Research on the Characteristics of Oscillation Combustion Pulsation in Swirl Combustor

Abstract

This study focuses on the center-staged swirl model combustion chamber, conducting experiments and numerical simulations to investigate the unstable combustion characteristics of diffusion flames under different Reynolds numbers and air–fuel ratios. The results were analyzed using methods such as Empirical Mode Decomposition (EMD), Fast Fourier Transform (FFT), and Proper Orthogonal Decomposition (POD). The research found that the first three intrinsic mode functions (IMFs) of the combustion chamber pressure fluctuation signal (DP) correspond to different physical fluctuation characteristics. Specifically, the 1st IMF represents the fluctuation characteristics of the heat release rate, corresponding to the flame shear region in the heat release rate field; the 2nd IMF represents the fluctuation characteristics of airflow swirl, corresponding to the swirl vortex structure region in the vorticity field; the 3rd IMF represents the flame detachment fluctuation characteristics, corresponding to the flame detachment region in the heat release rate field. Using the same experimental and numerical calculation methods to study another swirl model combustion chamber, the results also showed the aforementioned correspondence, further demonstrating the accuracy of the experimental results and the universality of this conclusion.

1. Introduction

As the aviation industry develops, pollutants in aircraft engine exhaust have a relatively serious impact on the human living environment [1]. Therefore, improving safety performance and reducing pollution has become the focus of research in the field of aircraft engines. Lean Premixed Prevaporized Combustion (LPP) technology has become the most widely applied low-emission combustion technology currently. In LPP technology, air cooling is used to reduce flame temperature, which, while reducing the generation of thermal NOx, can easily lead to combustion instability due to its relatively low fuel–air ratio and inherently small damping. Oscillatory combustion is a common phenomenon that frequently occurs in various combustion devices, including the combustion chambers of aero-engines, rocket engines, and gas turbine combustors [2]. This phenomenon can seriously affect the stable combustion performance of aircraft engines and even damage mechanical components of aircraft engines, leading to increased environmental pollution or even aviation accidents [3].

The swirl generator is the most commonly used method for stabilizing flames in aircraft engines because fuel needs to be burned stably and fully within a limited space, so most of this field adopts the method of injecting air into the combustion chamber in a swirling manner [4]. Domestic and foreign scholars have conducted a large number of studies on the influence of swirl generators. Different structures of swirl generators have a significant impact on flow field distribution, fuel atomization, combustion, and emissions [5]. The main principle of its stability is that air enters the combustion chamber after generating a certain radial velocity through the swirl generator, thereby generating a central recirculation zone in the combustion chamber to stabilize the flame. This further promotes the full mixing of air and fuel, making combustion more complete, the combustion efficiency higher, and the pollutant emissions lower [6].

In swirl combustion chambers, oscillatory combustion phenomena still occur and are complex in cause, including the influence of the chamber’s geometric structure, flow field, and fuel [7]. Enhancing the mixture of fuel and air within the combustion chamber while creating a stable ignition zone through pressure differentials achieves rapid, stable, and efficient combustion. However, this process leads to coupling between combustion and the precessing vortex core (PVC) as well as turbulence [8], resulting in severe deformation of the flame front. Locally, the flame may experience extinction and reignition, while globally, blowout, flashback, and oscillation may occur [9,10]. These not only affect combustion stability and efficiency but can also cause damage to the aero-engine itself. Many scholars have found that the formation of recirculation zones in swirl burners is a phenomenon of vortex breakdown, with the central recirculation zone also known as the vortex breakdown bubble [8,11,12,13,14]. Vortex breakdown can lead to pressure fluctuations in the flow field, and when the swirl intensity is high, it exhibits instability. The vortex precesses around the central axis at low frequencies, forming a typical PVC structure. The frequency of the PVC increases linearly with flow velocity along the direction of flow, but not necessarily consistently, which is also related to the rate of flow rotation [8].

The sources of instability that induce unstable combustion phenomena are numerous and exhibit a variety of differentiated mode characteristics. Firstly, there may be mutual coupling between different systems that can induce oscillatory combustion: Timo Buschhagen [15] studied the effects of inlet air temperature and equivalence ratio changes on oscillatory combustion under lean premixed high-pressure conditions; Nicholas A. Worth [16], Ahmed E. E. Khalil [17], Kazuaki Matsuura [18], among others have studied the effects of different equivalence ratios on oscillatory combustion. Secondly, there may also be pulsation sources in the structure of the combustion chamber, such as pressure pulsations caused by periodic vortex shedding: Timo Buschhagen [15] also studied the impact of vortex shedding on oscillatory combustion, with research indicating that the axisymmetric and asymmetric processes of vortex shedding correspond to longitudinal resonant modes and transverse instabilities, respectively.

In summary, the mechanism of inducing oscillatory combustion is extremely complex. In order to establish strategies for suppressing oscillatory combustion, it is essential to reveal the impact of different pulsation sources on oscillatory combustion. This paper primarily focuses on the engineering-level centrally swirler stage combustor and swirl model combustor as research objects, conducting experimental studies and numerical simulations on oscillatory combustion, investigating the pulsation sources within the swirl combustion chambers, and revealing the interplay between different pulsation sources and oscillatory combustion. Consequently, this can provide certain reference significance for the design work of combustion chambers, thereby avoiding the occurrence of oscillatory combustion phenomena.

2. Introduction to the Experimental System

2.1. Centrally Swirler Stage Combustor

2.1.1. Experimental Research Object

The experiment focuses on a centrally swirler stage combustor (Lean Premixed Prevaporized, LPP), with its geometric structure illustrated in Figure 1. This centrally swirler stage combustor employs a single-tube combustion chamber layout, where the combustor head consists of a primary radial swirler (main stage) and two secondary axial swirlers (pilot stages). The main stage of the combustor is fueled through direct injection nozzles distributed circumferentially, while the pilot stages are fueled via swirl atomizing nozzles. Additionally, cooling holes are configured in both the head and the flame tube to provide high-temperature protection for the combustor walls.

2.1.2. Layout of Experimental System

The centrally swirler stage combustor test system is shown in Figure 2. The test system consists of a centrally staged combustor, intake and exhaust ducts, an air supply system, a fuel supply system, and a data acquisition system. The test fuel used is RP-3 aviation kerosene. Air from the compressor is heated using an electric heater and enters the combustion chamber via an intake pipeline. The high-temperature flue gases produced during combustion are cooled through water spraying and then treated by a gas processing unit before being discharged [19].

Intake pressure pulsations, combustion chamber pressure pulsations, and fuel pressure pulsations are measured using dynamic pressure sensors, model PCB 113B28(PCB Piezotronics, New York, NY, USA), with a sensitivity of 15 mV/kPa, a range of 34.47 kPa, and an uncertainty of ≤0.3%F.S. The fluctuation in the heat release rate can be used to determine the combustion status, which is indirectly measured by measuring the CH* chemiluminescence intensity of the flame [20]. In this paper, a bandpass filter at 435 nm ± 5 nm combined with a Hamamatsu Photonics CH348 photomultiplier tube is employed to capture the CH* chemiluminescence signals. All the above dynamic signals are connected to an NI multichannel data acquisition system for synchronous acquisition.

2.1.3. Operating Conditions

Under atmospheric pressure, variable fuel–air ratio experiments were conducted with three different inlet airflow rates: 100.2 g/s (Marked A), 130.1 g/s (Marked B), and 140 g/s (Marked C). For each set of inlet airflow rates, experiments were carried out by gradually decreasing from a high fuel–air ratio to a low one, as shown in

Table 1. Operating conditions table for oscillation combustion test of centrally swirler stage combustor.

Test Number	Air Intake Flow Rate/(g/s)	Intake Air Temperature/K	Imported Re	FAR
A01	100.2	426	40,400	0.063
A02	100.2	426	40,400	0.057
A03	100.2	426	40,400	0.050
A04	100.2	426	40,400	0.046
A05	100.2	426	40,400	0.038
A06	100.2	426	40,400	0.033
B01	130.1	423.4	52,000	0.054
B02	130.1	423.4	52,000	0.052
B03	130.1	423.4	52,000	0.048
B04	130.1	423.4	52,000	0.046
B05	130.1	423.4	52,000	0.044
B06	130.1	423.4	52,000	0.038
C01	140.0	434	56,800	0.050
C02	140.0	434	56,800	0.048
C03	140.0	434	56,800	0.045
C04	140.0	434	56,800	0.044
C05	140.0	434	56,800	0.040
C06	140.0	434	56,800	0.038

.

2.2. Swirl Model Combustor

2.2.1. Experimental Research Object

The swirl model combustor utilizes a single-stage axial swirler, with its geometric structure shown in Figure 3. A fuel nozzle is placed at the center of the swirler, and the nozzle head has 12 jet orifices of 1.0 mm diameter distributed evenly around its circumference for ejecting propane gas fuel. The incoming air, after passing through the inclined vanes of the swirler, forms a central recirculation zone in the downstream combustion chamber to stabilize the flame.

2.2.2. Layout of Experimental System

Figure 4 illustrates the overall layout of the single-stage swirl model combustor test system. The test system primarily consists of an air intake pipeline, a fuel supply line, a combustion chamber, and a synchronous measurement system. Tests are conducted under normal temperature and pressure conditions, with air supplied by an external blower flowing from left to right. The main airflow enters the combustion chamber through a pipe with an outer diameter of 50 mm via the axial swirler. The average inlet velocity of air entering the combustion chamber is measured using a flowmeter. The fuel used is propane, supplied from an external gas cylinder, which enters the combustion chamber through jet orifices in the circumferential direction of the fuel supply line nozzle within the axial swirler, with this fuel supply line having a diameter of 12 mm. The combustion chamber is cuboid in shape, with an axial length a = 300 mm. Its cross-sectional shape is square, with a side length of l = 100 mm. A quartz glass observation window is set on the side of the combustion chamber for capturing dynamic flame images. The high-temperature flue gas is treated before being discharged at ambient pressure [21].

2.2.3. Operating Conditions

The experiments were conducted using a swirler with a blade angle of 50°. The swirl number S can typically be estimated using the following formula with some simple structural parameters of the swirler:

$$S={\displaystyle \frac{2}{3}}\left[{\displaystyle \frac{1-{\left(\frac{R_h}{R_n}\right)}^3}{1-{\left(\frac{R_h}{R_n}\right)}^2}}\right]\tan \theta$$

(1)

where $R_n$ and $R_h$ are the inner and outer radii of the swirl vane, respectively, and $\theta$ is the inclination angle of the swirl vane. Therefore, the swirl number of this swirler is 0.885. The inlet air mass flow rate is 9.44 g/s (Re = 11,000), and the inlet fuel mass flow rate is 0.139 g/s (FAR = 0.015), with temperature and pressure at ambient conditions, respectively.

3. Numerical Framework

3.1. Centrally Swirler Stage Combustor

In our study, grid division was completed using ICEM. For the two different swirl models, we adopted different grid strategies to accommodate their respective geometric features and flow characteristics. For the central staged swirl combustor, as shown in Figure 5, due to the complex swirl structure at the head, we chose unstructured grids to mesh the geometry, ensuring good grid quality, with a total grid number of 14 million. The numerical simulation employs Large Eddy Simulation (LES) for the turbulence model and a non-premixed combustion model, using the Discrete Phase Model (DPM) to simulate the breakup and evaporation process of RP-3 kerosene in the combustor as a gas–liquid two-phase phenomenon. This paper adopts the SIMPLE algorithm to solve for the velocity field and pressure field. The computational modeling is based upon an in-house CFD code known as the general equation and mesh solver [22]. The Navier–Stokes equations along with a single energy equation and five species equations are solved numerically. The LES turbulence model is used to compute large eddies directly. The Subgrid-Scale model used in this study is the Smagorinsky–Lilly model. The scheme is second-order-accurate in time. A physical time step of 5 × 10⁻⁵ s is used for all simulations. Simulations are started from quiescent conditions at atmospheric pressure and a temperature of 426 K. At the beginning of the simulation, both the fuel and oxidizer enter the combustor simultaneously, exposing the combustor to the incoming propellant and atmospheric backpressure. The entrance boundary condition of the combustor is a mass flow rate inlet, with an airflow rate of 100.2 g/s, a temperature of 426 K, operating at atmospheric pressure, and a total fuel flow rate of 5.71 g/s (FAR = 0.057). The convergence criterion is set with a computational residual of less than 0.001 as the standard.

3.2. Swirl Model Combustor

For the swirl model combustor, as shown in Figure 6, the head’s single-stage swirler remains complex, but the rear half of the combustor is merely a simple rectangular structure, so a mixed grid of unstructured and structured elements was used, with a total grid number of 4 million. The numerical simulation also employs Large Eddy Simulation for the turbulence model, with the combustion model being a partially premixed FGM (Finite-Rate Gaseous Mixture) model [23] to numerically simulate gaseous fuel propane. The solution algorithm and discretization accuracy are the same as those set for the centrally swirler stage combustor, and the boundary conditions are set to be the same as those described in Section 2.2.3 for the experimental conditions.

4. Data Processing Methods

4.1. Signal Processing Method

Empirical Mode Decomposition (EMD), proposed by N.E Huang et al. [24], is a method for processing non-stationary signals. The process decomposes the original signal based on its intrinsic characteristics, resulting in several Intrinsic Mode Functions (IMFs) and a residue. Each IMF captures different fluctuation characteristics of the original signal, enabling the extraction of its features. Unlike the Fast Fourier Transform (FFT), which calculates the overall fluctuation characteristics of the signal, EMD decomposes the signal based on its own intrinsic properties. During the decomposition process, curve interpolation is performed on local maxima and minima to form upper and lower envelope lines [25].

Currently, EMD has been widely applied in fault diagnosis across various scenarios. For example, Ge et al. combined EMD with HMM to propose a fault diagnosis model for equipment, using the energy of each IMF component and modal spectral entropy to construct a feature vector set as input for HMM classification, effectively achieving fault diagnosis [26]. Shen et al. integrated fault feature extraction based on EMD with fault reasoning based on directed factor graphs, providing a viable and effective means for fault diagnosis under conditions of information uncertainty and incompleteness [27].

4.2. Image Processing Method

Proper Orthogonal Decomposition (POD) is a powerful analytical tool for identifying coherent structures in vector or scalar fields, capable of extracting spatial patterns of flame fluctuations and their temporal distribution. This technique is extensively applied in flame dynamics research. Wang et al. applied POD to CH* chemiluminescence images corresponding to 40 oscillation cycles to explore detailed changes in flame dynamics during transition periods [28]. Fu et al. similarly applied POD to OH* chemiluminescence images of 1000 consecutive flame images to analyze detailed flame dynamics under three unstable conditions at different thermal powers [29]. Liu et al. utilized the POD method to process flame images, investigating the changing process of flame structures and studying the phase relationship between pressure waves and heat release fluctuations [30].

The aforementioned literature primarily explores flame structures using POD. This study further explores the dominant frequencies of pulsations in different flame structures based on the exploration of flame structures, a part rarely mentioned in previous literature, hence possessing certain novelty. Moreover, the POD algorithm adopted in this study has been validated through data in reference [31]. Therefore, this paper employs the POD method to process numerically simulated flame images [32].

If the parameter sequence of a flow field at a certain moment is represented as $L_i\in R^{n_p\times 1}$, and after extracting the characteristic information from M snapshots to construct matrix X, then X can be expressed as follows:

$$X=\left(L_1,L_2,\dots ,L_{n_t}\right)\in R^{n_p\times n_t}$$

(2)

where p represents the size of the spatial domain, which is much larger than time t. The process involves using Singular Value Decomposition (SVD) to decompose the transposed matrix $X^T$, as follows:

$$[U,S,V]=X^T$$

(3)

where U is the orthogonal matrix, and V is the orthogonal eigenvector matrix of $X^T$, which is also known as the POD mode matrix. S is the singular value matrix corresponding to V, that is, $S=diag\left(s_1,s_2,\dots ,s_r\right)$, where the elements are arranged in order of energy of the orthogonal bases in matrix V, which represents the POD as s_i, thus having $s_1>s_2>\dots >s_r$. Among these, the energy percentage of the m-th order POD mode is given by the following:

$$E^{(i)}=s_m^2/\sum _{m=1}^M{s}_m^2$$

(4)

5. Results and Discussion

5.1. Analysis of Experimental Results of Centrally Swirler Stage Combustor

Since the original signal in the time domain of each working condition contains rich information about multiple physical processes within the combustion chamber, this paper employs EMD to decompose its pressure fluctuation signals. Taking working condition A02 as an example, its pressure fluctuation signals and spectral graph are shown in Figure 7.

Upon performing EMD decomposition, a total of seven orders of components are obtained, with the energy primarily concentrated in the first three orders; the amplitude and dominant frequency of the other lower-order components are very small. The waveforms and spectra of the first three orders of components are shown in Figure 8, presented from top to bottom as the signals for 1st–3rd IMF and their spectral results. The waveform of the 1st IMF is similar to that of the DP waveform and amplitude, both having consistent dominant fluctuation frequencies, which represent the main characteristics of the original signal, although there is no secondary peak at 71.3 Hz; the waveform of the 2nd IMF still exhibits strong intermittency, with its fluctuation energy concentrated in a broader frequency band around 53 Hz; the dominant fluctuation frequency of the 3rd IMF is centered in a low-frequency band around 23 Hz. It is generally considered that the three components obtained after EMD decomposition have relative independence, corresponding to three separate physical processes.

Following the above-mentioned processing method, a statistical analysis of other working conditions in the experiment was conducted to obtain the variation in pressure fluctuation components at different mass flow rates, as shown in Figure 9. The fluctuation frequency of the 1st IMF changes significantly under Group A air intake, with the dominant fluctuation frequency higher during flame instability (FI) states at high fuel-to-air ratios than during combustion instability (CI) states at low fuel-to-air ratios; under CI conditions, the influence of the inlet air mass flow rate on the 1st IMF is minimal, with its main frequency varying around the system’s acoustic transverse oscillation eigenfrequency of 120 Hz. For the 2nd IMF, given a constant inlet air mass flow rate, its fluctuation dominant frequency exhibits minor variations around a fixed base value; as the airflow increases, the base values for various working conditions also gradually increase. In Group A working conditions, when transitioning from an FI state to a CI state, the fluctuation dominant frequency of the 3rd IMF gradually rises from 17 Hz to 23 Hz until it saturates at 26 Hz. Through the above analysis, it is evident that the dominant frequencies of the first three IMFs of pressure fluctuations under FI and CI states exhibit distinct characteristics of change: the dominant frequency of the 1st IMF tends towards the system’s natural frequency under lean CI conditions across all air intakes, whereas the dominant frequencies of the 2nd IMF and 3rd IMF show a clear positive correlation with the airflow/Re, indicating that the physical processes corresponding to these components are positively related to the mean velocity of the flow field.

5.1.1. Heat Release Rate Analysis

In this paper, the CH* filter is used in conjunction with a phototube to collect information on heat release rate fluctuations. After statistical analysis of the dominant fluctuation frequencies of CH* under all working conditions, the changes in the dominant fluctuation frequencies of CH* at three different air mass flow rates are shown in Figure 10. It can be seen from the figure that the dominant fluctuation frequency of CH* under high fuel-to-air ratio FI states gradually decreases as the fuel-to-air ratio decreases and stabilizes around 120 Hz in the CI state; comparing the dominant fluctuation frequency of CH* with the dominant fluctuation frequency of the 1st IMF for DP in Figure 8a, it is found that the frequency changes in both are consistent, leading to the inference that the 1st IMF fluctuation component of DP can represent the characteristics of changes in heat release rate fluctuations.

5.1.2. Cold State Pressure Signal Analysis

In the combustion flow field, the second largest influencing factor of pressure fluctuation is the macroscopic fluctuation caused by the flow field structure. After the inlet air enters the combustion chamber through a multi-stage swirler and undergoes swirl action, the resulting flow field exhibits non-uniform distribution, generating fluctuations. To analyze the influence of the internal flow field structure on DP, the DP signal in the cold state combustion chamber without ignition is analyzed. Taking Group A as an example, after filtering the original signal and then performing FFT calculations, its dimensionless spectrum is shown in Figure 11 below. It can be seen from the figure that there exists a dominant fluctuation frequency near 50 Hz in the low-frequency part, which may be related to the inherent characteristics of the combustion chamber.

Following the above-mentioned method, the results of the changes in the dominant fluctuation frequency caused by flow field structure fluctuations in other working conditions are shown in Figure 12. It can be observed that as the inlet air mass flow rate increases, the dominant fluctuation frequency of DP in the cold state gradually increases; at the same time, this frequency change deviates from a linear increase with the inlet air mass flow rate. The changes in the dominant frequency of the cold state DP under different inlet airflow rates are approximately consistent with the changes in the dominant fluctuation frequency of the 2nd IMF mentioned above, indicating that the 2nd IMF contains macro fluctuation information about the cold state flow field structure at that specific airflow rate.

5.1.3. Fire Frequency Analysis

Flame detachment is one of the significant factors contributing to changes in DP. During combustion, as the flame moves downstream with the main airflow, its position gradually stretches, leading to flame detachment. Detachment alters the position of high-temperature clusters within the combustion chamber, resulting in an uneven spatial temperature distribution and further causing DP variations. From a set of 150 frames capturing flame changes, 40 frames showing instances of flame detachment were selected. It was observed that the phenomenon of flame surface shedding occurred approximately twice, clearly indicating periodic alternations of light and dark in the reaction zone within the combustion chamber. The shooting frequency was 2000 Hz, with the frequency of occurrence estimated at about 2 × 2000/150 ≈ 26.7 Hz.

After statistical analysis of the detachment frequencies for Groups B and C using the above method, it was found that during CI states, the detachment frequency fluctuates around 29 Hz and 35 Hz, indicating that the flame detachment frequency increases with the increase in inlet air mass flow rate during CI states. This change pattern is consistent with the fluctuation frequency changes in DP signal’s 3rd IMF during combustion, suggesting that the variations in the 3rd IMF contain information on the patterns of flame detachment.

5.2. Analysis of Numerical Simulation Results for Centrally Swirler Stage Combustor

In the combustor, there exist complex fluctuation characteristics. This paper employs the Proper Orthogonal Decomposition (POD) method to decompose the results of numerical simulations. Due to the axisymmetric structure of the combustor, for the convenience of data analysis, only the two-dimensional map distributed along the axial direction of the combustor is recorded. As shown in Figure 13a, the diagrams represent the first two orders of POD decomposition pulsation characteristics. On the left is the result of the first-order mode, where a distinct axial pulsation characteristic along the central axis of the combustion chamber can be observed. On the right is the result of the second-order mode, primarily characterized by the pulsation of flame tail edge curling upstream. In Figure 13b, which presents the spectrum of the first-order mode of the POD decomposition of the heat release field within the combustion chamber, it is evident that there is a dominant fluctuation frequency around 33 Hz and another around 180 Hz. Based on the analysis presented earlier, the fluctuation characteristic at 33 Hz could be related to the phenomenon of flame detachment, while the fluctuation characteristic at 180 Hz should be associated with the fluctuations in the flame’s heat release rate.

To further analyze the related characteristics of these two fluctuation signals’ information, image FFT processing was applied to this heat release field. Figure 14 shows the frequency and phase diagrams of the FFT. Near the flame shear layer, where chemical reactions are most intense, there exist strong fluctuations in the heat release rate. It can be seen from the frequency diagram that the fluctuation frequency at the position of the flame shear layer is mainly around 150 Hz, which is consistent with the dominant fluctuation frequency of the heat release rate analyzed in Section 5.1.1 of the experimental results. Similarly, the phase diagram at this shear layer position also exhibits small-scale fluctuation characteristics of the flame. Near the central position along the axis of the combustion chamber, the frequency distribution is primarily dominated by low frequencies of 33 Hz. From the phase diagram, it can be observed that near the central axis, there is an influence of large-scale structures in space, causing disturbances to be in phase over a wide area.

5.2.1. Analysis of Heat Release Rate Characteristics

For the flame shear layer region where the primary chemical reactions occur, POD decomposition is conducted as shown in Figure 15a. It can be seen from Figure 15b that in this heat release area, its dominant fluctuation frequency is mainly around 180 Hz, which is not significantly different from the dominant fluctuation frequency of CH* obtained from experiments, indirectly verifying that the 1st IMF fluctuation component of DP can represent the characteristics of changes in heat release rate fluctuations. The most important source of pressure fluctuations in the combustion flow field is the instantaneous pressure change when premixed gas micro-clusters undergo intense chemical reactions (combustion), constituting a monopole source term. The entire combustion zone contains a large number of high heat release rate micro-clusters forming a composite pressure fluctuation source term. The coupling of heat release rate fluctuations with pressure fluctuations may lead to an increase in combustion instability, resulting in thermoacoustic oscillations that affect the normal operation of the combustion chamber.

5.2.2. Analysis of Flame Detachment Characteristics

To further understand the main fluctuation characteristics in the region near the central axis, POD decomposition was performed on the local area of the heat release field as shown in Figure 16a, and its first-order mode spectrum is displayed in Figure 16b. From the spectrum, it can be observed that the dominant fluctuation frequency in this area is 29 Hz, which is quite consistent with the detachment frequency mentioned earlier, indirectly verifying that the 3rd IMF fluctuation component of DP can represent the fluctuation characteristics of the flame detachment phenomenon. There are many reasons for the occurrence of this flame surface shedding, including the stretching of the flame surface due to the action of swirl shear on the mainstream air, the uneven distribution of air density caused by pressure fluctuation changes further feeding back to the pressure fluctuation mechanism, making the flame surface discontinuous, and the effect of recirculation zones on the flame surface, among others.

5.2.3. Cold State Characteristic Analysis

To further explore the characteristics of macro fluctuations in the cold state flow field structure, Large Eddy Simulation (LES) calculations were conducted on the centrally swirler stage combustor. Since large-scale vortex structures might be generated by swirling action, POD analysis was applied to the vorticity field, ${\lambda }_2$ criterion vortex structure, and Q criterion vortex structure near the central axis at the outlet of the swirler, as shown in Figure 17a. The first-order mode spectrum diagrams are shown in Figure 17b–d. From these, it can be seen that all three different vortex structure identification methods exhibit a dominant fluctuation frequency around 44 Hz. It is believed that this macro fluctuation structure is caused by the PVC structure formed when the inlet air passes through the swirl vanes and is subjected to swirl shear. Thus, it is verified that the 2nd IMF fluctuation component of DP contains the PVC fluctuation characteristics of the cold state flow field in the swirl combustion chamber under that airflow rate.

To gain a more intuitive understanding of the structural characteristics related to PVC, Figure 18 shows a schematic diagram of the PVC structure in the cold state flow field for the calculated operating condition. It starts from the outlet of the swirler and spirals around the central axis of the combustion chamber, extending downstream and gradually breaking up. In this structure, the direction of the spiral winding is opposite to the direction of the swirl (the same applies to axial and radial swirlers). However, the precession direction of the entire structure is the same as the global rotation direction of the flow. In summary, the cold state flow field is dominated by the fluid dynamics mode (PVC), with acoustics playing no role [33].

5.3. Experimental and Simulation Results Verification of Swirl Model Combustor

5.3.1. Analysis of Experimental Results

To further analyze the accuracy and universality of the above results, a verification analysis was conducted on the experimental and numerical calculation results of the swirl model combustor. The Empirical Mode Decomposition (EMD) method was also used to process the pressure fluctuation signals, thereby decomposing the complex information of multi-physical processes within the combustion chamber. Figure 19 shows the time-series signal and spectrum diagram of pressure fluctuations inside the combustion chamber under this experimental condition. From the diagram, it can be observed that under this condition, the combustion is in a stable state, and there exists a dominant fluctuation frequency with low amplitude.

After performing EMD decomposition, the energy is also concentrated in the first three orders, with the dominant frequency and amplitude of other order components being very small. The waveforms and spectra of the first three order components are shown in Figure 20, with the time-series signals and their corresponding spectrum diagrams for the 1st–3rd IMFs displayed from top to bottom. The waveform and spectrum of the 1st IMF are quite similar to those of the undecomposed DP signal, and the dominant frequency remains consistent, still representing the main characteristics of the original signal; the waveform of the 2nd IMF does not change significantly, but its fluctuation amplitude is noticeably reduced, with the fluctuation energy mainly concentrated in a wider band near 151 Hz; both the fluctuation amplitude and dominant frequency of the 3rd IMF are further reduced, mainly concentrated in a band near 74 Hz. Compared with the EMD results of the centrally swirler stage combustor, due to changes in the combustion chamber’s geometric structure, the dominant frequencies of each order component have changed, but the patterns and trends of changes from the 1st–3rd IMFs are consistent. It can also be considered that these three components obtained after EMD decomposition possess relative independence, corresponding to the three physical processes described above. The 1st IMF fluctuation component represents the characteristic changes in heat release rate fluctuations; the 2nd IMF represents the macro fluctuation information of the cold state flow field structure under that airflow rate, while the changes in the 3rd IMF contain information related to flame detachment.

5.3.2. Analysis of Numerical Calculation Results

Based on the conclusions drawn from the centrally swirler stage combustor, each order component of the EMD decomposition can correspond to a certain physical characteristic. Figure 21 shows the spectrum diagram obtained from POD processing of specific local areas in the heat release field and cold state vorticity field calculated numerically. The 1st IMF represents the fluctuation characteristics of the heat release rate, mainly reflected in the dominant fluctuation frequency of regions undergoing intense chemical reactions. Therefore, POD decomposition was performed on the heat release field in the flame shear layer area as shown in the left image of Figure 21a, with its first-order mode spectrum shown on the right. It can be seen that there is a dominant frequency near 314 Hz, which is quite close to the 315 Hz dominant fluctuation frequency of the 1st IMF. This further verifies that the 1st IMF component can somewhat represent the fluctuation characteristics of the heat release rate in the swirl combustion chamber. Similarly, local POD was performed on the cold state criterion vortex structure field and heat release field containing large-scale PVC vortex structures, also yielding spectrum diagrams with a clear dominant fluctuation frequency for both, as shown on the right in Figure 21b,c, corresponding to the cold state characteristics and flame detachment fluctuation characteristics of the 2nd IMF and 3rd IMF, respectively.

Figure 22 shows the dominant frequencies of each order component for both the centrally swirler stage combustor and the swirl model combustor under experimental and simulation results. It can be observed from the figure that as the order increases, the dominant frequency gradually decreases for both types of combustion chambers, and the numerical calculation results are in good agreement with the experimental results, verifying the accuracy and universality of the EMD components corresponding to different physical characteristics.

6. Conclusions

This paper focuses on two types of swirl combustion chambers as the research objects. Through experiments and numerical calculations, and by utilizing methods such as EMD, FFT, and POD, the pulsation characteristics within the swirl combustion chamber were studied. It was discovered that the third-order mode of the DP signal’s EMD in the combustion chamber could correspond to three different physical pulsation characteristics, leading to the following conclusions:

(1)

The 1st IMF can represent the pulsation characteristics of the heat release rate, mainly reflected in the flame shear zone of the heat release rate field in numerical calculations;

(2)

The 2nd IMF can represent the pulsation characteristics of airflow swirl, primarily manifested in the swirl vortex structure region of the vorticity field;

(3)

The 3rd IMF can represent the pulsation characteristics of flame detachment, mainly evident in the flame detachment zone of the heat release rate field.

The conclusions of this study possess a certain degree of universality. In the experiments and numerical results from another swirl model combustor, the third-order mode of EMD was also found to correspond to three different physical pulsation characteristics. This further validates the accuracy of these results.