Karrar S. Hasan*
| Hyder H. Balla
© 2026 The authors. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).
OPEN ACCESS
This study experimentally investigates the thermodynamic and exergy behavior of waste cooking oil (WCO) biodiesel blends (B10–B50) in an unmodified single-cylinder diesel engine operating at 1500 rpm under loads from 25% to 100%. First-law performance parameters, including brake specific fuel consumption (BSFC), brake thermal efficiency (BTE), exhaust gas temperature (EGT), and air-fuel ratio (AFR), together with exergy efficiency (ηex) and exergy destruction, were evaluated. Experimental uncertainty was determined using the root-sum-square (RSS) method. Biodiesel blends at increased load levels raised EGT by approximately 6.8% and BSFC by approximately 10.7% due to differences in heating value and viscosity. Under full-load conditions, the AFR and volumetric efficiency of biodiesel blends were approximately 8.3% and 3.1% lower, respectively, than those of pure diesel (D100). ηex increased with engine load, reaching 21.34% for pure diesel at full load. Higher exergy destruction in B50 (18.52 kW) compared to D100 (15.13 kW) indicates greater thermodynamic irreversibility within the adopted exergy-based evaluation framework as the blending ratio of biodiesel is increased. The uncertainty in the derived thermodynamic parameters did not exceed 2–3%, indicating acceptable experimental reliability. The results indicate that low and medium biodiesel blends (B10-B20) can be used in a conventional diesel engine without modification while maintaining acceptable thermodynamic performance.
alternative fuels, biodiesel blends, compression ignition engine, exergy analysis, exergy destruction, experimental uncertainty, thermodynamic irreversibility, Waste Cooking Oil biodiesel
Waste cooking oil (WCO) biodiesel is considered a suitable alternative to petroleum diesel in compression-ignition engines. It is renewable and naturally biodegradable. In addition, it can be used in conventional diesel engines with little or no mechanical modification [1, 2]. Fuel shortages and harmful exhaust emissions have increased interest in cleaner and more sustainable fuels [3]. In addition to saving costs, recycling WCO to make biodiesel also contributes to a reduction in environmental pollution and better energy recovery. There are various fuel properties that influence the combustion behavior of biodiesel blends, such as density, viscosity, oxygen content and heating value. These properties affect the spray formation, ignition delay, combustion stability and heat release within the cylinder [4, 5]. Biodiesel blends are generally associated with lower carbon monoxide and hydrocarbon emissions. However, the higher the biodiesel ratio, the more fuel that will be consumed, and under certain operating conditions, the combustion temperature will also increase. Thus, it is still necessary to identify appropriate blending ratios for ensuring the desired thermodynamic performance and stable engine operation without changing the engine system.
Exergy analysis has become an effective method for evaluating the thermodynamic performance of biodiesel-fueled diesel engines because it provides deeper insight into energy quality and system irreversibility [6, 7]. Exergy analysis can also identify the thermodynamic losses that occur in combustion and heat transfer systems and quantify the loss of useful energy in them, unlike conventional energy analysis. The previous studies also revealed that an integrated energy and exergy analysis offers a comprehensive insight into the behavior of a diesel engine under practical operating conditions [8]. In addition, biodiesel–diesel blends were found to improve thermodynamic behavior and reduce exergy destruction under suitable operating conditions [9, 10]. The effect of biodiesel blends on engine performance and emissions has been the subject of several studies. In general, biodiesel fuels contribute to cleaner combustion because of their oxygenated structure [11, 12]. Experimental studies reported improvements in combustion behavior and thermal performance at medium engine loads when suitable biodiesel blending ratios were used [13]. Other studies showed that increasing the biodiesel ratio may increase BSFC and combustion temperature, particularly at high engine loads [14, 15]. Similar observations were reported by Hossain et al. [8], Abed et al. [16], Sayyed et al. [17], and Mathew et al. [18], where biodiesel blends reduced some harmful emissions but also affected fuel consumption and combustion characteristics under different operating conditions. Recent investigations further highlighted the importance of combining energy, exergy, and sustainability assessments for biodiesel-powered diesel engines [19, 20].
Despite the large number of studies on biodiesel utilization in compression-ignition engines, most previous investigations focused mainly on first-law performance indicators, BTE and BSFC. These approaches do not fully explain thermodynamic losses and internal irreversibility within the engine system. In addition, many previous studies investigated high biodiesel blending ratios or required engine modifications to achieve lower emissions [21-23]. Limited attention has been given to medium-range biodiesel blends (B10–B50) operating in unmodified diesel engines under practical conditions. Furthermore, the combined assessment of thermodynamic performance, exergy behavior, and experimental uncertainty remains insufficiently explored [24, 25]. Therefore, the exergy approach to the energy degradation and irreversibility of the useful energy is more informative, and if it is not used, a comprehensive interpretation of the thermodynamics of the diesel engine is limited [26, 27]. In diesel engines, exergy analysis is a second law-based approach to the determination of the magnitude and distribution of thermodynamic losses and has proven to be a useful tool for assessing the performance under varying operating conditions [28]. The present study integrates the methods of energy analysis, exergy analysis, and uncertainty quantification for WCO biodiesel blends in an unmodified diesel engine, whereas most of the previous studies have concentrated on the first-law approach. The study examines the biodiesel blends from B10 to B50 in practical operating conditions of the engine with the aim of evaluating the thermodynamic behavior and practical application of the biodiesel blends without the engine's mechanical modification.
2.1 Preparation of waste cooking oil biodiesel blend
This study involved the laboratory preparation of biodiesel from WCO through a base-catalysed transesterification process, as depicted in Figure 1. The procedure commenced with the refinement of the WCO. One litre of WCO was passed through a fine membrane filter to remove impurities and solid particulates. To prevent saponification during the transesterification process, the filtered oil was heated to 65 ℃ for 30 min and subsequently dried to remove any residual moisture [29].
Figure 1. Schematic illustration of the waste cooking oil (WCO) biodiesel production process and biodiesel–diesel blend preparation
Table 1. Detailed volumetric composition of experimental fuel blends (per 1000 mL)
|
Fuel Designation |
Base Diesel (mL) |
Waste Cooking Oil (WCO) Biodiesel (mL) |
Total Volume (mL) |
|
D100 |
1000 |
0 |
1000 |
|
B10 |
900 |
100 |
1000 |
|
B20 |
800 |
200 |
1000 |
|
B30 |
700 |
300 |
1000 |
|
B40 |
600 |
400 |
1000 |
|
B50 |
500 |
500 |
1000 |
Table 2. Physicochemical properties of experimental fuel blends
|
Fuel / Blend |
Biodiesel (vol.%) |
Density @20 ℃ (kg/m³) |
Calorific value (kJ/kg) |
Flash point (℃) |
Pour point (℃) |
Cetane Index (–) |
Kinematic viscosity @40 ℃ (mm²/s) |
|
D100 |
0 |
830 |
43000 |
68 |
−16 |
53.4 |
2.70 |
|
B10 |
10 |
836 |
42650 |
78 |
−14 |
53.7 |
2.92 |
|
B20 |
20 |
841 |
42300 |
92 |
−12 |
54.1 |
3.15 |
|
B30 |
30 |
846 |
41950 |
108 |
−10 |
54.6 |
3.39 |
|
B40 |
40 |
852 |
41600 |
128 |
−8 |
55.1 |
3.66 |
|
B50 |
50 |
858 |
41250 |
150 |
−6 |
55.9 |
3.98 |
|
B100 |
100 |
885 |
39250 |
181 |
−3 |
56.7 |
4.87 |
The first treatment was followed by transesterification with methanol and sodium hydroxide (NaOH) as alcohol and base catalyst, respectively. 100 mL of 99.8% methanol with 3 g of NaOH (molar ratio of methanol: oil of 5:1) was prepared for every 500 mL of filtered WCO. The methanol / NaOH solution was stirred for 30 min at 65 ℃ with a stirring rate of 700 rpm and then mixed with WCO. The reaction mixture was then kept under continuous magnetic stirring (700 rpm) and heating (65 ℃) for another 30 min to confirm the complete transesterification process. Upon completion of the reaction, the mixture was transferred into a separating funnel and allowed to stand for 24 h. Gravity-induced phase separation produced a lower glycerol layer and an upper crude biodiesel layer. The crude biodiesel was subsequently washed with water to remove residual catalyst, methanol, soap, and other impurities. The washed biodiesel was then heated at 100–110 ℃ for 40 min to remove residual moisture and obtain purified biodiesel suitable for engine testing [30]. The five biodiesel mixtures were ultimately prepared as illustrated in Table 1. Before engine testing, all biodiesel–diesel blends (B10–B50) were allowed to homogenize and stabilize for 6 h to ensure uniform fuel properties throughout the experiments.
The prepared biodiesel blends were subjected to various physicochemical property analysis in the laboratories of the Aeronautical Technical Department of Najaf Technical Institute by employing the respective ASTM standard methods as listed in Table 2. The measured values were then compared to the requirements of ASTM D6751 and EN 14214. The kinematic viscosity remained within the acceptable range reported in previous studies (1.9–6.0 mm²/s), while the remaining fuel properties also satisfied the specified standards [31, 32]. Figure 2 shows the biodiesel blends prepared for testing, and Table 2 summarizes their measured physicochemical properties.
Figure 2. Prepared waste cooking oil (WCO) biodiesel–diesel blends (B10–B50) used in the experimental investigation
2.2 Engine configuration and test rig
All experiments were conducted in the Combustion Laboratory of the Aeronautical Technical Department at Najaf Technical Institute, Al-Furat Al-Awsat Technical University. An Altaj SA-100 diesel engine was used, as detailed in Figure 3; Figure 4 shows its schematic. The engine was a single-cylinder, four-stroke, air-cooled, direct-injected engine. A control panel that included gauges was a must in order to make the experiments possible. This panel featured switches for the fuel loads, a voltmeter/ammeter, a tachometer and a graduated cylinder to measure fuel consumption. Also installed in this system were an air filter, a calibrated orifice meter, and a digital, differential manometer for measuring the air-flow rate into the system. The engine's technical specifications are shown in Table 3.
Figure 3. Photograph of the experimental diesel engine test rig
Figure 4. Schematic diagram of the experimental diesel engine test rig
Table 3. Specifications of the experimental diesel engine
|
Specification |
Value |
|
Model |
SA-100 |
|
Type |
Single Cylinder, 4-Stroke, Air-Cooled |
|
Combustion System |
Direct Injection (DI) |
|
Bore × Stroke |
102 × 110 mm |
|
Displacement Volume |
899 cc |
|
Rated Output |
7.35 kW (10 hp) @ 1500 rpm |
|
Compression Ratio |
17:1 |
|
Lubrication |
Force feed and splash lubrication |
|
Net Weight |
180 kg |
2.2.1 Measurement instruments and data acquisition
During the experiments, a number of measuring instruments were used, and their characteristics and technical specifications are shown in Table 4.
Table 4. Technical characteristics of auxiliary measurement instrumentation
|
Specification / Model |
Parameter Measured |
Instrument |
|
Model: EHDIS, Range: ±2.999 psi |
Intake Manifold Pressure |
Digital Manometer |
|
Digital sensor |
Engine Speed |
Tachometer |
|
Calibrated volumetric burette (pipette) |
Fuel Consumption |
Fuel Gauge |
|
K-type thermocouples |
EGT, Fuel, Air Temp |
Temperature Sensors |
|
Model: HT-9815 |
Records data from sensors (e.g., Temp.) |
Data Logger |
The intake air flow rate was measured using a calibrated orifice meter connected to a digital differential manometer. The orifice geometry is illustrated in Figure 5 (D = 40 mm, d = 20 mm, β = 0.5, Cd = 0.6). The measured differential pressure was subsequently used to determine the intake air mass flow rate.
Figure 5. Schematic diagram of the orifice meter used to measure the intake air-flow rate
2.3 Experimental procedure
All experiments were conducted with consistent operating conditions using a single-cylinder diesel engine to ensure accuracy, repeatability, and feasibility of the experiments. The engine speed and compression ratio were maintained at 1500 rpm and 17:1, respectively, during the test. The performance and emission data were then taken with the engine at 0%, 25%, 50%, 75%, and 100% of its maximum capacity. The reference fuel and baseline fuel were diesel fuel (D100), and it was blended with WCO biodiesel at volumetric concentrations from B10 to B50 to be compared. The methodology was replicated with different fuel formulations to enhance the accuracy of the test and increase confidence in the data obtained. The study included analyses of fuel consumption rates, braking power, exhaust gas temperature (EGT), and pollutant concentrations. Specific equations were used in Microsoft Excel to perform accurate calculations, facilitating the assessment of BSFC and BTE. The gathered data were utilised to conduct both first-law and second-law thermodynamic analyses. This approach facilitated the utilization of an unaltered mechanical engine, attaining a balance between emission reduction and thermodynamic efficiency.
3.1 Energy-based performance analysis
3.1.1 Electrical power output
The engine load was represented by the electrical power output of the coupled single-phase synchronous generator, which was calculated from the measured voltage and current according to Eq. (1). Since the generator operated at a unity power factor (cosφ = 1.0), the electrical power output was determined directly from the measured electrical parameters.
$P=\frac{V \cdot I}{1000}$ (1)
where, P = electrical power output (kW), V is the measured voltage (V), and I is the measured current (A).
3.1.2 Brake Specific Fuel Consumption
In the present study, BSFC was calculated using the measured electrical power output of the coupled synchronous generator, which was considered as the useful engine output:
$B S F C=\frac{m_f}{P_{\text {elec }}}$ (2)
In g/kWh, the following relation was used:
$\operatorname{BSFC}(\mathrm{g} / \mathrm{kWh})=\frac{m_f\left(\frac{\mathrm{~kg}}{\mathrm{~s}}\right) \cdot 3600}{P_{\text {elec }}}$ (3)
where, $m_f$ is the fuel mass flow rate, and $\mathrm{P}_{\text {elec }}$ is the measured electrical power output.
3.1.3 Brake Thermal Efficiency
The BTE expresses the ratio of useful electrical power output to the fuel energy input.
$B T E=\frac{P_{\text {elec }}}{L H V \cdot m_f}$ (4)
where, LHV = The lower heating value of the fuel blends (kJ/kg).
3.1.4 Air-Fuel ratio
The intake air mass flow rate was experimentally measured using a calibrated orifice meter installed in the engine intake system and connected to a digital differential manometer. The air mass flow rate was determined from the measured pressure drop across the orifice according to:
$m_a=C_d A_0 \sqrt{2 \rho_a \Delta P}$ (5)
where, $C_d$ is the discharge coefficient, $\mathrm{A}_0$ is the orifice area, $\rho_{\mathrm{a}}$ is the ambient air density, and $\Delta \mathrm{P}$ is the measured differential pressure. The AFR was then calculated as:
$A F R=\frac{m_a}{m_f}$ (6)
3.1.5 Volumetric efficiency
The measured intake air mass flow rate was used to determine the volumetric efficiency ( $\eta_v$ of the four-stroke diesel engine based on the following:
$\eta_v=\frac{m_a}{\rho_a V_d N / 2}$ (7)
where, $V_d$ is the engine displacement volume, and N is the engine speed. The factor of 2 in the denominator accounts for the four-stroke operating cycle, where one intake event occurs every two crankshaft revolutions.
3.2 Exergy-based thermodynamic analysis
Exergy analysis accounts for energy quality and system irreversibility during combustion and heat transfer processes.
3.2.1 Reference state and assumptions
To perform the second-law analysis (exergy analysis), the reference environment was assumed at $\mathrm{T}_o$ = 298 K and $\mathrm{P}_o$ = 1 atm. Exergy is defined relative to the reference environment, since no useful work can be extracted once equilibrium is reached. A chemical exergy factor (X = 1.04) was adopted for the fuel blends to account for the difference between chemical exergy and lower heating value. The specific heat capacity of exhaust gases was assumed constant (Cp = 1.1 kJ/kg·K), which is a common approximation for diesel engine exhaust analysis.
3.2.2 Fuel chemical exergy
The fuel exergy rate, Ėxfuel, represents the available work potential from the fuel during complete combustion relative to the environment. It was calculated as:
$\dot{E} x_{\text {fuel }}=m_{f \cdot L H V \cdot X}$ (8)
where, $\mathrm{m}_{ \mathrm{f}}$ is the fuel mass flow rate (kg/s), and LHV is the lower heating value (kJ/kg). The chemical exergy factor X accounts for deviations between chemical exergy and heating value.
3.2.3 Electrical power exergy rate
The useful electrical power output of the engine–generator system was determined from the measured voltage and current. The electrical exergy rate was assumed equal to the electrical power output because electrical energy can be completely converted into useful work under ideal conditions.
$\dot{\mathrm{E}} x_{\text {elec }}=P_{\text {elec }}$ (9)
3.2.4 Physical exergy of exhaust gases
The physical exergy of exhaust gases was estimated based on the temperature difference between exhaust gases and the reference environment, and it was estimated as follows:
$\dot{E} x_{e x h}=\dot{m}_{e x} . C p\left[\left(T_{e x h}-T_o\right)-T_o \ln \left(\frac{T_{e x h}}{T_o}\right)\right]$ (10)
where, the exhaust mass flow rate (ṁex) is the sum of fuel ($m_f$) and air ($m_a$) mass flow rates:
$\dot{m}_{e x} \approx m_f+m_a$ (11)
$\dot{m}_a=A F R . m_f$ (12)
Exhaust exergy indicates the recoverable work potential available for waste heat recovery systems (WHRs) [24].
3.2.5 Exergy destruction
Exergy destruction (Ėxdest) represents the portion of fuel exergy irreversibly lost due to internal entropy generation within the engine. It was determined using the steady-state exergy balance:
$\dot{\mathrm{E}} x_{\text {dest }}=\dot{\mathrm{E}} x_{\text {fuel }}-\left(\dot{\mathrm{E}} x_{\text {elec }}+\dot{\mathrm{E}} x_{\text {exh }}\right)$ (13)
where, Ėxelec is the useful electrical power output exergy and Ėxexh is the physical exergy associated with the exhaust gases. A higher exergy destruction rate indicates greater thermodynamic irreversibility and reduced system effectiveness [33].
A simplified exergy balance was used to evaluate the thermodynamic performance of the diesel engine in the present study. The exergy destruction was calculated as the difference between the exergy input of the fuel and the useful electrical power output, and the physical exergy of exhaust gases. The cooling loss, lubrication loss, unburned fuel loss and the chemical exergy of the exhaust gas have not been calculated explicitly in the exergy balance but have been included in the calculated exergy destruction term. The simplified method was also followed to ensure the same operating conditions for all blends of biodiesel to be evaluated similarly.
3.2.6 Exergetic efficiency
Exergetic efficiency (ηex) is the ratio of the useful ratio of the useful electrical power output to the fuel exergy input. It was defined as:
$\eta_{e x}(\%)=\left(\frac{\dot{E} x_{\text {elec }}}{\dot{E} x_{\text {fuel }}}\right) \cdot 100$ (14)
Unlike BTE, ηex accounts for energy quality and irreversibility. Therefore, it provides a more realistic indicator of thermodynamic performance. Higher ηex reflects improved utilisation of the fuel's work potential and reduced internal losses [25].
3.3 Experimental uncertainty analysis
3.3.1 Instrument accuracy and measurement uncertainty
Instrument accuracies/resolutions were taken from the experimental setup specifications and used to quantify measurement uncertainty and propagate it to derived performance and exergy metrics. The specifications and measurement accuracies of the instruments used in this study are summarized in Table 5.
3.3.2 Root-Sum-Square-based uncertainty propagation
Uncertainty propagation was performed using the root-sum-square (RSS) method. For a derived quantity y = f(x₁, x₂, …, xₙ), the combined relative uncertainty is:
$\frac{U_y}{y}=\sqrt{\sum_{i=1}^n\left(\frac{\partial \ln y}{\partial \ln x_i}\right)^2\left(\frac{U_{x i}}{x i}\right)^2}$ (15)
where, $\frac{U_y}{y}$ is the relative uncertainty of the derived parameter y, $\frac{U_{x i}}{x i}$ is the uncertainty associated with the measured variable xi.
Table 5. Technical specifications, precision, and measurement uncertainties of the experimental instrumentation
|
Instrument |
Measured Quantity |
Accuracy/Resolution |
Unit |
|
Stopwatch |
Time, Δt |
±1 |
s |
|
Thermocouple (K-type) |
Exhaust gas temperature, EGT |
±1.5 |
℃ |
|
Tachometer |
Engine speed, N |
±(0.05% of reading + 1 digit); resolution 1 rpm |
rpm |
|
Fuel burette |
Fuel volume, ΔVf |
±1 |
mL |
|
Digital voltmeter |
Voltage, V |
±1% of reading |
V |
|
Digital ammeter |
Current, I |
±1% of reading |
A |
|
Fuel density (from reference/measurement) |
Fuel density, ρf |
±0.5 |
kg/m³ |
|
Calorific value measurement |
C.V |
±0.1% of reading |
kJ/kg |
3.3.3 Propagated uncertainty of derived parameters
The uncertainties associated with the derived parameters were evaluated using the RSS method [33, 34].
Fuel mass flow rate uncertainty. The fuel mass flow rate was determined from the measured fuel volume, fuel density, and consumption time:
$\left(\frac{U_{m_f}}{m_f}\right)=\sqrt{\left(\frac{U_\rho}{\rho}\right)^2+\left(\frac{U_V}{V}\right)^2+\left(\frac{U_t}{t}\right)^2}$ (16)
where, $\mathrm{U}_{\mathrm{m} \cdot \mathrm{f}}$ indicate uncertainty in the fuel mass flow rate, $\mathrm{U}_\rho$ indicate the uncertainty in fuel density, $\mathrm{U}_{\mathrm{V}}$ denotes uncertainty in fuel volume measurement, and $\mathrm{U}_{\mathrm{t}}$ denotes the uncertainty in time measurement.
Electrical power output uncertainty. The useful electrical power output was determined from the measured voltage and current of the coupled synchronous generator. The corresponding relative uncertainty was calculated as:
$\left(\frac{U_{\text {Pelec }}}{P_{\text {elec }}}\right)=\sqrt{\left(\frac{U_V}{V}\right)^2+\left(\frac{U_I}{I}\right)^2}$ (17)
where, $\mathrm{U}_{\mathrm{P}_{\text {elec }}}$ is the uncertainty in the electrical power output, $\mathrm{U}_{\mathrm{V}}$ indicate uncertainty in voltage measurement, $\mathrm{U}_{\mathrm{I}}$ indicate uncertainty in the current measurement.
Brake Specific Fuel Consumption uncertainty. Since BSFC depends on fuel mass flow rate and electrical power output. Its propagated uncertainty is given by:
$\left(\frac{U_{B S F C}}{B S F C}\right)=\sqrt{\left(\frac{U_{m\cdot f}}{m_{\cdot f}}\right)^2+\left(\frac{U_{P_{\text {elec }}}}{P_{\text {elec }}}\right)^2}$ (18)
where, $\mathrm{U}_{\mathrm{BSFC}}$ indicate uncertainty in BSFC, $\mathrm{U}_{\mathrm{m}^{\cdot} \mathrm{f}}$ indicate uncertainty in the fuel mass flow rate, and $\mathrm{U}_{\mathrm{P}_{\text {elec }}}$ indicate uncertainty in the measured electrical power output.
Brake Thermal Efficiency (ηth) uncertainty. The uncertainty in ηth brake thermal efficiency (BTE) depends on the measured electrical power output, fuel mass flow rate, and lower heating value, $\mathrm{U}_{\mathrm{m}^{\cdot} \mathrm{f}}$ and fuel heating value. The relative uncertainty is expressed as:
$\left(\frac{U_{B T E}}{B T E}\right)=\sqrt{\left(\frac{U_{\text {Pelec }}}{P_{\text {elec }}}\right)^2+\left(\frac{U_{m_f}}{m_f}\right)^2+\left(\frac{U_{L H V}}{L H V}\right)^2}$ (19)
where, $\mathrm{U}_{\mathrm{BTE}}$ indicate uncertainty in BTE, $\mathrm{U}_{\mathrm{m}^{\cdot} \mathrm{f}}$ indicate uncertainty of fuel mass flow rate, $\mathrm{U}_{\mathrm{P}_{\text {elec }}}$ indicate uncertainty in the measured electrical power output, and $\mathrm{U}_{\mathrm{LHV}}$ indicate uncertainty of the lower heating value.
Exergy Efficiency (ηex) Uncertainty. The uncertainty associated with ηex was calculated from the useful electrical exergy output and the fuel exergy input. Therefore, its propagated uncertainty was evaluated using the same RSS formulation, accounting for uncertainties in the fuel mass flow rate, heating value, and measured thermodynamic quantities.
$\left(\frac{U_{\eta_{e x}}}{\eta_{e x}}\right)=\sqrt{\left(\frac{U_{P_{e l e c}}}{P_{\text {elec }}}\right)^2+\left(\frac{U_{m \cdot f}}{m_{\cdot f}}\right)^2+\left(\frac{U_{\varepsilon_f}}{\varepsilon_f}\right)^2}$ (20)
The term εf denotes the specific fuel exergy, and $\mathrm{U}_{\varepsilon_f}$ is its associated uncertainty. The calculated propagated uncertainties of the derived parameters are presented in Tables 6-10.
Table 6. Relative uncertainty of fuel mass flow rate
|
Load (%) |
D100 |
B10 |
B20 |
B30 |
B40 |
B50 |
|
25 |
2.07 |
2.08 |
2.08 |
2.09 |
2.09 |
2.09 |
|
50 |
2.12 |
2.13 |
2.14 |
2.14 |
2.15 |
2.16 |
|
75 |
2.19 |
2.19 |
2.20 |
2.22 |
2.22 |
2.24 |
|
100 |
2.29 |
2.31 |
2.31 |
2.35 |
2.37 |
2.39 |
Table 7. Relative uncertainty of brake specific fuel consumption (BSFC)
|
Load (%) |
D100 |
B10 |
B20 |
B30 |
B40 |
B50 |
|
25 |
2.51 |
2.51 |
2.52 |
2.52 |
2.52 |
2.52 |
|
50 |
2.55 |
2.56 |
2.56 |
2.57 |
2.57 |
2.58 |
|
75 |
2.61 |
2.61 |
2.61 |
2.63 |
2.64 |
2.65 |
|
100 |
2.69 |
2.71 |
2.71 |
2.74 |
2.76 |
2.78 |
Table 8. Relative uncertainty of brake thermal efficiency (BTE)
|
Load (%) |
D100 |
B10 |
B20 |
B30 |
B40 |
B50 |
|
25 |
2.51 |
2.51 |
2.52 |
2.52 |
2.52 |
2.53 |
|
50 |
2.55 |
2.56 |
2.56 |
2.57 |
2.58 |
2.58 |
|
75 |
2.61 |
2.61 |
2.62 |
2.63 |
2.64 |
2.65 |
|
100 |
2.69 |
2.71 |
2.71 |
2.75 |
2.76 |
2.78 |
Table 9. Relative uncertainty of fuel exergy rate
|
Load (%) |
D100 |
B10 |
B20 |
B30 |
B40 |
B50 |
|
25 |
2.07 |
2.08 |
2.09 |
2.09 |
2.09 |
2.09 |
|
50 |
2.13 |
2.13 |
2.14 |
2.15 |
2.15 |
2.16 |
|
75 |
2.19 |
2.19 |
2.20 |
2.22 |
2.23 |
2.24 |
|
100 |
2.29 |
2.31 |
2.32 |
2.35 |
2.37 |
2.40 |
Table 10. Relative uncertainty of exergy efficiency (ηex)
|
Load (%) |
D100 |
B10 |
B20 |
B30 |
B40 |
B50 |
|
25 |
2.51 |
2.51 |
2.52 |
2.52 |
2.52 |
2.53 |
|
50 |
2.55 |
2.56 |
2.56 |
2.57 |
2.58 |
2.58 |
|
75 |
2.61 |
2.61 |
2.62 |
2.63 |
2.64 |
2.65 |
|
100 |
2.69 |
2.71 |
2.71 |
2.75 |
2.76 |
2.78 |
The propagated uncertainties of BSFC, BTE, and ηex are relatively similar because these parameters are derived from the same primary measured variables, namely fuel mass flow rate, voltage, current, and fuel calorific value. Among these variables, the uncertainty associated with fuel mass flow rate represents the dominant contribution to the overall propagated uncertainty, whereas the contributions of voltage, current, and fuel calorific value measurements are comparatively smaller. Consequently, the overall propagated uncertainties remained below 3%, indicating acceptable experimental reliability and measurement consistency.
4.1 Exergy analysis results
4.1.1 Exergy efficiency
Figure 6 depicts the variation in ηex when an engine operates on a biodiesel blend sourced from WCO under various loads. The results show that ηex progressively increases with increasing load across all utilised fuel types. This behavior may be associated with improved utilisation of fuel exergy and reduced relative thermodynamic losses at higher engine loads. Exergy losses are notably substantial when functioning at a low load of 25%. This behavior may be associated with higher relative heat-transfer losses and increased thermodynamic irreversibility at low-load operation. Consequently, ηex is comparatively low. As the engine load increases toward full-load operation, ηex reaches its highest value. Pure diesel (D100) had the highest ηex and lowest exergy destruction, while medium blends of biodiesel (B10–B20) had a relatively small ηex penalty over diesel. On the other hand, fuel consumption increased, and thermodynamic irreversibility increased with higher biodiesel blends (B30–B50), which led to a progressive decrease in ηex and an increase in exergy destruction.
Figure 6. Variation of exergy efficiency (ηex) with engine load
4.1.2 Exergy destruction analysis
The variation of available energy loss rate (exergy destruction rate, Ėxdest) of the diesel and biodiesel blends obtained from WCO with respect to the engine loading is illustrated in Figure 7. For all the tested fuel samples, Ėxdest is generally found to rise with the engine load. The increasing trend shows that the internal irreversibility is still the main source of thermodynamic losses on the engine's efficiency. A large part of the chemical energy of the fuel is not available under full load conditions. This increase could be related to thermodynamic irreversibilities and heat transfer losses in the engine system. An increase in the load also increases the exergy-destruction rates and the fuel-exergy input. The increase in loads also results in better engine performance; overall, it is generally related to an increase in thermodynamic irreversibility and an increase in entropy generation as reported in previous studies. In the previous study, the oxygenated content of WCO biodiesel has been reported to be more complete, but it was not directly tested in the current study.
Figure 7. Variation of exergy destruction at different loads
4.1.3 Exergy distribution at full load
A maximum-load distribution of available fuel energy at maximum load is displayed in Figure 8, showing the distribution for different exergy components. It shows that the internal irreversibility of the fuel energy is the major source of loss of energy during full load operation. In the meantime, a lower percentage of energy is lost in the exhaust gases. At full load, the exergy of the exhaust gases increased in importance as a result of the higher Texh, which could make waste-heat recovery applications possible in the future.
Figure 8. Exergy distribution at full load for diesel and biodiesel blends
4.1.4 Comparative exergy assessment
Table 11 summarises the exergy performance of diesel fuel and WCO biodiesel blends at maximum engine load. D100 exhibited the highest ηex and the lowest absolute exergy destruction rate among all tested fuels. With the increase in blending ratio of biodiesel, the absolute exergy destruction rate (kW) and the exergy destruction percentage increased, and the ηex gradually decreased. It is important to note that the rise in absolute exergy destruction must be taken in conjunction with the rise in fuel exergy consumption and not as a stand-alone measure of poorer thermodynamic performance. In the recent exergy analysis of a diesel engine, similar observations have been reported in which the Ėxdest and ηex have been correlated and interpreted together so as to give a balanced view of the thermodynamics [28]. Medium biodiesel blends (B10–B20) recorded only a slight decrease in the ηex and a little increase in exergy destruction percentage with respect to pure diesel fuel, while the higher biodiesel blends (B30–B50) recorded higher exergy loss as the biodiesel percentage increased. These findings show that as the concentration of biodiesel increases, the utilization factor of fuel exergy will be gradually decreased under full load operating conditions.
Table 11. Summary of exergy parameters and destruction rates at maximum engine load
|
Fuel |
ηex (%) |
Ėxdest (kW) |
Ėxdest (%) |
Ėxexh(%) |
|
D100 |
21.338 |
15.132 |
73.38 |
5.28 |
|
B10 |
20.646 |
15.755 |
73.93 |
5.42 |
|
B20 |
20.456 |
15.921 |
74.02 |
5.53 |
|
B30 |
19.312 |
17.18 |
75.4 |
5.28 |
|
B40 |
18.86 |
17.704 |
75.89 |
5.26 |
|
B50 |
18.17 |
18.522 |
76.49 |
5.34 |
4.2 Impact of waste cooking oil biodiesel blends on engine performance
4.2.1 Exhaust Gas Temperature behavior
Figure 9 illustrates the change in exhaust temperature with varying engine loads. The use of pure diesel fuel (D100) and the five biodiesel blends (B10-B50) clearly demonstrate an increase in Texh for all fuel types as the load increases. This behavior may be associated with the higher fuel supply required at increased engine loads, which is generally associated with elevated in-cylinder temperatures, as reported in previous studies. The exhaust temperature when using biodiesel was approximately 6.8% higher than when using pure diesel, especially under full loads. Similar trends have also been reported for WCO biodiesel blends, where the oxygenated nature of biodiesel may influence combustion behavior and EGT under increasing engine loads [34].
Figure 9. Comparison of exhaust gas temperatures (EGT) of diesel - waste cooking oil (WCO) biodiesel blends at different loads
4.2.2 Engine power characteristics
Figure 10 demonstrates that engine power is influenced by fuel type and is directly proportional to engine load. This behavior may be attributed to the increased energy demand required to satisfy higher engine loading conditions, as reported in previous studies [34]. The results of the tests showed that the electrical power input to the engine–generator system was about 4.9% greater to reach the tested loading conditions, especially for full load. The observed behavior could also be due to the LCV of biodiesel as compared to conventional diesel, which typically needs a higher ṁ f to produce an equivalent electrical power output [35]. A further consideration is the relatively greater density of the biodiesel that could lead to increased fuel delivery per injection as observed in previous studies [35].
Figure 10. Comparison of electrical power output of diesel - waste cooking oil (WCO) biodiesel blends at different loads
4.2.3 Brake Specific Fuel Consumption behavior
The BSFC results for the engine were documented using various fuel types and loads, as illustrated in Figure 11. At full engine loads, both pure diesel and biodiesel blends showed a lower BSFC value. This trend could correspond with higher fuel-energy efficiencies at higher loads as found in earlier studies [36]. The blends of biodiesel used over-consumed fuel by about 10.7%, primarily due to the LHV of the blends, which meant that the same power output could not be obtained with the same ṁf. In addition, the slightly higher viscosity of biodiesel could affect fuel spray performance and fuel-to-mixture mixing due to the fact that this has been suggested in previous studies [37]. Despite the increase in BSFC, the tested biodiesel blends remained operationally suitable for use in the unmodified diesel engine under the investigated operating conditions.
Figure 11. Comparison of brake specific fuel consumption (BSFC) of diesel - waste cooking oil (WCO) biodiesel blends at different loads
4.2.4 Air-Fuel Ratio behavior
Figure 12 illustrates that both fuel type and elevated load substantially affect the air-fuel ratio (AFR). As the load increases, this ratio typically decreases because a greater fuel injection rate is required to maintain constant torque. This leads to a greater fuel mass than the relatively constant intake air mass under stable operating conditions. Under elevated loads, the AFR was approximately 8.3% lower with biodiesel than with diesel fuel. Moreover, the oxygenated nature of biodiesel fuels may influence combustion characteristics under fuel-rich operating conditions, as suggested in previous studies [35]. This behavior has been associated with lower concentrations of incomplete-combustion products in biodiesel-fuelled diesel engines; however, such emissions were not measured in the present study [13].
Figure 12. Comparison of air-fuel ratio (AFR) of diesel - waste cooking oil (WCO) biodiesel blends at different loads
4.2.5 Brake Thermal Efficiency behavior
BTE varies with the fuel used and engine load, as shown in Figure 13. BTE increased with increasing engine load for both pure diesel and biodiesel blends. This behavior may be associated with improved utilization of the fuel energy input at higher engine loads and a reduced relative significance of heat losses, as reported in previous studies [36]. The biodiesel blends exhibited approximately 3.6% higher BTE than pure diesel under certain operating conditions. This behavior may be associated with the oxygenated nature of biodiesel fuels, which has been reported to influence combustion characteristics in diesel engines [38]. Conversely, at full loads, the BTE of biodiesel is lower than that of pure diesel. This behavior may be associated with the LHV and relatively higher viscosity of biodiesel fuels, which can influence fuel preparation and combustion processes, as suggested in previous investigations [37]. The results indicate that low- and medium-biodiesel blends can be utilised in the unmodified diesel engine while maintaining acceptable thermal performance under the investigated operating conditions.
Figure 13. Comparison of brake thermal efficiency (BTE) of diesel - waste cooking oil (WCO) biodiesel blends at different loads
4.2.6 Volumetric efficiency behavior
Figure 14 illustrates the variation of volumetric efficiency (VE) in a diesel-biodiesel blend with respect to load. Volumetric efficiency decreased with increasing load for all tested fuels. This behavior may be associated with the higher thermal conditions developed at elevated engine loads, which can influence the density of the inducted air charge, as reported in previous studies [36]. Compared with diesel fuel, the 
of the biodiesel blend decreased by approximately 3.1% under high-load conditions. This reduction may also be associated with the higher exhaust-gas temperatures observed for biodiesel blends, which may affect the intake process under high-load operating conditions, as suggested in previous investigations [38]. The results indicate that WCO biodiesel blends can be utilised in conventional diesel engines while maintaining acceptable volumetric-efficiency characteristics under the investigated operating conditions.
Figure 14. Comparison of volumetric efficiency (VE) of diesel - waste cooking oil (WCO) biodiesel blends at different loads
The present investigation was conducted using a single-cylinder, naturally aspirated diesel engine operating at a constant speed under steady-state conditions. Hence, the results obtained might vary in transient operation or for multi-cylinder engines. Further, there was no in-cylinder pressure analysis carried out, nor a detailed combustion analysis included in the present study, which restricts detailed combustion interpretation. The study also did not include an examination of the long-term durability of the engine, injector deposits or the effects of lubrication during the use of biodiesel for a long period of time. Moreover, the physical exergy of exhaust gases is only taken into account in the exergy analysis; the chemical exergy of the exhaust species is not incorporated in the present analysis. Future investigations may include advanced combustion analysis, transient engine operation, waste heat recovery integration, and long-term durability assessment to provide a more comprehensive thermodynamic evaluation of biodiesel-fuelled diesel engines.
An experimental thermodynamic and exergy assessment of WCO biodiesel blends was conducted using an unmodified single-cylinder diesel engine under different operating loads. The investigation employed first-law analysis, second-law analysis, and uncertainty propagation to evaluate the thermodynamic performance of biodiesel blends (B10–B50). The results indicated that increasing engine load increased ηex and improved overall thermodynamic performance. The EGT increased by approximately 6.8% for biodiesel blends relative to diesel fuel under high-load conditions, which may be associated with the oxygenated nature and fuel properties of biodiesel blends. The BSFC increased by nearly 10.7% with increasing biodiesel concentration owing to the LCV and higher viscosity of biodiesel blends. Meanwhile, the AFR and volumetric efficiency decreased by approximately 8.3% and 3.1%, respectively, under full-load operation.
Exergy analysis revealed that ηex improved with increasing load and reached a maximum value of 21.34% for D100 at full load. In contrast, exergy destruction increased progressively with increasing biodiesel concentration, rising from 15.13 kW for D100 to 18.52 kW for B50. The exergy distribution analysis further indicated that the major portion of fuel exergy was associated with exergy destruction within the adopted exergy-based thermodynamic assessment, whereas exhaust exergy remained within the range of 5.26–5.53%, suggesting potential opportunities for future waste heat recovery applications.
The uncertainty analysis confirmed acceptable reliability of the experimental measurements and calculated parameters, with propagated uncertainty values remaining within approximately 2–3%. Overall, the study demonstrates that low- and medium-WCO biodiesel blends (B10–B20) can be applied in conventional diesel engines under practical operating conditions with only a modest thermodynamic performance penalty compared with pure diesel. In contrast, higher biodiesel blends (B30–B50) exhibited progressively lower ηex and higher exergy destruction. Therefore, low- and medium-biodiesel blends represent a practical compromise between thermodynamic performance and reduced dependence on conventional petroleum diesel fuel.
|
A0 |
Orifice area |
|
AFR |
Air-fuel ratio |
|
BSFC |
Brake specific fuel consumption, g/kWh |
|
BTE |
Brake thermal efficiency, % |
|
VE |
Volumetric efficiency |
|
Cp |
Specific heat capacity at constant pressure, kJ/kg·K |
|
CV |
Calorific value, kJ/kg |
|
I |
Current, A |
|
LHV |
Lower heating value, kJ/kg |
|
LCV |
Lower calorific value, kJ/kg |
|
N |
Engine speed, rpm |
|
P₀ |
Reference pressure (dead state), atm |
|
Pelec |
Electrical power output, kW |
|
T |
Temperature, K |
|
T₀ |
Reference temperature (dead state), K |
|
Texh |
Exhaust gas temperature, K |
|
Ux |
Uncertainty of the measured parameter, % |
|
Uy |
Uncertainty of the derived parameter, % |
|
V |
Voltage, V |
|
Δt |
Time interval, s |
|
ΔVf |
Fuel volume consumed, mL |
|
Ėxdest |
Exergy destruction rate, kW |
|
Ėxpelec |
Electrical exergy rate, kW |
|
Ėxexh |
Exhaust exergy rate, kW |
|
Ėxfuel |
Fuel exergy rate, kW |
|
ṁa |
Air mass flow rate, kg/s |
|
ṁexh |
Exhaust gas mass flow rate, kg/s |
|
ṁf |
Fuel mass flow rate, kg/s |
|
X |
Chemical exergy factor |
|
Greek symbols |
|
|
ηex |
Exergy efficiency, % |
|
ηV |
Volumetric efficiency, % |
|
ρf |
Fuel density, kg/m³ |
|
Subscripts |
|
|
WCO |
Waste cooking oil |
|
D |
Diesel |
|
B |
Biodiesel |
|
DI |
Direct injection |
|
CR |
Compression ratio |
|
RPM |
Revolutions per minute |
|
EGT |
Exhaust gas temperature |
|
CO |
Carbon monoxide |
|
CO₂ |
Carbon dioxide |
|
HC |
Hydrocarbon |
|
NOx |
Nitrogen oxides |
|
PM |
Particulate matter |
|
RSS |
Root-sum-square method |
|
CI |
Compression ignition |
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