Performance and emission multi-objective optimization of γ-Al₂O₃ nanoparticle-enhanced E10 bioethanol–gasoline combustion in spark-ignition engines

Abstract

Driven by the transition toward green energy, bioethanol is a primary substitute for fossil fuels in spark-ignition engines; however, its high latent heat of vaporization limits thermal efficiency. This study presents an initial investigation into the catalytic and thermophysical effects of ultra‑low concentrations (10–30 ppm) of γ‑Al₂O₃ nanoparticles on the combustion of a gasoline–ethanol blend containing 10% ethanol and 90% gasoline (E10), using Response Surface Methodology (RSM). These specific dosages were selected to leverage the particles’ thermal bridge effect and high surface acidity while minimizing knock and agglomeration risks. The dispersed nanoparticles enhanced fuel atomization and mitigated ethanol’s cooling effect via micro-explosions and hydrocarbon oxidation. Engine testing demonstrated that 20 ppm γ-Al₂O₃ increased Brake Torque (BT) and Brake Thermal Efficiency (BTE) by 7.67% and 3.02%, respectively, compared to the E10 baseline. Brake Specific Fuel Consumption (BSFC) decreased by 5.95% at 3000 rpm. The 10 ppm concentration maximized emission reductions at 3000 rpm, decreasing CO and HC by 14.88% and 6.57%, respectively. Conversely, elevated cylinder temperatures at 20 ppm increased NO_x emissions by 17.08% via the Zeldovich mechanism. Multi-objective optimization identified a global optimum operating point at 2471.87 rpm and 5.88 ppm. At high engine speeds, the nanoparticles stabilized operation by altering heat release dynamics. These findings establish a practical approach for developing optimized, eco-friendly fuel blends.

Introduction

In recent years, the growing demand for sustainable energy has accelerated the search for cleaner and more efficient alternatives to conventional fossil fuels. Spark-ignition (SI) engines, which still rely mainly on gasoline, remain a notable source of greenhouse gas emissions. As a result, improved fuel formulations that enhance combustion efficiency while lowering harmful exhaust emissions have become an active research area^1–3.

Among liquid biofuels, ethanol is widely recognized as a renewable, oxygenated additive that can improve combustion processes and reduce pollutant formation^4–6. Ethanol–gasoline blends containing 3–10% ethanol are now encouraged or mandated in many regions⁷. In particular, a gasoline–ethanol blend containing 10% ethanol and 90% gasoline (E10) has shown higher octane ratings, increased oxygen content, and lower regulated emissions compared with E5⁴. Recent thermodynamic studies, including those by Örs et al.⁸, have also indicated that incorporating alcohols such as ethanol or methanol into gasoline may reduce thermal and exergetic efficiency, highlighting the need for more advanced fuel modification strategies. One challenge arises from ethanol’s relatively high latent heat of vaporization, which can cause charge cooling, incomplete combustion, and reduced combustion stability, especially under high-load or high-speed conditions⁹. Nevertheless, E10 remains a practical compromise between efficiency and compatibility without requiring major engine modifications¹⁰.

To further enhance the properties of biofuel blends, recent studies have examined the use of metal-oxide nanoparticles as fuel additives to improve catalytic and thermo-physical characteristics^10,11. Nanoparticles such as MgO, CeO₂, Mn₂O₃, Fe₂O₃, and TiO₂ have been reported to increase combustion efficiency, lower unburned hydrocarbon (HC) and carbon monoxide (CO) emissions, and in some cases improve power output^12–15. A growing body of work also highlights the interaction between fuel chemistry and engine operating parameters. For example, assessments by Gülcan et al.¹⁶ on TiO₂, Ag₂O, and CeO₂ additives demonstrated improvements in exergetic performance and provided better management of the trade-off between fuel consumption and emissions. The effectiveness of TiO₂ has also been shown in specialized applications such as jet engines¹⁷, where it enhances oxidation and fuel economy. Research on blends of amyl alcohol and TiO₂¹⁸ has indicated that exergy efficiency can be improved by optimizing the compression ratio. Similarly, work with waste-derived fuels, including waste-tyre pyrolysis oil combined with TiO₂-assisted ethylene glycol¹⁹, has demonstrated gains in performance and exergy indicators along with reduced environmental impact. Despite these advancements, most existing studies have focused on relatively high nanoparticle concentrations, which may lead to agglomeration, increased engine wear, and higher fuel preparation costs²⁰.

Although response surface methodology (RSM) has been applied in some studies to determine optimal nanoparticle dosages^12,14,15, the literature remains limited in two key areas: most existing work has focused on different fuels or on non-γ phases of Al₂O₃, and there is little information on ultra-low nanoparticle concentrations in the 10–30 ppm range. In particular, the impact of such low dosages on the thermal bridge effect within E10 blends is not well established. This study addresses these gaps by examining the catalytic and thermophysical behavior of γ-Al₂O₃ nanoparticles at these specific concentrations. The γ-phase of Al₂O₃ is of particular interest because of its high surface area, thermal stability, and moisture-adsorption capability^21,22, which can support combustion stability in ethanol-containing fuels. At the same time, keeping nanoparticle levels low helps avoid issues such as agglomeration, increased viscosity, and potential health or environmental concerns^23,24.

To address these gaps, this study makes two primary contributions. First, it provides a focused investigation of the catalytic effects of γ-Al₂O₃ nanoparticles at ultra-low concentrations (10–30 ppm), leveraging the thermal bridge effect while maintaining stability for ethanol-containing SI engine fuels. Second, it presents the first multi-objective optimization of γ-Al₂O₃ in gasoline-based fuels using a D-optimal RSM framework, enabling a quantitative assessment of performance–emission trade-offs under environmental and economic constraints for potential industrial application.

Materials and sample preparation

The gasoline used in this study is a commercially available fuel obtained from local filling stations. Bioethanol with a volumetric purity of 99.8% was employed as the oxygenated additive. The key physicochemical properties of the gasoline and bioethanol are presented in Table 1. The γ-Al₂O₃ nanoparticles, with a purity of 99.5%, were selected for this investigation based on their high surface area, thermal stability, and moisture adsorption capacity, as detailed in Table 2. These characteristics are utilized to stabilize the ethanol-blended fuels and mitigate degradation phenomena typically associated with such mixtures. Furthermore, the catalytic activity and heat transfer properties of the γ-Al₂O₃ nanoparticles are intended to enhance combustion efficiency under the investigated engine operating conditions²⁵.

Table 1.

The physical and chemical characteristics of the gasoline and bioethanol used in this study.

Specifications	Unit	Gasoline	Bioethanol
Chemical symbol	-	CxHy	C2H5OH
Molecular weight	g/mol	-	46.01
Density at 16 °C	Kg/m3	747.5	785
Specific Gravity	g/ml	0.713	0.98
Octane Index (MON)	-	83.6	-
Octane Index (RON)	-	87.3	109
Octane Index (AKI)	-	85.45	-
Flash point	°C	-43	13
Lower heating value	MJ/kg	43.5	26.8
Latent heat of vaporization	kJ/kg	350	854

Table 2.

Physicochemical properties of γ-Al₂O₃ nanoparticles.

Specifications	Unit	Values
Structure	-	Gamma (γ)
Type	-	Powder
Average particle size	nm	20
Morphology	-	Almost spherical
Density	Kg/m3	3.97
Specific surface area	m2/g	85.45
Melting point	°C	2040
Boiling point	°C	2980

Engine and experimental set-up

Experiments were conducted on a production four-cylinder SI engine (model XU7JP/L3). The geometric and performance specifications of the engine are listed in Table 3.

Table 3.

Technical specifications of the engine.

Parameter	Details
Engine type	Spark-ignition, 4-cylinder
Engine model	XU7JP/L3
Displacement	1761 cm3
Bore × Stroke	83 mm × 81.4 mm
Compression ratio	9.25:1
Number of valves	8 (2 per cylinder)
Maximum power	74.57 kW @ 6000 rpm
Maximum torque	153 N.m @ 3000 rpm
Fuel system	Multi-point fuel injection (MPFI)
Cooling system	Water-cooled (with cooling tower)

A cooling tower was integrated into the test facility to regulate system temperatures, and an oil temperature sensor was utilized to ensure the lubricant temperature remained below 95 °C. Engine torque and power were measured using a 130 kW eddy current dynamometer mechanically coupled to the engine. The dynamometer was operated via a control panel and computer interface (Fig. 1a). The test bed components, including the control panel, engine-dynamometer coupling, emission analyzer, and fuel measurement system, are shown in Fig. 1b and f. Exhaust emissions were quantified using a CAP 3200 gas analyzer (Fig. 1e). Fuel consumption was recorded using a gravimetric measurement system (Fig. 1f). The operating ranges and sensitivities of the instrumentation are detailed in Table 4.

Fig. 1.

Experimental setup: (a) schematic diagram of the engine and instrumentation; (b) overview of the engine and dynamometer test bed; (c) control panel and data acquisition system; (d) engine-dynamometer coupling and torque sensor; (e) exhaust gas emission analyzer; and (f) fuel tank and consumption measurement system.

Table 4.

List of measurement systems, operating ranges, and sensitivities.

Measurement system	Parameter	Operating range	Sensitivity / Resolution
Eddy current dynamometer	Torque	0–600 N.m	0.1 N.m
Magnetic pickup sensor	Engine speed	0–7000 rpm	1 rpm
Gravimetric fuel flow meter	Fuel consumption	1000–20000 g/hr	0.1 g/hr
Capelec CAP 3200 (NDIR)	CO / CO2	0–15% / 0–20% vol.	0.01% / 0.1% vol.
Capelec CAP 3200 (Electrochemical)	NOx	0–5000 ppm	1 ppm
Capelec CAP 3200 (FID)	HC	0–10,000 ppm	1 ppm
K-type thermocouples	Temperature	0–1000 °C	0.1 °C

Fuel preparation and experimental procedure

Experiments were conducted at an ambient laboratory temperature of 25 °C. The base fuel consisted of 10% (v/v) bioethanol and 90% commercial gasoline. Blends were prepared in 1 L batches to accommodate the capacity limits of the ultrasonic homogenizer. Solid nanoparticle volumetric displacement was accounted for during dosing to ensure concentration accuracy.

The nanoparticle-fuel blending procedure is outlined in Fig. 2. γ-Al₂O₃ nanoparticles (Fig. 2a) were added at concentrations of 10, 20, and 30 ppm (10, 20, and 30 mg/L, respectively). Nanoparticles were initially dispersed in the bioethanol fraction (Fig. 2b) using a probe ultrasonic homogenizer (Bandelin SONOPULS HD 3200) for 20 min (Fig. 2c). Following visual verification of suspension stability (Fig. 2d), the mixture was blended with gasoline (Fig. 2e). The complete formulation was homogenized using a magnetic stirrer (IKA C-MAG HS 7) for 30 min (Fig. 2f). The final blends were stored under static conditions for 24 h (Fig. 2g). Visual inspection confirmed no sedimentation, verifying the colloidal stability of the fuels.

Fig. 2.

Sequential stages of nano-fuel preparation: (a) γ-Al₂O₃ nanoparticles, (b) bioethanol, (c) ultrasonic homogenization, (d) nanoparticle-bioethanol suspension, (e) addition to gasoline, (f) magnetic stirring, and (g) final stable E10 nano-fuel blends.

Prepared batches were aggregated to meet the total volume required for engine testing. Trials were executed at wide-open throttle across four engine speeds: 1500, 2000, 2500, and 3000 rpm. Upon reaching steady-state operation, brake torque (BT), brake thermal efficiency (BTE), brake specific fuel consumption (BSFC), and exhaust gas emissions were measured for subsequent analysis.

Statistical analysis and model construction

A D-optimal experimental design was implemented using Design-Expert^® software (version 11.0). This approach was utilized to minimize the determinant of the covariance matrix of estimated parameters (D-criterion), thereby maximizing data acquisition from a limited number of experimental runs²⁵. The D-optimal method accommodates the bounded ranges of the independent variables—engine speed and nanoparticle concentration—providing precise parameter estimates suitable for the constrained experimental domain compared to conventional factorial or central composite designs²⁶. Consequently, this design enabled significant reductions in experimental time and cost while maintaining high model accuracy and predictive reliability^27,28.

For regression analysis, actual experimental variables () were transformed into dimensionless coded values () using Eq. (1):

1

where x̅ denotes the average of the actual variable, and d is the step size (the absolute difference between levels). The response variable (Y) was modeled as a function of the coded variables via multiple regression utilizing the least squares method, based on a second-order polynomial expression (Eq. (2)):

2

In this formulation, Y represents the predicted response, n is the number of factors, and X_i and X_j denote the independent coded variables. The coefficients β₀, β_i, β_ii, and β_ij correspond to the intercept, linear, quadratic, and interaction terms, respectively. For this study, X₁ correspond to engine speed (rpm) and X₂ represents nanoparticle concentration (ppm).

Regression model adequacy was evaluated using statistical indicators. Term significance was established using p-values, with criteria set at p < 0.05. Lack-of-fit tests were executed to verify model assumptions. Predictive reliability and optimal polynomial model selection were validated using the coefficient of determination (R²), adjusted R², predicted R², and the coefficient of variation (CV). The experimental factor levels and variable coding framework are summarized in Table 5.

Table 5.

The independent variables used for response surface modeling, showing both their actual and coded values.

Variable	Type	Level
		Actual	Coded
Engine speed (rpm)	X 1	1500	-1
		2000	− 0.333
		2500	0.333
		3000	1
Concentration of nanoparticles (ppm)	X 2	0	-1
		10	− 0.333
		20	0.333
		30	1

Error analysis

An uncertainty analysis was performed to quantify potential deviations between measured and true values, accounting for both instrument precision and measurement resolution. Instrument accuracies and their corresponding relative uncertainties, based on manufacturer specifications, are detailed in Table 6. Directly measured parameters were recorded in triplicate to ensure data reliability. The combined standard uncertainty (u_c) was calculated via the Root Sum of Squares (RSS) method²⁹, integrating the instrument accuracy (u_inst) and the standard deviation of the repeated measurements (u_rep):

3

Table 6.

Measurement parameters, their operating ranges, instrument accuracies, and associated percentage uncertainties used in the experimental setup.

Measurements	Operating range	Instrument accuracy )	Relative uncertainty (%)
Engine speed (rpm)	0-7000	1	0.13
Engine load (N.m)	0-600	0.01	1.5
Fuel flow measurement (g/hr)	1000–20,000	0.2%	0.20
Time (s)	-	0.1	-
Temperature (°C)	-	1	-
BT (N.m)	-	-	1.5
BTE (%)	-	-	0.47
BSFC (g/kW.hr)	-	-	0.47
CO2 (% vol.)	0–20	0.1	1.97
CO (% vol.)	0–15	0.01	4.5
HC (ppm)	0-10000	1	1.72
NOx (ppm)	0-5000	1	0.36

For derived parameters, including BTE and BSFC, uncertainties were evaluated using the Gaussian law of error propagation³⁰. For a derived variable R dependent on independent variables (V₁, V₂, …, V_n), the total propagated uncertainty (U_R) is determined by:

4

where u_i denotes the uncertainty of the individual independent variables. Accordingly, the uncertainty for BSFC was propagated from the measured uncertainties of the fuel flow rate and brake power. Detailed numerical procedures and statistical analyses for the repeated trials are documented in Appendices A.1, A.2, A.3, A.4, and the total combined uncertainties are compiled in Table 6³¹.

Appendix A.1.

Repeated measurements of fuel flow rate (g/hr).

Engine speed (rpm)	Test 1	Test 2	Test 3	Mean	SD
1500	3870	3845	3856	3857	12.7
2000	5258	5241	5250	5249.8	8.7
2500	7195	7183	7191	7189.6	6.0
3000	8543	8557	8552	8550.9	7.0

Appendix A.2.

Repeated measurement of Brake Power (kW).

Engine speed (rpm)	Test 1	Test 2	Test 3	Mean	SD
1500	16.65	16.72	16.68	16.68	0.036
2000	22.34	22.38	22.36	22.36	0.021
2500	29.20	29.26	29.23	29.23	0.030
3000	34.32	34.36	34.34	34.34	0.021

Appendix A.3.

Repeated measurements of Brake Thermal Efficiency (%).

Engine speed (rpm)	Test 1	Test 2	Test 3	Mean	SD
1500	37.15	37.23	37.25	37.21	0.05
2000	36.5	36.71	36.8	36.67	0.15
2500	34.8	35.1	35.4	35.1	0.3
3000	34.3	34.65	34.82	34.59	0.27

Appendix A.4.

Summary of relative uncertainty values (%) for calculated parameters.

Engine speed (rpm)	Relative uncertainty of fuel flow (%)	Relative uncertainty of BP (%)	Relative uncertainty of BTE (%)	Relative uncertainty of BSFC (%)
1500	0.20	0.52	0.56	0.55
2000	0.20	0.07	0.21	0.22
2500	0.20	0.85	0.87	0.88
3000	0.20	0.14	0.24	0.25
Mean	—	0.4	0.47	0.47

The final dataset, bounded by these uncertainty estimates, was utilized in the Design-Expert^® software environment to construct regression models and determine the optimal operating conditions for the nanoparticle-enhanced fuel blends.

Results and discussion

Prior to each experimental run, the fuel system underwent thorough flushing to purge residual mixtures, thereby mitigating any potential cross-contamination between tests. To ensure statistical reliability, all experiments were executed in triplicate under consistent operating conditions; consequently, the data presented in Table 7 reflect the arithmetic mean of these repeated trials.

Table 7.

Experimental conditions and corresponding results for engine performance and exhaust emissions. Each value represents the average of three repeated trials conducted under steady-state operation at wide-open throttle.

Variable			Response
			Engine performance			Emissions
Run	Speed (rpm)	Concentration (ppm)	BT (N.m)	BTE (%)	BSFC (g/kW.hr)	CO2 (%Vol.)	CO (%Vol.)	HC (ppm)	NOx (ppm)
1	1500	0	106.46	37.03	232.4	9.1	3.03	178	739
2	1500	0	106.31	37.21	231.3	8.8	2.87	182	743
3	2000	0	106.82	34.59	234.7	9.5	3.46	175	791
4	2500	0	111.73	36.67	245.2	10.8	3.21	163	789
5	3000	0	109.38	35.1	248.8	11.4	3.83	137	814
6	1500	10	111.63	37.38	230.2	9.2	2.63	177	822
7	2000	10	111.87	36.59	235.2	9.6	3.2	170	869
8	3000	10	115.75	35.44	242.8	11.3	3.26	128	922
9	1500	20	112.45	38.15	225.6	9.3	2.76	178	849
10	2000	20	113.06	36.36	230.3	9.8	3.35	173	897
11	2500	20	118.12	37.37	236.7	11.3	3.04	159	889
12	3000	20	117.08	36.76	234.1	11.6	3.42	130	953
13	1500	30	112.27	37.98	226.6	9.1	2.75	179	843
14	1500	30	112.2	35.66	226	9.2	2.82	180	841
15	2000	30	112.06	36.13	233.4	9.5	3.46	173	857
16	2500	30	116.81	36.04	241.3	11.1	3.37	166	840
17	3000	30	115.03	38.08	238.2	11.2	4.03	143	911
18	3000	30	115.12	36.87	238.8	11.4	4.12	139	907

The acquired experimental dataset was processed via Design-Expert software to formulate regression models elucidating the dependencies of performance metrics and exhaust emissions on engine speed and nanoparticle concentration. These predictive models were subsequently utilized to determine the optimal operational parameters for the γ-Al₂O₃–E10 fuel blends. The ensuing subsections delineate the statistical validation of model adequacy, encompassing the analysis of variance (ANOVA), followed by a comprehensive evaluation of the engine’s performance and emission characteristics.

The engine performance results

Brake torque (BT)

As depicted in the 3D response surface contours (Fig. 3a) and mathematically articulated in Eq. (5), the interaction between engine speed (X₁) and nanoparticle concentration (X₂) exhibits a pronounced non-linear relationship.

5

Fig. 3.

Response surface 3D plots illustrating the interactive effects of engine speed (X₁) and γ-Al₂O₃ nanoparticle concentration (X₂) on engine performance: (a) BT, (b) BTE, and (c) BSFC.

To adequately capture the observed reduction in torque at elevated rotational speeds, the regression model incorporates quadratic and cubic terms, specifically X₁² and X₁³. This degradation in torque output, consistent with findings reported by^12,32, primarily stems from a deterioration in volumetric efficiency coupled with an exacerbation of mechanical frictional losses. Experimental results yielded a maximum BT of 118.12 N.m under the operating conditions of 2500 rpm and a 20 ppm dosage of γ-Al₂O₃, representing a substantial 7.67% enhancement relative to the baseline E10 fuel. Such an improvement aligns with the enhanced burning velocities documented by³³ and is fundamentally driven by elevated in-cylinder pressures combined with a robust energy release phase, which collectively augment the Indicated Mean Effective Pressure (IMEP)^17,18.

Beyond the alterations in combustion dynamics, the incorporation of nanoparticles at the 20 ppm threshold facilitates the formation of a protective tribological film^34–36. This localized mending effect effectively mitigates parasitic frictional losses between the piston rings and the cylinder liner³⁴. Conversely, increasing the nanoparticle loading beyond 20 ppm yields a plateau in performance, subsequently followed by a notable decline. This phenomenon is likely attributable to nanoparticle agglomeration; the progressive clustering of particles increases the kinematic viscosity of the fuel blend, thereby interfering with the atomization process and spray momentum^37–40. Consequently, these agglomerated formations disrupt optimal combustion phasing and diminish torque output, a behavioral trend that corroborates observations in concurrent nanofuel investigations^39,40.

The statistical robustness of the applied regression analysis is corroborated by the model selection criteria summarized in Table 8. Furthermore, the estimated coefficients and goodness-of-fit metrics, derived via the least-squares method, are detailed in Table 9. To ensure methodological consistency and analytical reliability, this identical modeling framework was systematically applied to the evaluation of all subsequent engine performance parameters.

Table 8.

Analysis of variance (ANOVA) results for the response surface model predicting BT as a function of engine speed and  γ−Al₂O₃ nanoparticle concentration.

Model	Sum of squares	Degree of freedom	Mean square	F-value	p value Prob > F
Mean vs. total	2.276E + 05	1	2.276E + 05
Linear vs. mean	149.88	2	74.94	17.50	0.0001
2FI vs. linear	0.6712	1	0.6712	0.1478	0.7064
Quadratic vs. 2FI	39.81	2	19.90	10.05	0.0027
Cubic vs. quadratic	23.57	4	5.89	240.12	< 0.0001 (Suggested)
Quartic vs. Cubic	0.1234	3	0.0411	2.82	0.1465
Residual	0.0729	5	0.0146
Total	2.278E + 05	18	12657.52

Table 9.

Least-squares regression coefficients and statistical parameters for the response surface model of BT as a function of engine speed and γ-Al₂O₃ nanoparticle concentration.

Source	Sum of squares	Degree of freedom	Mean square	F-value	p value Prob > F
Model	213.92	9	23.77	968.76	< 0.0001 (significant)
X 1	38.88	1	38.88	1584.69	< 0.0001
X 2	0.7571	1	0.7571	30.86	0.0005
X 1 X 2	0.0076	1	0.0076	0.3083	0.5939
X 1 2	3.95	1	3.95	160.80	< 0.0001
X 2 2	45.54	1	45.54	1855.89	< 0.0001
X12X2	0.2171	1	0.2171	8.85	0.0177
X1X22	1.35	1	1.35	55.13	< 0.0001
X 1 3	22.28	1	22.28	908.00	< 0.0001
X 2 3	0.9490	1	0.9490	38.68	0.0003
Residual	0.1963	8	0.0245
Cor total	214.12	17

Brake thermal efficiency (BTE)

As illustrated in Fig. 3b, the Brake Thermal Efficiency (BTE) variations across the tested fuels indicate that the 20 ppm γ-Al₂O₃ blend achieved a maximum efficiency of 38.15% at 1500 rpm. Relative to the baseline E10 fuel, this constitutes a 3.02% enhancement, a trend mathematically captured by the complex variable interactions delineated in Eq. (6):

6

Within the established regression model, the negative higher-order terms corresponding to nanoparticle concentration (− 0.492 × ₂² and − 1.12 × ₂³) substantiate the Law of Diminishing Returns observed as the dosage approaches 30 ppm^41,42. Furthermore, the non-linear interaction between engine speed and nanoparticle concentration is accurately represented by the model’s coupling terms, specifically 0.459 × ₁² × ₂, which indicates that the efficacy of the nano-additive is fundamentally contingent upon rotational speed.

Mechanistically, this improvement in thermal efficiency primarily stems from the capacity of the nanoparticles to mitigate the evaporative cooling penalty inherently associated with ethanol^43,44. Although the high latent heat of vaporization of ethanol typically prolongs the ignition delay (ID) period, the superior thermal conductivity characteristic of γ-Al₂O₃ facilitates an accelerated heat flux throughout the combustible mixture. Consequently, this promotes rapid vaporization and shortens the ID, an observation that aligns with the literature^45–47. As a direct result, a larger fraction of the fuel-air charge is consumed during the premixed combustion phase, thereby effectively elevating the Heat Release Rate (HRR).

An additional contributing factor to these efficiency gains is the micro-explosion phenomenon. In this context, the suspended nanoparticles function as nucleation sites, triggering the abrupt internal vaporization of ethanol within the individual fuel droplets⁴⁸. This disruptive process yields secondary atomization and substantially enhanced fuel dispersion. Such improved atomization characteristics become particularly vital at elevated engine speeds (2500–3000 rpm), where the time window available for complete oxidation is strictly constrained and fine spray characteristics are a necessity⁴⁹. Conversely, increasing the nanoparticle dosage beyond the 20 ppm optimum resulted in a performance plateau rather than yielding marginal gains. This behavior is likely due to the fact that high nanoparticle loadings promote particle agglomeration, which subsequently reduces the effective surface area and compromises spray quality. This phenomenon represents a classic case of diminishing returns, corroborating previous empirical observations in nanofuel research^39,40 and fundamentally validating the negative cubic coefficients derived in the statistical model.

Brake specific fuel consumption (BSFC)

The 3D contours presented in Fig. 3c illustrate a distinct efficiency valley regarding fuel consumption across the evaluated blends. The empirical relationship defining BSFC as a function of engine speed (X₁) and nanoparticle concentration (X₂) is mathematically characterized by the cubic polynomial detailed in Eq. (7):

7

Specifically, at an operational speed of 3000 rpm, the 20 ppm γ-Al₂O₃ formulation facilitated a maximum BSFC reduction of 5.95%. Despite the inherently low Lower Heating Value (LHV) of ethanol, the incorporation of nanoparticles effectively mitigates this baseline energy deficit. This enhancement in fuel conversion efficiency correlates consistently with the energy recovery trends documented in the literature^16,50,51. Mechanistically, by advancing the peak HRR closer to Top Dead Center (TDC), the nano-additives ensure that a substantially greater proportion of the available chemical enthalpy is converted into useful mechanical work^51,52.

While this performance advantage remains relatively marginal under low-turbulence conditions (1500–2000 rpm), it becomes significantly more pronounced at elevated engine speeds. The primary driver for this high-speed efficacy is the enhanced atomization quality, a mechanism corroborated by⁵¹. Conversely, escalating the nanoparticle dosage beyond 30 ppm introduces a distinct fuel consumption penalty. At these elevated concentrations, the augmented fuel viscosity impedes the development of a homogeneous combustible mixture. Consequently, the engine dictates increased fuel input to compensate for the ensuing combustion inefficiencies. This saturation phenomenon, previously identified by^53,54 concerning the deterioration of spray momentum, demonstrates that excessive additive loadings ultimately yield counterproductive outcomes.

Emissions

Carbon dioxide (CO₂)

CO₂ emissions inherently serve as a robust indicator of carbon conversion efficiency within the combustion chamber. As depicted in the 3D response surface plot of Fig. 4a, the simultaneous influence of engine speed and γ-Al₂O₃ concentration substantially dictates this emission profile. The experimental data reveals a maximum CO₂ elevation of 5.68% at an additive loading of 20 ppm and a speed of 1500 rpm; notably, this upward trend persists across higher operational speeds. This behavior is primarily attributed to the synergistic interaction between intensified in-cylinder turbulence and the inherent redox activity of the nanoparticles⁵⁵. Specifically, the γ-Al₂O₃ phase facilitates the provision of localized lattice oxygen, thereby diminishing the activation energy required for carbon oxidation and promoting the generation of highly reactive hydroxyl radicals. The establishment of these catalytic pathways correlates directly with the mechanistic observations reported by⁵⁶, wherein radical-induced oxidation effectively drives the complete conversion of HC fragments into stable CO₂, mitigating the survival of incomplete, partially oxidized intermediates^16,51. The empirical relationship defining how engine speed and nanoparticle concentration govern these emission characteristics is mathematically represented by the regression model in Eq. (8):

8

Fig. 4.

Response surface plots showing the combined effects of engine speed and γ-Al₂O₃ nanoparticle concentration on exhaust emissions: (a) CO₂, (b) CO, (c) HC, and (d) NO_x.

Carbon monoxide (CO)

The influence of engine speed and nanoparticle dosage on CO emissions is graphically depicted in Fig. 4b. Fundamentally, CO serves as a primary indicator of incomplete combustion, representing a fraction of available chemical energy that remains unextracted⁵⁷. The experimental data reveals a general mitigation of CO emissions following the introduction of γ-Al₂O₃ nanoparticles into the base E10 fuel. Notably, the 10 ppm formulation achieved a maximum reduction of 14.88% at 3000 rpm, surpassing the performance of the 20 ppm mixture. This enhanced efficacy at a lower concentration is primarily attributed to superior nanoparticle dispersion within the fuel matrix, which sustains a highly active catalytic surface area^50,53. Furthermore, the nanoparticles supply localized lattice oxygen that facilitates the subsequent oxidation of CO into CO₂, an oxidative mechanism corroborated by the findings of⁵⁸. Within the current experimental matrix, the minimum CO emission levels directly correlated with the operating points demonstrating peak BTE. This inverse relationship suggests that the nanoparticulate additives effectively aid in extracting thermal energy from partially oxidized combustion intermediates^59,60. Conversely, scaling the additive dosage to 30 ppm precipitated an upward trend in CO exhaust fractions. This deterioration in emissions is likely due to localized nanoparticle agglomeration combined with elevated fuel viscosity, factors that collectively hinder optimal spray atomization and exacerbate incomplete combustion phenomena^15,61. The corresponding regression model defining CO emission behavior is detailed in Eq. (9):

9

Unburned hydrocarbons (HC)

As illustrated by the 3D response surface plot in Fig. 4c, a distinct inverse correlation exists between HC emissions, nanoparticle concentration, and engine speed. A maximum emission reduction of 6.57% was achieved at 3000 rpm utilizing the 10 ppm γ-Al₂O₃ blend. This substantive improvement stems from intensified in-cylinder turbulence coupled with elevated combustion chamber wall temperatures; these physical conditions synergistically thin the flame quench layer and promote robust post-combustion oxidation^52,53. Consequently, the nanoparticulate additives facilitate the recovery of chemical enthalpy that would otherwise remain unextracted within unburned fuel fragments, a mechanism corroborated by the findings of^50,62. Conversely, scaling the additive concentration beyond the 20 ppm threshold introduces an adverse combustion penalty. At elevated dosages, nanoparticle agglomeration exacerbates wall wetting phenomena, thereby establishing a localized thermal barrier that impedes the critical heat transfer required for complete HC oxidation^52,63. The empirical regression model governing HC emissions, formulated as a function of engine speed and nanoparticle concentration, is defined in Eq. (10):

10

Nitrogen oxides (NO_x)

The formation of NO_x is fundamentally dictated by the thermal Zeldovich mechanism⁶⁴. As illustrated by the 3D response surface plot in Fig. 3d, a robust positive correlation exists between NO_x emissions and engine speed irrespective of the nanoparticle dosage. Empirical observations indicate a progressive escalation in NO_x levels up to an additive concentration of 20 ppm, where emissions reach a maximum of 645 ppm—constituting a 17.08% surge relative to the E10 baseline. Consistent with established literature, this pronounced increment is a direct thermodynamic manifestation of the inherent BSFC- NO_x trade-off¹⁶, stemming from a curtailed ID⁶⁵ and a more vigorous premixed combustion phase¹⁶, phenomena that collectively drive peak in-cylinder temperatures upward^16,65. Such an inverse relationship between CO and NO_x characteristics remains a pervasive challenge within nanofuel optimization⁵¹. Conversely, escalating the additive concentration to 30 ppm induces a noticeable reduction in NO_x levels, an outcome primarily attributed to a localized thermal quenching effect. At this elevated dosage, nanoparticle agglomeration and augmented fuel viscosity impede the heat release intensity, thereby functioning as a thermal sink that mitigates NO_x generation, albeit at the expense of deteriorated thermal efficiency⁴³. The empirical regression model capturing NO_x emissions as a function of engine speed and nanoparticle concentration is formulated in Eq. (11):

11

Model adequacy evaluation

The predictive capability of the regression models was assessed through a comparison of predicted values to the corresponding experimental measurements, as illustrated in Fig. 5. A strong linear correlation was observed across all performance and emission responses—including BT, BTE, BSFC, and exhaust emissions (CO₂, CO, HC, NO_x). R² ranged from 0.98 to 1, indicating excellent agreement between the observed data and the model’s predicted values. These results confirm the adequacy and robustness of the response surface models in capturing the underlying behavior of the system and validating their reliability for optimization and prediction purposes. The validated regression equations provide robust tools for predicting engine responses under untested conditions. Their high R² values (> 0.98) and low CVs (< 3%) support their use in simulation-based fuel design, performance mapping, and emission trade-off analysis.

Fig. 5.

Predicted versus actual value plots for the developed regression models: (a) BT, (b) BTE, (c) BSFC, (d) CO₂, (e) CO, (f) HC, and (g) NO_x emissions. The strong linear alignment across all responses indicates excellent agreement between model predictions and experimental observations, supporting the models’ accuracy and predictive capability for nanoparticle-enhanced fuel blends.

As illustrated in Fig. 6, four key validation metrics—R², adjusted R², predicted R², and CV—were analyzed to assess model robustness. For all responses, both the R² and adjusted R² values were above 0.97, thereby confirming that the fitted models explain more than 97% of the variability in the experimental data. Additionally, a strong concordance was found between the predicted R² and the adjusted R², confirming the model’s generalization capability and predictive reliability beyond the experimental dataset. Furthermore, the CV for all models remained below 3%, reflecting a high degree of experimental precision and model stability. These validation results affirm the suitability of the developed models as reliable tools for predicting and optimizing trade-offs between engine performance and emissions, as well as for guiding the formulation of bioethanol–gasoline blends containing γ-Al₂O₃ nanoparticles.

Fig. 6.

Statistical performance metrics for the developed regression models, including R², adjusted R², predicted R², and CV for all performance and emission responses. High R² values (all > 0.97) and low CV values (< 3%) confirm strong model fitting, predictive accuracy, and experimental consistency across engine speed and nanoparticle concentration conditions.

Model validation and optimization

The optimization framework aimed to determine the optimal parameters for the independent variables—engine speed and γ-Al₂O₃ nanoparticle concentration—to maximize BT and BTE while concurrently minimizing BSFC and exhaust emissions, including CO₂, CO, HC, and NO_x. During the multi-response optimization, relative weights were assigned to each target parameter; notably, mitigating NO_x emissions was prioritized given its substantial environmental detriment. Table 10 delineates the specific optimization targets and constraints applied to each response, whereas Table 11 presents a summary of the numerical optimization, detailing six distinct candidate solutions. Among these alternatives, Solution 1 demonstrated the most advantageous compromise across all performance and emission metrics, characterized by the lowest standard error. Consequently, the predicted parameters corresponding to Solution 1 were selected as the optimal operating conditions, as this configuration achieved the maximum desirability function. These findings substantiate the utility of RSM in isolating balanced operational regimes that simultaneously augment mechanical output and suppress pollutant formation. The formulated empirical models offer considerable practical utility, enabling the accurate projection of engine performance and emission characteristics based on speed and nanoparticle dosage, thereby reducing the need for exhaustive empirical testing. Ultimately, the capacity of RSM to execute robust multi-objective optimization highlights its critical role in the ongoing development of clean-fuel technologies.

Table 10.

Lower and upper bounds and target objectives for each response variable used in the multi objective optimization process. Higher importance was assigned to NOx reduction due to its environmental impact.

Name	Goal	Lower	Upper	Lower	Upper	Importance
		Limit	Limit	Weight	Weight
Engine speed	Is in range	1500	3000	1	1	3
Concentration of nanoparticles	Is in range	0	30	1	1	3
BT	Maximum	106.31	118.12	1	1	5
BTE	Maximum	6.56	36.76	1	1	5
BSFC	Minimum	225.6	248.8	1	3	3
CO	Minimum	2.63	4.12	1	4	4
CO2	Minimum	8.8	11.6	1	2	2
HC	Minimum	128	182	1	4	4
NOx	Minimum	739	953	1	5	5

Table 11.

Optimal operating conditions and predicted responses for engine performance and exhaust emissions determined using RSM. Among the obtained solutions, Solution 1 achieved the highest composite desirability, representing the best trade-off between performance enhancement and emission reduction.

Solution	X1	X2	BT	BTE	BSFC	CO2	CO	HC	NOx	Desirability
1	2430.598	5.28	114.823	35.311	243.556	10.741	2.929	161.022	834.42	0.144 (Selected)
2	1500	6.98	110.419	37.04	232.412	9.062	2.7	177.473	800.49	0.127
3	1500	6.74	110.322	37.028	232.483	9.056	2.704	177.502	798.773	0.127
4	2480.389	25.81	117.39	36.273	237.33	11.166	3.235	163.105	870.345	0.105

Study limitations and future perspectives

The present investigation is subject to several limitations that delineate critical avenues for future research:

• Short test duration: The empirical evaluations were conducted over a one-month testing period. Although sufficient for establishing baseline performance and emission trends, this timeframe precludes a comprehensive assessment of long-term component wear and cumulative carbon deposit formation. Future investigations should incorporate extended endurance cycles to adequately evaluate engine longevity.

• Fixed engine settings: Experimental protocols were executed utilizing baseline factory calibrations for ignition timing and fuel injection. Consequently, the reported data reflects engine behavior exclusively within these predefined maps; the optimization of dynamic parameter tuning was beyond the scope of this study.

• Nanofluid stability: Although ultrasonic dispersion facilitated initial homogeneity, sustaining a uniform colloidal suspension at nanoparticle concentrations of 10–30 ppm over extended periods poses a distinct technical challenge. Translating these findings to practical applications necessitates rigorous characterization of long-term stability beyond the temporal testing window utilized herein.

• Scope of emission analysis: The current emissions characterization was restricted to gaseous pollutants, specifically CO, HC, and NO_x. The quantification of Particulate Matter (PM) was not undertaken in this phase and remains an imperative objective for subsequent environmental assessments.

• Steady-state focus: Data acquisition was strictly confined to steady-state loads and engine speeds. Given that real-world driving scenarios encompass transient cycles and rapid load variations, dynamic engine performance may deviate from the steady-state metrics documented in this work.

• Economic feasibility: The scope of this study was inherently confined to technical performance, omitting industrial-scale economic evaluations. A comprehensive cost-benefit analysis, accounting for nanoparticle synthesis and the energy penalty associated with mixing, is required prior to commercial deployment.

Conclusion

This study evaluated the addition of γ-Al₂O₃ nanoparticles to optimize the performance and emission characteristics of a SI engine operating on an E10 fuel blend. Experimental data was coupled with an RSM-based multi-objective approach to identify optimal operating parameters. The main findings are summarized below:

• Performance and Fuel Economy: At a concentration of 20 ppm, BT and BTE improved by maximums of 7.67% and 3.02%, respectively. These gains are attributed to a tribological mending effect on reciprocating parts and an increase in peak in-cylinder pressure. BSFC decreased by up to 5.95% at 3000 rpm. The nanoparticles acted as a thermal bridge, shifting heat release closer to TDC to offset ethanol’s latent heat penalty, while micro-explosions helped maintain combustion quality at higher speeds.

• Emission Characteristics: Exhaust analysis indicated that a 10 ppm dosage was the most effective for toxic emission mitigation. CO and HC levels dropped by 14.88% and 6.57%, respectively, while CO₂ increased by 5.68%. These trends suggest that lower nanoparticle concentrations facilitate more complete oxidation and avoid the combustion degradation associated with agglomeration at higher doses.

• Model Reliability and Optimization: The regression models demonstrated strong agreement with the experimental data, yielding R² > 0.97 and a CV of < 3% for all measured responses. Multi-objective optimization identified 2471.87 rpm and a 5.88 ppm nanoparticle concentration as the ideal operating point to maximize engine performance while keeping NO_x formation and additive costs at their lowest limits.

• Future Outlook: Practical industrial application of this fuel modification depends on resolving the long-term colloidal stability of the blends. Future research should prioritize characterizing the structural morphology of PM emissions and assessing the long-term tribological effects of γ-Al₂O₃ on component wear during extended durability testing.

Nanoparticle

γ-Al₂O₃

Gamma-aluminum oxide

Engine and fuel parameters

BT

Brake torque (N.m)

BTE

Brake thermal efficiency (%)

BSFC

Brake specific fuel consumption (g/kW.hr)

E10

Gasoline with 10% bioethanol by volume

Pollutants

CO

Carbon monoxide emissions (ppm)

CO₂

Carbon dioxide emissions (ppm)

HC

Unburned hydrocarbon emissions (ppm)

NO_x

Nitrogen oxides emissions (ppm)

Abbreviations

SI

Spark-ignition

rpm

Revolutions per minute

ppm

Parts per million

RSM

Response surface methodology

MPFI

Multi-point fuel injection

IMEP

Indicated mean effective pressure

ID

Ignition delay

HRR

Heat release rate

LHV

Lower heating value

TDC

Top dead center

PM

Particulate matter

Subscripts

i

Index of independent variables

j

Index of independent variables (distinct from i)

Statistical and modeling parameters

Y

Response (dependent) variable

Coded value of a variable for analysis

Actual (measured) value before coding

X₁

Coded value of engine speed

X₂

Coded value of nanoparticle concentration

X̄

Sample mean; average of data points

Intercept (constant term in regression)

Linear regression coefficients

Quadratic regression coefficients

Interaction regression coefficients

R²

Coefficient of determination

Adj. R²

Adjusted coefficient of determination

Pred. R²

Predicted coefficient of determination

ANOVA

Analysis of variance

CV

Coefficient of variation (%)

d

Absolute difference or standardized effect size

D-criterion

Design criterion maximizing determinant of information matrix

SD

Standard deviation

RSS

Root sum of squares

GUM

Guide to the expression of uncertainty in measurement

U_c

Combined standard uncertainty

U_inst

Instrument accuracy/uncertainty

U_rep

Standard deviation of repeated measurements

U_R

Total propagated uncertainty

R

A function of independent variables

V_i

Independent variables

U_i

Uncertainty of each independent variable

Author contributions

R.E.B., M.N.K., F.O., and K.M. contributed to the conceptualization, methodology, validation, and writing of the review and editing of the manuscript. R.E.B. and M.N.K. performed the formal analysis, investigation, data curation, and visualization. R.E.B. also handled the software and project administration. F.O. and K.M. provided resources and supervision. F.O. and K.M. were responsible for the project administration. R.E.B. prepared the original draft. All authors read, reviewed, and approved the final manuscript.

Data availability

The datasets generated and analysed during the current study are fully included within the published article, specifically in Table 5. All data necessary to support the findings of this study are available within the article. Any further inquiries concerning data availability should be directed to the corresponding author, Dr Ramtin Elkaei Behjati.

Declarations

Competing interests

The authors declare no competing interests.