Prediction of Temperature Distribution with Deep Learning Approaches for SM1 Flame Configuration

Abstract

This study investigates the application of deep learning (DL) techniques for predicting temperature fields in the SM1 swirl-stabilized turbulent non-premixed flame. Two distinct DL approaches were developed using a comprehensive CFD database generated via the steady laminar flamelet model coupled with the SST k-ω turbulence model. The first approach employs a fully connected dense neural network to directly map scalar input parameters—fuel velocity, swirl ratio, and equivalence ratio—to high-resolution temperature contour images. In addition, a comparison was made with different deep learning networks, namely Res-Net, EfficientNetB0, and Inception Net V3, to better understand the performance of the model. In the first approach, the results of the Inception V3 model and the developed Dense Model were found to be better than Res-Net and Efficient Net. At the same time, file sizes and usability were examined. The second framework employs a U-Net-based convolutional neural network enhanced by an RGB Fusion preprocessing technique, which integrates multiple scalar fields from non-reacting (cold flow) conditions into composite images, significantly improving spatial feature extraction. The training and validation processes for both models were conducted using 80% of the CFD data for training and 20% for testing, which helped assess their ability to generalize new input conditions. In the secondary approach, similar to the first approach, studies were conducted with different deep learning models, namely Res-Net, Efficient Net, and Inception Net, to evaluate model performance. The U-Net model, which is well developed, stands out with its low error and small file size. The dense network is appropriate for direct parametric analyses, while the image-based U-Net model provides a rapid and scalable option to utilize the cold flow CFD images. This framework can be further refined in future research to estimate more flow factors and tested against experimental measurements for enhanced applicability.

1. Introduction

Gaseous fuels are often used in industrial combustion systems because they produce fewer emissions, are easier to manage when they burn, and are cheaper than liquid and solid fuels. The focus of previous studies has been to cut down on emissions and make combustion more efficient. Many studies are focused on developing advanced flame stabilization ways to help with this. Non-premixed turbulent flames have gotten a lot of attention since they are very efficient and may be used in many ways. It is a widely used method to enhance flame stability in these systems by including swirl, which generates recirculating zones that enhance fuel–air mingling and facilitate flame stabilization [1].

Swirl-stabilized flames are present in gas turbines, industrial furnaces, and internal combustion engines. The recirculation zones enhance combustion stability and lower emissions [2].

The complex behavior of swirl flames is still being studied despite their extensive use. Challenges arise from phenomena such as flow instabilities and vortex breakdown [3].

These dynamics can be effectively captured by Large Eddy Simulation (LES), but it comes at a high computational cost. An alternative that strikes a good balance between accuracy and efficiency is the combination of probability density function (PDF) combustion models and Reynolds-Averaged Navier–Stokes (RANS) models [4].

Kalt et al. found that the SST k-ω turbulence model works well with experiments. Their results were similar to LES for temperature and species fields, but they cost a lot less [5]. Boke et al. looked at turbulence models for swirl flow in another study and compared how well the SST k-ω, RNG k-ε, and LES models work. The SST k-ω model was very similar to actual data and gave findings that were similar to those of LES for combustion variables like temperature and species mass fractions, but at a lower cost [6].

The SM1 flame is a well-established benchmark case representing a swirl-stabilized turbulent non-premixed flame. It is included in the Sydney swirl flame dataset, which was developed as part of the Turbulent Non-Premixed Flames (TNF) workshop. This flame configuration is widely used for validating turbulence-chemistry interaction models due to its clearly defined boundary conditions, systematic experimental setup, and strong relevance to real-world combustion applications.

In the SM1 case, methane is injected through a central nozzle surrounded by annular air flow. A swirl number of 0.5 is imposed by tangential air injection. This creates two main recirculation zones: a central vortex breakdown and an outer corner vortex. These structures improve flame stabilization by enhancing fuel–air mixing [7].

Recurrent Neural Networks (RNNs) and Convolutional Neural Networks (CNNs) are both prevalent deep learning architectures that depend on extensive datasets to efficiently acquire intricate feature representations. CNNs have done very well in recognizing patterns and images. Their layered structure uses convolutional kernels to find local spatial patterns. This helps cut down on the number of parameters and solves the curse of dimensionality, which is a problem where adding more parameters can make errors worse. CNNs were first created for analyzing images, and they have also been used in combustion research. Some of these are modeling unresolved flame surface wrinkling, forecasting scalar variances, and calculating chemical rate constants from shock-tube studies [8].

Convolutional Neural Networks (CNNs) have been instrumental in the revolutionization of computational fluid dynamics (CFD) by deep learning in recent years. There has been significant progress in this area. These networks excel in capturing intricate flow patterns, managing complex structures, and efficiently processing large datasets. Consequently, CNNs have proven effective in forecasting fluid dynamics. Classical CFD has some problems, like high processing costs and long modeling times [9].

Deep learning improvements in image processing and pattern recognition have shown that methods based on data can be used to create complicated flame structures. Convolutional Neural Networks (CNNs) have emerged as a pivotal instrument in this domain due to their exceptional capability in feature extraction. Zhang et al.’s study demonstrates that CNN architectures may effectively capture significant flow characteristics, highlighting their potential utility in fluid dynamics research [10].

Zhang et al. combined a super resolution CNN (SRCNN) and U-Net and built a model named SRUNet to reconstruct flow images. They successfully performed an increase in the model accuracy rather than U-Net and SRCNN [11].

ANN applications of combustion have generally focused on acceleration of chemical kinetics, combustion kinetics uncertainty, discovery of unknown reaction paths, and building surrogate solvers for simulations [12].

Ding et al. developed the hybrid flamelet/random data—multiple multilayer perception (HFRD-MMP) method to build chemical kinetic tables. This method improves chemical calculations 12× faster. This model only utilizes the CPU 19.9% [13]. In addition, Ding et al. made some improvements on the model for NOx formation. The Multiple Multilayer Perceptron—II” (MMLP-II) model calculates the chemical calculations 15× faster [14]. Nguyen et al. built an ANN model to calculate chemical calculations rapidly. Before training, a stochastic micro-mixing model diluted with thermal losses and burnt gases was simulated. Neural networks were trained by processing chemical composition data using clustering methods. The results show that chemistry analysis with ANN requires only 60% more CPU power than traditional simulations, and the results are consistent with experimental data [15].

Li et al. used machine learning (ML) techniques to solve the memory requirements of the Flamelet Generated Manifold (FGM) method. Four different ML models, namely two Artificial Neural Networks (ANN), Random Forest (RF), and Gradient Boosted Trees (GBT), were trained and compared to predict the source term and transport properties of the propagation variable. Data preprocessing played an important role in improving model performance. RF and GBT models exhibited high training efficiency and acceptable accuracy, while ANN models had lower error rates but longer training times [16].

An et al. proposed a methodology to represent complex hydrocarbon chemistry with artificial neural networks (ANNs). These networks were trained on a comprehensive dataset generated by the Latin hypercube sampling (LHS) method. Chemical kinetic mechanisms were represented by thermochemical sample data, and the model was built to cover the entire pressure/temperature/species space in different turbulent flames. The methodology was used to represent 30-species methane chemical mechanisms and validated with non-mixed turbulent flame (DLR_A) and partially mixed turbulent flame (Flame D) simulations. The results showed that ANN-based chemical kinetics do not compromise accuracy while reducing the computational cost by more than two orders of magnitude. This approach holds great potential for complex hydrocarbon fuels [17].

U-Net is a fully convolutional neural network that is specifically engineered for image segmentation tasks. It converts input photos into the same sized output images immediately. Assembled in a symmetric encoder-decoder design, the encoder shrinks the picture, makes the receptive field bigger, and downsamples to bring out low-frequency details. The decoder subsequently upsamples the input and employs skip connections to maintain information from all encoding steps, maintaining critical visual details. Traditional convolutional networks use fully connected layers to turn extracted features into outputs. U-Net, on the other hand, directly regresses from 2D inputs to 2D outputs, which makes it better at generalization. The Computer Science Department at the University of Freiburg created U-Net to help with biological image segmentation. Since then, it has been used in many other image segmentation tasks because it works so well [18].

Li et al. introduced a U-Net architecture for forecasting temperature and CO₂ concentration distributions in flames. This approach provides multiple significant benefits for the reconstruction of flame scalar fields. Initially, it necessitates solely spectral data obtained along the axial centerline of the flame, so considerably diminishing the requirement for comprehensive experimental observations. Second, prior knowledge of flame characteristics can be effectively incorporated into the training dataset, allowing the U-Net to achieve high reconstruction accuracy through offline training. Finally, the U-Net performs direct image-to-image mapping between the measured spectral optical thickness and the two-dimensional scalar fields of the flame, preserving spatial continuity more effectively than traditional line-of-sight reconstruction methods. These features demonstrate the U-Net’s strong capability as a reliable tool for flame reconstruction [19].

In the study by An et al., a deep learning-based turbulent combustion simulation framework is proposed to overcome the high costs of high-resolution CFD simulations. CFDNN, an optimized deep convolutional neural network (CNN) inspired by the U-Net architecture and inception module, is trained to simulate hydrogen combustion. The CFDNN solver provides more than two orders of magnitude speedup compared to traditional CFD solvers, while excellent agreement is achieved in spatial and temporal dynamics. This method offers new possibilities for low-cost, high-accuracy simulations and real-time control of combustion systems [20].

Maged et al. used deep learning methods to estimate combustion pressure from flame images that provide more information than traditional pressure sensors. Five different models, namely EfficientNetB4, ResNet50, Ensemble Adversarial Inception ResNet, CNN, and CNN-XGBoost, were trained using flame images from a single-cylinder optical gasoline direct injection (GDI) engine. EfficientNetB4 model showed the best performance with R2 of 0.94 and RMSE of 0.70. Furthermore, the deep learning approach achieved higher accuracy than pressure sensors for tracking cycle-to-cycle variations [21].

Artificial neural networks also can be used for prediction for combustion instabilities.

The study by Zhou et al. investigated the application of deep learning methods to monitor combustion instabilities based on time-averaged flame images. In the experiments conducted on a BASIS burner, a Convolutional Neural Network (CNN) called BIM (BASIS Image Monitor) was designed to extract features from flame shapes and predict thermoacoustic states. The BIM, trained in images of 112 different operating conditions, achieved 99% accuracy after a short training period. The features visualized by the CAM method reveal the connections between flame images and instabilities. The BIM has been shown to be a potential leading model for monitoring and controlling combustion instabilities by providing accurate results under unknown operating conditions [22].

In the study conducted by Li et al., a convolutional neural network (CNN)-based method supported by long short-term memory (LSTM) and attention mechanisms is proposed for thermoacoustic instability (TAI) detection. Thermoacoustic modes are classified into five different regimes, namely low and high frequency and low and high amplitude. While CNN extracts spatial features from flame images, LSTM captures temporal dynamics, and the attention mechanism focuses on important time steps. The model successfully detects dynamic instabilities of flames in both spatial and temporal dimensions. In addition, the model provides an effective solution for real-time detection and classification of thermoacoustic modes by accurately determining regime transitions at different time scales [23].

Pan et al. addressed the multimodality detection of combustion instabilities in swirl flames using convolutional neural networks (CNNs). One hundred twenty-nine sets of flame images obtained under different operating conditions were classified by Proper Orthogonal Decomposition (POD), Fast Fourier Transform (FFT), and Phase Space Reconstruction (PSR). The model was trained with K-fold cross-validation, and the best performing model was selected. The results show that ResNet18 model exhibits the best performance under unknown operating conditions. The focus of the model is visualized with Class Activation Mapping (CAM) and it is demonstrated that the model accurately captures not only the flame structure but also the flow field structures and thermo-flow interactions [24].

Deep learning modeling is also used in flame imaging technologies. In some studies, deep learning methodology has been used to generate flame front structures without using laser. In the study conducted by Han et al., a deep neural network-based method has been proposed to generate flame front structures without using laser. CH-PLIF and chemiluminescence images of turbulent premixed methane/air flames were recorded simultaneously and training was done with conditional generator adversarial network (CGAN). Two different generators, Resnet and U-net, were evaluated, and it was determined that Resnet performed better. The trained model can generate CH-PLIF images from chemiluminescence images with 91% accuracy and can effectively estimate flame surface density at high Reynolds numbers [25].

The research indicates that artificial neural networks (ANNs) present numerous applications. The improvement of chemical reaction calculations and their applications in tabular chemistry are highly significant. Moreover, numerous works examine AI-assisted instruction of time-dependent flame imagery via targeted preprocessing. Nonetheless, a practical methodology for instructing CFD outcomes for natural gas burners in industrial contexts is absent. The work we have conducted addresses this deficiency. The main objectives of this study can be shown as follows:

• A model based on input parameters for temperature distribution image prediction from input parameters
• Temperature distribution image prediction from cold image-based RGB fusion.
• To assess and compare the accuracy, efficiency, and size of DL models.
• To provide a practical method that supports faster and reliable combustion temperature predictions.

The primary aim is to create models that depict general flame behavior and high-temperature areas in temperature forecasts and to evaluate them against existing artificial intelligence models. In literature, investigations have predominantly utilized Res-Net and U-Net, while comparative analyses involving Efficient Net and InceptionV3 Net have not been observed. The RGB Fusion approach produced integrated graphics from cold flow (none-reacting) CFD visuals, although their incorporation into industrial-level artificial intelligence remains unaddressed in the literature. The study also analyzed the file sizes and prediction periods of the models regarding their suitability for industrial application.

2. Description of SM1 Case and CFD Modeling Methods

2.1. Experimental Setup for SM1 Case

A schematic representation of the burner used in these investigations is provided in Figure 1. Swirl is aerodynamically induced into the primary (axial) air stream 300 mm upstream of the burner exit. This process is achieved through three tangential air swirl ports, each with a diameter of 7 mm, positioned circumferentially at 120° intervals and inclined 15° upward relative to the horizontal plane. Additionally, two diametrically opposed ports, located upstream of the tangential inlets and along the burner periphery, supply the axial air streams. This design ensures a relatively simple configuration with well-defined and uniform boundary conditions, making it suitable for experimental and computational studies [26].

Laser Doppler Velocimetry (LDV) was used to measure time-averaged axial and tangential velocities, along with their fluctuations and shear stresses. The LDV system was powered by a Spectra-Physics Stabilite-2017 ion laser, providing 200 mW of power. Additionally, a combined Raman-Rayleigh-Laser-Induced Fluorescence (LIF) system was utilized for temperature and species mass fraction measurements, including methane, oxygen, carbon dioxide, water vapor, OH, CO, and NO. Mixture fraction data were obtained using Bilger’s formulation, providing insight into the flame structure and combustion process [27].

U_j represents the bulk jet flow velocity, while U_s and W_s correspond to the axial and swirl air velocity components, respectively. Additionally, U_e denotes the co-flow air velocity component. S_g is defined as swirl ratio and defined as S_g = Ws/U_s. Methane is used as fuel, and there is no change with experimental results; properties are given in

Table 1. SM-1 case description.

Case	Fuel	Uj (m/s)	Us (m/s)	Ws (m/s)	Ue (m/s)	Sg (m/s)	Re
SM-1	CH4	32.7	38.2	19.1	20	0.5	7200

.

2.2. Mathematical Model of K-Omega and SLF Combustion Model

In this study, the SST k-ω turbulence model was selected as the mathematical model for turbulence simulations. The SST k-ω model is an effective turbulence model, particularly in regions with high-pressure gradients and flow separation [28]. Equations of the SST-k-w turbulence model are given as follows in Equations (1) and (2) [29]:

$${\displaystyle \frac{\partial \left(\rho k{u}_j\right)}{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}[\mu +{\sigma }_k{\mu }_t\left({\displaystyle \frac{\partial k}{\partial x_j}}\right)]+P_k-\beta *\rho k\omega$$

(1)

$${\displaystyle \frac{\partial \left(\rho \omega u_j\right)}{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\mu +{\sigma }_k{\mu }_t\left({\displaystyle \frac{\partial \omega }{\partial x_j}}\right)\right]+{\alpha {\displaystyle \frac{\omega }{k}}P}_k-\beta \rho {\omega }^2+2(1-F_1)\rho {\displaystyle \frac{{\sigma }_{w2}}{w}}{\displaystyle \frac{\partial k}{\partial x_j}}{\displaystyle \frac{\partial w}{\partial x_j}}$$

(2)

In these equations, µ_t represents the turbulent eddy viscosity, and P_k represents the production of turbulent kinetic energy. β* and β are model constants. σ_k and σ_w are the Prandtl numbers. F₁ is the blending function for the near-wall treatment, ensuring correct behavior. The model constants are adjustable, and α = 5/9, β = 3/40, β* = 0.09, σ_k = 0.85, and σ_ω = 0.5 are the default values, respectively.

A steady laminar flamelet model is used for the turbulence-chemistry interaction. The mixture fraction (Z) and scalar dissipation (χ) rate are key parameters calculated in physical space to describe non-premixed flames, where combustion is predominantly governed by mixing. The mixture fraction effectively characterizes the mixing of fuel and oxidizer, exhibiting rapid variations perpendicular to the flame front, making it a critical scalar in analyzing such flames [30].

Mixture fraction, mixture fraction variance, and energy equation can be described by Equations (3)–(5), respectively [31]:

$$\nabla \left(\rho ·\dot{u}·\overline{Z}\right)=\nabla ·(\left({\displaystyle \frac{k_l}{C_p}}+{\displaystyle \frac{{\mu }_t}{{\sigma }_t}}\right)\nabla \overline{Z})$$

(3)

where k_l is the laminar thermal conductivity of the mixture, C_p is the specific heat of the mixture, σ_t is the Prandtl number, and µ_t is the turbulent viscosity.

$$\nabla ·\left(\rho ·\dot{u}·{\overline{Z}}^2\right)=\nabla ·\left(\left({\displaystyle \frac{k_l}{C_p}}+{\displaystyle \frac{{\mu }_t}{{\sigma }_t}}\right)\nabla \overline{Z^2}\right)+C_g{\mu }_t{\left(\nabla \overline{Z}\right)}^2-C_d\rho {\displaystyle \frac{\epsilon }{k}}{\overline{Z}}^2$$

(4)

where the k is the turbulent kinetic energy, ε is the turbulent dissipation rate, and σ_t, C_d, and C_g are model coefficients, which are 0.85, 2.86, and 2.0, respectively.

$$\nabla ·\left(\rho ·\dot{u}·\overline{H}\right)=\nabla ({\displaystyle \frac{k_t}{c_p}}\nabla \overline{H})$$

(5)

The scalar dissipation rate at the flame surface, given in Equation (6), serves as a measure of the deviation from equilibrium. With dimensions of [s⁻¹], it can be interpreted as the inverse of a characteristic diffusion time or as a diffusivity in the mixture fraction space.

$$\chi =2D_z(\nabla \mathrm{Z}·\nabla \mathrm{Z})$$

(6)

Flamelet equations, derived as a simplified form of species and energy transport equations, assume that the reaction layer is thin. This allows the transformation of transport equations from physical space into a flamelet-specific coordinate space. One of these coordinates is assumed to be normal to the flame front and is represented by the mixture fraction. In this transformed space, tangential gradients relative to the flame front are considered negligible compared to normal gradients, following asymptotic observations. The flamelet equations are given in Equations (7) and (8) [32].

$$\rho {\displaystyle \frac{\partial Y_i}{\partial \tau }}+0.25\left(1-\left({\displaystyle \frac{1}{{Le}_i}}\right)\right)\left({\displaystyle \frac{\partial \rho \chi }{\partial Z}}+{\displaystyle \frac{\rho \chi c_p}{\lambda }}{\displaystyle \frac{\partial }{\partial Z}}\left({\displaystyle \frac{\lambda }{c_p}}\right)\right){\displaystyle \frac{\partial Y_i}{\partial Z}}={\displaystyle \frac{\chi \rho }{2{Le}_i}}{\displaystyle \frac{{\partial }^2{Y}_i}{\partial Z^2}}+{\dot{w}}_i$$

(7)

$$\rho {\displaystyle \frac{\partial T}{\partial \tau }}-{\displaystyle \frac{\rho \chi }{2c_p}}({\displaystyle \frac{\partial c_p}{\partial Z}}+\sum _{i=1}^{n_{sp}}{\displaystyle \frac{c_{p,i}}{{Le}_i}}{\displaystyle \frac{\partial Y_i}{\partial Z}}){\displaystyle \frac{\partial T}{\partial Z}}={\displaystyle \frac{\rho \chi }{2}}{\displaystyle \frac{{\partial }^{2}T}{\partial Z^2}}-{\displaystyle \frac{1}{c_p}}\sum _{i=1}^{n_{sp}}{h}_i{\dot{w}}_i-{\displaystyle \frac{\dot{q_R}}{c_p}}$$

(8)

In this context, the specific heat capacity (c_p,i) of each species is represented by the specific heat of the i-th species, h_i the specific enthalpy of each species is denoted by the specific enthalpy, and the temperature (T) is represented as the temperature. The net mass production rate per unit volume (w) of each species, resulting from chemical reactions, is expressed as the net rate of mass production. The mass fraction of each species is indicated as the mass fraction (Y_i), and the time is denoted as the time. These parameters collectively describe the thermodynamic and reaction properties critical for modeling combustion processes.

3. Numerical Analyses

3.1. Geometry, Mesh, and Parametric Case Description

A two-dimensional, asymmetrical model of the SM1 combustor was prepared for analysis. The length (L) and outer diameter (D_out) of the computational domain, presented in Figure 2, were chosen to be 3.0 m and 0.250 m, respectively.

Quad elements are used, and the aspect ratio values of cells are nearly 1.0 at the combustion zone. The numerical mesh is shown in Figure 3.

To provide mesh independence in the analyses, four different mesh structures containing different numbers of structural elements were created: 125,000 (Mesh-1), 250,000 (Mesh-2), 500,000 (Mesh-3), and 1 million (Mesh-4) element meshes were used. These mesh structures were numerically analyzed with the SST k-ω turbulence model, appropriate boundary conditions, and solution methods. The temperature changes in the radial direction in the x/D = 0.8 plane are given in Figure 4. According to the data in Figure 4, it was observed that the difference between the analysis results of the 500,000-elements mesh and the 1 M element mesh was quite small. In line with this observation, it was decided to use the 500,000-elements mesh structure in all future analyses.

The analyses were conducted parametrically, involving a total of 430 simulations with 11 different equivalence ratios, 13 different swirl numbers, and 3 different fuel flow rates. Methane was used as the fuel, while the oxidizer consisted of 77% nitrogen and 23% oxygen by mass. The mixture fraction theory was applied, where the mixture fraction at the fuel inlet was set to Z = 1 and at the air inlet and co-flow inlet to Z = 0. The co-flow air velocity was kept constant throughout all simulations. For equivalence ratio calculations, the stoichiometric mixture fraction (Z_st) was assumed to be 0.0578. Detailed information about the input parameters used in the study is provided in

Table 2. Parameter design table.

Parameters	Values
Swirl Ratio (Ws/Us)	0.35, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95
Equivalence Ratio (1/φ)	5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10.0
Fuel Velocity (m/s)	32.7, 40.0, 45.0

.

The inverse equivalence ratio (1/φ) was selected within the range of 5.0 to 10.0, as observed variations in flame structure were present within this range. At lower equivalence ratios, the occurrence of flame lift-off may become a possibility [33]. The swirl ratio was set to 0.5 for the validation case. In the experimental studies conducted within the scope of the TNF Workshop, a maximum swirl ratio of 1.6 was selected for flames using natural gas and natural gas-air mixtures. In this study, the maximum swirl ratio was limited to 0.95 [7]. In the TNF Workshop Data Series, the SM2 flame, which exhibits the same behavior as the SM1 flame, is performed at a fuel velocity of 88.4 m/s. It is shown that SM2 has similar characteristics to SM1. With this similarity, it was observed that increasing the fuel speed did not have a detrimental effect on the flame character. Therefore, to stay on the safe side, the flame speed was selected as a maximum of 45 m/s [7].

CFD analyses were performed in two different modes: cold flow and reactive flow. In the cold flow studies, the species transport method was employed, while reactions were neglected. In the hot flow studies, combustion analyses were conducted using the steady laminar flamelet method, and deep learning studies were performed based on the obtained data. Turbulence effects were included in both studies.

The flow simulations were performed on ANSYS Fluent 2022 R2 based on the SIMPLE algorithm. The governing equations are discretized as a cell-based finite volume method. The PRESTO method was selected for pressure discretization in swirl-dominated flows. The energy equation is accounted for in the equation set. All equations are solved as second-order discretization. Simulations are performed while the residuals are below 10⁻⁵ [34].

3.2. Numerical Validations

In literature, studies on the SM1 flame have identified two distinct flow regions, referred to as the primary recirculation zone (PRZ) and the secondary recirculation zone (SRZ). Experimental measurements of the PRZ indicate a value of approximately 43 mm. The SRZ begins 65 mm downstream of the bluff body surface [35]. In this study, the diameter (D) is taken as 50 mm, and R is taken as 25 mm, and experimental results were obtained from TNF Workshop Data Archives [7].

Figure 5 shows the comparison between experimental and CFD-predicted axial velocity profiles at different axial positions (x/D = 0.4, 0.8, 1.2, and 2.0) using the SST k-ω turbulence model coupled with the steady laminar flamelet combustion model. Overall, the CFD results capture the main features of the velocity distribution and show good agreement with the experimental data, especially at positions further downstream (x/D ≥ 0.8).

MAPE (%), N-RMSE, and R² values are represented for axial velocity at

Table 3. Error metrics for axial velocity.

Location (x/D)	MAPE (%)	R2	N-RMSE
0.4	115.4069	0.896131	0.30547
0.8	48.88532	0.881266	0.229019
1.2	15.45042	0.878356	0.19543
2	97.39403	0.908819	0.216707

. As can be clearly seen, when the error metrics specific to the axial velocity are examined, it is seen that the experimental results are in high compliance with the SST k-w Steady Laminar Flamelet model. The reason for the high MAPE (%) values is that the percentage of difference is high when the velocity values approach zero. When the R² values are examined, it is seen that the minimum is 0.87.

Figure 6 presents the comparison between experimental measurements and CFD predictions of tangential velocity profiles at various axial locations normalized by the burner diameter (x/D = 0.4, 0.8, 1.2, and 2.0) using the SST k-ω turbulence model coupled with the steady laminar flamelet combustion model. The CFD results capture the overall shape and magnitude of the tangential velocity distribution along the radial direction with good accuracy. At all axial positions, the model effectively predicts the peak tangential velocities near the mid-radius region and the general decay towards both the centerline (r/D = 0) and the outer domain (r/D = 1). Some minor discrepancies are observed at specific radial locations, which can be attributed to the limitations of RANS-based turbulence modeling in resolving complex flow phenomena. Nevertheless, the close agreement between CFD and experimental data across multiple axial positions validates the effectiveness of the turbulence and combustion models in simulating swirl-induced tangential velocity fields in the SM1 flame configuration.

Tangential speed values are examined in terms of error metrics and presented in

Table 4. Error metrics for tangential velocity.

Location (x/D)	MAPE (%)	R2	N-RMSE
0.4	151.6819	0.761195	0.390649
0.8	54.0488	0.962425	0.185189
1.2	68.32376	0.975864	0.153151
2	38.37038	0.788708	0.299069

. The SST k-w Steady Laminar Flamelet model gives similar results to experimental data. The lowest R² value was determined as 0.76. The flame shows stable behavior between x/D = 0.4 and x/D = 2.0. Therefore, the error values in this region are much lower.

Figure 7 presents the comparison between experimental and CFD-predicted temperature profiles at different axial locations normalized by the burner diameter (x/D = 0.2, 0.4, 0.8, and 1.5) using the SST k-ω turbulence model combined with the Steady Laminar Flamelet combustion model. The CFD results generally capture the overall trend of the temperature distribution along the radial coordinate, including the peak temperatures near the mid-radius region and the decay towards the centerline (r/R = 0) and outer radius (r/R = 1). While the model tends to overpredict the maximum temperatures at several axial positions, the spatial distribution and qualitative shape of the temperature profiles show reasonable agreement with the experimental data. Some discrepancies, particularly in regions closer to the burner (x/D = 0.2 and 0.4), may be associated with modeling assumptions and simplifications inherent to the RANS-based approach and the Steady Flamelet model. Overall, the results demonstrate that the selected turbulence and combustion models provide a consistent representation of the temperature field evolution within the SM1 flame, supporting their suitability for CFD simulations of turbulent combustion in this configuration.

MAPE (%), N-RMSE and R² values are represented for temperature at

Table 5. Error metrics for temperature.

Location (x/D)	MAPE (%)	R2	N-RMSE
0.4	18.26	0.40	0.21
0.8	12.10	0.94	0.11
1	35.26	0.71	0.29
1.5	33.41	0.86	0.24

. In the stable flame area (0.4 < x < 1.2), the error metrics for temperature indicate that the experimental results align closely with the SST k-w SLF model. In the area where x/D = 0.4, despite the low R2 values, the CFD results exhibit similarities to the experimental findings according to MAPE result.

Figure 8 shows the comparison between experimental and CFD-predicted mixture fraction profiles at various axial locations normalized by the burner diameter (x/D = 0.2, 0.4, 0.8, and 1.5) using the SST k-ω turbulence model coupled with the Steady Laminar Flamelet combustion model. The CFD results generally capture the decreasing trend of the mixture fraction along the radial direction from the centerline (r/R = 0) to the outer radius (r/R = 1). The model predicts the high mixture fraction values near the centerline effectively, with reasonable agreement to the experimental data, especially at downstream positions. Overall, the CFD predictions provide a consistent and qualitatively accurate representation of the mixture fraction distribution across the domain, supporting the applicability of the chosen modeling framework for simulating the SM1 flame configuration.

4. ANN Architecture

Two different approaches were developed to predict temperature fields in the SM1 flame configuration. In order to better compare the performance of the models created in both approaches, a comparison was made with Res-Net, Efficient Net, and Inception V3 models, and the efficiency of the models was determined by giving comparative results in both approaches.

The first approach employs a fully connected dense neural network that maps scalar input parameters—fuel velocity, swirl ratio, and equivalence ratio—directly to temperature contour images. This model is trained on labeled CFD data, enabling temperature field prediction based solely on these physical input variables.

The second approach uses a convolutional neural network (CNN) with an encoder-decoder architecture for image-to-image translation. It takes as input composite RGB images generated by fusing cold flow scalar fields—velocity magnitude, methane mass fraction, and turbulence time scale—using an RGB Fusion technique. The network outputs predicted temperature contour images. This method leverages the computational efficiency of cold flow CFD simulations and spatial feature extraction capabilities of CNNs to estimate temperature fields.

Both models were trained using an 80/20 train-test split of the CFD dataset. While the first model relies on explicit physical parameters and dense layers, the second utilizes hierarchical convolutional layers for improved spatial feature learning and reduced model size.

4.1. Input Parameters to Image Learning Application (First Approach)

In the first approach of the study, a deep learning model was developed to predict temperature contours directly from three input parameters: fuel velocity, swirl ratio, and equivalence ratio (Table 2). In this approach, four models were performed. These models are Dense Model, Res-Net, Efficient Net, and Inception V3.

Dense Model was implemented using the TensorFlow and Keras libraries. Its architecture, shown in Figure 9, consists of fully connected (dense) layers that process the input vector and generate high-resolution temperature contour images. The input layer receives a three-dimensional vector corresponding to the physical parameters. This is followed by three dense layers, each with 256 neurons activated by the ReLU function to capture nonlinear relationships. A dropout layer with a 10% rate is included after the first dense layer to reduce overfitting and improve generalization. The final dense layer outputs a vector reshaped into a 256 × 256 × 3 tensor representing the predicted temperature image in RGB format. A sigmoid activation function is applied to normalize pixel values between 0 and 1. The model was compiled with the Adam optimizer, employing Mean Squared Error (MSE) as the loss function. Mean Absolute Error (MAE) was used as an additional metric to monitor training and validation performance. Training was performed using mini batches, with an early stopping criterion applied to halt training if validation loss did not improve over five consecutive epochs, preventing overfitting and reducing computation time. The dataset was partitioned into training and testing subsets using an 80/20 split ratio. Specifically, 80% of the available data was allocated for model training to enable the neural network to learn the underlying relationships between input parameters and temperature contours. The remaining 20% was reserved as an independent test set to rigorously evaluate the model’s generalization capability on unseen data. This standard data partitioning approach helps prevent overfitting and provides an unbiased assessment of model performance, ensuring the robustness and reliability of the predictive results.

The Res-Net model utilizes a framework that incorporates deep learning attributes trained on ImageNet. The Res-Net layers have been immobilized, with just the last layers of the model undergoing training. The model’s advantages include the utilization of residual connections to mitigate gradient loss. The EfficientNet network has been evaluated to provide a more efficient network design for industrial applications. EfficientNet has undergone training on ImageNet. It has been designed for mobile platform utilization. The Inception V3 model, trained on ImageNet, employs smaller filters and multi-scale learning techniques. The performance of multi-learning has been evaluated.

4.2. Cold Flow Image to Output Image Learning Application (Second Approach)

In the study’s second approach, four distinct ANN models were employed, similar to the first approach. The models include U-Net, ResNet, EfficientNet, and InceptionNet.

Firstly, it was developed to predict temperature contours using input derived from cold flow CFD simulations. Steady-state simulations were performed using the SST k-ω turbulence model and the species transport model, with combustion reactions neglected.

Equations of the SST k-ω turbulence model are given as follows Equation (9) [29]:

$$\nabla ·\left(\rho u{Y}_i\right)=-\nabla ·(-\rho D_i\nabla Y_i)$$

(9)

In Equation (9), ρ represents the density of the mixture (kg/m³), D is the diffusion coefficient, and Y is the mass fraction of species i.

Scalar fields such as velocity magnitude, methane mass fraction, and turbulent time scale (k/ε) were extracted from the non-reacting CFD results [36].

These scalar fields were converted into grayscale images by normalizing their values between 0 and 1. The grayscale images were then assigned to the red, green, and blue channels, respectively, creating composite RGB images that encode multiple physical fields in a single representation. This preprocessing technique, referred to as RGB Fusion, facilitates the integration of diverse flow information into a unified format suitable for deep learning. A schematic diagram of the image preprocessing pipeline is presented in Figure 10.

The resulting 256 × 256 × 3 RGB images were used as input to the CNN model. The U-Net architecture employed consists of an encoder-bottleneck-decoder structure. The encoder includes two downsampling levels, each containing convolutional layers with ReLU activation functions and batch normalization, followed by max pooling layers. The bottleneck comprises convolutional layers with 512 filters. The decoder mirrors the encoder with upsampling via transposed convolutions and includes skip connections to retain spatial context from earlier layers. A final 1 × 1 convolution with a sigmoid activation function produces the normalized RGB output image representing the predicted temperature field. Model architecture is represented in Figure 11

The model was compiled using the Adam optimizer and trained using Mean Squared Error (MSE) as the loss function. Mean Absolute Error (MAE) was also monitored to assess model accuracy. The dataset was partitioned into 80% training and 20% testing subsets to evaluate the model’s generalization to unseen data. Training was conducted with a batch size of 16 for up to 200 epochs.

To prevent overfitting and ensure training efficiency, an early stopping mechanism was applied. If the validation loss did not improve for 10 consecutive epochs, training was halted, and the model weights corresponding to the lowest validation loss were restored. This training strategy enabled efficient convergence while maintaining robust performance.

5. Results

5.1. CFD Results

A systematic variation of fuel velocity, mixture fraction, equivalence ratio, and swirl ratio was conducted to investigate their impact on the flow and scalar fields. While these parametric dependencies were characterized through detailed CFD simulations, the present manuscript is primarily concerned with the application of deep learning techniques for temperature field prediction. Accordingly, this study focuses exclusively on the analysis of temperature distributions and their sensitivity to varying input parameters, with comprehensive examination of other scalar quantities considered outside the scope of the current work.

Temperature contours are given in Figure 12. At low swirl ratios, the flame was observed to detach from the burner. When the swirl ratio reached 0.5, the flame exhibited complete attachment to the burner. However, as the swirl number increased beyond this point at the same equivalence ratio, the flame attachment became unstable again. Furthermore, at lower swirl numbers, the flame adopted a conical shape, whereas at higher swirl numbers, it transitioned into a cylindrical structure [33]. At high swirl ratios, it was observed that reducing the air flow rate is necessary to maintain flame attachment to the burner [37].

5.2. ANN Results

5.2.1. Results of Input Parameters to Image Learning Application

The training and validation loss histories of the ANN models such as DenseModel, ResNet, EfficientNet, and InceptionV3, presented in Figure 13, demonstrate a rapid decrease in Mean Squared Error (MSE) during the initial epochs, followed by a stable convergence beyond 250 epochs. The close alignment between training and validation loss curves indicates effective learning without overfitting.

An 80/20 train-test split was utilized, with early stopping applied to prevent overfitting by terminating training if the validation loss did not improve over 10 consecutive epochs. This training strategy ensured robust generalization and efficient convergence.

Table 6. Performance parameters of ML model for input parameters to image learning study (first approach).

Predicted Output (Temperature)	Training Loss	Mean Absolute Error	Validation Loss	Validation Mean Absolute Error
DenseModel	4.30 × 10−4	0.0042	1.7 × 10−4	0.0035
ResNet 50	6.00 × 10−4	0.0059	4.0 × 10−4	0.0044
EfficientNet B0	6.64 × 10−4	0.0059	5.0 × 10−4	0.0048
InceptionV3	2.95 × 10−4	0.0047	9.4 × 10−5	0.0025

summarizes the performance metrics, where the final minimum training loss and validation loss are 2.95 × 10⁻⁴ and 9.4 × 10⁻⁵, for Inception V3, respectively. Corresponding Mean Absolute Errors (MAEs) of 0.0042 (training) and 0.0035 (validation) further confirm the predictive accuracy for DenseModel.

In this study, the Normalized Difference method has been employed to compare CFD images with AI-generated output images. Normalized Difference involves the normalization of the absolute pixel value differences between two images. This process allows for the comparison of distinct images and facilitates the visualization of the differences in a scaled manner. Typically, in such analyses, the goal is to compress the differences into a specific range, which aids in the clearer visual understanding of the discrepancies. Normalized difference is described in Equation (10).

$$Normalized Difference\left(x,y\right)={\displaystyle \frac{\left|I_{real}\left(x,y\right)-I_{predicted}(x,y)\right|}{\mathrm{m}\mathrm{a}\mathrm{x}\left(I_{real}\left(x,y\right)\right)}}$$

(10)

In this equation, I_real and I_predicted are pixel values at (x,y) location. In this approach, the absolute difference between corresponding pixels of the real image and the predicted image is computed. Subsequently, the differences are normalized by dividing them by the maximum pixel value from the real image. This normalization process ensures that the differences between pixel values are scaled to a consistent range, enhancing the clarity of any discrepancies.

Figure 14 presents both the temperature distribution from finite volume simulations and the images predicted by the dense model. Upon comparison of the CFD results with the ML-predicted images, noticeable differences can be observed at the boundaries, particularly in the transition regions. Despite these discrepancies, the model effectively captures realistic behaviors across various flame regimes. The attachment of the flame to the burner surface and the locations of maximum temperature points are clearly identifiable from the predicted images, demonstrating the model’s capacity to reflect key flame characteristics.

Figure 15 provides a comparison of finite volume simulations and Res-Net predictions. It has been noted that the predictability at the contour boundaries of the Res-Net model is lower than that of the dense model.

Upon examining the Efficient Net model (Figure 16), it was noted that the resolution at the contour boundaries in the elevated flame temperature zone diminished. Nonetheless, while evaluating the overall flame behavior, no significant disparity was noted in comparison to the CFD data.

Figure 17 presents a comparison between the InceptionV3 model and the results of the finite volume simulation. The Inception V3 model has the lowest rates of training and validation loss. Furthermore, the accuracy at the contour boundaries can be characterized as the model that most closely approximates the dense model. It unequivocally illustrates flame dynamics.

5.2.2. Results of Cold Flow Image to Output Image Learning Application

Figure 18 presents the training and validation loss curves of the ANN models (U-Net, Res-Net, Efficient Net, and InceptionV3) tasked with predicting temperature contours from RGB-fused cold flow images. The Mean Squared Error (MSE) shows a rapid decline during the initial epochs, with the validation loss stabilizing after approximately 20 epochs for the U-Net model.

Table 7. Performance parameters for preprocessed RGB Fusion image to image prediction model metrics (second approach).

Predicted Output (Temperature)	Training Loss	Mean Absolute Error	Validation Loss	Validation Mean Absolute Error
U-Net	1.0 × 10−4	2.1 × 10−3	2.89 × 10−5	2.3 × 10−3
Res-Net	1.3 × 10−4	3.4 × 10−3	1.2 × 10−3	7.0 × 10−3
EfficientNetB0	6.2 × 10−4	6.3 × 10−3	13.2 × 10−3	25.1 × 10−3
InceptionV3	5.62 × 10−4	7.6 × 10−3	1.8 × 10−3	9.7 × 10−3

summarizes the quantitative performance metrics of the trained models. For training loss and validation loss, the U-Net model gives the best results compared to other models. The EfficientNetB0 model had the worst validation and training loss metrics.

As shown in Figure 19, the model demonstrates a high performance in predicting the flame temperature distribution. Upon examining the normalized difference, it can be observed that diffusion is only present at the contour boundaries and in the post-flame region, with minimal impact on the results.

Figure 20 illustrates that the Res-Net model yielded performance results comparable to those of the U-Net model. The Res-Net model can accurately anticipate flame behavior and high-temperature zones. Figure 21 reveals substantial discrepancies between the anticipated and real photos for EfficientNetB0, indicating that the flame behavior was inaccurately forecasted in some instances.

Figure 22 presents a comparison between finite volume and anticipated images generated by the Inception V3 model. The model’s performance exhibits findings comparable to those of Res-Net and U-Net. Nonetheless, the normalized difference values were determined to be superior to those of the images generated using U-Net and Res-Net. However, this discrepancy did not result in a significant margin of error in identifying the flame’s high-temperature areas.

5.2.3. Comparison of ANN Results

The performances of the two developed approaches were systematically compared in terms of training efficiency, model size, and predictive accuracy. In total, four ANN methods were performed at each approach. Validation MAE errors are given in Figure 23 for the first approach. The initial analysis reveals that the Inception V3 model has the lowest validation MAE value. The Efficient Net model exhibited the highest error rate. The Inception model operates by integrating multi-layered and multi-scale architecture. This enables the model to concurrently learn features at various resolutions. While the Efficient Net model reflects the overall characteristics of the flame, distortions have emerged at the contour boundaries.

Figure 24 illustrates the distribution of file sizes. Upon comparison of file sizes, it was noted that the Res-Net model exhibited the largest value. The Dense Model has the smallest file size.

Table 8. Comparison of models for first approach.

Model	Validation MAE	File Capacity (MB)	Average Prediction Time (s)	IoU	F1 Score
Dense Model	0.0035	580	<1 × 10−3	0.98	0.97
Res-Net	0.0044	675	<1 × 10−3	0.98	0.97
EfficientNet	0.0048	600	<1 × 10−3	0.98	0.97
InceptionV3	0.0025	670	<1 × 10−3	0.98	0.97

presents the Intersection over Union (IoU) and F1 score metrics for the models. A high F1 score signifies an effective equilibrium between precision and recall in the model. F1 score and Intersection over Union (IoU) are two metrics that have an important place in model evaluation and are widely used especially in classification and segmentation problems. F1 score is the harmonic mean of precision and recall metrics and measures the effectiveness of the model’s true positive predictions. F1 score provides more reliable results than using only accuracy by reflecting the overall performance of the model more accurately, especially when there is an imbalance between classes (for example, when there are too many negative classes). IoU is a metric often used in image segmentation and similar applications. IoU calculates the intersection ratio of the model’s predicted area with the true area. While the intersection indicates the pixels that the model correctly predicted, the union indicates the sum of all positive pixels of the predicted and true area. A high IoU indicates that the model performs the segmentation task correctly.

F1 and Intersection over Union can be represented by Equations (11) and (14).

F1 = 2 × (Precision × Recall)/(Precision + Recall)

(11)

Precision = TP/(TP + FP)

(12)

Recall = TP/(TP + FN)

(13)

Intersection over Union (IoU) = TP/(TP + FP + FN)

(14)

The secondary strategy essentially entailed preparing the computational fluid dynamics images acquired without reaction solutions through the RGB fusion technique to generate reconstructed images, which were subsequently input into the prediction model. This methodology involved sequential testing of U-Net, Res-Net, Efficient Net, and Inception Net models.

Figure 25 presents the validation MAE results. The maximum value is observed in the Efficient Net model, consistent with the initial method. The U-Net model has the lowest value. This score signifies the efficacy of the U-Net model in segmentation tasks. Res-Net exhibits a somewhat elevated error value; however, it does not demonstrate a substantial disparity in forecasting flame behavior and high-temperature areas. Due to its multi-layered architecture, Inception V3 can process the dataset at a specific scale. Efficient Net exhibits a decline in performance during dataset training due to overgeneralization.

Figure 26 illustrates the distribution of file sizes for the models. The U-Net model exhibits the smallest file size. The model, around 50 MB in size, possesses the greatest predictive capability. According to

Table 9. Comparison of models for second approach.

Model	Validation MAE	File Capacity (MB)	Average Prediction Time (s)	IoU	F1 Score
U-Net Model	0.0023	50	0.07	0.98	0.97
Res-Net	0.007	854	0.07	0.98	0.97
EfficientNet	0.025	630	0.11	0.96	0.94
InceptionV3	0.0097	834	0.08	0.98	0.96

, the mean prediction time for all models, excluding Efficient Net, is 0.07 s. The model exhibits the lowest F1 and IoU scores for Efficient Net. As demonstrated in the models, as the F1 score drops below 0.95, the predictive performance of the model diminishes, while its generalization capability enhances.

These results highlight the advantage of utilizing convolutional architectures with image-based inputs, which not only streamline the learning process but also improve scalability for practical applications. The reduced model size and training duration offer substantial benefits for deployment in industrial combustion simulations, where computational efficiency is paramount. Overall, the complementary nature of these two approaches provides valuable flexibility: the first model leverages explicit physical parameters for rapid parametric exploration, while the second exploits spatial flow features from cold flow simulations for detailed temperature field reconstruction. This dual framework broadens the applicability of deep learning in turbulent combustion modelling.

6. Conclusions

This study presents a novel integration of deep learning techniques with CFD simulations for the prediction of temperature fields in the SM1 swirl-stabilized turbulent flame. Initial CFD analyses using the SST k-ω turbulence model coupled with a Steady Laminar Flamelet combustion model provided a robust database for training.

Two distinct deep learning frameworks were developed and evaluated. The first model directly maps scalar input parameters—fuel velocity, swirl ratio, and equivalence ratio—to high-resolution temperature contours, enabling efficient parametric studies. In the first approach four models were performed. These are Dense Model, Res-Net, Efficient Net, and InceptionV3 model.

The preliminary analysis revealed that the InceptionV3 model and our Dense Model offered a superior solution. Due to its multi-layered architecture, the InceptionV3 model has surpassed the Dense Model in predictive performance. Upon examining the model dimensions, it is evident that all models possess comparable sizes. The Dense Model, Res-Net, and Inception V3 models have excelled at predicting contour borders.

In the second approach, cold flow (non-reacting) computational fluid dynamics images underwent pre-processing through the RGB fusion technique to generate composite images. The images were processed using U-Net, Res-Net, Efficient Net, and Inception V3 networks, and the prediction outcomes were disseminated. In the second technique, U-Net excels in both file size and predictive performance. Efficient Net exhibited the poorest model performance. The Efficient Net model has demonstrated notable variations within the temperature contour borders. It is inadequate for ascertaining overall conduct. The Res-Net model is the most appropriate choice following U-Net.

The model tends to produce reliable results only within the range of parameters presented during training, and due to its nature as a non-physics-based model, the ability to directly interpret the physical consistency of the results may be limited. By design, the model focuses more on steady-state conditions rather than time-dependent transient behaviors. Future work will focus on extending the deep learning framework to predict pollutants and emissions. In addition, the turbulence model’s effect on flame behavior is investigated. The presented approach represents a significant step toward data-driven combustion modeling, promising substantial benefits in terms of computational cost reduction and design efficiency.