Impedance mismatch design method for multi-can annular combustor of gas turbine

Abstract

The application discloses a method for impedance mismatch design of a multi-flame tube combined flame system of a gas turbine combustion chamber, comprising the following steps: based on graph theory, 12 flame tubes in a gas turbine are combined through a combined flame pipe to form a combustion chamber, modeling is performed as a cycle graph, and an adjacency matrix and a Laplace matrix are constructed; based on the angular frequency of the flame tube and the coupling strength of the combined flame pipe, a system matrix is constructed; eigenvalues and eigenvectors of the system matrix are calculated, oscillation frequency and vibration mode are determined, and degenerate modes are identified; by modifying the coupling strength of at least one combined flame pipe, the eigenvalues and eigenvectors of the system matrix are recalculated, degenerate frequency splitting is performed, and symmetry is broken; according to the split frequency and mode, the parameters of the combustion chamber are adjusted to optimize the combustion stability. The application simplifies the modeling of a complex system based on a graph theory method, reduces the calculation cost, breaks the symmetry of the system by modifying the coupling strength of the combined flame pipe, splits the degenerate frequency, and relieves the combustion instability.

Description

Technical Field

[0001] This invention relates to the field of gas turbine technology, and more specifically to an impedance mismatch design method for a multi-flame tube combined flame system in a gas turbine combustion chamber. Background Technology

[0002] Modern gas turbine combustors typically employ a multi-flame tube structure, with two flame tubes connected by a connecting tube. When the gas turbine ignites, the spark igniters of two adjacent flame tubes ignite the premixed gas within them. The ignited gas expands at high temperature and propagates through the connecting tube to the adjacent flame tube, eventually reaching pressure equilibrium under the influence of the connecting tube (the function of the connecting tube).

[0003] Therefore, the overall stability of the combustion chamber is achieved by the combined flame tube system. When the combined flame tube is designed in the same way to reduce costs, the uniformity and periodic repetition of the system's ascent symmetry (frequency and modal shape) will lead to the collective amplification and continuous propagation of thermoacoustic oscillations, which may eventually lead to the overall instability of one ring of the flame tube.

[0004] For the combustion chambers of heavy-duty gas turbines using cyclones, low-to-mid-frequency thermoacoustic oscillations (100-800Hz) are common within a single combustion chamber. When using a combined jet tube, because the combined jet tube can balance the overall pressure of the turbine, and because the acoustic impedance and boundaries lack reflection or dissipation mechanisms (which is intended by the combined jet tube geometry to reduce pressure loss, etc.), the combined jet tube may transmit some frequencies. When these frequencies are the same as or close to the natural frequency of the jet tube, oscillating mode coupling will occur, leading to structural damage and major accidents. The initial design goal of the combined jet tube geometry is to find a balance between jet depth and pressure loss, which gives the combined jet tube cross-sectional area a geometric design range.

[0005] Currently, the design of the combined flame tube follows an older design, meaning that early designs did not include lean premixing and thermoacoustic oscillation. Furthermore, since the flame in the combustion chamber is broadband, this means that multiple frequencies may occur within the combustion chamber. However, since it is unknown what frequency oscillation will occur in the flame tube due to various reasons (the causes of thermoacoustic oscillation are varied), there is a need for a system or device that can reduce thermoacoustic oscillation and reduce multiple frequencies. Summary of the Invention

[0006] The present invention provides an impedance mismatch design method for a multi-flame tube interconnected system of a gas turbine combustor based on graph theory to analyze and control combustion instability in the gas turbine combustor, thereby mitigating combustion instability. This method can at least solve one of the above-mentioned technical problems.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] The impedance mismatch design method for a multi-flame tube combined flame system in a gas turbine combustor includes the following steps:

[0009] S1. Based on graph theory, the 12 flame tubes in the gas turbine are connected by flame tubes to form a combustion chamber, which is modeled as a cycle graph C. 12 And construct the adjacency matrix A and the Laplace matrix L;

[0010] S2. Construct the system matrix K based on the angular frequency ω0 of the flame tube and the coupling strength k of the flame tube;

[0011] S3. Calculate the eigenvalues ​​and eigenvectors of the system matrix K, determine the oscillation frequency and vibration mode, and identify degenerate modes;

[0012] S4. By modifying the coupling strength of at least one flame tube to k′, updating the adjacency matrix A and the Laplace matrix L, recalculating the eigenvalues ​​and eigenvectors of the system matrix K, the degenerate frequency splits, and the symmetry is broken.

[0013] S5. Adjust the combustion chamber parameters according to the frequency and mode after splitting to optimize combustion stability.

[0014] Furthermore, in S1, each flame tube is a node, and there are 12 nodes in total, numbered sequentially as v1, v2, ..., v12. Each flame tube is an edge connecting two adjacent nodes vi and vi+1, wherein v12 is connected to v1.

[0015] Furthermore, in S1, the adjacency matrix A is a 12×12 matrix, defined as:

[0016] When the nodes are connected via a flame-connecting tube, A ij =k, where i represents the row index, j represents the column index, j=i+1 or i-1, the matrix modulus is 12, and k is the coupling strength of the flame tube, which is directly related to impedance matching in thermoacoustic oscillation;

[0017] In other cases, A ij =0;

[0018] For the cycle graph C 12 The adjacency matrix A is expressed in the form of:

[0019] ;

[0020] The Laplacian matrix L is L=DA, where D is the degree matrix. Each node is connected to two edges;

[0021] For the cycle graph C 12 The Laplace matrix L is expressed in the form of:

[0022] .

[0023] Furthermore, in S2, the dynamic behavior of the multi-flame tube combined flame system is described by the following second-order differential equation:

[0024]

[0025] Where K is the system matrix, This represents the oscillation displacement of each flame tube, where T is the transpose of the matrix;

[0026] The system matrix K is expressed in the following form:

[0027]

[0028] Where ω0 is the angular frequency of the flame tube, ω0=2πf0, f0 is the natural frequency of the flame tube, k is the coupling strength of the combined flame tube, and I is the identity matrix.

[0029] Furthermore, in S3, the eigenvalues ​​of the system matrix K Corresponding oscillation frequency eigenvalues The expression form is:

[0030]

[0031]

[0032] Where j = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, represents the different vibration modes of the 12 flame tubes in the combined flame system, with each j value corresponding to a specific vibration mode, λ j These are the eigenvalues ​​of the Laplace matrix L;

[0033] Oscillation frequency The expression form is:

[0034]

[0035] because For modes j=1,2,…,5, modes j and 12-j have the same frequency and constitute degenerate modes.

[0036] Furthermore, in S4, the symmetry is broken, and the degenerate frequency... It splits into two new frequencies, namely and .

[0037] The beneficial effects of this invention are reflected in:

[0038] This invention models the combustion chamber as a cyclic graph in graph theory, using the flame tube as nodes and the connecting tube as edges. A system matrix is ​​constructed using the Laplace matrix to calculate modal frequencies and vibration modes. By modifying the coupling strength of the connecting tube, the system symmetry is broken, degenerate frequencies are split, and combustion instability is mitigated. This invention not only provides an efficient computational tool that simplifies the modeling of complex systems and reduces computational costs, but also offers a tool for combustion chamber design optimization, applicable to the typical combustion instability frequency range of 100-80 Hz. Attached Figure Description

[0039] The accompanying drawings, which are provided to further illustrate this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application.

[0040] Figure 1 This is a schematic diagram of the overall process of the method in the embodiment of the present invention.

[0041] Figure 2 This is a schematic diagram of modal comparison in the degeneracy mode of the uniform ring according to an embodiment of the present invention.

[0042] Figure 3 This is a schematic diagram of modal comparison after modifying the impedance of the flame tube to obtain a new k value according to an embodiment of the present invention.

[0043] Figure 4 This is a structural block diagram of a computer device according to an embodiment of the present invention. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] It should be noted that the meaning of "and / or" throughout the text includes three parallel solutions. Taking "A and / or B" as an example, it includes solution A, solution B, or a solution that simultaneously satisfies A and B. Furthermore, "multiple" refers to two or more. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0046] See Figure 1This invention provides an impedance mismatch design method for a multi-flame tube combined combustion system in a gas turbine combustor, comprising the following steps:

[0047] S1. Based on graph theory, the 12 flame tubes in the gas turbine are connected by flame tubes to form a combustion chamber, which is modeled as a cycle graph C. 12 And construct the adjacency matrix A and the Laplace matrix L;

[0048] S2. Construct the system matrix K based on the angular frequency ω0 of the flame tube and the coupling strength k of the flame tube;

[0049] S3. Calculate the eigenvalues ​​(corresponding to oscillation frequencies) and eigenvectors (corresponding to vibration modes) of the system matrix K, determine the oscillation frequencies and vibration modes, and identify degenerate modes;

[0050] S4. By modifying the coupling strength of at least one flame tube (e.g., by adjusting the coupling strength of the flame tube). ), update the adjacency matrix A and the Laplace matrix L, recalculate the eigenvalues ​​and eigenvectors of the system matrix K, degenerate frequency splits, and symmetry is broken;

[0051] S5. Adjust combustion chamber parameters (e.g., tandem tube geometry or material) based on the frequency and mode after splitting to optimize combustion stability.

[0052] In this embodiment, in S1, each flame tube is a node, and there are 12 nodes in total, numbered v1, v2, ..., v12 in sequence. Each flame tube is an edge connecting two adjacent nodes vi and vi+1, wherein v12 is connected to v1.

[0053] In this embodiment, in S1, the adjacency matrix A is a 12×12 matrix, defined as:

[0054] When the nodes are connected via a flame-connecting tube, A ij =k, where i represents the row index, j represents the column index, j=i+1 or i-1, the matrix modulus is 12, and k is the coupling strength of the flame tube, which is directly related to impedance matching in thermoacoustic oscillation;

[0055] In other cases, A ij =0;

[0056] For the cycle graph C 12 The adjacency matrix A is expressed in the form of:

[0057] ;

[0058] The Laplacian matrix L is L=DA, where D is the degree matrix. Each node is connected to two edges;

[0059] For the cycle graph C12 The Laplace matrix L is expressed in the form of:

[0060] .

[0061] In this embodiment, the dynamic behavior of the multi-flame tube combined flame system in step S2 is described by the following second-order differential equation:

[0062]

[0063] Where K is the system matrix, This represents the oscillation displacement (or physical quantities such as pressure and temperature) of each flame tube, and T is the transpose of the matrix.

[0064] The system matrix K is expressed in the following form:

[0065]

[0066] Where ω0 is the angular frequency of the flame tube, ω0=2πf0, f0 is the natural frequency of the flame tube (e.g., 180Hz), k is the coupling strength of the flame tube, and I is the identity matrix.

[0067] In this embodiment, in S3, the eigenvalues ​​of the system matrix K Corresponding oscillation frequency eigenvalues The expression form is:

[0068]

[0069]

[0070] in:

[0071] j=0,1,2,3,4,5,6,7,8,9,10,11, representing different vibration modes in the 12 flame tubes connected to the flame system, with each j value corresponding to a specific vibration mode;

[0072] λ j These are the eigenvalues ​​of the Laplace matrix L, which represent the following in this multi-flame tube combined combustion chamber system:

[0073] 1. The strength of the coupling effect:

[0074] Describe the degree of coupling between adjacent flame tubes in the j-th vibration mode;

[0075] This reflects the restraining effect of the combined flame tube on the vibration of this mode.

[0076] 2. Modal Stiffness Contribution

[0077] λ jThe larger the value, the stronger the coupling constraint on that mode;

[0078] This is equivalent to adding extra "spring stiffness" to the system.

[0079] When j=0 (uniform mode), all flame tubes vibrate in phase, there is no relative flow in the flame tube, and the coupling effect is zero.

[0080] When j=6 (anti-phase mode), adjacent flame tubes vibrate in completely opposite phases, the flow in the combined flame tube is the most intense, and the coupling effect is the strongest.

[0081] λ j =0, this mode is not affected by the combined flame tube and retains its original frequency;

[0082] λ j >0, the combined flame tube increases the effective stiffness of this mode and increases the vibration frequency;

[0083] λ j The magnitude of the value determines the degree of frequency shift.

[0084] Therefore, λ j The "enhancing" effect of the flame tube combined flame system on the overall vibration frequency was measured in the j-th vibration mode.

[0085] Oscillation frequency The expression form is:

[0086]

[0087] because For modes j=1,2,…,5, modes j and 12-j have the same frequency and constitute degenerate modes.

[0088] In this embodiment, in step S4, the symmetry is broken, and the degeneracy frequency... It splits into two new frequencies, namely and .

[0089] To further verify the feasibility and superiority of this method, the present invention is analyzed and illustrated with the following practical application case:

[0090] In constructing the 200MW gas turbine combustor, 12 flame tubes were used, each with a natural frequency. The coupling strength of the flame tube is calculated based on the impedance. To achieve impedance mismatch, the system matrix is ​​calculated. From the eigenvalues ​​and eigenvectors, the modal frequencies are further obtained as follows:

[0091] Mode j=0: f0≈180Hz (uniform mode, non-degenerate);

[0092] Mode j=1,11: f1=f11≈200Hz (degeneracy);

[0093] Mode j=2,10: f2=f10≈246Hz (degenerate);

[0094] Modes j=3,9: f3=f9≈297Hz (degeneracy);

[0095] Modes j=4,8: f4=f8≈343Hz (degenerate);

[0096] Modes j=5,7: f5=f7≈369Hz (degenerate);

[0097] Mode j=6: f6≈382Hz (non-degenerate);

[0098] The above values ​​are consistent with characteristic frequencies commonly found in gas turbines.

[0099] The coupling strength of the flame tube between nodes v1 and v2 is changed to half of the original coupling strength, that is... The system matrix K is recalculated, and the degenerate frequency splits, at which point the symmetry is broken.

[0100] Based on the frequency and mode after splitting, adjust the geometry (such as pipe diameter or length) or material properties of the flame tube to change the coupling strength k′, avoid the frequency from coinciding with the resonant frequency of the combustion chamber, and thus alleviate combustion instability.

[0101] If other degenerate frequencies (such as j=2,10 or j=3,9) are desired to be closer to 400Hz or 600Hz, k can be further increased, or for example, f0=300Hz, k can be recalculated. That is, the required k value is calculated from the desired frequency, and the impedance of the combined flame tube can be modified accordingly. Furthermore, the coupling strength of multiple combined flame tubes can be modified to obtain more complex frequency splitting, thereby eliminating global oscillation.

[0102] If precise quantification of the magnitude of frequency splits is required, perturbation theory can be used to calculate the eigenvalue changes within the degenerate subspace.

[0103] like Figure 2 As shown, in the degeneracy mode of the uniform ring:

[0104] Mode j=0: Non-degenerate (uniform mode), all flame tubes oscillate in phase (equal amplitude), all points have the same size (uniform oscillation).

[0105] Modes j=1,2,3,4,5 form degenerate pairs with modes j=11,10,9,8,7 respectively, where:

[0106] Modes j=1,11: Simple parallel wave modes, the amplitude forms a sine / cosine distribution (clockwise / counterclockwise) of one wavelength on the ring, that is, the size and color of the points are sinusoidal (traveling wave).

[0107] Modes j=2,10: Simple parallel wave modes, with amplitudes forming a two-wavelength distribution, a sinusoidal distribution of two wavelengths;

[0108] Mode j=1,11: f1=f 11 ≈200Hz (degenerate);

[0109] Mode j=2,10: f2=f 10 ≈246Hz (degenerate);

[0110] Modes j=3,9: f3=f9≈297Hz (degeneracy);

[0111] Modes j=4,8: f4=f8≈343Hz (degenerate);

[0112] Modes j=5,7: f5=f7≈369Hz (degenerate).

[0113] Mode j=6: Non-degenerate mode, the amplitude forms a six-wavelength standing wave on the ring.

[0114] like Figure 3 As shown, by modifying the impedance of the flame tube to eliminate the flame tube-flame tube matching, a new k value is obtained, and the frequency and mode are then calculated:

[0115] The splitting of degenerate modes (e.g., j=1,11) causes the amplitude distribution to no longer be a perfect traveling wave, and may become a standing wave or a mixed mode.

[0116] For example, the original traveling wave mode may show local amplitude variations near v1 and v2 (where the flame tube changes). That is, modes 1 and 11 (the original degenerate modes): the amplitude distribution is no longer uniform and may show significant changes near v1-v2.

[0117] This invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the impedance mismatch design method for the multi-flame tube combined flame system of a gas turbine combustor as described above.

[0118] See Figure 4 The present invention also provides a computer device, including a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor performs the steps of the impedance mismatch design method for the multi-flame tube combined flame system of the gas turbine combustor described above.

[0119] This invention also provides a computer program product containing instructions that, when run on a computer, cause the computer to perform the steps of the impedance mismatch design method for the multi-flame tube combined flame system of a gas turbine combustor as described above.

[0120] It is understood that the systems, devices and storage media provided in the embodiments of the present invention correspond to the methods provided in the embodiments of the present invention, and the explanations, examples and beneficial effects of the relevant contents can be referred to the corresponding parts of the impedance mismatch design method of the multi-flame tube combined flame system of the gas turbine combustor described above.

[0121] It should be noted that those skilled in the art will understand that all or part of the steps implemented in the embodiments of the present invention can be implemented entirely or partially by software, hardware, firmware, or any combination thereof. When implemented in hardware, it can be implemented entirely or partially by purchasing standard parts or modifications. When implemented in software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid state disks (SSDs)).

[0122] In summary, this invention provides a graph theory-based analysis and control method to alleviate the problem of global thermoacoustic oscillations in existing combustion chambers. This method is used for analyzing global combustion instability in gas turbine combustion chambers composed of multiple (for example, 12) flame tubes connected by connecting tubes. Specifically, the connecting tube dimensions are designed to disrupt global frequencies, allowing only specific frequencies to propagate. Furthermore, impedance mismatch is created through the connecting tube dimensions, ensuring that these specific frequencies can only be transmitted to adjacent flame tubes, thus preventing global thermoacoustic oscillations. Finally, to prevent connecting tubes from being placed at incorrect nodes, identical connecting tubes are placed at geometrically different positions by 60°.

[0123] It should be understood that the examples and embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Those skilled in the art can make various modifications or changes based on them. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the protection scope of the invention.

Claims

1. An impedance mismatch design method for a multi-flame tube combined flame system in a gas turbine combustor, characterized in that, Includes the following steps: S1. Based on graph theory, the 12 flame tubes in the gas turbine are used as nodes and the flame tubes are used as edges to connect and form the combustion chamber, which is modeled as a cyclic graph C. 12 And construct the adjacency matrix A and the Laplace matrix L; S2. Based on the angular frequency ω0 of the flame tube and the coupling strength k of the connecting tube, and based on the adjacency matrix A and the Laplace matrix L, construct the system matrix K; S3. Calculate the eigenvalues ​​and eigenvectors of the system matrix K, determine the oscillation frequency and vibration mode, and identify degenerate modes; S4. By modifying the coupling strength of at least one flame tube to k′, updating the adjacency matrix A and the Laplace matrix L, recalculating the eigenvalues ​​and eigenvectors of the system matrix K, the degenerate frequency splits, and the symmetry is broken. S5. Adjust the combustion chamber parameters according to the frequency and mode after splitting to optimize combustion stability.

2. The impedance mismatch design method for a multi-flame tube combined combustion system in a gas turbine combustor as described in claim 1, characterized in that, In S1, each flame tube is a node, and there are 12 nodes in total, numbered v1, v2, ..., v12 in sequence. Each flame tube is an edge connecting two adjacent nodes vi and vi+1, wherein v12 is connected to v1.

3. The impedance mismatch design method for a multi-flame tube combined combustion system in a gas turbine combustor as described in claim 2, characterized in that, In S1, the adjacency matrix A is a 12×12 matrix, defined as follows: When the nodes are connected via a flame-connecting tube, A ij =k, where i represents the row index, j represents the column index, and j = i + 1 or i 1. The matrix has a modulus of 12, and k is the coupling strength of the flame tube, which is directly related to impedance matching in thermoacoustic oscillations; In other cases, A ij =0; For the cycle graph C 12 The adjacency matrix A is expressed in the form of: ； The Laplacian matrix L is L=DA, where D is the degree matrix. Each node is connected to two edges; For the cycle graph C 12 The Laplace matrix L is expressed in the form of: 。 4. The impedance mismatch design method for a multi-flame tube combined combustion system in a gas turbine combustor as described in claim 1, characterized in that, In S2, the dynamic behavior of the multi-flame tube combined flame system is described by the following second-order differential equation: Where K is the system matrix, This represents the oscillation displacement of each flame tube, where T is the transpose of the matrix; The system matrix K is expressed in the following form: Where ω0 is the angular frequency of the flame tube, ω0=2πf0, f0 is the natural frequency of the flame tube, k is the coupling strength of the combined flame tube, and I is the identity matrix.

5. The impedance mismatch design method for a multi-flame tube combined combustion system in a gas turbine combustor as described in claim 1, characterized in that, In S3, the eigenvalues ​​of the system matrix K Corresponding oscillation frequency eigenvalues The expression form is: Where j = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, represents the different vibration modes of the 12 flame tubes in the combined flame system, with each j value corresponding to a specific vibration mode, λ j These are the eigenvalues ​​of the Laplace matrix L; Oscillation frequency The expression form is: because For modes j=1,2,…,5, modes j and modes 12 j have the same frequency and form a degenerate mode.

6. The impedance mismatch design method for a multi-flame tube combined combustion system in a gas turbine combustor as described in claim 1, characterized in that, In S4, the symmetry is broken, and the degenerate frequency... It splits into two new frequencies, namely and .

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