*2.3. Results Processing*

A merit function [36] was used to select the best operating conditions in each one of the different studies. The merit function (MF) is defined as shown in Equation (2):

$$\text{MFF} = \sum\_{i} \max\left(0, \frac{x\_i}{x\_i^\*} - 1\right) \tag{2}$$

where *xi* is the value of the *i*th constrained parameter at the given conditions, *xi*\* is the constraint of the *i*th parameter and *i* is the index over all the constraints.

The values of the constraints used to calculate the merit function were NOx = 0.4 g/kWh, soot = 0.01 g/kWh, and maximum pressure rise rate (PRR) of 15 bar/CAD. These limitations were aimed to fulfill ultra-low emissions while preserving the engine mechanical integrity. Thus, the contribution to the merit function from a given variable will be zero if only the measured value is less than or equal to the specified limit. When the merit function is non-zero, the contribution from each constrained parameter can be examined separately to quantify the severity of its non-compliance.

If various operating conditions fulfilled all the constraints for the same specific study (which results in a merit function value of zero), the best condition among these was considered the one that minimized the fuel consumption.

### **3. Paths for Increasing RCCI Efficiency**

During RCCI combustion, the fuel energy is typically apportioned in the ranges shown in Figure 2, where the exact values obtained depend on the specific operating conditions and engine characteristics. The present work investigates the effectiveness of different ways to modify the energy outgoing flow path for minimizing the energy losses, thus providing the guidelines to maximize the efficiency of this

combustion concept. The different paths are studied in a progressive way, so that the best solution coming from a previous path was maintained for the following steps.

**Figure 2.** Typical apportionment of the fuel energy among the different outgoing energy paths during RCCI combustion.

The first path studied to increase the RCCI efficiency is the reduction of the losses associated to incomplete combustion. As seen in Figure 2, this source of energy loss is not very relevant if compared to the others, as it only represents the 5% of the input energy in the worst case. However, the incomplete combustion results in very high levels of HC and CO emissions, which can compromise the effectiveness of the aftertreatment systems and other subsystems. As the literature demonstrates, higher combustion losses occur at low loads, where lower in-cylinder pressure and temperature occur [22]. The solution explored in this work to minimize combustion losses is the optimization of the engine settings, because it is the most straightforward solution to manage the in-cylinder reactivity.

The second way proposed for increasing the gross indicated efficiency is the reduction of the heat transfer losses. In this sense, it is expected that only a portion of the recovered energy will be extracted as additional gross work, while the rest will be merely rejected as thermal exhaust loss due to the higher exhaust temperature. In any case, rising the exhaust temperature is more desirable than rejecting the heat to the coolant, because it contributes to increasing the conversion efficiency of the aftertreatment systems.

The third path to maximize RCCI efficiency relies on the fuel properties modification to look for a proper in-cylinder fuel reactivity that enhances the combustion propagation. In this sense, several studies confirm that, in order to achieve high efficiency while reducing NOx and soot emissions, the higher portion of the energy should come from the low reactivity fuel [22,26]. This fact suggests that the low reactivity fuel characteristics and its amount in the blend must have a key role on the in-cylinder reactivity, so this will be the fuel source varied during the investigation.
