The homogeneous sulfuric acid–water nucleation rate in conditions
related to vehicle exhaust was measured and modeled. The measurements were
performed by evaporating sulfuric acid and water liquids and by diluting and
cooling the sample vapor with a sampling system mimicking the dilution
process occurring in a real-world driving situation. The nucleation rate
inside the measurement system was modeled inversely using CFD (computational
fluid dynamics) and the aerosol dynamics code, CFD-TUTMAM (Tampere University
of Technology Modal Aerosol Model for CFD). The nucleation exponents for the
concentrations of sulfuric acid and water and for the saturation vapor
pressure of sulfuric acid were found to be

Airborne particles are related to adverse health effects

Vehicles equipped with internal combustion engines generate nonvolatile
particles

An important characteristic of fine particles is the particle size
distribution, as it determines the behavior of particles in the atmosphere
and particle deposition to the respiratory system. Modeling studies provide
information on the formation and evolution of exhaust-originated particles in
the atmosphere

The detailed nucleation mechanism controlling particle formation in cooling
and diluting vehicle exhaust is currently unknown

Particle formation due to

Conversely, the nucleation rates of the other nucleation mechanisms are
typically modeled as

The first step in examining nucleation mechanisms, other than the CNT, in
vehicle exhaust using experimental data was performed by

Inverse modeling is a preferable method in obtaining nucleation rates in a
diluting domain over the method based on calculating

Ammonia (

In this paper, an improved aerosol dynamics model, CFD-TUTMAM (Tampere
University of Technology Modal Aerosol Model for CFD), based on our previous
model, CFD-TUTEAM (Tampere University of Technology Exhaust Aerosol Model for
CFD), which is described in

Laboratory experiments designed for nucleation rate modeling purposes are
presented in which the examination of the nucleation rate was aimed towards
pure

The pure

The formulation obtained from this study helps in finding the nucleation
mechanisms occurring in real vehicle exhaust or in the atmosphere. Similarly,
it can be used to examine particle formation in coal-fired power plant
exhaust, which is also known to contain

The experimental setup used to generate artificial exhaust and
sample it with a diluting sampling system. The top part of the figure
represents the artificial raw exhaust generation, which contains mixing and
heating

Laboratory experiments were designed to enable the examination of the effects
of three parameters ([

The artificial raw exhaust sample was generated (the top part of
Fig.

The computational domain in the CFD simulation shown in the bottom part of
Fig.

The temperature of the raw sample was 243

The temperature of the

The determination of [

The sampling system used to dilute and cool the raw exhaust, presented in the
bottom part of Fig.

Dilution air used with the PTD and the ejector diluter was filtered
compressed air. The ejector diluter used only dry (

In this experiment, the residence time in the aging chamber was made adjustable by a movable sampling probe inside the aging chamber. The sampling probe was connected to the ejector diluter with a flexible Tygon hose. The residence time from before the PTD to after the ejector diluter was altered within a range of 1.4–2.8 s. Using a movable probe to alter the residence time has only a minor effect on the flow and temperature fields compared to altering the residence time with changing the flow rate in the aging chamber. Maintaining constant flow and temperature fields when studying the effect of the residence time is important because variable fields would alter the turbulence level and temperatures in the aging chamber, both having effects on the measured particle concentration and thus causing difficulties in separating the effect of the residence time from the effect of turbulence or temperature on measured particle concentrations.

The dilution ratio of the PTD was controlled by the excess flow rate after
the aging chamber and calculated by the measured [

Particle number concentration and size distribution were measured after the
ejector diluter using Airmodus PSM A11 (Airmodus Particle Size Magnifier A10 using Airmodus Condensation Particle Counter A20 as the particle counter), TSI
CPC 3775 (Ultrafine Condensation Particle Counter), and TSI Nano-SMPS (Nano
Scanning Mobility Particle Sizer using TSI CPC 3776 as the particle counter).
The PSM and the CPC 3775 measure the particle number concentration
(

The detection efficiencies of the PSM, with five different saturator
flow rates used in this experiment, and of the condensation particle counters (CPCs). The curves are
exponential fittings based on the detection efficiencies reported by the
manufacturers of the devices, excluding the CPC 3776 curve, which is based on
the efficiency measured by

Due to particle number concentrations that are too high for the PSM, aerosol measured
with the PSM and the CPC 3775 was diluted with a bridge diluter. It dilutes
the concentration of larger particles (

The dilution ratio of the bridge diluter with different particle diameters.

By varying [

The varied conditions of the measurements are presented in
Table

The varied conditions of the measurement points.

Figure

Examples of particle size distributions after the ejector
diluter, measured with different

It can be observed that, though the Nano-SMPS data are in a nearly log-normal
form, there are also size distributions in the PSM+CPC diameter range.
Particles generated with lower

The particle number concentrations measured with the highest saturator flow
rate of the PSM (

The measured number concentrations of the particles larger than

The effect of humidity on the particle concentration (set 2) is shown in
Fig.

The measured number concentrations of the particles larger than

The effect of

The measured number concentrations of the particles larger than

The effect of the residence time on the particle concentrations is presented
in Table

The ratios of the measured number concentrations and mass concentrations with the residence times of 1.4 and 2.8 s, in measurement set 4. The values are corrected with the dilution ratio of the bridge diluter and with the diffusional losses in the sampling lines after the ejector diluter; thus, the values correspond with the distributions existing after the ejector diluter.

Every measurement point presented in Table

The CFD simulations to solve the flow and the temperature fields for every simulation case were performed with a commercially available software, ANSYS Fluent 17.2. It is based on a finite volume method in which the computational domain is divided into a finite amount of cells. Governing equations of the flow are solved in every computational cell iteratively until sufficient convergence is reached. In this study, the governing equations in the first phase are continuity, momentum, energy, radiation, and turbulence transport equations.

The computational domain in the CFD simulations is an axial symmetric
geometry consisting of the PTD, the aging chamber, and the ejector diluter
(Fig.

In contrast to our previous study

Flow rate and temperature boundary conditions for the simulated sampling
system were set for the each simulation case to the measured values. Due to
steady-state conditions and high computational demand, all governing
equations were time averaged; thus, the simulations were performed with a
steady-state type. Turbulence was modeled using the SST-

The main functionality of the CFD-TUTMAM based on the previous aerosol model,
CFD-TUTEAM, is described by

The CFD-TUTMAM adds three governing equations per distribution (denoted by

After each iteration step of the CFD-TUTMAM simulation, the parameters of the
distributions are calculated for every computational cell by using three
moment concentrations. The parameters for the PL distribution are the number
concentration (

The nucleation source terms in Eq. (

Diffusion, condensation, and coagulation are modeled as described in

Intermodal particle transfer includes condensational transfer and
coagulational transfer from the PL distribution to the LN distribution. In
contrast to a constant condensational transfer factor

Deposition of particles and condensation of vapors onto the inner walls of
the sampling lines have a direct effect on the aerosol concentrations at the
measurement devices. The particle deposition was modeled by setting the
boundary conditions for the aerosol concentrations at the walls to zero,
which represents deposition driven by diffusion and turbulence. Condensation
of

The main trend of the RH inside the sampling system is an increasing trend due to
decreasing temperature. This results in an increasing water uptake rate during
the particle growth process, which can be modeled by the condensation rate of

All the simulated particle size distributions outputted by the CFD-TUTMAM
were corrected to correspond with the water amount that would be in the conditions
after the ejector diluter (

Examples of particle diameters in different humidities in the
temperature of 23

The particle size distributions outputted by the CFD-TUTMAM and corrected with the
dry particle model were also corrected according to the penetration and
detection efficiency model. Particle penetration in the sampling lines
between the ejector diluter and the measurement devices was calculated with
the equations of

The simulated number concentrations measurable by the PSM with different
saturator flow rates and by the CPC 3775 and the simulated size distributions
measurable by the Nano-SMPS were compared with the measured ones during
inverse modeling. The exponents

Due to the uncertainties involved in the measurement of

The uncertainties involved in modeling turbulence and the condensation of the
vapors onto the walls affect the number and mass concentrations in the
measurement devices. Nevertheless, these uncertainties become partially
insignificant because

In this section, the outputs of the simulations performed using the nucleation rate function with the best correspondence between the measured and the simulated data are described firstly. Finally, the used nucleation rate function is presented.

Figure

Simulated sulfuric acid concentrations in the raw sample compared to the theoretical concentrations with different sulfuric acid evaporator temperatures. The concentrations are presented as the concentrations in NTP (normal temperature and pressure) conditions rather than in a hot raw sample.

Examples of measured and simulated particle concentrations and size
distributions of measurement set 1 are presented in
Fig.

Examples of measured and simulated

Figure

Examples of measured and simulated particle size distributions after the ejector diluter. The measured data are corrected with the dilution ratio of the bridge diluter and with the diffusional losses in the sampling lines after the ejector diluter. Additionally, all concentrations are multiplied by the total dilution ratio of the diluting sampling system. See the Supplement for error bars.

The requirement of the PL+LN model can be observed from
Fig.

Figure

The black dots in Fig.

Comparison of the particle number concentrations and the diameters with the average mass after the ejector diluter simulated using the LN distribution only and using both the PL and the LN distributions.

Comparison of the simulated and the measured

Table

The ratios of the simulated number concentrations and mass
concentrations after the ejector diluter with the residence times of 1.4 and
2.8 s, in measurement set 4. The values in parentheses denote the
measured values as presented in Table

The nucleation rate function with the best correspondence between the
measured and the simulated data having a type of
Eq. (

The parameters of the nucleation rate function with the best correspondence between the measured and the simulated data. The ranges of variation represent the resolution with which the exponents were altered during inverse modeling.

The environmental parameter ranges within which the nucleation rate function was applied.

Because

The exponent

The nucleation rate was the highest in the PTD, where the hot sample and the cold
dilution air met. The major part of nucleation occurred in the beginning part
of the aging chamber. No noticeable nucleation occurred in the ejector
diluter, though the temperature reaches

Homogeneous

The measurements were simulated with the aerosol dynamics code CFD-TUTMAM
using the nucleation rate, which is explicitly defined as a function of
temperature and the concentrations of

The raw sample was generated by evaporating

In these measurements, particle formation was not observed with the

The obtained exponent

Data are available upon request from the corresponding author (miska.olin@tuni.fi).

The supplement related to this article is available online at:

MO, JA, TR, and MDM designed the experiments, and MO and JA carried them out. MO analyzed the measurement data, developed the model code, and performed the simulations. MRTP designed the IC analysis. MO prepared the paper, with contributions from all co-authors.

The authors declare that they have no conflict of interest.

The authors thank CSC and TCSC for the computational time. We also thank Prof. Mikko Sipilä from the University of Helsinki for lending the chemical ionization inlet for the atmospheric pressure interface time-of-flight mass spectrometer, the tofTools team for providing tools for mass spectrometry analysis, and M. Sc. Kalle Koivuniemi for ion chromatography measurements.

This research has been supported by the graduate school of Tampere University of Technology and the Maj and Tor Nessling Foundation (grant no. 2014452).

This paper was edited by Neil M. Donahue and reviewed by two anonymous referees.