2.1 Influence of the forcing amplitude on the conversion process126 5.2.2.2 Influence of the pulsation frequency on the conversion pro-cess . . . 127

5.3 Conclusion . . . 129

6 Optimisation strategies 133 6.1 Parameters influencing the system’s efficiency . . . 133

6.2 Flow uniformity control . . . 134

CONTENTS

6.2.2 Boundary layer thickness effect on the upstream flow . . . 139

6.2.3 Optimisation methodology for substrate geometry designs . . . 139

6.3 Conclusion . . . 140

7 Conclusion and perspectives 143 7.1 Conclusion . . . 143

7.2 Perspectives . . . 144

APPENDICES 145 A Test cases’ implementation in Gerris 147 A.1 Lamb-Oseen vortex . . . 147

A.2 Growth of random noise perturbations in a shear layer . . . 150

A.3 Energy decay in isotropic turbulence . . . 152

A.4 Regular boundary layer for a scalar quantity . . . 154

B Sub-grid models’ implementation in Gerris 157 B.1 Sub-grid pressure jump model implementation in Gerris . . . 157

B.2 Sub-grid reaction model implementation in Gerris . . . 160

List of Figures

1.1 Typical catalytic converter structure. Stainless steel casing and honey-comb with numerous parallel channels. The transformation of the main pollutants to the less toxic substances occur at the catalytic walls of the channels. . . 28 1.2 Schematic representation of diesel particulate filter (DPF) channels. Gas

loaded with particulate matter P M is filtered when it flows through porous walls. The clean flow (light blue arrows) passes to adjacent channels while P M , in dark blue, is stored in the blocked channels. . . 29 1.3 The mechanism of NOx trap according to Toyota [59]. (a) Lean condition

where N Ox are stored as N O3− forms. (b) Rich condition where reducing agents demonstrated as R induces a dissociation of N O₃− and N Ox is re-leased. Then released N Ox reacts over the rhodium to form nitrogen and carbon dioxide. . . 30 1.4 Schematic representation of a passenger car equipped with Urea-SCR

sys-tem. The system includes a urea tank, a piping, a SCR control system, a Urea injector and a SCR converter. The system yields high N Oxconversion rate. However it requires additional cost and specific servicing. . . 31 1.5 Different possible configurations of after treatment devices in the exhaust

line. (a) DPF is located downstream of DOC as DOC supplies the necessary temperature to clean DPF. (b) LNT can be included in the DOC. (c ) Urea-SCR system is usually located after DOC and DPF systems. . . 33 1.6 Conversion efficiency of CO, HC and N Oxas function of the air/fuel ration

in TWC [48]. . . 34 1.7 Cumulative CO, HC and N O_x emissions of a 21 gasoline car in the new

European driving centre [48]. . . 35 1.8 Cross sectional metallic and ceramic substrates. . . 36 1.9 Typical flow profiles throughout catalytic converter [66]. . . 37 1.10 Geometry changes in automotive catalytic converter and resulting flow

fea-tures. (a) Example of catalytic converter geometry. (b) Typical flow pat-terns inside a catalytics converter (Re=10000) in the symmetric plane. A shear layer forming right after the expansion point and a large recirculation region are observed in the diffuser region. The flow is re-laminarized inside the catalytic channels. . . 38

1.11 Streamfunctions at the diffuser and monolith channel entrance (Reynolds number is 20000 based on inlet pipe diameter). (a) Streamfunctions at the inlet diffuser. Recirculation region and vortices are formed due to turbulent expansion flow. (b) Zoom into the channel entrances near the catalyst edge. Enlarged recirculation zones are observed due to high entrance angle of inlet velocities. . . 39 1.12 Different scales of monolith reactor and physical/chemical processes

occur-ring in a single monolith channel. . . 41 1.13 Steps in heterogeneous catalytic reaction. . . 41 1.14 Schematic representation of gas diffusion from bulk flow to the solid-gas

interface in monolith reactors [49]. . . 42

2.1 Nondimensional pressure drop obtained by the full numerical solution of the Navier-Stokes equations as a function of the Reynolds number (_{) for} a pipe geometry. For reference, the pressure drop predicted by the Hagen-Poiseuille pressure drop model is included (-). . . 55 2.2 Pressure distribution in the full geometry and reduced geometry proposed

in this work. The catalytic converter is replaced by an interface where we apply a pressure jump as a function of the velocity according to the Hagen-Poiseuille pressure drop model. . . 55 2.3 Concentration distribution in the complete channel geometry and reduced

channel geometry proposed in this work. The substrate channel length is reduced to a thin region where we apply a source term containing a reaction model to obtain the exit concentration. (a) Concentration profile obtained from the Direct Numerical simulation of a half plane in axisymmetric co-ordinates. (b) Concentration jump obtained from applying a simplifed sub-grid model. . . 57 2.4 Illustration of AMR grid distribution on the upstream flow region before

the catalyst in automotive catalytic converters. . . 59 2.5 Example of quadtree discretisation (left) and corresponding tree

represen-tation (right) [68]. . . 60 2.6 Discretisation constraints in Gerris. The dotted lines represents the

nec-essary refinements to conform the given constraints: the levels of direct neighbouring cannot differ by more than one (left), the levels of diago-nal neighbouring cannot differ by more than one (centre) and all the cells directly neighbouring a mixed cell should be at the same level (right) [68]. 61

3.1 Different numerical integration methods to calculate the global error of a spatial parameter. Red points represent the numerical values in the cells. The black curve is the exact solution. (a) Nodal integration method. The integral is calculated by adding the multiplication of the cell size (h) and the absolute value of the difference between the exact and numerical solutions (_|fexact− fnumeric|) of the each cell in the computational domain. (b) Exact integration method. The integral is calculated as the area between the theoretical and the numerical results. . . 68

LIST OF FIGURES

3.2 Example of a problem with the analytical and numerical solutions and different integration methods to calculate the error. The error is obtained to be 0 according to the nodal integration method for a given level of refinements l (a) and l_{− 1 (b). With the exact integration method, the} numerical error is not 0 (c). Higher resolution results in less error with the exact integration method (d). . . 69 3.3 Radial velocity norm distribution for various non-dimensional times for

Lamb-Oseen vortex (a) and the azimuthal velocity snapshot obtained by the numerical simulation (b). The characteristic length of the problem is chosen to be the radial distance at which the velocity norm is maximal for the solution where νt0=0.5. . . 70 3.4 Error convergence (a) and converged value (b) with a fix and AMR mesh

for the Lamb-Oseen vortex test case. For AMR simulations, the equivalent grid size is defined as ∆x = Lbox/

√

Ncells . . . 73 3.5 Different convergence tendencies of the velocity based h-refinement

esti-mator method adapted based on L1 and L∞. For a given resolution, the method adapted by L_∞ norm provides approximately 10 times less error. 74 3.6 Grid distribution in the whole computational domain (at left) and in the

area (Lbox/lc = 6)very close to the vortex center (at right) obtained by L1 (a) and L_∞ (b) norms. The total number of cells is chosen to be approxi-mately the same (_{≈ 155000 nodes) for the different norms. . . 74} 3.7 Local error efficiency measurements for the Lamb-Oseen vortex test case.

(a)Predicted error εestimated versus true error εtrue for all the resolutions tested. (b)Coefficient of determination as a function of the grid resolution. 75 3.8 Inviscid vortex test case. A random perturbation is imposed in a shear

layer. The small perturbation initially imposed in the solution grow in time creating coherent structures corresponding to the most unstable mode for which a theoretical growthrate can be obtained. . . 76 3.9 Grid size distribution, velocity vectors and perturbation isolines (V ) for

the instability growth in a shear layer. Grid cells preferentially concentrate on the velocity shear layer region. (a)Grid distribution for the instability growth in a shar layer. The color scale represents the level of refinement l defined as 2l = Lbox/∆x. (b)Zoom into the shear layer region . . . 77 3.10 Error convergence (a) and converged values (b) with a fix and AMR mesh

for the instability growth in a shear layer. For AMR, the equivalent grid size is obtained as ∆x =

q

Lbox,x×Lbox,y

Ncells . . . 77

3.11 Comparison of convergence tendendcies obtained by the same estimator method basen on the L1 and the L∞ norms. The same convergence ten-dencies are obtained for this example. . . 78 3.12 Temporal evolution of the system’s kinetic energy (a) and Taylor’s scale as

a function of level of refinement for ReL= 375 (b). The energy decays and the Taylor microscale increases as the energy is dissipated. Figure source: Fuster (2013)[30]. . . 79 3.13 Snapshot of the non-dimensional λ2 isosurface-a way to characterise

vor-tices (isosurface _{∼ 5 × 10}4) and vorticity for bottom, left and right planes at _Ltu0

3.14 Convergence of temporally integrated values for fixed mesh and different hessian based error estimators at L1 norm. ∆x = Lbox/

√

Ncells is the grid size and κ is Kolmogorov lengthscale equal to 0.0028. (a) Temporally in-tegrated total kinetic energy. (b) Temporally inin-tegrated second order of transversal momentum. (c) Temporally integrated third order of transver-sal momentum. (d) Temporally integrated fourth order of transvertransver-sal mo-mentum. . . 83 3.15 Convergence of temporally integrated values for fixed mesh and different

error estimator methods at L1 norm. ∆x = Lbox/ √

Ncells is the grid size and κ is Kolmogorov lengthscale equal to 0.0028. (a) Temporally integrated total kinetic energy. (b) Temporally integrated second order of transversal momentum. (c) Temporally integrated third order of transversal momen-tum. (d) Temporally integrated fourth order of transversal momenmomen-tum. . 84 3.16 Convergence of temporally integrated values for fixed mesh and different

error estimator methods at L_∞ norm. ∆x = Lbox/ √

Ncells is the grid size and κ is Kolmogorov lengthscale equal to 0.0028. (a) Temporally integrated total kinetic energy. (b) Temporally integrated second order of transversal momentum. (c) Temporally integrated third order of transversal momen-tum. (d) Temporally integrated fourth order of transversal momenmomen-tum. . 85 3.17 Scalar quantity field for the given problem. The Sherwood number is 100. . 86 3.18 Error convergence of the scalar quantity for fix and AMR mesh. (a) Error

is measured based on the L_∞ norm. (b) Error is measured based on the L₁ norm. For AMR simulations, the equivalent grid size is defined as ∆x = Lbox/√Ncells, Ncells being the total number of cells in the domain. . 87 3.19 Grid distribution for the regular boundary layer of a scalar quantity. The

same error estimator adapted by the L_∞ norm (left) and the L1 norm (right). The total number of cells is chosen to be approximately the same (_{≈ 20000) for the different adaptation norms. . . 88} 3.20 Comparison of the error convergence of the scalar quantity obtained by

dif-ferent estimation methods: scalar quantity based hessian error estimator (ηhes(T )) and scalar quantity gradient indicator (ηgrad(T )). For high reso-lution simulations, hessian based error estimator provides more accurate results than the gradient error indicator. . . 88 3.21 Local error efficiency measurements for the regular boundary layer test

case. (a)Predicted error εestimated versus true error εtrue for all the resolu-tions tested. (b)Coefficient of determination R2 as a function of the grid resolution. . . 89 3.22 Correlation between the estimated error and the true error for different

numerical steps tested for the scalar quantity based hessian estimator method. 90

4.1 Simplified solid implementation with tracer approach. (a) Tracer region demonstrated in red color represents the solid parallel channels of monolith substrate. Velocity components are not allowed in tracer region. (b) Tracer region in red color represents the inlet pipe and diffuser geometry for 3-D simulation. . . 94

LIST OF FIGURES

4.2 Different substrate geometry implementation. Colours represent pressure. (a) Flow relaminarisation by solid approach. (b) Flow relaminarisation by tracer approach. (c) Flow relaminarisation by porous medium approach. (d) Velocity profile evolution at the upstream obtained by different solid implementation. Reynolds number based on inlet pipe diameter is 2500 and uniform velocity profile is applied at the inlet pipe. (e) Computational time required to achieve the same simulation time for different solid imple-mentations. Same uniform discretisation scheme (level of refinement l=10) is applied. . . 96 4.3 Different diffuser geometry implementations. Colours represent the

vortic-ity and grey lines are the streamfunctions. Reynolds number based on inlet pipe diameter is 5745 and uniform velocity profile is applied at the inlet pipe. (a) Diffuser geometry by using the traditional solid approach. (b) Diffuser geometry by using the tracer approach. . . 97 4.4 Comparison of the radial velocity profile (a), the total number of cells (b)

and the resulting computational times (c) for the simulations with different outer solid geometry implementations. . . 97 4.5 3-D simulation of flow in an expansion flow with the tracer approach for the

outer geometry. Reynolds number based on inlet pipe diameter is 80000. 128 processors are used for the parallel computation. . . 98 4.6 Sequence of vorticity snapshots obtained without (a) and with (b) the

pressure jump model. Diffuser and substrate properties are as shown in Table 4.1. The Reynolds number based on inlet pipe diameter is 10000. The model is able to capture the effect of the substract on the flow upstream and to block the pass of vortices throughout the catalytic region as observed in the full simulation (Figure 1.10)and experimental observations from [10]. 99 4.7 Experimental visualisation of the upstream flow in automotive catalytic

converters provided by Benjamin (2003) [10]. . . 99 4.8 Convergence tendencies of different grid designs at different regimes. . . 102 4.9 Non-uniformity for different regimes and substrate lengths . . . 102 4.10 Temporal evolution of the total grid points (tsimulation=tU0/Rmax) and the

radial velocity profile at Re = 79900 (based on inlet pipe diameter). The simulation results reproduce relatively well experimental results of [11]. (a) Number of total grid points as a function of the AMR tolerance (Table 4.3). (b) Converged radial velocity profile. . . 103 4.11 Grid size distribution (a) and non-dimensional vorticity (b) obtained by

3D simulation. The color scale for grid distribution represents the level of refinement, l, so that 2l = Dmax

∆x . The non-dimensionless vorticity is cal-culated as $Dmax

u0 . The grid is preferentially concentrated in those regions

where the vortical structures are present. . . 104 4.12 Grid size distribution (a) and non-dimensional vorticity (b) snapshots. The

color scale for grid distribution represents the level of refinement, l, so that 2l = Dmax

∆x . The non-dimensionless vorticity is calculated as $ Dmax

u0 .

The grid is preferentially concentrated in those regions where the vortical structures are present. . . 106

4.13 Comparison of computational times for fixed and AMR mesh. The use of AMR techniques allow us to obtain results approximately 10 times faster compared to uniform fixed mesh for a given level of accuracy. . . 106 4.14 Velocity profiles at the entrance of the substrate using a uniform grid and

the AMR grid. Level of refinement employed for uniform grid is l=9 so that Dmax

∆x = 2

9_{. Vorticity based Hessian estimator is used as AMR criterion. . 107} 4.15 Fourier transform of the velocity amplitude and Strouhal number St located

at different radial distances for Re_D = 20000 (a) and Re_D = 80000 (b). . . 107 5.1 Schematic representation concentration profiles in a single monolith

chan-nel at low temperature (a) and high temperature (b). cA0 is the reactant concentration at the entrance of the tube. . . 110 5.2 Conversion as a function of catalyst’s temperature [25]. . . 111 5.3 Mass transfer and reaction kinetics impact on the conversion process. . . . 113 5.4 Flow and diffusion impact on the conversion process. . . 115 5.5 Schematic representation of pipe flow with boundary conditions . . . 116 5.6 Laminar pipe flow involving slow (a) and fast (b) catalytic wall reaction.

Colours represent concentration and black lines are concentration isolines. Block and parabolic concentration profiles are obtained for slow and fast wall reactions respectively. The axis of symmetry is placed at the bottom part of the figure, the wall is at the top. . . 117 5.7 Averaged concentration with respect to the axial distance for steady state

laminar pipe flow with slow heterogenous wall reactions (kinetic regime). Numerical results are coherent with the analytical solutions for the case DaII << 1. Lines represent the theoretical solution for a given DaII and points represent the numerical solutions. . . 117 5.8 Sectionally averaged concentration with respect to axial distance for steady

state laminar pipe flow with fast heterogenous wall reaction (mass transfer regime). The results with DaII >> 1 are converged to the theoretical solution. Line represents the theoretical solution at DaII _{→ ∞ and points} represent the numerical solutions. . . 118 5.9 Reduced geometry for channel flow with reaction. (a) Region where source

term including reaction is applied. (b) Species concentration from inlet to outlet. Colours represent the concentration. Concentration variation where the source is imposed. . . 119 5.10 Outlet concentration for varions numerical simulations of complete and

reduced geometry for channel flow with reaction model (DaII = 0.1) . . . . 120 5.11 Pulsating flow characteristics. (a) non-dimensionalised velocity amplitude

with respect to Reynolds and Strouhal numbers. With increasing ResSt, velocity amplitude decreases. (b) Phase lag between velocity and pressure fluctuation versus Reynolds and Strouhal numbers. With increasing ResSt, phase of lag increases. . . 122 5.12 Schematic representation of pipe flow with boundary conditions . . . 123 5.13 Velocity profile snapshots at ResSt = 12.6. The dimensionless parameter

of forcing amplitude φ is chosen to be 5. Reynolds and Strouhal numbers are defined as shown in Equation 5.46 and 5.47 respectively. . . 123

LIST OF FIGURES

5.14 Comparison of theoretical and numerical results of pulsating flow. (a) Am-plitude of velocity ∆u/¯u normalized by forcing amplitude φ as a function of Re_sSt. (b) phase ϕ normalized by forcing amplitude φ as a function of ResSt. Reynolds and Strouhal numbers are defined as shown in Equation 5.46 and 5.47 respectively. Dimensionless parameter of forcing amplitude φ is chosen to be 2.2. . . 124 5.15 Illustration of pipe geometry and flow conditions of pulsating flow with

heterogenous reaction at pipe wall. . . 125 5.16 Theoretical comparison of concentration profiles as function of RecSc under

pulsating flow induced by different forcing amplitude (St_{≈ 0.0024). . . 127} 5.17 Enhancement of overall conversion. Numerical results confirm the 0thorder

theoretical solution for a given Strouhal number (St_{≈ 0.24). . . 128} 5.18 Enhancement of overall conversion obtained by 0th order theoretical

solu-tion for z/R=100. . . 128 5.19 Frequency effect on effective enhancement of the pulsation εc. (a)

Di-mensionless velocity amplitude, ∆u/u0 is fixed to 0.88. (b) Dimensionless forcing amplitude, φ is fixed to 2.20. Pipe radius based Re is 50 and Sc is chosen to be 0.2. . . 130 5.20 Frequency effect on effective enhancement of the pulsation εc obtained by

0th order theoretical solution for z/R=100. (a) Dimensionless velocity am-plitude, ∆u/u0 is fixed to 0.88. (b) Dimensionless forcing amplitude, φ is fixed to 2.20. Pipe radius based Re is 50 and Sc is chosen to be 0.2. . . . 130 6.1 Radial velocity profile at the substrate at ReD = 79000 (based on inlet

pipe diameter). At the catalyst centre, velocity is high which decreases the conversion efficiency according to simplified transport model proposed in Chapter 5. At the catalyst periphery, velocity is low increasing the conversion efficiency. However, the catalyst is poorly used in this region. . 135 6.2 Pressure drop effect on flow distribution. (a) Radial velocity profile

ob-tained by substrate configurations. As the pressure drop increases, the flow becomes more uniform. (b) Pressure drop versus flow non-uniformity index. (Re=20000) . . . 137 6.3 Comparison of the numerical axial velocities obtained by the largest (left)

and smallest (right) channel diameters. Colours represent the non-dimensional axial velocity where the characteristic velocity is defined as uc = _Lνc_c with Lc = 100mm and νc = 15.11 10−6m2/s for air at 20◦C. We observe the flow deceleration in the jet flow due to the increased pressure drop in the substrate, uniforming the inlet flow profile. . . 138 6.4 Channel diameter versus non-uniformity index obtained by simulations

with and without the boundary layer thickness at the inlet pipe. Intro-ducing a boundary layer thickness increases the non-uniformity index. . . . 139 6.5 Channel diameter distribution as a function of radius (a) resulting radial

velocity distribution (b) and the minimum channel diameter at the axial centre versus flow non-uniformity index ψ (c) at the substrate for uniform inlet velocity profile and ReD = 80000. As axial the channel diameter decreases, upstream flow becomes more uniform until reaching an optimal distribution for which the uniformity index is minimal. . . 141

A.1 Decomposition of azimuthal velocity uθ into velocity components U and V which represent the velocity component in x and y directions respectively in Cartesian coordinates. . . 147

List of Tables

1.1 Emission limits for passenger cars below 2500 kg according to European

standards [35]. . . 27

1.2 Commercial ceramic substrates used in automotive converters [88]. . . 36

1.3 Modeling and simulation approaches in the literature for automotive cat-alytic converters. . . 49

3.1 Error estimation methods, estimator norms and corresponding estimator function used for the Lamb-Oseen vortex. . . 71

3.2 Error estimators, estimator norms and corresponding estimator function used for the isotropic turbulence. . . 81

3.3 Error estimators, estimator norms and corresponding estimator function used for the Regular boundary layer for a scalar quantity. . . 87

4.1 Simulation conditions used to test the subgrid model in Figure 4.6. . . 100

4.2 Axisymmetric 2D simulation of experimental set-up . . . 100

4.3 Simulations for radial velocity profile convergence . . . 103

4.4 3D simulation of experimental set-up . . . 104

4.5 The non-uniformity index ψ convergence for 3D simulations. . . 105

5.1 The first five constants and eigenvalues for the evalution of the equation 5.22115 5.2 Non-dimensional simulation parameters for laminar pipe flow with wall reactions . . . 116

5.3 Axisymmetric 2D simulation of experimental set-up . . . 120

6.1 Substrate design criteria. . . 134

Nomenclature

AO open frontal area of the monolith substrate cA concentration of the reactant A (ppm)

cA,steady concentration of the reactant A under steady flow (ppm) cA,pulse concentration of the reactant A under pulsating flow (ppm) ci concentration of the ith component (ppm)

ci0 inlet concentration of the ith component (ppm) cis outlet concentration of the ith component (ppm) d monolith channel diameter (m)

D diffusion coefficient (m2_·s−1)

DAB binary molecular diffusion coefficient (m2·s−1) Din inlet pipe diameter (m)

Dmax catalyst diameter (m) DaII second Damk¨ohler number E(k) energy spectra (kg_·s−2)

E(K) total kinetic energy over the whole computational domain (kg_·m2_·s−2) f frequency (s−1)

Fext external forces (kg·m−2·s−2)

h cell size (m)

H helicity (m_·s−2)

HR(~x) function that applies the source term on the defined region

i complex number

IK temporally integrated total kinetic energy over the whole domain (kg·m2·s−2) IM2 temporally integrated second order moment over the whole domain (m

3_·s−2₎ IM3 temporally integrated third order moment over the whole domain (m

3_·s−3₎ IM4 temporally integrated fourth order moment over the whole domain (m

3_·s−4₎ J0() zeroth order Bessel function

k wavenumber (m−1)

bk1 reaction rate constant (m·s−1)

K steady part of the pressure gradient in oscillatory pipe flow (m_·s−2) l level of refinement

lc characteristic length of the Lamb-Oseen vortex (m) L monolith channel length (m)

Lint integral length (m) Lbox simulation box length

Lr length of the reactive pipe wall (m)

LR characteristic length of the reactive zone (m) L₁ error norm which reduces error integral L_∞ error norm which reduces maximum error

n normal vector

N number of components

Ncells total number of cells in the computational domain

M2 second order moment over the whole computational domain (m3·s−2) M₃ third order moment over the whole computational domain (m3_·s−3) M4 fourth order moment over the whole computational domain (m3·s−4) p pressure (kg_·m−1_·s−2)

P e_M Peclet number for mass transfer

R pipe radius (m)

R2 coefficient of determination R_c recirculation radius (m) Ri reaction rate (ppm·s−1) Rin inlet pipe radius (m) R_max catalyst radius (m)

ReD Reynolds number based on the inlet pipe diameter ReL Reynolds number based on the integral length Lint

Re_c Reynolds number based on the monolith channel diameter

Res Reynolds number based on the channel radius and steady part of the velocity Re() real part of the complex number

S source term in the Navier-Stokes equation (kg_·m−2_·s−2) Si source term in the transport equation (ppm·s−1)

Sc Schmidt number

St Strouhal number based on the angular frequency and channel radius

t time (s)

t0 initial time (s) t_sim simulation time

T numerical scalar quantity (e.g temperature, concentration etc.) u velocity vector (m_·s−1)

u_θ azimuthal velocity (m_·s−1)

u0 inlet velocity at the inlet pipe (m·s−1) U, V, W velocity components (m_·s−1)

x_c cell centred coordinates x, y, z Cartesian coordinates z, r, θ Axisymmetric coordinates α universal Kolmogorov constant

αci growth rate of perturbation in a shear layer (m−1) δ boundary layer thickness at the inlet pipe diameter (m) δ_s Dirac delta function

δc velocity shear layer thickness (m) D deformation tensor (s−1)

 dissipation rate (kg_·m−1_·s−4)

η AMR tolerance

LIST OF TABLES

ηgrad(T ) scalar quantity gradient error indicator ηvort vorticity error indicator

η_hes(u) velocity based hessian error estimator ηhes(ω) vorticity based hessian error estimator ηhes(H) helicity based hessian error estimator

η_hes(φ) energy dissipation based hessian error estimator ηhes(T ) scalar quantity based hessian error estimator ηres(N S) velocity based residual error estimator

γ surface tension (kg_·s−2) Γ circulation (m2_·s−1) κ Kolmogorov scale (m) λ Taylor scale (m) µ dynamic viscosity (kg_·m−1_·s−1) ν kinematic viscosity (m2_·s−1) ω angular frequency (2πf ) (s−1) Ω computational domain (m3) ΩR reactive zone (m3)

φ dimensionless forcing amplitude in oscillatory pipe flow

ψ non-uniformity index

ρ density (kg_·m−3)

σ_v variance of velocity (m_·s−1)

τ inverse of the characteristic time in the reactive zone (s−1) Θ energy dissipation (kg_·m−1_·s−3)

ε numerical error

ε0 porosity

ε00 cell density

ε_c effective enhancement of the overall conversion

ϕ phase lag between velocity and pressure in oscillatory pipe flow $ vorticity (s−1)

Chapter

1

Introduction

Contents

1.1 A brief historical background . . . 26 1.2 Development of automotive catalysts . . . 28 1.2.1 Diesel Particulate Filter (DPF) . . . 28 1.2.2 Diesel Oxidation Catalyst (DOC) . . . 29 1.2.3 NOx aftertreatment systems . . . 29 1.2.3.1 Lean NOx Trap (LNT) . . . 30 1.2.3.2 Urea Selective Catalytic Reduction (Urea-SCR) . . . 30 1.2.4 Three-Way Catalyst (TWC) . . . 31 1.2.5 Latest developments in autocatalysts and other emission control

systems . . . 32 1.3 Factors affecting system’s efficiency . . . 32 1.3.1 Air/Fuel ratio . . . 34 1.3.2 Cold start emission . . . 34 1.3.3 Substrate technology . . . 35 1.3.4 Flow uniformity at the catalyst inlet . . . 36 1.4 Description of the physical and chemical problem . . . 37 1.4.1 Flow features . . . 37 1.4.2 Transport and reaction mechanisms inside a monolith substrate

channel . . . 40 1.4.2.1 Reaction mechanisms . . . 40 1.4.2.2 Mass transfer . . . 42 1.4.2.3 Heat transfer . . . 43 1.5 Modelling and simulation approaches . . . 44 1.6 Objective and structure of the present study . . . 50

1.1

A brief historical background

The drastic rise in the use of passenger vehicles over the past decades has led to an in-crease in harmful exhaust gas emissions. These emissions give rise to the formation of greenhouse gases, respiratory illness, and depletion of the earth’s ozone layer [65]. This problematic has led governments to establish very stringent conditions to control auto-motive emissions. Typical pollutants are hydrocarbons (HC), carbon monoxide (CO), nitrogen oxides (N Ox) and particulate matter (P M ). The main characteristics can be resumed as follows:

• CO formation results from the incomplete combustion of hydrocarbons due to the lack of oxygen in the air/fuel mixture [15]. CO constitutes the major part of the pollutants in the exhaust gas. The toxicity of CO is well known as it reduces the oxygen level in the blood even at low concentrations.

• HC come either from incomplete combustion or evaporation of the fuel before the combustion. They consist not only of alkanes, alkenes, aldehydes, alcohols, but also of aromatic compounds present in the fuel [27]. They have carcinogenic and mutagenic effects caused by benzene and aromatics compounds.

• NOx (N O, N O2, N2O2 etc.) formation is a consequence of high temperature re-action between nitrogen and oxygen [15]. In addition to the thermal N Ox forma-tion, prompt N Ox can be formed in some combustion environments, such as in low-temperature, fuel-rich conditions and short residence times [6]. Also, nitrogen-containing organic compounds present in the fuel can contribute to the total N Ox formation during the combustion. N Ox tends to bond the hemoglobin in blood as CO. The most undesirable toxic effect is the fact that N Ox joins with the moisture in the lungs to form dilute nitric acid and it is very harmful for respiratory systems. It is also one of the components of photochemical smog.

• Particulate matter - soot (P M) is formed as a results of heterogeneous nature of combustion in diesel engines. P M is formed due to poor fuel atomisation in the combustion chamber. Indeed, the non-vaporised fuel molecules are transformed into hard carbonaceous compounds due to high temperature in the combustion chamber. They usually consist of a core of carbon and agglomeration of several compounds coming from the combustion [4]. The effects of soot particles are multiple: harmful to health, climate and environment. P M is also believed to have mutagenic activity in the pulmonary mucosa.

In order to decrease the emissions of the harmful pollutants, consecutive emission norms have been imposed by European standards. The first generation of Euro I stan-dards was introduced in 1993. Table 1.1 shows the evolution of maximum emission limits for the pollutants. Because of the differences in the combustion process in gasoline and diesel engines, the composition of the exhaust emissions are different as well. N Ox and P M are the most problematic compounds for diesel vehicles while for gasoline vehicles, the objective is to reduce HC and CO emissions. Therefore, the standards introduce different emission limits for diesel and gasoline vehicles based on the Euro II norm. As can be seen in the table, there is a significant decrease in the emission limits of the main pollutants imposed by the recent norms. To illustrate this, 60% and 90% decrease in CO

1.1. A BRIEF HISTORICAL BACKGROUND

Table 1.1: Emission limits for passenger cars below 2500 kg according to European stan-dards [35].

Standard Limit values [g/km]

CO HC + N Ox P M

Petrol Diesel Petrol Diesel Petrol Diesel

1993, Euro I 2.72 2.72 0.97 0.97 - - - 0.14

1996, Euro II 2.20 1.00 0.50 0.7/0.9 - - - 0.08/0.1

CO HC N Ox P M

Petrol Diesel Petrol Diesel Petrol Diesel Petrol Diesel

2000, Euro III 2.30 0.64 0.20 - 0.15 0.50 - 0.05

2005, Euro IV 1.00 0.50 0.10 - 0.08 0.25 - 0.025

2008, Euro V 1.00 0.50 0.10 - 0.06 0.20 0.005 0.005

2014, Euro VI 1.00 0.50 0.10 - 0.06 0.08 0.005 0.005

and HC emissions for gasoline vehicles have been imposed in last 20 years. Similarly, approximately 85% decrease in N Ox emission for diesel vehicles has been imposed from the Euro III to the Euro VI norm.

In order to fulfil the emission limits, automotive industries have developed several technologies to control exhaust emissions. Some of them are briefly presented here. (i) The air injection technology is one of the first developed exhaust emission control system. This system was used to inject air into the engine’s port to provide more oxygen so that unburnt hydrocarbons in the exhaust are burned completely. The injection technology was sufficient to control exhaust gas emission to respect Euro II norms. (ii) Afterwards, an oxidation catalyst (DOC) was developed to reduce CO and HC emissions since it was impossible to respect the emission limits imposed by Euro III norms by a simple air injection into the engine’s port [17]. (iii) An Exhaust Gas Recirculation (EGR) system was also introduced as N Ox reduction technology which consist of recovery of a part of exhaust gas from the exit of the engine to reinject to the engine. This system was de-veloped to reduce the injected oxygen quantity to dilute air/fuel ratio and to decrease the temperature of combustion chamber. N Ox forms when the mixture of N2 and O2 is subjected to high temperature in the combustion chamber; hence, decreasing the tem-perature reduces the formation of N Ox. The shortcoming of this technology is that it increases the particle formation. Finally, EGR technology is a compromise between P M and N Ox as it decreases N Ox formation causing increase in P M .

The Euro IV norm imposed a significant reduction in P M and N Ox emissions which led to an optimisation of EGR technologies as well as developments of new injection sys-tems (such as the Common Rail injection system). Passing from the Euro IV to the Euro V norm imposed further decreases in P M and N Ox emissions. This necessitated lower combustion temperature to decrease N Ox formation (iv) while a filter technology had to be developed to decrease particle formation especially for diesel vehicles. However, the real challenge of depollution is introduced with the Euro VI norm which has been applied on September 2014. Current technologies are not sufficient to fulfil the emission limits imposed by the Euro VI norm which requires a combined use of new engine technologies with more efficient combustion, EGR and after-treatment systems in the exhaust gas line.

In Section 1.2 the after-treatment system will be introduced more in detail.

1.2

Development of automotive catalysts

Among the different technologies presented in the previous section, the most common and effective exhaust after-treatment method is the catalytic converter. Passenger vehichles equipped with catalysts were first introduced in USA in 1974 and in European roads in 1985. In 2000 more than 275 million of the world’s 500 million cars and over 85% of all cars manufactured worldwide were equipped with autocatalysts systems [55]. Figure 1.1 shows the structure of a catalytic converter. The converter is composed of two main parts: an outer stainless steel cylindrical or oval-shaped casing and a honeycomb matrix core within the casing. The honeycomb consists of many parallel channels in which the exhaust gas flows and is transformed into less toxic substances. The honeycomb substrate is usually made from either ceramic or metallic material able to resist high temperatures. The substrate is coated with highly porous alumina (Al2O3) washcoat which provides a rough surface and increases the effective surface area. The washcoat is impregnated with noble metals as catalysts. Usually, platinum (P t), rhodium (Rh) and palladium (P d) are used as catalyst materials. In the following subsections we present different catalyst tech-nologies used in diesel and gasoline vehicles as well as latest developments in autocatalyts.

Figure 1.1: Typical catalytic converter structure. Stainless steel casing and honeycomb with numerous parallel channels. The transformation of the main pollutants to the less toxic substances occur at the catalytic walls of the channels.

1.2.1

Diesel Particulate Filter (DPF)

The decrease in P M emissions limits imposed by the Euro V norm necessitates a devel-opment in filter technologies in Diesel vehicles. Today, most of the modern diesel vehicles use diesel particulate filter (DPF) to respect the imposed norms. The filter is located in the vehicle exhaust line and stocks particulate matter. DPF is a reactor made of ceramic, mainly cordierite or silicon carbide. It comprises numerous channels. The channels are blocked alternatively at one end or the other and they are connected to adjacent channels via porous walls. Figure 1.2 shows the schematic representation of DPF channels. The

1.2. DEVELOPMENT OF AUTOMOTIVE CATALYSTS

gas loaded with particulate matter is filtered when flowing through porous walls while the clean flow passes to adjacent channels. As a result, gases are forced to flow through the porous walls which act as filters for the particulate matter. The system must be cleaned every 500 km by raising the temperature (between 450◦_{C and 600}◦_{C depending on the}

support material) in the presence of oxygen. This process is called DPF active generation [1].

Figure 1.2: Schematic representation of diesel particulate filter (DPF) channels. Gas loaded with particulate matter P M is filtered when it flows through porous walls. The clean flow (light blue arrows) passes to adjacent channels while P M , in dark blue, is stored in the blocked channels.

1.2.2

Diesel Oxidation Catalyst (DOC)

Oxidation catalyst systems were the first after-treatment systems used in the automotive industry. They have been widely developed since mid-70s for gasoline engines because of the high CO and HC emissions. Catalysts used for diesel applications appeared later since they have relatively lower values of CO and HC emissions when compared to gaso-line vehicles. However the strict emission limits led to the use of diesel oxidation catalysts (DOC). Generally, the species are treated by a platinum-based catalyst. The presence of DOC also reduces P M mass being the reason why DOC is currently used in diesel after-treatment systems. In addition, the oxidation reaction of HC and CO is highly exothermic. Thus, DOC is used to control the temperature in the exhaust line and also to increase the temperature needed for DPF active regeneration mentioned in Subsection 1.2.1. This explains why DOC is commonly placed upstream of the DPF in the exhaust line.

1.2.3

NOx aftertreatment systems

In diesel engines, the expected Euro VI standard implies the use of a NOx after-treatment system to meet the N Ox emmission limits. Two technologies: Lean NOx Trap (LNT)

and Urea Selective Catalytic Reduction (Urea-SCR) have been developed to face N Ox

1.2.3.1 Lean NOx Trap (LNT)

In the technology, alumina washcoat coated on the monolith substrate bears a barium-based trap and a platinum and rhodium barium-based catalyst. The system requires the gases to switch to rich conditions1 _{for a few seconds every few minutes. Generally, the rich} mixture is created by in-cylinder late post-injection. This causes extra fuel consumption.

The conversion process is described as follows. During the lean phases, the N Ox

compounds are adsorbed in platinum-based catalysis. N O is oxidised to form N O2. Then

N O2 reacts with barium and stored as nitrate form (N O−3). The process is schematically represented in Figure 1.3-(a). During the first phase, the catalyst is exposed to the flow that is rich in reducing agents (CO, H2, HC). This flow induces a dissociation of nitrates and N Ox is released. Then, released N Ox react over the rhodium to form nitrogen and

carbon dioxide. The schematic representation of this process is depicted in Figure 1.3-(b)[59].

(a) Lean condition

(b) Rich condition

Figure 1.3: The mechanism of NOx trap according to Toyota [59]. (a) Lean condition where N Ox are stored as N O−3 forms. (b) Rich condition where reducing agents demon-strated as R induces a dissociation of N O−₃ and N Ox is released. Then released N Ox

reacts over the rhodium to form nitrogen and carbon dioxide.

1.2.3.2 Urea Selective Catalytic Reduction (Urea-SCR)

The SCR technology is already in use among heavy duty applications. It is also recently used in passenger cars to meet N Ox emission limits imposed by the Euro VI norm.

Al-though this system yields high N Ox conversion rates, it requires additional cost and

spe-cific servicing. Figure 1.4 shows the schematic representation of passenger cars equipped 1_{the air to fuel ratio is below stoichiometry (explained more in detail in Subsection 1.3.1)}

1.2. DEVELOPMENT OF AUTOMOTIVE CATALYSTS

with Urea-SCR system. The Urea-SCR system is composed of a tank containing urea, which is injected to exhaust line through a circuit. Then it is decomposed into ammonia (N H3) which reacts with N Ox on the SCR catalyst. The catalyst can be T iO2, V2O5, Fe-Ze, Cu-Ze, etc...

Figure 1.4: Schematic representation of a passenger car equipped with Urea-SCR system. The system includes a urea tank, a piping, a SCR control system, a Urea injector and a SCR converter. The system yields high N Ox conversion rate. However it requires

additional cost and specific servicing.

1.2.4

Three-Way Catalyst (TWC)

As already mentioned, when the catalytic converter was first introduced, it was designed for the oxidation of HC and CO to CO2 and H2O only. The shortcoming of this system is that N Ox pass through the catalyst without being treated. In addition, oxygen atoms

available for oxidation reaction are combined with nitrogen atoms forming N Ox. This

reduces the efficiency of the oxidation reaction.

The next generation of catalytic converters was introduced in 1979 with Rh as a reduc-tion catalyst. Reducreduc-tion catalyst releases the oxygen atoms which previously combined as N Ox. The oxygen atoms released by the reduction of N Ox simultaneously oxidise HC

and CO. Therefore, the three main harmful pollutants (HC, CO and N Ox) are treated

when passing through the catalytic channels and their emissions to the atmosphere is significantly reduced. This kind of catalyst is referred to as the “Three-Way Catalyst” (TWC).

1.2.5

Latest developments in autocatalysts and other emission

control systems

As seen above, various autocatalysts have been developed for different engine technolo-gies. DOC, DPF and NOx after treatment systems have been proposed to reduce N Ox and P M emissions in diesel vehicles. Different possible configurations of after treatment devices in the exhaust line are presented in Figure 1.5. As mentioned earlier, DOC is used to reduce HC and CO emissions as well as to control temperature in the exhaust line. The temperature needed to clean DPF is supplied by DOC, for this reason, DPF is located downstream of DOC as shown in Figure 1.5-(a). To respect N Ox emission limits imposed by the Euro VI norm, either LNT or Urea-SCR should be used in the exhaust line. LNT can be included either in DOC or in DPF systems as can be seen in Figure 1.5-(b). The Urea-SCR system is usually located after DOC and DPF systems as shown in Figure 1.5-(c ).

In gasoline engines, N Ox emissions are lower than in diesel engines. In this later case HC and CO emissions are more problematic. Therefore TWC is an appropriate system for this type of vehicles to face Euro norms. To achieve the best simultaneous oxidation and reduction reactions, TWC are equipped with one or more oxygen sensors and a com-puterized closed-loop feedback fuel injection system2.

In addition, the automotive catalysts coupled with other advanced emission control methods have also been developed. Close Coupled Catalyst3 (CCC) combined with Under Body Catalyst4 (UBC) for Ultra Low Emission Vehicle5 (ULEV) application, electrically-heated catalysts6, in-cylinder catalysts7, catalyst-coated piston crowns, exhaust gas igni-tion systems8(EGI), insulated exhaust pipes, secondary air-rich fuel mixture systems9 are some examples of these developments. However, to develop further the efficiency of these systems, it is fundamental to understand the factors and parameters that influence the performance of the catalytic converter. Especially, the flow distribution and its impact on the conversion process must be studied and optimised.

1.3

Factors affecting system’s efficiency

Catalytic converter technologies are complicated due to the complex physical and chem-ical phenomena controlling the system’s efficiency. In the following subsections, some important factors effecting the catalytic converter’s efficiency are presented [48, 7, 88, 47, 16, 81, 12, 37, 2].

2_{will be explained more in detail in Subsection 1.3.1}

3_{catalytic converter located near the engine’s exhaust manifold which heats up quickly to increase the} conversion efficiency

4_{catalytic converter located after CCC}

5_{motor vehicle that emits extremely low levels of emissions}

6_{heated catalyst disc which is supported by insulating pins installed in front of the main catalyst} 7_{catalytic coating inside of the cylinder head for improved burn rate and flame propagation}

8_{when the engine operates initially with very rich fuel condition, the remaining unburnt fuel is ignited} at the catalyst inlet face by this system

9_{secondary current of air after the exhaust valves is injected to overcome lack of oxygen in catalytic} converter when the engine operates at rich fuel conditions during cold start

1.3. FACTORS AFFECTING SYSTEM’S EFFICIENCY

(a)

(b)

(c)

Figure 1.5: Different possible configurations of after treatment devices in the exhaust line. (a) DPF is located downstream of DOC as DOC supplies the necessary temperature to clean DPF. (b) LNT can be included in the DOC. (c ) Urea-SCR system is usually located after DOC and DPF systems.

1.3.1

Air/Fuel ratio

The air/fuel ratio (AFR) is the mass ratio of air to fuel present in an internal combustion engine. AFR influences greatly the exhaust gas composition. When enough oxygen is provided to completely burn the fuel, this air/fuel ratio is referred as stoichiometric mix-ture (AFR _{∼ 14.6). Figure 1.6 depicts the conversion efficiency of NO, CO and HC as} function of the AFR. As can be seen in the Figure, there is a narrow AFR interval (the width of the interval is about 0.1) in which high conversion efficiencies are achieved for all the pollutants. This interval is called “operating (lambda) window”.

To obtain the best simultaneous conversions for N O, CO, and CH, the AFR has to be fixed within the operating window. To this end, an oxygen (lambda) sensor is placed at the upstream of the catalytic converter so that the oxygen concentration is measured to calculate the AFR. Then the oxygen sensor sends a feedback to the closed-loop engine management/fuel injection systems in order to adjust the AFR so that the catalytic converter operates within the operating window condition [48].

0 20 40 60 80 100 14.4 14.5 14.6 14.7 14.8 Catalyst efficiency [%] Air/fuel ratio Operating window CO HC NO_x

Figure 1.6: Conversion efficiency of CO, HC and N O_x as function of the air/fuel ration in TWC [48].

1.3.2

Cold start emission

Temperature is an important controlling factor in the automotive catalytic converter’s performance. It is known that TWC is not active when the temperature is below the light-off temperature. The light-off temperature is defined as the temperature where the conversion of inlet species attains 50% [48].

The study of Becker et al [7] illustrates quantitatively the cumulative HC emissions during cold engine start. The study describes four operation phases. Phase 1 is the warm-up phase where there is essentially no chemical reaction because the temperature is below light-off. Phase 2 is the light-off phase where reaction rates increase by increasing temperature. Phase 3 is the hot operation regime where reactions occur very fast and

1.3. FACTORS AFFECTING SYSTEM’S EFFICIENCY

the conversion is controlled by mass transfer. Phase 4 is the restart after a ten minute hot soak and is described as warm start. Over 44% of HC emissions occur during phase 1. Figure 1.7 presents the cumulative CO, HC and N O_x emissions recorded during the European driving cycles10. Most of the emissions occur approximately for the first 100 seconds, which corresponds to cold engine start.

0 2 4 6 8 10 12 14 200 400 600 800 1000 1200 Cumulative emissions (g) Time (s) CO HC NO_x

Figure 1.7: Cumulative CO, HC and N Ox emissions of a 21 gasoline car in the new European driving centre [48].

To conclude, minimizing cold-start time is crucial in order to increase the efficiency of catalytic converters. Therefore, special techniques have been developed referred as fast light-off techniques (FLTs). FLTs may be categorized as passive systems employing exhaust system design changes (positioning the catalytic converter closer to the engine, using pre-catalysts or HC traps etc..) and active systems which rely on the controlled supply of additional energy to raise exhaust gas temperature rapidly (electrically heated catalyst, burner, exhaust gas ignition with secondary air injection etc...) [48].

1.3.3

Substrate technology

Substrate design is one of the major controlling factors as it influences the overall conver-sion efficiency. As mentioned in the previous section, the honeycomb monolith substrate is usually made from either ceramic cordierite (2M gO _{· 2Al2}O3 _{· 5SiO2}) or folded metal foil. Figure 1.8 shows the metallic and ceramic substrate (without washcoat). Generally ceramic substrates have square cross sectional shape while metallic substrates have sinu-soidal or triangle shapes. Both metallic and ceramic substrates can present either circular or elliptical cross sectional shapes. The advantage of ceramic substrates is that they have lower thermal expansion compared to metallic substrates. Metallic substrates heat up faster than ceramic substrates as their heat capacity and thermal mass are lower. Thus they are used as start-up catalysts in close-coupled positions. Metallic substrates have also thinner walls and higher cell density than ceramic ones, however they are usually

more expensive.

Figure 1.8: Cross sectional metallic and ceramic substrates.

Table 1.2 shows the typical ceramic substrate dimensions. The trend is towards de-creasing wall thickness and inde-creasing cell density. High cell densities are desirable to increase the surface area where wash coat is applied for a given substrate volume. This provides better conversion efficiency and durability. The shortcoming of high cell density substrates is that they increase the pressure drop induced by narrow substrate channels decreasing the combustion efficiency in the engine. Small wall thickness systems minimize the pressure losses due to high cell density and reduce the thermal capacity.

Table 1.2: Commercial ceramic substrates used in automotive converters [88]. Cell density Wall thickness Geometric surface area Open frontal

(cpsi) (mm) (cm2_{/ccm) area} 25 0.889 6.51 0.681 50 0.635 9.17 0.678 100 0.381 13.39 0.723 200 0.267 18.98 0.725 300 0.203 23.51 0.742 400 0.102 27.09 0.846 600 0.102 31.01 0.787 900 0.051 43.11 0.834

1.3.4

Flow uniformity at the catalyst inlet

In an ideal situation, the flow at the converter inlet should be uniform. However, in practical cases, the flow is non-homogeneous and non-uniform at the inlet converter. The reasons are the following: On one side a significant portion of the pressure drop of the total exhaust system is induced by the catalytic converter. This influences the engine perfor-mance and the fuel economy. In order to reduce the pressure drop induced by the catalytic converter, the monolith substrate is dimensioned as short as possible. This necessitates high substrate diameters to increase the total surface area where catalytic reactions take place. Typical cylindrical monoliths have diameters of ∼100mm and lengths of ∼150mm.

On the other side, packaging constraints do not permit the use of long diffusers which can distribute the flow uniformly between the inlet pipe and the substrate. Eventually, the

1.4. DESCRIPTION OF THE PHYSICAL AND CHEMICAL PROBLEM

abrupt expansion in diffuser lead to flow separation. Figure 1.9 illustrates typical flow profiles troughout the catalytic converter. In the diffuser, the flow separates right after the expansion point inducing a jet flow close to the axis of symmetry and a recirculation region at the expansion region where the inverse pressure gradient leads to a backflow. In addition to this, high Reynolds numbers, pulsating flow coming from the engine and the impact of porous media contribute to the flow non-uniformity at the converter inlet [11].

Figure 1.9: Typical flow profiles throughout catalytic converter [66].

The flow non-uniformity influences pressure drop, warm-up, light-off time, aging, de-activation and conversion efficiency [90, 47, 16, 81, 11, 12, 37, 2]. For a given substrate geometry, the minimum pressure drop is obtained when the catalyst inlet velocity profile is uniform and axial. When the velocity is not uniform at the catalyst inlet, the high velocity entering the substrate creates a local high pressure drop decreasing the system’s efficiency. In addition to this, different inlet velocities in substrate’s channels result in premature degradation of the catalyst in areas of high flow rates and poor volume utili-sation of catalyst in areas of low flow rates, which turns into a decrease of the system’s efficiency [11, 47]. It is also known that flow non-uniformities adversely affect the local balance between heat generation and heat convection rates, leading to severe degradation of the light-off performance [90].

1.4

Description of the physical and chemical problem

In catalytic converters, we find various physical and chemical processes occurring simul-taneously throughout the system. In the next subsections, we examine these physical and chemical phenomena and we discuss their importance under certain operating conditions.

1.4.1

Flow features

Different flow patterns are observed in automotive catalytic converters due to the changes in geometry. Figure 1.10-(a) shows a typical geometry of the system that we use in our simulations without the presence of the empty rooms between the diffuser and the cata-lyst substrate as well as between two catacata-lyst substrates. Figure 1.10-(b) represents the resulting flow features. The inlet diffuser increases the pressure and reduces the kinetic energy. The increasing pressure in the diffuser induces an unfavourable gradient causing the viscous boundary layers to break away from the walls [87]. This leads to flow sep-aration. Indeed, the flow separation occurs right after the expansion point for diffusers with high angles and short lengths. The separation forms a turbulent free shear layer

as demonstrated in Figure 1.10-(b). This shear layer divides the flow into two regions. A main jet flow appears close to the axis of symmetry whereas a recirculation flow re-gion appears between the expansion rere-gion and the monolith substrate as observed in Figure 1.10-(b). When there is an empty room between the diffuser and the substrate, the vortices in the recirculation region are advected until they impinge on the substrate. The intense recirculation induces high energy dissipation rates within the separated flow region [29]. In addition to this, when the flow expands, it becomes turbulent [62, 75, 82]. We find highly turbulent regimes and pulsating flow generated by the combustion engine. This leads to large range of scales and energetic structures in the upstream flow.

(a) (b)

Figure 1.10: Geometry changes in automotive catalytic converter and resulting flow fea-tures. (a) Example of catalytic converter geometry. (b) Typical flow patterns inside a catalytics converter (Re=10000) in the symmetric plane. A shear layer forming right after the expansion point and a large recirculation region are observed in the diffuser region. The flow is re-laminarized inside the catalytic channels.

Although the upstream regime is highly turbulent, the flow is laminarized by viscous forces inside the narrow channels (of the order of 1 mm). This induces a significant pres-sure drop across the channels compared to inlet diffuser and outlet nozzle.

At the entrance of the substrate channels, we find a uniform velocity profile rather than a parabolic velocity profile. This corresponds to a “developing laminar flow”. In this flow region, a hydrodynamic boundary layer starts to develop. Viscous forces slow down the fluid near the wall, causing a velocity drop near the wall and higher velocity in the centre of the pipe. This leads to a pressure increase as the fluid flows through the pipe. Thus, the development of the flow causes an additional pressure drop. After some distance, a parabolic velocity profile is established reaching a “fully developed flow”. The flow transition occurs only in the first few millimetres after the monolith entrance.

Figure 1.11-(a) depicts an example of streamfunctions found in the diffuser. The streamfunctions illustrate the recirculation zone and vortices due to turbulent expansion flow. The recirculation zone and vortices lead to large angles of velocity vectors at the entrance of the catalyst channels. The velocity vector misalignment causes an enlarged recirculation zone at the channel entrance and an additional pressure drop occurs. Fig-ure 1.11-(b) illustrates the streamfunctions found at the catalyst channel entrance. An enlarged recirculation zone is observed. Quick laminarization right after the recirculation region occurs due to viscous forces in the narrow channels.