*3.5. Temperature and Heat Results*

To assess the complete model, experimental tests were conducted in five operating points from the test matrix. Modelled outlet temperature *Tg*, *out* and heat loss through the exhaust pipe . *Q* are compared with experimental results in the five calibrating points (see Table 9).


**Table 9.** Experimental versus model thermal results in calibration engine modes.

The remaining four operating points of the test matrix are used to evaluate the model out of training points. Results are shown in Table 10.

**Table 10.** Experimental versus model thermal results out of calibration engine modes.


### *3.6. Flow Temperature Distribution at the DOC Outlet*

As commented in Section 2.2.3, it is suggested that energy recovery processes should take place downstream of after-treatment devices in order not to interfere with their operation. However, they should also occur sufficiently close in order to minimize further thermal energy dissipation to the surroundings. Therefore, the analysis of the flow abandoning the DOC is essential to know the working conditions of energy-harvesting devices.

Low uniformity in inlet flow occurring in most catalysts leads to different flow paths with different residence times. Flow inside the DOC is subject to cooling because external convection and heating because of chemical reactions in the DOC. These different paths (see Figure 11) caused by the inlet cone cause a gradient of temperature in the outlet section of the catalytic converter, as can be seen in Figure 12.

**Figure 11.** Streamlines and inlet velocity distribution in the monolith. An example of usual bad flow uniformity caused by inlet cones in automotive catalysts can be seen.

Coefficient of variation (standard deviation divided by mean value) of temperature distribution across the DOC outlet area (distribution shown in Figure 12b) was calculated from results of the CFD model. This statistical coefficient accounts for the dispersion from the average temperature flow. As can be seen in Figure 13, variation in temperature is enhanced in engine conditions with low mass flows, since flow thermal inertia is also lower. Engine modes in which catalytic reactions are active (see black dots in Figure 13) present more uneven distribution than those in which they are inactive (see white dots in Figure 13).

**Figure 12.** Temperature distribution for the 2400 rpm–110 Nm mode in (**a**) monolith, outlet cone and exhaust pipe and (**b**) cross-section of DOC outlet (before exhaust pipe).

**Figure 13.** Plot for coefficient of variation in temperature distribution at DOC outlet. White dots represent engine modes in which chemical processes were not active.

### *3.7. Temperature Loss along the Exhaust Pipe*

Sometimes, because of limitations in available space or ease of installation, the selected place for energy recovery devices moves away from the location with the maximum temperature available (immediately before the after-treatment systems). Average temperature of the exhaust gas in the first 50 cm downstream of the DOC was obtained from the validated model to quantify the loss in temperature when moving the energy recovery device away from the DOC.

Test-bench results with natural convection were compared with external forced convection (as in a moving vehicle with velocity *<sup>v</sup>*∞). Forced convection was simulated as boundary condition in pipe walls. Two different modes (lowest and highest engine power within the test matrix) were studied for each external condition. Forced convection coefficients were calculated with external parallel flow correlations [38] taking into account velocities of the vehicle at those engine conditions. Notice that natural convection conditions can also be relevant in moving vehicles since the part of the exhaust pipe adjacent to the DOC could not be in contact with car underbody air.

Average temperature decreases ( Δ *T*/*L*) for external natural convection (test-bench) range from 0.9 ◦C/dm in the lower power mode to 1.2 ◦C/dm in the higher power mode. For forced convection, decrease in temperature ranges from 1.2 ◦C/dm to 2.6 ◦C/dm (see Table 11).

**Table 11.** Cooling in the exhaust gas for the part of the pipe adjacent to the DOC (first 50 cm).

