Abstract A physics based one-dimensional transient seven partial differential equation model is proposed to study the oxygen storage dynamics and cold start behavior of a three-way catalytic converter. The model uses the recently published simplified kinetic model, is computationally efficient and may be used for offline TWC outer loop controller design and validation. The proposed TWC model is validated using emissions data collected in a vehicle over multiple drive cycles including FTP cycles. The internal mass transfer approximation is confirmed by comparing with a detailed washcoat diffusion–reaction model and is observed to be consistent for all practical purposes. The results are also used to study the qualitative and quantitative errors in emission and oxygen storage predictions caused by axially averaging thus identifying the region of applicability of the simpler axially averaged seven ordinary differential equation model.
Abstract Analysis of limiting models of a Diesel Particulate Filter (DPF) provides insight on its design and operating conditions. Analytical expressions for predicting the filtration velocity, pressure drop, filter heat-up time and speed and width of the temperature front in a DPF are presented. A more uniform filtration velocity with a lower pressure drop can be obtained by either decreasing the inlet velocity, increasing the channel hydraulic diameter or by increasing the DPF aspect ratio (D/...
Abstract We study the effect of the substrate material (ceramic versus metallic) on the steady-state and transient performance of monolith reactors using a one-dimensional two-phase model with position dependent transfer coefficients. When the operation of the reactor is on the ignited branch, it is shown that monoliths with metallic substrate clearly lead to a superior steady-state performance compared to those with ceramic substrate. In such cases, the ignited branch extends to lower inlet gas...
Abstract We propose a low-dimensional model of the three-way catalytic converter (TWC) that would be appropriate for real-time fueling control and TWC diagnostics in automotive applications. The model reduction is achieved by approximating the transverse gradients using multiple concentration modes and the concepts of internal and external mass transfer coefficients, spatial averaging over the axial length and simplified chemistry by lumping the oxidants and the reductants. The reduced order mod...
A four-mode low-dimensional model for the in-cylinder combustion process in an internal combustion engine is developed. The lumped parameter ordinary differential equation model is based on two mixing times that capture the reactant mixing limitations inside the cylinder and mixing limitations caused by the input and exit stream distribution. For a given inlet and operating conditions, the model predicts the exhaust composition of regulated gases (total unburned HCs, CO, and NOx) as well as the ...
We review and compare the literature correlations for estimating the heat and mass transfer coefficients as well as pressure drop in catalytic monoliths with simultaneously developing velocity, concentration and temperature profiles. We present accurate correlations for estimating the local Nusselt and Sherwood numbers for developing flows with constant flux (slow reaction) and constant wall concentration or temperature (fast reaction) cases for a channel of arbitrary shape. These new correlatio...
Abstract We utilize the recently developed concept of internal or intraphase mass transfer coefficient to simplify the problem of diffusion and reaction in more than one spatial dimension for a washcoated monolith of arbitrary shape. We determine the dependence of the dimensionless internal mass transfer coefficient ( Sh i ) on washcoat and channel geometric shapes, reaction kinetics, catalyst loading and activity profile. It is also reasoned that the concept of intraphase transfer coefficient i...
Abstract A global kinetic model for NOx storage and reduction for the case of anaerobic regeneration with hydrogen is developed, based on parallel experimental studies [R.D. Clayton, M.P. Harold, V. Balakotaiah, Appl. Catal., B 84 (2008) 616; R.D. Clayton, M.P. Harold, V. Balakotaiah, C.Z. Wan, Appl. Catal., B 90 (2009) 662.]. The existence of two different types of BaO storage sites on the catalyst is proposed, which differ in their storage as well as regeneration activity. The two-site model e...
We present accurate low-dimensional models for real time simulation, control, and optimization of monolithic catalytic converters used in automobile exhaust treatment. These are derived directly by averaging the governing equations and using the concepts of internal and external mass transfer coefficients. They are expressed in terms of three concentration and two temperature modes and include washcoat diffusional effects without using the concept of the effectiveness factor. The models reduce t...
A heterogeneous one-dimensional model is used to simulate a three way catalytic converter (TWC). The mathematical model consists of mass and energy balance equations in the gas and solid phases and accounts for 15 heterogeneous chemical reactions. Langmuir−Hinshelwood type kinetics is used to represent most of the reaction rates. In this work, the kinetic parameters of the various reactions occurring in a TWC are estimated using vehicle data based on a genetic-algorithm-based optimization. The m...
Abstract We present a general solution of the diffusion–reaction problem for linear kinetics and an expression for the effectiveness factor ( η ) in terms of the shape normalized Thiele modulus ( Φ ) for a catalyst particle of arbitrary shape and with an arbitrary activity profile. We also show that the Sherwood number ( Sh Ω ) or the dimensionless mass transfer coefficient between the interior of a particle or region (denoted by Ω ) and its boundary ( ∂ Ω ) is related to the effectiveness facto...
We propose a delay-dependent sampled-data output-feedback LPV control technique to address the air-fuel ratio (AFR) regulation problem in spark ignition (SI) engines. AFR control and advanced fueling strategies are essential for maximizing fuel economy while minimizing harmful exhaust emissions. The fuel path of the SI engine, as well as the three-way catalyst (TWC) simplified dynamics, have been captured by a continuous-time linear parameter-varying (LPV) system with varying time delay, where t...
Abstract We use the Lyapunov-Schmidt (L-S) reduction technique of bifurcation theory to develop reduced order models for monolith reactors with catalytic reactions in the washcoat layer and homogeneous reactions in the flow channel, and with thermal effects. The L-S technique eliminates the two transverse coordinates and converts the detailed models expressed in terms of three spatial coordinates and time to multi-mode models in axial coordinate and time. The reduced order models are expressed i...
This article introduces a physical model of a three-way catalytic converter oriented to engine cold-start conditions. Computational cost is an important factor, particularly when the modelling is oriented to the development of engine control strategies. That is why a one-dimensional one-channel real-time capable model is proposed. The present model accounts for two phases, gas and solid, respectively, considering not only the heat transfer by convection between both, but also the water vapour co...
Abstract We present a novel and accurate reduced order model with local property dependent internal and external mass transfer coefficients for real time simulations of monolith reactors. We compare the accuracy of the present approach with other reduced order models in the literature and with exact (numerical) solution of the detailed washcoat diffusion model. We illustrate the application of the reduced order models with three examples: a four reaction model of a three-way catalytic converter ...
Abstract NOx Storage and Reduction (NSR) conducted at higher cycling frequency enables enhanced conversion of NOx emitted by lean burn gasoline and diesel vehicles. Ting et al. (2018) reported data using a Pt/Rh/BaO/CeO2/Al2O3 showing that stored NOx utilization is primarily responsible for enhanced NOx conversion during fast cycling. In this study a low-dimensional, two-phase monolith reactor model comprising a network of reactions with global kinetics using C3H6 as the reductant is developed. ...
#1Rajbala(IITD: Indian Institute of Technology Delhi)H-Index: 2
#2Divesh Bhatia(IITD: Indian Institute of Technology Delhi)H-Index: 8
A model incorporating crystallite-scale features of a catalyst is developed to predict the oxygen storage capacity (OSC) of a Pd-containing three-way catalyst. The model predicts the effect of Pd crystallite size, Pd-ceria interfacial contact, and Pd dispersion on the spillover and reverse-spillover of oxygen between Pd and ceria, and the resulting OSC with H2 and CH4 as reductants. Consistent with the experimental findings, the model predicts that H2 results in a higher OSC than CH4. The depend...
#1Carlos Guardiola(Polytechnic University of Valencia)H-Index: 24
#2Héctor Climent(Polytechnic University of Valencia)H-Index: 18
Last. Marcelo Real(Polytechnic University of Valencia)H-Index: 2
view all 4 authors...
The purpose of this paper is to introduce a grey-box model of three-way catalytic converter, which is capable of estimating the oxygen storage level to aid the fuel-to-air ratio control in spark ig...
We present numerical and experimental investigation on the existence of diffusion-induced compositional variations in a reservoir fluid in the absence of convective mixing. New pressure-decay experimental data are presented for ethane in contact with stock tank oil, and the values of diffusivity and solubility parameters are obtained by using the one-dimensional transient diffusion model and integral-based regression method. We show the variation in oil composition through composition-height mea...