Patent Publication Number: US-2023160343-A1

Title: Unit cell resonator networks for gas turbine combustor tone damping

Description:
FIELD 
     The present disclosure relates generally to attenuation structures for reducing acoustic noise and, more particularly, to acoustic panels for reducing noise generated within the combustors of gas turbine engines or propulsion systems. 
     BACKGROUND 
     Acoustic panels may be used for noise suppression or attenuation in aerospace applications and other fields. The panels typically comprise two skin surfaces that sandwich between them at least one layer of a core material or structure. The two skins and the core structure may be bonded together or cured or otherwise formed together, but mechanical fastening is also used in some applications. The core structure ties the skins together structurally and can form a very rigid, efficient and lightweight structure for noise suppression or attenuation useful in aerospace applications, such as for example, in cabins or other areas of passenger aircraft. The panels may be given acoustic properties by perforating one skin (typically an air washed side of the panel) with specifically sized volumes. This enables the cells of the core structure to act like individual Helmholtz or quarter-wave resonators that attenuate a certain tone or tones, at specific or broadband frequencies or wavelengths, of noise generated outside an aircraft—e.g., by an engine or airflow over the fuselage—or noise generated within an aircraft—e.g., by personal audio/visual equipment, galley equipment or air management equipment. These acoustic panels, where the resonators are sandwiched by a single pair of skins, are typically referred to as single-degree of freedom (SDOF) liners or panels. Acoustic panels may also be constructed as double-degree of freedom (DDOF) or multiple-degree of freedom (MDOF) liners or panels, comprising two or more layers of resonators, that provide broader frequency noise reduction. 
     SUMMARY 
     A noise attenuation panel for a structure within a propulsion system is disclosed. In various embodiments, the noise attenuation panel includes a first plurality of unit cells; and a second plurality of unit cells, the second plurality of unit cells merged within the first plurality of unit cells, the first plurality of unit cells including a first periodic structure having a first unit cell, a second unit cell, a third unit cell and a fourth unit cell, each of the first unit cell, the second unit cell, the third unit cell and the fourth unit cell including a central body interconnected via a plurality of lateral tubes extending from the central body, the first periodic structure forming a first lateral layer of unit cells. 
     In various embodiments, the first plurality of unit cells defines a plurality of volumes and the second plurality of unit cells is merged within the first plurality of unit cells by positioning the second plurality of unit cells within the plurality of volumes. In various embodiments, exterior surfaces of the first plurality of unit cells and the second plurality of unit cells are spaced apart to form a spacing between the exterior surfaces. In various embodiments, the spacing provides a flow path for a cooling fluid to flow between the exterior surfaces of the first plurality of unit cells and the second plurality of unit cells. 
     In various embodiments, the first plurality of unit cells defines a first noise attenuation flow path and the second plurality of unit cells defines a second noise attenuation flow path. In various embodiments, the first noise attenuation flow path and the second noise attenuation flow path are configured to attenuate different frequency ranges. 
     In various embodiments, the plurality of volumes includes a first volume having a first volume size and a second volume having a second volume size different from the first volume size. 
     In various embodiments, the first unit cell includes a first central body and a first axial tube disposed on the first central body and a second axial tube disposed on the first central body, opposite the first axial tube, each of the first axial tube and the second axial tube being in fluid communication with one another through the first central body. In various embodiments, the first unit cell includes a first lateral tube, disposed on and in fluid communication with the first central body, and a second lateral tube, opposite the first lateral tube and disposed on and in fluid communication with the first central body. 
     In various embodiments, the first unit cell includes a third lateral tube, disposed on and in fluid communication with the first central body, and a fourth lateral tube, opposite the third lateral tube and disposed on and in fluid communication with the first central body and wherein each of the first axial tube, the second axial tube, the first lateral tube, the second lateral tube, the third lateral tube and the fourth lateral tube are in fluid communication with each other via the first central body. 
     In various embodiments, the first axial tube exhibits a first axial tube size, the second axial tube exhibits a second axial tube size, the first lateral tube exhibits a first lateral tube size, the second lateral tube exhibits a second lateral tube size, the third lateral tube exhibits a third lateral tube size and the fourth lateral tube exhibits a fourth lateral tube size and at least one of the first axial tube size, the second axial tube size, the first lateral tube size, the second lateral tube size, the third lateral tube size or the fourth lateral tube size exhibits a first size and at least one of the first axial tube size, the second axial tube size, the first lateral tube size, the second lateral tube size, the third lateral tube size or the fourth lateral tube size exhibits a second size that is different from the first size. 
     In various embodiments, at least one of the first axial tube, the second axial tube, the first lateral tube, the second lateral tube, the third lateral tube or the fourth lateral tube is completely sealed via a wall configured to block a flow of fluid therethrough. In various embodiments, at least one of the first axial tube, the second axial tube, the first lateral tube, the second lateral tube, the third lateral tube or the fourth lateral tube is partially sealed. 
     A combustor for a gas turbine engine is disclosed. In various embodiments, the combustor includes a combustion chamber; and a noise attenuation panel, including a first plurality of unit cells, and a second plurality of unit cells, the second plurality of unit cells merged within the first plurality of unit cells, the first plurality of unit cells including a first periodic structure having a first unit cell, a second unit cell, a third unit cell and a fourth unit cell, each of the first unit cell, the second unit cell, the third unit cell and the fourth unit cell including a central body interconnected via a plurality of lateral tubes extending from the central body, the first periodic structure forming a first lateral layer of unit cells. In various embodiments, the combustion chamber is in the form of a rotating detonation engine. 
     In various embodiments, the first plurality of unit cells defines a plurality of volumes and the second plurality of unit cells is merged within the first plurality of unit cells by positioning the second plurality of unit cells within the plurality of volumes. In various embodiments, exterior surfaces of the first plurality of unit cells and the second plurality of unit cells are spaced apart to form a spacing between the exterior surfaces. In various embodiments, the spacing provides a flow path for a cooling fluid to flow between the exterior surfaces of the first plurality of unit cells and the second plurality of unit cells. 
     In various embodiments, the first plurality of unit cells defines a first noise attenuation flow path and the second plurality of unit cells defines a second noise attenuation flow path. In various embodiments, the first noise attenuation flow path and the second noise attenuation flow path are configured to attenuate different frequency ranges. 
     The foregoing features and elements may be combined in any combination, without exclusivity, unless expressly indicated herein otherwise. These features and elements as well as the operation of the disclosed embodiments will become more apparent in light of the following description and accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The subject matter of the present disclosure is particularly pointed out and distinctly claimed in the concluding portion of the specification. A more complete understanding of the present disclosure, however, may best be obtained by referring to the following detailed description and claims in connection with the following drawings. While the drawings illustrate various embodiments employing the principles described herein, the drawings do not limit the scope of the claims. 
         FIG.  1    is a schematic representation of a gas turbine engine used as a propulsion system on an aircraft, in accordance with various embodiments; 
         FIGS.  2 A and  2 B  are schematic illustrations of noise attenuation panels for use in a gas turbine engine, in accordance with various embodiments; 
         FIGS.  3 A and  3 B  are schematic illustrations of noise attenuation panels for use in a gas turbine engine, in accordance with various embodiments; 
         FIGS.  4 A and  4 B  are schematic illustrations of noise attenuation panels for use in a gas turbine engine, in accordance with various embodiments; 
         FIGS.  5 A and  5 B  are schematic illustrations of noise attenuation panels for use in a gas turbine engine, in accordance with various embodiments; 
         FIGS.  6 A,  6 B,  6 C and  6 D  are schematic views of the noise attenuation panels of the present disclosure and performance graphs illustrating improvements over more conventional single-degree of freedom cell-based structures, in accordance with various embodiments; 
         FIGS.  7 A and  7 B  are schematic views of a noise attenuation panel of the present disclosure and a performance graph illustrating improvements over conventional single-degree of freedom cell-based structures, in accordance with various embodiments; 
         FIGS.  8 A,  8 B and  8 C  are schematic views of various embodiments of the noise attenuation panels of the present disclosure illustrating relative performance, in accordance with various embodiments; 
         FIGS.  9 A,  9 B and  9 C  are schematic illustrations of a noise attenuation panel of the present disclosure, in accordance with various embodiments; 
         FIGS.  10 A,  10 B and  10 C  are schematic illustrations of a noise attenuation panel of the present disclosure, in accordance with various embodiments; 
         FIGS.  11 A,  11 B and  11 C  are schematic illustrations of a noise attenuation panel of the present disclosure, in accordance with various embodiments; 
         FIGS.  12 A and  12 B  are schematic illustrations of a noise attenuation panel of the present disclosure, in accordance with various embodiments; 
         FIG.  13    is a schematic illustration of a noise attenuation panel of the present disclosure, in accordance with various embodiments; 
         FIG.  14    is a schematic illustration of a noise attenuation panel of the present disclosure, in accordance with various embodiments; 
         FIGS.  15 A,  15 B,  15 C,  15 D and  15 E  are schematic illustrations of various unit cell arrangements for a noise attenuation panel of the present disclosure, in accordance with various embodiments; 
         FIGS.  16 A,  16 B,  16 C and  16 D  are schematic illustrations of various facesheets or septa or perforate structures for a noise attenuation panel of the present disclosure, in accordance with various embodiments; 
         FIGS.  17 A,  17 B,  17 C and  17 D  are schematic illustrations of various components of a noise attenuation panel, in accordance with various embodiments; 
         FIGS.  18 A,  18 B,  18 C,  18 D,  18 E,  18 F and  18 G  are schematic illustrations of the solid lattice component and the fluid lattice component of the noise attenuation panel illustrated at  FIGS.  17 A- 17 D , in accordance with various embodiments; 
         FIGS.  19 A,  19 B,  19 C and  19 D  are schematic illustrations of a combustor having a noise attenuation panel, in accordance with various embodiments; 
         FIGS.  20 A and  20 B  are schematic illustrations of a combustor having a noise attenuation panel, in accordance with various embodiments; and 
         FIG.  21    is a schematic illustration of a combustor having a noise attenuation panel, in accordance with various embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     The following detailed description of various embodiments herein makes reference to the accompanying drawings, which show various embodiments by way of illustration. While these various embodiments are described in sufficient detail to enable those skilled in the art to practice the disclosure, it should be understood that other embodiments may be realized and that changes may be made without departing from the scope of the disclosure. Thus, the detailed description herein is presented for purposes of illustration only and not of limitation. Furthermore, any reference to singular includes plural embodiments, and any reference to more than one component or step may include a singular embodiment or step. Also, any reference to attached, fixed, connected, or the like may include permanent, removable, temporary, partial, full or any other possible attachment option. Additionally, any reference to without contact (or similar phrases) may also include reduced contact or minimal contact. It should also be understood that unless specifically stated otherwise, references to “a,” “an” or “the” may include one or more than one and that reference to an item in the singular may also include the item in the plural. Further, all ranges may include upper and lower values and all ranges and ratio limits disclosed herein may be combined. 
     Referring now to  FIG.  1   , a side cutaway illustration of a gas turbine engine  100  is provided. The gas turbine engine  100  extends along an axial centerline A between an airflow inlet  102  and a core exhaust system  104 . The gas turbine engine  100  includes a fan section  106 , a low-pressure compressor section  108  (LPC), a high-pressure compressor section  110  (HPC), a combustor section  112 , a high-pressure turbine section  114  (HPT) and a low-pressure turbine section (LPT)  116 . The various engine sections are typically arranged sequentially along the axial centerline A. In various embodiments, the low-pressure compressor section  108  (LPC), the high-pressure compressor section  110  (HPC), the combustor section  112 , the high-pressure turbine section  114  (HPT) and the low-pressure turbine section  116  (LPT) form a core  118  (or an engine core) of the gas turbine engine  100 . 
     Air enters the gas turbine engine  100  through the airflow inlet  102 , and is directed through the fan section  106  and into a core gas flow path C and a bypass gas flow path B. The air within the core gas flow path C may be referred to as “core air.” The air within the bypass gas flow path B may be referred to as “bypass air.” The core air is directed through the low-pressure compressor section  108 , the high-pressure compressor section  110 , the combustor section  112 , the high-pressure turbine section  114  and the low-pressure turbine section  116  and exits the gas turbine engine  100  through the core exhaust system  104 , which includes an exhaust center body  120  surrounded by an exhaust nozzle  122 . Within the combustor section  112 , fuel is injected into and mixed with the core air and ignited to provide a hot airstream that drives the turbine sections. The bypass air is directed through the bypass gas flow path B, and out of the gas turbine engine  100  through a bypass exhaust nozzle  124  to provide forward engine thrust. The bypass air may also or alternatively be directed through a thrust reverser, positioned, for example, at or proximate the bypass exhaust nozzle  124 , to provide reverse engine thrust. A fan nacelle  126  is typically employed to surround the various sections of the gas turbine engine  100  and a core nacelle  128  is typically employed to surround the various sections of the core  118 . The gas turbine engine  100  is typically secured to an airframe (e.g., a fuselage or a wing) via a pylon  130 . 
     Referring now to  FIGS.  2 A and  2 B , schematic views of a noise attenuation panel (or an acoustic attenuation structure) are provided; the noise attenuation panels described and illustrated in these figures are oversimplified to explain various features of the panels. Referring specifically to  FIG.  2 A , a noise attenuation panel  200  is illustrated having a unit cell  202  sandwiched between a facesheet  204  and a back plate  206 . The facesheet  204  typically includes a plurality of perforations or openings  208  to communicate acoustic waves or energy to the unit cell  202 , which acts as a resonator to damp or attenuate the acoustic waves or energy. The back plate  206  typically is non-perforated and, together with the facesheet  204 , provides a support structure for the unit cell  202 ; note that while the back plates described and illustrated in this disclosure are described as typically being non-perforated, there is no requirement that perforations may not be incorporated into or through the back plates. In various embodiments, and as will be described in further detail below, the unit cell  202  includes a pair of axial tubes, including, for example, a first axial tube  210  connected to the facesheet  204  and a second axial tube  212 , opposite the first axial tube  210  (e.g., the first axial tube  210  being axially aligned with the second axial tube  212 ), connected to the back plate  206 . In various embodiments, the unit cell  202  further includes a first pair of lateral tubes, such as, for example, a first lateral tube  214  and a second lateral tube  216 , opposite the first lateral tube  214  (e.g., the first lateral tube  214  being axially aligned with the second lateral tube  216 ). In various embodiments, the unit cell  202  further includes a second pair of lateral tubes, such as, for example, a third lateral tube  218  and a fourth lateral tube  220 , opposite the third lateral tube  218  (e.g., the third lateral tube  218  being axially aligned with the fourth lateral tube  220 ). As also described further below, while the various tubes (or tubular structures) are illustrated in  FIG.  2 A  as having an opening into a central body  222  of the unit cell  202 , the various tubes may be connected to the tubes of adjacent unit cells (see, e.g.,  FIG.  2 B ) or may be completely or partially closed (or sealed) via a wall or a mesh, which may include a perforated or a similar structure, the wall or the mesh being configured to block or partially restrict, respectively, a flow of fluid therethrough. 
     Further, it is noted that while the unit cell  202  may comprise a structure that exhibits various degrees of symmetry (e.g., a cubic symmetry typical of a Schwarz P surface), the various tubes or central bodies among a plurality of interconnected unit cells may be sized or shaped identically or exhibit different sizes or shapes among such plurality of interconnected unit cells. For example, the first axial tube  210  may exhibit a first axial tube size (e.g., a first diameter or first length), the second axial tube  212  may exhibit a second axial tube size (e.g., a second diameter or second length), the first lateral tube  214  may exhibit a first lateral tube size (e.g., diameter or length), the second lateral tube  216  may exhibit a second lateral tube size (e.g., diameter or length), the third lateral tube  218  may exhibit a third lateral tube size (e.g., diameter or length) and the fourth lateral tube  220  may exhibit a fourth lateral tube size (e.g., diameter or length) and at least one of the first axial tube size, the second axial tube size, the first lateral tube size, the second lateral tube size, the third lateral tube size or the fourth lateral tube size exhibits a first size and at least one of the first axial tube size, the second axial tube size, the first lateral tube size, the second lateral tube size, the third lateral tube size or the fourth lateral tube size exhibits a second size that is different from the first size. 
     Note also that in various embodiments, each of the first axial tube  210 , the second axial tube  212 , the first lateral tube  214 , the second lateral tube  216 , the third lateral tube  218  and the fourth lateral tube  220  are in fluid communication with each other via the central body  222 . 
     Referring now to  FIG.  2 B , with continued reference to  FIG.  2 A , a noise attenuation panel  230  is illustrated having a plurality of unit cells  232 , each having the shape of the unit cell  202 , interconnected and sandwiched between a facesheet  234  and a back plate  236 . In various embodiments, the plurality of unit cells  232  is formed by interconnecting adjacent lateral tubes of adjacent unit cells together. For example, as illustrated in  FIG.  2 B , a first unit cell  231  having a first lateral tube  233  may be interconnected to a second unit cell  235  having a second lateral tube  237  by interconnecting the first lateral tube  233  to the second lateral tube  237 . In similar fashion, a third unit cell  241  and a fourth unit cell  243  may be interconnected to each other and to, respectively, the first unit cell  231  and to the second unit cell  235 . In such fashion, a periodic structure having a plurality of resonators configured to damp or attenuate acoustic waves or energy results. As described in further detail below, note the periodic structure of the plurality of unit cells  232 , interconnected as described, results in a volume  245  at the center of the periodic structure and extending axially between the facesheet  234  and the back plate  236 . In various embodiments, the volume  245  may be sized to damp or attenuate acoustic waves or energy at different frequencies as do the plurality of unit cells  232 . 
     Referring now to  FIGS.  3 A and  3 B , schematic views of a noise attenuation panel  300 , similar to the noise attenuation panels described above, are provided. The noise attenuation panel  300  is illustrated as having a plurality of unit cells  302  sandwiched between a facesheet  304  and a back plate  306 . The facesheet  304  typically includes a plurality of perforations or openings  308  to communicate acoustic waves or energy to the plurality of unit cells  302 , which acts as a resonator to damp or attenuate the acoustic waves or energy. The back plate  306  typically is non-perforated and, together with the facesheet  304 , provides a support structure for the plurality of unit cells  302 . Each member of the plurality of unit cells  302  has properties and characteristics similar to the unit cell  202  and to the plurality of unit cells  232  described above with reference to  FIGS.  2 A and  2 B , and so such properties and characteristics, including the manner of interconnecting the unit cells within the plurality of unit cells  302  is not repeated here. 
     One difference between the embodiments described with reference to  FIGS.  2 A and  2 B  and those described with reference to  FIGS.  3 A and  3 B  is the layered structure exhibited by the noise attenuation panel  300 . For example, while the noise attenuation panel  230  described above with reference to  FIG.  2 B  comprises a single layer of unit cells (or a first periodic structure), the noise attenuation panel  300  comprises a plurality of layers of unit cells, including, for example, a first lateral layer of unit cells  351  (or a first periodic structure), a second lateral layer of unit cells  352  (or a second periodic structure), a third lateral layer of unit cells  353  (or a third periodic structure) and a fourth lateral layer of unit cells  354  (or a fourth periodic structure). In various embodiments, each lateral layer of unit cells exhibits an N×M structure of unit cells, where N is the number of unit cells in a first direction (e.g., a first unit cell, a second unit cell . . . an Nth unit cell in the x-direction) and M is the number of unit cells in a second direction (e.g., a first unit cell, a second unit cell . . . an Mth unit cell in the y-direction). A similar arrangement applies to the layers of unit cells in the axial or the z-direction, which may be P in number, and include a first axial layer of unit cells  361  (or a first periodic structure), a second axial layer of unit cells  362  (or a second periodic structure), a third axial layer of unit cells  363  (or a third periodic structure) and a fourth axial layer of unit cells  364  (or a fourth periodic structure). Note that while each of M, N and P equals four (4) in  FIGS.  3 A and  3 B , there is no requirement that M, N and P equal one another in any particular noise attenuation panel or embodiment thereof. 
     With primary reference now to  FIG.  3 B , and with continued reference to  FIG.  3 A , the second lateral layer of unit cells  352  is illustrated from an overhead (or axial or z-direction) perspective. Given the generally periodic structure of the noise attenuation panel  300 , the second lateral layer of unit cells  352  may be considered representative of any of the lateral or axial layers of unit cells identified above. The layer of unit cells comprises an N×M plurality of unit cells  370  interconnected together (via a plurality of lateral tubes as described above) and an (N−1)×(M−1) plurality of volumes  372  disposed between the unit cells. The layer also comprises an N×M plurality of axial tubes  374  that extend into an N×M plurality of central bodies  376  of the unit cells (e.g., a first central body, a second central body . . . an N×Mth central body). As discussed further below, one or more of the individual members of the (N−1)×(M−1) plurality of volumes  372 , the N×M plurality of axial tubes  374  and the plurality of lateral tubes may be either completely or partially sealed or restricted to tune the noise attenuation panel  300  to attenuate various frequencies of the acoustic energy spectrum that the noise attenuation panel  300  is being subjected during operation. 
     Referring now to  FIGS.  4 A and  4 B , sectional schematic views of a portion of a noise attenuation panel  400 , similar to any of the noise attenuation panels described above, are provided. Referring to  FIG.  4 A , for example, a schematic view of a volume  445 , similar to the volume  245  illustrated in  FIG.  2 B  or one of the (N−1)×(M−1) plurality of volumes  372  illustrated in  FIG.  3 B , is provided. As described above, the volume  445  is defined by a plurality of unit cells  402  that are interconnected via the interconnecting of lateral or axial tubes associated with the plurality of unit cells  402 . As illustrated, the volume  445  is partially restricted via a volume filler  447 , disposed throughout the space exterior to the unit cells, that is configured to act as a bulk absorber to reduce or restrict the flow of air through the volume  445 . Note that in various embodiments, the volume filler  447  may comprise a plurality of layers of mesh-like materials, perforated structures or even acoustic foams so the resulting structure exhibits properties of a bulk material or a foam that either partially restricts or completely restricts the flow of air (or acoustic waves) within the space that is exterior to the plurality of unit cells  402 . The partial or complete restriction provided by the volume filler  447  facilitates additional tuning of the noise attenuation panel  400  to attenuate over a broader frequency range of the acoustic energy spectrum. Similarly, referring to  FIG.  4 B , a schematic view of an isolated one of the plurality of unit cells  402 , similar to one of the plurality of unit cells  232  illustrated in  FIG.  2 B  or one of the plurality of unit cells  302  illustrated in  FIG.  3 A , is provided. As described above, the isolated one of the plurality of unit cells  402  includes a tube  403 , either lateral or axial, depending on the orientation of the unit cell. As illustrated, the tube  403  is partially restricted via a tube mesh  449 , which may include properties similar to those identified for the volume filler  447 , that is configured to reduce or restrict the flow of air through the tube  403 . 
     The partial restriction provided by the tube mesh  449  facilitates tuning the noise attenuation panel  400  to attenuate specific frequencies of the acoustic energy spectrum the noise attenuation panel  400  is being subjected to during operation. 
     Referring now to  FIGS.  5 A and  5 B , a model  501  that facilitates mathematical design of a noise attenuation panel  500  is described. As illustrated, the model  501  approximates the behavior or response of the noise attenuation panel  500  via a dynamical system that includes (i) a mass (e.g., M 1  and M 2 ) that represents the mass of air associated with an acoustic wave  503  that oscillates within a tube of a unit cell; (ii) a stiffness (e.g., K 1  and K 2 ) that represents the density of the air within the central body of the unit cell; and (iii) a dashpot (e.g., R 1  and R 2 ) that represents the energy dissipation associated with the air moving in the tubes. The dynamical system facilitates development of a set of differential equations that may be solved to approximate the behavior or response of the noise attenuation panel  500 . The dynamical system may also account for complete or partial restriction of the various axial or lateral tubes associated with the unit cell. While the model  501  illustrated in  FIG.  5 B  is representative of a simple two unit-cell system as illustrated in  FIG.  5 A , such models may be extended to arbitrarily large numbers of unit cells. 
     Referring now to  FIGS.  6 A,  6 B,  6 C and  6 D , computational results are provided that illustrate various benefits of the noise attenuation panels presented and described in this disclosure. Referring to  FIGS.  6 A and  6 B , a graph  681  showing absorption coefficient as a function of frequency is illustrated for a conventional single degree of freedom noise attenuation panel  680  (SDOF) having a facesheet  602  and a back plate  604  defining a height (h) of the panel, filled with a honeycomb structure  605 . By way of comparison,  FIGS.  6 C and  6 D  illustrate a graph  683  showing absorption coefficient as a function of frequency for a noise attenuation panel  682  (NAP) having the same facesheet and a back plate as employed in the conventional single-degree of freedom noise attenuation panel  680 . 
     As indicated in the graph  683 , the noise attenuation panel  682  provides a greater magnitude of noise attenuation at the design frequency and an extended attenuation bandwidth with more broadband absorption at higher frequencies, than the conventional single-degree of freedom noise attenuation panel  680  having a height (h) less than 50% of the height (h) of the conventional panel, thus providing a substantial space and potential weight savings and an increase in attenuation of noise over the conventional panel. 
     Referring now to  FIGS.  7 A and  7 B , schematic views of a noise attenuation panel of the present disclosure and a performance graph illustrating improvements over more conventional single-degree of freedom cell-based structures are provided, in accordance with various embodiments. Referring to  FIG.  7 A , a noise attenuation panel  782 , similar to the noise attenuation panel  682  described above, is depicted. Rather than having a height (h) equal to 0.45h of the height (h) of the conventional single-degree of freedom noise attenuation panel  680 , also described above, the noise attenuation panel  782  has a height (h) equal to the height (h) of the conventional single-degree of freedom noise attenuation panel  680 . This enables a more direct comparison between the noise attenuation panel  782  and the conventional single-degree of freedom noise attenuation panel  680  when constructed to have the same dimension (e.g., the same height (h)). As illustrated in  FIG.  7 B , for example, a graph  783  showing absorption coefficient as a function of frequency for the noise attenuation panel  782  (NAP) and the conventional single-degree of freedom noise attenuation panel  680  (SDOF) is provided. As indicated in the graph  783 , the noise attenuation panel  782  provides a greater magnitude of noise attenuation at the design frequency and at both higher and lower frequencies surrounding the design frequency than the conventional single-degree of freedom noise attenuation panel  680 , thus providing an extended attenuation bandwidth with more broadband absorption at both higher and lower frequencies than the design frequency where the two noise attenuation panels share the same dimensional characteristics. 
     Referring now to  FIGS.  8 A,  8 B and  8 C , schematic views of various embodiments of the noise attenuation panels of the present disclosure, and a graph illustrating relative performance, are provided. Referring to  FIGS.  8 A and  8 B , a first noise attenuation panel  881  and a second noise attenuation panel  882  are illustrated. Similar to the various embodiments described above, both the first noise attenuation panel  881  and the second noise attenuation panel  882  include a plurality of unit cells  802  and a plurality of volumes  872  defined by the spaces in between the individual unit cells comprising the plurality of unit cells  802 . The only difference between the first noise attenuation panel  881  and the second noise attenuation panel  882  is each of the plurality of volumes  872  in the second noise attenuation panel  882  is partially restricted or completely restricted via a volume filler  847 , similar to the volume filler  447  described above. Note that where complete restriction is provided, the volume filler  847  may be completely solid—e.g., the space exterior to the plurality of unit cells  802  is completely filled with material. Referring now to  FIG.  8 C , a graph  883  showing absorption coefficient as a function of frequency for the first noise attenuation panel  881  and the second noise attenuation panel  882  is provided. As depicted in the graph  883 , the second noise attenuation panel  882  exhibits an extended attenuation bandwidth with greater broadband absorption throughout the range of frequencies, which illustrates the enhanced noise absorption characteristics provided by the volume filler  847  used to partially restrict the flow of air through each of the plurality of volumes  872 . 
     Referring now to  FIGS.  9 A,  9 B and  9 C , schematic illustrations of a noise attenuation panel  900  are provided, in accordance with various embodiments. Similar to the various embodiments described above, the noise attenuation panel  900  includes a plurality of unit cells  902  sandwiched between a facesheet  904  and a back plate  906 . The facesheet  904  typically includes a plurality of perforations or openings  908  to communicate acoustic waves or energy to the plurality of unit cells  902 . Each member of the plurality of unit cells  902  has properties and characteristics similar to the unit cell  202  and to the plurality of unit cells  232  described above with reference to  FIGS.  2 A and  2 B , and so such properties and characteristics, including the manner of interconnecting the unit cells within the plurality of unit cells  902  is not repeated here. In various embodiments, the noise attenuation panel  900  includes a gap  909  adjacent the back plate  906  at each of the unit cells positioned adjacent the back plate  906 , where the gap  909  provides an opening or spacing away from the back plate  906 , thereby allowing fluid communication between the interior of the unit cells positioned adjacent the back plate  906  and the exterior of the unit cells comprising the plurality of unit cells  902 . 
     Referring more particularly now to  FIGS.  9 B and  9 C , and with continued reference to  FIG.  9 A , a panel section  920  of the noise attenuation panel  900  is illustrated as comprising a single row of unit cells sandwiched between the facesheet  904  and the back plate  906 . As illustrated, during operation, acoustic waves or energy impinge upon the facesheet  904  and enter the first unit cell of the panel section  920  via a perforation  903  (or via a plurality of such perforations). The acoustic waves or energy then traverse the plurality of unit cells  902  where acoustic attenuation occurs as described above. In various embodiments, the acoustic waves or energy then exit the interiors of the plurality of unit cells at the gap  909  adjacent the back plate  906 . Once exited, the acoustic waves or energy then traverse back to the facesheet  904  via a plurality of volumes  972  defined by the spaces in between the individual unit cells comprising the plurality of unit cells  902 . The acoustic waves or energy then may exit the facesheet  904  via the plurality of perforations or openings  908 . Note that in various embodiments, one or more or even all of the plurality of perforations or openings  908  may be closed to alter the frequency range of attenuation. In the case where all of the plurality of perforations or openings  908  is completely closed or sealed, it is possible to shift the peak absorption frequency to a lower frequency range than would otherwise occur. In such case, the volume of space exterior to the plurality of unit cells  902 —i.e., the plurality of volumes  972 —acts as a closed volume or resonator. 
     Referring now to  FIGS.  10 A,  10 B and  10 C , schematic illustrations of a noise attenuation panel  1000  are provided, in accordance with various embodiments. Similar to the various embodiments described above, the noise attenuation panel  1000  includes a plurality of unit cells  1002  sandwiched between a facesheet  1004  and a back plate  1006 . The facesheet  1004  typically includes a plurality of perforations or openings configured to communicate acoustic waves or energy to the plurality of unit cells  1002 . Each member of the plurality of unit cells  1002  has properties and characteristics similar to the unit cell  202  and to the plurality of unit cells  232  described above with reference to  FIGS.  2 A and  2 B , and so such properties and characteristics, including the manner of interconnecting the unit cells within the plurality of unit cells  1002  is not repeated here. In various embodiments, various members of the plurality of unit cells  1002  exhibit different sizes and, particular to the illustrated embodiment, different sized tubes used to interconnect the unit cells comprising the plurality of unit cells  1002  (e.g., the axial tubes and the lateral tubes described above with reference to the various figures). For example, as illustrated with reference to a panel section  1020 , a plurality of lateral tubes includes a first lateral tube  10741 , a second lateral tube  10742 , a third lateral tube  10743  and a fourth lateral tube  10744 , with each of the lateral tubes disposed between and surrounded by various members of a plurality of volumes  1072 . Each of the first lateral tube  10741 , the second lateral tube  10742 , the third lateral tube  10743  and the fourth lateral tube  10744  exhibit a tube size (e.g., a diameter) that decreases from a first tube size associated with the first lateral tube  10741  to a fourth tube size associated with the fourth lateral tube  10744 . While the various lateral tubes are illustrated as having tube sizes that decrease in diameter proceeding from the facesheet  1004  to the back plate  1006 , the disclosure contemplates alternative embodiments, such as, for example, tube sizes that increase in diameter proceeding from the facesheet  1004  to the back plate  1006  or tube sizes that both decrease and increase in diameter proceeding from the facesheet  1004  to the back plate  1006 . 
     Referring now to  FIGS.  11 A,  11 B and  11 C , schematic illustrations of a noise attenuation panel  1100  are provided, in accordance with various embodiments. Similar to the various embodiments described above, the noise attenuation panel  1100  includes a plurality of unit cells  1102  sandwiched between a facesheet  1104  and a back plate  1106 . The facesheet  1104  typically includes a plurality of perforations or openings configured to communicate acoustic waves or energy to the plurality of unit cells  1102 . Each member of the plurality of unit cells  1102  has properties and characteristics similar to the unit cell  202  and to the plurality of unit cells  232  described above with reference to  FIGS.  2 A and  2 B , and so such properties and characteristics, including the manner of interconnecting the unit cells within the plurality of unit cells  1102  is not repeated here. In various embodiments, various of the plurality of unit cells  1102  exhibit different sizes and, particular to the illustrated embodiment, different sized tubes used to interconnect the unit cells comprising the plurality of unit cells  1102  (e.g., the axial tubes and the lateral tubes described above with reference to the various figures). For example, as illustrated with reference to a panel section  1120 , a plurality of axial tubes includes a first axial tube  11801 , a second axial tube  11802 , a third axial tube  10803 , and a fourth axial tube  11804 , with each of the axial tubes disposed between and surrounded by various members of a plurality of volumes  1172 . Each of the first axial tube  11801 , the second axial tube  11802 , the third axial tube  10803  and the fourth axial tube  11804  exhibit a tube size (e.g., a diameter) that decreases from a first tube size associated with the first axial tube  11801  to a fourth tube size associated with the fourth axial tube  11804 . The panel section terminates at a fifth axial tube  11805 , which may be positioned adjacent the back plate  1106 . While the various tubes are illustrated as having tube sizes that decrease in diameter from the facesheet  1104  to the back plate  1106 , the disclosure contemplates alternative embodiments, such as, for example, tube sizes that increase in diameter from the facesheet  1104  to the back plate  1106  or tube sizes that both decrease and increase in diameter from the facesheet  1104  to the back plate  1106 . Further, while the illustrations show an outer diameter or exterior of each axial tube being sized the same, with the internal diameter having different sizes (e.g., progressively decreasing internal diameters from the first tube size to the fourth tube size), the disclosure contemplates size variations of the exteriors of the axial tubes to vary in the same or a similar manner as the above-described lateral tubes. 
     Referring now to  FIGS.  12 A and  12 B , schematic illustrations of a noise attenuation panel  1200  are provided, in accordance with various embodiments. Similar to the various embodiments described above, the noise attenuation panel  1200  includes a plurality of unit cells  1202  sandwiched between a facesheet  1204  and a back plate  1206 . The facesheet  1204  typically includes a plurality of perforations or openings configured to communicate acoustic waves or energy to the plurality of unit cells  1202 . Each member of the plurality of unit cells  1202  has properties and characteristics similar to the unit cell  202  and to the plurality of unit cells  232  described above with reference to  FIGS.  2 A and  2 B , and so such properties and characteristics, including the manner of interconnecting the unit cells within the plurality of unit cells  1202  is not repeated here. In various embodiments, the plurality of perforations or openings in the facesheet  1204  exhibit different sizes. For example, as illustrated with reference to  FIGS.  12 A and  12 B , the facesheet  1204  includes a first perforation  12081 , a second perforation  12082 , a third perforation  12083 , a fourth perforation  12084  and a fifth perforation  12085 . Each of the first perforation  12081 , the second perforation  12082 , the third perforation  12083 , the fourth perforation  12084  and the fifth perforation  12085  exhibit a perforation size (e.g., a diameter) that decreases from a first perforation size associated with the first perforation  12081  to a fifth perforation size associated with the fifth perforation  12085 . While the various perforations are illustrated as having perforation sizes that decrease in diameter proceeding from a left side (or an upstream side) of the facesheet  1204  to a right side (or a downstream side) of the facesheet  1204 , the disclosure contemplates alternative embodiments, such as, for example, perforation sizes that increase in diameter proceeding from the left side of the facesheet  1204  to the right side of the facesheet  1204 , or perforation sizes that both decrease and increase in diameter proceeding from the left side of the facesheet  1204  to the right side of the facesheet  1204 . 
     Referring now to  FIG.  13   , a schematic illustration of a noise attenuation panel  1300  is provided, in accordance with various embodiments. Similar to the various embodiments described above, the noise attenuation panel  1300  includes a plurality of unit cells  1302  sandwiched between a facesheet  1304  and a back plate  1306 . The facesheet  1304  typically includes a plurality of perforations or openings configured to communicate acoustic waves or energy to the plurality of unit cells  1302 . Each member of the plurality of unit cells  1302  has properties and characteristics similar to the unit cell  202  and to the plurality of unit cells  232  described above with reference to  FIGS.  2 A and  2 B , and so such properties and characteristics, including the manner of interconnecting the unit cells within the plurality of unit cells  1302  is not repeated here. In various embodiments, various of the plurality of unit cells  1302  exhibit different sizes and, particular to the illustrated embodiment, different sized tubes used to interconnect the unit cells comprising the plurality of unit cells  1302  (e.g., the axial tubes and the lateral tubes described above with reference to the various figures) and different sized volumes that surround the exterior surfaces of the unit cells comprising the plurality of unit cells  1302 . 
     For example, a plurality of lateral tubes includes a first lateral tube  1374   1 , a second lateral tube  1374   2 , a third lateral tube  1374   3  and a fourth lateral tube  1374   4 . Each of the first lateral tube  1374   1 , the second lateral tube  1374   2 , the third lateral tube  1374   3  and the fourth lateral tube  1374   4  exhibit a tube size (e.g., a diameter) that decreases from a first tube size associated with the first lateral tube  1374   1  to a fourth tube size associated with the fourth lateral tube  1374   4 . While the various lateral tubes are illustrated as having tube sizes that decrease in diameter proceeding from a left side (or an upstream side) of the noise attenuation panel  1300  to a right side (or a downstream side) of the noise attenuation panel  1300 , the disclosure contemplates alternative embodiments, such as, for example, tube sizes that increase in diameter proceeding from the left side of the noise attenuation panel  1300  to the right side of the noise attenuation panel  1300 , or tube sizes that both decrease and increase in diameter proceeding from the left side of the noise attenuation panel  1300  to the right side of the noise attenuation panel  1300 . 
     Still referring to  FIG.  13   , the volumes that surround the exterior surfaces of the unit cells exhibit different sizes. For example, a plurality of volumes includes a first volume  1372   1 , a second volume  1372   2 , a third volume  1372   3 , a fourth volume  1372   4  and a fifth volume  1372   5 . Each of the first volume  1372   1 , the second volume  1372   2 , the third volume  1372   3 , the fourth volume  1372   4  and the fifth volume  1372   5  exhibit a volume size (e.g., a characteristic dimension) that increases from a first volume size associated with the first volume  1372   1 , to a second volume size associated with the second volume  1372   2  . . . to a fifth volume size associated with the fifth volume  1372   5 . While the various volumes are illustrated as having volume sizes that increase in characteristic dimension proceeding from a left side (or an upstream side) of the noise attenuation panel  1300  to a right side (or a downstream side) of the noise attenuation panel  1300 , the disclosure contemplates alternative embodiments, such as, for example, volume sizes that decrease in characteristic dimension proceeding from the left side of the noise attenuation panel  1300  to the right side of the noise attenuation panel  1300 , or volume sizes that both decrease and increase in characteristic dimension proceeding from the left side of the noise attenuation panel  1300  to the right side of the noise attenuation panel  1300 . Note that where the volumes comprising the plurality of volumes are of varying or different sizes, in general, the unit cells comprising the plurality of unit cells that define the various volumes will also be of different sizes (e.g., where one or more of a first unit cell size, a second unit cell size, a third unit cell size or a fourth unit cell size exhibits a different characteristic dimension or dimensions from that of its neighboring unit cells). 
     Referring now to  FIG.  14   , a schematic illustration of a noise attenuation panel  1400  is provided, in accordance with various embodiments. Similar to the various embodiments described above, the noise attenuation panel  1400  includes a plurality of unit cells  1402  sandwiched between a facesheet  1404  and a back plate  1406 . The facesheet  1404  typically includes a plurality of perforations or openings configured to communicate acoustic waves or energy to the plurality of unit cells  1402 . Each member of the plurality of unit cells  1402  has properties and characteristics similar to the unit cell  202  and to the plurality of unit cells  232  described above with reference to  FIGS.  2 A and  2 B , and so such properties and characteristics, including the manner of interconnecting the unit cells within the plurality of unit cells  1402  is not repeated here. In various embodiments, various of the plurality of unit cells  1402  exhibit different sizes and, particular to the illustrated embodiment, different sized tubes used to interconnect the unit cells comprising the plurality of unit cells  1402  (e.g., the axial tubes and the lateral tubes described above with reference to the various figures) and different sized volumes that surround the exterior surfaces of the unit cells comprising the plurality of unit cells  1302 . 
     For example, a plurality of lateral tubes includes a first lateral tube  1474   1 , a second lateral tube  1474   2 , a third lateral tube  1474   3  and a fourth lateral tube  1474   4 . Each of the first lateral tube  1474   1 , the second lateral tube  1474   2 , the third lateral tube  1474   3  and the fourth lateral tube  1474   4  exhibit a tube size (e.g., a diameter) that decreases from a first tube size associated with the first lateral tube  1474   1  to a fourth tube size associated with the fourth lateral tube  1474   4 . While the various lateral tubes are illustrated as having tube sizes that decrease in diameter proceeding from the facesheet  1404  to the back plate  1406 , the disclosure contemplates alternative embodiments, such as, for example, tube sizes that increase in diameter proceeding from the facesheet  1404  to the back plate  1406  or tube sizes that both decrease and increase in diameter proceeding from the facesheet  1404  to the back plate  1406 . 
     Still referring to  FIG.  14   , the volumes that surround the exterior surfaces of the unit cells exhibit different sizes. For example, a plurality of volumes includes a first volume  1472   1 , a second volume  1472   2 , a third volume  1472   3 , a fourth volume  1472   4  and a fifth volume  1472   5 . Each of the first volume  1472   1 , the second volume  1472   2 , the third volume  1472   3 , the fourth volume  1472   4  and the fifth volume  1472   5  exhibit a volume size (e.g., a characteristic dimension) that increases from a first volume size associated with the first volume  1472   1  to a fifth volume size associated with the fifth volume  1472   5 . While the various volumes are illustrated as having volume sizes that increase in characteristic dimension proceeding from the facesheet  1404  to the back plate  1406 , the disclosure contemplates alternative embodiments, such as, for example, volume sizes that decrease in characteristic dimension proceeding from the facesheet  1404  to the back plate  1406  or volume sizes that both decrease and increase in characteristic dimension proceeding from the facesheet  1404  to the back plate  1406 . 
     Referring now to  FIGS.  15 A,  15 B,  15 C,  15 D and  15 E , schematic views of various noise attenuation panels (or acoustic attenuation structures) are provided; the noise attenuation panels described and illustrated in these figures are oversimplified to explain various features of the panels, but the disclosure contemplates that any or all of the various acoustic attenuation structures illustrated in  FIGS.  15 A- 15 E  may be incorporated into the noise attenuation panels described above and below. Referring, for example, to  FIG.  15 A , a noise attenuation panel  1500  is illustrated having a first unit cell  1501  and a second unit cell  1503  sandwiched between a facesheet  1504  and a back plate  1506 . The facesheet  1504  typically includes a plurality of perforations or openings to communicate acoustic waves or energy to the first unit cell  1501  and then to the second unit cell  1503 , which together act as a resonator to damp or attenuate the acoustic waves or energy. The back plate  1506  typically is non-perforated and, together with the facesheet  1504 , provides a support structure for the noise attenuation panel  1500 . In various embodiments, a septum  1505  separates the first unit cell  1501  and the second unit cell  1503 , with the septum  1505  including a plurality of perforations or openings to communicate acoustic waves or energy between the first unit cell  1501  and the second unit cell  1503 . In various embodiments, a connector  1507  (e.g., a tubular member) is used to connect the first unit cell  1501  and the second unit cell  1503 , with the septum  1505  being disposed between the connector  1507  and the second unit cell  1503 . Note, as illustrated, the first unit cell  1501  and the second unit cell  1503  may exhibit different shapes or sizes to further assist in tuning the noise attenuation panel  1500 . 
     Referring now to  FIG.  15 B , a noise attenuation panel  1510  is illustrated having a first unit cell  1511  and a second unit cell  1513  sandwiched between a facesheet  1514  and a back plate  1516 . The facesheet  1514  typically includes a plurality of perforations or openings to communicate acoustic waves or energy to the first unit cell  1511  and then to the second unit cell  1513 , which together act as a resonator to damp or attenuate the acoustic waves or energy. The back plate  1516  typically is non-perforated and, together with the facesheet  1514 , provides a support structure for the noise attenuation panel  1510 . In various embodiments, a septum  1515  separates the first unit cell  1511  and the second unit cell  1513 , with the septum  1515  including a plurality of perforations or openings to communicate acoustic waves or energy between the first unit cell  1511  and the second unit cell  1513 . In various embodiments, a connector  1517  (e.g., a tubular member) is used to connect the first unit cell  1511  and the second unit cell  1513 , with the septum  1515  being disposed between the connector  1517  and the first unit cell  1511 . 
     Referring now to  FIG.  15 C , a noise attenuation panel  1520  is illustrated having a unit cell  1522 , a facesheet  1524 , a back plate  1526  and a septum  1525 . The facesheet  1524  typically includes a plurality of perforations or openings to communicate acoustic waves or energy to an open chamber  1529  and then to the unit cell  1522 , which together act as a resonator to damp or attenuate the acoustic waves or energy. The back plate  1526  typically is non-perforated and, together with the facesheet  1524 , provides a support structure for the noise attenuation panel  1520 . In various embodiments, the septum  1525  separates the unit cell  1522  and the open chamber  1529 , with the septum  1525  including a plurality of perforations or openings to communicate acoustic waves or energy between the unit cell  1522  and the open chamber  1529 . In various embodiments, a connector  1527  (e.g., a tubular member) is used to connect the unit cell  1522  and the open chamber  1529 , with the septum  1525  being disposed between the connector  1527  and the open chamber  1529 . 
     Referring now to  FIG.  15 D , a noise attenuation panel  1530  is illustrated having a unit cell  1532 , a facesheet  1534 , a back plate  1536  and a septum  1535 . The facesheet  1534  typically includes a plurality of perforations or openings to communicate acoustic waves or energy to an open chamber  1539  and then to the unit cell  1532 , which together act as a resonator to damp or attenuate the acoustic waves or energy. The back plate  1536  typically is non-perforated and, together with the facesheet  1534 , provides a support structure for the noise attenuation panel  1530 . In various embodiments, the septum  1535  separates the unit cell  1532  and the open chamber  1539 , with the septum  1535  including a plurality of perforations or openings to communicate acoustic waves or energy between the unit cell  1532  and the open chamber  1539 . In various embodiments, a connector  1537  (e.g., a tubular member) is used to connect the unit cell  1532  and the open chamber  1539 , with the septum  1535  being disposed between the connector  1537  and the open chamber  1539 . Note, in contrast with the noise attenuation panel  1520 , the unit cell  1532  may not, in various embodiments, have a tube (e.g., a lateral tube  1538 ) in contact with the back plate  1536 . 
     Referring now to  FIG.  15 E , a noise attenuation panel  1540  is illustrated having a first unit cell  1541 , a second unit cell  1543 , a facesheet  1544 , a back plate  1546  and a septum  1545 . The facesheet  1544  typically includes a plurality of perforations or openings to communicate acoustic waves or energy to an open chamber  1549  and then to the first unit cell  1541  and to the second unit cell  1543 , which together act as a resonator to damp or attenuate the acoustic waves or energy. The back plate  1546  typically is non-perforated and, together with the facesheet  1544 , provides a support structure for the noise attenuation panel  1540 . In various embodiments, the septum  1545  separates the first unit cell  1541  and the open chamber  1549 , with the septum  1545  including a plurality of perforations or openings to communicate acoustic waves or energy between the first unit cell  1541  and the open chamber  1549 . 
     Note, in contrast with, for example, the noise attenuation panel  1510 , the noise attenuation panel  1520 , the noise attenuation panel  1530 , and the noise attenuation panel  1540 , the first unit cell  1541  and the second unit cell  1543  are smaller in comparison to the sizes of the unit cells comprising the previous attenuation panels, thereby allowing for attenuation of noise at relatively higher frequencies. 
     Referring briefly now to  FIGS.  16 A,  16 B,  16 C and  16 D , schematic views of various structures used for the facesheets and septa and other perforated structures described throughout the disclosure are provided. Referring to  FIG.  16 A , for example, a perforated structure  1600  (e.g., a facesheet or a septum) includes a slot  1602  (or a plurality of slots) that is aligned in a generally axial direction with respect to a longitudinal axis A. In various embodiments, the slot  1602  exhibits an aspect ratio that may vary from a generally square-shaped configuration (e.g., 1:1 aspect ratio) to an elongated rectangular-shaped configuration (e.g., 10:1 aspect ratio). Referring to  FIG.  16 B , a perforated structure  1610  includes a slot  1612  (or a plurality of slots) that is aligned in a generally non-axial direction (or angled direction) with respect to a longitudinal axis A. In various embodiments, the slot  1612  exhibits an aspect ratio that may vary from a generally square-shaped configuration (e.g., 1:1 aspect ratio) to an elongated rectangular-shaped configuration (e.g., 10:1 aspect ratio). Further, the disclosure contemplates the non-axial direction may exhibit an angle  1614  with respect to the axial direction from plus ninety degrees (+90°) to minus ninety degrees (−90°). Referring to  FIG.  16 C , a perforated structure  1620  includes a plurality of perforations  1622  (e.g., circular holes) spaced about the surface of the perforated structure  1620 . The plurality of perforations  1622  may exhibit a regular spacing (as illustrated) or a non-regular orientation. Referring to  FIG.  16 D , a perforated structure  1630  includes a mesh structure  1632 . In various embodiments, the mesh structure  1632  may be formed by weaving various materials to have warp and weft interaction (e.g., longitudinal warp materials interwoven with transverse weft materials). Without loss of generality, each of the perforated structures just described may exhibit various percent openings with respect to the non-open portions of the perforated structures. For example, in various embodiments, the percent openings may range from about two percent (2%) to about ninety percent (90%) or any range of values therebetween. 
     The foregoing disclosure provides an acoustic metamaterial (e.g., a material engineered to have a property or properties not found in naturally occurring materials) consisting of a periodic lattice structure made of a unit cell bulb-like structure that divides a space into two or more separated but intertwined fluid networks (e.g., the volumes and the tubes described above). The fluid networks are locally coupled at the junctions of the lattice structure to create arrays of resonator networks. The resonator networks may be varied in length, width or height to satisfy particular target frequencies for maximum sound absorption or attenuation. Distributed networks of various dimensions may be constructed for broadband absorption. Hybrid concepts include various forms of restrictions or space fillers for tuning the resulting noise attenuation panel. These space-fillers can act as bulk absorbers to extend the bandwidth and frequency range of acoustic attenuation or they can be partially or completely solid (or filled) for improved structural performance. Further, the unit cells may be constructed of different forms, sizes or shapes or may have similar, repeating shapes of the same size, such as, for example, including the Schwarz P periodic minimal surface. Advantageously, the various resonator networks, including networks exhibiting repeating and identically shaped unit cells, or networks exhibiting non-repeating and non-identically shaped unit cells, or networks comprising various restrictions (complete or partial) distributed throughout various tubes or volumes described above, may be fabricated using additive manufacturing techniques and dynamically modeled via acoustic performance analysis prior to manufacture. Other benefits of the disclosure include noise attenuation panels exhibiting greater damping or attenuation per unit volume as compared to conventional honeycomb liners. This benefit translates into potential weight reduction or fuel savings over existing technology. The noise attenuation panels described herein also provides an ability to replace conventional structural honeycomb liners with liners having better attenuation and structural properties. Additional embodiments of noise attenuation panels that include many of the features described above are described below, followed by applications in various combustors for gas turbine engines. 
     Referring now to  FIGS.  17 A,  17 B,  17 C and  17 D , schematic illustrations of various components of a noise attenuation panel  1700  are provided. The noise attenuation panel  1700  ( FIG.  17 D ) is illustrated as having a first plurality of unit cells  1702  ( FIG.  17 B ) and a second plurality of unit cells  1703  ( FIG.  17 A ) merged within the first plurality of unit cells  1702 . More specifically, the first plurality of unit cells  1702  takes the form, for example, of the first plurality of unit cells  302  described above with reference to  FIG.  3 A  and includes a plurality of volumes  1772  disposed between the unit cells, similar to the plurality of volumes  372  described above with reference to  FIG.  3 B . The second plurality of unit cells  1703  is merged within the first plurality of unit cells  1702  by disposing a unit cell (from the second plurality of unit cells  1703 ) within a volume (from the plurality of volumes  1772 ), such that each of the plurality of volumes  1772  has a unit cell disposed within its interior space. In addition, the size of the exterior surface of each unit cell disposed within the second plurality of unit cells  1703  is sized smaller than the corresponding volume within which the unit cell resides or is disposed. The relative sizing provides a space between the exterior surfaces of the first plurality of unit cells  1702  and second plurality of unit cells  1703 . The spacing provides a flow path  1705  ( FIG.  3 C ) or a cooling fluid flow path for a cooling fluid to flow between the exterior surfaces of the first plurality of unit cells  1702  and the second plurality of unit cells  1703 . To be clear, each of the first plurality of unit cells  1702  and the second plurality of unit cells  1703  is a solid lattice structure while the flow path  1705  is a fluid lattice structure (e.g., an open spacing or volume between the first plurality of unit cells  1702  and the second plurality of unit cells  1703 ). In various embodiments, the open spacing or volume is attributable to the additive manufacturing process used to construct the noise attenuation panel  1700 , whereby the first plurality of unit cells  1702  and the second plurality of unit cells  1703  are constructed simultaneously with the flow path  1705  resulting thereby. 
     During operation, acoustic waves or energy  1710  impinge upon the noise attenuation panel  1700  (e.g., upon a facesheet  1704  of the noise attenuation panel  1700 ). The acoustic waves or energy enter a first plurality of axial tubes  1712  of the first plurality of unit cells  1702  and traverse the interiors of the various unit cells as indicated by a first noise attenuation flow path  1714 . Similarly, the acoustic waves or energy  1710  enter a second plurality of axial tubes  1716  of the second plurality of unit cells  1703  and traverse the interiors of the various unit cells as indicated by a second noise attenuation flow path  1718 . At the same time, a cooling fluid traverses the flow path  1705  between the first plurality of unit cells  1702  and the second plurality of unit cells  1703  as indicated by a cooling fluid flow path  1720 . Further operational details are provided in the drawings that follow to clarify operation of the noise attenuation panel  1700 . Note that while the disclosure describes the cooling fluid traversing the flow path  1705 , the disclosure contemplates other manners of cooling the noise attenuation panel  1700 . For example, in various embodiments, the cooling fluid may be introduced directly through the interior of a single one of the first plurality of unit cells  1702  and the second plurality of unit cells  1703 , while the other of the first plurality of unit cells  1702  and the second plurality of unit cells  1703  is used for noise attenuation. 
     Referring now to  FIGS.  18 A,  18 B,  18 C,  18 D,  18 E,  18 F and  18 G , a noise attenuation panel  1800 , similar to the noise attenuation panel  1700 , is illustrated. The noise attenuation panel  1800  includes a first plurality of unit cells  1802  and a second plurality of unit cells  1803  merged within the first plurality of unit cells  1802  with a flow path  1805  existing between the exterior surfaces of the first plurality of unit cells  1802  and the second plurality of unit cells  1803 . During operation (referring to  FIGS.  18 A and  18 B ), acoustic waves or energy  1810  impinge upon the noise attenuation panel  1800  (e.g., upon a facesheet  1804  of the noise attenuation panel  1800 ). The acoustic waves or energy enter a first plurality of axial tubes  1812  of the first plurality of unit cells  1802  and traverse the interiors of the various unit cells as indicated by a first noise attenuation flow path  1818  Similarly (referring to  FIGS.  18 C and  18 D ), the acoustic waves or energy  1810  enter a second plurality of axial tubes  1816  of the second plurality of unit cells  1803  and traverse the interiors of the various unit cells as indicated by a second noise attenuation flow path  1818 . At the same time (referring to  FIGS.  18 E,  18 F and  18 G ), a cooling fluid traverses the flow path  1805  between the first plurality of unit cells  1802  and the second plurality of unit cells  1803  as indicated by a cooling fluid flow path  1820 , which, in various embodiments, completely fills the volume of space exiting between the exterior surfaces of the first plurality of unit cells  1802  and the second plurality of unit cells  1803 . Benefits of the dual noise attenuation flow paths and cooling fluid flow path, based on the differing sizes of the unit cells comprising the first plurality of unit cells  1802  and the second plurality of unit cells  1803 , include being able to cool the two pluralities of unit cells and the ability to attenuate different frequency ranges within the acoustic waves or energy  1810 , with the larger of the unit cells (e.g., the first plurality of unit cells  1802 ) attenuating lower frequencies than the smaller of the unit cells (e.g., the second plurality of unit cells  1803 ). 
     Referring now to  FIGS.  19 A,  19 B,  19 C and  19 D , cross-sectional and axial views of a combustor  1900 , similar to the combustor section  112  described above with reference to  FIG.  1    are provided. Referring more specifically to  FIGS.  19 A and  19 B , in various embodiments, the combustor  1900  may generally include an outer liner assembly  1902 , an inner liner assembly  1904  and a diffuser case module  1906  that surrounds the outer liner assembly  1902  and the inner liner assembly  1904 . A combustion chamber  1908 , positioned within the combustor  1900 , has a generally annular configuration, defined by and comprising the outer liner assembly  1902 , the inner liner assembly  1904  and a bulkhead liner assembly  1910 . The outer liner assembly  1902  and the inner liner assembly  1904  are generally cylindrical and radially spaced apart, with the bulkhead liner assembly  1910  positioned generally at a forward end of the combustion chamber  1908 . The outer liner assembly  1902  is spaced radially inward from an outer diffuser case  1912  of the diffuser case module  1906  to define an outer annular plenum  1914 . The inner liner assembly  1904  is spaced radially outward from an inner diffuser case  1916  of the diffuser case module  1906  to define, in-part, an inner annular plenum  1918 . Although a particular combustor is illustrated, it should be understood that this disclosure is also applicable to other combustor types having various combustor liner arrangements, various of which are described below. During operation, compressed air from a core flow path C enters the forward section of the combustion chamber  1908  and is mixed with fuel while the remainder of the compressed air enters the outer annular plenum  1914  and the inner annular plenum  1918 . 
     Still referring to  FIGS.  19 A and  19 B , the combustor includes one or more pairs of noise attenuation panels, including for example, a forward outer cooling flow noise attenuation panel  1920  and a forward inner cooling flow noise attenuation panel  1922 , an aft outer cooling flow noise attenuation panel  1924  and an aft inner cooling flow noise attenuation panel  1926 , and an outer diffuser case noise attenuation panel  1928  and an inner diffuser case noise attenuation panel  1930 . As illustrated in  FIG.  19 B , the pairs of noise attenuation panels, in various embodiments, are spaced about the combustor  1900  in the circumferential direction (e.g., at 120° intervals, as illustrated in  FIG.  19 B , or at other suitable intervals), but the disclosure contemplates other configurations, including embodiments where one or more noise attenuation panels are configured to extend up to the entire 360° about the combustor. In addition, while not expressly illustrated in the figures, the disclosure contemplates perforations placed in or through the various liner assemblies and diffuser cases such that the acoustic waves or energy generated in the combustion chamber  1908  (e.g., combustor tones  1931 ,  1932  and  1933 ) is able to interact with the noise attenuation panels. Note that while pairs of noise attenuation panels are described and illustrated, the disclosure contemplates the use of single noise attenuation panels as well, positioned in the various locations just described. Further, while any of the noise attenuation panels previously described may be employed in the combustor  1900  to attenuate acoustic waves or energy generated in the combustion chamber  1908  (e.g., combustor tones  1931 ,  1932  and  1933 ), beneficially, the forward outer cooling flow noise attenuation panel  1920  and the forward inner cooling flow noise attenuation panel  1922  and the aft outer cooling flow noise attenuation panel  1924  and the aft inner cooling flow noise attenuation panel  1926  may be cooled by the compressed air from the core flow path C by employing the structures described above with reference to  FIGS.  17 A- 17 D  and  FIGS.  18 A- 18 G . The outer diffuser case noise attenuation panel  1928  and the inner diffuser case noise attenuation panel  1930  are considered far enough away from the combustion chamber  1908  such that no cooling is required, but cooling may be incorporated nonetheless—e.g., via compressed air supplied by a low-pressure or high-pressure compressor. In addition, one potential advantage of using one or more of the aft outer cooling flow noise attenuation panel  1924 , the aft inner cooling flow noise attenuation panel  1926 , the outer diffuser case noise attenuation panel  1928  or the inner diffuser case noise attenuation panel  1930  is these panels exhibit reduced or eliminated pressure drop through the outer annular plenum  1914  and the inner annular plenum  1918  when compared with the pressure drop introduced by use of one or both of the forward outer cooling flow noise attenuation panel  1920  and the forward inner cooling flow noise attenuation panel  1922 . 
     Referring now more specifically to  FIGS.  19 C and  19 D , and with continued reference to  FIGS.  19 A and  19 B , the combustor  1900  may include a noise attenuation panel  1940 , such as, for example, one or more of the forward outer cooling flow noise attenuation panel  1920 , the forward inner cooling flow noise attenuation panel  1922 , the aft outer cooling flow noise attenuation panel  1924  and the aft inner cooling flow noise attenuation panel  1926  described above. The noise attenuation panel  1940  is typically positioned in one of the outer annular plenum  1914  and the inner annular plenum  1918 . Attached to the noise attenuation panel  1940  and positioned radially outside of the diffuser case module  1906  is an extended noise attenuation panel  1942 , which provides additional attenuation of acoustic waves and energy (e.g., combustor tones  1931 ). For example, where lower frequency ranges are targeted for attenuation, it is beneficial to increase the volume of the noise attenuation panel  1940 , which may be accomplished via addition of the extended noise attenuation panel  1942 . As described above, while any of the noise attenuation panels previously described may be employed in the combustor  1900  to attenuate acoustic waves or energy generated in the combustion chamber  1908 , beneficially, the noise attenuation panel  1940  (as well as the extended noise attenuation panel  1942 ) may be cooled by the compressed air from the core flow path C by employing the structures described above with reference to  FIGS.  17 A- 17 D  and  FIGS.  18 A- 18 G . 
     Referring now to  FIGS.  20 A and  20 B , a combustor  2000  is illustrated and described. In various embodiments, the combustor  2000  may be employed downstream of the combustor section  112  described above or may be used as a stand-alone unit. In various embodiments, the combustor  2000  may generally include an annular liner assembly  2002  surrounded by and spaced radially from an annular casing  2004 , which together define an annular cooling passage  2006  that extends radially and longitudinally between the annular liner assembly  2002  and the annular casing  2004 . A combustion chamber  2010  is provided radially inward of the annular liner assembly  2002 . In various embodiments, the combustion chamber  2010  receives fuel from a plurality of injectors  2012  positioned upstream of the combustion chamber  2010  and the annular cooling passage  2006  receives compressed air from a core flow path C, where the compressed air is used to both cool the annular liner assembly  2002  and to provide an oxidant to the combustion chamber  2010 . Similar to the combustor  1900  described above, the combustor  2000  may include one or more noise attenuation panels, such as, for example, a first cooling flow noise attenuation panel  2014  and a second cooling flow noise attenuation panel  2016  spaced radially opposite the first cooling flow noise attenuation panel  2014 . As illustrated, the first cooling flow noise attenuation panel  2014  and the second cooling flow noise attenuation panel  2016 , in various embodiments, are spaced about the combustor  2000  in the circumferential direction (e.g., at 180° intervals, as illustrated, or at other suitable intervals). Note that while any of the noise attenuation panels previously described may be employed in the combustor  2000  to attenuate acoustic waves or energy generated in the combustion chamber  2010  (e.g., combustor tones  2031 ), beneficially, the first cooling flow noise attenuation panel  2014  and the second cooling flow noise attenuation panel  2016  may be cooled by the compressed air from the core flow path C by employing the structures described above with reference to  FIGS.  17 A- 17 D  and  FIGS.  18 A- 18 G . 
     Referring now to  FIG.  21   , a combustor  2100  is illustrated and described. In various embodiments, the combustor  2100  is disposed downstream of a compressor section (e.g., the high-pressure compressor section  110  (HPC)) and upstream of a turbine section (e.g., the high-pressure turbine section  114  (HPT)). In various embodiments, the combustor  2100  may generally include an annular inner casing  2106  surrounded by and spaced radially from an annular outer casing  2108 , which together define an annular combustion chamber  2110  that extends radially and longitudinally between the annular inner casing  2106  and the annular outer casing  2108 . In various embodiments, the combustor  2100  in the form described is representative of a rotating detonation engine  2112 , which receives fuel and oxidant and supports a detonation wave that travels circumferentially about the annular combustion chamber  2110 . As illustrated, upstream running combustor tones  2114  and downstream running combustor tones  2116  are generated by the combustion occurring in the annular combustion chamber  2110 . An outer forward noise attenuation panel  2118  and an inner forward noise attenuation panel  2120  may be positioned radially outside and radially inside, respectively, of a core flow path C and configured to attenuate the upstream running combustor tones  2114 . Similarly, an outer aft noise attenuation panel  2122  and an inner aft noise attenuation panel  2124  may be positioned radially outside and radially inside, respectively, of an exhaust flow path E and configured to attenuate the downstream running combustor tones  2116 . As with the foregoing embodiments, note that while any of the noise attenuation panels previously described may be employed in the combustor  2100  to attenuate acoustic waves or energy generated in the combustion chamber  2010  (e.g., the upstream running combustor tones  2114  and the downstream running combustor tones  2116 ), beneficially, one or more of the outer forward noise attenuation panel  2118 , the inner forward noise attenuation panel  2120 , the outer aft noise attenuation panel  2122  and the inner aft noise attenuation panel  2124  may be cooled by the compressed air from the core flow path C by employing the structures described above with reference to  FIGS.  17 A- 17 D  and  FIGS.  18 A- 18 G . 
     Benefits, other advantages, and solutions to problems have been described herein with regard to specific embodiments. Furthermore, the connecting lines shown in the various figures contained herein are intended to represent exemplary functional relationships and/or physical couplings between the various elements. It should be noted that many alternative or additional functional relationships or physical connections may be present in a practical system. However, the benefits, advantages, solutions to problems, and any elements that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as critical, required, or essential features or elements of the disclosure. The scope of the disclosure is accordingly to be limited by nothing other than the appended claims, in which reference to an element in the singular is not intended to mean “one and only one” unless explicitly so stated, but rather “one or more.” Moreover, where a phrase similar to “at least one of A, B, or C” is used in the claims, it is intended that the phrase be interpreted to mean that A alone may be present in an embodiment, B alone may be present in an embodiment, C alone may be present in an embodiment, or that any combination of the elements A, B and C may be present in a single embodiment; for example, A and B, A and C, B and C, or A and B and C. Different cross-hatching is used throughout the figures to denote different parts but not necessarily to denote the same or different materials. 
     Systems, methods and apparatus are provided herein. In the detailed description herein, references to “one embodiment,” “an embodiment,” “various embodiments,” etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but every embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to affect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described. After reading the description, it will be apparent to one skilled in the relevant art(s) how to implement the disclosure in alternative embodiments. 
     Numbers, percentages, or other values stated herein are intended to include that value, and also other values that are about or approximately equal to the stated value, as would be appreciated by one of ordinary skill in the art encompassed by various embodiments of the present disclosure. A stated value should therefore be interpreted broadly enough to encompass values that are at least close enough to the stated value to perform a desired function or achieve a desired result. The stated values include at least the variation to be expected in a suitable industrial process, and may include values that are within 10%, within 5%, within 1%, within 0.1%, or within 0.01% of a stated value. Additionally, the terms “substantially,” “about” or “approximately” as used herein represent an amount close to the stated amount that still performs a desired function or achieves a desired result. For example, the term “substantially,” “about” or “approximately” may refer to an amount that is within 10% of, within 5% of, within 1% of, within 0.1% of, and within 0.01% of a stated amount or value. 
     Furthermore, no element, component, or method step in the present disclosure is intended to be dedicated to the public regardless of whether the element, component, or method step is explicitly recited in the claims. No claim element herein is to be construed under the provisions of 35 U.S.C. 112(f) unless the element is expressly recited using the phrase “means for.” As used herein, the terms “comprises,” “comprising,” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. 
     Finally, it should be understood that any of the above described concepts can be used alone or in combination with any or all of the other above described concepts. Although various embodiments have been disclosed and described, one of ordinary skill in this art would recognize that certain modifications would come within the scope of this disclosure. Accordingly, the description is not intended to be exhaustive or to limit the principles described or illustrated herein to any precise form. Many modifications and variations are possible in light of the above teaching.