*2.2. Theoretical Background*

L-category regulation provides the equations for gaseous pollutants measured from the dilution tunnel with bags. In our case, we used the integrated signal from the analyzers in order to compare real time signals as well. Equations from the tailpipe can be found in passenger cars regulations at the RDE (Real-Driving Emissions) regulation or at the heavy-duty engines regulation and were summarized elsewhere for gaseous pollutants [34]. Here, the equations for SPN will be given for both the tailpipe and the dilution tunnel, because there is lack of information and it is the most complex case (see also [18]). In addition, we will expand them to take into account the extracted flow from the tailpipe (bleed off). Other topics that can influence the results and have been mentioned in the literature will also be shortly presented.

#### 2.2.1. Solid Particle Number (SPN) Emissions

The tailpipe instantaneous particle number flow rate *SPNTP,i* [p/s] can be determined by multiplying the instantaneous particle number concentration *CTP,i* [p/m3] (normalized to 0 ◦C and 101.3 kPa) by the instantaneous exhaust mass flow rate *Qexh,i* [kg/s] (aligned to each other), and by dividing with the density of the exhaust gas ρ*exh* [kg/m3] at 0 ◦C. A density of 1.2931 kg/m<sup>3</sup> was used for gasoline (E10) (Regulation (EU) 2017/1154). The total tailpipe emissions *SPNTP* [p/km] were calculated by integrating the *SPNTP,i* rate over the test cycle and dividing by the distance covered *D* [km] (7.6 km in our tests).

$$SPN\_{TP,i} = C\_{TP,i} \ Q\_{cxh,i} / \rho\_{exh} \tag{1}$$

$$SPN\_{TP} = \Sigma \text{ } SPN\_{TPj}/D \tag{2}$$

When a flow is extracted from the exhaust gas, the equation is still valid if the *Qexh* includes this extracted flow rate.

The CVS instantaneous particle number flow rate *SPNCVS,i* [p/s] was calculated as above using the CVS flow rate *QCVS* [kg/s] and the density of air ρ*air* [kg/m3] at 0 ◦C. The total tailpipe emissions *SPNCVS* [p/km] were calculated by integrating the *SPNCVS,i* rate over the test cycle and dividing by the distance covered *D* [km].

$$\text{SPN}\_{CVS,i} = \text{C}\_{CVS,i} \text{ Q}\_{CVS,i} / \rho\_{air} \tag{3}$$

$$\text{SPN}\_{\text{CVS}} = \Sigma \text{SPN}\_{\text{CVS},j}/D \tag{4}$$

When a flow is extracted from the dilution tunnel, the equation is still valid if the *QCVS* includes this extracted flow rate; however, the correction is usually negligible.

The final *SPNCVS* result is equivalent to the one in the passenger cars and trucks regulations. The time alignment is less critical in this case:

$$\text{SPN}\_{\text{CVS}} = \text{C}\_{\text{CVS}, \text{mr}} \text{ } V\_{\text{CVS}}/D \tag{5}$$

where *VCVS* [l] is the volume of the diluted exhaust gas (normalized to 0 ◦C and 101.3 kPa) and *CCVS,ave* [p/m3] is the mean concentration during the cycle duration (normalized to 0 ◦C and 101.3 kPa) (Regulation (EU) 2017/1151).

The particles extracted from the tailpipe *SPNextr,i* were calculated using the instantaneous particle number concentration *CTP,i* [p/m3] (normalized to 0 ◦C and 101.3 kPa) and the instantaneous flow rate of the instruments sampling from the tailpipe *Qinstr,i* [kg/s]. In our case, the total extracted flow rate was constant and equal to 19–23 l/min due to the SPN instrument(s) and the gas analyzers. The total particle emissions extracted from the tailpipe *SPNextr* [p/km] were calculated by integrating the *SPNextr,i* rate over the test cycle and dividing by the distance covered *D* [km].

$$\text{SPN}\_{\text{extr};i} = \text{C}\_{\text{TP};i} \, \text{Q}\_{\text{instr};i} / \rho\_{\text{exh}} \tag{6}$$

$$SPN\_{\rm extr} = \Sigma \text{ } SPN\_{\rm extr,j}/D \tag{7}$$

The corrected CVS results *SPNCVS,corr,i* were calculated by adding the SPN emissions of the dilution tunnel *SPNCVS,i* and the SPN extracted from the tailpipe *SPNextr,i*.

$$SPN\_{CVS, \text{corr}, i} = SPN\_{CVS, i} + SPN\_{\text{extr}, i} \tag{8}$$

For completeness, another way to calculate the SPN emissions due to the extracted flow from the tailpipe, when no tailpipe SPN measurements are available, is to recalculate every second of the concentrations at the dilution tunnel by using the "true" dilution ratio at the CVS as if no flow had been extracted. The reason is that the extraction of a flow from the tailpipe results in higher dilution in the dilution tunnel, which is not considered in the calculations. This is equivalent to increasing the exhaust flow that would enter the dilution tunnel by the flow extracted by the instruments connected to the tailpipe. As an example, using the di fference between CVS total ( *QCVS*) and dilution air flow (*Qair*) rates as a proxy of the exhaust flow, the final SPN concentration would be:

$$\text{SPN}\_{\text{CVS}\varphi\text{orr},i} = \text{SPN}\_{\text{CVS},i} / (\text{Q}\_{\text{CVS}} - \text{Q}\_{\text{air},i}) \times (\text{Q}\_{\text{CVS}} - \text{Q}\_{\text{air},i} + \text{Q}\_{\text{instr},i}) \tag{9}$$

Details about other methods determining the exhaust flow rate or the dilution factor are given in the next paragraph.

For the open transfer tube case, the same tailpipe equations can be used as long as the tailpipe SPN measurements are taken before the dilution at the tailpipe and the exhaust flow rate is estimated correctly.

The results of the SPN emissions at the tailpipe need correct time alignment between the SPN signal and the exhaust flow rate. Misalignment of a few seconds can have a significant e ffect [35]. Here, the e ffect of misalignment was checked by moving the SPN signal for ±1 second. Long sampling lines might result in signal deformation due to mixing and di ffusion and need advanced mathematical models to "reconstruct" the original signal [36–38]. The tailpipe measurements due to the short sampling lines should not have this issue. It should be mentioned though that the deformation of the signal from the engine to the tailpipe is not of importance in this paper, because only tailpipe with dilution tunnel results are compared [39].

#### 2.2.2. Exhaust Flow Rate

The exhaust flow rate *Qexh* can be determined with various methods. The direct measurements with exhaust flow meters are sensitive to the exhaust gas fluid conditions, such as the temperature, flow rate, composition, and pressure [40]. In small one- or two-cylinder gasoline engines, there is also a problem with pulsating flows especially during idling, which can even include reverse flow direction. For this reason, today, there are no exhaust flow meters for mopeds and small motorcycles and indirect methods are used. In the case of non-road, small utility purpose engines, for example, the sum of intake air mass and fuel mass flow is used as the exhaust mass flow [41]. Alternatively, one of these two flows can be calculated from the other with the measurement of the air/fuel ratio obtained with a lambda sensor.

Here, we used three methods applicable in the laboratory: The instantaneous di fference between total CVS flow *QCVS* (corrected for any flows extracted from the dilution tunnel) and dilution air flow (*Qair*) (Equation (10)), the CVS flow and the instantaneous dilution factor (*DF*) calculated by the CO2 tracer method (Equation (11)), or the carbon balance method (CB) (Equation (12)).

$$Q\_{\rm cxl,air,i} = Q\_{\rm CVS} \cdot Q\_{\rm air,i} \tag{10}$$

$$Q\_{c\text{cyl},\text{CO2},i} = Q\_{CVS} / DF\_{\text{CO2},i\prime} \tag{11}$$

$$Q\_{\rm cxbh,CB,i} = Q\_{\rm CVS} / DF\_{\rm CB,i} \tag{12}$$

$$\text{D}F\_{\text{CO2},i} = \text{C}\_{\text{CO2},\text{TP},\text{j}} \text{C}\_{\text{CO2},\text{CVS},i\text{\textprime}} \tag{13}$$

$$DF\_{\rm CB,i} = 13.4 \langle \mathbf{C\_{CO2,CVS,i}} + \mathbf{C\_{CO,CVS,i}} + \mathbf{C\_{HC,CVS,i}} \rangle \tag{14}$$

where *C* is the concentration [%] of the pollutant in the dilution tunnel (CVS) or tailpipe (TP) for each second *i*. The concentrations should refer to the wet exhaust (i.e., the dry-to-wet correction should be applied [42]) and should also be corrected for the dilution air background. The dry-to-wet correction is important for the tailpipe concentrations, while the dilution air background correction is important for the dilution tunnel concentrations. The 13.4 is the theoretical CO2 concentration for a gasoline engine, around 13.4%, which is obtained with the average composition of gasoline fuel (C8H15) [40]. Note also that the CO2 tracer method needs a CO2 analyzer sampling from the tailpipe beyond that at the dilution tunnel, and this extracted flow has to be considered in the calculations. The extracted flow rate has to be added to the equations above to find the actual exhaust flow rate.

$$Q\_{cxh,i} = Q\_{cxh, 
mathcal{,i}} + Q\_{i 
subset r, i} \tag{15}$$

## 2.2.3. Cold Start

During cold start condensation can take place and this has an effect up to 10% on the results of instruments measuring on dry basis (e.g., CO2 or CO) [42]. According to our knowledge there are no SPN instruments measuring in dry basis. Therefore, the correction is not needed.

## 2.2.4. Particle Dynamics

The main aerosol processes from the tailpipe to the full dilution tunnel are agglomeration, diffusion, and thermophoresis [18,43,44].

Agglomeration arises from particle to particle collisions where the colliding particles are attached together, but retain their identity and shape. Agglomeration changes the number concentration and size of particles, but not the total particle mass concentration. The extent of agglomeration depends on the initial particle concentration and, to a smaller degree, on particle size and surrounding temperature.

Diffusion is the net movement of particles (or gas molecules) from high to low concentration. Smaller particles diffuse faster than larger particles. Therefore, diffusion is most important for particles smaller than about 50 nm in diameter. Particle concentration decreases in the exhaust transfer lines due to diffusional deposition of particles on the surfaces.

Thermophoresis is the motion of a particle in a temperature gradient. Due to the higher rate of collisions of gas molecules on the hotter side the particle, thermophoresis results in particle movement towards the colder side (i.e., particles in high temperature exhaust gas to the colder walls).

Other transport losses (e.g., gravitational deposition, inertial impaction, electrophoretic) and sampling losses (due to anisoaxial and anisokinetic extraction of sample) were considered negligible as they affect larger particles than those emitted of the moped of this study (<1 μm) [44]. A detailed presentation of the topics is out of the scope of this paper. Details can be found in the literature [18,43,44].

This study focused on measurements of solid particles carried out following the current EU legislation (Regulation (EU) 2017/1151) and on the related uncertainty. The measurements of total particles (including volatiles) are not included in the legislation, both in the laboratory and on the road (Regulation (EU) 2017/1154). They depend on many parameters, such as the dilution ratio and the dilution air temperature, which can result in orders of magnitude difference between different settings [45]. This topic has been discussed in the literature [46] and was beyond the scope of this study.
