Particle sampling efficiency for the PPS

Particles within the exhaust gas stream will have to overcome a 90^◦ turn in order to enter the Pegasor Particle Sensor inlet port for both probe configura-tions A and B, shown in Figure 3.10. However, with particle sample extrac-tion efficiency being strongly dependent on the sampling method and the particle size range, calculations were made to characterize possible sample concentration deficiencies due to the chosen method of installation of the PPS. Anisokinetic sampling and probe misalignment (i.e. anisoaxial sam-pling⇒sample velocity direction is different from stream velocity) are two primary factors, influencing representative particle collection and leading to either possible over or under estimation of the measured particle concentra-tions (Hinds, 1999; Von der Weiden et al., 2009; Giechaskiel et al., 2011).

Anisokinetic sampling occurs by virtue of a velocity difference between the gas stream in the exhaust stack or transfer pipe (v_exh⁸) and the sample flow within the sample probe (v_s), whereas misalignment (i.e. anisoaxial sam-pling) is defined as the angle (θ) between the streamlines of the exhaust gas stream and the streamlines within the sampling probe (Hinds, 1999; Von der

8pipe diameter averaged flow velocity.

Weiden et al., 2009). Both phenomena can be described as a function of the Stokes number (Stk), hence, are ultimately a function of particle size de-scribed by their aerodynamic diameter. According to a comprehensive re-view of methods used in the automotive sector for quantifying combustion engine derived particulate matter emissions, sampling for particle number measurements is typically done sub-isokinetically with ratios v_exh/v_s = 1.4-4.1, whereas, particulate matter mass is sampled at super-isokinetic condi-tions (i.e. v_exh/vs = 0.3-0.9) (Giechaskiel et al., 2012a). Table 3.5 lists typical exhaust and PPS sample flow parameters from heavy-duty and light-duty vehicles used as part of this study. It has to be noted that exhaust gas tem-peratures provided in Table 3.5 were measured at the location of sample ex-traction for the PPS and are thus, representative for the local gas properties.

Temperatures will be higher immediately downstream the after-treatment components.

The Stokes number can be defined as shown by Equation 3.4 (Hinds, 1999) with v_exhbeing the exhaust flow velocity (i.e. free stream velocity) in [m/s], Dsthe internal probe diameter and τ the relaxation time in [sec].

Stk= ^{τ vexh}

D_s (3.4)

The relaxation time characterizes the time required for a particle to adjust or relax its velocity to a new condition of external forces and is described as the product of particle mass (mp) and particle mobility (bp) (Hinds, 1999). Alter-natively, the relaxation time can be defined in terms of the standard particle density⁹ (ρ₀) in [kg/m³], the sample gas viscosity (η_s) in [Pa·s], the aero-dynamic particle diameter (d_a) in [m], and the Cunningham slip correction factor (Cc) as shown by Equation 3.5.

τ= ^ρ0da

2C_c 18 ηs

(3.5) The Cunningham slip correction factor was further defined according to the expression developed by Allen and Raabe (1985) for solid particles as a function of the physical particle diameter (d_p) in [m], and the mean free path (λ) of the sample gas as shown in Equation 3.6.

9standard particle density of 1g/cm³.

Table 3.5: Typical exhaust and sample flow parameters for heavy-duty (data from Thiruven-gadam et al. (2015)) and light-duty (data from Thompson et al. (2014)) applications; exhaust pipe diameter (D_s) for heavy-duty: 5in, and light-duty: 2in; pressure of exhaust (P_exh) and sample (Ps) streams both 101,325Pa; differentQsfor PPS versions V1 through V3.

Heavy-Duty Light-Duty

Min. Max. µ Min. Max. µ

Q_exh [m³/min] 2.42 42.48 15.63 0.26 8.50 3.65

v_exh [m/s] 3.19 55.88 20.56 2.13 69.86 30.01

T_exh [C] 85.08 272.45 183.29 94.45 197.18 145.24

ρ_exh [kg/m³] 0.99 0.65 0.77 0.96 0.75 0.84

η_exh [Pa·s] 2.14E-5 2.90E-5 2.56E-5 2.19E-5 2.61E-5 2.40E-5 Reexh [-] 18,596 158,629 78,949 4,763 101,959 53,530

Ts [C] 200 200

For simplicity, ideal air rather than real exhaust gas properties have been assumed in order to estimate the mean free path according to Equation 3.7, with R being the universal gas constant in [J/(mol·^{K)], N}A the Avogadro’s number in [1/mol], dm the collision diameter for air molecules in [m], and Ps

and Ts the sample gas pressure in [Pa] and temperature in [K], respectively (Hinds, 1999). The sample gas viscosity (η_s) in [Pa·s] was calculated using Sutherland’s formula with the coefficients chosen for air (i.e. T0= 291.15, η0

= 18.27x10⁻⁶, C = 120).

λ= √ ^R Using the empirical Equations 3.8 and 3.9 provided by Durham and Lundgren (1980) the particle concentration ratio (C/C_{0, isoaxi}) due to anisoaxial sam-pling can be calculated as a function of the probe misalignment angle (θ) in [deg]. According to Hinds (1999) the empirical Equation 3.8 is valid between 0^◦ ≤ ^θ ≤ ^90◦ and for isokinetic sampling flow conditions with Stokes num-bers in the range of 0.01 < Stk < 6. It can be noticed from Table 3.5 that sampling under all considered conditions was performed sub-isokinetically.

However, for the purpose of estimating C/C_{0, isoaxi} in this analysis it was assumed that the sample flow rate was of similar magnitude as the exhaust flow rate (i.e. v_exh≡^vs).

Assuming a properly aligned sampling probe (i.e. θ = 0^◦), Belyaev and Levin (1974) provide an empirical expression to calculate the concentration ratio (C/C_{0, isokin}) due to anisokinetic sampling conditions given by Equa-tion 3.10. According to Von der Weiden et al. (2009) this formula is valid for Stokes numbers between 0.051 ≤ ^Stk ≤ 2.03 and velocity ratios between 0.17≤ ^vexh/vs ≤ 5.6, however, has also been applied outside this range by Giechaskiel et al. (2012a) for estimation of particle sampling efficiencies from CVS dilution tunnel or raw exhaust stack.

C Figure 3.11 depicts the square root of the Stokes number as a function of particle diameter on the right y-axes along with the concentration ratio for anisoaxial flow conditions as a function of Stokes number on the left y-axes for a probe misalignment angle of θ =90^◦ (i.e. conditions expected for sam-pling probes A and B). The data shown is representative of average exhaust flow and sampling conditions for a heavy-duty engine application (see Ta-ble 3.5) and was plotted for particle diameters ranging from 1nm to 40µm

at standard pressure conditions of 101.325kPa and at an exhaust gas temper-ature of∼^183◦C. The dotted line provides a visual aid to identify the Stokes number representative of a particle with diameter 1µm for the given exhaust gas properties.

In parallel, Table 3.6 gives an overview of the concentration ratios for 1µm particles due to anisokinetic and anisoaxial sampling conditions for the range of typical parameters provided in Table 3.5 for both heavy- and light-duty applications as well as the three different Pegasor Particle Sensors (i.e.

their respective sample flow rates). On one hand it can be observed that particle concentrations inside the sampling probe are slightly reduced by a factor of 0.98 and 0.97 for heavy-duty and light-duty vehicles, respectively, due to probe misalignment. On the other hand however, calculations indi-cate an enrichment of particles in the sampling probe due to sub-isokinetic sampling on the order of 1.15 to 1.33 for heavy- and light-duty applications, respectively. These values are estimated for 1µm particles. In a compre-hensive analysis of typical exhaust particle size distributions from diesel and gasoline fueled engines, Harris and Maricq (2001) showed that count mode mobility diameters are ranging within 80-100nm for both non-filter equipped diesel and direct injected spark-ignition (DISI) engines, and are considerably lower between 20-30nm for port-fuel injected (PFI) gasoline en-gines. Therefore, when considering 200nm diameter particles, C/C_{0, isoaxi} in-creases to 0.99 for both heavy- and light-duty, whereas C/C_{0, isokin}is reduced to 1.008 and 1.017 for heavy- and light-duty applications, respectively.

The analysis provided herein was based on the assumption of isokinetic flow conditions when estimating concentration ratios due to probe misalignment and vice-versa, a properly aligned probe to calculate sampling efficiencies due to anisokinetic flow conditions. In the present case of the PPS with a combination of probe misalignment (θ=90^◦) and anisokinetic sampling due to the changing exhaust flow rates during engine operation while the sam-pling flow rate is kept constant, a more general analysis described by Brock-mann (1993) might be applicable. In case of a combination of anisokinetic and anisoaxial sampling conditions Hinds (1999) introduces the limiting con-centration ratio where the overestimation due to sub-isokinetic sampling is canceling the underestimation due to probe misalignment.

Furthermore, Giechaskiel et al. (2012a) showed in a similar analysis as pre-sented herein, that for Stokes numbers between ∼^{10−3 and 10−4 the} over-or underestimation of both particle number over-or particulate matter mass pen-etrations is within 2% for all evaluated cases and therefore, negligible even

10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰ 10¹

Figure 3.11: Effect of anisoaxial probe alignment on the concentration ratio (C/C0, isoaxi) for θ=90^◦; medium values for typical heavy-duty engine with 5in exhaust stack; assuming isokinetic sampling conditionsv_exh≡^vs (v_exh =20.6m/s); dotted line indicating√

Stk for 1µm particles.

for particles up to 1µm diameter. Results indicated that even extreme cases of anisokinetic sampling lead to a penetration of only 102% for 100nm par-ticles. Similarly, Ntziachristos and Samaras (2002) estimated that deviations from isokinetic sampling are insignificant for number concentrations during chassis dynamometer testing of light-duty vehicles. The study reports∼^4%

higher number concentrations for a maximum deviation ratio of 1.32.

Based on the results obtained from this analysis, and supported by litera-ture, it was concluded that anisoaxial sampling conditions for probe config-urations A and B as well as the expected impact of changing exhaust flow rates on isokinetic conditions will not noticeably affect the ability of the PPS to measure particulate matter directly from the exhaust stack, and can there-fore be neglected.