Open AccessArticle

Study on the Dynamic Combustion Characteristics of a Staged High-Temperature Rise Combustor

Meng Li

^1,2,3,

Jinhu Yang

^4,*

Cunxi Liu

^2,3

Fuqiang Liu

⁴

Kaixing Wang

^2,3,

Changlong Ruan

⁴,

Yong Mu

⁴ and

Gang Xu

^2,3

Fluid Machinery Engineering Technology Research Center, Jiangsu University, Zhenjiang 212013, China

Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China

National Key Laboratory of Science and Technology on Advanced Light-Duty Gas-Turbine, Beijing 100190, China

⁴

Qingdao Aeronautical Technology Research Institute, Qingdao 266000, China

Author to whom correspondence should be addressed.

Energies 2025, 18(3), 662; https://doi.org/10.3390/en18030662

Submission received: 19 December 2024 / Revised: 10 January 2025 / Accepted: 14 January 2025 / Published: 31 January 2025

(This article belongs to the Special Issue Advanced Research in Combustion Energy: Optimization, Applications, and Analysis)

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Browse Figures

Figure 1
Schematic of the combustion chamber: (a) combustion chamber; (b) triple swirler; (c) midplane. "> Figure 2
Grid independence verification. "> Figure 3
Mesh distributions: (a) combustor; (b) swirler. "> Figure 4
Courant number distribution. "> Figure 5
Percentage of resolved turbulent kinetic energy. "> Figure 6
Kinetic energy spectra. "> Figure 7
Comparison of experimental results and simulation results of average velocity field. "> Figure 8
Time-averaged velocity field (Case0): (a) axial velocity; (b) radial velocity. "> Figure 9
Axial velocity distribution under temperature fluctuation: (a) axial distribution; (b) radial distribution. "> Figure 10
Time-averaged temperature distribution in the midplane of the combustor (Case0). "> Figure 11
Comparison of time-averaged RTDF of combustion chamber outlet section. "> Figure 12
Instantaneous temperature evolution in the middle section of the combustor under inlet temperature fluctuation. "> Figure 13
Comparison of axial distribution of temperature fluctuation under different working conditions: (a) temperature pulsation; (b) air pulsation; (c) fuel pulsation. "> Figure 14
Frequency domain diagram of heat release rate pulsation under different working conditions: (a) temperature pulsation; (b) air pulsation; (c) fuel pulsation. "> Figure 15
Comparison of inlet parameters and outlet average temperature of combustion chamber with time under different operating conditions: (a) temperature pulsation; (b) air pulsation; (c) fuel pulsation. "> Figure 16
The outlet time-averaged temperature distribution under different operating conditions. "> Figure 17
Distribution of DOTDF. ">

Versions Notes

Abstract

Currently, steady-state analysis predominates in combustion chamber design, while dynamic combustion characteristics remain underexplored, and there is a lack of a comprehensive index system to assess dynamic combustion behavior. This study conducts a numerical simulation of the dynamic characteristics of the combustion chamber, employing a method combining large eddy simulation (LES) and Flamelet Generated Manifold (FGM). The inlet air temperature, air flow rate, and fuel flow rate were varied by 1%, 2%, and 3%, respectively, with a pulsation period of 0.008 s. The effects of nine different inlet parameter pulsations on both time-averaged and instantaneous combustion performance were analyzed and compared to benchmark conditions. The results indicate that small pulsations in the inlet parameters have minimal impact on the steady-state time-averaged performance. In the region near the cyclone outlet, which corresponds to the flame root area, pronounced unsteady flame characteristics were observed. Fluctuations in inlet parameters led to an increase in temperature fluctuations near the flame root. Analysis of the outlet temperature results for each operating condition reveals that inlet parameter fluctuations can mitigate the inherent combustion instability of the combustion chamber and reduce temperature fluctuations at the outlet hot spot.

Keywords:

large eddy simulation; staged combustion chamber; dynamic combustion characteristics

1. Introduction

The combustion process in the main combustion chamber of an aero-engine is inherently dynamic. Under steady operating conditions, the physical quantities and their spatial distribution within the combustion chamber fluctuate over time. Under transient operating conditions, the physical fields in the combustion chamber exhibit dynamic variations. As performance requirements for both military and civil aircraft continue to evolve, the design of hot-end components is increasingly focused on precision, with the performance indices now extending beyond steady-state parameters to include both steady-state and dynamic performance metrics. However, research on the dynamic combustion characteristics of the combustion chamber remains insufficient, and a comprehensive index system for evaluating these dynamic characteristics is lacking. To address this gap, this study presents a numerical simulation of the dynamic combustion characteristics of the combustion chamber, providing both data and methodological support for future fine-tuned design of combustion chambers based on dynamic combustion behavior [1].

With advancements in laser and combustion diagnostic technologies, detailed studies of dynamic combustion within combustion chambers have become increasingly feasible [2,3,4,5]. Fu et al. [6] utilized a high-speed camera and laser to measure OH* Chemiluminescence (CL), CH₂O, and SO₂-PLIF at a frequency of 20 kHz to capture the two-dimensional structure and heat release distribution of the flame. They observed that fluctuations in fuel mass flow rate fluctuation could extend blowoff limits. Stohr et al. [7,8] investigated the Lean Blowout (LBO) characteristics of partially premixed combustors using synchronized stereo Particle Image Velocimetry (PIV) and OH Planar Laser-Induced Fluorescence (PLIF) techniques. Their findings revealed that the flame root exhibits inherent instability near the LBO, characterized by frequent extinction and reignition events. These results underscore the critical role of the flame root and suggest that targeted modifications to the flow field or mixture fraction in this region could potentially extend the LBO limit. Zhao et al. [9] employed CH* chemiluminescence high-speed imaging technology to visualize spray flames in a multi-swirl staged combustor and applied Fast Fourier Transform (FFT) and Proper Orthogonal Decomposition (POD) methods to analyze high-speed imaging data collected at various time points prior to flame extinction. Their results identified key precursor phenomena leading to flame extinction. Broda et al. [10] utilized CH* chemiluminescence imaging to capture unstable flame dynamics in their experiments and investigated the impact of inlet temperature variations on the flame morphology of a premixed swirl burner. The experimental results demonstrated that, as the inlet temperature gradually increased beyond a critical threshold, the flame became unstable, with a shortened flame length that eventually entered the corner vortex recirculation zone. Guiberti and Boyette [11,12] conducted a series of experimental studies on high-pressure turbulent non-premixed jet flames, examining the variations in flame lift-off height and flame length with pressure at different inlet Reynolds numbers. Their findings indicated that an increase in pressure enhanced the stability of jet flames at high Reynolds numbers. Additionally, they observed that, as pressure increased, the flame reaction zone became thinner, and the flame front exhibited significantly enhanced wrinkling.

In numerical simulations, although the Reynolds-Averaged Navier–Stokes (RANS) method is widely used, it is unable to capture the detailed characteristics of complex transient flows. In contrast, LES can directly resolve the large-scale structures within the flow, accurately model the combustion field in the combustion chamber, and capture the transient behavior of the flow. LES has become a critical tool for dynamic combustion research [13,14,15,16,17]. Xu Jianguo et al. [18] conducted a large eddy simulation study on methane-air turbulent combustion in a dual-swirl combustor. They found that the recirculation zone velocity increased with pressure, the flame structure became more compact at higher pressures, and both the Precessing Vortex Core (PVC) frequency and the outlet gas temperature significantly increased with rising pressure. Nan Meng et al. [19] investigated the effects of flame tube structure on flame propagation and pressure fluctuations in the combustion field using LES and Power Spectral Density (PSD) coupling. Their results demonstrated that the presence of primary combustion and mixing holes in the combustion chamber increased the amplitude of pressure oscillations and heat release rate, with peak values occurring in the shear layer and vortex structure regions. Lv et al. [20] employed the FGM combustion model in combination with a Weighted-Model Large Eddy Simulation (WMLES) to examine the dynamic combustion characteristics of a coaxial staged combustor, varying the equivalence ratio of the pilot stage by adjusting the pilot fuel flow rate. Chen et al. [21] used LES to study the dynamic flame structure during stable and unstable combustion in a dual-swirl combustor, accurately capturing various flow dynamics induced by PVC and thermoacoustic oscillations. They identified the stagnation point caused by PVC as a critical factor in flame stabilization.

At present, most of the research on dynamic combustion explores the influence of combustion chamber structure and large-scale changes in inlet parameters on dynamic combustion. However, the influence of engine inlet parameter pulsations or speed fluctuations on the pulsation characteristics of the combustion chamber under stable operating conditions remains underexplored. Therefore, this paper presents a large eddy simulation study of a staged combustion chamber, coupled with the Flamelet Generated Manifold combustion model, to investigate the effects of inlet air flow, temperature, and fuel flow pulsations on dynamic combustion behavior. The findings of this study provide both data and methodological support for the future design optimization of combustion chambers based on dynamic combustion characteristics.

2. Computational Models and Methods

2.1. Physical Model and Meshing

This study investigates a single-head fan-shaped model of a three-swirl high-temperature rise combustor, as illustrated in Figure 1. The model consists primarily of a casing, head swirler, nozzle, and flame tube. Air enters the flame tube through the head swirler, the primary holes, the dilution holes, and the cooling holes, creating the required flow field structure and outlet temperature distribution for combustion. Specifically, 45.05% of the air enters through the head of the flame tube, forming a recirculation zone that organizes the combustion process. A total of 17% of the air enters through the primary holes, with part of it participating in the combustion within the main combustion zone, while the remainder contributes to the initial mixing of the combustion chamber’s temperature field. Another 17% of the air enters through the dilution holes, where it mixes with the upstream-burned high-temperature gas to achieve a uniform temperature distribution suitable for turbine acceptance. The remaining 21.05% of the air enters through the cooling holes, where it provides protection to the flame tube via adherent film cooling. There are 4 primary holes, 4 dilution holes, and 1655 cooling holes. The design parameters of the swirler are provided in Table 1. In the swirler design, the two-stage fuel nozzles consist of centrifugal nozzles and multi-point injection air atomizing nozzles, arranged from the innermost to the outermost stages. The pre-combustion fuel is discharged through the centrifugal nozzle and atomized by the air shear generated by the first and second-stage cyclones. The main combustion fuel is released through small holes in the wall of the third-stage cyclone. The fuel distribution between the pre-combustion and main combustion stages is 30% and 70%, respectively. The swirl number of the three-stage axial cyclones increases from the innermost to the outermost stages. The rotation directions are clockwise for the first stage, counterclockwise for the second, and counterclockwise for the third.

Due to the dense, multi-inclined hole design of the flame tube cooling holes, unstructured grids are employed to mesh the cyclone, combustion zone, and cooling holes, thereby reducing the overall grid count. This approach facilitates the meshing of the cyclone and flame tube, enabling accurate capture of the dynamic combustion process. Structured grids are used for the remaining areas.

Three sets of grids with varying numbers of elements were generated using the same method, and the axial velocity profile at Line 2 was selected to assess grid independence. The results are presented in Figure 2. After comparison, it was determined that the grid with 17.89 million elements was the most suitable. The grid distribution for the cross-section and the swirler within the combustion chamber is shown in Figure 3. The grid size for the flame tube and the head cooling hole is set to 0.2 mm, while the maximum grid size overall is 1.6 mm. The final grid contains 17.89 million elements.

2.2. Calculation Methods and Operating Conditions

In this paper, large eddy simulation is used for turbulence calculation. The filtered control equation is as follows:

\frac{\partial \bar{ρ}}{\partial t} + \frac{\partial \bar{ρ} {\tilde{u}}_{i}}{\partial x_{i}} = 0

(1)

\frac{\partial \bar{ρ} {\tilde{u}}_{i}}{\partial t} + \frac{\partial (\bar{ρ} {\tilde{u}}_{i} {\tilde{u}}_{j})}{\partial x_{j}} = \frac{\partial σ_{i j}}{\partial x_{j}} - \frac{\partial \bar{ρ}}{\partial x_{j}} - \frac{\partial τ_{i j}^{s g s}}{\partial x_{j}}

(2)

\frac{\partial \bar{ρ} \tilde{h}}{\partial t} + \frac{\partial (\bar{ρ} {\tilde{u}}_{j} \tilde{h})}{\partial x_{j}} = \frac{D \bar{p}}{D t} - \frac{\partial}{\partial x_{j}} (\bar{ρ} \tilde{u_{j} h} - \bar{ρ} {\tilde{u}}_{j} \tilde{h}) + \frac{\partial}{\partial x_{j}} (\bar{ρ} α \frac{\partial \tilde{h}}{{\partial x}_{j}}) + \bar{τ_{i j} \frac{\partial u_{i}}{\partial x_{j}}}

(3)

\frac{\partial \bar{ρ} {\tilde{Y}}_{k}}{\partial t} + \frac{\partial (\bar{ρ} {\tilde{Y}}_{k} {\tilde{u}}_{j})}{\partial x_{j}} = \frac{\partial}{\partial x_{j}} (\bar{ρ} {\tilde{D}}_{k} \frac{\partial {\tilde{Y}}_{k}}{\partial x_{j}}) - \frac{\partial}{\partial x_{j}} (\bar{ρ} \tilde{u_{j} Y_{k}} - \bar{ρ} {\tilde{u}}_{j} {\tilde{Y}}_{k}) + {\bar{ω}}_{k}

(4)

The Wale model is used to close the sub-grid stress, the combustion chamber is partially premixed combustion, and the FGM model is used to close the chemical reaction source term. The fuel is represented by n-decane, with a skeletal mechanism containing 77 components and 359 reactions [22]. The SIMPLE algorithm is employed for the numerical solution. The near-wall region is handled using the standard wall function. Fuel droplets are simulated using the Discrete Phase Model (DPM). The main combustion stage nozzle is a hollow cone, while the pre-combustion stage nozzle is a solid cone. The side walls of the fluid domain in the single-head annular combustor are modeled with a rotating periodic boundary condition, with a rotation angle of 18°.

Due to the detailed computational grid required by LES, the time step must be kept relatively small. The maximum time step for LES calculations must satisfy the following condition:

∆ t \leq \frac{∆ x}{U}

(5)

∆ x

represents the grid size, and

U

denotes the average flow velocity within the grid. Taking into account the difference between the instantaneous velocity and the average velocity, it is assumed that the Courant number is less than 0.5, which satisfies the requirements for LES calculations. The calculation formula for the Courant number is as follows:

C_{o} = \frac{U ∆ t}{∆ x}

(6)

To improve computational efficiency, LES calculations are performed based on the results of the RANS calculations. A time step of 10⁻⁶ s is selected, and the Courant number distribution across the combustion chamber cross-section is obtained. As shown in Figure 4, the global Courant number is less than 0.5, which satisfies the requirements for LES calculations.

The simulation conditions are summarized in Table 2. The inlet pressure of the combustion chamber is 500 kpa and the pressure drop is 6%. To investigate the impact of small pulsations in inlet parameters on the dynamic combustion characteristics of the combustion chamber, the inlet conditions are varied based on the benchmark conditions, with pulsations introduced as sine waves at amplitudes of 1%, 2%, and 3%. The pulsation frequency of the air and fuel boundary conditions, representing typical system-level pulsations, is simulated. The typical dynamic pulsation frequency of the combustion chamber is around 100 Hz, and the pulsation level does not exceed 3% of the mean value. Therefore, the pulsation period is selected as 0.008 s.

2.3. Model Evaluation

To verify the accuracy of the large eddy simulation and obtain high-resolution reactive flow simulation results, grid quality is crucial. Two LES turbulence criteria proposed by Professor Pope [23] are employed to assess the quality of the simulation: the grid resolution criterion and the power spectral density of the velocity. The turbulent kinetic energy of the large-scale structures is resolved by the LES, while the turbulent kinetic energy of the small-scale structures is resolved by the sub-grid scale model. The ratio of the turbulent kinetic energy of the large-scale structures to the total turbulent kinetic energy in LES is referred to as the turbulent kinetic energy resolution percentage:

p e r c e n t a g e = \frac{k_{r e s}}{k_{r e s} + k_{s g s}}

(7)

where

k_{s g s}

is the sub-grid turbulent kinetic energy, and

k_{r e s}

is the resolved turbulent kinetic energy.

k_{r e s}

can be obtained using the following formula:

k_{r e s} = \frac{1}{2} (\bar{u' u'} + \bar{v' v'} + \bar{w' w'})

(8)

where

u'

is the root mean square error of axial velocity,

v'

is the root mean square error of radial velocity, and

w'

is the root mean square error of tangential velocity.

In this study, LES calculations are performed for the reference condition. The turbulent kinetic energy resolution ratio at the cross-section of the combustion chamber and the velocity energy spectrum at a monitoring point 20 mm downstream of the pre-combustion stage nozzle are obtained, as shown in Figure 5. According to Professor Pope, a well-converged LES should resolve at least 80% of the turbulent kinetic energy. As shown in Figure 4, the turbulent kinetic energy resolution ratio in most regions of the combustion chamber exceeds 80%, indicating that the current grid quality and solver settings meet the requirements for LES calculations. Additionally, a region exhibiting a slope close to −5/3 is observed in the velocity energy spectrum in Figure 6, which aligns with the Kolmogorov turbulence theory [24]. This suggests that the current grid quality and solver settings are capable of capturing the multi-scale characteristics of the flow field.

To further validate the accuracy of the large eddy simulation method, both experiments and simulations were conducted for the multi-swirl staged combustion chamber. The numerical approach and model used are consistent with those presented in this paper. The experimental methodology is detailed in Ref. [25]. The multi-swirl staged combustion chamber adopts the centrally staged method, and the injector consists of a pilot stage and a main stage. The pilot stage consists of two counter-rotating axial swirlers and an air atomizing nozzle. The main stage contains one axial swirler and one radial swirler. Plain-orifice atomizers are equidistantly arranged on the sidewall of the 4th swirler. Figure 7 shows the distribution of the average axial velocity. The left side is the experimental result, and the right side is the simulation result. The red solid line marks the location where the average axial velocity is zero. From the comparison, it is evident that typical swirl flow field features, such as the recirculation zone and high-speed shear layers, are present in the combustion chamber. The size and position of the recirculation zone in the simulation results are in good agreement with the experimental observations, and the variation of the average axial velocity within the combustion chamber is accurately captured. These verification results demonstrate that the meshing and numerical simulation methods for the staged combustion chamber are reliable.

3. Results

Based on the reference condition (case 0), the inlet temperature, air flow rate, and fuel flow rate pulsate in the form of a sine wave by 1%, 2%, and 3%, respectively, and the pulsation period is 0.008 s. The results are compared to analyze the influence of small pulsations of inlet parameters on flow field characteristics, local high-temperature zone evolution, and outlet temperature distribution.

3.1. Time-Averaged Analysis

The characteristics of the recirculation zone are critical indicators of combustion performance within the combustion chamber. Figure 8 presents the time-averaged velocity field of the combustion chamber under reference conditions. The left panel shows the axial velocity field, while the right panel depicts the radial velocity field. Due to the combined effects of the three-stage swirler, a distinct confined swirl flow is generated downstream of the swirler head, exhibiting typical swirl combustion chamber flow features, including pilot swirl jets (Pilot SWJs), main swirl jets (Main SWJs), the central toroidal recirculation zone (CTRZ), the corner recirculation zone (CRZ), and the shear layer (SL). The red line in the axial velocity field indicates the location where the axial velocity is zero. A large-scale, low-velocity zone is formed downstream of the cyclone outlet, which promotes flame stability.

Figure 9 illustrates the axial distribution of the time-averaged axial velocity within the combustor under inlet temperature fluctuations, as well as the radial distribution curves at various axial positions along the flame tube. The dashed line indicates the point at which the axial velocity is zero. The position distribution of Line1–Line5 can be seen in Figure 1. From the figure, it is evident that the time-averaged axial velocity distributions of the combustion chamber under different temperature pulsations exhibit similar trends. The axial velocity distribution along the axial direction shows that the axial length of the recirculation zone remains relatively constant under different operating conditions, and the axial velocity profile within the main recirculation zone exhibits minimal variation.

The radial distribution curve of axial velocity at different axial positions reveals multiple velocity peaks at Line 1, which are attributed to the outlet velocities from the first, second, and third-stage cyclones, as well as the head cooling hole. Among these, the outlet velocity from the third-stage cyclone is the largest. As the axial distance increases, the velocity differences gradually diminish, and the radial distribution of axial velocity adopts an ‘M’ shape. Furthermore, as the axial distance increases, the asymmetry of the velocity distribution becomes more pronounced, with the axial velocity peak on the lower side of the flame tube significantly higher than that on the upper side. This asymmetry is primarily attributed to the structural design of the flame tube, where the number and area of cooling holes on the upper and lower sides are uneven. Additionally, the cross-sectional area of the inner ring flow is smaller than that of the outer ring, leading to an uneven distribution of air intake across the upper and lower sides of the flame tube. This results in a higher axial velocity on the lower side. At Line 4, the radial extent of the main recirculation zone reaches its maximum. The influence of intake flow and fuel flow pulsation on the steady-state flow field structure is similar, and is not analyzed further.

To quantitatively analyze the influence of different inlet parameters on the extent of the main recirculation zone, the length and width of the recirculation zone under various operating conditions were calculated, as presented in Table 3. From the table, it is evident that the width of the main recirculation zone under pulsating inlet conditions is smaller than that under the baseline operating conditions. Furthermore, as the degree of pulsation increases, the width of the main recirculation zone decreases. When the fuel flow pulsation reaches 3%, the width of the main recirculation zone attains its minimum value. By observing the length and width of the main recirculation zone in each operating condition, it is found that the difference is very small, and the change is not regular, which has little effect on the overall structure of the recirculation zone.

Figure 10 presents the time-averaged temperature distribution in the middle section of the combustion chamber under the reference condition (Case0). As shown in the figure, a ‘W’-shaped low-temperature zone is formed at the outlet of the head swirler due to the two-stage fuel injection and the swirling airflow. This swirling airflow creates a cooling film near the cooling hole of the flame tube, which serves to protect the flame tube and enhance its service life. The jet from the main combustion hole significantly reduces the high-temperature zone in the primary combustion region. Following the mixing jet, the high-temperature zone at the outlet of the combustion chamber is substantially diminished, resulting in a more uniform temperature distribution at the outlet. The fluctuation of inlet parameters has a minimal impact on the time-averaged temperature distribution within the combustion chamber and is therefore not analyzed further.

The uniformity of the outlet temperature distribution in the combustion chamber directly influences the service life of the turbine. The outlet temperature distribution OTDF and RTDF of each pulsating condition of the research object in this paper are analyzed. The temperature distributions for each operating condition are presented in Table 4. It is evident that the outlet temperature of the combustion chamber exhibits only slight variations across different conditions, suggesting that small pulsations in the inlet parameters have minimal impact on the time-averaged outlet temperature distribution. Compared with the reference condition, the fluctuation of inlet temperature and flow rate increases the steady-state OTDF, resulting in the increase of outlet hot spot temperature. Fuel flow pulsation has little effect on steady-state OTDF.

Figure 11 presents a comparison of the average radial temperature distribution at the combustion chamber outlet under different inlet parameter pulsations. The radial temperature distribution curves across the various operating conditions exhibit a similar ‘bimodal’ pattern, with high-temperature regions located at the upper and lower sections of the flame tube outlet. Notably, when the inlet fuel flow pulsation is 3%, the average radial temperature distribution at the combustion chamber outlet is more uniform compared to the other operating conditions.

3.2. Instantaneous Temperature Field Analysis

Figure 12 illustrates the instantaneous temperature evolution in the middle section of the combustion chamber over a cycle under inlet temperature fluctuations. The diagram reveals that the temperature distribution in the combustion chamber is similar across different operating conditions. In the main recirculation zone, the high-temperature region is more concentrated. Further downstream, the temperature fluctuations become more pronounced, primarily due to the mixing effects of the main combustion hole jet and the mixing hole jet. The mixing holes located in the rear section of the flame tube are arranged in a cross-pattern, allowing air to enter the flame tube through these holes and mix with the high-temperature gases. This mixing process helps to achieve a more uniform outlet temperature distribution. The interaction between the jet air around the primary holes and the dilution holes and the small eddy current in the combustion field inevitably causes a certain degree of temperature fluctuation.

To more intuitively illustrate the effect of inlet parameter pulsations on the temperature within the combustion chamber, the root mean square (RMS) value of the axial temperature over a period of 0.008 s is calculated. The formula is as follows:

T_{R M S} = \sqrt{\frac{I}{N} \sum_{i = 1}^{N} {(T - \bar{T})}^{2}}

(9)

where

T

is the instantaneous temperature and

\bar{T}

is the time-averaged temperature.

Figure 13 presents the axial distribution curve of temperature fluctuations over a cycle under different operating conditions. From the diagram, the temperature fluctuations are more clearly observed, with the root mean square value of the temperature being largest near the outlet of the cyclone. This is attributed to the stability of the flame in this region, which corresponds to the flame root, where unsteady characteristics are more pronounced. Fluctuations in the inlet parameters lead to enhanced temperature variations near the flame root. In the vicinity of the primary combustion hole, the root mean square value of temperature decreases overall; however, the axial temperature profile still exhibits significant fluctuations. This suggests that the fuel is influenced by the jet mixing near the primary combustion hole, which intensifies the temperature fluctuations. Conversely, near the mixing hole and towards the outlet of the flame tube, the temperature profile becomes smoother, indicating a reduction in localized high-temperature areas due to the mixing of cold and hot gases. As a result, the temperature distribution at the outlet becomes more uniform.

Figure 14 shows the frequency domain diagram of heat release rate pulsations under different operating conditions. The monitoring point is point 1, within the central recirculation zone. As seen in the figure, there are slight differences in the frequency domain characteristics of the heat release rate across the various operating conditions; however, the overall trends are similar. The primary difference is observed in the peak values. When the inlet fuel flow pulsation is 3%, the peak amplitude of the heat release rate reaches a maximum value of 5.6 × 10⁹ W·m⁻³ in each working condition. This shows that the fuel pulsation increases the unsteady pulsation characteristics of the flame, resulting in severe pulsation of the heat release rate. The primary peak frequency for each operating condition ranges from 100 to 200 Hz, which is consistent with the pulsation frequency of the inlet parameters. This suggests that the pulsations in this event are primarily governed by the inlet fluctuations.

3.3. Analysis of Outlet Temperature Fluctuation

Figure 15 illustrates the temporal variations of the inlet parameters and the average outlet temperature of the combustion chamber under different operating conditions. As shown in the figure, over a large time scale, the average outlet temperature for all conditions remains close to 1800 K, exhibiting varying degrees of pulsation over time. On a smaller time scale, the time distribution of the average outlet temperature for different inlet parameters follows a pattern similar to that of the reference condition. The key difference is that there is a phase shift, either “lead” or “lag”, relative to the reference condition, which is attributed to the average temperature variation induced by fluctuations in the inlet parameters. Positive fluctuations in inlet airflow, along with negative fluctuations in inlet temperature and fuel flow, result in a decrease in the average outlet temperature, and vice versa. Additionally, the average outlet temperature displays a sine wave-like fluctuation with a “decrease-increase-decrease” trend over time, which correlates with the sine wave oscillations of the inlet parameters, particularly in the case of inlet airflow and fuel flow rate.

To quantitatively characterize the response of the average outlet temperature fluctuation to the inlet parameter fluctuations, the transfer function (TF) is employed to describe the system behavior. The calculation formula is given as follows:

T F = \frac{\hat{T} / \bar{T}}{\hat{X} / \bar{X}} = G e^{i ∆ φ}

(10)

In the formula,

\hat{T}

and

\bar{T}

represent the fluctuation and average values of the average outlet temperature of the combustion chamber, respectively;

\hat{X}

and

\bar{X}

represent the fluctuation and average values of the inlet parameters (inlet temperature, air flow rate, and fuel flow rate), respectively;

G

denotes the gain;

i

is the imaginary unit; and

∆ φ

is the phase difference. The transfer functions for different operating conditions are calculated, and the corresponding gain and phase values are presented in Table 5. In general, under conditions of inlet temperature fluctuation, the amplitude of the outlet temperature fluctuation is larger, and the transfer function gain

G

is correspondingly higher. However, as the pulsation degree of the inlet parameters increases, the transfer function gain

G

exhibits a decreasing trend. This suggests that, when the pulsation magnitude is small, the inherent combustion instability of the combustion chamber amplifies the inlet pulsations, leading to a larger gain. Conversely, as the amplitude of the inlet pulsations increases, the gain does not increase proportionally. This shows that the pulsation of the inlet parameters has an inhibitory effect on the inherent combustion instability of the combustion chamber. The flow pulsation exhibits a phase difference of approximately 0.5 π, while the fuel pulsation phase difference is close to π. This is consistent with the phase difference observed between the outlet temperature fitting curve and the inlet pulsation curve in Figure 14. As the amplitude of the inlet parameter pulsations increases, the phase difference gradually decreases.

Figure 16 shows the distribution of the outlet time-averaged temperature under different operating conditions, with the blue point representing the location of the maximum outlet time-averaged temperature. As observed, the outlet temperature distribution of the combustion chamber exhibits similar patterns across various operating conditions. To quantitatively analyze the impact of inlet parameter fluctuations on outlet temperature variations, the dynamic outlet temperature distribution coefficient (DOTDF) is defined. The calculation formula is as follows:

D O T D F = \frac{T_{4 m a x, r m s}}{T_{4 a v e} - T_{3 a v e}}

(11)

Here,

T_{4 m a x, r m s}

represents the root mean square value at the location of the maximum time-averaged outlet temperature of the combustion chamber,

T_{3 a v e}

is the average inlet temperature, and

T_{4 a v e}

is the average outlet temperature of the combustion chamber. The dynamic outlet temperature distribution coefficient is calculated for each operating condition, with the results shown in Figure 17. According to the definition of the formula, a higher root mean square value for the maximum outlet temperature corresponds to a higher DOTDF, indicating a greater degree of outlet temperature fluctuation. As seen in the figure, the DOTDF for inlet parameter pulsations is lower than that for the reference condition. Additionally, under conditions involving inlet temperature and fuel flow pulsations, the DOTDF decreases with increasing pulsation amplitude. However, under airflow pulsation conditions, the DOTDF increases as the pulsation amplitude increases. This suggests that fluctuations in inlet parameters help suppress outlet hot spot temperature fluctuations, although excessive fluctuations in airflow should be avoided.

4. Conclusions

In this study, a method combining large eddy simulation and Flamelet Generated Manifold is employed to numerically simulate a three-swirl staged combustion chamber. The effects of nine different inlet parameter pulsations on the dynamic combustion behavior of the chamber are analyzed and compared with the reference conditions. The results are as follows:

(1): The steady-state time-averaged results of each working condition were analyzed. The three-swirl staged combustion chamber forms a large, low-speed recirculation zone that enhances flame stability. The flow field and temperature distribution for all operating conditions show minimal differences, indicating that, on a large time scale, small pulsations of the inlet parameters have no significant impact on the steady-state, time-averaged performance. Furthermore, as the pulsation intensity of the inlet parameters increases, the recirculation zone tends to expand horizontally.
(2): The transient temperature field results for each operating condition were analyzed, revealing a similar temperature distribution across all conditions. Near the outlet of the cyclone, the flame root region exhibits pronounced unsteady flame characteristics. Fluctuations in the inlet parameters lead to an increase in the temperature variations in this flame root area.
(3): The outlet temperature results for each operating condition were analyzed. It was observed that, when the inlet pulsation amplitude is small, the inherent combustion instability within the combustion chamber amplifies the inlet pulsations. As the inlet pulsation amplitude increases, the influence of inlet parameter fluctuations on the outlet pulsations becomes more pronounced, suggesting that inlet pulsations have a suppressive effect on the inherent combustion instability of the chamber. Analysis of the outlet dynamic OTDF reveals that fluctuations in the inlet parameters can mitigate the fluctuations in the outlet hot spot temperature.

Author Contributions

Conceptualization, J.Y.; methodology, M.L. and J.Y.; validation, C.L., Y.M., and G.X.; formal analysis, M.L.; investigation, M.L.; data curation M.L.; writing—original draft preparation, M.L.; writing—review and editing, C.L., Y.M., G.X., F.L., C.R., and K.W.; supervision, J.Y. and C.L.; project administration, J.Y.; funding acquisition, J.Y. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the National Science and Technology Major Project (J2019-III-0002-0045), National Natural Science Foundation of China (No. 52276141) and the Taishan Scholars Program.

Data Availability Statement

The data presented in this study are available on request from the corresponding author due to data confidentiality restrictions.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Schematic of the combustion chamber: (a) combustion chamber; (b) triple swirler; (c) midplane.

Figure 2. Grid independence verification.

Figure 3. Mesh distributions: (a) combustor; (b) swirler.

Figure 4. Courant number distribution.

Figure 5. Percentage of resolved turbulent kinetic energy.

Figure 6. Kinetic energy spectra.

Figure 7. Comparison of experimental results and simulation results of average velocity field.

Figure 8. Time-averaged velocity field (Case0): (a) axial velocity; (b) radial velocity.

Figure 9. Axial velocity distribution under temperature fluctuation: (a) axial distribution; (b) radial distribution.

Figure 10. Time-averaged temperature distribution in the midplane of the combustor (Case0).

Figure 11. Comparison of time-averaged RTDF of combustion chamber outlet section.

Figure 12. Instantaneous temperature evolution in the middle section of the combustor under inlet temperature fluctuation.

Figure 13. Comparison of axial distribution of temperature fluctuation under different working conditions: (a) temperature pulsation; (b) air pulsation; (c) fuel pulsation.

Figure 14. Frequency domain diagram of heat release rate pulsation under different working conditions: (a) temperature pulsation; (b) air pulsation; (c) fuel pulsation.

Figure 15. Comparison of inlet parameters and outlet average temperature of combustion chamber with time under different operating conditions: (a) temperature pulsation; (b) air pulsation; (c) fuel pulsation.

Figure 16. The outlet time-averaged temperature distribution under different operating conditions.

Figure 17. Distribution of DOTDF.

Table 1. Design characteristics of the triple swirler.

	Swirler Vane Angle	Swirl Number	Air Split Ratio
1st swirler	35°	0.59	13.1%
2nd swirler	−45°	0.86	29.8%
3rd swirler	−50°	1.06	57.1%

Table 2. Operating conditions.

Case	P/(kpa)	T/(K)	ma/(kg/s)	mf/(kg/s)
0	500	600	0.739	0.02733
1	500	600 ± 6	0.739	0.02733
2	500	600 ± 12	0.739	0.02733
3	500	600 ± 18	0.739	0.02733
4	500	600	0.739 ± 0.0074	0.02733
5	500	600	0.739 ± 0.0148	0.02733
6	500	600	0.739 ± 0.0222	0.02733
7	500	600	0.739	0.02733 ± 0.000273
8	500	600	0.739	0.02733 ± 0.000546
9	500	600	0.739	0.02733 ± 0.000819

Table 3. The range of the main recirculation zone under different operating conditions.

Case	0	1	2	3	4	5	6	7	8	9
Length/mm	66	64	64	68	67	62	67	63	64	66
Width/mm	65	64	62	62	64	63	62	61	65	56

Table 4. Time-averaged outlet temperature distribution.

Case	0	1	2	3	4	5	6	7	8	9
RTDF	0.10	0.10	0.10	0.10	0.11	0.11	0.11	0.10	0.12	0.09
OTDF	0.17	0.20	0.19	0.18	0.20	0.20	0.21	0.16	0.18	0.16

Table 5. Gain and phase of outlet temperature response under different operating conditions.

Case	$G$	$∆ φ$
1	1.51	0.92 π
2	1.37	0.45 π
3	0.76	0.48 π
4	1.68	0.44 π
5	1.12	0.62 π
6	0.99	0.25 π
7	1.77	0.99 π
8	1.63	0.80 π
9	1.56	0.82 π

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Li, M.; Yang, J.; Liu, C.; Liu, F.; Wang, K.; Ruan, C.; Mu, Y.; Xu, G. Study on the Dynamic Combustion Characteristics of a Staged High-Temperature Rise Combustor. Energies 2025, 18, 662. https://doi.org/10.3390/en18030662

AMA Style

Li M, Yang J, Liu C, Liu F, Wang K, Ruan C, Mu Y, Xu G. Study on the Dynamic Combustion Characteristics of a Staged High-Temperature Rise Combustor. Energies. 2025; 18(3):662. https://doi.org/10.3390/en18030662

Chicago/Turabian Style

Li, Meng, Jinhu Yang, Cunxi Liu, Fuqiang Liu, Kaixing Wang, Changlong Ruan, Yong Mu, and Gang Xu. 2025. "Study on the Dynamic Combustion Characteristics of a Staged High-Temperature Rise Combustor" Energies 18, no. 3: 662. https://doi.org/10.3390/en18030662

APA Style

Li, M., Yang, J., Liu, C., Liu, F., Wang, K., Ruan, C., Mu, Y., & Xu, G. (2025). Study on the Dynamic Combustion Characteristics of a Staged High-Temperature Rise Combustor. Energies, 18(3), 662. https://doi.org/10.3390/en18030662

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Study on the Dynamic Combustion Characteristics of a Staged High-Temperature Rise Combustor

Abstract

1. Introduction

2. Computational Models and Methods

2.1. Physical Model and Meshing

2.2. Calculation Methods and Operating Conditions

2.3. Model Evaluation

3. Results

3.1. Time-Averaged Analysis

3.2. Instantaneous Temperature Field Analysis

3.3. Analysis of Outlet Temperature Fluctuation

4. Conclusions

Author Contributions

Funding

Data Availability Statement

Conflicts of Interest

References

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