#### 3.1. Soot Load Determination

The results of the test are shown in

Figure 4. The numerals ① to ⑦ again represent the operation points of the engine. In the upper graph, the weighed soot load is plotted in

g/

l_{DPF} (open squares). As described above, the filter was weighed before and after the test run and once in the middle of the test.

The soot concentration as determined by the Pegasor sensing device in g/m

^{3} in each operation point was multiplied by the volumetric exhaust flow rate at the particular operation point and then integrated to get a soot mass inside the DPF. This soot mass is then divided by the DPF filter volume to get a soot load of the DPF in

g/

l_{DPF} (Equation (1)):

By doing this, it is assumed for simplification that no soot is being oxidized during the test and that all particles being present in the exhaust gas upstream of the DPF are trapped inside the filter. With this method, the gravimetrically determined actual soot load was slightly underestimated (ca. 16%), which is probably due to an insufficient calibration of the Pegasor sensing device. This is why the calculated soot load is divided by a factor of 0.84 (which is the quotient from the soot load at the end of the test determined by the Pegasor sensing device and that determined by weighing) to normalize the soot load with the gravimetrically determined values. Now, the curve of the soot load determined by the Pegasor sensing device represents the actual soot load during the experiment very well. It can be seen that the graph hits the weighed value at 2.6 h exactly, although only the value at the end was taken into account for the correction.

Very clearly, the single operation points with different particle contents in the exhaust can be distinguished in the slope of the curve with respect to the soot load of the DPF (

Figure 4, upper graph). Operation points with a higher average soot mass concentration induce faster filter loading. This can be seen, e.g., in the first half of the test, where by varying only the EGR rate, three different points with different soot mass emissions were adjusted. Operation point ② has the highest EGR rate, which leads also to the highest soot particle formation. The slope of the soot load curve is also the highest at this point. As a conclusion, it can be stated that, by integrating the signal of the Pegasor sensing device, a realistic soot load determination is possible, after calibration of the measuring system.

The question whether it is possible to detect the filter loading with a resistive soot sensor shall be investigated next. In

Figure 4, the soot load data derived from the resistive sensor are plotted. It was calculated as follows. At each operation point, an average value for the different slope values of the soot sensor current, d

I/d

t, was determined and correlated to the average soot concentration at this operation point, measured by the Pegasor sensing device. The signal slope of each soot-collecting period of the sensor was determined manually. In this way, each soot-collecting period evokes one measuring point. In each engine operation point, a varying number of collecting and regeneration cycles of the sensor are conducted (between one and four). The mean value of the slopes in each engine operation point is then used as a measure for the average soot mass concentration. The resistive type soot sensor was regenerated 18 times throughout the test run for a time of always 60–90 s. Thereby, the response time (the time until first soot paths have formed out and a current is measurable) varies from only seconds, up to minutes, depending on the soot content in the exhaust. Regeneration events are indicated in

Figure 4 by vertical bars.

Figure 5 shows the very good linear correlation between the sensor signal and the soot mass in the exhaust. Thereby, various test runs are considered for defining the linear regression curve, which are not shown here specifically. With this regression curve (

Figure 5), an average soot concentration can be determined for each operation point from the soot sensor signal. Now, this averaged soot mass concentration was again multiplied with the related exhaust flow and integrated over time (Equation (1)). This procedure is similar to the calculation of the DPF soot load from the signal of the Pegasor sensing device. Again, the correction factor of 0.84 was used to calculate the soot load.

The two curves in the upper graph of

Figure 4, the soot load as determined by the Pegasor sensing device and the soot load as determined by the resistive soot sensor, agree well. The different average soot mass concentrations in the exhaust of each operation point, which yields different slopes of the soot load curves, can be seen by both systems. However, the soot load, especially after operation point ⑤, is underestimated by the resistive soot sensor.

In the lower graph of

Figure 4, the microwave-derived frequency-averaged transmission parameter |

S_{21}| and the differential pressure, ∆

p, are plotted. The slopes of the curves at each operation point coincide quantitatively very well with the slope of the soot load of the DPF (upper graph). Both curves show a slight decrease in operation point ③, in contrast to the values calculated from the Pegasor sensing device and from the resistive soot sensor. This could most likely be due to soot oxidation inside the filter, resulting in a slightly decreased soot load in the DPF. Yet, in the exhaust gas upstream of the DPF, soot particles are still present and are detected by the resistive soot sensor and the Pegasor sensing device, which are located upstream of the filter. In contrast to that, the differential pressure and the microwave-derived transmission parameter are not affected by the soot mass concentration upstream of the filter, as both correlate to the soot

load of the filter.

The transmission parameter |

S_{21}| is averaged over frequency as described above. In

Figure 6, the value at the beginning of the test run (0 mg/

l_{DPF}) and the end of each operation point is plotted over the corresponding soot load (which is actually the trapped soot mass), which was taken from the accumulated (and corrected) Pegasor sensing device signal in

Figure 4. As can be seen in

Figure 6, the averaged |

S_{21}| depends linearly on the soot load of the filter. This confirms earlier results [

6]. In contrast to the previous study in [

6], the filter here was not soot loaded at one single constant engine operation point, but under changing engine parameters. It should be pointed out that there is no compensation of exhaust temperature, although this is an important noise factor [

6]. By compensating the temperature influence, the accuracy could have been enhanced even more.

#### 3.2. Soot Mass Concentration in the Exhaust Gas

In the previous section, the signals of two devices that were installed in the exhaust gas upstream of the filter to detect the actual soot mass concentration (Pegasor sensing device and resistive soot sensor) were integrated over time and correlated with the actual soot mass loading of the filter. The correlation between the microwave-based signal and the actual soot mass loading of the filter was also shown.

Now, in contrast to that, it shall be investigated, whether the microwave-based method can be applied to determine the actual soot mass concentration. This has already been described by Sappok et al. in [

7]. The results shall be proven here by similar tests with our own system for the first time. Here, the filter itself acts as the soot sensor. If one neglects second order effects, changes in the soot loading of the filter should be proportional to the actual soot mass concentration upstream of the filter. Hence, the time derivative of the soot mass may be a suitable means to monitor the soot concentration. This is similar to the gas dosimeter principle where both the accumulated amount and the instantaneous level can be measured even at low concentrations [

24]. In

Figure 7, the time derivative of the frequency-averaged transmission parameter |

S_{21}| is plotted against the averaged soot mass concentration in the exhaust gas, measured with the Pegasor sensing device. Each point in

Figure 8 is a result from one of the operation points ① to ⑦.

In

Figure 8, the time derivative of the differential pressure is plotted against the averaged soot mass concentration in the exhaust upstream of the DPF, measured with the Pegasor sensing device. Thereby the change in differential pressure is corrected to exhaust gas flow of this operation point, as it is well known, that the ∆

p signal is strongly affected by gas flow. With increasing volumetric gas flow, the differential pressure at constant filter loading increases as well [

2].

It can be seen that both signals depend similarly on the averaged soot mass concentration. With more soot being present in the exhaust, the soot load of the filter increases faster and hence the derived signal increases. In case of the microwave-based system, it seems that a certain soot mass concentration is needed to evoke a signal. One point (operation point ② at 50 mg/m

^{3}) seems to be too high and is not considered for the regression curve (dashed line) in

Figure 7. It is also striking that both systems (

Figure 7 and

Figure 8) indicate a slightly negative average soot mass concentration for the value derived from operation point ③ (very low soot concentration measured by the sensors). This may be due to the fact that both systems do not measure the soot mass concentration in the gas phase, but indirectly via the change of the soot load of the filter. Conditions promoting soot oxidation in the filter (elevated temperature, high NO

_{x} concentration) lead to a decrease of the signal below zero, despite the fact that a small amount of soot is emitted from the engine and is present in the exhaust even at these operation points. This leads to inaccuracies, especially at low soot mass concentrations. At higher soot contents in the exhaust, the correlation looks quite well. Here, the systems are suitable not only to monitor the filter state, but also to draw inferences about the soot mass concentration of the exhaust.

The before-shown results of the two signals differential pressure and microwave parameter for the averaged soot mass concentration are now compared with the actual soot mass in the exhaust (measured with the Pegasor sensing device) and the signal of the resistive soot sensor. Therefore, all four signals are shown together in

Figure 9 for the seven engine operation points. By means of the regression curves (

Figure 5,

Figure 7 and

Figure 8), the soot concentration,

c_{soot}, was calculated for each operation point out of the measured values from the resistive soot sensor, the microwave-based system and the differential pressure, respectively. In

Figure 9, the good agreement of the different sensor systems becomes obvious. It has to be noted that temperature correction was neither applied for the microwave-based system nor for the resistive soot sensor. Since exhaust gas temperature varies only around ca. 20 °C in maximum, the influence is not dominant, but temperature compensation may probably be important to increase accuracy. Again, an unrealistic negative value of the differential pressure sensors stands out. At operation point ③, a negative soot concentration of −34 mg/m

^{3} was calculated. As described above, this could retrieve from soot oxidation effects or inaccuracies in the measuring procedure, especially at very low soot concentrations. Further, at operation point ⑦, the ∆

p value diverges compared to the other systems. Apart from this behavior of the differential pressure in some operation points, all measuring devices show consistent soot concentration values. Only in operation point ⑤ do both measuring devices upstream (Pegasor and resistive soot sensor) agree very well, as do both filter sensing devices (microwave-based system and differential pressure sensor). However, it appears that the differentiated filter data do not coincide with the upstream soot concentration data. This has not been understood up to now.