## 3 Results and Discussion  
The first system to be studied was the simplest cooling system, as depicted in Figure 2.  
A similar scheme was previously studied for a slightly different purpose in [4; 5]. In this context, dependencies are derived for such a scheme to observe how \(M_{\Sigma}\) changes when regulating the consumption of ICC (Figure 3). When constructing graphs and conducting further analysis, the parameter \(\eta_{0}\) is utilized, representing the efficiency of the cooling system for cooling the charge air  
\[\eta_{0}\ =\ \frac{T_{1}-T_{\text{s}}}{T_{1}-T_{\text{inv1}}},\]  
where \(T_{1,\text{s}}\)--temperatures of charge air in front of the compressor and in the engine receiver, K; \(T_{\text{inv1}}\)--temperature of external circuit coolant (ECC) in front of the cooler, K.  
Figure 1: Scheme of the cooling system type A.  
Figure 2: Scheme of the simplest closed cooling system. The dependencies were plotted for various values of \(\eta_{0}\) and different external circuit coolant costs--\(G_{ww}\). The calculations were conducted for one of the modern medium-speed marine engines, and the necessary parameters for these calculations are provided in Table 1.  
In greater detail, the initial section of one of the curves in Figure 3 is illustrated in Figure 4. Here, it can be observed that it exhibits a characteristic bend, influencing the value of \(M_{\Sigma}\) at low ICC flow rates. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Designation** & **Items** & **Values** \\ \hline \(N_{\epsilon}\) & Engine output (kW) & 1000 \\ \(n\) & Engine speed (rpm) & 500 \\ \(p_{\mathrm{c}}\) & Boost pressure (bar) & 2.0 \\ \(G_{\mathrm{G}}\) & Charge air flow (kg s\({}^{-1}\)) & 0.9 \\ \(p_{0}\) & Ambient pressure (bar) & 1.0 \\ \(t_{0}\) & Ambient temperature (\({}^{\circ}\)C) & 40.0 \\ \(t_{1}\) & Air temperature after compressor (\({}^{\circ}\)C) & 181.35 \\ \(t_{ww1}\) & Sea water temperature in front of the pump (\({}^{\circ}\)C) & 30.0 \\ \(t_{2}\) & Air temperature in the receiver (\({}^{\circ}\)C) & 35.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main parameters of the engine for which the simplest cooling systems were calculated. Figure 4: Example of the calculated graph of the dependence of \(M_{\Sigma}\) on the flow rate of the ICC \(G_{w}\). Figure 3: Dependences of \(M_{\Sigma}\) for different constant values of \(\eta_{0}\) and for different values of \(G_{ww}\) on the ICC flow rate \(G_{w}\) in the circuit. Analysis of the dependencies in Figures 3 and 4 allows us to note the following features. 1. In a closed simple circuit, there is a significant variation in \(M_{\Sigma}\) depending on the flow of ICC through the heat exchangers. 2. As \(G_{w}\) increases from values close to zero, the value of \(M_{\Sigma}\) first decreases (Figure 4), and then consistently increases monotonically for any constant values of \(\eta_{0}\). 3. For all possible \(\eta_{0}\), the minimum values of \(M_{\Sigma}\) are achieved at relatively low values of the ICC flow rate \(G_{w}\). 4. The values of \(M_{\Sigma}\) decrease as \(G_{w}\) decreases and increase as \(G_{w}\) increases. 5. The increase in \(M_{\Sigma}\) depending on \(G_{w}\) varies for different values of \(\eta_{0}\); as \(\eta_{0}\) as \(\eta 0\) increases, the growth of \(M_{\Sigma}\) becomes more pronounced. 6. The ratios \(M_{\Sigma}\) for two different \(\eta_{0}\) increase as the values of \(\eta_{0}\) and the absolute value of \(M_{\Sigma}\) rise--they can exceed 1000% in the region of large values of \(G_{w}\) within practical ranges of \(G_{w}\) and \(\eta_{0}\). Next, an analysis was conducted on the position of the minimum points of \(M_{\Sigma}\) for the simplest cooling system, depending on the ratio of the energy capacities of the coolants in the charge air cooler \(S_{c}\).