# Numerical Analysis of the Forces on the Components of a Direct Diesel Engine
## 3 Kinetics and Dynamics of the Test Engine
### In-Cylinder Pressure and Friction Force Calculation  
During the operation of internal combustion engines, combustion is an irreversible process that uses the reactions of fuel with an oxidizer to convert chemical energy into sensible energy, which also works to form products. In practice, carbon dioxide (CO\({}_{2}\)), nitrogen, and water are the main products of the combustion process. However, other species, including nitric oxide, nitrogen oxide, carbon monoxide, hydrocarbon, and particulate matter, are also common products. The liquid state determination at each point in the process requires a detailed understanding of the intermediate reactions that change the original mixture into the final combustion products. However, in all cases, we can use the first law of thermodynamics to determine the correlation between the beginning and end of a combustion process. The application of this law does not require users to know the development of the intermediate stages of the process. The first law of thermodynamics expresses the relationship between the variation of the internal energy (or enthalpy) and that of heat and work. When applying this law to a system where the chemical composition changes, we need to determine the zero state of the internal energy or enthalpy of all the substances in the system. In specific cases, the calculation of combustion in internal combustion engines is based on the equation of the first law of thermodynamics:  
\[\frac{d(m_{c}u)}{da}=-p_{c}\frac{dV}{da}+\frac{dQ_{F}}{da}-\sum\frac{dQ_{w}}{ da}-h_{BB}\frac{dm_{BB}}{da}, \tag{1}\]  
where \(\frac{d(m_{c}u)}{da}\) is the change in internal energy inside the cylinder, \(-p_{c}\frac{dV}{da}\) is the work cycle, \(\frac{dQ_{F}}{da}\) is the heat input, \(\sum\frac{dQ_{w}}{da}\) is the heat loss through the wall, \(h_{BB}\frac{dm_{BB}}{da}\) is the enthalpy loss due to gas leakage, \(m_{c}\) is the volume of the liquid inside the cylinder, \(u\) is the internal energy, \(p_{c}\) is the pressure inside the cylinder, \(V\) is the cylinder volume, \(Q_{F}\) is the heat of the fuel supply, \(Q_{W}\) is the heat loss to the wall, \(\alpha\) is the angle of the crankshaft rotation, \(h_{BB}\) is the enthalpy value, and \(\frac{dm_{BB}}{da}\) is the variation in volumetric flow rate. Equation (1) applies to both internal and external composite engines. However, the changes in the composition of the two cases are different. In the case of the formation of a mixture inside a cylinder, if we assume that the fuel in the cylinder is burned immediately, the combustion mixture is immediately blended with the residual gas in the cylinder. The air-fuel ratio (A/F) decreases continuously from a high value at the starting point to a low value at the end of the combustion. After the transformation, Equation (1) becomes:  
\[ \begin{array}{l}\frac{dT_{c}}{da}=\frac{1}{m_{c}\left(\frac{\partial u}{ \partial\partial t}+\frac{\partial u}{\partial\partial t}\frac{\
abla}{c} \right)}\left[\frac{dQ_{F}}{da}\left(1-\frac{u_{c}+\frac{\partial u}{\partial p _{c}}}{H_{u}}\right)-\frac{dQ_{w}}{da}-\frac{dm_{BB}}{da}\right.\\ \left.\left(h_{BB}-u_{c}-p_{c}\frac{\partial u}{\partial p}\right)-m_{c}\frac{ \partial u}{\partial\lambda}\frac{\partial\lambda}{\partial x}-p_{c}\frac{dV_{ c}}{da}\left(1-\frac{\partial u}{\partial p}\frac{m_{c}}{V_{c}}\right)\right]\end{array} , \tag{2}\]  
where \(T_{c}\) is the cylinder temperature, \(m_{c}\) is the volume of the fluid in the cylinder, \(p_{c}\) is the pressure in the cylinder, \(u_{c}\) is the specific internal energy of the volume of liquid inside the cylinder, \(H_{c}\) is the low calorific value, \(\lambda\) is the air residue ratio (\(1/\Phi\)), \(\alpha\) is the equivalent ratio, and \(V_{c}\) is the cylinder volume. The solution of the above equation depends onexperimental and numerical methods. The in-cylinder pressure always changes according to the crankshaft angle. The in-cylinder pressure is nominal at the intake and exhaust strokes; however, it increases dramatically during the compression and power strokes.