Numerical and Experimental Analysis of the Potential Fuel Savings and Reduction in CO Emissions by Implementing Cylinder Bore Coating Materials Applied to Diesel Engines

Abstract

Currently, internal combustion engines contribute to the problem of global warming due to their need to use products derived from fossil resources. To mitigate the above problem, this study proposes the use of coatings on the cylinder bore in order to reduce fuel consumption and polluting emissions. Therefore, in the present study a numerical model is developed in which the tribological behavior, heat fluxes, and leakage of the combustion gases in the chamber are considered to evaluate the influence of the coating. Nickel nanocomposite (NNC) and diamond-like carbon (DLC) coatings are considered in the study. The results demonstrate that the NNC coating produces a 32% reduction in the total friction force of the compression ring. The estimated maximum temperatures for the lubricating oil were 214, 202, and 194 °C for the DLC, steel, and NNC materials. Increasing the temperature in the DLC coating can cause a reduction in the tribological performance of the lubricant. The estimates made show that the implementation of the NNC coating allows a maximum reduction of 5.28 ton of fuel and 39.30 kg of CO emissions, which are based on the global fleet of diesel engines forecast for the year 2025 (corresponding to one hundred and eighty million engines) and a test time of 1800 s. The proposed numerical model allows future analyses to be carried out for other types of materials used as coatings. Additionally, the model can be expanded and adapted to consider other systems that involve friction processes in the engine.

1. Introduction

Despite the harmful effects on the environment and human health, fuels derived from fossil products continue to be the main source of energy globally. However, alterations in climatic conditions have promoted actions to reduce the production of harmful emissions [1,2]. Additionally, the high dependence on fossil resources, especially in the automotive sector, causes an energy risk in the future because these types of resources are not renewable [3,4]. This situation has led to an interest in seeking alternatives that allow reductions in fuel consumption and minimize polluting emissions. In general, to achieve this purpose it is necessary to improve the efficiency of internal combustion engines (ICEs), which can be achieved through changes in mechanical design, new fuel alternatives, and operating conditions [5,6,7]. In the particular case of modern ICEs, it is observed that they are subjected to high thermal and mechanical conditions as a consequence of the high ratio between the power and the light weight of the engine components [8]. This causes an average loss of fuel energy of 9.5%, which is used to overcome the friction processes of the engine [9]. A significant portion of these friction losses is located in the piston rings, which represent between 40 and 55% of the total energy lost due to friction processes in the engine [10,11]. One way to improve the efficiency of engines is through tribological and thermal studies focused on the piston rings. This would allow an improvement in fuel economy and a reduction in polluting emissions [12,13,14].

Several investigations have experimentally studied the inefficiency in the piston ring assembly. However, there is a high difficulty in this type of methodology due to the modifications necessary for the measurement of friction losses under engine operating conditions [10]. Therefore, analysis using analytical models has been chosen, which allows a better understanding of the tribological behavior of piston rings [15,16]. Furthermore, this type of model allows the incorporation of studies focused on the continuity of the lubricant flow, regime, and transport. Studies of this type include the work developed by Mishra et al. [17,18], who formulated a thermo-elastohydrodynamic model for the study of the compression ring of the piston. The results indicated that the viscous effects of the lubricant could not be ignored. Additionally, they used elastohydrodynamic ring models to investigate the influence of ring asymmetry on friction losses [19]. Baker et al. [20] studied the elastodynamic behavior of flexible rings to evaluate their ability to adapt holes and prevent flue gas leaks. Morris et al. [21] constructed a thermal network model to estimate the contact temperature between the cylinder liner and the piston rings. The results showed that the model is in agreement with the findings of Mishra et al. [21]. Using the model, they investigated the change in temperature caused by friction in the rings. Rahmani et al. [22] concluded that fuel consumption is influenced by tribological characteristics and can be reduced by controlling the temperature inside the cylinder.

Modern ICEs are considered to be highly efficient heat engines. Therefore, to improve their efficiency, it is necessary to apply innovative technologies such as cylinder deactivation, surface texturing, the heat treatment of exhaust gases, and the use of advanced coatings [23,24,25]. The use of coatings applied to ICE engines has been studied largely experimentally for different operating conditions, including standard conditions, cold start, and wear [26]. The investigations carried out show that the application of surface coatings influences tribological and thermal behavior. Therefore, they can be used to minimize the wear problems produced in engine contact areas [27]. Dahotre and Nayak [28] investigated a coating based on graphite, Al₂O₃, and SiC. It was observed that this type of coating improves the lubrication properties and wear resistance of surfaces. In the case of nickel nanocomposite (NNC) coatings, improvements have been obtained in the tribological characteristics of cylinder holes [27]. Rejowski et al. [29] reported that diamond-like carbon (DLC) coatings reduce friction by 2.5%.

The pistons of ICE engines are exposed to high mechanical and thermal loads [30]. Therefore, wear is one of the main causes of engine piston failure [31]. Specifically, the cylinder liner supports high friction and wear forces as a consequence of lateral thrust forces [32]. Typically, pistons are made of aluminum-silicon alloys [33]. Improved engine energy efficiency requires better performing pistons [34]. However, the wear resistance of aluminum alloys is limited [35]. In order to improve the durability and reliability of the pistons in the engines, different coatings have been implemented based on carburized, spray-on, nitrided, microarc oxidation, and composite materials, among others [36,37,38,39]. Nguyen et al. [40] used a titanium nitride coating to increase resistance to corrosion and wear. Chen et al. [41] investigated the development of a self-lubricating carbide layer by electrical discharge. Wang et al. [42] studied iron-based coatings applied to Al-Si alloys. The results show a better wear resistance compared to Al-Si alloys.

Previous studies demonstrate the benefits of coating technology as an indirect means of minimizing the problems associated with the consumption of fossil resources and environmental impact. Additionally, the application of coatings implies an improvement in fuel economy. Due to this, it is necessary to develop tribological studies focused on quantifying the impact of this type of technology. However, the literature does not generally evaluate the effect of applying coatings on reducing emissions and saving fuel.

Due to the above, in the present study a numerical model is proposed to evaluate the effect of coating materials on reducing fuel and polluting emissions. For this, a model is developed in which the tribological behavior, heat flows, and exhaust of the combustion gases are considered. The study analyzes the properties of nickel nanocomposite (NNC) and diamond-like carbon (DLC) materials, which are compared with the steel surface of the cylinder liner. The study is based on the characteristics of a single-cylinder diesel engine. In this way, it seeks to contribute to the development of a methodology that allows estimating the effects of coating materials on the tribological characteristics, power loss, and thermal characteristics between the contact of the compression rings and the cylinder liner. Additionally, it seeks to evaluate the impact of this type of technology on fuel consumption and CO emission levels. This allows us to search for an improvement in the fuel economy of internal combustion engines.

2. Mathematical Model

To evaluate the effect of the properties of nickel nanocomposites (NNC) and diamond-like carbon (DLC), a mathematical model is developed. The model used is composed of kinematic analysis, lubricant properties, kinetics, leakage, and thermal losses applied to the compression ring. Each of these analyses is described in the following sections.

2.1. Kinematic Piston Model

To study the behavior of the compression ring, the primary movement that the piston experiences throughout the combustion cycle is described. This analysis is carried out considering the crankshaft—connecting rod—piston components as a sliding mechanism [43]. From the above, the displacement, velocity, and acceleration of the piston as functions of the crankshaft angle are determined. The description of the movement and the geometric parameters of the mechanism are shown in Figure 1.

Through an algebraic analysis, the velocity $\left(v_p\right)$ and acceleration $\left(a_p\right)$ of the piston are calculated by solving the system of equations shown below [44].

$$\left[\begin{array}{c}-l_{cr}\times {\omega }_{cr}\times \sin \left(\theta \right)\\ -l_{cr}\times {\omega }_{cr}\times \cos \left(\theta \right)\end{array}\right]=\left[\begin{array}{ll}{l}_{rod}\times \sin \left(\psi \right)& 1\\ l_{rod}\times \cos \left(\psi \right)& 0\end{array}\right]\left[\begin{array}{l}{\omega }_{rod/p}\\ v_p\end{array}\right],$$

(1)

$$\left[\begin{array}{c}-L_{cr}\times {\omega }_{cr}^2\times \cos \left(\theta \right)-L_{rod}\times {\omega }_{rod/p}^2\times \cos \left(\psi \right)\\ L_{cr}\times {\omega }_{cr}^2\times \sin \left(\theta \right)+L_{rod}\times {\omega }_{rod/p}^2\times \sin \left(\psi \right)\end{array}\right]=\left[\begin{array}{ll}{L}_{rod}\times \sin \left(\psi \right)& 1\\ L_{rod}\times \cos \left(\psi \right)& 0\end{array}\right]\left[\begin{array}{c}{\alpha }_{rod/p}\\ a_p\end{array}\right],$$

(2)

where $l_{cr}$ is the longitude of the crankshaft, $l_{rod}$ is the longitude of the connecting rod, $\theta$ is the angle of rotation of the crankshaft, ${\omega }_{cr}$ is the angular velocity of the crankshaft, ${\omega }_{rod/p}$ is the angular velocity relative to the motion between the connecting rod and the piston, and $\psi$ is the angle formed between the axis of movement of the connecting rod and the piston. This last parameter is calculated using Equation (3):

$$\psi ={\mathrm{sen}}^{-1}\left[\frac{d-\left(L_{cr}\times \cos \left(\theta \right)\right)}{L_{rod}}\right],$$

(3)

where $d$ is the horizontal distance between the axis of movement of the piston and the crankshaft. By solving Equations (1) and (2), the velocity and acceleration of the connecting rod are determined, allowing for the velocity and acceleration of the piston to be calculated as a function of the crankshaft angle.

2.2. Lubrication Properties

A two-phase condition is established for the mathematical model in the compression ring, which is distributed by 10% air and 90% lubricating oil. The initial thickness of the lubrication film is set at a value of 5 $\mathsf{\mu }\mathrm{m}$. This value is based on the empirical research developed by Lyubarskyy et al. [45]. The properties of the lubricating oil used are described in

Table 1. Lubrication oil properties.

Properties
Upper explosion limit	6.5 vol%
Lower explosion limit	0.6 vol%
Viscosity at 40 °C	91.76 mm2/s
Flashpoint	224 °C (DIN ISO 2592)
Density at 20 °C	0.864 g/cm3 (DIN 51757)
Pourpoint	−33 °C (ISO 3016)

.

Since the dynamic viscosity and density of the lubricating oil changes with pressure and temperature conditions, mathematical functions are defined to account for the variation in lubricant properties. In the case of density, the relationship established by Dowson and Higginson [46] is used, which is shown in Equation (4):

$$\rho =\left[{\rho }_o-{\rho }_o\times \beta \times \left(T-T_o\right)\right]+\frac{6\times {10}^{-10}·\left[{\rho }_o-{\rho }_o\times \beta \times \left(T-T_o\right)\right]\times \left(P-P_o\right)}{1+1.7\times {10}^{-9}\times \left(P-P_o\right)},$$

(4)

where $P$ and $\beta$ are the pressure in the combustion chamber and the coefficient of thermal expansion. The subscript $o$ indicates the environmental conditions.

For the change in the viscosity of the lubrication oil, the Houpert equation [47] is used, as described by Equation (5).

$$\eta ={\eta }_o{e}^{\ln \left(\frac{{\eta }_o}{{\eta }_{\infty }}\right)\times \left[{\left(1+\frac{P-P_o}{c_p}\right)}^Z{\left(\frac{T-138}{T_o-138}\right)}^{-S_o}-1\right]}.$$

(5)

where $c_p$ and ${\eta }_{\infty }$ are the model constants, defined as $1.98\times {10}^8 \mathrm{Pa}$ and $6.31\times {10}^{-5} \mathrm{Pa}·\mathrm{s}$, respectively. $S$ and $Z$ are the thermo-viscosity indices and lubricant piezo-viscosity, which are defined by Equations (6) and (7) [48].

$$S=\frac{{\beta }_o\left(T_o-138\right)}{\ln \left(\frac{{\eta }_o}{{\eta }_{\infty }}\right)},$$

(6)

$$Z=\frac{{\alpha }_o{c}_p}{\ln \left(\frac{{\eta }_o}{{\eta }_{\infty }}\right)},$$

(7)

where ${\beta }_o$ and ${\alpha }_o$ are the thermo-viscosity and piezo-viscosity at environmental conditions, respectively.

2.3. Kinetic Piston Model

The lubricating oil that coats the piston compression ring supports the ring loads. Therefore, the frictional forces are affected by the lubrication properties and the height of the lubrication film. To determine the forces acting on the compression ring, it is necessary to solve the equations that govern the fluid mechanics of the lubricant. Due to the above, the Reynolds equation is used, which establishes a relationship between the height of the film and the pressure of the lubricating oil. In the specific case of the present study, a two-dimensional approach is used, which implies that the lubrication parameters are found as a function of the piston position. From this condition, the Reynolds equation is defined as shown in Equation (8) [49].

$$\frac{\partial }{\partial y}\left(h^3\frac{\partial P}{\partial y}\right)=6\eta v_p\frac{\partial h}{\partial y}+12\eta \frac{dh}{dt},$$

(8)

where $h$ is the height of the lubrication film below the profile of the compression ring.

For the analysis of the radial and axial forces applied to the piston compression ring, the following considerations are established:

• Radial inertial forces are neglected due to the stiffness of the piston body, which is the consequence of the proper adjustment of the inner diameter of the ring [50].
• The axial damping force is determined by means of the Reynolds equation since this is the main equation used in the literature to describe the hydrodynamic behavior between the ring and the cylinder liner [45].
• The pressure and behavior of the combustion gases are considered in a steady state.
• Flow processes are considered isothermal. This consideration is appropriate because of the relatively low velocity of flow over the compression ring groove [51].

The aforementioned considerations are normally implemented in the literature for the analysis of piston ring dynamics [50].

In Equations (9) and (10), the dynamic forces applied to the compression ring in the axial and radial direction of the piston are described.

$$F_{hydro,axial}+F_{fric,axial}+F_{gas,axial}=m_r\times \frac{d^{2}y}{d{t}^2},$$

(9)

$$F_{hydro,radial}+F_{fric,radial}+F_{gas,radial}=m_r\times \frac{d^{2}x}{d{t}^2},$$

(10)

where $F_{hydro},F_{fric},$ and $F_{gas}$ are the damping force of the lubrication film, the friction force due to the interaction between the ring surface and the cylinder liner, and the force due to the combustion gases. $m_r$ is the mass of the compression ring.

The friction force ($F_{fric}$) is made up of two components, which correspond to the asperity force $\left(F_{asp}\right)$ caused by the lubricant’s shear effect and the hydrodynamic force $\left(F_{hydro}\right)$ caused by the lubricant’s viscosity, as shown in Equation (11).

$$F_{fric}=F_{asp}+F_{hydro}.$$

(11)

The asperity force $\left(F_{asp}\right)$ is defined by Equation (12) [52].

$$F_{asp}=c_f{{\displaystyle \int }}_{-b}^a{P}_{c}dx,$$

(12)

where $P_c$ and $c_f$ are the asperity contact pressure and pressure coefficient of boundary shear. $P_c$ is calculated by Equation (13).

$$P_c=\frac{16\sqrt{2}\pi }{15}\times \left({\sigma }_c^2+{\sigma }_r^2\right)\times r_c^2\times {\eta }^2\times E\times {\left({\sigma }_c^2+{\sigma }_r^2\right)}^{1/4}\times \frac{F_{5/2}}{{\left(r_c\right)}^{1/2}},$$

(13)

where ${\sigma }_r,{\sigma }_c,E,$ and $r_c$ are the surface roughness of the compression ring, the surface roughness of the cylinder liner, the composite Young’s modulus between the cylinder liner and the compression ring, and the radius of the curvature of asperities. $F_{5/2}$ is the commutation function calculated by means of Equation (14).

$$F_{5/2}=\left\{\begin{array}{c}4.4068\times {10}^{-5}{\left(4-H_s\right)}^{6.804}, H_s<4\\ 0, H_s\ge 4\end{array}\right.,$$

(14)

where $H_s$ is the film thickness ratio. The composite Young’s modulus between the cylinder liner and compression ring $\left(E\right)$ is calculated by means of Equation (15) [53].

$$\frac{2}{E}=\frac{1-{\vartheta }_c^2}{E_c}+\frac{1-{\vartheta }_r^2}{E_r},$$

(15)

where $E$ and $\vartheta$ are the elastic modulus and the Poisson ratio. The subscripts $c$ and $r$ indicate the cylinder liner and compression ring, respectively.

The hydrodynamic force shown in Equation (16) is determined, as shown in the following equation:

$$F_{hydro}=-{{\displaystyle \int }}_{-b}^a\left(v_p\frac{\eta }{h}+\frac{h}{2}\frac{\partial P}{\partial x}\right)dx.$$

(16)

The power loss due to friction processes is calculated using Equation (17) [54].

$$P_{loss}=\int \frac{h^3}{12\eta }{\left(\frac{\partial P}{\partial x}\right)}^{2}dA+\int \frac{\eta ·v_p^2}{h}dA.$$

(17)

2.4. Blow-By Losses Model

Equation (18) and (19) is used to determine the flow of flue gas leaking from the combustion chamber through the piston [55].

$${\dot{m}}_b={\left(\frac{P_{cc}}{P_{ups}}\right)}^{1/\gamma }\times \frac{P_{cc}\times c_d\times A_v}{{\left(R\times T_{in}\right)}^{1/2}}\times {\left(\frac{2\gamma }{\gamma -1}\times \left[1-{\left(\frac{P_{cc}}{P_{ups}}\right)}^{\left(\gamma -1\right)/\gamma }\right]\right)}^{1/2}, \frac{P_{cc}}{P_{ups}}>{\left(\frac{2}{\gamma +1}\right)}^{\gamma /\left(\gamma -1\right)},$$

(18)

$${\dot{m}}_b={\gamma }^{1/2}\times \frac{P_{cc}\times c_d\times A_v}{{\left(R\times T_{in}\right)}^{1/2}}\times {\left(\frac{2}{\gamma +1}\right)}^{(\gamma +1)/\left(2\gamma -2\right)}, \frac{P_{cc}}{P_{ups}}\le {\left(\frac{2}{\gamma +1}\right)}^{\gamma /\left(\gamma -1\right)},$$

(19)

where $T_{in}$ is the temperature of the fuel at the inlet valve, $P_{cc}$ is the combustion chamber pressure, $P_{ups}$ is the upstream pressure wave, $R$ is the gas constant, and $c_d$ is the coefficient of discharge $\left(c_d=0.55\right)$. $A_v$ and $\gamma$ are the engine valve area and the specific heat ratio, which are calculated using Equations (20) and (21) [56].

$$A_v=\frac{\pi ·D_v^2}{4},$$

(20)

$$\gamma \left(T\right)=1.46-1.63\times {10}^{-4}T+4.14\times {10}^{-8}{T}^2,$$

(21)

where $D_v$ is the diameter of the valve $\left(D_v=26 \mathrm{mm}\right)$.

2.5. Compression Ring Thermal Model

Figure 2 shows the model for the thermal analysis of the compression ring of the piston in order to observe the influence of the coating on heat transfer. For the analysis, it is considered that all the heat generated is a consequence of power losses due to friction processes $({\dot{Q}}_t=P_{loss})$.

The total heat generated is dissipated through the coated surface of the compression ring $\left({\dot{Q}}_r\right)$, by convection transfer to the lubricating oil $\left({\dot{Q}}_{lub}\right),$ and through the coated surface of the cylinder liner $\left({\dot{Q}}_c\right)$. The distribution of the total heat generated is shown in Equation (22).

$${\dot{Q}}_t=P_{loss}={\dot{Q}}_r+{\dot{Q}}_{lub}+{\dot{Q}}_c.$$

(22)

The heat flow is transmitted through different thermal resistances, which correspond to conduction through lubrication oil $\left(R_{lub}\right)$, convection through contact surfaces $\left(R_s\right),$ and conduction through coated surfaces $\left(R_{cs}\right)$. Each of these resistances are calculated using the following equations.

$$R_{lub}=\frac{h}{2k_{lub}·A},$$

(23)

$$R_s=\frac{1}{h_c·A},$$

(24)

$$R_{cs,i}=\frac{S_{f,i}}{k_i·A} , i=c,r,$$

(25)

where $h$ is the thickness of the lubrication film, $h_c$ is the convection coefficient, $k_{lub}$ is the thermal conductivity of the lubricant, and $S_{f,i}$ is the equivalent length. The subscripts $c$ and $r$ refer to the cylinder bore coating and compression ring.

2.6. Fuel Consumption and CO Emission Model

The mass flow of fuel is determined by Equation (26).

$${\dot{m}}_f=\frac{\dot{m}}{{\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$F$}\right.\right)}_{rr}+1},$$

(26)

where ${\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$F$}\right.\right)}_{rr}$ is the real air/fuel ratio, which is obtained from data obtained through experimental tests. $\dot{m}$ is the mass flow from the fuel–air mixture. The energy of the fuel flow is calculated by means of Equation (27).

$${\dot{E}}_f={\dot{m}}_f·Q_{LHV},$$

(27)

where $Q_{LHV}$ is the lower calorific value of the fuel. The variation in the fuel flow is calculated using Equation (28).

$$\mathrm{∆}{\dot{m}}_f=\frac{\mathrm{∆}{\dot{E}}_{loss}}{Q_{LHV}},$$

(28)

where $\mathrm{∆}{\dot{E}}_{loss}$ is the variation in the loss energy. This term will be influenced by the characteristics of each coating.

The index of CO emissions is calculated by means of Equation (29).

$$CO=\left\{\begin{array}{l}{e}^{\left(-8.395+5.518{\varphi }^2\right)}, \varphi <1\\ -2.725+2.78\varphi , \varphi \ge 1\end{array}\right\},$$

(29)

where $\varphi$ is the equivalence relation, which is shown in Equation (30).

$$\varphi =\frac{{\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$F$}\right.\right)}_{ss} }{{\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$F$}\right.\right)}_{rr} },$$

(30)

where (A/F) is the stoichiometric air/fuel ratio, defined by Equation (31).

$${\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$F$}\right.\right)}_{ss}=\frac{35.56·\left(4+x\right)}{12.011+1.008x}, x=\frac{b}{a},C_a{H}_b.$$

(31)

3. Numerical Methodology

3.1. Experimental Test Bench

Figure 3 shows the experimental test bench used as a reference for the numerical model.

The test bench consists of a single-cylinder, four-stroke, natural injection diesel engine.

Table 2. Technical characteristics of the test engine.

Model	SK-MDF300
Manufacturer	SOKAN
Cycle	4 Strokes
Bore x stroke	78 mm
Stroke	62.57 mm
Engine type	1 cylinder
Maximum power	3.43 kW
Compression ratio	20:1
Injection system	Direct injection
Intake system	Naturally Aspirated
Displaced volume	299 CC
Crankshaft radius	48 mm
Piston radius	39 mm
Length of connecting rod	106 mm

shows the technical characteristics and geometric properties of the engine.

An alternator coupled to the shaft is used to control the load conditions of the diesel engine. The intake air flow measurement is conducted by a mass flow sensor (BOSCH OE-22680 7J600). The pressure inside the cylinder is measured by a piezoelectric pressure transducer (KISTLER 7063-A) and a load amplifier (KISTLER 5015). The fuel flow is calculated using a gravimetric meter (OHAUS—PA313). To ensure synchronization between the combustion pressure signal and the crankshaft rotation angle, a TDC sensor (Top Dead Center) and angle encoder (BECK ARNLEY 180-0420) are used. The information from each of these sensors is used as input data for the model. Figure 4 describes the behavior of the combustion pressure and the velocity of the piston for a combustion cycle.

3.2. Uncertainty Analysis

In the development of experimental measurements, there are factors that induce errors in the measurement process, such as instrument calibration, environmental conditions, and human error, among others. Due to this situation, it is necessary to guarantee the reliability of the data obtained from the measurement. For this, an uncertainty analysis is carried out, in which the systematic error $\left(U_{sys,\left(x_i\right)}\right)$ due to the nature of the instrument and the random error $\left(U_{r,\left(x_i\right)}\right)$ due to uncontrollable external factors are considered. The calculation of the random error is performed by statistical analysis, as shown in Equation (32) [57].

$$U_{r,\left(x_i\right)}=\frac{1}{n^{1/2}}\times {\left(\frac{1}{n-1}\times {{\displaystyle \sum }}_{i=1}^n{\left(q_i-\overline{q}\right)}^2\right)}^{1/2}.$$

(32)

The total uncertainty $\left(U_t\right)$ is calculated from the square root of the mean due to random error and systematic error, as shown in Equation (33) [57].

$$U_t={\left({U_{r,\left(x_i\right)}}^2+{U_{sys,\left(x_i\right)}}^2\right)}^{1/2},$$

(33)

where $x_i$ is the best estimate of a set of measurements ($q_1, q_2, q_3, \dots , q_n$) and $n$ is the number of measurements made for each variable. For the research, a total of three repetitions $\left(n=3\right)$ were carried out, since an increase in the measurements can increase the error in the measurement due to external factors such as the change in environmental conditions. The technical characteristics and the uncertainty of the measuring instruments are shown in

Table 3. Technical characteristics and uncertainty of measuring instruments.

Instrument	Parameter	Manufacturer	Range	$\left({\mathit{U}}_{\mathit{r},\left({\mathit{x}}_{\mathit{i}}\right)}\right)$	${\mathit{U}}_{\mathit{s}\mathit{y}\mathit{s},\left({\mathit{x}}_{\mathit{i}}\right)}$	${\mathit{U}}_{\mathit{t}}$
Air mass sensor	Airflow	BOSCH OE-22680 7J600	0–125 g/s	±1.10	±1.02	±1.5
Piezoelectric transducer	Cylinder pressure	KISTLER type 7063-A	0–250 bar	±0.38	±0.32	±0.5
Gravimetric meter	Fuel measuring	OHAUS—PA313	0–310 g	±1.06	±0.91	±1.4
Crankshaft Position Sensors	Angle	Beck Arnley 180-0420	5–9999 RPM	±0.73	±0.68	±1.0
Temperature sensor	Temperature	Type K	−200–1370 °C	±0.52	±0.46	±0.7

.

3.3. Material Properties

For the study, the influence of the diamond-like carbon (DLC) and nickel nanocomposite (NNC) coatings on the cylinder bore is evaluated. The properties of these coatings are obtained from the information provided by the manufacturer [58]. The cylinder bore material is steel. The thermo-mechanical properties of the above materials are shown in

Table 4. Thermo-mechanical properties of coatings [58,59,60].

Parameter	Unit	Cylinder Bore Surface
		Steel 4340	NNC	DLC
Density	kg/m3	7850	5175	3510
Thermal conductivity	W/mK	34.3	42.1	4.5
Poisson’s ratio	-	0.31	0.31	0.22
Specific heat capacity	J/kgK	520	566	1300
Young’s modulus of elasticity	GPa	200	165	210
Pressure coefficient of boundary shear	-	0.170	0.149	0.219

.

In the case of the compression ring, it is coated with titanium nitride (TiN). The thermo-mechanical properties of the compression ring material are shown in

Table 5. Thermo-mechanical properties of the compression ring coating [58].

Parameter	Unit	TiN
Density	kg/m3	5220
Thermal conductivity	W/mK	19.2
Poisson’s ratio	-	0.25
Specific heat capacity	J/kgK	484.9
Young’s modulus of elasticity	GPa	251

.

Each of the thermo-mechanical properties shown in Table 4 and Table 5 directly affects the kinetics and thermal conditions of the piston. The above is due to the fact that these properties directly influence the asperity force and the heat flows within the combustion chamber, as shown in Equations (12), (13), (15), and (21).

3.4. Numerical Procedure

To solve the system of equations described in Section 2, the solver ode45 of the MATLAB software is used. In Figure 5, the diagram of the process used to analyze the influence of the coating on the cylinder bore is described.

The geometric characteristics of the test engine and the data recorded through the measurement instruments are used as input data in the numerical model. Based on this information, calculations are made to define the dynamic conditions of the compression ring, physical properties, heat flows, and leakage gas losses, which are shown in Section 2. Before analyzing the results, a validation of the estimates is made by the model through a comparison between the friction force of the piston obtained by the model and experimentally. This analysis is detailed in Section 4.1. Finally, the numerical model is used to study the influence of the coating on the cylinder bore.

For the validation of the numerical model, a comparison is made between the friction force supported by the piston for different angular positions of the crankshaft, obtained through the model and the experimental tests.

The measurement of the friction force is carried out by means of a strain gauge sensor, which allows the measurement of deformation and tension in the cylinder liner. For the installation of the sensor, a portion of the cooling fins of the engine is removed and fixed by means of a high-temperature adhesive. The sensor sends a pulse signal that indicates the deformation produced in the cylinder liner due to the passage of the piston. The sensor characteristics are shown in

Table 6. Characteristics of the strain gauge sensor.

Parameter	Value
Overall width	4.55 mm
Gauge resistance	120 $\mathrm{\Omega }$
Maximum operating temperature	1150 °C
Grid width	4.55 mm
Overall length	6.30 mm
Gage length	2.54 mm

. The measurement process is shown in Figure 6.

The friction force is calculated using Equations (34) and (35) [61].

$$\frac{V_1}{V_2}=-\frac{\epsilon ·G_f}{2}\left[\frac{1}{2+\epsilon ·G_f}\right],$$

(34)

$$F_{fric}=\epsilon \times A_s\times E_c,$$

(35)

where $E_c,\epsilon ,A_s,G_f,$ and $V$ are Young’s modulus of the cylinder liner, the longitudinal strain, the area of the strain gauge sensor, the sensor calibration factor $\left(G_f=2\right)$, and the voltage.

Since the deformation measured by the sensor includes the thermal deformation caused by the elevated temperatures of the chamber, a filtering process is carried out. For this, a coefficient of thermal expansion of 24 µstrain/°C is considered [62]. In this way, it is ensured that the measured deformation is a consequence of the friction process.

4. Results and Discussion

4.1. Experimental Validation

The results of the comparison between the experimental tests and the model estimates are shown in Figure 7.

The results show that the numerical model allows us to describe the behavior inside the combustion chamber. The relative error between the simulation and the mean value of the experimental data is 8%. However, when considering the minimum and maximum values of the measurement range for each point, maximum errors of 24% and 30% were obtained. The methodology used and the errors obtained are considered acceptable to analyze the behavior of the piston compression ring due to the difficulty of isolating the ring under engine operating conditions [63].

4.2. Friction Force Analysis

Figure 8 shows the behavior of the friction force during the combustion cycle for an uncoated surface, which is used as a basis to determine the influence of coating materials.

The results of Figure 8 show that the compression ring is mainly subjected to a hydrodynamic regime condition throughout the combustion cycle. The above indicates that viscous shear is the main source of friction during the stages of the combustion process. The force due to the pressure of the gases mainly affects the compression and combustion stage, causing the presence of a boundary friction force. This is attributed to a reduction in the thickness of the lubrication film, which decreases below the average height of the asperity of the contact surfaces.

In Figure 9, the influence of the coating material on the boundary friction force is shown. The DLC coating was observed to produce a considerable rise in friction force during the mixed lubrication regime condition. For the simulated conditions, an increase of 13.10 N was obtained compared to the reference condition (steel). This is mainly attributed to the smooth topography of the material, which produces high adherence. An opposite behavior was observed in the NNC coating, in which a decrease of 9.57 N was obtained in the boundary friction force.

Figure 10 shows the total friction force in the compression ring with DLC and NNC and without steel coatings in the cylinder bore.

The results show that the maximum magnitudes of the total friction force are 18.84, 29.35, and 37.19 N for the NNC, steel, and DLC materials, respectively. This maximum force in all conditions is located during the combustion stage, which is a consequence of the pressure generated by the combustion gases on the inner surface of the compression ring.

The change in material in the cylinder bore has a significant effect on the friction process. It was observed that when using the DLC carbon coating, there was a 27% increase in the maximum friction force compared to the cylinder bore without coating (Steel). In the case of the NNC coating, a reduction in the maximum friction force of 36% was observed compared to the cylinder bore without coating. The increase in friction force in the DLC material is attributed to its lower thermal conductivity and the higher coefficient of shear compared to the NNC, as shown in Table 4. The above causes a high adhesion surface when using DLC.

4.3. Temperature and Heat Flow Analysis

Figure 11 shows the temperature behavior of the compression ring for the different surfaces of the cylinder bore.

In Figure 11, it was observed that the change in the material in the cylinder bore caused a change in the temperature of the compression ring, which is a consequence of the different heat transfer coefficients of each material. The results show a reduction of 0.23% and an increase of 0.34% in the temperature of the compression ring when using coatings of NNC and DLC, respectively. This temperature reduction is a consequence of the thermal and tribological properties of the NNC coating.

Figure 12 shows the change in lubricant temperature for the different coatings. The increase in lubricant temperature is mainly due to the conduction heat transfer mechanism. The results show that the coating of NNC and DLC does not cause a considerable change in the temperature of the lubricant compared to steel.

Figure 13 describes the behavior of the heat flow when using the different materials in the cylinder bore.

In the case of the DLC coating, an 8.65% reduction in heat flow transferred through the cylinder liner was observed compared to steel. This behavior is attributed to the lower thermal conductivity of the DLC material, which allows the better insulation of the combustion chamber. The above behavior occurs during the combustion stage. However, it changes during the intake, compression, and exhaust stages because, in these conditions, the formation of heat prevails due to the thickness of the material, which is higher in the DLC coating. For the NNC coating, an inverse behavior to the DLC coating was observed, in which an increase of 4.61% and 14.52% was obtained in the heat flow transferred through the cylinder liner compared to steel and the DLC coating. This implies a greater loss of heat during the compression stage.

4.4. Power Loss Analysis

Figure 14 shows the behavior of energy loss during the combustion cycle for the different coating materials.

The results show that the highest energy losses occur in the DLC coating, compared to the steel and the NNC coating, respectively. This greater energy loss occurs mainly during the first half of the combustion stage due to the mixed regime condition and the high shear rate of the DLC material. The reduction in energy loss in the NNC material implies better tribological performance.

To analyze the effect of the cylinder bore coating on the mechanical power loss of the engine, the energy loss is evaluated for load conditions of 25%, 50%, 75%, and 100% at a constant rotation speed of 3600 rpm. The results of this analysis are shown in Figure 15.

The results obtained show that the maximum power loss for the NNC and DLC coatings are 330.70 W and 372.26 W, respectively. In the case of the cylinder bore without a coating (steel material), a maximum power loss of 349.96 W was obtained. In general, the NNC coating allows a 4.60% reduction in power loss. This behavior is attributed to the reduction in the total friction force, as shown in Figure 8.

4.5. Fuel Economy

The reduction in engine power loss implies a decrease in fuel consumption and CO emissions. The influence of the NNC and DLC coating on these parameters is shown in Figure 16. For the calculation, the estimate of the global diesel vehicle fleet for the year 2025 is considered, which corresponds to one hundred and eighty million engines [64].

The estimation is performed considering that the technical characteristics of these engines are similar to those of the test engine used in the present study. The calculation of fuel consumption and CO emissions is carried out using the air/fuel ratio and the equivalence ratio, as indicated in Equations (25) and (28). Additionally, through simulation an operating condition is established in the engine for 1800s in order to represent the characteristics of the WLTC test.

Figure 16 depicts the fuel savings and decreased CO emissions obtained by implementing an NNC coating on the cylinder bore. The results show average reductions of 4810 and 26.64 kg in the parameters of fuel consumption and CO emissions, respectively. However, these estimates are limited since only a single cylinder is being considered in the simulation conditions. Therefore, the potential for reducing fuel consumption and CO emissions would be greater when considering the savings in each cylinder.

Figure 17 shows the increase in fuel and CO emissions caused by the DLC coating due to the increase in power loss. Overconsumption of fuel and CO emissions of 8130 and 31.92 kg, respectively, were observed.

5. Summary

In the present study, a numerical model is carried out to evaluate the influence of the material used as a coating on a cylinder bore. The implemented model considers the tribological behavior, heat flows, and leakage of the combustion gases in the chamber. For the analysis, DLC and NNC materials are considered as alternatives for coating the cylinder bore.

The study shows that variations in coating properties cause a significant change in the friction force to which the compression ring is subjected. In general, the NNC coating produces a 32% reduction in the total frictional force of the compression ring throughout the combustion cycle. An opposite case occurs with the DLC coating, in which there is a 33% increase in the friction force. This behavior is a direct consequence of the higher shear coefficient of the DLC material.

The characteristics of the DLC material allow the greater thermal insulation of the combustion chamber, which reduces the associated losses due to heat transfer during the combustion stage. However, this insulation causes an increase in the temperature of the lubricant. For the tested conditions, maximum temperatures of 214, 202, and 194 °C were obtained in the lubrication oil for the DLC, steel (uncoated), and NNC materials. Increasing the temperature when using the DLC coating can cause a reduction in the tribological performance of the lubricant. In general, NNC and DLC coatings cause a reduction and an increase of 3.68% and 5.71% in the lubrication oil temperature.

The research shows that the application of an NNC coating on the cylinder bore allows a reduction of 4.60% of the power lost by the friction process between the compression ring and the cylinder liner compared to the case without coating. The properties of the DLC coating produce an increase in a power loss of 8.38%.

The reduction in power loss implies a decrease in fuel consumption and polluting emissions, such as carbon monoxide. The estimates made show a maximum reduction of 5280 kg of fuel and 39.30 kg of CO emissions when considering the diesel engine fleet for the year 2025. In the case of the DLC coating, the greater power loss causes a maximum increase of 8950 kg of fuel and 39.77 kg of CO emissions.

The proposed numerical model allows future analyses to be carried out for other types of materials used as coatings. Additionally, the model can be expanded and adapted to consider other systems that involve friction processes, such as valve and bearing systems in ICEs.