It is simplified as a one-dimensional steady flow unit with main losses of local pressure drop ΔP₁ and drag loss along the way ΔP₂[10].

Where ΔP₁, ΔP₂, ρ, l, d, P₀ are local pressure loss at the inlet, resistance loss along the way, air density, pipe length, pipe diameter and compressor inlet pressure respectively. The loss coefficient ε is 0.5; The air viscous coefficient is taken as λ = 0.00001983 pa ∙ s. Air flow rate is v= m_c/(ρA_r), obtained from the compressor mass flow rate. Inlet equivalent area of compressor A_r is 0.039. The air filter simulation model in Matlab/Simulink is shown in Figure 3.

Figure 3: 
Simulation model of air filter in Matlab/Simulink

According to a one-dimensional adiabatic compression model with a compressor characteristic curve, the outlet temperature of the compressor [11]

The obtained torque of the compressor is

where T_cin and T_cout are the inlet and outlet temperatures of the compressor, respectively. n_tc and π_c are the supercharger speed and compressor pressure ratio respectively. Here, π_c = P_clin/P₀, and η_cs and mc˙ are the adiabatic efficiency and air flow rate of the compressor, respectively. The polytropic compression index and gas constant k and R can be obtained with imported n_tc and π_c. The simulation model of the compressor in the MATLAB/Simulink is shown in Figure 4.

Figure 4: 
Simulation model of air compressor in Matlab/Simulink

Owing to its high heat exchange efficiency, the thermal inertia of the intercooler can be generally ignored, and only the cooling effect and pressure loss are considered, which are treated as a throttle cooling and pressure dropping unit [12]. With the cooling coefficient ε, the outlet temperature of the intercooler is

The pressure drop of the intercooler is related to the air flow rate, and the outlet air pressure of the intercooler can be expressed as [12]

where, T_clin, T_clout, and P_clin, P_clout are the air temperature and pressure at the intercooler inlet and outlet, respectively. T_w is the cooling water inlet temperature of the intercooler, ε is its cooling coefficient, and mc0˙ is the rated air flow rate of the intercooler. The initial air pressure loss of the intercooler P₀ is 400 Pa [13]. The simulation model of the intercooler in MATLAB/Simulink is shown in Figure 5.

Figure 5: 
Simulation model of inter-cooler in Matlab/Simulink

The scavenging tank is modeled using the volumetric method calculated by the energy, mass, and ideal gas law conservation equations. The air pressure in the scavenging tank is [14]

The outlet air temperature in the scavenging tank is obtained from the ideal gas law equation as

where, Plm˙ and T_im are the air pressure rate and temperature in the scavenging tank, respectively. Here, the scavenging tank volume V_im of the MAN B&W 6S35ME-B9 diesel engine was calculated to be 0.167 m³. m_d is the intake airflow of the engine. The scavenging tank simulation model in MATLAB/Simulink is shown in Figure 6.

Figure 6: 
Simulation model of scavenging tank in Matlab/Simulink

The intake air flow of a diesel engine is obtained from the theoretical airflow of the engine with a filled cylinder

where η_v is the charging efficiency of the engine, which is generally regarded as a single function of the running speed n_e of the diesel engine. Here, η_v = a₂ * n_e² + a₁ * n_e + a₀,here a₂ = −5.363 * 10⁻⁷, a₁ = 2.04 * 10⁻³, a₀ = 0.576107.

The exhaust gas temperature in the exhaust branch is expressed as

where, K and α are the increase factors of the exhaust gas temperature and excess air coefficient, respectively. The required air per fuel L₀ is 14.3. The exhaust gas temperature rise factor K is a function of the air-fuel ratio [13], which is interpolated with the excess air coefficient. In MATLAB/Simulink, the simulation model of the exhaust branch temperature of the diesel engine is shown in Figure 7.

Figure 7: 
Simulation model of exhaust branch in Matlab/Simulink

Output torque of diesel engine

Its fuel oil consumption

Where m_f, T_i, T_e, g_i are the fuel injection quantity per cylinder, output torque, exhaust gas temperature and fuel oil consumption rate of the diesel engine respectively. The lower fuel heat value H_u is 42700 kJ/(kgk).The evacuation volume per cylinder V_d is 0.87 m³. η_i is the indicated working efficiency of engine. The combustion dynamics and thermodynamic simulation model of combustion in the cylinder in Matlab/Simulink is shown in Figure 8.

Figure 8: 
Thermodynamic simulation model of combustion in Matlab/Simulink

The exhaust gas in the manifold is also modeled with the "Volumetric method" and exhaust gas pressure

The gas temperature in the exhaust manifold is obtained from the ideal gas equation law

where Pem˙ and T_em are the gas pressure rate and temperature in the exhaust manifold, respectively. Here, the mixed gases in the exhaust manifold m_out are m_d + m_f, and the exhaust pipe volume V_em is 0.3 m³. The exhaust manifold simulation model in MATLAB/Simulink is shown in Figure 9.

Figure 9: 
Simulation model of exhaust manifold in Matlab/Simulink

The turbine efficiency is fitted by the embedded RBF function in MATLAB by adopting the s-function from the turbine characteristic curve [14].

The turbine outlet temperature is

The turbine output torque is

The turbine is equivalent to a throttle nozzle for a simplified calculation. The gas flow, mt˙ is obtained as a one-dimensional isentropic expansion process:

When πt<kt+12ktkt-1 :

When πt≥kt+12ktkt-1 :

where, T_tout, M_t, m_t, η_ts, and F_res (A0 in the following figure) are the gas outlet temperature, turbine output torque, gas flow, turbine efficiency, and gas flow area, respectively. The turbine expansion ratio π_t was P_em/P_b. ψ, μ_T are the flow function and flow coefficient, respectively, where F_res is 0.039 and μ_T is 0.7. The turbine simulation model in MATLAB/Simulink is shown in Figure 10.

Figure 10: 
Simulation model of turbine in Matlab/Simulink

The turbocharger rotating speed can be obtained from the D'Alembert's principle as

where, η_m and I_tc are the turbocharger mechanical working efficiency and turbocharger rotating inertia, respectively, where η_m is 0.89 and I_tc is 16. The turbine rotor simulation model in MATLAB/Simulink is shown in Figure 11.

Figure 11: 
Simulation model of rotor in Matlab/Simulink

Owing to the different shipping routes, the influence of the engine room temperature cannot be ignored, and the engine inlet air temperature could be different. The relative deviations of the thermodynamic parameters under different running speeds and engine room temperatures are shown in Figure 12. It can be observed that when the engine room temperature rises, the decrease in inlet air density worsens the chamber combustion inside the cylinder. The exhaust air temperature T_e, exhaust gas temperature in manifold T_em, and turbine outlet gas temperature T_tout of the diesel engine increase significantly, whereas the intercooler inlet air pressure P_clin, air pressure in the scavenging tank P_im, and exhaust air pressure in the manifold P_em decrease. The most obvious change was the rise in the compressor outlet air temperature T_cout. With respect to the combined parameters, the turbine coefficient Nt₁ increases the most obviously, whereas the compressor coefficient Nc₁, compressor coefficient Nc₂, turbine coefficient Nt₂, intercooler flow coefficient Nc_f, and turbine flow coefficient Nt_f all decrease to varying degrees.

Figure 12: 
Relative deviation under different engine room temperatures and running speeds

Comparing Figure 12 (a) and Figure 12 (b), it can be observed that the variations in the various parameters under different running conditions are quite similar. This indicates that the performance failure behavior of characteristic parameters in terms of the relative deviation is quite clear and immovable, even under different running conditions of the diesel engine, which is greatly convenient for failure diagnosis.

The pressure drop due to resistance along the way of the filter mesh was simulated by changing the length diameter ratio of the filter (l/d) in Equation (2) to simulate the blockage of the air filter in the diesel engine.

Figure 13 shows the relative deviation of the characteristic parameters of the diesel engine when l/d is 1500 and 300 at different running speeds. It can be observed that when the air filter is blocked, the inlet air pressure of the intercooler P_clin, outlet air pressure of the intercooler P_clout, and exhaust gas pressure in manifold Pem decrease, whereas the exhaust gas temperature T_e, exhaust gas temperature in the manifold T_em, and turbine outlet gas temperature T_tout of the diesel engine increase, and the outlet air temperature of the compressor T_cout, intercooler outlet air temperature T_clout, and scavenger air temperature T_im do not change significantly. Additionally, the compressor coefficient N_c2, turbine coefficient N_t2, intercooler flow coefficient N_cf, and turbine flow coefficient N_tf decrease significantly. It was found that when the air filter is blocked, the most affected characteristic parameter is the inlet pressure of the compressor, resulting in insufficient air into the compressor and poor combustion inside the cylinder; thus, the exhaust gas temperature increases in the exhaust manifold.

Figure 13: 
Relative deviation under different air filter l/d and running speeds

The fouling in the intercooler water passage also has a direct impact on the intake air of diesel engines.

As shown in Figure 14, owing to the fouling on the water side of the intercooler, the cooling coefficient decreases, and it is difficult for air to exchange heat with the cooling water. The intercooler outlet air temperature T_clout, scavenging air temperature T_im, exhaust gas temperature T_e, exhaust gas temperature in manifold T_em, turbine outlet gas temperature T_tout, intercooler inlet air pressure P_clin, and air pressure in scavenging tank P_im all increase significantly. The compressor coefficient N_c1 and compressor coefficient N_c2 increase significantly, whereas the turbine coefficients N_t1, N_t2, and N_c decrease. The turbocharger speed increases slightly, which is similar to that of the extremely high intercooler cooling water temperature described below. Here, the intercooler cooling coefficient N_c decreases significantly, whereas it remains unchanged under other failures. Therefore, the intercooler cooling coefficient N_t could be used as a unique characteristic parameter for the intercooler water fouling failure at both the air and water sides.

Figure 14: 
Relative deviation under different intercooler cooling coefficients and running speeds

The intercooler has a direct impact on the intake air temperature of the diesel engine, especially on the intake air temperature of the cylinder. When the intercooler inlet cooling water temperature increases, the intake air flow slightly decreases, leading to an increase in the compressor outlet air temperature T_cout, intercooler outlet air temperature T_cout, scavenging air temperature T_im, exhaust gas temperature T_e, exhaust gas temperature in manifold T_em, turbine outlet gas temperature T_tout, intercooler inlet air pressure P_clin, and scavenging air pressure P_im. The compressor coefficient N_c1 and compressor coefficient N_c2 increase significantly, whereas the turbine coefficient N_t1, turbine coefficient N_t2, and intercooler flow coefficient N_cf decrease, and the turbocharger rotating speed increases slightly, as shown in Figure 15.

Figure 15: 
Relative deviation under different intercooler cooling water temperatures and running speeds

With the blockage of the scavenging port, the intake air flow into the cylinder decreases significantly, which worsens the fuel combustion inside the cylinder. The exhaust gas temperature T_e, exhaust gas temperature in the manifold T_em, and turbine outlet gas temperature T_tout increase significantly, whereas the intercooler inlet air pressure P_clin, scavenging air pressure P_im, and exhaust gas pressure in the manifold P_em decrease. The most obvious increase is the compressor outlet air temperature T_cout, as shown in Figure 16. The turbine coefficient N_t1 increases most obviously, whereas the compressor coefficients Nc₁, Nc₂, N_t2, N_cf, and N_tf all decrease to varying degrees. The characteristic behavior is similar to that of air filter fouling, turbocharger bearing wear, and high inlet air temperature.

Figure 16: 
Relative deviation under different scavenging port flowing coefficients and running speeds

Blocked turbine nozzles can block gas flow into the turbine, which significantly increases the exhaust gas pressure in the manifold P_em, whereas the exhaust temperature T_e of the diesel engine, exhaust manifold temperature T_em, and turbine outlet temperature T_tout slightly decrease. When the turbine nozzle is blocked, its most direct influence is on the exhaust gas pressure in the manifold P_em and turbine flow coefficient N_tf, which could be used as two characteristic parameters for turbine nozzle blockage failure, as shown in Figure 17.

Figure 17: 
Relative deviation under different nozzle flowing coefficients and running speeds

When the turbine rotor is mechanically worn out, its compressor air compression capacity and compressor air flow decrease, which cause an increase in the exhaust temperature T_e, exhaust gas temperature in manifold T_em, and turbine outlet gas temperature T_tout, whereas the inlet air pressure P_clin, scavenging air pressure P_im, exhaust gas pressure in the manifold P_em, and turbocharger rotating speed n_tc decrease significantly, similar to the case in the turbine outlet passage fouling failure, as shown in Figure 18 and 19.

Figure 18: 
Relative deviation under different turbocharger mechanical efficiencies and running speeds

Figure 19: 
Relative deviation under different turbine exhaust back pressures and running speeds

The turbine outlet passage fouling was simulated by increasing the back pressure during simulation. As shown in Figure 19, a higher back pressure of the turbine causes an increase in the exhaust gas temperature T_e, exhaust gas temperature in manifold T_em, and turbine outlet gas temperature T_tout. The most direct impact is the decrease in the turbine working capacity, which reduces the turbocharger speed n_tc, intercooler inlet air pressure P_clin, intercooler outlet air pressure P_clout, scavenging air pressure P_im, and exhaust gas pressure in manifold P_em. With respect to the combined parameters, the increase in the turbine coefficient N_t1 is the most obvious, whereas the compressor coefficient N_c1, compressor coefficient N_c2, turbine coefficient N_t2, intercooler flow coefficient N_cf, and turbine flow coefficient N_tf all decrease to some extent.

In conclusion, the characteristic parameters of extremely high inlet air temperature, intake air filter blockage, scavenging port fouling, worn turbocharger bearing, and turbine outlet passage fouling exhibit similar behavior even under different operating conditions of the diesel engine. However, when the engine room temperature is extremely high, the compressor outlet temperature T_cout increases significantly but decreases to a certain extent in the other failures, which provides a distinguishing parameter from other failures. The engine room temperature can be measured directly, the blocked air filter can be monitored with the differential pressure of the intake air filter, and the turbine back pressure can also be measured directly at the turbine outlet. Additionally, the worn turbocharger bearing can be judged from its vibration and scavenging port fouling can be detected by the pressure difference between the intercooler outlet air and scavenging air; thus, these different failures can be identified. The characteristic parameter behavior of the extremely high intercooler cooling water temperature is considerably similar to that of intercooler fouling at the water side, but the fouled intercooler can be determined directly by the intercooler cooling coefficient Nc, and the cooling water temperature in the intercooler can be measured directly. These two failures were the most easily distinguished. The most obvious characteristic of the turbine nozzle blockage is the obvious increase in the exhaust gas pressure in manifold P_em and turbine flow coefficient N_tf, which is not found in the other failures. In other words, the performance failure diagnosis of diesel engine turbocharging and gas-exchanging systems can be eventually realized with some other parameters and information.