Patent Publication Number: US-8966903-B2

Title: Combustor resonator with non-uniform resonator passages

Description:
BACKGROUND OF THE INVENTION 
     The subject matter disclosed herein relates to combustor assemblies and, more particularly, to a combustor resonator. 
     Gas turbine systems typically include at least one gas turbine engine having a compressor, a combustor assembly, and a turbine. The combustor assembly may use dry, low NOx (DLN) combustion. In DLN combustion, fuel and air are pre-mixed prior to ignition, which lowers emissions. However, the lean pre-mixed combustion process is susceptible to flow disturbances and acoustic pressure waves. More particularly, flow disturbances and acoustic pressure waves could result in self-sustained pressure oscillations at various frequencies. These pressure oscillations may be referred to as combustion dynamics. Combustion dynamics can cause structural vibrations, wearing, and other performance degradations. 
     BRIEF DESCRIPTION OF THE INVENTION 
     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. 
     In a first embodiment, a system includes a combustor assembly and an annular resonator shell disposed radially about the combustor assembly. The annular resonator shell has an annular outer wall. A distance between the annular outer wall and the combustor assembly is non-uniform. 
     In a second embodiment, a combustor resonator includes a flow sleeve and a resonator shell disposed about the flow sleeve. The resonator shell comprises an outer wall, and a distance between the outer wall and the flow sleeve is non-uniform. 
     In a third embodiment, a combustor resonator includes an inner annular wall and an outer annular wall disposed about the inner annular wall. A distance between the annular outer wall and the inner annular wall is non-uniform. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       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: 
         FIG. 1  is a block diagram of an embodiment of a gas turbine system including combustor assemblies, which each may include a combustor resonator having a resonator shell with a distance between the combustor assembly and the resonator shell that is non-uniform; 
         FIG. 2  is a schematic diagram of an embodiment of one of the combustor assemblies of  FIG. 1 , including a combustor resonator having a distance between the resonator shell and the combustor assembly that is non-uniform; 
         FIG. 3  is a cross-sectional side view of an embodiment of the combustor resonator of  FIG. 2 , illustrating a resonator shell having a distance between the resonator shell and the combustor assembly that is non-uniform, and resonator necks having lengths among the resonator necks that are non-uniform; 
         FIG. 4  is a cross-sectional side view of an embodiment of the combustor resonator of  FIG. 2 , illustrating resonator necks having alternating lengths among the resonator necks; 
         FIG. 5  is a cross-sectional side view of an embodiment of the combustor resonator of  FIG. 2 , illustrating resonator necks having increasing lengths among the resonator necks; 
         FIG. 6  is a cross-sectional side view of an embodiment of the combustor resonator of  FIG. 2 , illustrating resonator necks having diameters among the resonator necks that are non-uniform; 
         FIG. 7  is a graph illustrating an absorption coefficient for three different embodiments of combustor resonators with respect to the frequency of pressure oscillations; 
         FIG. 8  is a partial perspective view of an embodiment of the combustor resonator of  FIG. 2 , illustrating three rows of resonator necks disposed on a flow sleeve of the combustor assembly; 
         FIG. 9  is a partial perspective view of an embodiment of the combustor resonator of  FIG. 2 , illustrating four rows of resonator necks having a staggered configuration disposed on a flow sleeve of the combustor assembly; 
         FIG. 10  is a partial cross-sectional view of an embodiment of the combustor resonator of  FIG. 2 , illustrating resonator passages defined by ribs and holes formed in the flow sleeve of the combustor assembly; 
         FIG. 11  is a partial perspective view of an embodiment of the combustor resonator of  FIG. 2 , illustrating resonator passages defined by ribs and holes formed in the flow sleeve of the combustor assembly; and 
         FIG. 12  is a partial perspective view of an embodiment of the combustor resonator of  FIG. 2 , illustrating resonator passages partially defined by ribs and holes formed in an inner wall of the resonator shell. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     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. 
     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. 
     The present disclosure is directed toward a combustor resonator having a non-uniform annulus between a resonator shell and the combustor. As described above, gas turbine systems include combustor assemblies which may use a DLN or other combustion process that is susceptible to flow disturbances and/or acoustic pressure waves. Specifically, the combustion dynamics of the combustor assembly can result in self-sustained pressure oscillations that may cause structural vibrations, wearing, mechanical fatigue, thermal fatigue, and other performance degradations in the combustor assembly. One technique used to mitigate combustion dynamics is the use of a resonator, such as a Helmholtz resonator. Specifically, a Helmholtz resonator is a damping mechanism that includes several narrow tubes, necks, or other passages connected to a large volume. The resonator operates to attenuate and absorb the combustion tones produced by the combustor assembly. The depth of the necks or passages and the size of the large volume enclosed by the resonator may be related to the frequency of the acoustic waves for which the resonator is effective. 
     As described herein, the volume enclosed by the resonator, as well as the sizes and depths of the resonator necks or passages, may be varied to adjust the frequency range over which the resonator effectively attenuates and absorbs acoustic pressure waves produced by the combustor assembly. Certain embodiments of the present disclosure include a combustor resonator having an annulus with a non-uniform height. For example, in one embodiment, the combustor resonator includes a resonator shell disposed about a flow sleeve of the combustor assembly, wherein the annulus between the flow sleeve and the resonator shell may be non-uniform. The combustor resonator may also include a plurality of resonator necks or passages connecting the flow sleeve of the combustor assembly to the annulus between the flow sleeve and the resonator shell. In certain embodiments, the resonator necks or passages may also be non-uniform. Specifically, the lengths that the resonator necks or passages extend into the annulus of the combustor resonator may vary between the resonator necks or passages disposed around the circumference of the flow sleeve. Moreover, the diameters of the resonator necks or passages may also vary between the resonator necks or passages disposed around the circumference of the flow sleeve. In other embodiments, the resonator shell may be disposed about other areas of the combustor assembly, such as fuel nozzles of the combustor assembly. As described in greater detail below, the non-uniform height of the annulus and the non-uniform heights and diameters of the resonator necks or passage may help widen the frequency ranges over which the combustor resonator may be effective. As will be appreciated, embodiments of the present disclosure may include an annulus with a non-uniform height, non-uniform resonator necks or passages, or both in combination. 
     Turning now to the drawings,  FIG. 1  illustrates a block diagram of an embodiment of a gas turbine system  10 . The diagram includes a compressor  12 , combustor assemblies  14 , and a turbine  16 . In the following discussion, reference may be made to an axial direction or axis  42 , a radial direction or axis  44 , and a circumferential direction or axis  46  of the combustor  14 . The combustor assemblies  14  include fuel nozzles  18  which route a liquid fuel and/or gas fuel, such as natural gas or syngas, into the combustor assemblies  14 . As illustrated, each combustor assembly  14  may have multiple fuel nozzles  18 . More specifically, the combustor assemblies  14  may each include a primary fuel injection system having primary fuel nozzles  20  and a secondary fuel injection system having secondary fuel nozzles  22 . As described in detail below, a combustor resonator  40  (e.g., annular resonator and/or turbine combustor resonator) is coupled to each combustor assembly  14 , wherein the resonator  40  has an annular chamber defined by an annular resonator shell  50  partially extending around the combustor  14 . The resonator  40  may also include resonator necks  102  or resonator passages  208  extending into the annular chamber. Similarly, the primary and secondary fuel nozzles  20  and  22  may include resonators  40  having annular resonator shells  50  and resonator necks  102  or resonator passages  208 . As discussed below, the resonator  40  has a non-uniform height of the annular chamber, a non-uniform length among the necks or passages, and/or a non-uniform diameter among the resonator necks or passages to widen the frequency range of the resonator  40 . 
     The combustor assemblies  14  illustrated in  FIG. 1  ignite and combust an air-fuel mixture, and then pass hot pressurized combustion gasses  24  (e.g., exhaust) into the turbine  16 . Turbine blades are coupled to a common shaft  26 , which is also coupled to several other components throughout the turbine system  10 . As the combustion gases  24  pass through the turbine blades in the turbine  16 , the turbine  16  is driven into rotation, which causes the shaft  26  to rotate. Eventually, the combustion gases  24  exit the turbine system  10  via an exhaust outlet  28 . Further, the shaft  26  may be coupled to a load  30 , which is powered via rotation of the shaft  26 . For example, the load  30  may be any suitable device that may generate power via the rotational output of the turbine system  10 , such as a power generation plant or an external mechanical load. For instance, the load  30  may include an electrical generator, a propeller of an airplane, and so forth. 
     In an embodiment of the turbine system  10 , compressor blades are included as components of the compressor  12 . The blades within the compressor  12  are also coupled to the shaft  26 , and will rotate as the shaft  26  is driven to rotate by the turbine  16 , as described above. The rotation of the blades within the compressor  12  compress air from an air intake  32  into pressurized air  34 . The pressurized air  34  is then fed into the fuel nozzles  18  of the combustor assemblies  14 . The fuel nozzles  18  mix the pressurized air  34  and fuel 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. 
       FIG. 2  is a schematic diagram of an embodiment of one of the combustor assemblies  14  of  FIG. 1 , illustrating an embodiment of the resonator  40  with an annular resonator shell  50  disposed about the combustor assembly  14 . As described above, the compressor  12  receives air from an air intake  32 , compresses the air, and produces a flow of pressurized air  34  for use in the combustion process within the combustor  14 . As shown in the illustrated embodiment, the pressurized air  34  is received by a compressor discharge  48  that is operatively coupled to the combustor assembly  14 . As illustrated by arrows  52 , the pressurized air  34  flows from the compressor discharge  48  towards a head end  54  of the combustor  14 . More specifically, the pressurized air  34  flows through an annulus  56  between a liner  58  and a flow sleeve  60  of the combustor assembly  14  to reach the head end  54 . 
     In certain embodiments, the head end  54  includes plates  61  and  62  that may support the primary fuel nozzles  20  depicted in  FIG. 1 . In the embodiment illustrated in  FIG. 2 , a primary fuel supply  64  provides fuel  66  to the primary fuel nozzles  20 . Additionally, the primary fuel nozzles  20  receive the pressurized air  34  from the annulus  56  of the combustor assembly  14 . The primary fuel nozzles  20  combine the pressurized air  34  with the fuel  66  provided by the primary fuel supply  64  to form an air/fuel mixture. The air/fuel mixture is ignited and combusted in a combustion zone  68  of the combustor assembly  14  to form combustion gases (e.g., exhaust). The combustion gases flow in a direction  70  toward a transition piece  72  of the combustor assembly  14 . The combustion gases pass through the transition piece  72 , as indicated by arrow  74 , toward the turbine  16 , where the combustion gases drive the rotation of the blades within the turbine  16 . 
     The combustor assembly  14  also includes the resonator  40  with the annular resonator shell  50  extending circumferentially  46  around the combustor  14  (e.g., around the flow sleeve  60 ). In other words, the resonator  40  comprises an inner annular wall (e.g., the flow sleeve  60 ) and an outer annular wall (e.g., the annular resonator shell  50 ) disposed about the inner annular wall. In other embodiments, the inner annular wall of the resonator  40  may include the primary fuel nozzles  20  or the secondary fuel nozzles  22 . As described above, the combustion process produces a variety of pressure waves, acoustic waves, and other oscillations referred to as combustion dynamics. Combustion dynamics may cause performance degradation, structural stresses, and mechanical or thermal fatigue in the combustor assembly  14 . Therefore, combustor assemblies  14  may include the resonator  40 , e.g., a Helmholtz resonator, to help mitigate the effects of combustion dynamics in the combustor assembly  14 . In the illustrated embodiment, the annular resonator shell  50  of the resonator  40  extends completely around the flow sleeve  60  of the combustor assembly  14 . In other embodiments, the annular resonator shell  50  may be used in other locations within the combustor assembly  14 . For example, the annular resonator shell  50  may be disposed around the primary fuel nozzles  20 , as indicated by reference numeral  75 . 
     The annular resonator shell  50  is a generally cylindrical and hollow structure. As described in detail below, the radial  44  distance between the annular resonator shell  50  and the flow sleeve  60  of the combustor assembly  14  is non-uniform. In other words, a lateral cross-section of the combustor assembly  14  and the annular resonator shell  50  is non-uniform. In the illustrated embodiment, a central axis  76  of the annular resonator shell  50  is offset a distance  78  from a central axis  80  of the combustor assembly  14 . As a result, the distance between the annular resonator shell  50  and the flow sleeve  60  of the combustor assembly  14  varies circumferentially  46  about the flow sleeve  60  of the combustor assembly  14 . For example, a first portion  82  of an outer wall of the annular resonator shell  50  is disposed a first radial distance  84  from the flow sleeve  60 . Additionally, a second portion  86  of the outer wall of the annular resonator shell  50  is disposed a second radial distance  88  from the flow sleeve  60 , where the second distance  88  is shorter than the first distance  84 . The varying radial  44  distance between the flow sleeve  60  and the annular resonator shell  50  enables the annular resonator shell  50  to absorb oscillations across a wider frequency range than a single resonator with a uniform distance between the annular resonator shell  50  and the flow sleeve  60 . Additionally, the non-uniform shape of the annular resonator shell  50  offers the flexibility of accommodating the annular resonator shell  50  in irregular spaces that are common in combustors. For example, the annular resonator shell  50  may be accommodated around a curved portion  90  of the transition piece  72  of the combustor assembly  14 , or the annular resonator shell  50  may disposed around the primary fuel nozzles  20 . Furthermore, the annular resonator shell  50  may have a variety of different shapes. For example, the annular resonator shell  50  may be circular, oval, rectangular, polygonal, etc. 
       FIG. 3  is a cross-sectional side view of an embodiment of the combustor assembly  14 , taken along line  3 - 3  of  FIG. 2 , illustrating an embodiment of the resonator  40  with the annular resonator shell  50  disposed circumferentially  46  about the flow sleeve  60 , thereby defining an annulus  100  (e.g., annular resonator chamber) between the annular resonator shell  50  and the flow sleeve  60 . Additionally, the flow sleeve  60  includes resonator necks  102  (e.g., tubes, channels, or other passages) extending radially  44  outward from the flow sleeve  60  toward the annular resonator shell  50 . In certain embodiments, the resonator necks  102  are welded to the flow sleeve  60 . As described above, the annular resonator shell  50  is disposed about the flow sleeve  60  at a radial  44  offset. That is, the flow sleeve  60  and the annular resonator shell  50  are not concentric. Specifically, at a top portion  104  (or one side) of the combustor assembly  14 , the annular resonator shell  50  is a first distance  106  radially  44  away from the flow sleeve  60 . In other words, the radial height of the annulus  100  at the top portion  104  of the combustor assembly  14  is the first distance  106 . At a bottom portion  108  (or other side) of the combustor assembly  14 , the annular resonator shell  50  is a second distance  110  radially  44  away from the flow sleeve  60 , wherein the second distance  110  is greater than the first distance  106 . In other words, the radial height of the annulus  100  at the bottom portion  108  of the combustor assembly  14  is the second distance  110 . Because the height of the annulus  100  is greater at the bottom portion  108  than the top portion  104  of the combustor assembly  14 , the annulus  100  generally has a greater volume at the bottom portion  108  than at the top portion  104  of the combustor assembly  14 . Consequently, the frequency of the oscillations absorbed by the annular resonator shell  50  at the bottom portion  108  may be different than the frequency of the oscillations absorbed by the annular resonator shell  50  at the top portion  104 . 
     In the embodiment illustrated in  FIG. 3 , the flow sleeve  60  includes resonator necks  102  extending radially  44  outward from the flow sleeve  60  toward the annular resonator shell  50 . As described above, the resonator necks  102  may be welded to the flow sleeve  60 . Additionally, the geometries of the resonator necks  102  are different between resonator necks  102 . Specifically, in the illustrated embodiment, the lengths  112  of the resonator necks  102  are not uniform circumferentially  46  about the flow sleeve  60 . As described in detail below, other embodiments of the resonator necks  102  may have other variations in geometry. At the top portion  104  (or one side) of the combustor assembly  14 , the lengths  112  of the resonator necks  102  are shorter than the lengths  112  of the resonator necks  102  at the bottom portion  108  (or other side) of the combustor assembly  14 . More specifically, the lengths  112  of the resonator necks  102  incrementally increase from the top portion  104  to the bottom portion  108  of the combustor assembly  14  along each side of the flow sleeve  60  (e.g., in a direction  114  and in a direction  116  circumferentially  46  about the flow sleeve  60 ). As will be appreciated, the specific variation of the lengths  112  of the resonator necks  102  may vary between different embodiments. For example, in other embodiments, the resonator necks  102  with the longer lengths  112  may be located along the top portion  104  of the combustor assembly  14 . 
     Variations in the lengths  112  of the resonator necks  102  may allow the resonator necks  102  to mitigate and absorb different frequencies of combustion dynamics. Specifically, the resonator necks  102  with shorter lengths  112  (e.g., the resonator necks  102  at the top portion  104  of the combustor assembly  14  illustrated in  FIG. 3 ) may generally absorb higher frequency oscillations produced by combustion dynamics. Conversely, the resonator necks  102  with longer lengths  112  (e.g., the resonator necks  102  at the bottom portion  108  of the combustor assembly  14 ) may generally absorb lower frequency oscillations produced by combustion dynamics. The lengths  112  among the resonator necks  102  may vary by a factor of approximately 1.1 to 20, 1.5 to 10, or 2 to 5 from the shortest neck  102  to the longest neck  102 . 
     Furthermore, in the embodiment illustrated in  FIG. 3 , the annular resonator shell  50  is positioned about the flow sleeve  60 , such that a radial gap (i.e., a radial offset)  118  between a peripheral end  119  of each resonator neck  102  and the annular resonator shell  50  is constant. However, in other embodiments, the gaps  118  between each resonator neck  102  and the annular resonator shell  50  may not be constant. For example, in certain embodiments, the lengths  112  of the resonator necks  102  may vary circumferentially  46  about the flow sleeve  60 ; however, in contrast to the embodiment illustrated in  FIG. 3 , the flow sleeve  60  and the annular resonator shell  50  may be concentric. In such an embodiment, the gaps  118  between the resonator necks  102  and the annular resonator shell  50  may vary inversely proportional to variations in the lengths  112  of the resonator necks  102 . 
       FIGS. 4-6  are cross-sectional side views of various embodiments of the combustor assembly  14 , taken along line  3 - 3  of  FIG. 2 , illustrating various configurations of the resonator necks  102  extending radially outward from the flow sleeve  60 . The embodiments illustrated in  FIGS. 4-6  include similar elements and element numbers as the embodiment illustrated in  FIG. 3 . Additionally, while the annular resonator shell  50  is not shown in  FIGS. 4-6 , the embodiments of the resonator  40  illustrated in  FIGS. 4-6  may include the annular resonator shell  50 .  FIG. 4  illustrates an embodiment of the combustor assembly  14  having resonator necks  102  with lengths  112  that alternate about the circumference of the flow sleeve  60 . Specifically, the lengths  112  of the resonator necks  102  alternate between a shorter length  120  and a longer length  122  about the circumference of the flow sleeve  60 . For example, in certain embodiments, the shorter length  120  of certain resonator necks  102  may be approximately 0.25 to 0.75, 0.3 to 0.7, 0.4 to 0.6, or 0.45 to 0.5 inches. In certain embodiments, the longer length  122  of certain resonator necks  102  may be approximately 1.25 to 1.75, 1.3 to 1.7, 1.4 to 1.6, or 1.45 to 1.5 inches. Furthermore, in certain embodiments, the longer lengths  122  may be 1.05 to 50, 1.1 to 20, 1.5 to 10, or 2 to 5 times the shorter lengths  120 . As will be appreciated, the resonator necks  102  having the shorter length  120  may generally absorb oscillations of a higher frequency than the resonator necks  102  having the longer length  122 . 
       FIG. 5  illustrates a combustor assembly  14  having a flow sleeve  60  with resonator necks  102  extending radially  44  outward from the flow sleeve  60 . In the illustrated embodiment, the lengths  112  of the resonator necks  102  incrementally increase circumferentially  46  about of the flow sleeve  60 . Specifically, a resonator neck  130  at the top portion  104  of the combustor assembly  14  has the shortest length  112 . For example, in certain embodiments, the length  112  of the shortest resonator neck  130  may be approximately 0.25 to 0.75, 0.3 to 0.7, 0.4 to 0.6, or 0.45 to 0.5 inches. In a clockwise direction  132 , the length  112  of each subsequent resonator neck  102  gradually increases one after another circumferentially  46  about the flow sleeve  60 . In certain embodiments, the increases in the lengths  112  of the resonator necks  102  may be incremental at a constant rate or a variable rate. For example, in certain embodiments, the length  112  of each subsequent resonator neck  102  along the circumference of the flow sleeve  60  may increase by approximately 0.01 to 0.1, 0.02 to 0.8, 0.03 to 0.7, 0.04 to 0.6, or 0.05 to 0.5 inches, until a resonator neck  134  disposed adjacent to the resonator neck  130  has the longest length  112 . For example, in certain embodiments, the length  112  of the longest resonator neck  134  may be approximately 1.25 to 1.75, 1.3 to 1.7, 1.4 to 1.6, or 1.45 to 1.5 inches. In other embodiments, the lengths  112  of the resonator necks  102  may have percentage incremental increases. For example, the lengths  112  may increase 1 to 50, 5 to 25, or 10 to 15 percent from one neck  102  to another in a circumferential  46  direction. Further, the length  112  of the longest resonator neck  134  may be 1 to 1000, 2 to 500, 3 to 100, 4 to 50, or 5 to 25 times longer than the shortest resonator neck  130 . As will be appreciated, due to the varying lengths  112  of the resonator necks  102 , the resonator necks  102  may absorb different frequencies of oscillations produced by combustion dynamics. 
       FIG. 6  illustrates a combustor assembly  14  having a flow sleeve  60  with resonator necks  102  extending radially  44  outward from the flow sleeve  60 . In the illustrated embodiment, the resonator necks  102  have different cross-sectional diameters  150  (i.e., different passage diameters or widths). More specifically, the resonator neck  152  at the top portion  104  of the combustor assembly  14  has the smallest cross-sectional diameter  150 . For example, in certain embodiments, the diameter  150  of the most narrow resonator neck  152  may be approximately 0.2 to 1.0, 0.3 to 0.9, 0.4 to 0.8, or 0.5 to 0.7 inches. In the clockwise direction  132 , the cross-sectional diameter  150  of each subsequent resonator neck  102  gradually increases one after another circumferentially  46  about the flow sleeve  60 . In certain embodiments, the increases among the cross-sectional diameters  150  of the resonator necks  102  may be incremental at a constant rate or a variable rate. For example, in certain embodiments, the cross-sectional diameter  150  of each subsequent resonator neck  102  circumferentially  46  about the flow sleeve  60  may increase by approximately 0.005 to 0.1, 0.01 to 0.9, 0.02 to 0.8, 0.03 to 0.7, 0.04 to 0.6, or 0.05 to 0.5 inches, until a resonator neck  154  disposed adjacent to the resonator neck  152  has the largest cross-sectional diameter  150 . For example, in certain embodiments, the cross-sectional diameter  150  of the widest resonator neck  154  may be approximately 1.2 to 2.0, 1.3 to 1.9, 1.4 to 1.8, or 1.5 to 1.7 inches. In other embodiments, the cross-sectional diameters  150  of the resonator necks  102  may have percentage incremental increases. For example, the cross-sectional diameters  150  may increase 1 to 50, 5 to 25, or 10 to 15 percent from one neck  102  to another in a circumferential  46  direction. Further, the cross-sectional diameter  150  of the widest resonator neck  154  may be 1 to 1000, 2 to 500, 3 to 100, 4 to 50, or 5 to 25 times greater than the resonator neck  152 . As will be appreciated, due to the varying cross-sectional diameters  150  of the resonator necks  102 , the resonator necks  102  may absorb different frequencies of oscillations produced by combustion dynamics. 
       FIG. 7  is a graph  170  illustrating an absorption coefficient  172  for three different embodiments of resonators  40  for combustor assemblies  14  with respect to a frequency  174  of pressure oscillations produced by combustion dynamics. More specifically, the line  176  represents a relationship between the absorption coefficient  172  and the frequency  174  of pressure oscillations for a combustor assembly  14  where the radial distance from the annular resonator shell  50  to the flow sleeve  60  is constant or uniform. In other words, the annular resonator shell  50  and the flow sleeve  60  are concentric for the combustor assembly  14  represented by the line  176 . Specifically, for the combustor assembly  14  represented by line  176 , the distance between the annular resonator shell  50  and the flow sleeve  60  is the distance  110  shown in  FIG. 3 , and the distance  110  is uniform circumferentially  46  about the flow sleeve  60 . Additionally, the combustor assembly  14  represented by the line  176  includes resonator necks  102 , where each resonator neck  102  has the longer length  122  shown in  FIG. 4  (i.e., the resonator necks  102  are uniform and have the length  122 ), and each resonator neck  102  has the same (i.e., uniform) diameter. 
     The graph  170  also includes a line  178  which represents the relationship between the absorption coefficient  172  and the frequency  174  of pressure oscillations for a combustor assembly  14  where the distance between the annular resonator shell  50  and the flow sleeve  60  is constant. In particular, the distance between the annular resonator shell  50  and the flow sleeve  60  is the distance  106  shown in  FIG. 3 , and the distance  106  is uniform circumferentially  46  about the flow sleeve  60 . In other words, the annular resonator shell  50  and the flow sleeve  60  are concentric for the combustor assembly  14  represented by the line  178 . Additionally, the combustor assembly  14  represented by line  178  includes resonator necks  102 , where each resonator neck has the shorter length  120  shown in  FIG. 4  (i.e., the resonator necks  102  are uniform and have the length  120 ), and each resonator neck  102  has the same (i.e., uniform) diameter. 
     Furthermore, the graph  170  includes a line  180  representing the relationship between the absorption coefficient  172  and the frequency  174  of pressure oscillations for a combustor assembly  14  having the annular resonator shell  50  disposed at an offset around the flow sleeve  60  and resonator necks  102  having different lengths  112 . For example, the combustor assembly  14  represented by line  180  may have the annular resonator shell  50  and resonator necks  102  configuration shown in  FIG. 3 . In other words, the combustor assembly  14  represented by line  180  includes the resonator  40  with a non-uniform annulus  100 , non-uniform lengths  112  of the resonator necks  102 , and constant cross-sectional diameters  150  of the resonator necks  102 . 
     As shown by the graph  170 , the combustor assembly  14  represented by line  176  has an approximate effectiveness range  182 . In other words, the approximate effectiveness range  182  represents the range of frequencies  174  across which the resonator  40  of the combustor assembly  14  represented by line  176  (e.g., the combustor assembly  14  where the distance between the annular resonator shell  50  and the flow sleeve is constant and equal to the distance  110  shown in  FIG. 3  and where each resonator neck  102  has the longer length  122  shown in  FIG. 4 ) effectively absorbs oscillations produced by combustion dynamics. Similarly, the combustor assembly  14  represented by line  178  (e.g., the combustor assembly where the distance between the annular resonator shell  50  and the flow sleeve  60  is constant and equal to the distance  106  shown in  FIG. 3  and where each resonator neck has the shorter length  120  shown in  FIG. 4 ) has an approximate effectiveness range  184 . Furthermore, the combustor assembly  14  represented by line  180  has an approximate effectiveness range  186 . The approximate effectiveness range  186  of the combustor assembly  14  represented by line  180  (e.g., the combustor assembly  14  having the annular resonator shell  50  offset from the flow sleeve  60  and the resonator necks  102  with non-uniform lengths  112 ) is greater than the approximate effectiveness ranges  182  and  184  for the combustor assemblies  14  represented by lines  176  and  178 . As will be appreciated, the combustor assembly  14  having an off center annular resonator shell  50  and resonator necks  102  with non-uniform lengths  112  may absorb a wider range of frequencies (e.g., range  186 ) than the combustor assemblies  14  having the annular resonator shell  50  concentric to the flow sleeve  60  and resonator necks  102  with a uniform length  112  (e.g., ranges  182  and  184 ). 
       FIGS. 8 and 9  are partial perspective views of embodiments of the combustor assembly  14  illustrating the flow sleeve  60  having multiple rows of resonator necks  102  extending radially  44  outward from the flow sleeve  60  toward the annular resonator shell  50  (shown in dashed lines). Specifically,  FIG. 8  illustrates the flow sleeve  60  having three rows of resonator necks  102  extending radially  44  outward from the flow sleeve  60  toward the annular resonator shell  50 . While the illustrated embodiment shows three rows of resonator necks  102 , other embodiments may include more rows, or fewer rows, of resonator necks  102 . For example, the flow sleeve  60  may include 1, 2, 4, 5, or more rows of resonator necks  102 . In certain embodiments, the number of rows of resonator necks  102  may be selected based on the range of frequencies of oscillations to be absorbed. Each row may include 6, 8, 10, 12, 14, 16, 18, 20, or more resonator necks  102 . As discussed above, the resonator necks  102  may have different lengths  112  and/or cross-sectional diameters  150  circumferentially  46  about the flow sleeve  60  to enable the absorption of different frequencies of oscillations produced by combustion dynamics. Additionally, the resonator necks  102  in the illustrated embodiment are oriented in a rectangular grid configuration. As discussed below, other embodiments may include resonator necks  102  oriented in other configurations. 
     For example,  FIG. 9  illustrates an embodiment of the combustor assembly  14  having a flow sleeve  60  with resonator necks  102  oriented in a staggered configuration. More specifically, the illustrated embodiment includes four rows of resonator necks  102 , where each row is staggered with respect to adjacent rows of resonator necks  102 . While the illustrated embodiment includes four staggered rows of resonator necks  102  disposed on the flow sleeve  60 , other embodiments may include more or fewer rows. For example, other embodiments may include 2, 3, 5, 6, or more staggered rows of resonator necks. Additionally, each row may include 6, 8, 10, 12, 14, 16, 18, 20, or more resonator necks  102 . As discussed above, the resonator necks  102  may have different lengths  112  and/or cross-sectional diameters  150  circumferentially  46  about the flow sleeve  60  to enable the absorption of different frequencies of oscillations produced by combustion dynamics. Similarly, while  FIGS. 8 and 9  illustrate resonator necks  102  configurations for the flow sleeve  60 , the illustrated configurations may be used for other components of the combustor assembly  14  which may have resonator necks  102 , such as the fuel nozzles  20 . 
       FIG. 10  is a partial cross-sectional side view of an embodiment of the combustor assembly  14 , illustrating the combustor resonator  40  having resonator passages defined by ribs  200  (e.g., annular ribs) formed in the flow sleeve  60  of the combustor assembly  14 . The illustrated embodiment includes similar elements and element numbers as the embodiment shown in  FIG. 2 . A portion  202  of the flow sleeve  60  includes a plurality of ribs  200 , or grooves, formed circumferentially  46  about the flow sleeve  60 . For example, the portion  202  may be a separate structure fused to the flow sleeve  60 , e.g., by a welding or brazing process. Alternatively, the portion  202  may be integrally formed with the flow sleeve  60 . While the illustrated embodiment of the portion  202  includes three ribs  200  formed about the flow sleeve  60 , other embodiments may include 1, 2, 4, 5, 6, 7, 8, or more ribs  200 . In certain embodiments, the ribs  200  may be formed by a machining process, such as milling. As shown, the ribs  200  have a radial height  204 . In other words, the ribs  200  extend a distance (e.g., height  204 ) radially  44  outward from the flow sleeve  60 . The height  204  of the ribs  200  may be constant about the circumference  46  of the flow sleeve  60 , or the height  204  of the ribs  200  may vary. Additionally, holes  206  extend through the ribs  200 . More particularly, the holes  206  define resonator passages  208  through the ribs  200  radially  44  outward from the flow sleeve  60 . In this manner, the holes  206  and the ribs  200  represent the individual resonator necks  102  discussed above. In other words, the ribs  200  and holes  206  form resonator passages  208  between the annulus  56  and the annulus  100  (e.g., the resonator chamber). In certain embodiments of the combustor resonator  40 , the flow sleeve  60  may include the individual resonator necks  102  discussed above and resonator passages  208  formed by ribs  200  with holes  206 . As will be appreciated, the holes  206  may have similar or different diameters  210 . In this manner, the resonator passages  208  may be tuned to mitigate a specific frequency range of combustion dynamics. Similarly, each rib  200  may have any number of holes  206 . For example, each rib may have approximately 1-1000, 2 to 500, 3 to 250, 4 to 100, 5 to 50, or 6 to 25 holes  206 . As with the embodiments described above, the annular resonator shell  50  may be disposed about the portion  202  of the flow sleeve  60  to provide an annulus  100  with a non uniform height. 
       FIG. 11  is a partial perspective view of the combustor resonator  40 , illustrating an embodiment of resonator passages  208  formed by ribs  200  and holes  206 . Specifically, the illustrated embodiment shows the portion  202  of the flow sleeve  60  having three ribs  200 . As mentioned above, other embodiments of the combustor resonator  40  may include more or fewer ribs  200 . Additionally, each rib  200  includes a plurality of holes  206  to create the resonator passages  208 . As shown, the holes  206  extend through the ribs  200  in the radial  44  direction, thereby creating resonator passages  208  between the annulus  56  and the annulus  100  (e.g., the resonator chamber). As discussed above, the holes  206  may have different diameters  210 , and the ribs  200  may have different heights  204 , which may vary circumferentially  46  about the portion  202  of the flow sleeve  60  to enable the absorption of different frequencies of oscillations produced by combustion dynamics. Similarly, while  FIGS. 10 and 11  illustrate resonator passages  208  formed in the portion  202  of the flow sleeve  60 , resonator passages  208  may be formed by ribs  200  with holes  206  in other components of the combustor assembly  14 , e.g., fuel nozzles  20  with a combustor resonator  40 . 
       FIG. 12  is a partial perspective view of the combustor resonator  40 , illustrating an embodiment of the resonator passages  208  formed by ribs  200  and holes  206 . More specifically, in the illustrated embodiment, the ribs  200  and holes  206  are formed in an inner wall  220  of the annular resonator shell  50 . In other words, the ribs  200  extend from the inner wall  220  of the annular resonator shell  50  to the flow sleeve  60 . Additionally, the holes  206  extend through the flow sleeve  60  and the inner wall  220  of the annular resonator shell  50  in the radial  44  direction to form the resonator passages  208 . In this manner, the annulus  56  between the liner  58  and the flow sleeve  60  is operatively coupled to the annulus  100  of the combustor resonator  40  (e.g., the resonator chamber). As discussed above, the holes  206  may have different diameters  210 , and the ribs  200  may have different heights  204 , which may vary in the axial  42  direction, as shown, to enable the absorption of different frequencies of oscillations produced by combustion dynamics. Similarly, the diameters  210  and heights  204  may vary circumferentially  46  about the inner wall  220  of the annular resonator shell  50 . 
     As discussed above, the described embodiments provide a combustor resonator  40  having an annulus  100  with a non-uniform height. For example, the resonator  40  includes an annular resonator shell  50  which may be disposed about various components of the combustor assembly  14 , such as the flow sleeve  60  or fuel nozzles  20 . The combustor resonator  40  may also include resonator necks  102  or resonator passages  208  which are non-uniform. In other words, the resonator necks  102  or resonator passages  208  may have variable lengths and diameters. The non-uniform height of the annulus  100  and the non-uniform lengths and diameters of the resonator necks  102  or resonator passages  208  may help widen the frequency ranges over which the combustor resonator  40  is effective. In other words, embodiments of the combustor resonator  40  described herein may enable attenuation of combustion dynamics over a wider range of frequencies. 
     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.