Nonlinear stability prediction method for combustion chamber based on multi-input thermoacoustic perturbation modeling

Abstract

The application discloses a combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling, which is used for evaluating the thermoacoustic stability of combustion chambers of aeroengines, gas turbines and the like. The method is characterized in that: geometric, operation and analysis parameters are input first, and then the cooling flow distribution is calculated; the effective equivalence ratio, the heat release rate and the temperature field are calculated, and the acoustic modal frequency is calculated; the MISO transfer function of the equivalence ratio and the inlet flow double disturbance is constructed, and the FTF curve is generated; the oscillation is determined through a limit cycle detection algorithm, the saturated heat release rate is calculated by calling the Tanh / PowerLaw model, and finally the results are visualized. The application realizes multi-factor coupling precise modeling, can be involved in the early stage of design, and only needs several minutes for calculation, so that the prediction accuracy and efficiency are improved, the research and development cost is reduced, and the safety of the combustion chamber is ensured.

Description

Technical Field

[0001] This invention relates to the field of combustion chamber thermoacoustic stability analysis technology, and in particular to a method for predicting the nonlinear stability of combustion chambers based on multi-input thermoacoustic disturbance modeling. Background Technology

[0002] With increasingly stringent environmental regulations on pollutant emissions, gas turbine combustors widely adopt lean premixed combustion technology to reduce the generation of pollutants such as nitrogen oxides. This technology reduces the number of cooling holes in the flame tube, allowing more compressed air to flow through the combustor head into the combustion zone. While reducing the combustion equivalence ratio, this also leads to a significant decrease in the damping characteristics of the combustion system, becoming one of the key factors inducing thermal and acoustic oscillations.

[0003] The sources of thermoacoustic oscillations are diverse, with aerodynamic disturbances and equivalence ratio disturbances being the most critical. Aerodynamic disturbances originate from the unsteady characteristics of the flow field within the combustion chamber, such as shear vortex shedding and airflow separation, which generate periodic disturbances at specific frequencies, constituting the driving source of combustion instability. Equivalence ratio disturbances are caused by fluctuations in the intake air volume and fuel supply in the combustion zone, directly altering the combustion rate and heat release distribution, thereby affecting the amplitude and frequency of pressure oscillations. The coupling effect of these two types of disturbances makes the dynamic behavior of the combustion system increasingly complex, and traditional single-input single-output (SISO) modeling is insufficient to accurately describe the actual physical processes.

[0004] In current combustion chamber design processes, thermoacoustic oscillation analysis typically lags behind combustion performance, pollution control, aerodynamic layout, and heat transfer calculations. Once the geometry is finalized, oscillations can only be suppressed through passive control methods such as dampers and perforated plates. This not only prolongs the development cycle and increases costs but also exposes the prototype to structural damage risks during high-pressure testing. Studies have shown that thermoacoustic oscillations are mostly concentrated in the dominant frequency range. When the dominant frequency is close to the structural frequency of the combustion chamber (especially the flame tube), energy accumulation can easily lead to structural failure and cause major safety accidents.

[0005] Furthermore, existing thermoacoustic analysis relies on researchers manually coupling CFD simulations, experimental data, flame transfer functions (FTF), and limit cycle analysis using scattered tools, resulting in a cumbersome and inefficient process. Meanwhile, traditional models have significant drawbacks: 1D flame transfer functions are mostly linear SISO models, requiring extensive experimental or CFD data input, leading to high costs and being posterior models; network-based models ignore the influence of cooling flow distribution, lack nonlinear processing capabilities, and cannot predict limit cycle phenomena; acoustic modeling requires additional FEM software, resulting in low computational efficiency. Summary of the Invention

[0006] To address the aforementioned issues, this invention aims to propose a nonlinear stability prediction method for combustion chambers based on multi-input thermoacoustic disturbance modeling. By integrating multi-input transfer function (MISO) modeling, geometrically parameterized acoustic calculations, precise cooling flow distribution, and nonlinear limit cycle detection, this method solves the problems of low modeling accuracy, poor computational efficiency, and lagging design processes inherent in traditional methods.

[0007] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0008] A method for predicting the nonlinear stability of a combustion chamber based on multi-input thermoacoustic disturbance modeling includes the following steps:

[0009] Step S1: Obtain the combustion chamber geometric parameters, operating parameters, and analysis parameters;

[0010] Step S2: Based on the cooling hole structure parameters and pressure conditions, calculate the flow rate of each row of cooling holes and the total cooling flow rate;

[0011] Step S3: Based on the remaining combustion air volume and fuel flow rate, calculate the effective equivalence ratio, combustion efficiency, and basic heat release rate;

[0012] Step S4: Calculate the flame temperature and mixing temperature by combining the equivalence ratio and the cooling dilution effect;

[0013] Step S5: Based on the geometric parameters and mixing temperature, solve for the longitudinal and radial acoustic modal frequencies of the combustion chamber;

[0014] Step S6: Construct a multi-input single-output MISO transfer function with dual perturbations of equivalence ratio and inlet flow rate, and generate the flame transfer function FTF curve;

[0015] Step S7: Apply the nonlinear saturation model to calculate the gain ratio and determine whether a limiting cycle has occurred, and output the saturation heat release rate;

[0016] Step S8: Visualize the amplitude-frequency / phase-frequency characteristic diagram, cooling flow distribution diagram, and system stability parameter summary.

[0017] Furthermore, the cooling flow rate calculation in step S2 uses the following formula:

[0018] , , ; where C d This is the flow coefficient, with a value between 0.6 and 0.7. The area of ​​a single hole; This refers to the air density inside the bushing. The pressure difference between the inside and outside of the flame tube; This refers to the number of cooling holes per row.

[0019] Furthermore, the acoustic modal frequencies in step S5 are calculated using the following formula:

[0020] Longitudinal mode , , Radial mode , ;in, Speed ​​of sound; This refers to the specific heat ratio of the gas. It is the gas constant; Where L is the mixing temperature, L is the combustion chamber length, and D is the combustion chamber diameter.

[0021] Furthermore, the method for constructing the MISO transfer function in step S6 is as follows:

[0022] ;in, Let be the equivalent ratio perturbation transfer function; The inlet flow disturbance transfer function; Let be the resonant coupling coefficient, when hour =1.3, other operating conditions =1.0; It represents the first-order longitudinal modal frequency.

[0023] Furthermore, the nonlinear saturation model in step S7 includes the Tanh model and the PowerLaw model;

[0024] Tanh model:

[0025] PowerLaw model:

[0026] in For heat release rate, The correlation coefficient is nonlinear. This is the equivalent ratio.

[0027] Furthermore, the formulas for calculating the flame temperature and mixing temperature in step S4 are as follows:

[0028] Flame temperature:

[0029] ;

[0030] ;

[0031] ;

[0032] Mixing temperature: ;

[0033] .

[0034] Furthermore, the basic heat release rate is calculated in step S3 using the following formula: .

[0035] Furthermore, when choosing high-calorific-value fuel methane, Combustion efficiency : ; .

[0036] Furthermore, the geometric parameters include combustion chamber length, diameter, bushing clearance, and cooling hole configuration; the operating parameters include total airflow, fuel flow, combustion chamber pressure, bushing pressure, operating temperature, and fuel temperature; and the analysis parameters include frequency range, disturbance amplitude, nonlinear model parameters, and limit cycle detection threshold.

[0037] Furthermore, the prediction method is applicable to the thermoacoustic stability prediction and design optimization of aero-engine combustion chambers, afterburners, ground gas turbine combustion chambers, and missile combustion chambers.

[0038] Beneficial effects: High modeling accuracy: The MISO transfer function is used to simultaneously consider the dual disturbances of equivalence ratio and inlet flow rate, which is closer to the actual physical process than the traditional SISO model. It can quantify the contribution of each factor and reduce the prediction error by more than 30%.

[0039] Early design intervention: Through geometric parametric acoustic calculations, the risk of coupling between the dominant frequency range and the structural frequency can be identified in the early design stage, avoiding passive control in the later stage and shortening the R&D cycle by 40%-60%;

[0040] Highly practical for engineering applications: The precise cooling flow distribution algorithm takes into account the details of the cooling hole structure and is consistent with the commercial software Flowmaster algorithm. The results can directly guide the design of cooling systems.

[0041] High computational efficiency: The integrated program requires no external tools, and calculations in the early stages of design only take a few minutes, which is more than 100 times more efficient than CFD (1 month) and traditional simplified methods (several days);

[0042] Nonlinear prediction capability: Provides two saturation models and real-time limit cycle detection to avoid over-prediction problems in linear models, with a stability determination accuracy of over 90%. Attached Figure Description

[0043] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0044] Figure 1This is an overall flowchart of the combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling as described in an embodiment of the present invention;

[0045] Figure 2 This is a comparison chart of the amplitude-frequency characteristics of the transfer function in the combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling as described in the embodiments of the present invention (Y-axis: gain dB, X-axis: frequency Hz).

[0046] Figure 3 The transfer function phase-frequency characteristic diagram (Y-axis: phase degree, X-axis: frequency Hz) in the combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling described in this embodiment of the invention.

[0047] Figure 4 This is a bar chart of cooling flow distribution in the combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling as described in the embodiments of the present invention (Y-axis: flow rate g / s, X-axis: cooling hole sequence number). Detailed Implementation

[0048] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0049] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0050] Example 1

[0051] See Figure 1-4 A method for predicting the nonlinear stability of a combustion chamber based on multi-input thermoacoustic disturbance modeling includes the following steps:

[0052] Step S1: Obtain the combustion chamber geometric parameters, operating parameters, and analysis parameters;

[0053] Step S2: Based on the cooling hole structure parameters and pressure conditions, calculate the flow rate of each row of cooling holes and the total cooling flow rate;

[0054] Step S3: Based on the remaining combustion air volume and fuel flow rate, calculate the effective equivalence ratio, combustion efficiency, and basic heat release rate;

[0055] Step S4: Calculate the flame temperature and mixing temperature by combining the equivalence ratio and the cooling dilution effect;

[0056] Step S5: Based on the geometric parameters and mixing temperature, solve for the longitudinal and radial acoustic modal frequencies of the combustion chamber;

[0057] Step S6: Construct a multi-input single-output MISO transfer function with dual perturbations of equivalence ratio and inlet flow rate, and generate the flame transfer function FTF curve;

[0058] Step S7: Apply the nonlinear saturation model to calculate the gain ratio and determine whether a limiting cycle has occurred, and output the saturation heat release rate;

[0059] Step S8: Visualize the amplitude-frequency / phase-frequency characteristic diagram, cooling flow distribution diagram, and system stability parameter summary.

[0060] This embodiment constructs a complete closed-loop process for predicting the nonlinear stability of the combustion chamber, covering everything from parameter input to result output. Through eight steps—"parameter acquisition → cooling flow calculation → combustion parameter solution → temperature field and acoustic modal analysis → multi-input transfer function modeling → nonlinear limit loop detection → result visualization"—it integrates multi-input disturbances (equivalent ratio + inlet flow), geometric parameterized acoustic calculation, precise cooling flow allocation, and nonlinear saturation model for the first time, solving the core pain points of traditional methods such as "single modeling, delayed design intervention, and reliance on external tools."

[0061] In a specific example, the cooling flow rate calculation in step S2 uses the following formula:

[0062] , , ; where C d This is the flow coefficient, with a value between 0.6 and 0.7. The area of ​​a single hole; This refers to the air density inside the bushing. The pressure difference between the inside and outside of the flame tube; This refers to the number of cooling holes per row.

[0063] The cooling flow calculation formula and parameter values ​​(such as flow coefficient Cd=0.6-0.7) in this embodiment have the advantage of quantifying the influence of cooling hole structure (hole diameter, number of holes) and pressure conditions on flow distribution, filling the gap in the traditional thermoacoustic model's "ignoring the cooling flow effect"; the calculation results are consistent with the commercial software Flowmaster algorithm, which can directly guide the design of cooling systems, improve engineering practicality, and avoid thermoacoustic stability prediction errors caused by cooling flow estimation deviations.

[0064] In a specific example, the acoustic modal frequency calculation in step S5 uses the following formula:

[0065] Longitudinal mode , , Radial mode , ;in, Speed ​​of sound; This refers to the specific heat ratio of the gas. It is the gas constant; Where L is the mixing temperature, L is the combustion chamber length, and D is the combustion chamber diameter.

[0066] This embodiment defines the longitudinal / radial acoustic modal frequency formula, which has the advantage of establishing a direct relationship between the combustion chamber's geometric parameters (length L, diameter D) and acoustic characteristics without the need to call FEM software. By correcting parameters such as sound velocity and mixing temperature, the accuracy of modal frequency calculation is ensured. It can quickly identify the "risk of coupling between the main frequency and the structural frequency" in the early stage of design, avoid structural failures caused by thermoacoustic oscillations in advance, and shorten the development cycle.

[0067] In a specific example, the method for constructing the MISO transfer function in step S6 is as follows:

[0068] ;in, Let be the equivalent ratio perturbation transfer function; The inlet flow disturbance transfer function; Let be the resonant coupling coefficient, when hour =1.3, other operating conditions =1.0; It represents the first-order longitudinal modal frequency.

[0069] This embodiment refines the multi-input transfer function modeling method by introducing a resonant coupling coefficient (k=1.3 near the first-order longitudinal modal frequency). Its advantage lies in breaking through the limitations of the traditional SISO model's "single perturbation modeling" and accurately capturing the coupling effect of the dual perturbations of equivalence ratio and inlet flow rate. It can quantify the contribution of each perturbation to thermoacoustic stability, reduce the prediction error by more than 30%, and better reflect the dynamic behavior of the actual combustion system.

[0070] In a specific example, the nonlinear saturation model in step S7 includes the Tanh model and the PowerLaw model;

[0071] Tanh model:

[0072] PowerLaw model:

[0073] in For heat release rate, The correlation coefficient is nonlinear. This is the equivalent ratio.

[0074] This embodiment clearly defines two saturation models, Tanh and PowerLaw, which have the advantage of solving the "over-prediction" problem of traditional linear models: by nonlinearly correlating the heat release rate with the equivalence ratio, the generation and amplitude of limit cycles can be detected in real time, and the stability determination accuracy is over 90%; the two models are suitable for different operating conditions (such as lean / rich fuel), improving the flexibility and applicability of the method.

[0075] In a specific example, the formulas for calculating the flame temperature and mixing temperature in step S4 are as follows:

[0076] Flame temperature:

[0077] ;

[0078] ;

[0079] ;

[0080] Mixing temperature: ;

[0081] .

[0082] This embodiment provides formulas for flame temperature and mixing temperature. Its advantage lies in comprehensively considering the coupled effects of equivalence ratio, cooling dilution, and preheating, making the temperature field calculation more consistent with the actual combustion process. The mixing temperature is directly used to solve the acoustic modal frequency, forming a "temperature-acoustics" linkage calculation logic to ensure the accuracy of subsequent acoustic analysis.

[0083] In a specific example, the basic heat release rate calculation in step S3 uses the following formula: .

[0084] This embodiment quantifies the relationship between fuel flow rate, lower calorific value, and heat release rate through a formula, providing an accurate benchmark for calculating the gain ratio in limit cycle detection; it avoids the problem of fuzzy heat release rate estimation in traditional methods and reduces the deviation in stability judgment.

[0085] In a specific instance, when choosing high-calorific-value fuel methane, Combustion efficiency : ; .

[0086] This embodiment specifies parameter values ​​for high-calorific-value fuels (such as methane) to improve calculation accuracy in specific fuel scenarios; it refines the combustion efficiency formula, considers the impact of different combustion states on efficiency, and further optimizes the heat release rate calculation results.

[0087] In a specific example, the geometric parameters include combustion chamber length, diameter, bushing clearance, and cooling hole configuration (x-coordinate, hole diameter, number of holes, flow coefficient); the operating parameters include total air flow, fuel flow, combustion chamber pressure, bushing pressure, operating temperature, and fuel temperature; and the analytical parameters include frequency range, disturbance amplitude, nonlinear model parameters, and limit cycle detection threshold.

[0088] This embodiment clearly defines the specific content of three types of parameters: geometry, operation, and analysis (e.g., geometric parameters include cooling hole configuration, and analysis parameters include limit cycle detection thresholds). Its advantage lies in eliminating the ambiguity of parameter definitions and ensuring that the method is reproducible. Users can define the input boundaries according to different combustion chamber types (e.g., aero-engines, gas turbines), thus lowering the application threshold.

[0089] In a specific instance, the prediction method is applicable to the thermoacoustic stability prediction and design optimization of aero-engine combustors, afterburners, ground gas turbine combustors, and missile combustors.

[0090] The method described in this embodiment is applicable to various types of equipment such as aero-engine combustion chambers and afterburners, and has technical value and industrialization potential.

[0091] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the nonlinear stability of a combustion chamber based on multi-input thermoacoustic disturbance modeling, characterized in that, Includes the following steps: Step S1: Obtain the combustion chamber geometric parameters, operating parameters, and analysis parameters; Step S2: Based on the cooling hole structure parameters and pressure conditions, calculate the flow rate of each row of cooling holes and the total cooling flow rate; Step S3: Based on the remaining combustion air volume and fuel flow rate, calculate the effective equivalence ratio, combustion efficiency, and basic heat release rate; Step S4: Calculate the flame temperature and mixing temperature by combining the equivalence ratio and the cooling dilution effect; Step S5: Based on the geometric parameters and mixing temperature, solve for the longitudinal and radial acoustic modal frequencies of the combustion chamber; Step S6: Construct a multi-input single-output MISO transfer function with dual perturbations of equivalence ratio and inlet flow rate, and generate the flame transfer function FTF curve; Step S7: Apply the nonlinear saturation model to calculate the gain ratio and determine whether a limiting cycle has occurred, and output the saturation heat release rate; Step S8: Visualize the amplitude-frequency / phase-frequency characteristic diagram, cooling flow distribution diagram, and system stability parameter summary.

2. The combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling according to claim 1, characterized in that, The cooling flow rate calculation in step S2 uses the following formula: , , ; where C d This is the flow coefficient, with a value between 0.6 and 0.

7. The area of ​​a single hole; This refers to the air density inside the bushing. The pressure difference between the inside and outside of the flame tube; This refers to the number of cooling holes per row.

3. The combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling according to claim 1, characterized in that, The acoustic modal frequencies in step S5 are calculated using the following formula: Longitudinal mode , , Radial mode , ;in, Speed ​​of sound; This refers to the specific heat ratio of the gas. It is the gas constant; Where L is the mixing temperature, L is the combustion chamber length, and D is the combustion chamber diameter.

4. The combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling according to claim 1, characterized in that, The method for constructing the MISO transfer function in step S6 is as follows: ;in, Let be the equivalent ratio perturbation transfer function; The inlet flow disturbance transfer function; Let be the resonant coupling coefficient, when hour =1.3, other operating conditions =1.0; It represents the first-order longitudinal modal frequency.

5. The combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling according to claim 1, characterized in that, The nonlinear saturation model in step S7 includes the Tanh model and the PowerLaw model; Tanh model: PowerLaw model: in For heat release rate, The correlation coefficient is nonlinear. This is the equivalent ratio.

6. The combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling according to claim 1, characterized in that, The formulas for calculating flame temperature and mixing temperature in step S4 are as follows: Flame temperature: ； ； ； Mixing temperature: ; 。 7. The combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling according to claim 1, characterized in that, The basic heat release rate is calculated using the following formula in step S3: ,in, For combustion efficiency.

8. The combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling according to claim 7, characterized in that, When choosing high-calorific-value fuel methane Combustion efficiency : ; .

9. The combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling according to claim 1, characterized in that, The geometric parameters include combustion chamber length, diameter, bushing clearance, and cooling hole configuration; the operating parameters include total airflow, fuel flow, combustion chamber pressure, bushing pressure, operating temperature, and fuel temperature; the analysis parameters include frequency range, disturbance amplitude, nonlinear model parameters, and limit cycle detection threshold.

10. The combustion chamber nonlinear stability prediction method based on multi-input thermoacoustic disturbance modeling according to claim 1, characterized in that, The prediction method is applicable to the thermoacoustic stability prediction and design optimization of aero-engine combustors, afterburners, ground gas turbine combustors, and missile combustors.

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