## 2 Numerical Model Description  
### Engine Modeling  
In this study, the GT-POWER program (Gamma Technologies, Westmont, IL, USA) was used to predict the reduction of NOx at partial engine load under the engine speed of 1200 rpm, as shown in Table 1. Cam-in-cam, the variable valve scheme used in this study, is an electronically variable valve device, and the inside of the variable cam is retarded to about 30 degrees. An extensive GT-POWER model of the base R-engine with internal EGR created by variable exhaust valve actuation was built in this study.  
Among the five points on the operation map of the R-engine, as shown in Figure 1a, the standard value (hereinafter referred to as \"Base\" case) is selected when the engine of the basic cam follows the injection strategy according to the operating map. Figure 1b shows the prototype cam-in-cam system used in this study and variable valve profile.  
\begin{table}
\begin{tabular}{c c} \hline
**Low Load** & **Low, Middle Load** \\ Fuel Injection Quantity: 12 mg & Fuel Injection Quantity: 12 \& 19.8 mg \\ \hline
**Idle + Low Speed** & **Middle Speed** \\ Engine speed: 800 rpm & Engine speed: 1200–2000 rpm \\ \hline \end{tabular}
\end{table}
Table 1: Operating points on map in R-engine.  
Figure 1: Engine map and variable valve device. (**a**) Five operating points on map in R-engine; (**b**) Prototype cam-in-cam system (MAHLE).  
Commercial R-engine has 4-cylinder and 4-valve per cylinder. Cylinder pressure was measured at 1-cylinder only for combustion analysis. Engine crank shaft connected with a DC dynamometer and high-pressure fuel injected in the cylinder by signal of injection device. Table 2 shows specification of R-engine used in this study.  
The GT-POWER program is a commercial engine analysis program widely used as an industry standard for vehicle and powertrain simulation software. It is a next-generation integrated CAE application that is becoming increasingly important in the industry due to its functions for engine evaluation, such as cooling system operations, as well as fuel consumption, noise, etc. under an arbitrary driving condition. It provides a fast solver for 1D and 3D simulations, making realistic simulations of large-scale systems possible. It also has the advantage of containing detailed information on valves, cylinders, and combustion behavior (predictive or data-based functions) for engine combustion calculations. The numerical full-circuit model developed by this study consists of the engine part (single cylinder, valves, pipes, etc.), valve train part (cam, camshaft, valve rod, etc.), and fuel injection part (piezo actuator, nozzle, rod, needle, orifice, etc.). The valve part in the engine system has received a valve profile from rotating the cam by the valve train model linked with the engine model. The injector model is built up with internal construction of a third piezo injector and linked with an engine model. The engine combustion model uses DIPUSE because NO\({}_{x}\) prediction is possible with improved accuracy. The heat transfer model uses WoschniGT.  
The fuel injection model was designed with a third piezo injector and verified through comparing experimental injection data obtained by the Bosch-tube method. The Bosch-tube measurement principle is to feed the fuel into the pipe with a cross-sectional area A and select the fuel control volume in the pipe flowing at the speed of sound as c when the fuel in the pipe moves at a speed of u. By knowing the sonic velocity and fuel density in the pipe and determining the amount of change in pressure in the chamber, the injection rate can be calculated [12].