Introduction

Fuel has always been a critical driver of the global economy. Nevertheless, the huge dependence of various industries, particularly the logistics, on fossil fuel and its by-products has brought us to the edge of their depletion. This reliance raises concerns about the negative impacts, including pollution and contributions to global warming through fuel emissions. Consequently, there’s an urgent need to establish a robust framework to measure these harmful emissions. Addressing this challenge involves initiatives aimed at developing alternative fuel sources. Recent trends have witnessed a significant upsurge in Bio-fuel research due to its diverse advantages. Beyond reduced emission levels, the ease of manufacturing presents another notable benefit. Various methodologies are being utilized to improve Bio-fuel efficiency and identify the most suitable blends of fossil fuels. Predictive modeling by AI-ML (Artificial Intelligence-Machine Learning) of engine emissions plays a pivotal role in the quest for the optimal fuel blend. Predictive modeling encompasses generating outcomes through statistical methods and principles of probability. To yield accurate results, this approach necessitates specific input data. The accuracy of a prediction increases with the quantity of test data supplied to the model. The precision of a prediction is a key aspect of determining the model’s precision. Additionally, this paper delves into recent technological innovations in the realm of Machine Learning, which synergizes with AI to create a successful precise and concise model.

Ghobadian et al.1 constructed an ANN trialed model aimed at focusing on the performance and engine emissions as the output with waste vegetable cooking oil based biofuel. The experimental procedure initiated with the production of biofuel after gathering used vegetable cooking oil. This biofuel was introduced to a 2 cylinder diesel engine with emissions and performance parameters were recorded and computed. Diverse blends of biofuels were formulated, with each blend undergoing the same standardized testing protocol. This method generated a substantial volume of data utilized for training the ANN. Following the creation and evaluation of the model, the outcomes demonstrated that the back-propagation algorithm effectively predicted performance parameters. The calculated RMSE root mean error approached 0.0004, closely resembling the ideal value, indicating the accuracy of the predictions made.

Azeez et al.2 employed an enhanced artificial neural network model for estimating the carbon monoxide (CO) emissions and creating daily restricted maps of a specific area. The exhaust data used in this research originated from the traffic vehicles operating in the designated ___location. The study introduced hybrid models that integrated data mining and Geospatial Information System (GIS) with a focus on designing, analyzing, and storing various spatial data, etc. In addition, the prediction maps were generated to facilitate the analysis of localized CO emission levels. The model achieved an impressive accuracy rate of 86%, making it a valuable tool for monitoring localized emission predictions from daily traffic vehicles. This model proves highly beneficial in understanding emission patterns, especially when emissions peak, offering valuable insights into harmful emissions’ temporal trends. In 2013, a similar approach was adopted3, yielding the predictions for a turbocharged engine, encompassing both performance analysis and engine emissions. Similar ANN models were used by various researchers for predicting the performance and emission spectrums4,5,6.

Uslu et al.7 employed an ANN technique for evaluating the brake power and torque of a SI engine. The research highlighted the scarcity of information concerning the use of iso-amyl alcohol-based fuel. Test rigs were used in experiments to gather exhaust spectrum. Data sets were constructed using altering specific input data, such as throttle, speed, and adjustments in the CR (compression ratio). This dataset was further utilized to train the ANN. For the refinement of the ANN model’s performance, they utilized Response Surface Methodology (RSM). The determined correlation factor ranged from 0.94 to 0.99.

Multiple methods, including modeling and simulation, have been employed to estimate diesel engine emissions, broadly sorted for 4 categories: (1) PM and NOxsensor calibration8 ; (2) MAP (Mean average precision) -based look-up methods9 ; (3) 0 (or) 3 dimensional modeling10 ; (4) data-driven ML prediction techniques11. Radio frequency sensors were also appended by researchers to monitor the DPF (Diesel Particulate Filter), leading to enhanced DPF durability and reduced SFC12.

Nevertheless, sensor measurement techniques face challenges such as high expenses and complex structures13,14. The commonly used MAP method requires extensive calibration and significant experimental resources, particularly for obtaining precise emission characteristics during transient operations15. While modeling methods effectively reduce research time and expenses, they necessitate a deep understanding of complex theories, demanding high expertise from researchers and equipment. Among these methods, data-driven ML approaches have attracted interest owing to benefits: shorter computation time reduced cost, high predictive accuracy, and robustness16,17.

This involves using diverse machine learning algorithms to create opaque models for predicting diesel engine emissions without considering operational mechanisms18. Machine learning methods provide a balanced trade-off between model accuracy and computational resources during the modeling process, significantly simplifying the complexity of emission prediction19. Machine learning techniques have found widespread application across diverse domains, including autonomous driving19, electric vehicle charging prediction20, language processing21,22, face recognition23, and traffic flow forecasting24. Sangharatna et al.25 utilized the neural networks (NN) to diagnose faults by detecting and diagnosing engine component status through fault-related signals. Machine learning has been employed to predict diesel emissions since Atkinson26 developed a NN based prediction model in 1998. Due to the non-linear fitting and generalization capabilities of machine learning methods, they simplify efficient engine optimization16, leading to increasing interest from researchers. Table 1presents an extensive review of literature on the performance and emissions in engine characteristics (not limited to diesel engines) using ML techniques. Early studies mainly relied on data collected from lab engine operations during stable conditions, with the ANN algorithm being predominant26,27,28. Tables 2 and 3 indicate the significance of bowl geometries and nano additives in engine characteristics respectively.

Table 1 Overview of model used along with test dataset values.
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Table 2 Overview of various bowl geometries and their significances35,36,37,38,39,40
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Table 3 Overview of a variety of nano additives and their influence on characteristics of engine41,42,43,44,45,46,47
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The fuel spray characteristics study is also gaining prominence in recent years as it considers various key factors such that could alter the primary jet formation and atomization process48. With higher fuel density, the impinging inertia is improved drastically which could slow down the spray velocity along with higher surface tension which induces cohesive forces and larger Sauter Mean Diameter (SMD) of fuel droplets49. Some studies also reveals that, higher fuel viscosity has significant effect on hampering the aerodynamic thrust of the fuel surface and could cause much dawdle in break-up of fuel spray48. Highly viscous fuels such as B50 and above could eventually result in higher surface tension and become tough to break up on interaction with air/gas followed by higher STP, lowered SCA and increased SMD50. In general, biofuels were blended with volatile fuels to improve the spray properties51. Geng et al.52 found that pure biofuel had a 33.59% higher smoke point (STP) and a 33.08% larger droplet size (SMD) compared to diesel (B0). The addition of 30% ethanol to biodiesel resulted in a substantial decrease in its kinematic viscosity and surface tension, leading to a notable improvement in the spray breakup. Hence, the B70E30 exhibited a decrease of 22.05% in its STP and a decrease of 20.88% in its SMD, when compared to B100. Multiple studies have shown that biodiesel has ↑STP, ↓SCA, ↑SMD, and less velocity of fuel injection with respect to mineral diesel53,54. For instance, Raghu et al.55 examined spray properties of biofuels and verified that biofuels have ↑STP and ↓SCA compared to diesel55.

Novelty of the current research

In spite of several investigations delved into alternative fuel with machine learning, this particular study aims to explore quaternary fuel as the primary fuel doped with nano particle with various bowl geometries. With limited prior research delving into the combination of biofuel and nano additives, key focus of present work is to analyze the impact of introducing the nano biofuel in various bowl geometries on diesel engine behavior and performance. Apart from standard hemispherical bowl, toroidal, shallow depth and toroidal re-entrant profiles were evaluated. The gathered data underwent analysis using a machine learning approach that utilized the Long Short-Term Memory (LSTM) model within an artificial neural network framework across various engine loading conditions. Also, using Diesel-RK combustion simulation software, the fuel spray characteristics were studied for various bowl profiles and the results were compared.

Materials and methods

Test fuel preparation

The test fuel employed for the current experimentation is a quaternary blend of diesel/biodiesel/vegetable oil/pentanol and termed as DBOP blend. The DBOP blend is comprised of 50% diesel (vol%) + 5% biodiesel (vol%) + 5% vegetable oil (vol%) + 40% (vol%) pentanol. This combination is selected based on fuel properties and experimentation from previously published data56. DBOPN is prepared by blending 20ppm TiO2 nano additives with DBOP blend. TiO2 nano additives were chosen as specific additive due to its improved oxidation at higher cylinder temperatures so that it can acts as a buffer O2 for promoting oxidation. Also, the 20ppm concentration is opted based on experimentation and fuel property analysis. The blends were initially prepared using magnetic stirrer followed by ultrasonication. The blends were then checked for stability. The blends were initially found to be stable for 48 h. Then, surfactant Span80 + Tween 20 was added to the blend at concentration of 5 mg/L. After this, the blends were found to be stable for more than 120 h. The fuel properties of the test fuel blend, physio-chemical properties and properties of test fuel blends were displayed in Tables 4, 5 and 6. The above blend has been chosen owing to the fact that it has highest Brake thermal efficiency than other blend concentrations, lowered BSFC, HC, CO and Smoke opacity (indicated by Ref56). However, the NOx profile of DBOP40 is higher for which the current work employs the usage of various bowl geometries and nano additives and their influence is studied and validated by LSTM (Long Short Term Memory) machine learning algorithm.

Table 4 Physical properties of diesel, Jatropha vegetable oil and Jatropha biodiesel (Data sourced from56).
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Table 5 Physio-chemical properties of test fuels (Data sourced from56).
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Table 6 Properties of fuel blends with nano particle.
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Nanoparticle preparation and characterization

First, the precursor ingredient, titanium tetraisopropoxide, is neutralised with ethanol, hydrochloric acid, and deionised water. This was followed by thirty minutes of vigorous stirring to lower the pH of the liquid to 1.5. The pH level was then raised to six after two hours of continuous stirring and the addition of 10 mL of deionised water at room temperature. Once another titration with demonized water was completed, cladigel was produced; its pH was 8. Next, for a whole day at 150 °C, the cladigel was dried and calcined. TiO2 nanoparticles were finally produced by heating the dried samples to 300 °C for two hours. The manufactured TiO2 nanoparticles’ physical properties are described in more detail in Table 7.

Table 7 TiO2 nano particle properties (Data sourced from57).
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Distinct lattice fringes were revealed by HR-TEM and TEM morphology (Fig. 1a, b) using the JEM-3010 ultra-high-resolution analytical electron microscope, showing the presence of nano crystalline TiO2 particles. An inconsistent spherical distribution of nano particles with mild aggregation was apparent in the SEM picture (Fig. 1c) produced using the VEGA3-TESCAN preparation. Figure 2 depicts the outcomes of the energy dispersive spectrum analysis (EDX) of TiO2 nano particles (Make: INCA Energy 250 micro analysis equipment), which verifies that the composition contains just titanium and oxygen components and does not contain any observable contamination.

Fig. 1
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(a) HR-TEM, (b) TEM, (c) SEM of TiO2nano particles57

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Fig. 2
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Energy dispersive spectrum analysis (EDX) of TiO2nano particles57

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Experimental setup

An agricultural based single-cylinder, four-stroke compression–ignition engine is used in this investigation. The engine configuration is depicted in Fig. 3, and the test engine’s parameters are listed in Table 8. Emission, performance, and combustion characteristics of the engine when running on a blend of DBOP enhanced with TiO2 nano additions are the primary objectives. A dynamometer is connected to the engine, and the position of the crank angle is continuously monitored by a crank angle encoder. Water cooling systems are installed in both the engine and the dynamometer. On the vertical surface of the cylinder, an in-cylinder pressure transducer is mounted in order to measure the maximum pressure. Furthermore, a system that incorporates an electronic control unit to regulate crucial engine operating parameters, such as the IT (injection timing) and IP (injection pressure). A high-speed Data Acquisition System (DAS) is utilized for the collection and recording of combustion-related data, encompassing cylinder pressure fluctuations, Heat Release Rate (HRR), and Cumulative Heat Release Rate (CHRR). The quantification of regulated emissions such as HC, CO, CO2, NOx, and smoke is conducted through AVL gas analyzers and a Bosch smoke meter.

Fig. 3
figure 3

Schematic of the experimental setup.

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Table 8 Test engine specification.
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Combustion bowl alteration

The main reason for combustion chamber geometry in the cylinder piston is to enhance the turbulence results in better mixing of air/fuel. During the first two strokes, suction of air takes place at a very high-pressure and has several motion turbulences which eventually results in a heated air. These typical erratic motions were widely dependent on bowl geometries as the movement of air is pretty random in topmost area of piston. At the end of the second stroke, only the fuel is supplied where these turbulent air mixtures uphold evaporation and vaporization phenomenon. For the present experimentation, different bowls were considered namely TCC, TRCC and SDRCC with a constant volume of 661 cc equivalent to that of standard HCC. Hence, compression ratio is also held constant. The different combustion chamber geometries were illustrated in Fig. 4.

Fig. 4
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Pictorial representations of modified piston bowl geometries58

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LSTM network—an overview

Time series data is a frequently encountered data format. Among the various sectors and applications that LSTM covers are finance, health monitoring, demand and supply forecasting, and other disciplines. In the context of time series analysis, a common task involves forecasting future values by utilizing historical data, typically when presented with a historical array of time series values. Time series forecasting techniques branches into two primary domains: those that rely on machine learning models and those that adhere to traditional statistic methods. While the latter recurrent neural networks (RNNs), is commonly utilized to detect, classify, and forecast anomalies in time series data.

RNNs are purposefully crafted to improve the processing of sequential data by considering the intrinsic sequential structure of the dataset. Within a conventional RNN network, the calculation proceeds sequentially from the initial sequence element to the last one, advancing one step at a time. At each step, it takes in two inputs: In the context of a basic LSTM, the input consists of current succession element and the output generated by the preceding sequence element. These inputs may be represented as numerical values or textual descriptions. The LSTM layer is usually sandwiched amid input &output layers. A deep LSTM network’s LSTM layer configuration can be altered to meet the requirements of a given application. Deep LSTM performs well over the basic LSTM due to the fact that it can process input values through time in a single LSTM cell as well as across numerous LSTM layers.

Thus, each time step’s inputs undergo a thorough processing due to the layers’ equitable distribution of the input variables. Recurrent Forecast Layer (RFL) is a subset of LSTM. To address the computational complexity issues associated with employing a conventional LSTM RNN at each time step, this novel architectural design was created. The final design (Deep LSTM with a Recurrent Projection Layer) has some LSTM layers with separate projection layers for each LSTM layer. Due to its ability to progress the model’s efficiency with greater depth, this arrangement is quite advantageous when handling excess storage demands. Increased depth also acts as a safeguard against over-fitting in models since it necessitates inputs to pass through a variety of non-linear functions in these networks.

LSTM models require intensive training by related datasets before they are suitable for use in real-world applications. Word sequences can be processed for purposes such as language modeling and text production. Linguistic models can operate effectively about multiple levels and even entire page. Also, noteworthy use pertains to processing of characters/images, where an input image undergoes analysis to create captions and sentences customized to that image. This entails the utilization of a dataset containing a multitude of images for training a specially crafted LSTM model, in conjunction with its associated descriptive captions. Following this, when new sets of images are presented to the model, it generates captions for these images. The model’s accuracy is contingent upon a range of parameters, encompassing the quantity of secreted layers, duration of training epoch and solver optimization.

LSTMs find another application akin to their role in text generation, and this pertains to the ___domain of music generation. In this scenario, LSTM networks predict musical notes by scrutinizing combinations of input notes. When it comes to language translation, LSTM’s facilitate the mapping of the sequence order of phrases from one language to its corresponding order in another language. Model training involves using a refined subset of the dataset that includes phrases and their translations after data cleaning. Before being produced as a transformed version, the input data undergoes conversion into a vector representation through an LSTM model. Generally, RNNs employ multiple layers, each encompassing functions like sigmoid, multiplication, and addition.

Within this architecture, data moves sequentially, transitioning from Ct−1till Ct, and this process involves the utilization of various parameters such as tan h, the sigma function, the value 1 (which allows data to pass through a sigmoid layer), and the value 0 (which prevents data transfer between consecutive stages). LSTM, as a subtype of recurrent neural networks, relies on long-term memory and has garnered substantial popularity across diverse fields when related with alternative models. In an ideal scenario, RNN incorporates multiple layers, each containing a 1 layer sigmoid function, multiplication, and subtraction. The math-model is displayed following the guidelines outlined in Ref59.

The LSTM architecture is shown clearly in Fig. 4. Within an LSTM, there are three gates which are controlled by the sigmoid activation function, functioning within a range from 0 to 1. In this range, a value of 0 acts as a barrier preventing incoming data, while a value of 1 allows data to pass freely. This function is purposefully crafted to generate a positive output, ensuring accurate and precise outcomes.

$${{\text{i}}_{\text{t}}}\,=\,{\text{s}}({{\text{w}}_{\text{i}}}[{{\text{A}}_{t - {\text{1}}}},{\text{ }}{{\text{S}}_{\text{t}}}]\,+\,{{\text{b}}_{\text{i}}})$$
(1)
$${{\text{f}}_{\text{t}}}\,=\,{\text{s}}({{\text{w}}_{\text{f}}}[{{\text{A}}_{{\text{t}} - {\text{1}}}},{\text{ }}{{\text{S}}_{\text{t}}}]\,+\,{{\text{b}}_{\text{f}}})$$
(2)
$${{\text{o}}_{\text{t}}}\,=\,{\text{s}}({{\text{w}}_{\text{t}}}[{{\text{A}}_{{\text{t}} - {\text{1}}}},{\text{ }}{{\text{S}}_{\text{t}}}]\,+\,{{\text{b}}_{\text{t}}})$$
(3)

In the provided equations, the left-hand side (LHS) represents the input, forget, and output gates, denoted by the variables ‘i’, ‘f’, and ‘o’. The symbol sigma (σ) is used to signify the sigmoid activation function. The symbol ‘w’ stands for the weights assigned to the neurons within these respective gates. ‘At-1’ corresponds to the hidden state of the previous unit at time, ‘t-1’, while ‘St’ represents the input at the current time step. The symbol ‘b’ represents the biases linked to the three gates, as indicated in Fig. 5 with values 0, 1, 2, and 3.

Fig. 5
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LSTM architecture.

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Additionally, Eq. (1) delineates how the input gate determines the nature of the information to be carried forward. Equation (2) quantifies the degree to which the current unit should forget past information from the previous unit. Lastly, Eq. (3) governs the activation of the output gate for the current time step.

$${\widetilde {C}_t}{\text{ }}={\text{tan h}}({w_c}\left[ {_{{{\text{At}} - {\text{1}}}},{{\text{S}}_{\text{t}}}} \right]{\text{ }}+{b_c})$$
(4)
$${C_t}={f_t} * {C_{t - 1}}+{i_t} * {\widetilde {C}_{\text{t}}}$$
(5)
$${A_t}={o_t} * {\text{tan h}}({C_t})$$
(6)

The variable Ct stands for the memory information at the present time step, and \({\widetilde {C}_t}\) represents the candidate for the current cell state. The symbol ‘*’ indicates element-wise multiplication of the given vectors.

Upon scrutiny of Eqs. (4)–(6), it becomes apparent that the activation function in Eq. (8) assumes a vital role in deciding what information to discard and in shaping the final output, based on the previous memory state.

LSTM comparing to other models, has layer memory, and each output rely upon prior outputs which has potential to exploit the dependencies between time series data. In engine emission prediction, LSTM will be an add-on benefit as it has gated mechanism, long term-dependency handling, versatility and lesser gradient problems.

Diesel RK—software: fuel spray visualization

Diesel-RK simulation software is a top-notch tool for optimizing parameters linked to Compression Ignition (CI) engines because it is primarily made to imitate the real-world operational scenarios of diesel engines. Estimating diesel engine performance, combustion dynamics, and emission characteristics is the primary use. It operates on both conventional diesel fuel and a wide range of biodiesel categories. In particular, Diesel-RK is able to replicate the running cycles of a number of diesel engines without much dependence on empirical coefficients. These coefficients hold constant for a wide range of engine types and operating situations. Modern models for combustion and emission production are included in the strategy, along with strategies for optimization that insure adherence to existing emission regulations. It permits optimal emission control and conforms with current regulations.

Diesel-RK is unique in that it can imitate several combustion chamber geometries, encompassing nozzle, spray placement, swirl profiles, and multiple fuel injections. It is also a beneficial tool for maximizing piston bowl shapes that comply with certain design specifications. Also, the software provides dynamic visualizations that demonstrate connections between adjacent sprays, air swirl patterns, and chamber walls and fuel sprays. A range of fuel substitutes enable an in-depth evaluation of diesel engine properties, such as thermal efficiency, in-cylinder pressure, heat release rates, ignition delays, and concentrations of soot, CO, and NOx. Therefore, by correlating these simulation results with experimental test data, exact inferences can be made. Without modifying the engine’s running conditions, Diesel-RK makes it less difficult to generate piston bowls with Hemispherical Combustion Chambers (HCC) that meet testing requirements during the experimental phase.

Fig. 6
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Multi zone-fuel spray model developed by Diesel-RK simulation58

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By using default data on widely accepted technical solutions for internal combustion engines and general diesel engine knowledge, Diesel-RK streamlines the development of input data files. This simplifies the process of entering data and calibrating the engine model. It is regarded as a professional tool of the industry, which makes it indispensable for researchers working on projects with tight deadlines and sparse experimental data. It uses combustion modeling and spray evolution simulations to take use of the physical characteristics of biofuel blends. Additionally, users can designate distinct fuels for different engine running modes and preserve bespoke fuel attributes in the internal database of the software. It introduces an alternative concept known as the multi-Zone quasi-dimensional model (as shown in Fig. 6), which partitions sprays into distinct zones based on a combination of geometric principles and considerations related to mixture formation and evaporation conditions. The figure provides a comprehensive overview of the multi-zone fuel spray model, which reveals the existence of seven distinct characteristic zones that correspond to specific evaporation and combustion conditions. Before the fuel jet makes contact with the surface (jet impingement), there are only three zones in the spray:

  1. 1.

    The free spray’s thick axial core.

  2. 2.

    The free spray’s thick forward front.

  3. 3.

    An outer sleeve that is diluted and encircles the free spray.

However, once the jet impinges on a nearby surface, the flow becomes more homogeneous and denser, leading to a further classification into four zones:

  1. 4.

    An axial conical core of the near-wall flow.

  2. 5.

    The flow’s thick core approaches the wall.

  3. 6.

    The near-wall flow’s dense forward front.

  4. 7.

    A diluted outer zone encircling the flow close to the wall.

Throughout its development, the spray eventually reaches both the cylinder liner and the cylinder head, completing its trajectory. Figure 7 illustrates the design of piston bowl for (a) HCC (b) SDCC, (c) TCC and d)TRCC with Diesel-RK software.

Fig. 7
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Different combustion chamber geometries design using DIESEL-RK software.

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The capacity of the engine simulation program DIESEL-RK to forecast the performance, combustion dynamics, and emission features of diesel engines running on different fuels under optimal conditions has recently brought it notoriety. Using the extensive thermodynamic engine simulation program DIESEL-RK, Al-Dawody and Bhatti60 investigated creative methods for cutting NOx emissions. They recommended designing deeper piston bowls with smaller diameters based on their simulation tests, which showed a considerable reduction in nitrogen oxide emissions.

In an alternative investigation, Kuleshov61 conducted a thorough examination of diesel engine performance and emission characteristics under typical operating settings using DIESEL-RK simulation software. They found that the software may be a very useful tool for changing a lot of engine characteristics, such as fuel injection, nozzle count, exhaust gas recirculation, and piston bowl shape. Additionally, Venu et al.’s study62 looked at how emissions, combustion, and diesel engine performance are affected by the architecture of the combustion chamber. They performed engine experiments and simulations under similar operating conditions using the simulation system. With regard to the combustion chamber design, their work expands the body of knowledge regarding the software’s ability to analyze performance and optimize emissions of diesel engines.

Uncertainty analysis

Errors and uncertainties can emerge from various factors like selection and calibration of instruments, changing environment conditions, tests and observations, etc. In general, uncertainty can be grouped into two major factors, namely fixed errors and random errors. The former scenario deals with repeatability while the latter deals with the analytical measurements. In this current work, the uncertainty of measured variable (ρX) is evaluated by Guassian distribution as shown in Eq. (7) within the confidence limits of ± 2σ. 2σ is the mean limit in which the 95% of measured values rely upon.

$$\Delta {X_i}=\frac{{2{\sigma _i}}}{{{X_i}}} \times 100,$$
(7)

where Xi is the number of readings, \(\overline{X} _{i}\) denotes the experimental reading and \(\sigma _{i}\) represents standard deviation. The uncertainties of calculated parameters were assessed using the expression given below:

$$R\,=\,f({X_1},{\text{ }}{X_2},{\text{ }}{X_3}, \ldots {X_n})$$
(8)
$$\Delta R=\sqrt {\left[ {{{\left( {\frac{{\partial R}}{{\partial {X_1}}}\Delta {X_1}} \right)}^2}+{{\left( {\frac{{\partial R}}{{\partial {X_2}}}\Delta {X_2}} \right)}^2}+{{\left( {\frac{{\partial R}}{{\partial {X_3}}}\Delta {X_3}} \right)}^2}+ \cdots {{\left( {\frac{{\partial R}}{{\partial {X_n}}}\Delta {X_n}} \right)}^2}} \right]} ,$$
(9)

where R in Eq. (8) represents the function of X1, X2,…Xn and X1,X2,…Xn represents number of readings taken. Hence “ρR” is computed by RMS (root mean square) of errors associated with measured parameters. The uncertainties of various measuring instruments were illustrated in Table 9. By using Eq. (9), the uncertainties in various measured parameters were evaluated and tabulated in Table 10.

Table 9 Uncertainty values of instruments.
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Table 10 Uncertainty values of parameters.
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Results and discussion

Performance characteristics

BSFC (brake specific fuel consumption)

The variation of BSFC for DBOPN in different combustion chamber geometries for the examined fuel samples were shown in Fig. 8. It is inferred that with increment in load, the BSFC was decreased owing to elevated cylinder temperature at peak loads thus requiring less fuel to maintain a constant speed. Among different geometries, it is found that, apart from HCC, the TCC geometry exhibits higher fuel consumption due to lacking pace in induction of swirl. At full engine load condition, the BSFC of DBOPN-TCC, DBOPN-SDCC and DBOPN-TRCC were lower than DBOPN-HCC by about 3.74%, 5.63% and 8.65% respectively. The toroidal re-entrant bowl profile boosted the engine performance due to improvements in air-fuel mixture formation and more of this mixture is being directed concerning with ignition zone and better mixing of fuel/air mixture. Overall, contemplating BTE and BSFC variation, DBOPN-TRCC is considered the best blend for improved performance.

Fig. 8
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Variation of BSFC with respect to engine load.

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These are on par with the findings of Jaichandar and Annamalai63 and Wickman et al.40. With toroidal re-entrant bowl geometry, the BSFC is found to increase in the literature of Lalvani et al.64. However, some contradictory results with toroidal re-entrant bowl geometry giving rise to lowered BSFC such as Mamilla et al.65, Bapu et al.66 and Venkateswaran and Nagarajan67 which is a result of abnormal fluctuation in swirl and turbulence resulting in reduced combustion efficiency and more fuel enters the combustion chamber to maintain engine speed constant giving rise to lowered BSFC profile.

BTE (brake thermal efficiency)

Figure 9illustrates the variation in Brake Thermal Efficiency (BTE) for DBOPN across various combustion chamber geometries in relation to engine load. The results highlight the crucial role of the combustion chamber in enhancing engine efficiency. In comparison to DBOPN-HCC, DBOPN-TRCC, DBOPN-SDCC, and DBOPN-TCC demonstrated higher BTE values by approximately 8.4%, 5.89% and 3.11% respectively, at full engine load conditions. This improvement is attributed to enhanced swirl and squish motion, facilitating improved air-fuel mixing with the modified chamber geometry. Notably, the TRCC bowl stands out as consistently yielding higher BTE across the entire engine load range among the various combustion chamber configurations; Brake thermal efficiency of DBOPN-TRCC is more than DBOPN-HCC and DBOP by about 8.4% and 11.97% respectively. This is because the re-entrant profile of TRCC offers fuel turbulence with an enhanced swirl. DBOPN-TRCC exhibits 33.484% BTE at 100% engine load condition with impact of fuel bound oxygen atoms in BFB improving efficiency of combustion along with higher BTE. These results are on par with the findings of Jaichandar and Annamalai63 and Venkateswaran and Nagarajan67. With toroidal re-entrant bowl geometry, the BTE is found to increase in the literatures of Mamilla et al.65, Bapu et al.66 and Venkateswaran and Nagarajan67. However, some contradictory results with toroidalre-entrant bowl geometry giving rise to lowered BTE were reported such as Lalvani et al.64.However, some contradictory results with toroidal re-entrant bowl geometry giving rise to lowered BTE due to abnormal fluctuation in swirl and turbulence resulting in reduced combustion efficiency followed by lowered BTE profile as reported such as Lalvani et al.64.

Fig. 9
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Variation of BTE with respect to engine load.

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Emission characteristics

Carbon monoxide (CO)

The CO emission fluctuation for DBOPN in different piston bowl geometries with engine load is delineated in Fig. 10. From the figure, it is found that D100 emits more CO when compared to oxygenated additives since it has less built-in O2and can convert more easily into CO2 during oxidation. All other geometries show lower CO emissions when compared to DBOPN-HCC. The CO emissions of DBOPN-TCC, DBOPN-SDCC, and DBOPN-TRCC are, at 100% engine load, approximately 48.85%, 5.96%, and 90.16% lower than those of DBOPN-HCC. The O2 present in BBOPN mixes, which may have increased CO oxidation and thus reduced CO emission, and improved air circulation within the combustion chamber are responsible for this enormous reduction in CO emissions. Maximum CO reduction is evident for DBOPN-TCC and DBOPN-TRCC due to potential utilization of inbuilt O2, quick fuel molecule breaking and swirl improvement along with squish formation which causes the fuel to be directly concerned with the combustion chamber. Overall, DBOPN-TRCC results in reduced CO emission throughout the load. Reduced CO emission with such a re-entrant profile is confirmed with the results revealed by Wickman et al.40 and Venkateswaran and Nagarajan67. With toroidal re-entrant bowl geometry, CO is found to increase in the literature of Benajes et al.68. However, some contradictory results with toroidal re-entrant bowl geometry giving rise to lowered CO were reported such as Mamilla et al.65, Li et al.20, Jaichandar and Annamalai63, Dolak et al.69, Lalvani et al.64 and Venkateswaran and Nagarajan67 which could be attributed to poor utilisation of inbuilt O2, difficulty in fuel molecule breaking and poor swirl development which causes the fuel to be poorly oxidized and reduced CO levels.

Fig. 10
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Fluctuation in carbon monoxide (CO) levels in relation to engine load.

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HC (hydrocarbon)

Figure 11 portrays the fluctuation of HC emission for DBOPN in different piston bowl geometries with engine loads. The deduction is that the alteration of the combustion chamber can significantly contribute to the reduction of Hydrocarbon (HC) emissions. HC emissions are highest for D100, while the lowest HC is reported for DBOPN-TRCC throughout the engine load condition. At 100% load, DBOPN-TRCC exhibits HC emission of about 0.02 g/kWh which is lower than DBOPN-HCC, DBOPN-TCC and DBOPN-SDCC by about 59.95%, 57.78% and 41.63% respectively. TRCC bowl supports the turbulent kinetic energy of the fuel mixture and therefore channels to the combustion zone. This occurrence, therefore, lowers the possibility of formation of fuel-rich zones followed by HC emission reduction. Even though DBOPN-TCC is comparatively lesser HC than DBOPN-HCC, the quantum of emissions is higher than other chambers such as SDRCC and TRCC which could be possibly attributed to TCC due to absence of re-entrant geometry causes wall wetting tendency followed by higher HC emission. The reduced Hydrocarbon (HC) emissions, particularly evident with the TRCC geometry, align closely with the research findings of Jaichandar et al.70 and Wickman et al.40. With toroidal re-entrant bowl geometry, the HC emissions are found to increase in the literatures of Benajies et al.68. However, some contradictory results with toroidal re-entrant bowl geometry giving rise to lowered HC emissions were reported such as Mamilla et al.65, Lalvani et al.64 and Venkateswaran and Nagarajan67 as a result of lowered rich mixture zones in crevice areas of the combustion chamber due to the presence of swirl in combustion chamber.

Fig. 11
figure 11

Changes in hydrocarbon (HC) levels with engine load.

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NOx (oxides of nitrogen)

NOx fluctuation for DBOPN with relation to engine load is shown in Fig. 12 for various combustion chamber designs. D100 is the mix that shows the least amount of NOx when the engine is running. At engine loads of 25%, 50%, 75%, and 100%, respectively, the NOx emissions of DBOPN-HCC were approximately 45.8%, 57.43%, 47.46%, and 57.18% higher than those of D100. When using a DBOPN mix, all of the four bowl geometries—TCC, SDRCC, and TRCC—show greater NOx levels than HCC. At 100% load, the NOx liberated by DBOPN-TCC, DBOPN-SDRCC and DBOPN-TRCC were about 17.56 g/kWh, 18.03 g/kWh and 18.81 g/kWh respectively, while DBOPN-HCC emits only 17.09 g/kWh. Consequently, the DBOPN-TCC configuration achieved the lowest NOx emissions due to reduced swirl and squish fuel motion. This directs the fuel spray away from the combustion zone, thereby lowering the adiabatic temperature and resulting in reduced NOx emissions. Higher NOx emissions of DBOPN-TRCC are merely compensated for improved BTE and the lowered CO, HC emissions with respect to other geometries. Higher NOxemissions with TRCC are reported by few researchers65,70.

Fig. 12
figure 12

Changes in nitrogen oxide (NOx) levels in correlation with engine load.

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While some contradiction results with lowered NOx with TRCC is also reported by Wei et al.71, Prasad et al.72 and Wickman et al.40. With toroidal re-entrant bowl geometry, the NOx emissions are found to increase in the literatures of Mamilla et al.65, Jaichandar and Annamalai63,70, Li et al.20, Lalvani et al.64 and Venkateswaran and Nagarajan67. However, some contradictory results with toroidal re-entrant bowl geometry giving rise to lowered NOx emissions were reported such as Wickman et al.40, Lim and Min73 and Wei et al.71. This can be attributed to a reduction in swirl and squish fuel motion, directing the fuel spray away from the combustion zone, thereby reduced adiabatic temperature and poor O2utilization lowering the NOx emission subsequently.

Smoke opacity

The fluctuation smoke opacity for DBOPN in various combustion chamber designs in relation to engine load is shown in Fig. 13. As most of the literature points out, it can be seen as a trade-off feature between smoke opacity and NOx emissions. For D100, the maximum smoke opacity is seen at all engine load conditions. When comparing DBOPN-TCC, DBOPN-SDCC, and DBOPN-TRCC to DBOPN-HCC, the smoke opacity of each is approximately 2.71%, 3.58%, and 15.48% lower, respectively, at 100% engine load. This can be attributed to the various bowl shapes that provide efficient spray penetration, enhanced evaporation, and rapid precursor burning, all of which reduce the likelihood of undesired fuel accumulation and the air shortfall in the combustion zone, giving rise to lowered smoke emissions. DBOPN-TRCC achieved highest smoke reduction throughout the load could be attributed to enhanced fuel swirl thereby lessening the soot precursor formation, improved oxidation followed by lowered smoke. Lowered smoke capacity with the usage of re-entrant bowl profile was on par with similar research findings of Wei et al.71. Results with toroidal re-entrant bowl geometry giving rise to lowered smoke emissions were reported such as Mamilla et al.65, Jaichandar and Annamalai63,70, Lalvani et al.64 and Venkateswaran and Nagarajan67 and Dolak et al.69.

Fig. 13
figure 13

Variation of smoke opacity with respect to engine load.

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LSTM algorithm prediction

The results have been included into the LSTM network to examine how various fuel mixes operate and what kind of emissions they produce under full engine load (80–100%) condition. To validate the model, the collected data is used for training and subsequently compared to the values generated by the LSTM network. For most parameters, a second-order function was applied to ensure consistency, and the dataset was constructed to encompass Brake Thermal Efficiency (BTE), Brake Specific Fuel Consumption (BSFC) and the concentrations of Carbon Dioxide (CO2), Carbon Monoxide (CO), Nitrogen Oxides (NOx), and smoke opacity. Table 11 presents the regression model coefficients (P, Q, R, S) associated with various parameters (BTE, BSFC, HC, CO, NOx and smoke opacity). In each case, coefficient P holds no significance. These regression coefficients are employed to prepare and subsequently train the dataset in conjunction with LSTM. Figures 14 and 15 have been included to depict the comparison of regression models with Long Short-Term Memory (LSTM) specifically for Brake Thermal Efficiency (BTE) and Hydrocarbon emissions (HC). Similarly, this methodology can be extended to predict various parameters. Table 12 displays the Root Mean Square Error (RMSE) values for the LSTM model concerning different parameters for the test fuels. Upon the obtained predicted data, LSTM could act as an effective tool for the present state of art problems. Also, LSTM can be effectively implemented in optimizing the sourced data from the diesel engine with lesser RMSE values.

Table 11 Aggression model coefficients for various test parameters.
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Table 12 Root mean square error (RMSE) values for the LSTM model.
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Fig. 14
figure 14

Prediction verses measured BTE for LSTM machine learning model.

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Fig. 15
figure 15

Prediction versus measured HC for LSTM machine learning model.

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Diesel RK—fuel spray visualization

The DBOP blend is a blend consisting of diesel/Jatropha biodiesel, vegetable oil and pentanol with different concentrations. To enhance its properties, it has been enriched with alumina nano additives at a concentration of 20 parts per million (ppm). The resulting fuel is referred to as DBOPN. Subsequently, the properties of HPF are utilized as inputs, which run over identical working environment to those of a typical diesel engine. The software analyzes the performance of the engine using different combustion chamber geometries, including HCC (Homogeneous Charge Compression), SDRCC (Swirl Direct Re-Entrant Combustion Chamber), TCC (Turbulence Charge Compression), and TRCC (Toroidal Re-Entrant Combustion Chamber). The simulation within Diesel-RK focuses on fuel spray occurrence and combustion phenomenon within the various bowl profiles, as illustrated in Fig. 16. Among these geometries, the TRCC design stands out as the most effective in terms of enhancing performance and optimizing combustion parameters. This superiority is attributed to the TRCC’s ability to generate a potent squish effect along with efficient air movement, resulting in improved air-fuel interaction.

Fig. 16
figure 16figure 16

Simulation of fuel spray formation and combustion for different bowl geometries.

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The outcomes derived from the Diesel-RK simulation are compared with actual experimental data obtained under identical operating conditions. The comparison involves the utilization of DBOPN blend and various bowl strategies. Table 13 presents the comparative analysis of these results. It is evident that the TRCC geometry consistently outperforms the other combustion chamber designs in several key aspects, including BTE, BSFC, higher Pcyl, and an increased HRR. This excellence is mainly credited to the generated squish effect and swirled air movement within the TRCC design, which significantly contributes to turbulence generation and, consequently, enhances the combustion efficiency. Notably, the simulation outcomes are closely aligned with the experimental values, underscoring the accuracy of the Diesel-RK software in predicting engine performance. However, it should be noted that the theoretical simulation values tend to be slightly higher than the actual values due to the omission of factors such as heat losses and friction in the simulation model. In a related study, Al-Dawody and Bhatti60 conducted a thorough investigation using the DIESEL-RK simulation software to optimize strategies for reducing nitrogen oxide (NOx) emissions in diesel engines. Their findings highlighted that a deeper piston bowl with a smaller diameter had a significant mitigating effect on NOx emissions. Similar reports were reported by Kuleshov61 with modified piston bowl having the greater turbulence shown higher performance of the diesel engine.

Table 13 Synopsis of (a) test results and (b) Diesel-RK simulation findings of CI engine with DBOPN.
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Conclusion

The present work explores the integration of nanotechnology and Long Short-Term Memory (LSTM) machine learning algorithms to enhance the understanding and optimization of fuel spray dynamics in compression ignition (CI) engines with varying bowl geometries.

  • The test fuel used is a quaternary fuel (50% diesel (vol%) + 5% biodiesel (vol%) + 5% vegetable oil (vol%) + 40% (vol%) pentanol) with various combustion bowl strategies such as hemispherical, toroidal, shallow depth and toroidal re-entrant chambers.

  • DBOPN-TRCC is found to exhibit 8.13% higher BTE and 8.65% lowered BSFC than the conventional HCC bowl. DBOPN-TRCC is found to have 90.16% lowered CO, 59.95% lowered HC and 15.48% lowered smoke owing to improved spray penetration and faster burning of soot precursors. However, NOx emissions of DBOPN-TRCC were found to be higher (by 10.01% in comparison with DBOPN-HCC at full load).Overall, DBOPN-TRCC blend is found to have improved performance and minimized emission characteristics.

  • The outcomes were trained and validated using LSTM networks. The regression coefficients indicate that the LSTM approach is effective in predicting both performance and emissions across a wide range of loading conditions. Application of toroidal re-entrant bowl geometry (TRCC) in quaternary fuel could be regarded as a promising substitute for traditional fossil fuels. Diesel-RK results also highlighted that a deeper piston bowl with a smaller diameter had a significant mitigating effect on NOx emissions74.

Scope for future work

The work can be extended to study the behavior of gaseous fuels or dual fuels with different combustion geometries. Also, microscopic analysis of fuel spray with photographs can be an interesting add on to the existing work.