Abstract:
A system includes a gas turbine engine having a first combustor and a second combustor. The first combustor includes a first fuel conduit having a first plurality of injectors. The first plurality of injectors are disposed in a first configuration within the first combustor along a first fuel path, and the first plurality of injectors are configured to route a fuel to a first combustion chamber. The system further includes a second combustor having a second fuel conduit having a second plurality of injectors. The second plurality of injectors are disposed in a second configuration within the second combustor along a second fuel path, and the second plurality of injectors are configured to route the fuel to a second combustion chamber. The second configuration has at least one difference relative to the first configuration.

Description:
BACKGROUND 
       [0001]    The subject matter disclosed herein relates generally to gas turbine systems, and more particularly, to systems and methods for reducing combustion dynamics, and more specifically, for reducing modal coupling of combustion dynamics within a gas turbine engine. 
         [0002]    Gas turbine systems generally include a gas turbine engine having a compressor section, a combustor section, and a turbine section. The combustor section may include one or more combustors (e.g., combustion cans), each combustor having a primary combustion zone and a secondary combustion zone (e.g., late lean injection (LLI) system) downstream from the primary combustion zone. A fuel and/or fuel-air (e.g., oxidant) mixture may be routed into the primary and secondary combustion zones through fuel nozzles, and each combustion zone may be configured to combust the mixture of the fuel and oxidant to generate hot combustion gases that drive one or more turbine stages in the turbine section. 
         [0003]    The generation of the hot combustion gases can create combustion dynamics, which occur when the flame dynamics (also known as the oscillating component of the heat release) interact with, or excite, one or more acoustic modes of the combustor, to result in pressure oscillations in the combustor. Combustion dynamics can occur at multiple discrete frequencies or across a range of frequencies, and can travel both upstream and downstream relative to the respective combustor. For example, the pressure waves may travel downstream into the turbine section, e.g., through one or more turbine stages, or upstream into the fuel system. Certain downstream components of the turbine section can potentially respond to the combustion dynamics, particularly if the combustion dynamics generated by the individual combustors exhibit an in-phase and coherent relationship with each other, and have frequencies at or near the natural or resonant frequencies of the components. In general, “coherence” refers to the strength of the linear relationship between two dynamic signals, and is strongly influenced by the degree of frequency overlap between them. In certain embodiments, “coherence” can be used as a measure of the modal coupling, or combustor-to-combustor acoustic interaction, exhibited by the combustion system. 
         [0004]    Accordingly, a need exists to control the combustion dynamics, and/or modal coupling of the combustion dynamics, to reduce the possibility of any unwanted sympathetic vibratory response (e.g., resonant behavior) of components in the turbine system. 
       BRIEF DESCRIPTION 
       [0005]    Certain embodiments commensurate in scope with the originally claimed invention are summarized below. These embodiments are not intended to limit the scope of the claimed invention, but rather these embodiments are intended only to provide a brief summary of possible forms of the invention. Indeed, the invention may encompass a variety of forms that may be similar to or different from the embodiments set forth below. 
         [0006]    In a first embodiment, a system includes a gas turbine engine having a first combustor and a second combustor. The first combustor includes a first fuel conduit having a first plurality of injectors. The first plurality of injectors are disposed in a first configuration within the first combustor along a first fuel path, and the first plurality of injectors are configured to route a fuel to a first combustion chamber. The system further includes a second combustor which includes a second fuel conduit having a second plurality of injectors. The second plurality of injectors are disposed in a second configuration within the second combustor along a second fuel path, and the second plurality of injectors are configured to route the fuel to a second combustion chamber. The second configuration has at least one difference relative to the first configuration. 
         [0007]    In a second embodiment, a system includes a second combustor having a second fuel conduit, which includes a second plurality of fuel injectors with a second arrangement. The second plurality of fuel injectors are configured to route the fuel to a second secondary combustion zone of the second combustor. The second plurality of fuel injectors comprises a third injector having at least one difference relative to a fourth injector. 
         [0008]    In a third embodiment, a method includes controlling a first combustion dynamic of a first combustor or a first flame dynamic of a first set of fuel injectors of the first combustor with a first arrangement of the first set of fuel injectors. The method further includes controlling a second combustion dynamic of a second combustor or a second flame dynamic of a second set of fuel injectors of the second combustor with a second arrangement of the second set of fuel injectors. The first arrangement comprises at least one difference relative to the second arrangement. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]    These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein: 
           [0010]      FIG. 1  is a schematic of an embodiment of a gas turbine system having a plurality of combustors, where each combustor of the plurality of combustors is equipped with a late lean injection (LLI) fuel circuit having a plurality of LLI injectors in a LLI injector arrangement; 
           [0011]      FIG. 2  is a cross-sectional schematic of an embodiment of one of the combustors of  FIG. 1 , where the combustor is operably coupled to the LLI fuel circuit and a controller; 
           [0012]      FIG. 3  is a schematic of an embodiment of the gas turbine system of  FIG. 1 , illustrating a plurality of combustors each having a plurality of late lean injectors, where the arrangement of the late lean injectors in each of the plurality of combustors varies between combustors to control combustion dynamics and therefore modal coupling of combustion dynamics, thereby reducing the possibility of unwanted vibratory responses in downstream components; 
           [0013]      FIG. 4  is a cross-sectional schematic of an embodiment of a first combustor in the system of  FIG. 3 , wherein the first combustor includes a first circumferential distribution of injectors; 
           [0014]      FIG. 5  is a cross-sectional schematic of an embodiment of a second combustor in the system of  FIG. 3 , wherein the second combustor includes a second circumferential distribution of injectors that is different than the first circumferential distribution; and 
           [0015]      FIG. 6  is a cross-sectional schematic of an embodiment of a third combustor in the system of  FIG. 3 , wherein the third combustor includes a third circumferential distribution of the injectors  18  that is different than the first and second circumferential distribution. 
       
    
    
     DETAILED DESCRIPTION 
       [0016]    One or more specific embodiments of the present invention will be described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. 
         [0017]    When introducing elements of various embodiments of the present invention, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. 
         [0018]    The present disclosure is directed towards reducing combustion dynamics and/or modal coupling of combustion dynamics, to reduce unwanted vibratory responses in downstream components. As described above, a combustor within the gas turbine system combusts an oxidant-fuel mixture to generate hot combustion gases that drive one or more turbine stages in the gas turbine. In some situations, the combustion system may create combustion dynamics due to the combustion process, characteristics of intake fluid flows (e.g., fuel, oxidant, diluent, etc.) into the combustor, and various other factors. The combustion dynamics may be characterized as pressure fluctuations, pulsations, oscillations, and/or waves at certain frequencies. Collectively, the combustion dynamics can potentially cause vibratory responses and/or resonant behavior in various components upstream and/or downstream from the combustor. For example, the combustion dynamics (e.g., at certain frequencies, ranges of frequencies, amplitudes, combustor-to-combustor phases, etc.) can travel both upstream and downstream in the gas turbine system. If the gas turbine combustors, upstream components, and/or downstream components have natural or resonant frequencies that are driven by these pressure fluctuations (i.e. combustion dynamics), then the pressure fluctuations can potentially cause vibration, stress, fatigue, etc. The components may include combustor liners, combustor flow sleeves, combustor caps, fuel nozzles, turbine nozzles, turbine blades, turbine shrouds, turbine wheels, bearings, fuel supply assemblies, or any combination thereof. The downstream components are of specific interest, as they are more sensitive to combustion tones that are in-phase and coherent. Thus, reducing coherence specifically reduces the possibility of unwanted vibrations in downstream components. 
         [0019]    As discussed in detail below, the disclosed embodiments may vary the position and/or location of one or more injectors (e.g., late lean injectors) within a fuel supply assembly (e.g., late lean injection (LLI) fuel circuit) within, between, and/or among one or more combustors of the gas turbine system. More specifically, the disclosed embodiments may vary the position of the late lean injectors via axial staggering and/or circumferential grouping to modify the fuel-air ratio of each injector, or a group of injectors, and/or the distribution of the heat release, modifying the flame dynamics, and therefore the combustion dynamics of the gas turbine combustor (e.g., varying the frequency, amplitude, range of frequencies, or any combination thereof). In addition, modifying the arrangement of late lean injectors may also alter the geometries of the fuel volumes, and therefore, may alter the acoustic response of the fuel system. Referred to in the art as fuel system impedance, modifying the acoustic response of the late lean injector fuel system can affect the interaction between the flame dynamics and the acoustic response of the combustor, which can, in turn, alter the combustion dynamics amplitude and/or frequency, coherence, range of frequencies, or any combination thereof). As noted above, a gas turbine system may include one or more combustors (e.g., combustor cans, combustors, etc.), and each combustor may be configured with a primary combustion zone and a secondary combustion zone. Specifically, in some embodiments, the secondary combustion zone may include an LLI fuel circuit configured to route a secondary fuel into a secondary combustion zone for combustion. In certain embodiments, each LLI fuel circuit includes one or more fuel lines configured to provide the secondary fuel to one or more fuel injectors (e.g., LLI injectors) that route the secondary fuel into the secondary combustion zone. In particular, the position of each LLI injector among the plurality of LLI injectors within a combustor may be varied relative to the other LLI injectors within the same combustor, between LLI injectors of an adjacent combustor, and/or among the LLI injectors of any of the plurality of combustors within the gas turbine system. In some embodiments, the LLI injectors may be varied via axial staggering such that the LLI injectors are shifted along an axial axis within the combustor and/or between combustors. In some embodiments, the LLI injectors may be varied via circumferential grouping such that the LLI injectors are distributed or grouped differently on a plane in the circumferential direction within the combustor and/or between combustors. 
         [0020]    In certain embodiments, varying the arrangement, configuration, and/or function of the LLI injectors of the gas turbine system may change the heat release energy distribution and/or flame shape, thereby driving different flame dynamic behavior in each combustor and shifting the combustion dynamics frequency between the combustors of the system. Since coherence may be indicative of the similarity of the combustion dynamics frequency between the combustors, shifting the combustion dynamics frequency between the combustors of the system may decrease coherence between combustors. In certain implementations, the combustor tone may be smeared or spread out over a greater frequency range, reducing combustion dynamics amplitude and potentially reducing coherence. Particularly, varying the arrangement of LLI injectors of a particular combustor relative to the LLI injectors of another combustor within the system may vary both the heat release distribution, as well as, that particular combustor&#39;s fuel side impedance relative to other combustors, thereby changing the coupling between the acoustic and heat release perturbations, driving a flame dynamic behavior that is different than the flame dynamic behavior of one or more of the other combustors of the system. Accordingly, the resulting combustion dynamics frequencies between the combustors are different, thereby reducing coherence and therefore, modal coupling of the combustors. 
         [0021]    With the forgoing in mind,  FIG. 1  is a schematic of an embodiment of a gas turbine system  10  having a plurality of combustors  12 , wherein each combustor  12  is equipped with a secondary fuel circuit, such as a LLI fuel circuit  14 . In certain embodiments, one or more of the combustors  12  of the system  10  may not be equipped with a secondary fuel circuit. The LLI fuel circuit  14  may be configured to route a secondary fuel  16 , such as a liquid and/or gas fuel into the combustors  12 . For example, the secondary fuel  16  may be routed to one or more secondary fuel injectors of the combustor  12 , such as the LLI fuel injectors  18 . In particular, the arrangement of the LLI fuel injectors  18  for one or more combustors  12  may be varied relative to the LLI fuel injectors  18  of other combustors  12  within the system  10 . As noted above and as further described in detail below, varying the arrangement and/or configuration of the LLI injectors  18  within the system  10  may change the heat release energy distribution and/or flame shape between the combustors  12 , thereby driving different flame dynamic behavior in each combustor  12  and shifting the combustion dynamics frequency between the combustors  12  of the system  10 . Accordingly, the resulting combustion dynamics frequencies between the combustors  12  are different, thereby reducing coherence and therefore, modal coupling of the combustors  12 . 
         [0022]    The gas turbine system  10  includes one or more combustors  12  having the plurality of injectors  18  (e.g., 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more injectors  18 ), a compressor  20 , and a turbine  22 . The combustors  12  include primary fuel nozzles  24  which route a primary fuel  26 , such as a liquid fuel and/or a gas fuel into the combustors  12  for combustion within a primary combustion zone  28 . Likewise, the combustors  12  include the LLI injectors  18  which route the secondary fuel  16  into the combustors  12  for combustion within a secondary combustion zone  30 . The combustors  12  ignite and combust an oxidant-fuel mixture, and then hot combustion gases  32  are passed into the turbine  22 . The turbine  22  includes turbine blades that are coupled to a shaft  34 , which is also coupled to several other components throughout the system  10 . As the combustion gases  32  pass through the turbine blades in the turbine  22 , the turbine  22  is driven into rotation, which causes the shaft  34  to rotate. Eventually, the combustion gases  32  exit the turbine system  10  via an exhaust outlet  36 . Further, the shaft  34  may be coupled to a load  38 , which is powered via rotation of the shaft  34 . For example, the load  38  may be any suitable device that may generate power via the rotational output of the turbine system  10 , such as an external mechanical load. For instance, the load  38  may include an electrical generator, the propeller of an airplane, and so forth. 
         [0023]    In an embodiment of the turbine system  10 , compressor blades are included as components of the compressor  20 . The blades within the compressor  20  are coupled to the shaft  34 , and will rotate as the shaft  34  is driven to rotate by the turbine  22 , as described above. The rotation of the blades within the compressor  20  compress air (or any suitable oxidant)  40  from an air inlet  42  into pressurized air  44  (e.g., pressurized oxidant). The pressurized oxidant  44  is then fed into the primary fuel nozzles  24  and the secondary fuel nozzles (i.e. late lean injectors  18 ) of the combustors  12 . The primary fuel nozzles  24  and the secondary fuel nozzles (i.e. late lean injectors  18 ) mix the pressurized oxidant  44  and fuel (e.g., the primary fuel  26 ) to produce a suitable mixture ratio for combustion (e.g., a combustion that causes the fuel to more completely burn) so as not to waste fuel or cause excess emissions. 
         [0024]    In some embodiments, the physical location of one or more LLI injectors  18  may vary relative to LLI injectors  18  within and/or between combustors  12 . For example, the position and/or arrangement of the LLI injectors  18  of a first combustor  13  may be different than the position and/or arrangement of the LLI injectors  18  of another combustor  12 , such as an adjacent (or non-adjacent) second combustor  15 . In the illustrated embodiment, the LLI injectors  18  of the first combustor  13  are disposed closer to the exit of the combustor  46  (and further from a head end  48 ) compared to the LLI injectors  18  of the second combustor  15 . In other words, the LLI injectors  18  of the combustor  12  may be shifted along an axial direction or axis  50  (e.g., a longitudinal axis), such that the position of the LLI injectors  18  may vary between the combustors  12 . It should be noted that in other embodiments, the position of the LLI injectors  18  may be varied along a circumferential direction or axis  54 . As noted above, varying the arrangement of the LLI injectors  18  of one combustor  12  relative to another may change the heat release energy distribution and/or flame shape at each LLI injector  18 , thereby driving different flame dynamic behaviors and shifting the frequency response between the combustors  12 . 
         [0025]    In some embodiments, the system  10  may include a controller  56  configured to regulate the one or more LLI circuits  14 , where each LLI circuit  14  is associated with the combustor  12 . The controller  56  (e.g., industrial controller, or any suitable computing device, such as desktop computer, tablet, smart phone, etc.) may include a processor and a memory (e.g., non-transitory machine readable media) suitable for executing and storing computer instruction and/or control logic. For example, the processor may include general-purpose or application-specific microprocessors. Likewise, the memory may include volatile and/or non-volatile memory, random access memory (RAM), read only memory (ROM), flash memory, hard disk drives (HDD), removable disk drives and/or removable disks (e.g., CDs, DVDs, Blu-ray Discs, USB pen drives, etc.), or any combination thereof. 
         [0026]    In certain embodiments, the controller  56  may be useful in regulating the secondary fuel  16  routed to one or more LLI injectors  18  via the one or more LLI fuel circuits  14 . For example, in some embodiments, the controller  56  may be configured to bias the secondary fuel  16  routed through the LLI fuel circuit  14  to the LLI injectors  18  of a particular combustor  12 . For example, for a particular combustor  12 , the controller  56  may route more secondary fuel  16  to certain LLI injectors  18  than others. Indeed, in certain embodiments, the controller  56  may be configured to bias the secondary fuel  16  such that one or more LLI injectors  18  of a particular combustor  12  receive the secondary fuel  16  while the remaining LLI injectors  18  of the combustor  12  do not. The LLI fuel circuit  14  may include one or more circuits supplying one or more cans, or valves, to facilitate injector-level fuel flow control. 
         [0027]    In addition, in some embodiments, the controller  56  may be configured to bias the secondary fuel  16  routed to one or more LLI injectors  18  of different combustors  12  of the system  10 . For example, the controller  56  may route more secondary fuel  16  to one or more LLI injectors  18  of the first combustor  13  than one or more LLI injectors  18  of the second combustor  15 . In such embodiments, the position and/or configuration of the LLI injectors  18  of the first combustor  13  and the second combustor  15  may be approximately the same, but the LLI injectors  18  may have a different operation based in part on how the controller  56  is configured to regulate the LLI circuits  14  and/or the secondary fuel  16  associated with each combustor  12 . In this manner, the controller  56  may be configured to change the operation of the LLI injectors  18  to reduce combustion dynamics without necessarily varying the arrangement and/or configuration of the injectors  18 . For example, the controller  56  may be configured to vary the function of the LLI injectors  18  in a manner that changes the heat release energy distribution and/or flame shape of the injectors  18  between the combustors  12 , such that different flame dynamic behavior is driven and the resulting combustion dynamics frequencies are shifted. 
         [0028]      FIG. 2  is a schematic of an embodiment of one of the combustors  12  of  FIG. 1 , where the combustor  12  is operatively coupled to the LLI fuel circuit  14  and the controller  56 . As noted above, the LLI fuel circuit  14  may be configured to route the secondary fuel  16  to the one or more LLI injectors  18  of the combustor  12 . Further, the controller  56  may be configured to regulate the LLI fuel circuit  14  and/or the secondary fuel  16  routed to the one or more LLI injectors  18 . In certain embodiments, the position and/or configuration of the LLI injectors  18  may be varied relative to the LLI injectors  18  of other combustors  12  within the system  10 . Further, in some embodiments, such as in the illustrated embodiment, the controller  56  may be configured to control the operation of one or more LLI injectors  18  of a particular combustor  12 , such that the LLI injectors  18  of the combustor  12  have different heat release energy distributions and/or flame shapes, such that different flame dynamic behaviors are driven and the resulting combustion dynamics frequencies are shifted. In this manner, the combustor  12  may be regulated to have reduced coherence behavior (as described in detail below), and therefore may reduce the possibility of modal coupling between and/or among the combustors  12  within the system  12  (as described in detail with respect to  FIG. 3 ). 
         [0029]    The combustor  12  includes the head end  48  having an end cover  60 , a combustor cap assembly  62 , the primary combustion zone  28 , and the secondary combustion zone  30 . The end cover  60  and the combustor cap assembly  62  may be configured to support the primary fuel nozzles  24  in the head end  48 . In the illustrated embodiment, the primary fuel nozzles  24  route the primary fuel  26  to the primary combustion zone  28 . Further, the primary fuel nozzles  24  receive the pressurized oxidant (e.g., pressurized air)  44  from the annulus  66  (e.g., between liner  68  and flow sleeve  70 ) of the combustor  12  and combine the pressurized oxidant  44  with the primary fuel  26  to form an oxidant/fuel mixture that is ignited and combusted in the primary combustion zone  28  to form combustion gases (e.g., exhaust). The combustion gases flow in a direction  72  to the secondary combustion zone  30 . The LLI fuel circuit  14  provides the secondary fuel  16  to the one or more LLI injectors  18 , which may be configured to route the secondary fuel  16  to the secondary combustion zone  30 . In particular, the LLI injectors  18  receive and route the secondary fuel  16  into the stream of combustion gases in the secondary combustion zone  30 , flowing in the downstream direction  72 . Further, the LLI injectors  18  may receive the pressurized oxidant  44  from the annulus  66  of the combustor  12  and/or directly from the compressor discharge, and combine the pressurized oxidant  44  with the secondary fuel  16  to form an oxidant/fuel mixture that is ignited and combusted in the secondary combustion zone  30  to form additional combustion gases. More specifically, the pressurized oxidant  44  flows through the annulus  66  between the liner  68  and the flow sleeve  70  of the combustor  12  to reach the head end  48 . The combustion gases flow in the direction  72  towards the exit  46  of the combustor  12 , and pass into the turbine  22 , as noted above. 
         [0030]    As described above, combustion dynamics (e.g., generation of hot combustion gases) within the primary combustion zone  28  and/or the secondary combustion zone  30  may lead to unwanted vibratory responses in downstream components. Accordingly, it may be beneficial to control the combustion dynamics, and/or the modal coupling of the combustion dynamics between various combustors  12  of the system  10 , to help reduce the possibility of any unwanted sympathetic vibratory responses (e.g., resonant behavior) of components within the system  10 . In certain embodiments, the controller  56  may be configured to regulate the LLI fuel circuit  14  and control the secondary fuel  16  routed to one or more LLI injectors  18  of the combustor  12 . For example, in the illustrated embodiment, the controller  56  may be configured to bias the amount of secondary fuel  16  routed to a first injector  19 , a second injector  21 , a third injector  23 , and a fourth injector  25 . In particular, the controller  56  may be configured to regulate the LLI circuit  14  in order to bias the secondary fuel  16  such that the first injector  19  and the third injector  23  receive more secondary fuel  16  than the second injector  21  and the fourth injector  25 . Accordingly, the heat release energy distribution and/or the flame shape of the first and third injectors  19 ,  23  may be different than the heat release energy distribution and/or the flame shape of the second and fourth injectors  21 ,  25 . Further, the flame shape of the first and third injectors  19 ,  23  may be different than the flame shape of the second and fourth injectors  21 ,  25 . In some situations, the controller  56  may be configured to bias all (or almost all) of the secondary fuel  16  away from one or more injectors  18 , such that one or more injectors  18  contribute minimally to the combustion gases generated in the secondary combustion zone  30 . In some situations, the controller  56  may be configured to bias some of the secondary fuel  16  away from one or more injectors  18  of the combustor, such that the injectors  18  contribute in various amounts to the combustion gases generated in the secondary combustion zone  30 . 
         [0031]    In some embodiments, the controller  56  may be configured to vary the arrangement of the functioning LLI injectors  18  by controlling the LLI fuel circuit  14  and regulating the amount of secondary fuel  16  routed to each injector  18  of the combustor  12 . In certain embodiments, the controller  56  may bias the secondary fuel  16  to the first and second injectors  19 ,  21  in the first combustor  13 , and may bias the secondary fuel  16  to the third and fourth injectors  23 ,  25  in the second combustor  15 , as further described with respect to  FIG. 3 . In this manner, the controller  16  may be configured to regulate and/or vary the heat release energy distribution and/or the flame shape of the injectors  18  within one or more combustors  12 , thereby driving different flame dynamic behaviors within and between combustors  12  of the system  10 . In this manner, the combustion dynamics frequency within and/or between combustors  12  may be shifted, such that there is decreased coherence between the combustors  12 . 
         [0032]      FIG. 3  is a schematic of an embodiment of the gas turbine system  10  of  FIG. 1 , illustrating a plurality of combustors  12  each equipped with the LLI fuel circuit  14  having a plurality of LLI injectors  18  (e.g., 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more injectors  18 ). In the illustrated embodiment, the gas turbine system  10  includes four combustors  12  coupled to the turbine  22 . In some embodiments, the system  10  may include any number of combustors  12 , such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more combustors  12  coupled to the turbine  22 . In addition, one or more of the LLI fuel circuits  14  associated with the combustors  12  may be operatively coupled to the controller  56 . In particular, in certain embodiments, the one or more LLI injectors  18  of each combustor  12  may have a particular arrangement (e.g., configuration, position, etc.) and/or may be controlled by the controller  56  to have a particular operation configured to help reduce coherent behavior within the system  10 , as further described in detail below. More specifically, the arrangement and/or the operation of the LLI injectors  18  may vary within and/or between the combustors  12  of the system, such that the LLI injectors  18  are driven at different flame dynamic behaviors and have varied fuel system impedances, thereby generating combustion dynamics frequencies that are shifted between the combustors  12  of the system  10 . Since coherence may be indicative of the similarity of the combustion dynamics frequencies between the combustors, shifting the combustion dynamics frequencies between the combustors of the system may reduce coherence between combustors  12 . 
         [0033]    In certain embodiments, the position of one or more LLI injectors  18  may be shifted along the axial direction or axis  50  of the system, such that the position of the LLI injectors  18  vary between the combustors  12 . For example, the LLI injectors  18  of the first combustor  13  may be disposed approximately a first distance  80  from the endcover  60  of the first combustor  13 . In addition, the LLI injectors  18  of the second combustor  15  may be disposed approximately a second distance  82  from the endcover  60  of the second combustor  15 , where the second distance  82  may be greater than the first distance  80 . It should be noted that in some embodiments, the second distance  82  may be less than and/or approximately the same as the first distance  80 , such that the LLI injectors  18  of the second combustor  15  are closer to the head end  48  than the LLI injectors  18  of the first combustor  13 , or such that the LLI injectors  18  of the first and second combustors  13 ,  15  are approximately the same. 
         [0034]    In some embodiments, the position of one or more LLI injectors  18  may be shifted along the axial direction or axis  50 , such that the position of the LLI injectors  18  vary within, as well as between the combustors  12 . For example, each LLI injector  18  of a third combustor  81  may be disposed at a different distance from the endcover  60  of the third combustor  81 . In addition, each LLI injector  18  of a fourth combustor  83  may be disposed at approximately a different distance from the endcover  60  of the fourth combustor  83 . For example, in the third combustor  81 , a third distance  84  from the endcover  60  to the third injector  23  may be less than a fourth distance  86  from the endcover  60  to the fourth injector  25 . It should be noted that in some embodiments, the third distance  84  may be greater than the fourth distance  86 . 
         [0035]    In some embodiments, the distance between various pairs of injectors  18  of a particular combustor may vary within that particular combustor. For example, a fifth distance  88  between the third and fourth injectors  23 ,  25  may be greater than a sixth distance  90  between the first and second injectors  19 ,  21  of the third combustor  81 . In this manner, the injectors  18  of the third combustor  81  may be axially staggered along the axial direction  50  within the combustor  81 . It should be noted that the distance between the injectors  18  (e.g., the fifth or sixth distances  88  and  90 ) may be any distance. Further, in some embodiments, the injectors  18  of the third combustor  81  may be axially staggered relative to the injectors  18  of the fourth combustor  83 . For example, the fifth distance  88  between the third and fourth injectors  23 ,  25  may be greater than the sixth distance  90  between a fifth and a sixth injector  85 ,  87 , respectively. In this manner, varying the position of the injectors  18  via axial staggering along the axial direction  50  between and/or within the combustors  12  (e.g., the first and second combustors  13 ,  15  and/or the third and fourth combustors  81 ,  83 , etc.) may vary the heat release energy distribution and/or flame shape, thereby driving different flame dynamic behaviors between combustors  12 . Accordingly, different flame dynamic behavior is driven and the resulting combustion dynamics frequencies are shifted between the combustors  12 . 
         [0036]    In certain embodiments, the controller  56  may be operatively coupled to one or more LLI circuits  14  associated with one or more combustors  12 . In particular, the controller  56  may be configured to control a particular LLI circuit  14  by regulating the amount of secondary fuel  16  routed and/or biased to the one or more injectors  18  of the combustor  12  associated with that particular LLI circuit  14 . For example, in the illustrated embodiment, the controller  56  may be operatively coupled to a third LLI fuel circuit  14  associated with the third combustor  81  and a fourth LLI fuel circuit  14  associated with the fourth combustors  83 . In some situations, the controller  56  may be configured to bias the secondary fuel  16  routed to the injectors  18  of the third and fourth combustor  81 ,  83  according to a particular arrangement, such that only the injectors  18  in specific positions are fueled. For example, the controller  56  may be configured to route secondary fuel  16  to the second injector  21 , the third injector  23 , the sixth injector  87 , and a seventh injector  89  and away from the first injector  19 , the fourth injector  25 , the fifth injector  85 , and an eighth injector  91 . Accordingly, as illustrated, the heat release distribution and/or the flame shape of the injectors  18  biased with more secondary fuel  16  may be different than the injectors  18  biased with less secondary fuel  16 , thereby driving different flame dynamic behaviors between combustors  12 . As such, different flame dynamic behavior is driven and the resulting combustion dynamics frequencies are shifted between the third and fourth combustors  81 ,  83 . 
         [0037]    In some embodiments, the system  10  may include one or more groups (e.g.,  1 ,  2 ,  3 ,  4 ,  5 , or more) of combustors  12 , where each group of combustors  12  includes one or more combustors  12  (e.g.,  1 ,  2 ,  3 ,  4 ,  5 , or more). In some situations, each group of combustors  12  may include identical combustors  12  that differ from one or more other groups of combustors  12  within the system  10 . For example, a first group of combustors  12  may include identical combustors  12  having a particular arrangement of LLI injectors  18 , and a second group of combustors  12  may include identical combustors  12  having a second arrangement of LLI injectors  18 . Further, the first and second arrangements of LLI injectors  18  may be different in one or more ways, as described above. Accordingly, the first group of combustors  12  may produce a flame dynamic behavior and a fuel system impedance that is different from the flame dynamic behavior and the fuel system impedance of the second group of combustors  12  within the system  10 , thereby generating combustion dynamics frequencies that are shifted between the combustors  12  of the system  10 . 
         [0038]    For example, in certain embodiments, a first group of combustors  12  may include identical combustors  12  each having a first arrangement of LLI injectors  18 , a second group of combustors  12  may include identical combustors  12  each having a second arrangement of LLI injectors  18 , and a third group of combustors  12  may include identical combustors  12  each having a third arrangement of LLI injectors  18 . Further, the arrangements of the LLI injectors  18  of each group of combustors may be different from each other in one or more ways, as described with respect to  FIGS. 3-6 . Accordingly, the LLI injectors  18  of the first group of combustors  12  may be arranged to achieve a first flame dynamic behavior or fuel system impedance, the LLI injectors  18  of the second group of the combustors  12  may be arranged in a configuration different from the baseline configuration to achieve a second flame dynamic behavior or fuel system impedance, and the LLI injectors  18  of the third group of the combustors  12  may be arranged in a configuration different form the baseline configuration to achieve a third flame dynamic behavior or fuel system impedance. The first, second, and third flame dynamic behavior or fuel system impedance may be different from one another. As a result, the combustion dynamics frequencies are shifted between the different groups of combustors  12  of the system  10 . In certain embodiments, the controller  56  may be configured to control the configuration of the LLI injectors  18  within each group of combustors  12 , as further described above. Though three groups and three frequencies are described, it should be clear that any number of groups and/or frequencies may be employed. 
         [0039]    In some embodiments, in addition to axial staggering of injectors  18 , the position and/or arrangement of the injectors  18  may be varied within, between, and/or among one or more combustors  12  of the system  10  via circumferential grouping, as further described with respect to  FIGS. 4 ,  5 , and  6 . For example, the grouping and/or distribution of the LLI injectors  18  along one or more axes in the circumferential direction  54  may be varied between combustors  12 , as further described in detail with respect to  FIGS. 4-6 . 
         [0040]      FIG. 4  is a cross-sectional schematic of an embodiment of the first combustor  13  in the system  10  taken along line  4 - 4  of  FIG. 3 , wherein the first combustor  13  includes a first circumferential distribution  92  of the injectors  18  along a particular axis in the circumferential direction  54 . For example, in the illustrated embodiment, a first set  94  having three injectors  18  and a second set  96  having one injector  18  are circumferentially disposed (e.g., arranged, configured, etc.) approximately along a first circumferential axis  98 , as shown in  FIG. 3 . Each set of injectors  18  may be configured to route the secondary fuel  16  to the secondary combustion zone  30  of the first combustor  13 . In particular, varying the configuration and/or arrangement of the injectors  18  within the combustor  12  and/or between combustors  12  (e.g., the first combustor  13  and the second combustor  15 ) may vary the heat release energy distribution and/or flame shapes, thereby driving different flame dynamic behaviors and shifting the frequency response between the combustors  12 . For example, in some embodiments, the injectors  18  of the first combustor  13  may be disposed along the first circumferential axis  98  in a manner that is different than the position and/or arrangement of the injectors  18  of the second combustor  15 . More specifically, the first set  94  of injectors  18  may be spatially disposed and/or grouped away from the second set  96  of injectors  18  along the same circumferential axis  98  of the first combustor  13 . Indeed, each injector  18  may be spaced at any circumferential distance from another injector  18  of the first combustor  13 , such that certain injectors  18  may be spaced closer to each other than other injectors  18 . In some embodiments, the circumferential grouping of the injectors  18  in the first combustor  13  may differ from the circumferential grouping of the injectors  18  in an adjacent combustor  12 , such as the second combustor  15 , as further described in detail with respect to  FIG. 5  and  FIG. 6 . 
         [0041]      FIG. 5  is a cross-sectional schematic of an embodiment of the second combustor  15  in the system  10  taken along line  5 - 5  of  FIG. 3 , wherein the second combustor  15  includes a second circumferential distribution  100  of the injectors  18  along a particular axis in the circumferential direction  54 . For example, in the illustrated embodiment, the second circumferential distribution  100  comprises four injectors  18  configured to route the secondary fuel  16  to the secondary combustion zone  30  of the second combustor  15 . In particular, the second circumferential distribution  100  may include one or more injectors  18  (e.g., a first circumferential injector  102 , a second circumferential injector  104 , a third circumferential injector  106 , and a fourth circumferential injector  108 ) having approximately the same circumferential distance between them. For example, the first, second, third and fourth circumferential injectors  102 ,  104 ,  106 ,  108  may be disposed at 90 degree increments along a circumferential axis  54 , such that the first injector  102  and the third injector  106  are oppositely disposed (e.g. separated by approximately 180 degrees in the circumferential direction  54 ), and the second injector  104  and the fourth injector  108  are also oppositely disposed (separated by approximately 180 degrees in the circumferential direction  54 ) as shown in  FIG. 5 . Accordingly, any two circumferential injectors in the illustrated embodiment may be disposed at approximately a first angle  110 , such as the first angle  110  at approximately 90 degrees. It should be noted that in other embodiments, the first angle  110  separating any two injectors  18  may be any suitable angle, such as between approximately 1 to 359 degrees, 5 to 10 degrees, 10 to 20 degrees, 20 to 45 degrees, 45 to 90 degrees, 90 to 180 degrees, 180 to 360 degrees, etc. For example, in the illustrated embodiment, the first circumferential injector  102  may be disposed at approximately 45 degrees from the second circumferential injectors  104 , rather than at approximately 90 degrees. In addition, the first angle  110  between any two circumferential injectors  102 ,  104 ,  106 , or  108  may be varied between the combustors  12  for different circumferential configurations and/or arrangements between combustors  12 , as further described with respect to  FIG. 6 . 
         [0042]    In this manner, the injectors  18  of the first combustor  13  may be configured and/or arranged differently than the injectors  18  of the second combustor  15 . Indeed, as noted above, varying the configuration and/or arrangement of the injectors  18  within the combustor  12  and/or between combustors  12  (e.g., the first combustor  13  and the second combustor  15 ) may vary the heat release energy distribution and/or flame shapes, thereby driving different flame dynamic behaviors and shifting the frequency response between the combustors  12 . 
         [0043]      FIG. 6  is a cross-sectional schematic of an embodiment of the third combustor  81  in the system  10  taken along line  6 - 6  of  FIG. 3 , wherein the third combustor  81  includes a third circumferential distribution  112  of the injectors  18  along a particular axis in the circumferential direction  54 . For example, in the illustrated embodiment, the third circumferential distribution  112  comprises four injectors  18  configured to route the secondary fuel  16  to the secondary combustion zone  30  of the third combustor  81 . In particular, the arrangement of the first injector  19 , the second injector  21 , the third injector  23 , and the fourth injector  25  of the third combustor  81  may be different than the arrangement of the first circumferential injector  102 , the second circumferential injector  104 , the third circumferential injector  106 , and the fourth circumferential injector  108  of the second combustor  15 . For example, similar to the injectors  18  of the second combustor  15 , the injectors  18  of the third combustor  81  may be disposed at 90 degree increments along a circumferential direction  54 , such that the first injector  19  and the third injector  23 , and the second injector and the fourth injector  25 , are approximately 180 degrees apart. However, each of the injectors  18  of the third combustor  81  may be offset by approximately a second angle  113  relative to each of the injectors  18  of the second combustor  15 . For example, the first injector  19  of the third combustor  81  may be offset approximately by the second angle  113  (e.g., approximately 45 degrees) relative to the first circumferential injector  102  of the second combustor  15 . It should be noted that in other embodiments, the second angle  113  is representative of the angle offset between any two combustors  12  and may be any suitable angle, such as between approximately 1 to 359 degrees, 5 to 10 degrees, 10 to 20 degrees, 20 to 45 degrees, 45 to 90 degrees, 90 to 180 degrees, 180 to 360 degrees, etc. 
         [0044]    In this manner, the injectors  18  of the second combustor  15  may be configured and/or arranged differently than the injectors  18  of the third combustor  81 . Indeed, as noted above, varying the configuration and/or arrangement of the injectors  18  within the combustor  12  and/or between combustors  12  (e.g., the second combustor  15  and the third combustor  81 ) may vary the heat release energy distribution and/or flame shapes, thereby driving different flame dynamic behaviors and shifting the frequency response between the combustors  12 . 
         [0045]    Technical effects of the disclosure include varying the position and/or location of the one or more injectors  18  of the fuel supply circuit  14  associated with each of the one or more combustors  12  of the system  10 . Specifically, the position and/or arrangement of the injectors  18  may be varied within, between, and/or among the one or more combustors  12  via axial staggering and/or circumferential grouping to modify the heat release energy distribution and/or the fuel system impedance of the LLI fuel system, and therefore the combustion dynamics of the gas turbine combustor (e.g., varying the frequency, amplitude, combustor-to-combustor coherence, range of frequencies, or any combination thereof). For example, the injectors  18  of a particular combustor  12  may be shifted along the axial direction or axis  50  (e.g., a longitudinal axis) of that combustor  12 , such that the position of the injectors  18  may axially vary between the combustors  12  of the system  10 . Likewise, the injectors  18  of a particular combustor  12  may be circumferentially grouped and/or distributed along the circumferential direction  54  of that combustor  12 , such that the position and/or arrangement of the injectors  18  may circumferentially vary between the combustors  12  of the system  10 . It should be noted that in certain embodiments, the injectors  18  of the system  10  may be varied axially and/or circumferentially between the combustors  12 . 
         [0046]    In certain embodiments, the controller  56  may be may be utilized to regulate the secondary fuel  16  routed to one or more LLI injectors  18  via the LLI fuel circuit  14 . For example, in some embodiments, the controller  56  may be configured to bias the secondary fuel  16  routed through the LLI fuel circuit  14  to the LLI injectors  18  of a particular combustor  12 . In this manner, the controller  56  may be configured to change the operation of the LLI injectors  18  to reduce combustion dynamics without necessarily varying the arrangement and/or configuration of the injectors  18 . 
         [0047]    This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.