A new exhaust aerosol model CFD-TUTEAM (Tampere University of Technology Exhaust Aerosol Model for Computational Fluid Dynamics) was developed. It is based on modal aerosol dynamics modeling with log-normal assumption of particle distributions. The model has an Eulerian sub-model providing detailed spatial information within the computational domain and a computationally less expensive, but spatial-information-lacking, Lagrangian sub-model. Particle formation in a laboratory sampling system that includes a porous tube-type diluter and an aging chamber was modeled with CFD-TUTEAM. The simulation results imply that over 99 % of new particles are formed in the aging chamber region because the nucleation rate remains at a high level in the aging chamber due to low dilution ratio and low nucleation exponents. The nucleation exponents for sulfuric acid in sulfuric-acid–water nucleation ranging from 0.25 to 1 appeared to fit best with measurement data, which are the same values as obtained from the slopes of the measured volatile nucleation mode number concentration vs. the measured raw exhaust sulfuric acid concentration. These nucleation exponents are very low compared to the nucleation exponents obtained from the classical nucleation theory of binary sulfuric-acid–water nucleation. The values of nucleation exponent lower than unity suggest that other compounds, such as hydrocarbons, might have a significant role in the nucleation process.

Ultrafine particles are related to adverse health effects

Fuel combustion generates solid particles, such as soot, ash, core

The particle size distribution controls aerosol deposition to the respiratory
system and its behavior in the atmosphere. Modeling studies can provide
information on vehicle exhaust particle formation and evolution in the
atmosphere. To model particle concentration and the size of nucleation mode,
the actual nucleation rate needs to be known. In addition, modeling of
vehicle exhaust particle formation can also provide insight on nucleation and
particle formation processes in more dilute environments. The detailed
nucleation mechanism controlling particle formation in vehicle exhaust is
currently unknown. Studies have shown that nucleation particles contain at
least water, sulfuric acid, and hydrocarbons

Particle formation and dilution in vehicle exhaust and in laboratory sampling
systems have been studied by several authors

In this paper, an exhaust aerosol model for application in CFD modeling of
realistic vehicle exhaust and its applicability to study particle formation
involving sulfuric acid in diesel exhaust using previously published data

The CFD code used was a commercially available software ANSYS FLUENT 14.0. It
can be used to solve, e.g., flow, mass, heat, and radiation transfer
problems. It is based on a finite volume method

The aerosol dynamics model CFD-TUTEAM is based on the
former aerosol model TUTEAM

The parameters of log-normal distributions (number concentration

CFD-TUTEAM consists of an Eulerian- and a Lagrangian-type sub-model. In the
Eulerian model, the moment variables are connected to the CFD model by
solving the scalar transport equations of type
Eq. (

The Eulerian aerosol model is two-way coupled with the CFD model: (1) the
properties on the fluid side affect on the transport equation of the particle
variables Eq. (

Temperature, gas species concentrations, and particle distribution parameters in hot exhaust and cold dilution air are the boundary conditions that are used at the domain boundaries in the corresponding inlets. Computation of the CFD model and the Eulerian aerosol model provide the solution for flow and particle parameters inside the simulation domain and their values at the outlet.

The simulation domain is a two-dimensional axial symmetric geometry. The measurement setup to be modeled had no time dependence in the results in a short timescale, which allows a computationally more efficient steady-state simulation.

The Lagrangian aerosol model is a Matlab code in which the differential
equations Eq. (

The path lines contain no spatial information in the Lagrangian model, but temporal information exist. However, the Lagrangian model can also be considered a steady-state simulation, because the inputs are obtained from a steady-state CFD simulation. Due to fewer dimensions in the Lagrangian model compared to the Eulerian model, a very high temporal resolution can be simulated with the same computational cost. The output from the Eulerian model is actually interpolated to a higher resolution to match the input required for the Lagrangian model. However, the Lagrangian model has, in principle, the same resolution for temperature and gas species concentrations as the Eulerian model because the solution has been calculated using the lower resolution. The higher resolution is, however, used for particle dynamics in the Lagrangian model. Therefore, comparing the particle distribution results from both models provides information on the sufficiency of the spatial resolution of the Eulerian model. A high resolution is required for particle dynamics processing due to the non-linear and exponential nature of the equations controlling particle dynamics.

Running the Lagrangian aerosol model provides the particle distribution parameters as a function of time for different path lines. The values at the ends of the different path lines can be averaged to get information on the particle parameters at the outlet.

Modeled aerosol processes are shown in Fig.

“Nucleation” is a key process controlling particle number concentration in
diluting exhaust particle formation, which is generally considered
sulfur-driven, more specifically sulfuric-acid-driven. Binary homogeneous nucleation (BHN) of water and sulfuric acid
has been used as a nucleation mechanism in previous diesel exhaust modeling
studies

However, the actual nucleation rate, which is the rate of the formation of
new stable molecule clusters

In atmospheric modeling studies, activation- and kinetic-type nucleation rates
have been used in the following forms

Correction factors for nucleation rate obtained from CNT as a function of raw
exhaust sulfuric acid vapor concentration. Figure adapted from

The nucleation term in Eq. (

“Condensation” in the model is assumed to occur by sulfuric acid, water, and hydrocarbon vapors. The condensation term for sulfuric acid is

“Coagulation” modeling is based on the model of

“Diffusion” is modeled as laminar and turbulent parts. The laminar
diffusion coefficient for particles

Modeled aerosol processes, modes, components, and phases. Detailed
information on them are explained in Sect.

“Deposition” onto the surfaces is assumed to occur only due to diffusion, because thermophoresis was found to have only a minor role on deposition due to low thermal gradients. Deposition is modeled by setting all moments to 0 on the walls.

To demonstrate the applicability of the CFD-TUTEAM, we applied it to
a laboratory sampling system for which data have already been published by

The part of the measurement setup relevant for the simulations. The computational domain consists of a PTD and an aging chamber only due to an approximation that the ejector diluter has a minor effect only on the particle distribution.

In both measurements

The measurements performed with 100

The computational domain. It is an axial symmetric geometry where the raw exhaust is input from the left, and the dilution air is supplied radially from a cylindrical boundary in the PTD region. The PTD is insulated but the latter part lies in stagnant external fluid. Only the ends of the aging chamber are shown, but the length of it is 1 m in reality. The figure is scaled vertically with a factor of 5. The yellow (PTD) and the green (aging chamber) boxes present the regions in which the contour plots are plotted in the following figures.

The sampling system seen in Fig.

The domain was divided into

Boundary conditions for the simulations.

Internal fluid was modeled as a mixture of air, water vapor, sulfuric acid vapor, and the hydrocarbon mixture. Particle scalars were also within the internal fluid but were not connected to the fluid properties. The external fluid was modeled as air, the insulation zone as wool, and the solid zones of the PTD and the aging chamber as steel.

The boundary conditions are described in Table

The water vapor mole fraction in exhaust was calculated from combustion
reaction stoichiometry and with a lambda value (the fraction of injected air
mass compared to the air mass required for the stoichiometric combustion) of
1.54. The water vapor concentration in dilution air was obtained by assuming
that dilution air RH was 10

Deposition was implemented in the CFD model by setting the mole fraction for
a depositing vapor at the boundary to 0; for non-depositing vapor, a zero
flux at the boundary was implemented. A vapor was considered depositing when
its saturation ratio exceeded unity near the boundary and non-depositing
otherwise. For sulfuric acid vapor, saturation never exceeded unity in these
simulations; hence the zero flux assumption was always used. In reality,
dilution air cools the PTD; however, the cooling was not simulated because it
would require the modeling of the dilution air outside the dilution air inlet
boundary. This would have increased the complexity of the simulation due to
the porousness of the diluter and due to the requirement for a
three-dimensional
simulation. We estimate that exhaust temperatures in the sampling pipe of the
PTD would be lower and the dilution air temperatures higher near the boundary
where the hot exhaust and cold dilution air are mixed. Hence, sulfuric acid
vapor might condense on the cooled inner walls of the sampling pipe of the
PTD. A saturation ratio of more than unity for hydrocarbons was calculated as
a fraction of condensing hydrocarbons

For the volatile nucleation mode,

Due to steady-state simulations, all governing equations were
Reynolds-averaged, i.e., time-averaged. The averaging of the momentum
transport equations causes additional terms, called Reynolds stresses, to
appear. Turbulence models are used to model the Reynolds stresses, but the
calibration of the turbulence models has been done with experimental data,
and the calibration may not be suitable in cases with different geometries,
fluid mixture, and boundary conditions. In this case, shear-stress-transport–

All cases were simulated with two nucleation exponents for sulfuric acid
vapor:

Temperature in the PTD region. The gray lines represent the path lines used in the Lagrangian simulation. Blue and red lines in the beginning of the path lines are the color coding of them. The figure is scaled vertically with a factor of 10.

Nucleation rate in the PTD region when there is

Figures

Temperature and nucleation rate at the axis when there is

The volatile nucleation mode concentration in the aging chamber region when
there is

In R cases, the volatile nucleation mode number concentration was decreased
by 3–9

The volatile nucleation mode CMD in the aging chamber region when
there is

The core mode CMD in the aging chamber region when there is

Figures

Measured and simulated

Modeled values of

The required hydrocarbon vapor amount is also shown in
Fig.

In A cases with

Modeled proportions of sulfuric acid existing in different modes and remaining in the gas phase (%) at the end of the aging chamber.

In reality, the shape of the region of highest nucleation rates would be
different and probably transferred towards the inner wall of the sampling
pipe of the PTD due to the cooling of exhaust gas by dilution air, which was
not modeled. DBP nucleation simulations of

Particle liquid part composition (mass %) and the maximum saturation vapor pressures of hydrocarbons at the end of the aging chamber.

A simulation performed by the Eulerian model of A case with raw exhaust
sulfuric acid vapor concentration of

Nucleation rate and particle concentration as a function of time on the path lines. Nucleation rate profiles are the same in both simulations. Note the different timescales; the left plots show the very beginning of the curves as zoomed.

Figure

Particle concentration in the aging chamber region when there is

Comparing the particle concentrations between the Eulerian and the Lagrangian
simulations, it can be observed that the concentrations in the Eulerian
simulations are higher in the beginning. That is caused by the diffusion
influx of the particles from the surrounding areas of a path, which cannot be
modeled with the Lagrangian model but is modeled in the Eulerian model. The
region where the particle concentration jumps rapidly to a high level is the
expander region of the aging chamber. The diffusion influx to the paths in
that region can be seen in Fig.

The concentrations at the ends of all the paths are, however, almost the
same, except for 20

CMD in the aging chamber region when there is

It can be seen from Fig.

Although the behavior of the Eulerian model during the fluctuating flow is not very smooth, the model is capable of approaching realistic values after that region. The fluctuation behavior can probably be smoothed by increasing the spatial resolution in that region. However, the values at the inlet and the outlet are of the main interest in this study; therefore, as the modeled outlet values for both models are approximately the same, the spatial resolution may be sufficient.

The Lagrangian model appears to produce almost equal results compared to the Eulerian model, when the output particle distribution is of interest only, despite the path line chosen for the simulation. However, in the inner areas of the sampling system, the Lagrangian model may produce unrealistic results if diffusion fluxes have strong effects on the particle distribution, which is especially seen in a turbulent flow. The Lagrangian model can be executed with very high time resolution without being computationally expensive. However, it requires cooling and dilution profiles obtained from the CFD model, if proper results are required. Additionally, the coupling of the fluid species with the aerosol dynamics is required to be modeled when the aerosol processes are limited by the vapor concentrations, not by time. Conversely, the Eulerian model can produce more detailed spatial information compared to the Lagrangian model, and the diffusion is also included in simulations. However, it is computationally more expensive and, therefore, the spatial resolution may remain too low to be able to produce realistic results when the same computational effort as for the Lagrangian model is considered.

It can be seen from Fig.

However, particle concentrations in A cases may have been underestimated
because of very low particle sizes (

The measured and simulated volatile nucleation mode concentrations as
a function of raw exhaust sulfuric acid vapor concentration. Particle
concentrations are normalized to raw exhaust by dilution ratio 12.
Measurement data for R cases are obtained from

The nucleation exponent

For our cases, the nucleation exponents

The reason for different nucleation exponents between A and R cases is not obvious, and further research is required to examine that. The difference could be accounted for by different sulfuric acid vapor concentration ranges, different particle size ranges, or another reason that cannot be seen from the measurements or the simulations studied here. Sulfuric acid vapor concentration range could cause the difference if the nucleation exponent were dependent on the sulfuric acid vapor concentration in a way that the nucleation exponent decreases with increasing sulfuric acid vapor concentration, which is actually seen in CNT. Different particle size range could explain the difference due to decreased counting efficiency with decreasing particle size; particle sizes were lower in A cases compared to R cases.

The CFD-TUTEAM model was used to simulate the particle formation process in a laboratory-scale diesel exhaust sampling system, consisting of a porous tube-type diluter and an aging chamber. Eulerian- and Lagrangian-type sub-models were used, and both models produced almost the same particle distributions at the outlet of the aging chamber, but it was seen that the Lagrangian model may not produce realistic results in the inner areas of the sampling system. The Lagrangian model is computationally less expensive compared to the Eulerian model; thus, it can be modeled with a higher temporal resolution with the same computational cost. However, cooling and dilution profiles from the Eulerian model are required as inputs for the Lagrangian model. Conversely, the Eulerian model produced more detailed spatial information inside the sampling system, and it includes diffusion modeling. The main advantage of the modal aerosol model is that it can be used to examine particle formation spatially with lower computational cost compared to sectional aerosol models. The drawback of it relates to the assumption that the particle distributions remain log-normal, which is not true, especially when nucleation and condensation occur simultaneously.

The highest nucleation rates were found to exist in the region where hot
exhaust and cold dilution air encounter. However, due to low dilution ratio
and low nucleation exponents, the nucleation rate remains high in the aging
chamber where the dilution process is already finished. Hence, the major
part (over 99

The nucleation exponents for sulfuric acid vapor in the range from 0.25 to 1 appeared to fit best with the measurement data, according to the simulations. In this range of condensation and coagulation sinks resulting from solid particles, the nucleation exponents can be estimated directly from the measurement data through the slope of the volatile nucleation mode number concentration vs. the raw exhaust sulfuric acid vapor concentration. Due to the nucleation exponents below unity, it is probable that there are other compounds, such as organics, affecting the nucleation rate. The reason for different nucleation exponents between the cases is not obvious, and further research is required to examine that.

According to the simulations, the major part of deposition occurs in the region of the expander of the aging chamber. Turbulence increases in the expander, which increases the effective diffusion coefficient; therefore, deposition rate increases. The expander had higher influence on the core and soot mode compared to the volatile nucleation mode, because the major part of the volatile nucleation mode particles was formed after the expander.

Modeled particle diameters range from a molecule diameter to below
1

The mass growth rate of a single particle in mode

Kelvin factor for water and sulfuric acid is calculated by

Liquid parts in particles are considered two immiscible phases: sulfuric-acid–water phase (sa-w) and hydrocarbon (hc) phase. The
phase with lower volume fraction is assumed to form a lens on the surface of
the other phase

Due to a wide range of different hydrocarbons in diesel exhaust, it is not
reasonable to model them all. A new method to model hydrocarbons is
implemented in the model. According to

Assuming the diesel exhaust organic aerosol volatility distribution measured
by

The properties of tetracosane (

A particle in water equilibrium is defined as a particle onto which no
condensation occurs and from which no evaporation of water vapor occurs. Therefore,
the following equation is satisfied:

The factor for water equilibrium

For the Lagrangian model, water equilibrium is maintained by altering water
content in the particles artificially after every time step in such a manner
that Eq. (

This work was funded by the Maj and Tor Nessling foundation (project number 2014452), by the Finnish Funding Agency for Technology and Innovation, Tekes (TREAM project), and by Dinex Ecocat Oy, Neste Oil Oyj, AGCO Power, and Ab Nanol Technologies Oy. Edited by: A. Virtanen