## 2 Materials and Methods
### ESC Test  
Exhaust emissions from internal combustion engines are dependent on engine operating states, both static and dynamic. Awareness of the dependence of the emission of toxic components from internal combustion engines on their operating states has led to the need to develop tests that correspond to actual engine operating conditions. This has led to the development of several static and dynamic tests typically used in approval procedures. The ESC (European Stationary Cycle) test is one of the more extensive static tests. ESC is a 13-phase, steady-state procedure, which has also been called the OICA or ACEA cycle [43]. Engine testing in the ESC test is a procedure that evaluates the emissions and fuel efficiency of engines. The test simulates urban driving conditions, where stopping and acceleration are common. During the test, the engine is run stationary and subjected to various load cycles that simulate typical city driving conditions [44]. The ESC test cycle was introduced along with the European Load Response (ELR) test and the European Transient Cycle (ETC) test as part of the Euro III emissions [45]. For this test, engine tests are conducted on an engine dynamometer at steady state. The engine must run for a specified time in each mode, reaching full speed and load changes within the first 20 s [46; 47; 48]. Circumferential torque must be maintained within \(\pm\)2% of maximum torque, while the specified speed  
Figure 1: Test stand: (**a**) AVL CEB II exhaust gas analyzer, (**b**) apparatus for measuring particulates, (**c**) SCHENCK brake, and (**d**) Perkins 854E-E34 TA engine. must be maintained within \(\pm\)50 rpm. Emissions of toxic exhaust components are averaged over the cycle using weighting factors. Emissions results are expressed in g/kWh. Table 4 shows the test modes of the ESC test. To determine the speeds \(A\), \(B\), and \(C\), it is necessary to determine two speeds. The speed of the motor at 70% of maximum power must be specified. This speed is denoted as \(n_{hi}\). The motor speed for 50% of maximum power is then determined. This speed is denoted as \(n_{lo}\). This makes it possible to calculate motor speeds \(A\), \(B\), and \(C\)[45; 46]:  
\[ \begin{array}{l}A=n_{lo}+0.25(n_{hi}-n_{lo})\\ B=n_{lo}+0.50(n_{hi}-n_{lo})\\ C=n_{lo}+0.75(n_{hi}-n_{lo})\\ \end{array} \]  
High average load factors and high exhaust gas temperatures characterize the ESC test. Figure 2 graphically shows the process of conducting an ESC test on a dynamometer bench at Warsaw University of Technology. Due to the fact that the test stand is equipped with the AVL IndiSmart system, it is possible to determine the pressure in the Perkins engine cylinder. The relative error of measurement of the gas pressure in the combustion chamber of the Perkins engine is about \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mode** & **Weight, \%** & **Engine Speed** & **Load, \%** \\ \hline
1 & 15 & Low idle & 0 \\
2 & 8 & A & 100 \\
3 & 10 & B & 50 \\
4 & 10 & B & 75 \\
5 & 5 & A & 50 \\
6 & 5 & A & 75 \\
7 & 5 & A & 25 \\
8 & 9 & B & 100 \\
9 & 10 & B & 25 \\
10 & 8 & C & 100 \\
11 & 5 & C & 25 \\
12 & 5 & C & 75 \\
13 & 5 & C & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ESC test modes [49]. Figure 2: The sequence of steps and weights of individual measurement points in the ESC test on the Warsaw University of Technology test bench. \(\delta=0.25\%\). This makes it possible to calculate the amount and rate of relative heat release in the combustion process. The formula to calculate the heat release rate is as follows [50]:  
\[HRR=\frac{\kappa}{\kappa-1}p\frac{dV}{d\varphi}+\frac{1}{\kappa-1}V\frac{dp}{d \varphi}\ \ \ \ \ \left[\frac{J}{CAD}\right] \tag{1}\]  
where  
\[\frac{c_{p}}{c_{v}}=\kappa \tag{2}\]  
The temperature in the cylinder can be determined using the equations of state of a perfect gas. Another parameter that can be calculated is specific fuel consumption (SFC).