Investigation of Hot Spot Migration in an Annular Combustor Using the SAS Turbulence Model

Abstract

Unsteady simulations were performed to investigate hot spot migration in an annular recirculation combustor equipped with two different swirler configurations. The Scale-Adaptive Simulation (SAS) turbulence model was applied, using steady-state results as the initial condition. The simulations reveal that (1) in both configurations, high-temperature gases are divided into two regions by the high-velocity jets from the primary holes, forming a primary and a secondary recirculation zone; (2) with Swirler Configuration 1, the hot spot in the primary recirculation zone is more stable, and the hot spot temperature on the combustor liner is lower; (3) with Swirler Configuration 2, the hot spot exhibits a broader axial distribution, with higher temperatures on the wall of exhaust transition piece and at the outlet.

1. Introduction

With the continuous advancement of aeronautical technology, the requirements for aero-engine performance, safety, and efficiency have been steadily increasing. The rise in combustor outlet temperature poses severe challenges to the high-temperature resistance of hot-section components. Currently, nickel-based superalloys are the primary materials used in hot-section components of aero-engines, but they can withstand temperatures of only about 1150 °C. The application of thermal barrier coatings (TBCs) effectively reduces the temperature of the substrate metal, enabling the engine to operate in environments beyond the melting point of the base superalloy [1].

As a key technology for protecting superalloys, TBCs are composite systems of high-temperature, thermally insulating ceramic materials with the substrate. By reducing the surface temperature of hot-section components and improving their resistance to high-temperature oxidation and corrosion, TBCs significantly enhance the thrust-to-weight ratio and thermal efficiency of engines, while also extending the service life of hot-section components under high-temperature conditions. However, during actual service, TBCs often suffer from premature cracking, spallation, and other failure modes, which critically undermine engine reliability and durability. In combustors, the primary cause of TBC failure is corrosion by CMAS (mainly composed of CaO, MgO, Al₂O₃, and SiO₂) [2,3,4]. This type of failure is closely associated with the non-uniform distribution and dynamic migration characteristics of high-temperature gases inside the combustor.

The excessive local thermal load in combustors is primarily caused by internal high-temperature hot spots. The formation, distribution, and morphology of these hot spots are closely related to the jets from the primary holes, the characteristics of the recirculation zones, and the swirler geometry. The dynamic migration of hot spots directly affects the thermo-mechanical load distribution on the combustor liner, exhaust transition piece, and turbine guide vanes. Conventional experiments are limited in measuring the transient temperature of hot spots inside combustors and cannot capture their migration process, making numerical simulations an effective approach to study this complex phenomenon.

Regarding turbulence modeling, the Reynolds-Averaged Navier–Stokes (RANS) approach is the most widely used in industry, primarily for predicting overall outlet temperature trends. However, Christopher et al. [5] reported that RANS tends to overpredict total temperature diffusion and fails to preserve turbulence anisotropy. While RANS offers low computational cost, it cannot resolve the dynamic evolution of hot spot [6,7,8]. Large-Eddy Simulation (LES) provides higher accuracy but requires extremely fine grids and vast computational resources, limiting its applicability in engineering problems with complex geometries. The Scale-Adaptive Simulation (SAS) method introduces the von Kármán length scale into the turbulence dissipation equation, enabling automatic detection of unsteady flow regions. This approach significantly reduces computational cost while maintaining accuracy [9], making it more suitable for simulating complex flows such as those in annular combustors. Andreini et al. [10] compared three turbulence models for combustor–turbine interaction and found that SAS results were consistent with LES predictions but required much lower computational resources.

In this study, unsteady flow and combustion simulations were performed for an annular recirculation combustor with two swirler configurations using the SAS turbulence model. The focus is on analyzing how swirler geometry influences the hot spot formation mechanisms and migration characteristics in the combustor, providing theoretical guidance for optimizing combustor design and improving the service environment of thermal barrier coatings.

2. Numerical Method

The Scale-Adaptive Simulation (SAS) model is developed on the basis of the Shear Stress Transport (SST) turbulence model, in which the von Kármán length scale is introduced as a second length scale. This additional length scale is incorporated into the source term of the specific turbulence dissipation rate equation [11]. By adding the SAS source term, the excessive damping of high-frequency flow structures inherent in RANS is avoided. The value of the von Kármán length scale can be used to determine flow stability and to automatically identify regions that have entered unsteady flow. In separated flow regions, once the criterion is satisfied, the SAS term is activated, and the model locally degenerates into a Large-Eddy Simulation (LES) mode. In these unsteady regions, the eddy viscosity is automatically reduced to resolve larger-scale turbulent fluctuations. The transport equations of the SST-based turbulence model are given as follows:

$${\displaystyle \frac{\partial \rho k}{\partial t}}+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho u_{i}k\right)=G_k-\rho c_{\mu }k\omega +{\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right){\displaystyle \frac{\partial k}{\partial x_j}}\right]$$

(1)

$${\displaystyle \frac{\partial \rho \omega }{\partial t}}+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho u_i\omega \right)=\alpha {\displaystyle \frac{\omega }{k}}{G}_k-\rho \beta {\omega }^2+Q_{SAS}+\left(1-F_1\right){\displaystyle \frac{2\rho }{{\sigma }_{\omega 2}}}{\displaystyle \frac{1}{\omega }}{\displaystyle \frac{\partial k}{\partial x_j}}{\displaystyle \frac{\partial \omega }{\partial x_j}}$$

(2)

where $t$ is time, $\rho$ is density, $k$ is the turbulence kinetic energy, $u$ is velocity, $G_k$ is the turbulence source term, $\mu$ is the dynamic viscosity, ${\mu }_t$ is the turbulent viscosity, $Q_{SAS}$ is the source term, and $x_i$ is the spatial coordinate with subscript $i$ denoting the coordinate direction. Detailed values of the model constants can be found in Ref. [12].

$$Q_{SAS}=max\left[\rho {\eta }_2\kappa S^2{\left[{\displaystyle \frac{L}{L_{\nu \kappa }}}\right]}^2-C\cdot {\displaystyle \frac{2\rho k}{{\sigma }_{\varphi }}}max\left[{\displaystyle \frac{1}{{\omega }^2}}{\displaystyle \frac{\partial \omega }{\partial x_j}}{\displaystyle \frac{\partial \omega }{\partial x_j}},{\displaystyle \frac{1}{k^2}}{\displaystyle \frac{\partial k}{\partial x_j}}{\displaystyle \frac{\partial k}{\partial x_j}}\right],0\right]$$

(3)

$$L=\sqrt{k}/\left(c_{\mu }^{1/4}\cdot \omega \right)$$

(4)

$$L_{\nu K}=\kappa \left|{\displaystyle \frac{U^{\prime }}{U^{″}}}\right|$$

(5)

In the equations, $S$ is the strain-rate tensor, $L$ is the modeled turbulence length scale, with the constants taken as ${\eta }_2$ = 3.51, ${\sigma }_{\varphi }$ = 2/3, and $C$ = 2.

3. Validation of Numerical Simulation

Extensive validation cases for the SAS turbulence model have been reported in Refs. [9,11]. To further verify its predictive accuracy in combustor simulations, the SAS model was applied to the EtF7 ethanol combustion case of the Sydney bluff-body burner (Sono-Tek, Milton, NY, USA) [13], and the temperature distribution was checked against experimental data [14].

In this study, the Sydney EtF7 ethanol spray flame case was selected to validate the numerical setup. Figure 1 shows the simplified configuration of the Sydney jet combustor. The combustor consists of three streams: a central stream carrying fuel droplets generated by an ultrasonic atomizer upstream, a middle stream with a pilot flame, and an outer co-flow of cold air. The central injection tube has a diameter of D = 10.5 mm, surrounded by the pilot flame with an outer diameter of 25 mm.

The computational domain for the numerical simulation is a cylinder with dimensions of 2π × 11D × 25D. An unstructured mesh with a polyhedral core was generated using Fluent Meshing 2020, with local refinement applied in the central combustion region to better capture the flow field variations. The fuel inlet was modeled as a surface nozzle, and the pilot flame was set as high-temperature air at 2100 K. The total mesh count was approximately 3 million. The boundary conditions are summarized in

Table 1. Inflow boundary conditions for case EtF7 (experiment set B) [14].

Inlet Conditions	Value
Bulk velocity of jet (m/s)	60
Liquid mass flow rate at jet exit (g/s)	1.167
Vapor fue flow rate at jet exit (g/min)	0.083
Temperature estimated at jet exit (K)	293
Carrier mass flow rate (g/s)	6.267
Equivalent ratio at jet exit	0.1

.

The predicted mean temperature radial distributions at different axial locations, x/D = 10, 20, and 30, are shown in Figure 2 [15,16].

The Sydney combustor was simplified, and the inlet conditions differ considerably from the experiment, resulting in a larger deviation at x/D = 10. At all three axial positions, the experimental temperature profiles exhibit an initial increase followed by a decrease along the radial direction. The numerical simulations successfully capture this trend, and the locations of peak temperature are consistent with the experimental measurements, showing good agreement overall. In the downstream region (x/D = 20 and 30), some differences are observed between the SAS and k-epsilon results. This discrepancy primarily arises from the fundamental differences between the two turbulence models: the k-epsilon model, being a fully RANS-based approach with isotropic eddy viscosity, tends to overdamp turbulent fluctuations and therefore predicts an overly diffused temperature field; in contrast, the SAS model transitions to a LES-like resolution when strong unsteady shear-layer structures develop downstream of the injector, allowing it to resolve large-scale coherent vortices and sharper thermal gradients. Consequently, SAS provides a more physically realistic description of turbulent mixing in the downstream region. Considering the overall agreement in trend and peak location with the experiment, the present numerical setup is considered reliable for simulating hot spot formation and migration within the combustor.

4. Numerical Simulation of a Practical Annular Combustor

4.1. Problem Description

Considering the premature cracking and spalling of typical combustor components during service, a flow and heat transfer simulation of the combustor with thermal barrier coatings (TBCs) was carried out from the perspective of aerothermal characteristics. The objective was to obtain the aerodynamic and heat transfer features on component surfaces under different operating conditions and configurations listed in

Table 2. Inlet and outlet parameters of typical combustor operating conditions.

Parameter	Design Point	Takeoff Condition	Ground Idle	Maximum Continuous
Inlet air pressure	1.000	0.965	0.376	0.907
Inlet air temperature	1.000	0.996	0.771	0.839
Total airflow	1.000	0.977	0.454	0.933
Liner airflow	1.000	0.977	0.456	0.932
Fuel flow rate	1.000	0.942	0.265	0.862

, thereby providing technical support for understanding the failure mechanisms of TBCs in combustors.

The design point condition was selected as the reference baseline. All physical quantities of the boundary conditions were normalized to a dimensionless value of 1. The other three operating conditions were also non-dimensionalized based on the corresponding parameters at the design point. The specific values are given in Table 2.

Based on the simulation results of combustor aerothermal performance under different operating conditions with Swirler Configuration 1 and Configuration 2, the formation of hot spots in the primary combustion zone and their downstream migration are analyzed. The study further considers different configurations of the thermal barrier coating (TBC) in the combustor, specifically: (1) the outer liner of combustor and exhaust transition piece casing in a concave annular surface exposed to hot gases, (2) the inner liner of combustor and exhaust transition piece casing in a convex annular surface exposed to hot gases, and (3) the dome region in a flat annular surface exposed to hot gases.

The investigated combustor is an annular recirculating combustor equipped with swirlers, as shown in Figure 3 and Figure 4 The swirlers enhance fuel-air mixing, generate recirculation zones, and improve flame stability. The two swirler configurations differ only at the outlet: Configuration 1 has guide vanes with an angle of 38°, resulting in a wider jet diffusion and a more open structure; Configuration 2 adopts a compound-cone design with a front angle of 18° and a rear angle up to 67°, leading to a significantly contracted outlet, as shown in Figure 3. To reduce computational cost, only 1/12 of the annular combustor is modeled, as illustrated in Figure 4. The combustor mainly consists of the swirler, combustor liner, and exhaust transition piece.

4.2. Simulation Setup and Mesh Generation

Numerical simulations were performed using ANSYS Fluent 2020. The combustion model employed was the Eddy Dissipation Model (EDM) with a two-step chemical reaction mechanism. The evaporation and trajectory of kerosene droplets (C₁₂H₂₃) were modeled using the Euler–Lagrange Discrete Phase Model (DPM), which accounts for the interactions between the continuous phase (fluid) and the discrete phase (droplets). In this approach, the continuous phase is solved by the Eulerian method using the Navier–Stokes equations to obtain the flow field, while the discrete phase is solved by the Lagrangian method to track the motion of individual particles, including droplet-fluid interactions. A conical injector was adopted, with a uniform droplet diameter of 0.05 mm.

For steady-state calculations, the realizable k-ε turbulence model with standard wall functions was used, while transient simulations were conducted with the Scale-Adaptive Simulation (SAS) model [12]. The time step for the unsteady simulation is 10⁻⁵ s, and the computation of a single case requires approximately 30 days.

The computational mesh was generated in Fluent Meshing using a hexahedral core. The diameter of film-cooling holes in the combustor liner is approximately 0.6 mm; to ensure accuracy, local mesh refinement was applied in this region, with cell sizes in the range of 0.2–0.3 mm. Since combustion occurs mainly in the liner and swirler region, a body of influence (BOI) refinement was applied in these areas to better capture fuel-air mixing. As shown in Figure 5, Simulations were performed using meshes of 2.4 million, 3.8 million, 6.6 million, and 9.6 million cells. When the mesh size exceeded 3.8 million cells, the differences in the results were small, with errors within 5%. Therefore, a mesh of 3.8 million cells was selected for the subsequent calculations. An unstructured mesh was generated for the fluid–structure coupled combustor, with a total of 25 million cells.

4.3. Results and Discussion

4.3.1. Temperature Distribution Under Different Operating Conditions

Figure 6 presents the relative temperature contours on the central axial plane of the combustor for the four operating conditions. It is observed that the high-temperature region, truncated by the primary holes, is mainly concentrated within the liner. Due to the presence of cooling holes, the gas temperature near the wall remains relatively low. From the design point to ground idle, the maximum temperature and its spatial extent in the primary zone gradually decrease with the reduction in fuel supply. Consequently, the design point condition serves as the most representative operating case for analyzing hot spot formation and migration within the combustor.

To reduce computational cost, steady-state simulations were first performed for four representative operating conditions using the RANS approach. The temperature fields were nondimensionalized by selecting the minimum temperature T_min in the computational domain as the reference scale, with the local temperature T converted into a nondimensional form.

4.3.2. Time-Averaged SAS Analysis

Based on the steady-state results, transient simulations were conducted with a time window from 0 to 20 ms and a time step of 0.01 ms. The inlet air entering the combustor was divided into three streams: (1) part of the air flows axially along the outer liner (out liner of combustor and out liner of exhaust transition piece), with a fraction entering the combustor through the outer-liner holes, while the rest passes through the swirler and into the inner liner (inner liner of combustor and inner liner of exhaust transition piece) via inner-liner holes; (2) another portion enters directly through the dome region; and (3) the remaining portion flows through the swirler, mixes with fuel, and then enters the combustor.

Velocity fields were nondimensionalized in the same way as temperature fields, with the maximum velocity V_max in the computational domain chosen as the reference scale. As shown in Figure 7, two recirculation zones with double-vortex structures are formed. The main mechanism of this dual-vortex structure is as follows: after stable combustion is established, a high-temperature region develops inside the liner, where the gas exhibits higher viscosity and lower density. Meanwhile, the fuel droplets are injected at relatively low temperature but high velocity, leading to strong shear interactions with the surrounding air. This fuel jet penetrates downstream toward the primary holes, where the high-momentum primary jets induce deep penetration into the flow field. Combined with the inflow through the liner wall holes, the recirculation is split into a primary and a secondary recirculation zone.

Between the dome and the primary holes, two relatively symmetric vortex structures are formed, creating the primary recirculation zone that provides a continuous ignition source for the flame. Downstream of the primary holes, the outer liner of the exhaust transition piece forms a concave surface with a larger contact area with the hot gas, inducing a stronger buoyancy effect of the thermal boundary layer and transverse backflow. This strengthens the vortex, resulting in two asymmetric secondary vortices that form a secondary recirculation zone. This allows high-temperature gases to stagnate in the secondary zone, which helps extend the residence time of the gases. And for Configuration 1, the recirculation structure shifts upstream, leading to combustion peaks concentrating near the front. Therefore, the swirl numbers of the two configurations in the combustor are 4, respectively. For Configuration 2, the primary recirculation zone extends downward, enhancing the mixing of fuel and air.

The central section chosen is the one passing through the primary holes of the combustor. As shown in Figure 8, hot spots inside the combustor are mainly concentrated along the axis of the flame tube, exhibiting a distinct high-temperature core structure. Upstream of the primary holes, hot spots display a good axisymmetric distribution, while downstream, the symmetry is weaker consistent with the vortex structures in the velocity streamline diagram.

For Configuration 1, the high-temperature zone exhibits a “funnel shape,” with hot spots located closer to the dome. As the flow develops downstream, the temperature remains relatively high, but the axial extension is limited, and the hot spots are constrained by the main recirculation zone. For Configuration 2, hot spots clearly shift downstream beyond the primary holes, with a wider axial spread, mainly located in the mid-to-rear section of the combustor liner. This indicates a downstream migration of the combustion center, with the hot spot region more uniformly dispersed and the temperature gradient relatively smoother.

The four selected cross-sections inside the combustor are the central section of the first row of cooling holes on the inner and outer liners, the central section of the primary holes on the inner and outer liners, the central section of the dilution holes on the inner and outer liners, and the central section of the third row of cooling holes on the exhaust transition piece. As shown in Figure 9, due to the existence of cooling holes, the gas temperature near the wall is significantly lower than that in the high-temperature core region, yet noticeable hot spots still appear in the regions between the holes.

For the configuration, the gas temperature downstream of the primary holes decreases significantly, indicating that the air entering through the dilution holes is mainly used to reduce the gas temperature. In contrast, for the configuration 2 swirler, the gas temperature downstream of the primary holes does not decrease, suggesting that the air entering through the dilution holes mainly participates in the combustion reaction, while the cooling air introduced through the cooling holes in exhaust transition piece is primarily responsible for lowering the gas temperature.

4.3.3. Instantaneous Analysis

The airflow enters the liner through multiple passages of the air holes. The droplet spray injected from the nozzles inside the swirlers interacts with the various airflow streams, and after full circulation, a stable vortex structure is formed, as shown in Figure 10. At different moments, the flow field structure inside the combustor still exhibits the distribution of the primary recirculation zone and the secondary recirculation zone. Within each recirculation zone, more small-scale vortex structures can be captured, and the fluid motion trajectories become increasingly complex. These small vortex structures are mainly located in the high-temperature core region of the combustor. This is because the high-temperature core region is accompanied by fuel droplet evaporation as well as intense and complex combustion chemical reactions. Meanwhile, the fluid itself has viscosity, and the velocity gradients in the flow field are oriented in multiple directions. Over time, the small vortex structures continuously dissipate and regenerate, while the large vortex structures remain essentially unchanged.

For Configuration 1, the symmetric vortex structures upstream of the primary holes and the two dominant vortex structures downstream of the primary holes persist throughout the process. For Configuration 2, the vortex structures upstream of the primary holes remain symmetric, but the vortex intensity is weaker than that of Configuration 1. This is because the smaller flare angle of Configuration 2 increases the axial jet momentum, thereby reducing the velocity gradients in the primary recirculation zone and suppressing strong vortex separation.

C₁₂H₂₃ is treated as gaseous fuel. As shown in Figure 11 and Figure 12, with the progression of time, the fuel gradually evaporates and mixes with the surrounding high-temperature gases. The low-concentration regions gradually develop downstream. The hot spots originate in the mixing region of fuel and air within the primary recirculation zone and subsequently migrate downstream along the mainstream direction during the combustion process. Since the fuel is almost completely evaporated and consumed in the primary combustion zone, the migration path of the hot spots in the mainstream region aligns closely with the distribution of the fuel mass fraction.

In terms of fuel distribution patterns, Configuration 1 exhibits a “C”-shaped structure with relatively clear boundaries, smaller fluctuations, and a more regular morphology, while little fuel is present directly opposite the primary holes. In contrast, Configuration 2 displays a “T”-shaped distribution with blurred boundaries, large fluctuations, and an irregular morphology, with more fuel located directly opposite the primary holes. The air jets entering through the primary holes in Configuration 1 impose weaker disturbances on the fuel distribution compared with Configuration 2. The results indicate that in Configuration 1, the jets from the primary holes divide the hot spots into two regions, with relatively clear boundaries and stable morphology in the primary combustion zone, showing little violent oscillation. In Configuration 2, however, the hot spots in the jet region fluctuate significantly under the influence of the primary hole jets, resulting in larger boundary fluctuations and more irregular shapes of hot spots in the mainstream region. Therefore, in the mainstream zone, the migration path of hot spots is jointly governed by both the fuel mass fraction distribution and the vortex structures.

4.3.4. Migration of Hot Spots on Wall Surfaces

High-temperature gases within the combustion chamber can respond almost instantaneously to variations in fuel concentration, flow disturbances, and changes in recirculation structures. During unsteady combustion, the evolution of vortex structures and local variations in mixture fraction can rapidly alter the flame propagation path. Consequently, hot spots in the fluid domain may “jump,” resulting in rapid migration; thus, both the location and extent of hot spots in the fluid domain exhibit pronounced temporal fluctuations.

In contrast, the solid wall possesses a significantly higher heat capacity and a much lower thermal diffusivity compared to the gas. Temperature changes in the wall require the accumulation of heat flux and propagate slowly along the wall thickness. As a result, hot spots cannot expand or migrate rapidly across the wall surface. On solid surfaces, hot spots therefore display a “passive” or “insensitive” behavior, which closely aligns with the time-averaged hot spot pattern. Examination of the wall temperature distribution indicates that the hot spot pattern in Configuration 1 is symmetric, whereas Configuration 2 exhibits weaker symmetry. In both configurations, the inner ring experiences higher hot spot temperatures than the outer ring.

Specifically, in Configuration 1 (Figure 13 and Figure 14), the inner-ring hot spots form a ring surrounding the central primary holes. Downstream of the primary holes, the hot spot region expands. The outer-ring hot spots are also concentrated around the primary holes, with a large axial extent but limited radial spread. In Configuration 2, inner-ring hot spots similarly surround the primary holes, but their area is larger and temperatures are higher compared to Configuration 1. The outer-ring hot spots in Configuration 2 occupy positions similar to Configuration 1, maintaining the same axial extent but exhibiting a wider radial distribution.

As shown in Figure 15 and Figure 16, the inner-ring hot spots in the exhaust transition piece are primarily concentrated downstream of the primary holes. Due to the convex shape of the inner ring, it remains in contact with the high-temperature gas for a longer duration, and the front portion is more susceptible to gas impingement, resulting in localized high-temperature regions that exhibit a crescent-shaped, attached distribution. For the outer ring, the concave region near the center is more exposed to high-temperature gas flow, so temperatures remain elevated near the central area, but the temperature gradient is relatively mild.

As shown in Figure 17, the hot spots in Configuration 2 are more pronounced at the outlet compared to Configuration 1. The hot spots exhibit significant fluctuations, primarily located near the inner half of the outlet region, and migrate circumferentially.

5. Conclusions

Based on the present study, the following conclusions can be drawn:

• In combustion chambers equipped with two different swirler configurations, the high-speed jets from the primary holes divide the high-temperature gas into two distinct regions. In the fluid domain, the high-temperature region in Configuration 1 is mainly concentrated within the primary recirculation zone, whereas in Configuration 2, high-temperature regions are extensively present in both the primary and secondary recirculation zones.
• In Configuration 1, the two symmetric vortex structures within the primary recirculation zone are more stable. Cool air entering through the cooling holes effectively envelops the high-temperature gas, resulting in lower hot spot temperatures on the combustor liner. In Configuration 2, fuel droplets and air exiting the swirler possess higher axial velocities. The vortex structures in the primary recirculation zone are less stable, and the jet from the primary holes induces strong disturbances in the fuel distribution, leading to higher wall temperatures.
• The temperature distribution at the outlet of Configuration 1 is relatively uniform, with no obvious hot spots. In Configuration 2, the axial extent of high-temperature gas within the combustion chamber is larger, making hot spots at the outlet more pronounced. These hot spots primarily occur within the inner half of the outlet region and migrate circumferentially.
• A larger swirler outlet diffusion angle promotes the formation of wide, low-momentum recirculation zones, which benefits flame stabilization and the development of a broad high-temperature region. The resulting lower outlet velocity leads to milder mixing, with hot spots located closer to the inner liner of combustor. Conversely, a smaller diffusion angle favors the generation of a compact, high-velocity central jet. Near the center axis, local high-temperature, strong recirculation zones form, and the interaction between the high-speed jet and surrounding low-speed gas creates intense shear layers, enhancing turbulence and accelerating mixing, which shifts hot spots closer to the jet region.

The results provide practical design guidance for swirler outlet angles and film-cooling layouts, showing how geometric parameters shift the flame center and modify TBC heat loads. This contributes directly to aero-engine combustor optimization.