**3. Fouling mechanisms in the EGR system**

The gas-particle multiphase flow and the formation of fouling layer inside the EGR system are complex phenomena in which several mechanisms are involved. Thermophoresis, diffusion, inertial impact, hydrocarbon condensation, gravitational settling, removal due to shear force, water vapor condensation, or turbulent burst are the main mechanisms that engage in the fouling process.

Excluding the thermal effects, other parameters, such as the particle diffusion, the gravitational settling, the inertial impact of the turbophoresis, play an important role in the EGR fouling formation. The particle diffusion is the dominant mechanism for the small particles, particles with dimensionless relaxation times (*t* þ *<sup>p</sup>* ) less than 0.1, while the transport of large particles, particles with dimensionless relaxation times (*τ*<sup>þ</sup> *<sup>p</sup>* ) more than 0.1, is dominated by inertial and gravitational effects [34].

Inside the EGR cooler, thermophoresis—induced by the temperature gradient drives the nanoparticles from the bulk gas flow to the near cool walls, causing the deposition of the soot particles over the heat exchanger surfaces. It has been reported by several authors that under non-isothermal conditions, thermophoresis is the primary mechanism of soot deposition in the particle size typically encountered in exhaust gas, 10 nm to 1 μm, and some correlations from literature, such as Brock-Talbot or Cha-McCoy-Wood, have been used to determine the thermophoretic velocity as a function of the particle diameter [13, 35–38].

The condensation of HC and acids, which are part of the exhaust flow, is significant on a mass basis compared to soot deposition, and it is an important issue in the deposit formation [39]. As exhaust gas is diluted and cooled, the condensation of hydrocarbons is particularly important inside the EGR system. Condensate, which is mixed with soot particles inside the fouling layer, modifies the microstructure of the soot deposit and changes the characteristics of the deposit, leading to an increase of the density and the thermal conductivity of the fouling layer [40].

The effect of shear force of the gas flow over the deposited particles, the turbulent burst, or the water vapor condensation have been identified as potential mechanisms that cause the removal of particles from the fouling layer [41, 42]. When the drag force over the particle is larger than the adhesion force, removal occurs. In the same way, the condensed water droplets can interact with the deposited particles, causing a washout of the dry soot deposit [43].

It has been extensively reported in literature that the formation of the fouling deposits depends on two simultaneous phenomena: the deposition and the removal of particles [13, 44–48]. Such categorization usually selects thermophoresis, particle diffusion, gravitational drift, inertial impact, or hydrocarbon condensation as deposition mechanisms. On the contrary, water vapor condensation, the shear force, or the turbulent burst are usually classified as removal mechanisms.

#### **4. Numerical approaches**

In the study of the fouling process of the EGR system, both experimental and numerical investigations have been carried out in order to analyze the effects of the

Analyzing the composition of the PM of the exhaust gas, the particles are a product of a mix of volatile and nonvolatile species. Volatile faction is composed by

elements (dCH2 + N, O and S). Nonvolatile fraction is composed by carbonaceous particles, commonly referred to as soot, and ash, formed by metals (Fe, Cr, Cu, Zn, Ca) and nonmetals (Si, P, S, Cl) [24]. Several factors, such as fuel and lubricant characteristics or engine work conditions, can influence the composition and proportion of these species, however, in most cases, elemental carbon accounts for around 90% of PM mass [25]. The primary particles—sizes typically between 15 and 30 nm—are composed by carbon and traces of metallic ash, and they aggregate forming complex irregular clusters together with adsorbed and condensed hydrocarbons (HC) [26, 27]. As **Figure 4** shows, the agglomeration of the primary particles causes the formation of clusters with a complex structure with nonuniform

When this particulate matter is deposited on the heat exchanger walls, it forms a fouling layer which coats the heat exchanger surface. The interaction between the particles and the metal surface during the early stages of the deposit formation, and the particle-particle interaction during fouling layer growth, leads to the accumulation of amorphous aggregates on the heat exchanger walls, causing a highly porous deposit (around 98% [18]). This fouling layer, with a complex nanostructure with multiple pores between the deposited aggregates, functions as an insulator between the gas flow and the heat transfer surface. According to the experimental measurements of Lance et al. [18], the fouling layer generated from the deposition of diesel particulate matter has a density around 0.035 g/cm<sup>3</sup> and a low thermal conductivity that is around 0.041 W/mK. However, in some cases, different phenomena, such as

+ metal nitrate), and organic

<sup>2</sup> + metal sulfate), nitrates (NO3

*Generalized size distribution for typical particles emitted by internal combustion engines.*

*Environmental Issues and Sustainable Development*

sulfates (SO4

*Agglomerate diesel particle.*

**Figure 4.**

**330**

**Figure 3.**

shape and compactness [28].

**5. 0-D models**

between both methods.

were verified.

Abarham et al. [49]

Garrido et al. [50]

**Table 1.** *0-D model.*

**333**

**Authors Mechanisms modeled**

Thermophoresis *Kth* <sup>¼</sup> <sup>2</sup>*CsCc*

• Water vapor condensation

condensation

• Acid

fouling layer effect in the EGR system.

*DOI: http://dx.doi.org/10.5772/intechopen.93062*

*Numerical Modelling of Fouling Process in EGR System: A Review*

**Table 1** summarizes the 0-D models that have been proposed to analyze the

Abarham et al. [49] proposed an analytical model for thermophoretic particle deposition that solves the mass conservation of particles and the energy equation of the gas flow for a single turbulent pipe flow. This approach considers the submicron particle deposition due to the thermophoretic effect, neglecting the diffusion and other deposition mechanisms. The model takes into consideration the pipe diameter reduction due to the growth of the fouling layer and considers different boundary conditions, such as the inlet temperature and mass flow rate of the gas, the inlet particle concentration, or the wall temperature. In this study, the properties of the soot layer, i.e., density, porosity, and thermal conductivity, have been taken from the experimental measurements of Lance et al. [18], and the soot particle diameter has been set at 57 nm, based on the study of Maricq and Harris [51]. This model computes the total mass deposited on the tube and evaluates the degradation of the

heat transfer effectiveness over time. To verify the results of this numerical approach, the data were compared with the experimental measurements obtained by the Oak Ridge National Laboratory, and an acceptable agreement was achieved

Garrido et al. [50] presented a theoretical analysis of the thermodynamics of exhaust gas condensation. They analyzed the condensation of different species that are part of the exhaust gas produced by gasoline engines, such as water vapor, ammonium, and sulfuric, nitrous, nitric, and chloric acids. The examination of the chemical reactions that takes place along the exhaust line and the analysis of the vapor-liquid equilibrium of the condensable species under different temperatures allow the study of their behavior and the calculation of their dew point. The experimental validation of the model showed that, although the collected condensate amount was slightly lower than the model predicted results, the general tendencies

Since the 0-D models do not provide any spatial resolution of the fouling parameters, their scope is deliberately more concise. Nevertheless, they can be used

**Main fouling equations Parameters**

*kg =kp*þ*CtKn* 1þ2*kg =kp*þ2*CtKn*

*m*\_ *cond* ¼ *m*\_ *<sup>g</sup>* ð Þ *wi*,*initial* � *wi*,*end* • Saturation

**analyzed**

• Deposited soot mass • Cooler effectiveness • Pipe diameter reduction

temperature • Condensation flux

**Model experiment**

General tendencies validated

In reasonable agreement **Remarks**

An analytical solution for thermophoretic deposition of submicron particles

Theoretical analysis of the thermodynamics of gasoline engine exhaust condensation

as essential tools in guiding the study of the fouling phenomenon.

1þ3*Cm Kn*

**Figure 5.**

*Main numerical models published from 1997 to 2020.*

deposit that grows on the heat exchanger walls. Although the amount of experimental studies have been larger and more frequent, the numerical models have become relevant since 2009, as **Figure 5** depicts, due to the increase in NOx emission regulation requirements.

The numerical approaches intend to reproduce and simulate the formation and evolution of the deposit inside the EGR system recreating the different mechanisms involved in the fouling process. Because of their significance in the prediction of the deposit, the deposition mechanisms have been implemented in 76.9% of the main numerical models that analyze the deposit formation inside the EGR system. By contrast, the numerical approaches that recreate removal mechanisms are slightly lower (50.0%), and only the 30.8% of the models are focused on the study of the condensation of volatile species. In many cases, several kinds of mechanisms are implemented and coupled in one single numerical approach, in order to achieve more complete simulation frameworks.

According to the complexity of the formulation of the models, they can be divided into three principal categories: the zero-dimensional (0-D), the onedimensional (1-D), and the multidimensional models.

The zero-dimensional models are focused on an overall heat and material balance of the system, and they do not include any analysis of the fluid dynamics. Following several assumptions and simplifications, they evaluate the overall fouling effects, and, although these numerical approaches avoid any spatial resolution of the variables involved in the process, they can give a fair indication about the fouling phenomenon.

The one-dimensional approach is the next level of complexity. In these models, only one spatial dimension is considered, dividing the fluid zone in different regions and analyzing the properties of the system in each region separately. Although this approach simplifies the number of equations, it can give a detailed evolution of the spatial changes of the fouling parameters.

The multidimensional models require the spatial discretization of the volume of the region and can provide a thorough analysis of the variables of the process. In this field, the use of computational fluid dynamics simulations has been increasing steadily since the 1990s, due to the availability of high-performance computing hardware and the development of user-friendly interfaces. The computer-based simulations make it possible to obtain a detailed solution of the fluid flow, both in two-dimensional (2-D) and three-dimensional (3-D) domains, and they can reproduce the evolution and formation of fouling layers.
