COMBUSTOR OF A GAS TURBINE ENGINE

FIELD OF THE INVENTION

The present invention relates in general to gas turbine engines and, more particularly, to acoustic damping systems for damping dynamics in combustors in gas turbine engines.

BACKGROUND OF THE INVENTION

Gas turbine engines typically include a plurality of combustor baskets positioned downstream from a compressor and upstream from a turbine assembly. During operation, longitudinal mode dynamics often occurs in the combustor baskets. The longitudinal mode dynamics usually originates at the inlet of the air flow path in a combustor basket and travels downstream to the turbine inlet. The dynamics restrict the tuning flexibility of the gas turbine engine in order to operate at lower emissions, which is an ever increasing requirement for newer gas turbines.

Resonators have been incorporated into combustors to damp the longitudinal mode dynamics. The resonators have been sized and configured to address specific acoustic tunes. Resonators with various configurations have been employed.

Typically, the resonators are positioned within the combustors in the area of highest heat release to be most effective. It is in this position where the resonators are exposed to significant temperatures and thermal gradients. Early configurations including welding resonators directly to the combustor, but often failed due to formation of cracks caused by residual stress, leading to high repair costs. Other solutions have been used with limited success because of cracking and significant repair costs. Thus, a need exists for a more efficient, less costly solution to damp longitudinal mode dynamics.

SUMMARY OF THE INVENTION

An acoustically dampened gas turbine engine having a gas turbine engine combustor with an acoustic damping resonator system is disclosed. The acoustic damping resonator system may be formed from one or more resonators formed from a resonator housing positioned within the gas turbine engine combustor at an outer housing forming a combustor basket and extending circumferentially within the combustor. In at least one embodiment, the resonator housing may include one or more resonator chambers that provide enhanced cooling with reduced risk of cracking and other damage. The resonator housing may include resonator exhaust orifices that are positioned closer to an area of maximum temperature within the combustor, thereby enabling the resonator to reduce the temperature gradient within the combustor. The resonator housing may be sized and configured to reduce stress found in conventional systems by increasing distances between resonator exhaust orifices and between resonator inlet impingement orifices, among others.

In at least one embodiment, the acoustic damping resonator system for a combustor of a turbine engine may include one or more resonator housings defining one or more inner channels with an inner surface and an outer surface on an opposite side of the resonator housing from the inner surface. The acoustic damping resonator system may include one or more resonator chambers extending radially outward from the resonator housing. The resonator chamber may include one or more resonator inlet impingement orifices in an outer wall of the resonator chamber and one or more resonator exhaust orifices extending through the resonator housing. The resonator exhaust orifice extending through the resonator housing may be offset axially upstream to place the resonator exhaust orifice closer to an area of maximum temperature within the combustor.

The resonator exhaust orifice may include a plurality of resonator exhaust orifices that are positioned closer to an upstream wall of the resonator chamber than a downstream wall of the resonator chamber. The plurality of resonator exhaust orifices may be separated from each other a distance equal to at least one and one half times a diameter of a smallest diameter of the plurality of resonator exhaust orifices. In another embodiment, the plurality of resonator exhaust orifices may be separated from each other a distance equal to at least two times a diameter of a smallest diameter of the plurality of resonator exhaust orifices. The plurality of resonator exhaust orifices may be collected into a pattern of an inverted triangle with a point of the triangle pointed downstream. In another embodiment, the plurality of resonator exhaust orifices are collected into a pattern of a rectangle. The resonator inlet impingement orifice may include a plurality of resonator inlet impingement orifices that are offset from the plurality of resonator exhaust orifices such that one or more of the plurality of resonator inlet impingement orifices are radially aligned with the resonator housing in which the plurality of resonator exhaust orifices are positioned such that cooling fluids flowing into the resonator chamber impinge on the resonator housing. The plurality of resonator inlet impingement orifices may form half as many rows as rows formed by the plurality of resonator exhaust orifices. The rows formed by the plurality of resonator inlet impingement orifices may extend circumferentially and may be aligned radially between rows of the plurality of resonator exhaust orifices beginning with a first upstream row of resonator exhaust orifices and moving downstream. The plurality of resonator inlet impingement orifices may form a first row that has one fewer orifices than a first row of resonator exhaust orifices. The plurality of resonator inlet impingement orifices may form a second row downstream from the first row of resonator inlet impingement orifices, whereby the second row of resonator inlet impingement orifices may have two fewer orifices than a second row of resonator exhaust orifices. The second row of inlet impingement orifices may skip a position in a middle of the second row of resonator exhaust orifices.

The plurality of inlet impingement orifices may be separated from each other a distance equal to at least one and one half times a diameter of a smallest diameter of the plurality of inlet impingement orifices. The plurality of inlet impingement orifices may be separated from each other a distance equal to at least two times a diameter of a smallest diameter of the plurality of inlet impingement orifices. A ratio of distance between the outer wall of the resonator chamber and the resonator housing and a diameter of the resonator inlet impingement orifice may be between about seven and about four. The outer wall may be sized in thickness such that a ratio of a length of the at least one resonator inlet impingement orifice extending radially inward to a diameter of the at least one resonator inlet impingement orifice is greater than one.

In another embodiment, an acoustic damping resonator system for a combustor of a turbine engine may include one or more resonator housings defining at least one inner channel with an inner surface and an outer surface on an opposite side of the resonator housing from the inner surface. The an acoustic damping resonator system may include one or more resonator chambers extending radially outward from the resonator housing, whereby the resonator chamber includes at least one resonator inlet impingement orifice in an outer wall of the resonator chamber and resonator exhaust orifice extending through the resonator housing. The acoustic damping resonator system may include a ratio of distance between the outer wall of the resonator chamber and the resonator housing to a diameter of the resonator inlet impingement orifice between about seven and about four. As such, the footprint of the resonator chamber is expanded. A maximum internal resonator dimension extending linearly within the at least one resonator chamber may be increased less than 12 percent while a footprint of the resonator chamber has been enlarged by between 40 percent and 100 percent relative to a resonator chamber having a ratio of greater than eight of a distance between the outer wall of a resonator chamber and a resonator housing to a diameter of a resonator inlet impingement orifice.

The acoustic damping resonator system may include resonator chambers having numerous different shapes configured to prevent a maximum internal resonator dimension extending linearly within the resonator chamber from being enlarged beyond a point at which the resonator chamber has a target cutoff frequency that is greater than an actual damping frequency. In at least one embodiment, a cross-sectional shape of outer sidewalls forming the resonator chamber forms a modified parallelogram in which a longest diagonal direction has been reduced via truncated intersections. The truncated intersections of the modified parallelogram may be formed with a first corner side at a first intersection and a second corner side at a second intersection, whereby the first corner side may extend between first and second sidewalls forming the modified parallelogram and wherein the second corner side may extend between third and fourth sidewalls forming the modified parallelogram. In another embodiment, a cross-sectional shape of outer sidewalls forming the resonator chamber may form a modified triangle in which at least two corners have been truncated with corner sides. In yet another embodiment, each corner of the modified triangle may have been truncated with at least one corner side such that a first corner side may extend between first and second sidewalls, a second corner side may extend between second and third sidewalls and a third corner side may extend between first and third sidewalls.

In another embodiment, a cross-sectional shape of outer sidewalls forming the resonator chamber may form a modified rectangle in which at least two corners have been truncated with corner sides. At least two corners of the modified rectangle may have been truncated with at least one corner side. Each corner of the modified rectangle may have been truncated with at least one corner side such that a first corner side may extend between first and second sidewalls, a second corner side may extend between second and third sidewalls, a third corner side may extend between third and fourth sidewalls and a fourth corner side may extend between first and fourth sidewalls. In at least one embodiment, at least one corner on at least one sidewall forming the resonator chamber may be curved.

These and other advantages and objects will become apparent upon review of the detailed description of the invention set forth below.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and form a part of the specification, illustrate embodiments of the presently disclosed invention and, together with the description, disclose the principles of the invention.

Figure 1 is partial cross-sectional side view of a combustors positioned within gas turbine engines.

Figure 2 is a cross-sectional side view of a combustor in the gas turbine engine taken as section line 2-2 in Figure 1 .

Figure 3 is a perspective view of a combustor liner with an acoustic damping resonator system.

Figure 4 is a schematic diagram of a combustor in the gas turbine engine with a conventional resonator.

Figure 5 is a cross-sectional side view of a resonator of the acoustic damping resonator system shown together with a conventional resonator with a larger height taken along section line 5-5 in Figure 3.

Figure 6 is a perspective, cross-sectional view of resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3. Figure 7 is a perspective, cross-sectional view of another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 8 is a cross-sectional side view of resonator chamber of the acoustic damping resonator system showing a reduced sized recirculation zone adjacent to and downstream of a resonator chamber, whereby a high heat transfer starting at a reattachment point is positioned closer to the resonator than in conventional systems taken along section line 5-5 in Figure 3.

Figure 9 is a cross-sectional side view of a conventional resonator chamber. Figure 10 is a cross-sectional side view of a resonator chamber of the acoustic damping resonator system taken along section line 5-5 in Figure 3.

Figure 1 1 is a cross-sectional side view of a conventional resonator chamber.

Figure 12 is a cross-sectional side view of a resonator chamber of the acoustic damping resonator system taken along section line 5-5 in Figure 3.

Figure 13 is a cross-sectional side view of another embodiment of a resonator chamber of the acoustic damping resonator system taken along section line 5-5 in Figure 3.

Figure 14 is a cross-sectional side view of yet another embodiment of a resonator chamber of the acoustic damping resonator system taken along section line 5-5 in Figure 3.

Figure 15 is a cross-sectional top view of a conventional resonator chamber.

Figure 16 is a cross-sectional top view of an embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 17 is a cross-sectional top view of another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 18 is a cross-sectional top view of an embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 19 is a cross-sectional top view of a conventional resonator chamber. Figure 20 is a cross-sectional top view of another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 21 is a cross-sectional top view of yet another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 22 is a cross-sectional top view of another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 23 is a cross-sectional top view of still another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 24 is a cross-sectional top view of another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 25 is a cross-sectional top view of a conventional resonator chamber. Figure 26 is a cross-sectional top view of another conventional resonator chamber.

Figure 27 is a cross-sectional top view of an embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 28 is a cross-sectional top view of another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 29 is a cross-sectional top view of yet another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 30 is a cross-sectional top view of another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3. Figure 31 is a cross-sectional top view of still another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 32 is a cross-sectional top view of another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

Figure 33 is a cross-sectional top view of another embodiment of the resonator chamber of the acoustic damping resonator system taken along section line 6-6 in Figure 3.

DETAILED DESCRIPTION OF THE INVENTION

As shown in Figures 1 -3, 5-8, 10, 12-14, 16-18, 20-24 and 27-33, an acoustically dampened gas turbine engine 10 having a gas turbine engine combustor 12 with an acoustic damping resonator system 14 is disclosed. The acoustic damping resonator system 14 may be formed from one or more resonators 16 formed from a resonator housing 18 positioned within the gas turbine engine combustor 12 at an outer housing 20 forming a combustor basket 22 and extending circumferentially within the combustor 12. In at least one embodiment, the resonator housing 18 may include one or more resonator chambers 24 that provide enhanced cooling with reduced risk of cracking and other damage. The resonator housing 18 may include resonator exhaust orifices 26 that may be positioned closer to an area of maximum temperature 28 within the combustor 12, thereby enabling the resonator 16 to reduce the temperature gradient within the combustor 12. The resonator housing 18 may be sized and configured to reduce stress found in conventional systems by increasing distances between resonator exhaust orifices 26 and between resonator inlet impingement orifices 30, among others.

In at least one embodiment, the acoustic damping resonator system 14 for a combustor 12 of a turbine engine 10 may include one or more resonator housings 18. The resonator housing 18 may extend for a portion of or entire around a combustor 12, as shown in Figures 2 and 3. In at least one embodiment, the resonator housing 18 may define one or more inner channels 32, as shown in Figures 2, 3 and 5, with an inner surface 34 and an outer surface 36 on an opposite side of the resonator housing 18 from the inner surface 34. In at least one

embodiment, the resonator housing 18 may be generally cylindrical, thereby forming a ring with a single inner channel 32 therein.

The acoustic damping resonator system 14 may include one or more resonator chambers 24 extending radially outward from the resonator housing 18. The resonator chamber 24 may have any appropriate shape. In at least one embodiment, as shown in Figures 16-18, 22-24, 27, 32 and 33, the resonator chamber 24 may be shaped as a quadrilateral with a somewhat triangular shape, a rectangular shape, as shown in Figures 20-21 and 31 , or other appropriate shape. As shown in Figures 12-14, the resonator chamber 24 may be formed from an outer wall 38 that may be supported by one or more sidewalls 40, such as upstream sidewall 42 and downstream sidewall 44. The resonator chamber 24 may include one or more resonator inlet impingement orifices 30 in the outer wall 38 of the resonator chamber 24 and one or more resonator exhaust orifices 26 extending through the resonator housing 18. The resonator exhaust orifice 26 extending through the resonator housing 18 may be offset axially upstream to place the resonator exhaust orifice 26 closer to an area of maximum temperature within the combustor 12.

In at least one embodiment, as shown in Figure 12, the resonator 16 may be shifted further in the upstream direction relative to the resonator housing 18 such that the resonator 16 is closer to an area of maximum temperature within the combustor 12. In at least one embodiment, as shown in Figure 14, the acoustic damping resonator system 14 may include a plurality of resonator exhaust orifices 26 that are positioned closer to an upstream wall 42 of the resonator chamber 24 than a downstream wall 44 of the resonator chamber 24. As shown in Figures 6, 7, 17, 18 and 21 , the resonator exhaust orifices 26 may be spaced further apart from each other than in conventional systems, as shown in Figures 15 and 19 to reduce the likelihood of cracking in the resonator housing 18. The plurality of resonator exhaust orifices 26 may be separated from each other a distance equal to at least one and one half times a diameter of a smallest diameter of the plurality of resonator exhaust orifices 26. In another embodiment, the resonator exhaust orifices 26 may be separated from each other a distance equal to at least two times a diameter of a smallest diameter of the resonator exhaust orifices 26. In at least one embodiment, the resonator exhaust orifices 26 may be collected into a pattern having a shape of a quadrilateral with a somewhat triangular shape as shown in Figures 16-18 and 22- 24, which may also be described as being an inverted triangle with a point of the triangle pointed downstream, a rectangular shape, as shown in Figures 20-21 , or other appropriate shape.

As shown in Figures 22-24 and 33, the acoustic damping resonator system 14 may include one or more resonator inlet impingement orifices 30 that are offset from the plurality of resonator exhaust orifices 26 such that at least one of the plurality of resonator inlet impingement orifices 30 is radially aligned with the resonator housing 16 in which the plurality of resonator exhaust orifices 26 are positioned such that cooling fluids flowing into the resonator chamber 24 impinge on the resonator housing 16. As shown in Figures 23-24 and 33, the resonator inlet impingement orifices 30 may form fewer rows 46 as rows 48 formed by the plurality of resonator exhaust orifices 26. In another embodiment, as shown in Figures 23-24, the resonator inlet impingement orifices 30 may form half as many rows 46 as rows 48 formed by the plurality of resonator exhaust orifices 26. The rows 46 formed by the plurality of resonator inlet impingement orifices 30 may extend circumferentially and may be aligned radially between rows 48 of the plurality of resonator exhaust orifices 26 beginning with a first upstream row 50 of resonator exhaust orifices 26 and moving downstream. The rows 46 formed by the plurality of resonator inlet impingement orifices 30 may be positioned closer to an upstream sidewall 42 than a downstream sidewall 44 to increase efficiency. In at least one embodiment, the plurality of resonator inlet impingement orifices 30 may form a first row 52 that has one fewer orifices 30 than a first row 50 of resonator exhaust orifices 50. As shown in Figure 24, the plurality of resonator inlet impingement orifices 30 may form a second row 54 downstream from the first row 52 of resonator inlet impingement orifices 30, whereby the second row 54 of resonator inlet impingement orifices 30 has at least two fewer orifices 30 than a second row 56 of resonator exhaust orifices 26. As shown in Figure 24, the second row 54 of inlet impingement orifices 30 may skip a position in a middle of the second row 56 of resonator exhaust orifices 26. In another embodiment, as shown in Figure 33, the plurality of resonator inlet impingement orifices 30 may form a second row 54 downstream from the first row 52 of resonator inlet impingement orifices 30, whereby the second row 54 of resonator inlet impingement orifices 30 has at least one additional orifice 30 than a first row 52 of resonator inlet impingement orifices 30. The second row 56 of resonator exhaust orifices 26 may also include at least one additional resonator exhaust orifice 26 compared to a first row 50 of resonator exhaust orifices 26. A third row 58 of the resonator inlet impingement orifices 30 may have at least one less orifice 30 than a second row 54 of resonator inlet impingement orifices 30. A third row 59 of the resonator exhaust orifices 26 may have at least one less orifice 26 than a second row 56 of resonator exhaust orifices 26. The remaining rows of resonator inlet impingement orifices 30 and resonator exhaust orifices 26 may reduce in number moving downstream towards the downstream sidewall 44.

In at least one embodiment, the plurality of inlet impingement orifices 30 may be separated from each other a distance equal to at least one and one half times a diameter of a smallest diameter of the plurality of inlet impingement orifices 30. In another embodiment, the plurality of inlet impingement orifices 30 may be separated from each other a distance equal to at least two times a diameter of a smallest diameter of the plurality of inlet impingement orifices 30.

In at least one embodiment, as shown in Figures 5, 8, 27-32, the resonator chamber 24 may be configured to increase cooling of the resonator housing 18 and the combustor 12 without increasing the amount of cooling air needed. In particular, the resonator chamber 24 may be reconfigured to extend for a larger distance axially with a smaller radial height, thereby keeping the volume within the resonator chamber 24 relatively unchanged in comparison to conventional systems but exposing a larger amount of surface area of the resonator housing 18 to cooling fluids. In addition, the resonator chamber 24 may extend further radially upstream than conventional systems, which enables the upstream sidewall 42 of the resonator chamber 24, resonator exhaust orifices 26 or resonator inlet impingement orifices 30, or any combination thereof, to be shifted upstream and closer to an area of maximum temperature 28 within the combustor 12. In at least one embodiment, a ratio of distance between the outer wall 38 of the resonator chamber 24 and the resonator housing 18 to a diameter of the resonator inlet impingement orifice 30 may be between about seven and about four. In another embodiment, the ratio of distance between the outer wall 38 of the resonator chamber 24 and the resonator housing 18 to the diameter of the resonator inlet impingement orifice 30 is about 6.5 in the middle of the resonator 16. By decreasing the height of the resonator chamber 24, resonator 16 experiences improved cold side cooling downstream, in relation to the cold side flow direction, of the resonators 16 because of formation of a smaller recirculation zone adjacent to the sidewall 40 than in conventional systems. As such, a smaller low heat transfer region develops adjacent the recirculation zone. Instead, the high heat transfer at the reattachment point develops closer to the resonator 16 than in conventional systems.

The outer wall 38 of the resonator chamber 24 may be configured to enhance the flow of cooling fluids through the resonator inlet impingement orifices 30 and enhance the impingement of cooling fluids on the resonator housing 18 within the resonator chamber 24. In at least one embodiment, as shown in Figure 10, the outer wall 38 of the resonator chamber 24 may be thicker than conventional systems, as shown in Figure 9, to increase the effectiveness of the resonator inlet impingement orifices 30. In at least one embodiment, the outer wall 38 may be sized in thickness such that a ratio of a length of the at least one resonator inlet impingement orifice 30 extending radially inward to a diameter of the resonator inlet impingement orifice 30 is greater than about 0.75. In another embodiment, the outer wall 38 may be sized in thickness such that a ratio of a length of the at least one resonator inlet

impingement orifice 30 extending radially inward to a diameter of the resonator inlet impingement orifice 30 is greater than about one.

In at least one embodiment, as shown in Figures 5, 8, 27-32, the acoustic damping resonator system 14 may be configured such that the footprint of the resonator chamber 24 may be enlarged relative to conventional resonators, yet prevent a maximum internal resonator dimension 60 extending linearly within the resonator chamber 24 from being enlarged beyond a point at which the resonator chamber 24 has a target cutoff frequency that is greater than an actual damping frequency. The shape of the resonator 16 may be adapted such that the maximum internal resonator dimension 60 is not increased in the same relation as the resonator footprint. With the adapted resonator shape, a shift of the cut off frequency to higher frequencies is enabled, which ensures reliable damping in the designed frequency range of the resonator 16. As such, the acoustic damping resonator system 14 may be formed from a resonator housing 18 with a one or more resonator chambers 24 as described above. A ratio of a distance between the outer wall 38 of the resonator chamber 24 and the resonator housing 18 to a diameter of the resonator inlet impingement orifice 30 may be between about seven and about four. As shown in Figures 29-31 , a maximum internal resonator dimension 60 extending linearly within the resonator chamber 24 may be increased less than 12 percent while a footprint of the resonator chamber 24 on the resonator housing 18 may have been enlarged by between 40 percent and 100 percent relative to a resonator chamber 24 having a ratio of greater than eight of a distance between the outer wall 38 of a resonator chamber 24 and a resonator housing 18 to a diameter of a resonator inlet impingement orifice 30. The resonator chamber 24 may have been enlarged and sized, as set forth above.

The acoustic damping resonator system 14 may include resonator chambers 24 having numerous different shapes configured to prevent a maximum internal resonator dimension 60 extending linearly within the resonator chamber 24 from being enlarged beyond a point at which the resonator chamber 24 has a target cutoff frequency that is greater than an actual damping frequency. In at least one embodiment, a cross-sectional shape of outer sidewalls 40 forming the resonator chamber 24 may form a modified parallelogram 66, as shown in Figure 30, in which a maximum internal resonator dimension 60 has been reduced via truncated intersections 64. The truncated intersections 64 of the modified parallelogram 66 may be formed with a first corner side 68 at a first intersection 70 and a second corner side 72 at a second intersection 74. The first corner side 68 may extend between first and second sidewalls 76, 78 forming the modified parallelogram 66. The second corner side 72 may extend between third and fourth sidewalls 80, 82 forming the modified parallelogram 66.

In another embodiment, as shown in Figure 29, a cross-sectional shape of outer sidewalls 40 forming the resonator chamber 24 may form a modified triangle 84 in which at least two corners 86 have been truncated with corner sides 88. In at least one embodiment, each corner of the modified triangle 84 may be truncated with at least one corner side 88 such that a first corner side 68 may extend between first and second sidewalls 76, 78, a second corner side 72 may extend between second and third sidewalls 78, 80 and a third corner side 90 may extend between first and third sidewalls 76, 80.

In yet another embodiment, as shown in Figure 31 , a cross-sectional shape of outer sidewalls 40 forming the resonator chamber 24 may form a modified rectangle 92 in which at least two corners 86 have been truncated with corner sides 88. At least two corners 86 of the modified rectangle 92 may have been truncated with one or more corner sides 88. In at least one embodiment, each corner 86 of the modified rectangle 92 may have been truncated with at least one corner side 88 such that a first corner side 68 may extend between first and second sidewalls 76, 78, a second corner side 72 may extend between second and third sidewalls 78, 80, a third corner side 90 may extend between third and fourth sidewalls 80, 82 and a fourth corner side 94 may extend between first and fourth sidewalls 76, 82. In at least one embodiment, the modified rectangle 92 may have equal length sides and be a square.

As shown in Figure 32, one or more corners 86 on one or more sidewalls 40 forming the resonator chamber 24 may be curved. In at least one embodiment, each corner 86 on each sidewall 40 forming the resonator chamber 24 may be curved.

The foregoing is provided for purposes of illustrating, explaining, and describing embodiments of this invention. Modifications and adaptations to these embodiments will be apparent to those skilled in the art and may be made without departing from the scope or spirit of this invention or the following claims.