# An Economical and Precise Cooling Model and Its Application in a Single-Cylinder Diesel Engine
## 4 Results and Discussion  
In this section, we compare the total power consumption of the two cooling systems and describe the performance of the DK32 engine, equipped with the electric cooling system. Several typical loads are chosen to calculate the power consumptions of the two cooling systems, that is \(\phi=(F,80\%,65\%)\) and \(T_{atm}=(40\,^{\circ}\)C, \(35\,^{\circ}\)C, \(30\,^{\circ}\)C). Here, \(F\) represents a full load. The power consumption curves for different loads at different engine speeds are shown in Figure 11. The results indicate that power consumption of a mechanical cooling system increases with the engine speed and is the same for all \(T_{atm}\). The power consumption of the electric cooling system increases with the engine speed and is lower for lower values of \(T_{atm}\) as expected; the power consumption is lower for the electric cooling system than the mechanical cooling system. In the case of \((n=2200,\phi=0.8)\), the power consumption of the electrical cooling system is \(300\) W, \(213\) W and \(117\) W for \(T_{atm}=40\,^{\circ}\)C, \(35\,^{\circ}\)C, and \(30\,^{\circ}\)C, respectively, whereas the power consumption of the mechanical cooling system is about \(680\) W. This trend becomes more apparent as \(\phi\) decreases, such as in the case of \(\phi=0.65\). In the common use case, this occurs in the region of the minimum BSFC \((n=1600,\phi=0.8)\) and \(T_{atm}=30\,^{\circ}\)C, where the total power consumptions of the electric and mechanical one are \(35\) W and \(290\) W, respectively. Therefore, the power saving of using the electric cooling system is \(255\) W, that is, the direct benefit of the electric cooling system is about \(1.9\%\) of the engine's power output. Figure 10: The plot ensures that the cooling system works well in all cases. The gray surface representing \(Q_{c}\) in Equation (14) is just above the colorful surface, which represents the heat rejection \(Q\) of the engine. The indirect benefit of the electric cooling system is much higher than the direct benefit. As mentioned above, in the common use case, the electric cooling system consumes 35 W output power of the engine and brings out about 7.2 kW heat rejection and ensures the target temperature of the coolant. However, in the mechanical cooling system, the excess power consumption drives the fan and water pump at excessive high speeds, resulting in overcooling of coolant and engine and thereby increasing the heat rejection of the engine to the ambient environment. The experimental data show that the mechanical cooling system results in 8.3 kW of heat rejection and the minimum BSFC is 211 g/(kW-h). Thus, under a part load, the mechanical cooling system uses a small proportion of the available engine power to incur high heat losses, which results in inefficiencies at part load of the engine-power curve, for details please refer to [2]. The amounts of exhaust pollutants of the DK32 engine are markedly different for the two kinds of cooling systems. The test results obtained by the National Automobile Quality Supervision and Test Center are listed in Table 1. It is evident that the engine with the electric cooling system meets the China-IV emission standard [23], whereas the engine with the mechanical cooling systems does not meet the standard because the CH + NOx value exceeds the limit. However, this engine can not meet EPA 3 standard because of the CH + NOx value. Additional technical measures, such as turbocharging or increasing fuel injection pressure or after-treatment, can improve the situation. Based on this mathematical model, the fan and water pump speeds can be predicted. For example, for \(T_{atm}=35\,^{\circ}\mathrm{C}\), the speeds are shown in Figures 12 and 13. The speed data can be stored in the ECU of the engine and are used to control the fan and water pump speed to ensure that the engine operates at the target temperature.