Edited by: Evangelos G. Giakoumis, National Technical University of Athens, Greece
Reviewed by: Christopher Harald Onder, ETH Zürich, Switzerland; Eduardo Ernesto Miro, Universidad Nacional del Litoral (FIQ-UNL), Argentina
This article was submitted to Engine and Automotive Engineering, a section of the journal Frontiers in Mechanical Engineering
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Today restrictions on pollutant emissions require the use of catalyst-based after-treatment systems as a standard both in SI and in Diesel engines. The application of monolith cores with a honeycomb structure is an established practice: however, to overcome drawbacks such as weak mass transfer from the bulk flow to the catalytic walls as well as poor flow homogenization, the use of ceramic foams has been recently investigated as an alternative showing better conversion efficiencies (even accepting higher flow through losses). The scope of this paper is to analyse the effects of foam substrates characteristics on engine performance. To this purpose a 0D “crank-angle” real-time mathematical model of an I.C. Engine developed by the authors has been enhanced improving the heat exchange model of the exhaust manifold to take account of thermal transients and adding an original 0D model of the catalytic converter to describe mass flows and thermal processes. The model has been used to simulate a 1.6l turbocharged Diesel engine during a driving cycle (EUDC). Effects of honeycomb and foam substrates on fuel consumption and on variations of catalyst temperatures and pressures are compared in the paper.
In the last decades the constant need to reduce pollutant emissions from Internal Combustion Engines (ICEs) led OEMs both to enhance existing subsystems (e.g., fuel injection, valve actuation systems, etc.) and to introduce innovative solutions (with particular reference to after-treatment devices). As a matter of fact, in order to allow these technologies to be really effective, a proper and concurrent design of plant layout, control systems and management strategies is needed.
The complexity of systems and the large number of control variables require a deep understanding of processes that determine the behavior of the controlled powertrain as a system as a whole. The design of system architecture and of its control devices definitely need a solid theoretical support from physical models to outline system overall behavior, which is mostly non-linear and therefore difficult to predict. Mathematical models are powerful tools to estimate the influence of system layout and control strategies on the final result thus shortening the way from design specifications to on-road testing (Guzzella and Onder,
The application of fast mathematical models in the design of powertrains and related management systems is well-known for more than a decade and several examples can be found in the literature (Gambarotta and Lucchetti,
This scenario highlights the significant role of fast mathematical models in the simulation of complex systems, whose overall behavior arises from the interactions of different components and processes in a complex and not trivial way. Following this consideration, and in order to investigate the effects of different catalyst substrates on powertrains performance, a model of the after-treatment system has been developed and coupled with a “crank-angle” engine model (Gambarotta and Lucchetti,
Open cell foams are cellular materials composed by interconnected solid struts arranged in cells that enclose void regions, and open window or pores. Such foams can be readily manufactured with different technologies and materials ranging from polymers, ceramics (Al_{2}O_{3}, cordierite, or SiC) and metals (Santoliquido et al.,
Recently, a variation of foam structure has been proposed based on the advances of additive manufacturing (AM) techniques. Such “foams” are composed by repeated unit cells with different shapes (Inayat et al.,
It is not straightforward to quantify the influence of catalyst substrate structure on engine performance due to the different dynamic behavior of honeycombs and foams during transients and to the high non-linearity of the overall engine system. To compare the influence of honeycomb and foam substrates an original 0D mathematical tool has been developed and used to model an up to date 1.6l turbocharged Diesel engine. Simulation results obtained with reference to an EUDC driving cycle are reported in the paper showing the effects of these different supports on catalyst thermal transients and on fuel consumption.
For the purpose of this work the engine model described in Gambarotta et al. (
Cycle averaged value of equivalence ratio φ is calculated from total intake air mass (obtained by integrating air mass flow rate over each cycle) and the total fuel mass injected per cycle (estimated from injected fuel flow rate). Mass flow rates of considered pollutants (CO, HC, and PM), required to calculate pollutant concentrations
The model and its causality scheme are described in Gambarotta et al. (
Heat transfer processes in the exhaust system have a key role in the simulation of ICEs due to the significant influence of exhaust gas temperature on after-treatment systems efficiency. Therefore, a careful description of heat exchange processes is fundamental especially during critical transients (e.g., catalyst “light-off,” particulate trap regeneration, etc.). Other emission critical phases of engine operation are long time operation at low load, when the after-treatment system is significantly cooled down, as well as at highest load, when temperatures are high enough but exhaust mass flow rates force the catalyst to operate under mass transfer deficiency. For this reason, although within the limitations imposed by a 0D approach, particular attention has been dedicated to the simulation of thermal behavior of the exhaust system.
Working fluid has been considered as a mixture of perfect gases defined through a vector of mass concentrations
Finally λ is obtained from the definition of
The mathematical model of the exhaust manifold has been developed following a F&E approach. Temperature and pressure are obtained from the equations of conservation of mass and energy applied to the manifold considered as a 0D volume. Estimating heat flow through manifold walls as suggested in Guzzella and Onder (
where
In the presented model the thermal inertia of the exhaust manifold has been considered assuming a defined overall mass
where
Schematic of the exhaust manifold flows.
To estimate
The term
where
and
where
and
Then convection coefficient and heat flux can be calculated, since:
and
where
The estimation of convective heat flux from manifold walls to ambient air is more difficult due to the component geometry and to external flow pattern. For the sake of simplicity, manifold geometry has been assumed as cylindrical and external flow field uniform and related to the vehicle speed. The model is based on the correlation proposed in Konstantinidis et al. (
where
and
From
and
where
External radiation heat flux
where
Total heat flux
A catalytic converter is a complex component from the point of view of both gas flow pattern and of chemical reactions. Fluid dynamics, heat and mass transfer processes have a significant role in its behavior and should be carefully considered. Taking account of the aims of the presented work, neither a 3D (e.g., Lucci et al.,
The model has been developed according to the causality reported in
Schematic and causality of the catalyst model.
Layout of the model of the catalyst core.
The “gas model” has been developed as shown in
where ρ and μ (as other fluid properties) are calculated at
where axial heat exchange and variation of kinetic and potential energy in the gas are neglected (as usually considered; Pontikakis et al.,
Structure of the “gas model” module (input and output variables are in green and red, respectively).
The convective heat exchange between gas and core is described as usual through a convection coefficient
Wall temperature of the monolith
Molecular diffusion of different species and chemical reactions in the gas mixture and in the core has not been considered. However, the overall effects of unburnt species oxidation are replicated in terms of generated heat through the following expression (in [W/m]):
which represents a 1D distribution of heat generation along the axial length of the core (between
The number
The term
Coefficients
and assuming that the ratio
The integration of energy conservation equation in 1D and in steady state between
Heat flux between gas and monolith in each time step can be estimated through the equation:
It should be noted that since properties of gas mixture are determined with reference to the average temperature in the core, the value of
For the estimation of changes of mean temperature of the monolith
In addition to the heat flux exchanged with gases
Even if different configurations can be found, the most common technique is to fit the monolith into a metal casing with a layer of interposed insulating material: this layout has been assumed in the developed model, as schematically shown in
where
Schematic of flow and heat exchange processes in the catalyst core.
Taking into account only the insulating material layer (i.e., neglecting the thermal resistance of the metal casing) and assuming a cylindrical geometry,
Forced convection to ambient air can be considered assuming a cylindrical casing with radius equal to
where
assuming a gain factor of 3/2 to take account of axial conduction in the metal casing.
The convection coefficient
where
As regards thermal radiation, assuming the external wall of metal casing as a gray body inside a large cavity, corresponding heat flux can be estimated as Incropera et al. (
from which
Finally, heat flux to external ambient air can be calculated as:
Parameters for forced and natural convection have been calculated with reference to fluid properties at the average temperature:
where
Therefore, the value of
The described procedure has been used for the simulation of different catalyst substrates (honeycombs or foams) by using suitable correlations to link mass flow rates and pressure changes in the catalyst core (concentrated flow resistance) and to determine
The presented model of the after-treatment system has been then calibrated with reference to specific core geometries, honeycombs, and foams. Flow resistance and heat transfer processes have been identified from correlations available in literature and standard physical and geometrical properties have been used.
In honeycombs, the gas has to move in channels of very small section, and therefore the flow is mainly laminar. Correlations that link mass flow rate with Δ
or, placing
as suggested in Incropera et al. (
As regards the foam, a first relation was derived from Giani et al. (
where in
A second correlation, suggested in Lucci et al. (
where χ is called “tortuosity” and represents the ratio between the length of the actual path followed by the fluid and the corresponding axial displacement. With reference of the complex geometry of foams, χ is usually far greater than 1. To fit the results of 3D simulations, drag coefficient
where
The estimation of heat flow between exhaust gases and the internal surface of the monolith has been based on the calculation of convection coefficient
where
For foams two correlations were used from the literature. The first one has been suggested in Giani et al. (
where
Three-dimensional and frontal view of a Kelvin cell (KC), from Lucci et al. (
A second correlation has been used for foams, derived from Lucci et al. (
where the Hagen number
It should be recalled that the first correlation (Giani et al.,
The second correlations (Lucci et al.,
In
Flow resistance and transport correlations used.
Honeycombs |
||
Foam |
||
Kelvin cell |
The total volume of the catalytic reactor is assumed to be 1.5 l with a reactor length of 15 cm. A standard honeycomb structure, identified in the following as “h_Giani,” is used as reference case and is characterized by a porosity of ε = 63%, a characteristic channel diameter of
Values of parameters assumed for the catalysts models.
0.01 | 0.01 | [m^{2}] | |
0.15 | 0.15 | [m] | |
0.001 | 0.002 | [m] | |
ε | 0.63 | 0.90 | [–] |
χ | – | 1.1 | [–] |
2,700 | 1,000 | [m^{2}/m^{3}] | |
0.006 | 0.006 | [m] | |
0.03 | 0.03 | [W/m/K] | |
ε | 0.6 | 0.6 | [–] |
300 | 300 | [K] | |
101325 | 101325 | [Pa] | |
2,600 | 3,920 | [kg/m^{3}] | |
1,050 | 800 | [J/kg/K] |
Thickness
However, it should be recalled that all the above-mentioned parameters can be easily changed in the model, allowing to test and compare different geometries.
The exhaust system and the catalyst models have been coupled with a 0D “crank-angle” model of a turbocharged Diesel engine. The structure of the model (alternating volume and non-volume blocks) avoided numerical problems and algebraic loops (Gambarotta and Lucchetti,
The model has been identified with reference to a 1.6l turbocharged Diesel engine (main technical data are reported in
Main technical data of the considered diesel engine.
Bore × stroke | 79.5 mm × 80.5 mm |
Compression ratio | 16.5 |
I/E valves | 2 intake valves with multiair® |
Injection system | Common rail multijet II® |
Intake system | Turbocharged with variable geometry turbine |
Exhaust gas recirculation | Low pressure system |
Input parameters are engine rotational speed, fuel mass flow rate, driving signals for VGT and EGR, ambient temperature and pressure. Outputs can be every single one of the parameters estimated by the engine model, e.g., torque,
In order to highlight the influence of substrate characteristics on engine behavior, the Extra Urban Driving Cycle (EUDC) section of the New European Driving Cycle (NEDC) was chosen. To this extent input parameters (rotational speed, fuel mass flow rate, VGT and EGR driving signals) were defined through an inverse model of the vehicle (developed in Guzzella and Sciarretta,
Thermodynamic parameters in the intake and exhaust systems obtained with different substrates were compared. As an example, in the following, several results are plotted with reference to the EUDC assuming the honeycomb substrate as a baseline (“h_Giani,” in solid red) and computed differences between the two open cell foam like structures (the real foam “f_Giani,” in solid green, and the Kelvin cell structure “f_Lucci,” in solid blue).
As expected, foam substrates lead to higher pressure losses. In
Calculated pressure losses through different catalysts substrates.
Calculated pressure changes through turbine.
Calculated pressure in the exhaust manifold.
Temperature profiles inside the catalytic reactor block are presented in
Calculated temperature of the substrates.
The model allowed to estimate instantaneous and cumulative fuel consumption on the considered EUDC: results are plotted in
Calculated cumulative fuel consumption during the EUDC.
The analysis of the instantaneous fuel consumption ṁ_{f} shows that, within the assumed conditions, lower values are reached for the honeycomb than for both open cell foam structures. However, differences in cumulative fuel consumption between the cases is lower than 0.20%. Furthermore, among the open cell substrates, fuel consumption with real foams (“f_Giani”) is slightly lower than that with Kelvin Cells structures (“f_Lucci”).
As previously shown, pressure drop through the catalytic converter is higher for open cell structures (
The maximum deviation observed in instantaneous fuel consumption between all the cases was 0.35%, appearing only during accelerations when higher torque is requested. During steady driving conditions at constant velocity the increased instantaneous fuel consumption due to the open cell structure substrate is lower (0.10% approximately). These variations result in an increase of only 0.20% in total injected fuel over the whole 400 s of the cycle.
Mathematical models represent an interesting (and often unavoidable) way to get a proper understanding of the behavior of complex systems. As a matter of fact, development of theoretical tools requires a good compromise between physical and empirical approaches to limit the CPU time.
In the paper a fast model of a catalytic converter for automotive application has been built up and integrated in a 0D “crank-angle” model of a turbocharged Diesel engine. After improving the heat exchange model for the exhaust manifold (to take account of thermal dynamics during transients), a 0D model of the catalyst has been developed to simulate related flow and thermal processes. Then the catalyst model has been coupled to an engine model to investigate the behavior of the overall system and the effects of catalyst substrate characteristics. To this extent an actual 1.6 l turbocharged Diesel engine with EGR has been simulated within an EUDC driving cycle comparing engine performance with different catalyst substrates.
The behavior of three different catalytic structures was analyzed: honeycomb, open cell foams and open Kelvin cell structures. It has been shown that, using reactors of the same volume, the increased pressure drop caused by open cell structures results in a total fuel consumption increase not higher than 0.20%. On the other side open cell structures show faster thermal transients due to their lower thermal inertial and thus are able to reach quickly light-off temperatures.
It should be noted that higher mass transfer properties of open cell structures may allow for more compact reactors compared to honeycombs. This may help to reduce the overall flow resistance of foams giving new possibilities to improve the efficiency of the after-treatment system lowering at the same time specific fuel consumption. The presented mathematical tool proved to be very effective to simulate the behavior of the comprehensive system (engine+after-treatment system) and will be used in the next future to explore exhaustively these topics.
It should be recalled that in the presented model working fluid has been considered as a mixture of 7 chemical species, i.e., N_{2}, O_{2}, CO_{2}, H_{2}O, CO, H_{2} NO. The number N and the type of involved pollutants depend on the specific application. In the presented model CO and one or more species representative of HC have been considered, since their oxidation reactions were assumed as the most significant in the determination of the catalyst temperature. Different after-treatment systems can be considered in the next future, e.g., three way catalysts (which represents a very interesting application for these new solutions). Modeling a three way catalyst however, is more complex since it involves the oxygen balance (gasoline engines are always near stoichiometric operation) and thus always operating under oxygen shortage. The presented approach can be used to attempt modeling a three way catalyst under real driving conditions in real-time.
Finally it should be emphasized that in the presented work the vehicle model has not yet been developed. Therefore, required input parameters (i.e., rotational speed, fuel mass flow rate, VGT and EGR driving signals) were defined through an inverse model of the vehicle (developed in Guzzella and Sciarretta,
The datasets generated for this study are available on request to the corresponding author.
AG, VP, and PD contributed to the design and implementation of the research, to the analysis of the results and to the writing of the manuscript.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The authors gratefully acknowledge financial support from the Swiss federal Office for the Environment (FOEN) for the projects, Exhaust After treatment system for the lowest environmental impact, Natural Gas powered delivery vehicle, Euro 7 and beyond (EAS7+), project no. UTF 584.13.18 and Katalysator simulation Vertrag Nr. 15.0002.PJ/S122-1359.
A | area [m^{2}] |
A' | specific area per unit length [m^{2}/m] |
AM | Additive Manufacturing |
brake mean effective pressure [Pa] | |
constant pressure specific heat [J/(kg·K)] | |
specific heat [J/(kg·K)] | |
CT | Computerized Tomography |
pressure drop [Pa] | |
characteristic channel diameter in honeycomb structure [m] | |
characteristic pore dimension [m] | |
ε | porosity, emissivity |
ET | Energizing Time [s] |
exh | exhaust |
EGR | Exhaust Gas Recirculation |
η | conversion efficiency |
F&E | Filling-and-Emptying |
enthalpy [J/kg], convection coefficient [W/(m^{2}·K)] | |
Hg | Hagen number |
HiL | Hardware-in-the-Loop |
HRR | Heat Release Rate [W] |
ICE | Internal Combustion Engine |
L | catalyst length [m] |
Lower Heating Value | |
ṁ | mass flowrate [kg/s] |
μ | dynamic viscosity [Pa·s] |
engine rotational speed [rad/s] | |
Nusselt number | |
Pr | Prandtl number |
rail pressure [Pa] | |
heat flux [J/s] | |
QSF | Quasi-Steady Flow |
radius [m] | |
thermal resistance [K/W] | |
Reynolds number | |
ρ | density [kg/m^{3}] |
Specific Surface Area [m^{2}/m^{3}] | |
temperature [K] | |
tur | turbine |
internal energy [J] | |
flow velocity [m/s] | |
vehicle speed [m/s] | |
walls | |
vector of mass concentrations of chemical species i | |
ϕ | equivalence ratio |
χ | tortuosity |