Keywords

1 Introduction

The growing problems of environmental pollution and global warming have been a concern for governments and other social institutions for the past decades. Emissions from the transportation sector are estimated to be one of the main sources of air pollution affecting human health and the environment [1, 2]. In addition, the global trend to adopt stricter vehicle emission standards [3, 4] makes it necessary to consider the possibility of using alternative environmentally friendly fuels to replace fossil diesel [5].

The use of simple combustion models, such as the Wiebe function [6], to analyze or predict the combustion process can accelerate knowledge and help optimize engine performance with alternative fuels. The diesel combustion phenomenon is usually divided into three phases, namely, premixed combustion, diffusion combustion, and late combustion phase [7]. Each of these phases has a different combustion rate, so no single Wiebe function can be applied for the characterization of the entire combustion process [6]. Serrano et al. [8] simulated the premixed, diffusion, and late combustion phases of a turbocharged diesel engine by combining three Wiebe functions. Xu et al. [9] used the triple Wiebe function (to represent the premixed, main, and late combustion phases) and found that the triple Wiebe function was more accurate and preferable in terms of predicting the evolution of the mass fraction burned. A similar observation was made by Awad et al. [10] who experimentally studied the three combustion phases of a diesel engine fueled with diesel and biodiesel.

This study models the experimental data of an unmodified four-cylinder Diesel engine consuming diesel/n-butanol blends using a single zone combustion model along with the modified triple Wiebe equation.

2 Materials and Methods

2.1 Experimental Setup

The experimental setup consists of an engine (Table 1), dynamometer control unit, fuel metering unit, eddy current dynamometer, in-cylinder pressure recording unit and data acquisition system.

Table 1. Engine specifications.
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In-cylinder pressure data acquisition was performed using a combustion analysis system (KiBox) consisting of an AVL GH14D cylinder pressure transducer, a charge amplifier, and a crankshaft angle adapter. Data were collected in KiBox for 100 consecutive cycles with a crankshaft angle resolution of 0.1°CA. The engine was preconditioned for 10 min following the procedure established in regulation 49 [11]. Then, it was run for the prescribed time in mode 11 of the World Harmonized Stationary Cycle at the speed of 1260 rpm and 50% load. All fuels were tested three times to ensure that the results were sufficiently repeatable.

Table 2. Physical and chemical properties of analyzed fuels.
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2.2 Fuels

Four fuels were tested. Pure diesel (called Diesel) as reference, and three binary blends: DBu5/10/20; with 5%, 10% and 20% n-butanol added to neat diesel (Table 2).

2.3 Wiebe Function for Combustion Model

The Wiebe function represents the evolution of the fuel burned fraction during combustion phenomena [7, 10, 12]. The triple Wiebe function used in this study is Eq. (1).

$${X}_{b}\left(\theta \right)={\sum }_{i+1}^{3}\frac{1+sign\left(\theta -{\theta }_{i}\right)}{2}{\beta }_{i}\left\{1-exp\left[-{a}_{i}{\left(\frac{\theta -{\theta }_{i}}{{\Delta \theta }_{i}}\right)}^{{m}_{i}+1}\right]\right\}$$
(1)

where for \(\theta >{\theta }_{i}\); \(sign\left(\theta -{\theta }_{i}\right)=1\), else. \(sign\left(\theta -{\theta }_{i}\right)=-1\); θ_i = crank angle at which ith phase of combustion starts; \(\Delta {\theta }_{i}\) = combustion duration of ith phase of combustion; \({a}_{i}\) = efficiency factor for the ith phase of combustion; \({m}_{i}\) = form factor for the ith phase of combustion; \({\beta }_{i}\) = total burn fraction for the ith phase of combustion.

The model approximation \(AHRR\) compared with experimentally calculated \(AHRR\). Equation (2) was used to predict the gross apparent heat release rate (\({Q}_{ch}\)) [7, 12].

$$ \frac{{dQ_{{ch}} }}{{d\theta _{{model}} }} = \frac{{dX_{b} (\theta )}}{{d\theta }}m_{f} \cdot LHV_{{fuel}} \cdot \eta _{{comb}} $$
(2)

where \({X}_{b}\) (\(\theta \)) is the burn fraction at a particular crank angle (\(\theta \)) predicted using triple Wiebe function, \({m}_{f}\) is the fuel consumption per cycle (g), \(LH{V}_{fuel}\) is the lower heating value of fuel (J/g), \({\eta }_{comb}\) is the combustion efficiency [7].

The modeled heat release rate data were used to predict in-cylinder pressure using Eq. 3 [12] derived from the analysis of the first law of thermodynamics.

$${p}_{i+i}={p}_{i}+\frac{\frac{\Delta {Q}_{n}}{\Delta \theta }-\left(\frac{\gamma }{\gamma -1}\right){p}_{i}\frac{\Delta V}{\Delta \theta }}{\left(\frac{1}{\gamma -1}\right)V}\Delta \theta $$
(3)

\(V\) is the in-cylinder volume, \(\gamma \) is the specific heat ratio, \(p\) is the in-cylinder pressure.

3 Results and Discussion

Figure 1 shows the comparison between experimental and simulated in-cylinder pressure values for diesel fuel. The combustion model was validated using the fitted Wiebe function to estimate the heat release rate, this rate was used to predict the in-cylinder pressure during the combustion process. The accuracy of each format of the triple Wiebe function was evaluated using the root-mean-square error (\(RMSE\)) to compare the predicted heat release rate and in-cylinder pressure to the experimental data. The RMSE values determined are ≤1.2 bar for all fuels. The max. in-cylinder pressure values (bar) for fuel DBu5/10/20 and diesel were 110.2, 111.0, 112.2 and 111.1 respectively. The max.in-cylinder temperatures (°C) were 2265, 2256, 2256 and 2262.

Fig. 1.
figure 1

Experimental vs. model pressure for reference diesel fuel.

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The parameters of the Wiebe triple function obtained by curve fitting of the experimental data on the combustion fraction are given in Table 3. The form factor values in the first stage (\({m}_{1}\)) of combustion are significantly larger than those in the second stage (\({m}_{2}\)) for diesel and binary blends. This is because the initial combustion is slower during the start of combustion, while the initial combustion is faster during the second stage of combustion, which is obvious from the nature of premixed combustion in the IC engine [10]. Moreover, the Wiebe triple function predicted the mass fraction burned (\({X}_{b}\)) with good accuracy (R2 = 0.99).

Table 3. Triple Wiebe function parameters.
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Figure 2 and 3 show the \({X}_{b}\) and \(AHHR\) profiles for all fuels, respectively. The \(AHRR\) calculated with the model is in good agreement with the experimental \(AHRR\) (\(RMSE\) ≤ 3.80 J/°CA). The low n-butanol contents in the binary mixture do not show considerable variations in the combustion process. It is important to note that the DBu20 blend leads to a slower initial combustion (Table 3) due to the lower CN of n-butanol.

The maximum AHRR value for diesel was 217.7 J/ºCA, which decreased to 211.8 J/ºCA when adding n-butanol (DBu20 fuel blend) due to the lower calorific value of the n-butanol blended fuel [13]. The maximum AHRR values of DBu5 (220.7 J/ºCA) and DBu10 (219.1 J/ºCA) are slightly increased without considerable variations, due to the proper atomization and air/fuel mixing of oxygenated fuels with n-butanol [14].

The combustion starts earlier and has a shorter ignition delay (6.1°CA) for diesel compared to DBu20 (7.1°CA). The addition of n-butanol increases the ignition delay from 6.1°CA to 7.1°CA. This is expected because n-butanol has a lower cetane number than diesel [15]. With the use of DBu5 and DBu10 blends the effect on ignition delay is less evident, with values of 6.1°CA and 6.7°CA, respectively.

Fig. 2.
figure 2

Experimental vs. model Burn faction (\({X}_{b}\)) [\(Xb\_exp\) – experimental burn fraction, \(Xb\_tw\) – burn fraction fitted applying triple Wiebe function, \(Xb\_f\) – burn fraction of first phase, \(Xb\_s\) – burn fraction of second phase, \(Xb\_t\) – burn fraction of third phase] for all fuels.

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Fig. 3.
figure 3

Experimental vs. model Apparent heat release rate (\(AHRR\)) [\(AHRR\_exp\) – experimental \(AHRR\), \(AHRR\_tw\) – AHRR calculated applying triple Wiebe function model] for all fuels.

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4 Conclusions

The zero-combustion model using Wiebe’s triple combustion fraction predicted the AHRR data with good accuracy for all fuels. The results show that the DBu5 and DBu10 blends did not alter the peak in-cylinder pressure and peak apparent heat release rate (AHRR) values, while slightly decreasing the peak in-cylinder temperature, with no significant changes in ignition delay and combustion duration. The DBu20 blend has no relevant variations in peak in-cylinder pressure and temperature, slightly reduced peak AHRR, also increased ignition delay and reduced combustion duration. The results may be beneficial to promote the use of n-butanol as an alternative renewable fuel in diesel engines to comply with emission control regulations.