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Numerical simulation of a diesel engine performance powered by soybean biodiesel and diesel fuels



The present study presents a 3-D numerical simulation of a direct injection diesel engine powered by base diesel oil and soybean biodiesel fuel at different load conditions. The modeling was performed using commercial computational fluid dynamics (CFD) software linked to a chemical solver. A chemical kinetic reaction mechanism was developed to simulate the combustion and fuel spray processes. Base diesel oil results were verified using a single-cylinder, 4-stroke diesel engine.


The study showed that the usage of the soybean biodiesel fuel caused a reduction in carbon monoxide (CO) and hydrocarbon (HC) emissions by about 42.38% and 41.35%, compared with base diesel and an increase in nitrogen oxides (NOx) and carbon dioxide (CO2) emissions of about 21.8% and 11.2%, respectively. Exhaust gas temperature (EGT) is reduced by an average value of 9.4%, the brake-specific fuel consumption (BSFC) is increased by an average value of 11.8% and the brake thermal efficiency (BTE) is dropped by an average value of 11.3% for soybean biodiesel fuel.


The CFD model showed the effect of the unsaturated fatty acid methyl esters present in soybean biodiesel on the spatial distributed values of NOx, oxygen and temperature during the combustion in engine cylinder. It was observed that the combustion of soybean biodiesel began about 3.89 CAD earlier than base diesel, and the in-cylinder peak pressure was dropped by 8.25%. Soybean biodiesel fuel was optimized by performing four starts of injection (SOI) at timings of − 18, − 16, − 15 and − 13,5 bTDC, and it was found that the combustion characteristics of soybean biodiesel are optimum at SOI = − 15 bTDC. These results indicate that the biodiesel fuel can be used as an alternative and environmentally friendly fuel in the engine without any modifications.

1 Background

The increasing demand for fossil fuels and the concerns about their harmful emissions have forced the scientific society to search for alternative fuels for internal combustion engines. Therefore, researchers have been developing new alternatives from different sources, biodiesel fuel is one of the best alternative fuels for diesel engines because of its high cetane number, low carbon fuel, non-toxic, biodegradable, lubricity, oxygenation nature, no aromatics and almost no sulfur content, so it is considered a renewable energy source and environmentally friendly [1,2,3,4].

Vegetable oils, animal fats and reused oils are the most common sources of biodiesel. Biodiesel fuel is produced by a common chemical method, namely transesterification; in this method, a chemical reaction occurs between the triglycerides (vegetable oil) and alcohol in the presence of a catalyst. If methanol alcohol is used, the reaction products will be fatty acid methyl esters (FAMEs; biodiesel) and glycerol. FAMEs may be saturated and unsaturated; their proportions in biodiesel fuel directly affect the physical and chemical properties [5,6,7].

Soybean biodiesel fuel is considered in the present study. However, the disadvantages of soybean biodiesel relative to base diesel oil, such as higher viscosity, higher density and lower volatility. So, the usage of biodiesel for a long term may cause engine durability problems such as poor fuel atomization, injector coking, piston ring sticking, a clogged fuel filter and higher pressure inside fuel lines [8]. Therefore, different experimental methods are required to make soybean biodiesel more suitable for diesel engines such as preheating at a wide range of temperatures, blending with base diesel, increasing injection pressure and adding additives [9]. CFD codes have recently gained popularity in the industry as a tool for facilitating and speeding up engine evaluation under various conditions. The purpose is to minimize the cost and prototyping time and have the ability to make several studies by changing individual parameters such as injection pressure, inflow temperature of the fuel and air, injection timing, fuel blends and the engine loads [10, 11].

A compression ignition (CI) engine is considered one of the most complex problems in fluid dynamics to model because the flow inside the cylinder is unsteady, compressible, turbulent and cyclic. All physical processes that take place inside the cylinder from the start of air entry to the end of combustion required a mathematical model to describe them. Turbulence, fuel spray, atomization, breakup, collision, coalescence, droplets vaporization, kinetic reaction mechanism (fuel chemistry), self-ignition, premixed and diffusion combustion, heat losses and emission development (NOx and soot)—all of these processes require subroutines that work together in order to simulate the engine [12, 13].

Many studies conducted on biodiesel fuel and its effect on engine performance, Zhang et al. [14] studied the performance and emission of a marine diesel engine fueled with natural gas ignited by biodiesel blends at different conditions of engine load and concluded that at all engine conditions, the NOx, CO and soot emissions decreased with increasing the natural gas fraction. According to EL-Seesy et al. [15], the addition of butanol to the diesel/jojoba oil blend lowers the mixture's viscosity compared to diesel/jojoba oil, increases the in-cylinder peak pressure and heat release rate (HRR), and also results in a reduction in NOx, CO and HC emissions compared to diesel fuel. Zhang et al. [16] conducted a study on the effect of assisted hydrogen on a diesel engine performance fueled with biodiesel fuel and reported that the in-cylinder pressure and temperature are increased by about 7.42% and 7.14%, respectively. Meanwhile CO and HC decreased but NOx emissions increased. Coughlin et al. [17] studied the combustion characteristics of soybean oil–butanol blends and found that the addition of alcohol could improve the soybean combustion characteristics. Ng HK et al. [18] studied the effect of palm, coconut and soybean biodiesel fuels on a diesel engine performance numerically using a CFD code, which was coupled to a chemical kinetic reaction mechanism including 80 species and 303 reactions. According this study, the biodiesel properties influence the formation of emissions; so, the soybean biodiesel fuel provided a greater thermal NOx than others because its higher unsaturation level. Al-Dawody et al. [19] carried out a 2-D numerical and experimental study on a DI diesel engine fueled with different blends of soybean biodiesel with diesel fuels. The effects of blending on the in-cylinder pressure, heat release rate (HRR), unburned hydrocarbon (UHC), carbon monoxide (CO), nitrogen oxides (NOx) and smoke opacity were calculated. He found that the use ofiesel results in lower smoke opacity up to 48.23% with higher brake-specific fuel consumption (BSFC) by 14.65%, compared to diesel fuel. For the blends of B20 (20% soybean biodiesel + 80% diesel fuel) and B100 (100% soybean biodiesel), the CO emissions reduced by 11.36% and 41.7% respectively, compared to diesel fuel. At blends of B20, B40 and B100, the unburnt hydrocarbon emissions were found to be 15%, 27% and 38.4% lower than that of diesel fuel, respectively. Also, he reported that at all blends the NOx emissions were observed to be higher than that of diesel fuel. The in-cylinder pressure for soybean biodiesel is lower than that of diesel fuel by about 2.98% due to the reduction in the heat supply for the blended fuel and the maximum pressure obtained for biodiesel is near to top dead center (TDC) than diesel fuel.

In contrast to conventional combustion, Ganesan et al. [20] investigated a light-duty diesel engine using the reactivity-controlled compression ignition technique by introducing cottonseed oil biodiesel as a high-reactivity fuel directly into the combustion chamber and n-pentanol as a low-reactivity fuel. In comparison with the neat cottonseed oil biodiesel, this method led to lower concentrations of NOx and smoke emissions by roughly 44.2% and 35.0%, as well as a higher thermal efficiency. Nayak et al. [21] investigated the performance, combustion and emission characteristics of a direct injection diesel engine running on biodiesel fuel produced from waste palm cooking oil and fish oil and reported that the biodiesel fuel resulted in a lower thermal efficiency and higher specific fuel consumption compared to diesel fuel. An experimental study carried out by Singh et al. [22] on a diesel engine running on Jatropha biodiesel at varied compression ratios. Jatropha biodiesel diesel blend (B30) and neat diesel fuel were used to power the diesel engine. According to the experimental study, using the B30 blend reduces HC and CO emissions from diesel by about 16.7% and 24%, respectively. However, using the B30 blend resulted in a notable increase in NOx and CO2 emissions. Gritsenko et al. [23] investigated how disconnecting some of the engine cylinders in low-load and idling modes increased fuel efficiency in cars and tractors. Experiment results indicate that when some engine cylinders are disconnected, the performance parameters of the car (tractor) are interdependent. It has also been established that the maximum reduction in hourly fuel consumption occurs when the engine is idling, and that it decreases as the load increases.

Due to its higher viscosity and lower calorific value, biodiesel causes CI engines to operate poorly and consume a lot of fuel. This issue can be solved by raising the injection temperature of biodiesel to a specific temperature. The results of an experimental study conducted by Kodate et al. [24] on a DI diesel engine running on preheated biodiesel fuel (at 95 °C) showed that the viscosity of the fuel decreases at higher temperatures, improving combustion characteristics and fuel atomization as well as fuel vaporization in a diesel engine, resulting in higher engine performance and lower CO and HC emissions with a slight increase in NOx and CO2 emissions when compared to unheated biodiesel fuel.

Biswas et al. [25] compared the performance, emissions and engine noise of a quadruple (early–pilot–main–after) injection strategy to three different triple [early–pilot–main and pilot–main–after] injection strategies in a heavy-duty BS-IV diesel engine with a 45% EGR fraction. According to this study, the quadruple injection strategy outperforms the promising triple injection strategy, which provides optimal results in terms of both performance and emissions. Using Fisher's primary breakup model, Beutler et al. [26] carried out numerical modeling on a spray of diesel and polyoxymethylene dimethyl ether in a high-pressure chamber at several variable parameters (ambient pressure, temperature and injection pressure) and compared it with the results of the experiments. Baek et al. [27] analyzed the spray behavior and the performance of a diesel engine powered by biodiesel and jet propellant-5 (JP-5) at multiple split injection strategies and reported that for all injection timings, biodiesel showed disadvantages as compared to JP-5 in terms of combustion and emission characteristics. Kuti et al. [28] used the Reynolds averaged Navier–Stokes model to simulate the spray combustion characteristics of waste bio-oils and traditional diesel fuel. They used a combination of n-heptane and n-tetradecane as surrogates for diesel fuel and a combination of methyl decanoate, methyl-9-decenoate and n-heptane as surrogates for the waste bio-oils. The results of the spray liquid length, ignition delay period, soot formation and flame lift-off length were compared to the experimental results, and good validity was found.

Although biodiesel derived from rice bran oil is seen to be a viable green fuel substitute for traditional diesel fuel, when utilized as fuel in diesel engines. Particularly in cold areas, the high free fatty acid concentration of rice bran biodiesel fuel is viewed as a significant disadvantage. More specifically, this undesirable characteristic causes noticeably higher viscosity, surface tension and higher density, which may then cause problems with fuel pumping, poor fuel spray and atomization, the formation of heterogeneous air–fuel mixtures and ultimately incomplete combustion [29]. The main factors causing wear, corrosion and abrasion in engines may be deposits created during the burning of biodiesel. In comparison with neat diesel, the use of biodiesel and plant oil-based fuels typically results in cylinder head carbon deposits, deposits on the injector tip and on the piston crown, degradation of lubricating oil and the formation of more deposits. This is especially true for long-term applications [30].

Fuel stability is a main procedural problem regarded in biodiesel manufacturing and is related to several issues like phase separation, polymerization, fuel degradation and oxidation. There are three types of biodiesel stability: oxidation, storage and thermal stability. When biodiesel is kept in storage for a long time, oxidation occurs. During the storage time, the free radicals attack the unsaturated lipids in biodiesel and produce lipid peroxide products. The oxidation of biodiesel fuel is brought on by the double and triple bonds that are present in the chains of fatty acid methyl esters. Some of the extrinsic elements that impact the oxidative stability of biodiesel include the presence of air, light, antioxidants, metal traces and storage container material [31].

Compared to the previous studies, the diesel engine simulation process saves the time and effort of practical experiments. It also enables us to conduct several parametric studies for engine development. From this perspective, this study was chosen to evaluate the performance of the diesel engine, where the numerical results of conventional diesel fuel were compared with the experimental results, and a good convergence was found. A suitable kinetic reaction mechanism was chosen to simulate soybean-derived biodiesel, and the combustion and emission results were compared with previous works, and good validity was attained. In order to accurately simulate the in-cylinder turbulence, fuel atomization, droplet vaporization, kinetic reaction mechanism, premixed and diffusion combustion, heat losses and exhaust emission generation, it is necessary for many subroutines to work together. The objective of the current work is to create a 3-D computational fluid dynamics (CFD) model to simulate the combustion and emissions of a direct injection (DI) diesel engine running on diesel and soybean biodiesel fuels at different load conditions.

2 Fuel properties

Table 1 shows the faty acid methyl ester (FAME) composition of soybean biodiesel. The properties of the tested fuels are given in Tables 2 and 3, according to the European Union EN 590 and EN 14,214 standards. Due to the difference in physical and chemical properties of biodiesel fuel, the combustion and emission characteristics will be changed. The oxygen concentration in soybean biodiesel fuel is about 10.7 wt% [32]. This percentage of oxygen will directly influence on combustion and emission development, especially NOx emissions. Also, properties such as cetane number will influence on the ignition delay period, as will viscosity, which is considered one of the most important parameters affecting the fuel spray, atomization and vaporization. Higher viscosity results in lower injection velocity, poor atomization, an increase in friction between the fuel boundary layer and fuel line surfaces, higher deposits and an increase in the power required for the fuel pump [33]. Soybean biodiesel fuel has a higher flash point than diesel fuel, which makes soybean biodiesel fuel safer during transporting and storing. The lower heating value of soybean biodiesel fuel is less than that of diesel fuel, thus HRR and BSFC may be decreased. Soybean biodiesel fuel has a chemical property known as an "acid number," which does not exist in diesel fuel properties. Acid number refers to the amount of free fatty acids (FFA) content in a fuel. FFA may be saturated or non-saturated, but its proportion will have a significant impact on the engine performance. Compared to diesel fuel, soybean biodiesel fuel is almost free from sulfur content, which is the main motives for using biodiesel fuel as an alternative fuel [34].

Table 1 Fatty acid methyl ester composition of soybean biodiesel
Table 2 Properties of base diesel fuel
Table 3 Properties of soybean biodiesel fuel

3 Experimental methodology

The present work has been conducted on a Petter PH1W single-cylinder, 4-stroke, naturally aspirated and water-cooled diesel engine with a hemispherical bowl in combustion chamber. The schematic diagram of the engine test bench is shown in Fig. 1. The engine specifications are tabulated in Table 4. A DC universal dynamometer is coupled to the diesel engine, which drives the engine at the start of operation and further absorbs the output power from the engine. A damping chamber with an orifice system is used to measure the inlet air mass flow rate supplied to the diesel engine and eliminate the pulsation effect at the engine suction. A piezoelectric sensor is used to measure the dynamic pressure inside the engine combustion chamber. A crankshaft position sensor is used to indicate the TDC position and the further intervals of crankshaft position. A 2-channel storage oscilloscope is used to present and record the in-cylinder pressure versus the crank angles. The exhaust gas temperature (EGT) is measured using a type K thermocouple with a sensitivity of 41 µV/oC and a standards error of ± 2.2 °C. The concentrations of CO, CO2, NO and HC emissions are measured using an ADC multi-gas analyzer. The tests have been conducted at a constant speed of 1500 rpm for a wide range of diesel engine load, starting from 20 up to 100% of the engine rated load. The characteristics of the equipment used are given in Table 5.

Fig. 1
figure 1

Schematic diagram of the engine test bench

Table 4 Engine specifications
Table 5 Accuracy and relative error of measured parameters

4 Numerical method

In the present study, numerical simulation is analyzed from intake valve closure (IVC) to exhaust valve opening (EVO); this simulation technique is known as closed cycle simulation (CCS). Due to the periodicity of the injector and the combustion chamber, the computational domain is divided into sectors in order to reduce the computational time. One eighth sector was taken to represent the full geometry. Piston bowl geometry, computational sector, sector mesh and the setting of nozzle orientation with the piston sliding motion inside the engine cylinder are shown in Fig. 2. Hexahedron mesh is generated through a commercial CFD code with a cell height of 1.6 mm, a cell expansion ratio of 1.01 from the piston and a cell expansion ratio of 1.01 from the head. Meshing can be automatically refined or coarsened based on the solution variables or geometrical features. Sub-processes such as a nozzle flow model, spray atomization, droplet breakup, droplet collision and coalescence, droplet vaporization and wall impingement have been needed to simulate the dynamics and interactions of the fuel spray. The nozzle orientation was adjusted according to the spherical coordinate system as θ = 134o and φ = 22.5°. For fuel details, a combination of methyl decanoate (MD), methyl-9-decanoate (MD9D) and n-heptane is utilized as a reaction mechanism to represent the saturated and non-saturated of the oxygenated hydrocarbon chain of biodiesel fuel, which includes 247 species and 1129 reactions [35]. N-heptane reaction mechanism with 117 species and 472 reactions by [36] was utilized as a surrogate fuel model to represent the chemical kinetics of the diesel fuel. The model used for NOx formation is based on thermal mechanism [37]. Fuel spray atomization and droplet breakup are modeled based on the Kelvin–Helmholtz / Rayleigh–Taylor (KH / RT) hybrid model, where the fuel spray is divided into two regions, the first region starting from the nozzle exit, during which the fuel jet still dense but some droplets are separated from the jet; this region is associated with Kelvin–Helmholtz modeling; see Fig. 3. At the end of the first region, the fuel jet turns entirely to droplets; this region is associated by Rayleigh–Taylor modeling; details and validation are available in [38].

Fig. 2
figure 2

geometry creating steps: a piston bowl, b computational sector, c piston sliding motion in the computational domain and d sector mesh

Fig. 3
figure 3

KH/RT breakup model of fuel spray

The transport equations of the turbulent reacting flow are formulated as follow:

  1. 1.

    Species conservation equation Eq. (1):

    $$\frac{{\partial \overline{\rho }_{k} }}{\partial t} + \nabla \left( {\overline{\rho }_{k} \tilde{u}} \right) = \nabla \left( {\overline{\rho }D \, \Delta \overline{y}_{k} } \right) + \nabla \phi + \overline{\rho }_{k}^{c} + \overline{\rho }_{k}^{s}$$

where \(\overline{y}_{k} = \frac{{\rho_{k} }}{\rho }\) and \(\varphi \, = \overline{\rho }_{k} \tilde{\user2{u}} - \overline{{\rho_{k} \tilde{\user2{u}}}}\).

  1. 2.

    Fluid continuity equation Eq. (2):

    $$\frac{{ \partial \overline{\rho }}}{\partial t} + \nabla \left( {\overline{\rho }{ }\tilde{\user2{u}}} \right) = \overline{\rho }^{s}$$
  2. 3.

    Momentum conservation equation Eq. (3):

    $$\frac{{ \partial \overline{\rho }{ }\tilde{\user2{u}}}}{\partial t} + \nabla \left( {\overline{\rho }{ }\user2{\tilde{u}\tilde{u}}} \right) - \nabla \overline{P}{ } + \nabla .\overline{\user2{\sigma }} - \Delta \Gamma + \overline{F}^{s} + \overline{{\rho {\varvec{g}}}}$$
  3. 4.

    Energy conservation equation Eq. (4):

    $$\frac{{ \partial \overline{\rho }{ }\tilde{\user2{I}}}}{\partial t} + \nabla \left( {\overline{\rho }{ }\user2{\tilde{u}\tilde{I}}} \right) = - \overline{P}\nabla \cdot \tilde{\user2{u}} - \nabla .\overline{J} - \nabla {\mathbf{H}} + \overline{\rho }{ }\tilde{\varepsilon } + \overline{Q}^{c} + \overline{Q}^{s}$$

where \(\overline{\user2{J}}\) = -λ \(\nabla \overline{T}\)\(\overline{\rho }{ }\) D \(\sum \widetilde{{{\varvec{h}}_{k} }}\) \(\nabla y_{k}\) and λ = \(\overline{\rho }{ }C_{p}\) α.

  1. 5.

    Gas-phase mixture equation of state Eq. (5):

    $$\overline{P} = R_{u} \overline{T}\sum \frac{{\overline{{\rho_{k} }} }}{{W_{k} }}$$

Turbulence is modeled by the renormalization group RNG k-ε [39] Eqs. (6,7).

$$\frac{{ \partial \overline{\rho } \widetilde{K}}}{\partial t} + \Delta \left( { \overline{\rho } \widetilde{u}\widetilde{K}} \right) = - \frac{2}{3}\overline{\rho }K\widetilde{K}\nabla \cdot \widetilde{u} + \left( {\sigma {-}\Gamma } \right):\;\nabla \cdot \widetilde{u} + \nabla \left[ {\frac{{\left( {\mu + \mu_{T} } \right)}}{{\Pr_{k} }}\nabla \widetilde{K}} \right] - \overline{\rho }\widetilde{\varepsilon } + \overline{W}^{s}$$
$$\frac{{ \partial \overline{\rho }{ }\tilde{\user2{\varepsilon }}}}{\partial t} + \nabla \cdot \left( {\overline{\rho }{ }\tilde{\user2{u}}\tilde{\varepsilon }} \right) = - \left( {\frac{2}{3 }C_{\varepsilon 1} - C_{\varepsilon 3} } \right) \cdot \overline{\rho }\tilde{\varepsilon }\nabla \cdot \tilde{\user2{u}} + \nabla \left[ {\frac{{\left( {\upsilon + \upsilon_{T} } \right)}}{{Pr_{\varepsilon } }}\nabla \tilde{\varepsilon }} \right] + \frac{{\tilde{\varepsilon }}}{{\tilde{\user2{K}}}}C_{\varepsilon 1} \left( {\overline{\user2{\sigma }}{ }{-}\Gamma } \right) \cdot \nabla \tilde{\user2{u}} - C_{\varepsilon 2 } \overline{\rho }\tilde{\varepsilon } + C_{s} \overline{W}^{s} - \overline{\rho }$$

where \(R = \frac{{C_{\mu } \eta^{3} \left( {1 - \eta /\eta_{0} } \right)}}{{1 + {\varvec{\beta}}\eta^{3} }} \cdot \frac{{\tilde{\varepsilon }^{2} }}{{\tilde{\user2{K}}}}\).

The values of model constants cs, cµ, cε1, cε2, cε3, 1/Prk, 1/Prε, η0 and β are given in Table 6. Boundary and initial conditions are given in Table 7.

Table 6 Values of RNG k-ε model constants
Table 7 Boundary and initial conditions

When the fuel droplets impinge the wall surface, this impingement will result in the following possibilities [40]:

  1. 1.

    Sticking if Wen ≤ 5

  2. 2.

    Rebound if 5 < Wen ≤ 10

  3. 3.

    Spread if Wen > 10 and Wen Ren0.5 < Hcr

  4. 4.

    Splash if Wen Ren0.5 ≥ Hcr

where Wen = \(\frac{{\rho U}^{2}d}{\sigma }\) , Ren = \(\frac{\rho Ud}{\mu }\) and Hcr = [1500 + \(\frac{650}{{\beta }^{0.42}}\)][1 + 0.1Ren0.5mim(δ,0.5)].

Splash impingement regime is employed in the present work. The net heat release rate can be calculated by the first low Eq. (8).

$$\frac{{dQ_{net} }}{d\theta } = \frac{\gamma }{\gamma - 1}\;{\text{P}}\;\frac{dV}{{d\theta }} + \frac{\gamma }{\gamma - 1}\;{\text{V}}\frac{dP}{{d\theta }}$$

4.1 Model validation

Figures 4, 5 and 6 show a comparison of simulation and experimental results for in-cylinder pressure, heat release rate and in-cylinder temperature at 100% of engine rated load using diesel fuel. The experimental and computational results were found to be in agreement. The peak pressure deviation was approximately 2.7%. The heat release rate (HRR) plot had two peaks because combustion in a diesel engine occurs in two phases: premixed and diffusion. The rapid combustion (first peak in pressure and HRR plots) is due to the premixed combustion phase. Any changes in temperature, HRR (second peak) and pressure after the first phase inside the cylinder are due to the diffusion phase, and this phase can be controlled by mixing fuel with air. In this context, the first peak in the HRR plot is due to the premixed combustion phase, and its wider width indicates good mixing and the consumption of a large amount of fuel during this phase. The second peak size in the HRR plot indicates how much fuel was consumed during this phase. The experimental and simulation results do not match at the second peak in the HRR plot, as shown in Fig. 5. In addition, as shown in Fig. 6, a divergence was observed between the ends of the experimental and theoretical temperature lines. This indicates that combustion continued in the practical experiment, which could be because the injector continued to inject fuel even after combustion ended. As a result, in the practical experiment, a development occurred in the diffusion combustion phase that differed from the diffusion combustion in the numerical simulation. Table 8 compares the numerical and experimental performance and emission results for conventional diesel fuel at 100% engine rated load. A numerical simulation was conducted on the biodiesel fuel fired the diesel engine using a combination of methyl decanoate (MD), methyl-9-decanoate (MD9D) and n-heptane, where the MD represent the saturation FAME and the MD9D represent the unsaturation FAME, the validation and details of this mechanism are available in literature [35]. Table 9 compares the numerical results to the experimental results reported in the literature [41] (Additional file 1).

Fig. 4
figure 4

In-cylinder pressure for the base diesel (BD) fuel at 100% of engine rated load

Fig. 5
figure 5

Heat release rate (HRR) of base diesel fuel at 100% of engine load

Fig. 6
figure 6

In-cylinder temperature of base diesel fuel at 100% of engine load

Table 8 Comparison of numerical and experimental results of the BD fuel at 100% of engine rated load
Table 9 Rate of change in the results for biodiesel fuel compared to diesel fuel

5 Results

5.1 Engine performance

Figures 7, 8 and 9 show the variation in mean pressure, heat release rate and temperature inside the engine cylinder at 100% of the engine rated load for biodiesel and base diesel fuel. As shown in Fig. 7, combustion of soybean biodiesel fuel begins earlier than combustion of base diesel fuel because the premixed phase of soybean biodiesel (SB) is shorter than that of base diesel (BD) or the biodiesel fuel has a shorter ignition delay period due to its higher cetane number. As a result, the in-cylinder pressure of the base diesel fuel increased because more fuel was injected during the premixed phase than in the soybean biodiesel fuel. Because of the lower heating value of soybean biodiesel fuel, the heat release rate HRR for biodiesel was reduced by an average of 21.8% at 100% of the engine rated load. These findings are consistent with those reported by [41, 42] (Additional file 2).

Fig. 7
figure 7

In-cylinder pressure for base diesel (BD) and soybean biodiesel (SB) fuels at 100% of engine rated load

Fig. 8
figure 8

Heat release rate (HRR) for base diesel (BD) and soybean biodiesel (SB) fuels at 100% of engine rated load

Fig. 9
figure 9

In-cylinder temperature for base diesel (BD) and soybean biodiesel (SB) fuels at 100% of engine rated load

Figures 10 and 11 depict the variations in brake-specific fuel consumption (BSFC) and brake thermal efficiency (BTE) for base diesel and soybean biodiesel fuels at each load. The BSFC for soybean biodiesel fuel was found to be 11.8% higher than that of base diesel fuel, owing to the lower heating value of soybean biodiesel, which is about 12.8% lower than that of base diesel fuel. As a result, in order to produce the same power as diesel fuel, the amount of soybean biodiesel fuel injected into the combustion chamber must be increased. The conversion efficiency of the chemical energy content in a fuel into useful work is represented by the BTE. As shown in Fig. 11, the BTE increases as engine load increases, but the BTE for biodiesel fuel was found to be lower than base diesel fuel by an average value of 11.3%. This reduction is due to the lower ignition delay period and less area between firing and non-firing pressure curves.

Fig. 10
figure 10

Brake-specific fuel consumption (BSFC)

Fig. 11
figure 11

Brake thermal efficiency (BTE)

5.2 Emission analysis

5.2.1 Carbon monoxide emission (CO)

Figure 12 depicts the CO emissions from the tested engine, which was powered by base diesel and soybean biodiesel fuels. It was found that increasing the engine load increases CO emissions for both diesel and soybean biodiesel fuels. At higher loads, CO emissions increase significantly due to a rich fuel mixture, which results in incomplete combustion. As illustrated in Fig. 12, soybean biodiesel fuel emits significantly lower CO emissions than diesel fuel over the entire engine load. The average reduction in CO emissions for soybean biodiesel fuel was approximately 42.389% when compared to base diesel fuel; this reduction is primarily due to the excess oxygen content, which improves combustion efficiency. According to Özener et al. [41] and Vellaiyan [42], biodiesel fuel reduces CO emissions by 46 and 33.8%, respectively.

Fig. 12
figure 12

CO emissions at different loads

5.2.2 Hydrocarbon (HC) emissions

The hydrocarbon (HC) emissions are produced when hydrocarbons such as CH4 do not burn completely and exhausted out the engine. Figure 13 clearly shows that the biodiesel fuel significantly reduces HC emissions compared to diesel fuel over the entire engine loads. On average, soybean biodiesel fuel reduces HC emissions by approximately 41.53% when compared to diesel fuel; this reduction is due to the higher cetane number and oxygen content of soybean biodiesel; this result is consistent with that reported by [42]. Furthermore, the higher the cetane number of biodiesel fuel, the shorter the ignition delay period, which influences the reduction of HC emissions.

Fig. 13
figure 13

HC emissions at different loads

5.2.3 Nitrogen oxide (NOx) emissions

As shown in Fig. 14, nitric oxide (NO) emissions increase as engine load increases due to an increase in in-cylinder temperature, which results in the decomposition of more nitrogen atoms from atmospheric air, and these nitrogen atoms interact with oxygen to form the nitrogen oxides NOx (NO and NO2). In the combustion of soybean biodiesel fuel, the higher in some spatial temperature inside the engine cylinder, excess oxygen content and faster reaction rate are attained when compared to diesel fuel. As a result, NOx formation in soybean biodiesel fuel is always greater than in diesel fuel. This study found that NO emissions increased by an average of 21.8% over the entire engine loads. The higher oxygen content of biodiesel is considered to be the main cause of higher NOx emissions. As shown in Fig. 15, some zones in the combustion chamber reached higher temperatures than diesel fuel due to the unsaturated fatty acids present in soybean biodiesel fuels, resulting in more thermal NOx formation. Because the intensity of the interaction of oxygen with carbon and nitrogen is greater in biodiesel fuel than in diesel fuel, regions with higher NO emissions have lower oxygen content.

Fig. 14
figure 14

NO emissions at different loads

Fig. 15
figure 15

Spatial distributed temperatures, NO and O2 emissions at 10 CAD and 30 CAD aTDC for diesel and soybean biodiesel fuels

5.2.4 Carbon dioxide (CO2) emissions and exhaust gas temperature (EGT)

Because of the higher oxygen concentration and lower carbon-to-hydrogen ratio in biodiesel fuel, the fuel oxidation process occurs in locally rich zones during the combustion of biodiesel fuel in a diesel engine, reducing the tendency to produce soot. CO2 emissions and EGT were calculated numerically for base diesel and soybean biodiesel fuels at different engine loads. As shown in Figs. 16 and 17, using biodiesel fuel increases Co2 emissions and decreases EGT over the entire engine load range by an average of 11.2% and 9.4%, respectively. The lower EGT is due to the earlier combustion and the lower heating value of soybean biodiesel fuel.

Fig. 16
figure 16

CO2 emissions at different loads

Fig. 17
figure 17

Exhaust gas temperature (EGT) at different loads

5.3 Optimization

This study showed that the combustion of biodiesel fuel began earlier than diesel fuel with a drop in peak pressure so, optimization of the injection timing of biodiesel is essential.

Soybean biodiesel fuel is optimized by conduction four SOI timings as shown in Table 10. Figure 18 shows the in-cylinder combustion pressure of soybean biodiesel at wide range of SOI timings. In the case of SOI = − 15 bTDC, the combustion began earlier than diesel fuel by 1.44 CAD and the peak pressure was dropped by 4.37%, which mean that the in-cylinder peak pressure and temperature are increased and resulting in a higher engine performance compared to other SOI timings. The combustion characteristics of soybean biodiesel is optimum at SOI = − 15 bTDC.

Table 10 Start of injection timings of biodiesel fuel
Fig. 18
figure 18

In-cylinder pressure of soybean biodiesel at a wide range of SOI timings

6 Discussion

The combustion process in diesel engines is divided into two phases, as shown in Figs. 7 and 8. The first phase is the premixed phase, which begins after the start of injection and involves the mixing of fuel and air to form combustible rich fuel zones. When a self-ignition occurs, multiple flames spread from various locations quickly consume all of the combustible mixture, causing pressure and temperature to rise rapidly and the combustion to transition to the second phase; diffusion phase. The premixed phase is responsible for the peak pressure and the first peak in the HRR diagram. The diffusion phase is governed by the mixing of air and fuel, which is responsible for any temperature change after the peak pressure, as illustrated in Fig. 9.

Diesel engine performance depends significantly on the fuel properties and the fuel injection system. Soybean biodiesel fuel is characterized by its higher viscosity, lower calorific value and the oxygenation nature so, these properties will affect fuel spray and combustion process. As shown in Fig. 7, the area between the firing and non-firing (motoring) pressure curves for the base diesel fuel is greater than that of soybean biodiesel fuel on the right-hand side, which this means the power delivered by the base diesel is higher than that of soybean biodiesel fuel.

Fuel spray is the process of forcing the liquid fuel out of a given container into a mass of small liquid droplets. In a DI diesel engine, the injector injects the fuel into the cylinder while it is still in the liquid phase. As soon as the injected liquid fuel enters the combustion chamber and comes into contact with the cylinder's air, the liquid phase instantly starts to disperse. This liquid phase evaporates, creating a combustible mixture that releases a considerable amount of energy inside the chamber. The entire process, which includes the atomization, evaporation and breakdown of the liquid fuel, is referred to as the spray evolution process. It is crucial to have a thorough understanding of spray evolution since it plays a significant role in the preparation of the mixture, which in turn affects how well the combustion and emission formation turn out. Using the particle-tracking tool in a CFD code, the spray behavior of the diesel and biodiesel fuels could be demonstrated in the current study in detail. The particle tracking of diesel and biodiesel sprays at TDC is shown in Fig. 19a and b. The two figures can be compared to demonstrate how much larger the spray cone angle of biodiesel is than that of diesel fuel and how much longer the liquid penetration length of biodiesel is than that of diesel. Additionally, the temperatures of diesel fuel droplets are higher than those of biodiesel fuel. These lower temperatures will have an impact on how well biodiesel evaporates, making it burn less efficiently than diesel.

Fig. 19
figure 19

Spray development of a diesel fuel and b biodiesel fuel

Generally, the formation of carbon monoxide and hydrocarbon emissions is affected by fuel type, equivalence ratio, swirling, injection timing, engine load and engine speed. CO emission increases due to poor fuel atomization (low turbulence kinetic energy), rich fuel mixtures, high engine load and low speed (idle mode). The NOx formation is greatly influenced by the combustion temperature, oxygen concentration and reaction rate. The oxygen content in the biodiesel fuel is considered the main reason for the increase in NOx emissions.

7 Conclusion

A 3-D computational fluid dynamics (CFD) study is carried out using a CFD code linked to a chemistry solver to analyze the performance and emission characteristics of a DI diesel engine fueled with base diesel (BD) and soybean biodiesel (SB) fuels. The diesel engine was verified and a good validity was found. The following are the main findings of this study:

  1. 1)

    At different engine loads, the developed CFD model predicted in-cylinder pressure, temperature, heat release rate and CO, HC, CO2 and NOx emissions.

  2. 2)

    Because soybean biodiesel fuel has a lower ignition delay period than diesel fuel, the combustion process begins earlier, which is the main reason for lowering the area between the firing and non-firing (motoring) pressure curves for biodiesel fuel on the right-hand side, which increases the power delivered by the base diesel than that of soybean biodiesel fuel, so retarding biodiesel fuel injection to an angle near the TDC is preferred to overcome this deficiency.

  3. 3)

    In comparison with base diesel fuel, BSFC increased by an average of 11.8%, while BTE decreased by an average of 11.3% for soybean biodiesel fuel.

  4. 4)

    When compared to diesel fuel, the heat release rate of soybean biodiesel fuel was found to be about 21.8% lower at 100% of engine rated load.

  5. 5)

    When compared to diesel fuel, soybean biodiesel fuel reduced CO and HC emissions by an average of 42.38% and 41.53%, respectively.

  6. 6)

    Because the oxygen content in biodiesel fuel improved combustion efficiency and improved CO2 conversion, NOx and CO2 emissions increased by 21.8% and 11.2%, respectively, when compared to diesel fuel.

  7. 7)

    The exhaust gas temperature (EGT) of soybean biodiesel fuel was reduced by 9.4% on average when compared to base diesel fuel.

  8. 8)

    Soybean biodiesel fuel was optimized by performing four starts of injection (SOI) at timings of − 18, − 16, − 15 and − 13,5 bTDC, and it was found that the combustion characteristics of soybean biodiesel are optimum at SOI = − 15 bTDC.

These findings indicate that biodiesel fuel can be used as an alternative and environmentally friendly fuel in the engine without requiring any modifications. Several strategies, such as exhaust gas recirculation (EGR) with fuel preheating and emulsion, can be used to address the problem of rising NOx emissions.

Availability of data and materials

The data used in the present study are available on request.



After top dead center


Before top dead center


Bottom dead center


Base diesel


Brake-specific fuel consumption (g/KWh)


Brake thermal efficiency


Crank angle degree

\({C}_{p}\) :

Heat capacity (J/K)


Droplet diameter (micron)


Diffusion coefficient


Direct injection


Exhaust gas temperature (K)


Fatty acid methyl esters

\({\overline{F} }^{s}\) :

Momentum gain per unit volume due to the spray


Specific body force (ms-1)


Specific enthalpy (J/kgK)

Hcr :

Splashing threshold


Heat release rate (J/CAD)

\(\widetilde{{\varvec{I}}}\) :

Specific internal energy (J/kgK)


Heat flux vector (W/m.2)


Turbulent kinetic energy (m2s.−2)


Species index


Pressure (N/m.2)

\({\overline{Q} }^{c}\) :

Chemical heat release source term

\({\overline{Q} }^{s}\) :

Spray interactions source term

Ren :

Reynolds number

\({R}_{u}\) :

Universal gas constant (J/Kmol.K)


Soybean biodiesel


Start of injection


Top dead center

\(\overline{T }\) :

Fluid temperature (K)


Volume (m.3)

Wen :

Weber number

\({\overline{W} }^{s}\) :

Eddies source term

\({W}_{k}\) :

Molecular weight (g/mol)

\({\overline{y} }_{k}\) :

Species mass fraction


Specific body force (ms.−1)


Surface roughness height-to-incident droplet diameter ratio


Specific heat ratio


Film thickness-to-incident droplet diameter ratio


Dissipation rate of the turbulent kinetic energy (m−2 s.−3)


Crank angle


Thermal conductivity (Wm−1 K.−1)


Viscosity (N s m.−2)


Turbulent kinematic viscosity (m2 s.−2)


Density (kg/m.3)

ρ ̅_k^c:

Chemical reaction source term

ρ ̅_k^s:

Spray evaporation source term


Viscous shear stress (N/m.2)


Thermal diffusivity (m2s.−1)


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The authors would like to thank and acknowledge the support offered by the staff of internal combustion engines laboratory, faculty of engineering, Al-Azhar University, for their contributions to the experiments.


The authors declare that they did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.

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MKA conducted the numerical simulation, visualization, conceptualization and investigation and wrote the manuscript. MMA supervised the laboratory experiments and structured. AME conducted the laboratory experiments, edited, read and reviewed the final manuscript. All authors read and approved the final manuscript.

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Correspondence to Mohamed Khaled Abdelrazek.

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Supplementary Information

Additional file 1. Simulation of diesel engine combustion using soybean biodiesel fuel.

Additional file 2. Simulation of diesel engine combustion using base diesel fuel.

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Abdelrazek, M.K., Abdelaal, M.M. & El-Nahas, A.M. Numerical simulation of a diesel engine performance powered by soybean biodiesel and diesel fuels. Beni-Suef Univ J Basic Appl Sci 12, 11 (2023).

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