Patent Publication Number: US-2023134727-A1

Title: Fan rotor for airfoil damping

Description:
FIELD OF THE DISCLOSURE 
     The present disclosure relates generally to gas turbine engines, and more specifically to rotors having airfoils for use in gas turbine engines. 
     BACKGROUND 
     Gas turbine engines are used to power aircraft, watercraft, power generators, and the like. Gas turbine engines typically include a compressor, a combustor, and a turbine. The compressor compresses air drawn into the engine and delivers high pressure air to the combustor. In the combustor, fuel is mixed with the high pressure air and is ignited. Products of the combustion reaction in the combustor are directed into the turbine where work is extracted by rows of rotating blades and non-rotating vanes to drive the compressor and, sometimes, an output shaft. Each blade and vane has an airfoil that interacts with gases as they pass through the engine. 
     Airfoils have natural vibration modes of increasing frequency and complexity of the mode shape. The simplest and lowest frequency modes are typically considered to be the bending modes and the torsion mode. The first bending mode is a motion normal to the working surface of an airfoil in which the entire space of the airfoil moves in the same direction. Subsequent bending modes are similar to the initial bending modes, but with a node line of zero motion somewhere along the span of the airfoil other than the root, so that the upper and lower portions of the airfoil may move in opposite directions. The first torsion mode is a twisting motion around an axis that is parallel to the span of the airfoil, in which the entire space of the airfoil, on either side of the axis moves in the same direction. 
     Blades may be subject to destructive vibrations induced by steady or unsteady interaction of the airfoils of those blades with gases passing through a gas turbine engine. One type of vibration is flutter, which is an aero-elastic instability resulting from interaction of the flow over the airfoils of the blades and the blades&#39; natural vibration tendencies. The lowest frequency vibration modes, i.e., the first bending mode and the first torsion mode, are often the vibration modes that are susceptible to flutter. When flutter occurs, the unsteady aerodynamic forces on the blade, due to its vibration and insufficient mechanical or aerodynamic damping, add energy to the vibration, causing the vibration amplitude to increase. The vibration amplitude can become large enough to cause damage to a blade. Another type of vibration is known as forced response, which is an aero-elastic response to inlet distortion or wakes from upstream airfoils, struts, or any other flow obstruction. The operable range, in terms of pressure rise and flow rate, of turbomachinery can sometimes be restructured by flutter and forced response phenomena. 
     The specific susceptibility of a blade to flutter may be increased if all the blades on a rotor are identical in terms of their vibration natural frequencies. Sometimes, intentional variations may be introduced into blades during manufacturing to create structural mistuning of a rotor and provided flutter resistance. 
     SUMMARY 
     The present disclosure may comprise one or more of the following features and combinations thereof. 
     An airfoil for use in a gas turbine engine according to the present disclosure includes an airfoil body and at least one passageway. The airfoil body extends radially outwardly relative to an axis and is configured to interact with gases surrounding the airfoil body, the airfoil body having a leading edge, a trailing edge opposite the leading edge, a pressure side, and a suction side opposite the pressure side. The airfoil body is formed to define a first cavity within the airfoil body and a second cavity within the airfoil body, the second cavity being spaced apart from the first cavity. The airfoil body includes a damping fluid disposed within at least one of the first cavity and the second cavity. 
     In some embodiments, the at least one passageway extends between and fluidly interconnecting the first cavity and the second cavity. The at least one passageway is sized to allow the damping fluid to move at least partially from one of (i) the first cavity to the second cavity and (ii) the second cavity to the first cavity in response to the airfoil experiencing a modal response during use of the airfoil so as to damp the airfoil and attenuate the modal response. 
     In some embodiments, at least one of (i) the at least one passageway is sized such that a rate of fluid transfer at which the damping fluid moves between the first cavity and the second cavity at least one of changes a frequency of the modal response of the airfoil and adds damping and (ii) the damping fluid viscosity causes a rate of fluid transfer at which the damping fluid moves between the first cavity and the second cavity to at least one of change a frequency of the modal response of the airfoil and add damping. 
     In some embodiments, the first cavity includes a first passageway sidewall through which the at least one passageway opens into the first cavity. The second cavity includes a second passageway sidewall through which the at least one passageway opens into the second cavity. The first passageway sidewall is spaced apart from the second passageway sidewall such that at least a portion of the airfoil body is disposed between the first passageway sidewall and the second passageway sidewall. 
     In some embodiments, the airfoil body includes a blade root located adjacent to the wheel and a blade tip spaced apart radially outward from the blade root. The first cavity is located radially outward of the second cavity and adjacent to the blade tip. The at least one passageway extends in a direction from the blade root to the blade tip. 
     In some embodiments, the at least one passageway includes a first passageway and a second passageway spaced apart from the first passageway in an axial direction. 
     In some embodiments, the airfoil body defines a camber line extending from the leading edge to the trailing edge. Each of the first passageway and the second passageway defines a center extending along a longitudinal extent of the passageway. The center of each of the first passageway and the second passageway intersects with the camber line of the airfoil body. 
     In some embodiments, the first cavity is located adjacent to the leading edge and the second cavity is located adjacent to the trailing edge such that the first cavity is spaced apart from the second cavity in the direction from the leading edge to the trailing edge. 
     In some embodiments, the at least one passageway extends in a direction from the leading edge to the trailing edge. 
     In some embodiments, at least one partial support wall is arranged within the first cavity and at least one partial support wall is arranged within the second cavity. Each partial support wall extends at least partially from a first sidewall of a respective cavity to a second sidewall of the respective cavity opposite the first sidewall. 
     In some embodiments, each partial support wall extends entirely from the first sidewall of the respective cavity to the second sidewall of the respective cavity. Each partial support wall includes at least one opening through which fluid is adapted to move throughout the respective cavity. 
     In some embodiments, the first cavity and the second cavity are arranged radially outwardly of a halfway point of a radial extent of the airfoil body. 
     In some embodiments, the airfoil body defines a camber line extending from the leading edge to the trailing edge. The first cavity and the second cavity are arranged on opposing sides of the camber line. The at least one passageway extends between the first cavity and the second cavity so as to intersect the camber line. 
     A rotor assembly for use in a gas turbine engine according to another aspect of the present disclosure includes a wheel arranged circumferentially about an axis and a first airfoil extending radially outwardly from the wheel relative to the axis and configured to interact with gases surrounding the first airfoil. The first airfoil includes a first airfoil body and at least one first passageway, the first airfoil body having a leading edge, a trailing edge opposite the leading edge, a pressure side, and a suction side opposite the pressure side, the first airfoil body formed to define a first cavity within the first airfoil body and a second cavity within the first airfoil body, the second cavity being radially spaced apart from the first cavity. The first airfoil body includes a first damping fluid disposed within at least one of the first cavity and the second cavity. 
     In some embodiments, the at least one first passageway extends between and fluidly interconnecting the first cavity and the second cavity. The at least one passageway sized to allow the first damping fluid to move at least partially from one of (i) the first cavity to the second cavity and (ii) the second cavity to the first cavity in response to the first airfoil experiencing a modal response during use of the first airfoil so as to damp the first airfoil and attenuate the modal response. 
     In some embodiments, the rotor further includes a second airfoil circumferentially offset from the first airfoil relative to the wheel, the second airfoil extending radially outwardly from the wheel relative to the axis and configured to interact with gases surrounding the second airfoil. In some embodiments, the second airfoil includes a second airfoil body and at least one second passageway. 
     In some embodiments, the second airfoil body includes a leading edge, a trailing edge opposite the leading edge, a pressure side, and a suction side opposite the pressure side. The second airfoil body is formed to define a third cavity within the second airfoil body and a fourth cavity within the second airfoil body, the third cavity being axially spaced apart from the third cavity. The second airfoil body includes a second damping fluid disposed within at least one of the third cavity and the fourth cavity. 
     In some embodiments, the at least one second passageway extends between and fluidly interconnecting the third cavity and the fourth cavity. The at least one second passageway is sized to allow the second damping fluid to move at least partially from one of (i) the third cavity to the fourth cavity and (ii) the fourth cavity to the third cavity in response to the second airfoil experiencing a modal response during use of the second airfoil so as to damp the second airfoil and attenuate the modal response. 
     In some embodiments, the first airfoil includes a blade root located adjacent to the wheel and a blade tip spaced apart radially outward from the blade root. The first cavity is located radially outward of the second cavity and adjacent to the blade tip. The at least one first passageway of the first airfoil extends in a direction from the blade root to the blade tip. The third cavity of the second airfoil is located adjacent to the leading edge and the fourth cavity is located adjacent to the trailing edge. The at least one second passageway of the second airfoil extends in a direction from the leading edge to the trailing edge. 
     In some embodiments, at least one of (i) the at least one passageway is sized such that a rate of fluid transfer at which the damping fluid moves between the first cavity and the second cavity at least one of changes a frequency of the modal response of the first airfoil and adds damping and (ii) the damping fluid viscosity causes a rate of fluid transfer at which the damping fluid moves between the first cavity and the second cavity to at least one of change a frequency of the modal response of the first airfoil and add damping. 
     In some embodiments, at least one partial support wall is arranged within each of the first cavity, the second cavity, the third cavity, and the fourth cavity. Each partial support wall extends at least partially from a first sidewall of a respective cavity to a second sidewall of the respective cavity opposite the first sidewall. 
     In some embodiments, each partial support wall extends entirely from the first sidewall of the respective cavity to the second sidewall of the respective cavity opposite the first sidewall. Each partial support wall includes at least one opening through which fluid passes freely throughout the respective cavity. 
     In some embodiments, the at least one first passageway includes a first passageway and a second passageway spaced apart from the first passageway in an axial direction. The first airfoil body defines a camber line extending from the leading edge to the trailing edge. Each of the first passageway and the second passageway defines a center extending along a longitudinal extent of the passageway. The center of each of the first passageway and the second passageway intersects with the camber line of the first airfoil body. 
     A method according to another aspect of the present disclosure includes a first operation of forming an airfoil having a leading edge, a trailing edge opposite the leading edge, a pressure side, and a suction side opposite the pressure side, a second operation of forming a first cavity within the airfoil and forming a second cavity within the airfoil, the second cavity being spaced apart from the first cavity, a third operation of at least partially filling at least one of the first cavity and the second cavity with a damping fluid, a fourth operation of forming at least one passageway extending between and fluidly interconnecting the first cavity and the second cavity, and a fifth operation inducing a modal response in the airfoil such that the damping fluid moves at least partially from one of (i) the first cavity to the second cavity and (ii) the second cavity to the first cavity so as to damp the airfoil and attenuate the modal response. 
     These and other features of the present disclosure will become more apparent from the following description of the illustrative embodiments. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a cutaway view of a gas turbine engine that includes a fan, a compressor, a combustor, and a turbine, the fan having a rotor including a wheel arranged around an axis of the engine and a plurality of blades arranged around the wheel that each extend radially outward from the wheel to interact with gases flowing through the engine and suggesting that at least some of the blades include a first cavity and a second cavity formed therein that contain damping fluid configured to move between the cavities via at least one passageway extending between and interconnecting the cavities; 
         FIG.  2    is a cross-sectional view of a portion of the plurality of blades included in the fan of  FIG.  1    showing that each of the illustrated blades is formed to define the first cavity and the second cavity, and further showing a damping fluid disposed within at least one of the first cavity and the second cavity, and showing that the blades further include at least one passageway extending between the cavities and sized to allow the damping fluid to move between the cavities in response to the blades experiencing a modal response so as to damp the blades and attenuate the modal response; 
         FIG.  3    is a cross-sectional view of one of the blades of  FIG.  2    showing that the first cavity is arranged radially outwardly of the second cavity and that the damping fluid is disposed within the second cavity; 
         FIG.  4    is a top view of a section of the blade of  FIG.  3    showing that the airfoil includes the two passageways that extend radially, and that the airfoil body defines a camber line extending from the leading edge to the trailing edge, and suggesting that a center of each of the first passageway and the second passageway intersects with the camber line of the airfoil body; 
         FIG.  5    is a cross-sectional view of another embodiment of a blade included in the fan of  FIG.  1    showing that the blade includes a first cavity that is axially spaced apart from a second cavity and that the damping fluid is disposed within the first cavity; 
         FIG.  6    is a top view of a section of the blade of  FIG.  5    showing that the blade includes the passageway that extends axially between the cavities, and that the blade defines a camber line extending from the leading edge to the trailing edge, and suggesting that the center of each of the first passageway and the second passageway is aligned with the camber line of the airfoil body; 
         FIG.  7    is a cross-sectional view of a portion of the plurality of blades included in the fan of  FIG.  1    including a blade as shown in  FIG.  3    and a blade as shown in  FIG.  5    arranged circumferentially adjacent the blade of  FIG.  3    along the wheel; 
         FIG.  8    is a cross-sectional view of a blade according to another aspect of the present disclosure showing that the blade is shaped as an airfoil, the airfoil body formed to define a first cavity within the airfoil body and a second cavity within the airfoil body, the second cavity being spaced apart from the first cavity, and showing that the first cavity and the second cavity are arranged radially outwardly of a halfway point of a radial extent of the airfoil body; 
         FIG.  9    is a top view of a blade according to another aspect of the present disclosure showing that the airfoil includes a passageway that extends axially between a first cavity and a second cavity, showing that each cavity includes a plurality of support walls extending between the sidewalls of the cavity, showing that the two sidewalls closest to the passageway are entirely solid so as to define smaller cavities within the main cavity, and showing that the damping fluid is contained to only the smaller cavities and may move therebetween; 
         FIG.  10    is a cross-sectional view of a blade according to another aspect of the present disclosure showing that the blade is shaped as an airfoil, the airfoil body formed to define a first cavity within the airfoil body and a second cavity within the airfoil body, the second cavity being spaced apart from the first cavity, and showing that the central walls of each cavity are angled in the same direction so as to be substantially parallel with each other; and 
         FIG.  11    is a top view of a blade according to another aspect of the present disclosure showing that the airfoil includes a passageway that extends in a direction from a chordwise midpoint of the pressure side of the blade to a chordwise midpoint of the suction side of the blade, and suggesting that a first cavity and a second cavity are arranged on opposing sides of a central camber line of the blade. 
     
    
    
     DETAILED DESCRIPTION OF THE DRAWINGS 
     For the purposes of promoting an understanding of the principles of the disclosure, reference will now be made to a number of illustrative embodiments illustrated in the drawings and specific language will be used to describe the same. 
     A bladed rotor  10  includes a plurality of blades  14  including first blades  16  and second blades  36  as shown in  FIG.  1   . The bladed rotor  10  is adapted for use in a gas turbine engine  110  that includes a compressor  112 , a combustor  113 , and a turbine  114 , and a fan  115  as shown in  FIG.  1   . The fan  115  is driven by the turbine  114  and provides thrust for propelling an aircraft. The compressor  112  compresses and delivers air to the combustor  112 . The combustor  113  mixes fuel with the compressed air received from the compressor  112  and ignites the fuel. The hot, high pressure products of the combustion reaction in the combustor  113  are directed into the turbine  114  to cause the turbine  114  to rotate about an axis  11  of the gas turbine engine  110  and drive the compressor  113  and the fan  115 . In the illustrative embodiment, the fan  115  includes the rotor  10 . 
     The rotor  10  includes a wheel  12  and the plurality of blades  14  as shown in  FIG.  1   . The wheel  12  is arranged around the axis  11 . The blades  16 ,  36  may each be comprised of a first material and are arranged around the wheel  12 . Each blade  16 ,  36  extends radially outwardly away from the wheel  12  relative to the axis  11  to interact with gases surrounding the rotor  10 . The first material is a metallic material in the illustrative embodiment. 
     The plurality of blades  14  may include at least some the first blades  16 , as shown in  FIGS.  2 - 4   , and at least some of the second blades  36 , as shown in  FIGS.  5 - 7   . In some embodiments, the plurality of blades  14  includes only first blades  16 , and in some embodiments, the plurality of blades  14  includes only second blades  36 . In some embodiments, the plurality of blades  14  may include some of the first blades  16 , some of the second blades  36 , and any additional numbers of groups of blades described in alternative embodiments of the blades described herein. For example, as shown in  FIG.  7   , the plurality of blades  14  may include at least one section having a first blade  16  directly adjacent a second blade  36 . Each of the first blades  16 , the second blades  36 , and the alternative blades described herein have external surfaces that are similarly sized and shaped for the particular gas turbine engine  110 . 
     Flutter may be a common aerodynamic phenomenon that may lead to excessive blade vibratory stress and eventual blade failure. Reducing the phenomenon may be difficult when combined with other requirements of the blades  16 ,  36 , such as structural strength and aerodynamic performance. In some instances, mistuning blades may include changing the existing airfoil shape of some of the blades about the rotor. Yet, such arrangements may cause conflicting issues with the other original blades, such as forced response. 
     In order to attenuate the modal response of the plurality of blades  14 , the present disclosure provides for blades having similar external shapes and having at least two cavities  22 ,  24  formed therein. The cavities include a damping fluid  30  disposed within at least one of the cavities  22 ,  24 . The damping fluid  30  is configured to move between the cavities  22 ,  24  via at least one passageway  26 ,  28  to vary the frequency response of the blade. Specifically, when the blade  16 ,  36  deforms or vibrates, the mode shape motion drives the damping fluid  30  to pass from one cavity to the other cavity. This motion damps the blade  16 ,  36  and thus attenuates the modal response. The cavities of the illustrative embodiment are partially filled with damping fluid  30 . The extent to which the cavities are filled with fluid  30  is dependent on the desired damping effect. The remainder of the cavity space may be filled with air or other gas. 
     Turning again to the plurality of blades  14 , the first blade  16 , also referred to as an airfoil, may include an airfoil body  20  as shown in  FIGS.  2  and  3   . The airfoil body  20  has an aerodynamic shape for accelerating air through the gas turbine engine  110 . The airfoil body  20  further includes a blade tip  21  spaced apart radially outward from a blade root  23 , the blade root  23  located adjacent to the wheel  12 . The airfoil body  20  has a leading edge  25 , a trailing edge  27  opposite the leading edge  25 , a pressure side external surface  31 , and a suction side external surface  33  opposite the pressure side  31  as shown  FIGS.  2 - 4   . 
     In the illustrative embodiment, the blade root  23  of the blade  16  is shaped to be received in a corresponding slot in the wheel  12  to couple the blade  16  to the wheel  12 . In some embodiments, the blade root  23  may be another suitable attachment method. In other embodiments, the rotor  10  is a blisk and the plurality of blades  16 ,  36 , as well as the additional arrangements of blades described herein, are integrally formed with the wheel  12 . 
     The blade  16  is formed to include a first cavity  22  within the airfoil body  20  and a second cavity  24  within the airfoil body  20  that is radially spaced apart from the first cavity  22  as shown in  FIGS.  2 - 4   . Specifically, the first cavity  22  is located radially outward of the second cavity  24  and adjacent to the blade tip  21 . The cavities  22 ,  24  are formed as hollowed-out spaces within the airfoil body  20 . In the illustrative embodiment, the cavities  22 ,  24  are formed generally centrally relative to the pressure side surface  31 , the suction side surface  33 , the leading edge  25 , and the trailing edge  27 . In some embodiments, the airfoil body  20  may include more than two cavities based on the operating conditions that the blades  16  will be experiencing. Moreover, in some embodiments, the cavities  22 ,  24  may include support walls  29  arranged therein to support the walls of the cavities  22 ,  24 . The cavities  22 ,  24  are entirely sealed within the airfoil body  20 . That is, the cavities  22 ,  24  are covered entirely by metallic material that forms an external surface of the airfoil body  20 . 
     The blade  16  further includes at least one passageway  26 ,  28  extending between and fluidly interconnecting the first cavity  22  and the second cavity  24  as shown in  FIGS.  2 - 4   . In particular, the at least one passageway  26 ,  28  includes a first passageway  26  and a second passageway  28  spaced apart from the first passageway  26  in a circumferential direction relative to the wheel  12 . The passageways  26 ,  28  may be formed as hollowed-out cylindrical cavities within the material of the airfoil body  20  or may be hollow tubes that are inserted into the airfoil body  20 . The passageways  26 ,  28  extend in a direction from the blade root  23  to the blade tip  21 . In some embodiments, the airfoil body  20  may include more than two passageways  26 ,  28  or only a single passageway  26  depending on the structural requirements of the blade  16  and the desired rate of fluid flow between the cavities  22 ,  24 . The passageways  26 ,  28  may be other shapes and may include tapers, angled surfaces, etc. 
     The airfoil body  20  further includes a damping fluid  30  disposed within at least one of the first cavity  22  and the second cavity  24  as shown in  FIGS.  2  and  3   . In the illustrative embodiment, the damping fluid  30  is an inert fluid which remains a liquid across a range of temperatures of operation of the blades  14 . For example, oils of varying viscosity levels are suitable for this purpose. Oils of different viscosity levels will have differing damping effects on the blade  16 , and choosing the appropriate viscosity level of the oil will enhance the damping effect in a given operating condition of the rotor  10  and gas turbine engine  110 . However, because oil viscosity may change with temperature, this factor can be taken into account when choosing the appropriate oil for a given operating condition of the gas turbine engine  110 . As a further example, the fluid used as the damping fluid  30  may be glycol. 
     The viscosity of the damping fluid  30  is chosen and the passageways  26 ,  28  are sized to allow the damping fluid  30  to move at least partially from one of the cavities  22 ,  24  to another cavity  22 ,  24  in response to the blade  16  experiencing a modal response during use of the blade  16  so as to damp the blade  16  and attenuate the modal response. 
     In the illustrative embodiment, the first cavity  22  is spaced apart from the second cavity  24  as shown in  FIGS.  2  and  3   . Specifically, the first cavity  22  includes a first passageway sidewall  34  through which the passageways  26 ,  28  open into the first cavity  22 . Similarly, the second cavity  24  includes a second passageway sidewall  35  through which the passageways  26 ,  28  open into the second cavity  24 . The first passageway sidewall  34  is spaced apart from the second passageway sidewall  35  such that at least a portion of the material that comprises the airfoil body  20  is disposed between the first passageway sidewall  34  and the second passageway sidewall  35 . The cavities  22 ,  24  are fully enclosed except for the opening in the sidewalls  34 ,  35  through which the passageways  26 ,  28  open into the cavities  22 ,  24 . 
     In some embodiments, the airfoil body  20  defines a camber line  60  extending from the leading edge  25  to the trailing edge  27  as shown in  FIG.  4   . Each of the first passageway  26  and the second passageway  28  defines a center extending along a longitudinal extent of the passageway  26 ,  28 . The center of each of the first passageway  26  and the second passageway  28  intersects with the camber line  60  of the airfoil body  20 . Aligning the center of each passageway  26 ,  28  with the camber line  60  of the airfoil body  20 , and thus generally centrally with each cavity  22 ,  24 , may allow for a maximum amount of damping fluid  30  to move between the cavities  22 ,  24 , increasing the efficiency of the damping. 
     In some embodiments, the airfoil body  20  further includes at least one partial support wall  29  arranged within the first cavity  22  and at least one partial support wall  29  arranged within the second cavity  24  as shown in  FIG.  4   . As illustrated, each cavity  22 ,  24  includes two partial support walls  29 , although in other embodiments, the airfoil body  20  may include additional or fewer support walls  29 , or no support walls  29 , depending on the structural needs of the blade  16 . 
     Each partial support wall  29  extends at least partially from a first sidewall of the cavity  22 ,  24  to a second sidewall of the cavity  22 ,  24  opposite the first sidewall so as to provide support for the cavity  22 ,  24 . Because the support walls  29  are formed as partial walls, the damping fluid  30  may flow freely within the cavity  22 ,  24 . In some embodiments, at least one support wall  29  extends entirely from the first sidewall of the cavity  22 ,  24  to the second sidewall of the cavity  22 ,  24  and includes at least one opening  32  through which fluid passes freely throughout the respective cavity  22 ,  24 . In some embodiments, every support wall  29  extends entirely from the first sidewall to the second sidewall of the cavity  22 ,  24  and includes an opening  32 . 
     In some embodiments, the plurality of blades  14  further includes the second blade  36 , also referred to as an airfoil, as shown in  FIGS.  5 - 7   . The blade  36  is formed similarly to the blade  36 , except that the blade  36  includes a different arrangement of cavities  42 ,  44 . The blade  36  includes an airfoil body  40  as shown in  FIGS.  5  and  6   . The airfoil body  40  has an aerodynamic shape for accelerating air through the gas turbine engine  110 . The airfoil body  40  further includes a blade tip  41  spaced apart radially outward from a blade root  43 , the blade root  43  located adjacent to the wheel  12 . The airfoil body  40  has a leading edge  45 , a trailing edge  47  opposite the leading edge  45 , a pressure side external surface  51 , and a suction side external surface  53  opposite the pressure side  51  as shown  FIGS.  5 - 7   . 
     In the illustrative embodiment, the blade root  43  of the blade  36  is shaped to be received in a corresponding slot in the wheel  12  to couple the blade  36  to the wheel  12 . In some embodiments, the blade root  43  may be another suitable attachment method. In other embodiments, the rotor  10  is a blisk, or in other words, having blades integrally machined with the a disk, and the plurality of blades  16 ,  36 , as well as the additional arrangements of blades described herein, are integrally formed with the wheel  12 . 
     The blade  36  is formed to include a first cavity  42  within the airfoil body  40  and a second cavity  44  within the airfoil body  40  that is axially spaced apart from the first cavity  42  as shown in  FIGS.  5  and  6   . Specifically, the first cavity  42  is located axially spaced apart from the second cavity  44 . The cavities  42 ,  44  are formed as hollowed-out spaces within the airfoil body  40 . In the illustrative embodiment, the cavities  42 ,  44  are formed generally centrally relative to the pressure side surface  51 , the suction side surface  53 , the leading edge  45 , and the trailing edge  47 . In some embodiments, the airfoil body  40  may include more than two cavities based on the operating conditions that the blades  36  will be experiencing. Moreover, in some embodiments, the cavities  42 ,  44  may include support walls  49  arranged therein to support the walls of the cavities  42 ,  44 . 
     The blade  36  further includes at least one passageway  46  extending between and fluidly interconnecting the first cavity  42  and the second cavity  44  as shown in  FIGS.  5  and  6   . In the illustrative embodiment, the at least one passageway  46  includes a single first passageway  46 . The passageway  46  may be formed as a hollowed-out cylindrical cavity within the material of the airfoil body  40  or may be a hollow tube that are inserted into the airfoil body  40 . The passageway  46  extends in a direction from the leading edge  45  to the trailing edge  47 . In some embodiments, the airfoil body  40  may include more than one passageway  46  depending on the structural requirements of the blade  36  and the desired rate of fluid flow between the cavities  42 ,  44 . 
     The airfoil body  40  further includes a damping fluid  50  disposed within at least one of the first cavity  42  and the second cavity  44  as shown in  FIGS.  5  and  6   . Similar to the blade  16 , the damping fluid  50  is an inert fluid which remains a liquid across a range of temperatures. The fluid used as the damping fluid  50  may be an oil or glycol. The viscosity of the damping fluid  50  is chosen and the passageway  46  is sized to allow the damping fluid  50  to move at least partially from one of the cavities  42 ,  44  to the other cavity  42 ,  44  in response to the blade  36  experiencing a modal response during use of the blade  36  so as to damp the blade  36  and attenuate the modal response. 
     In the illustrative embodiment, the first cavity  42  is spaced apart from the second cavity  44  as shown in  FIGS.  5  and  6   . Specifically, the first cavity  42  includes a first passageway sidewall  54  through which the passageway  46  opens into the first cavity  42 . Similarly, the second cavity  44  includes a second passageway sidewall  55  through which the passageway  46  opens into the second cavity  44 . The first passageway sidewall  54  is spaced apart from the second passageway sidewall  55  such that at least a portion of the material that comprises the airfoil body  40  is disposed between the first passageway sidewall  54  and the second passageway sidewall  55 . The cavities  42 ,  44  are fully enclosed except for the opening in the sidewalls  54 ,  55  through which the passageway  46  opens into the cavities  42 ,  44 . 
     In some embodiments, the airfoil body  40  defines a camber line  80  extending from the leading edge  45  to the trailing edge  47  as shown in  FIG.  6   . The first passageway  46  defines a center extending along a longitudinal extent of the passageway  46 . The center of the first passageway  46  is generally aligned with the camber line  80  of the airfoil body  40 . Aligning the center of the passageway  46  with the camber line  80  of the airfoil body  40 , and thus generally centrally with each cavity  42 ,  44 , may allow for a maximum amount of damping fluid  50  to move between the cavities  42 ,  44 , increasing the efficiency of the damping. 
     In some embodiments, the airfoil body  40  further includes at least one partial support wall  49  arranged within the first cavity  42  and at least one partial support wall  49  arranged within the second cavity  44  as shown in  FIG.  6   . The airfoil body  40  may include multiple support walls  49  in one or both of the cavities  42 ,  44 , a single support wall  49  in one or both of the cavities  42 ,  44 , or no support walls  49 , depending on the structural needs of the blade  36 . 
     Each partial support wall  49  extends at least partially from a first sidewall of the cavity  42 ,  44  to a second sidewall of the cavity  42 ,  44  opposite the first sidewall so as to provide support for the cavity  42 ,  44 . Because the support walls  49  are formed as partial walls, the damping fluid  50  may flow freely within the cavity  42 ,  44 . In some embodiments, at least one support wall  49  extends entirely from the first sidewall of the cavity  42 ,  44  to the second sidewall of the cavity  42 ,  44  and includes at least one opening  52  through which fluid passes freely throughout the respective cavity  42 ,  44 . In some embodiments, every support wall  49  extends entirely from the first sidewall to the second sidewall of the cavity  42 ,  44  and includes an opening  52 . 
     In operation, the damping fluid  30 ,  50  is configured to move between the cavities  22 ,  24 ,  42 ,  44  via the at least one passageway  26 ,  28 ,  46  to vary the frequency response of the blade. When the blade  16 ,  36  deforms or vibrates, the mode shape motion drives the damping fluid  30 ,  50  to pass from one cavity to another cavity. The size of the passageways  26 ,  28 ,  46  restricts the flow of the damping fluid  30  such that the rate of fluid transfer at which the damping fluid  30 ,  50  moves between the first cavity  22  and the second cavity  24  or between the third cavity  42  and the fourth cavity  44  changes a frequency of the modal response of the blade and/or adds damping. Moreover, the damping fluid  30 ,  50  viscosity is chosen to cause a rate of fluid transfer at which the damping fluid moves between the first cavity and the second cavity to change a frequency of the modal response of the blade and/or add damping. The energy absorbed to move the damping fluid  30 ,  50  between the cavities  22 ,  24 ,  42 ,  44  aids attenuation of the modal response and to change the frequency of the blade vibration to move it off resonance. Moreover, unsynchronized fluid flow relative to the blade mode frequency contributes to additional damping to attenuate the modal response. 
     In the illustrative embodiment, the blade  16 , which includes the radially spaced apart cavities  22 ,  24 , is arranged in this manner to damp the blade  16  in response to bending of the blade  16  in the spanwise direction. That is, when the blade  16  bends along an axis that extends from the leading edge to the trailing edge, the cavities  22 ,  24  being radially spaced apart improves the damping effect of the fluid  30 . The blade  36 , which includes the axially spaced apart cavities  42 ,  44 , is arranged in this manner to damp the blade  36  in response to torsion of the blade  36 . That is, when the blade  36  twists along an axis that extends from the blade root to the blade tip, the cavities  42 ,  44  being axially spaced apart improves the damping effect of the fluid  50 . Even further, the cavities  22 ,  24 ,  42 ,  44  may be arranged near a peak displacement for a particular mode or near a peak strain. 
     In some embodiments, the cavities  22 ,  24 ,  42 ,  44  are located within the blades  16 ,  36  in locations that accommodate specific deflection, bending, and/or torsion of the blades  16 ,  36 . Specifically, the cavities  22 ,  24 ,  42 ,  44  are located in areas of the blade  16 ,  36  in which significant deflection, bending, and/or torsion is occurring. For example, the blades  16 ,  36  described above are beneficial for deflection, bending, and/or torsion occurring in the blade  16 ,  36  in the general area of the cavities. Other embodiments may include cavities arranged in other areas of the blade, as well be described herein. 
     In some embodiments, the frequency of the blades  16 ,  36  in response to various operating conditions of the gas turbine engine  110  may be known prior to manufacturing the cavities such that a desired damping effect may be achieved based on operating conditions that the gas turbine engine  110  will experience. 
     Another embodiment of a blade  116  in accordance with the present disclosure is shown in  FIG.  8   . The blade  116  is substantially similar to the blade  16 ,  36  shown in  FIGS.  1 - 7    and described herein. Accordingly, similar reference numbers in the  100  series indicate features that are common between the blade  116  and the blade  16 . The description of the blade  16  is incorporated by reference to apply to the blade  116 , except in instances when it conflicts with the specific description and the drawings of the blade  116 . 
     The blade  116  includes an airfoil body  120  having an aerodynamic shape for accelerating air through the gas turbine engine  110 . The airfoil body  120  further includes a blade tip  121  spaced apart radially outward from a blade root  123 , a leading edge  125 , and a trailing edge  127  opposite the leading edge  125 . The airfoil body  120  further includes a pressure side external surface  131 , and a suction side external surface  133  opposite the pressure side  131  as shown  FIG.  8   . 
     The blade  116  is formed to include a first cavity  122  within the airfoil body  120  and a second cavity  124  within the airfoil body  120  that is radially spaced apart from the first cavity  122  as shown in  FIG.  8   . The cavities  122 ,  124  are formed similar to the cavities  22 ,  24 . Moreover, the blade further includes at least one passageway  126  extending between and fluidly interconnecting the first cavity  122  and the second cavity  124 . The airfoil body  120  further includes a damping fluid  130  disposed within at least one of the first cavity  122  and the second cavity  124 . 
     In the illustrative embodiment, the first cavity  122  is spaced apart from the second cavity  124  as shown in  FIG.  8   . Specifically, the first cavity  122  includes a first passageway sidewall  134  through which the passageway  126  opens into the first cavity  122 . Similarly, the second cavity  124  includes a second passageway sidewall  135  through which the passageway  126  opens into the second cavity  124 . The first passageway sidewall  134  is spaced apart from the second passageway sidewall  135  such that at least a portion of the material that comprises the airfoil body  120  is disposed between the first passageway sidewall  134  and the second passageway sidewall  135 . The cavities  122 ,  124  are fully enclosed except for the opening in the sidewalls  134 ,  135  through which the passageway  126  opens into the cavities  122 ,  124 . 
     The blade  116  differs from the blade  16  at least in that the first cavity  122  and the second cavity  124  are both located on a radially outer side of the blade  116  as shown in  FIG.  8   . In particular, the first cavity  122  and the second cavity  124  are both arranged radially outwardly of a halfway point of a radial extent of the airfoil body  120 . As discussed above, the cavities  122 ,  124  are located within the blade  116  in locations that accommodate specific deflection, bending, and/or torsion of the blade  116 . Thus, arranging both cavities  122 ,  124  radially outwardly of a halfway point of a radial extent of the airfoil body  120  is beneficial in operating conditions in which the blade  116  is experiencing greater deflection at the radially outer end of the blade  116 . 
     Another embodiment of a blade  236  in accordance with the present disclosure is shown in  FIG.  9   . The blade  236  is substantially similar to the blade  36  shown in  FIGS.  5 - 7    and described herein. Accordingly, similar reference numbers in the  200  series indicate features that are common between the blade  236  and the blade  36 . The description of the blade  36  is incorporated by reference to apply to the blade  236 , except in instances when it conflicts with the specific description and the drawings of the blade  236 . 
     The blade  236  includes an airfoil body  240  having an aerodynamic shape for accelerating air through the gas turbine engine  110 . The airfoil body  240  further includes a blade tip (not shown due to cross section) spaced apart radially outward from a blade root  243 , a leading edge  245 , and a trailing edge  247  opposite the leading edge  245 . The airfoil body  240  further includes a pressure side external surface  251 , and a suction side external surface  253  opposite the pressure side  251  as shown  FIG.  9   . 
     The blade  236  is formed to include a first cavity  242  within the airfoil body  240  and a second cavity  244  within the airfoil body  240  that is radially spaced apart from the first cavity  242  as shown in  FIG.  9   . The cavities  242 ,  244  are formed similar to the cavities  42 ,  44 . The cavities  242 ,  244  differ from the cavities  42 ,  44  at least in that the cavities  242 ,  244  are delimited by support walls  249  arranged in the cavity  242 ,  244 . Specifically, the first cavity  242  is delimited by a first passageway sidewall  254  through which the passageway  246  opens into the first cavity  242  and a first support wall  249  that extends entirely between all sides of the cavity  242  to seal off the cavity  242  from the remainder of any open space  248  within the airfoil body  240 . 
     Similarly, the second cavity  244  is delimited by a second passageway sidewall  255  through which the passageway  246  opens into the second cavity  244  and a first support wall  249  that extends entirely between all sides of the cavity  244  to seal off the cavity  244  from the remainder of any open space  248  within the airfoil body  240 . As discussed above, the cavities  242 ,  244  are located within the blade  236  in locations that accommodate specific deflection, bending, and/or torsion of the blade  236 . Thus, arranging both cavities  242 ,  244  near the central radially extending axis of the airfoil body  240  is beneficial in operating conditions in which the blade  236  is experiencing greater deflection around the central radially extending axis of the blade  236 . 
     Another embodiment of a blade  336  in accordance with the present disclosure is shown in  FIG.  10   . The blade  336  is substantially similar to the blade  36 ,  236  shown in  FIGS.  1 - 7  and  9    and described herein. Accordingly, similar reference numbers in the  300  series indicate features that are common between the blade  336  and the blade  36 ,  236 . The description of the blade  36 ,  236  is incorporated by reference to apply to the blade  336 , except in instances when it conflicts with the specific description and the drawings of the blade  336 . 
     The blade  336  includes an airfoil body  340  having an aerodynamic shape for accelerating air through the gas turbine engine  110 . The airfoil body  340  further includes a blade tip  341  spaced apart radially outward from a blade root  343 , a leading edge  345 , and a trailing edge  347  opposite the leading edge  345 . The airfoil body  340  further includes a pressure side external surface  351 , and a suction side external surface  353  opposite the pressure side  351  as shown  FIG.  10   . 
     The blade  336  is formed to include a first cavity  342  within the airfoil body  340  and a second cavity  344  within the airfoil body  340  that is axially spaced apart from the first cavity  342  as shown in  FIG.  10   . The cavities  342 ,  344  are formed similar to the cavities  42 ,  44 . Moreover, the blade further includes at least one passageway  346  extending between and fluidly interconnecting the first cavity  342  and the second cavity  344 . The airfoil body  340  further includes a damping fluid  350  disposed within at least one of the first cavity  342  and the second cavity  344 . 
     In the illustrative embodiment, the first cavity  342  is spaced apart from the second cavity  344  as shown in  FIG.  10   . Specifically, the first cavity  342  includes a first passageway sidewall  354  through which the passageway  346  opens into the first cavity  342 . Similarly, the second cavity  344  includes a second passageway sidewall  355  through which the passageway  346  opens into the second cavity  344 . The first passageway sidewall  354  is spaced apart from the second passageway sidewall  355  such that at least a portion of the material that comprises the airfoil body  340  is disposed between the first passageway sidewall  354  and the second passageway sidewall  355 . The cavities  342 ,  344  are fully enclosed except for the opening in the sidewalls  354 ,  355  through which the passageway  346  opens into the cavities  342 ,  344 . 
     The blade  336  differs from the blade  36 ,  236  at least in that first passageway sidewall  354  and the second passageway sidewall  355  are both angled at the same angle relative to the central radially extending axis of the blade  336  so as to be substantially parallel with each other as shown in  FIG.  10   . As discussed above, the cavities  342 ,  344  are located within the blade  336  in locations that accommodate specific deflection, bending, and/or torsion of the blade  336 . Thus, arranging the first passageway sidewall  354  and the second passageway sidewall  355  to be angled at the same angle relative to the central radially extending axis of the blade  336  is beneficial in operating conditions in which the blade  336  is experiencing greater deflection along the central radially extending axis of the blade  336 . 
     Another embodiment of a blade  436  in accordance with the present disclosure is shown in  FIG.  11   . The blade  436  is substantially similar to the blades  36 ,  136 ,  236 ,  336  described herein. Accordingly, similar reference numbers in the  400  series indicate features that are common between the blade  436  and the blades  36 ,  136 ,  236 ,  336 . The description of the blade  36 ,  136 ,  236 ,  336  is incorporated by reference to apply to the blade  436 , except in instances when it conflicts with the specific description and the drawings of the blade  436 . 
     The blade  436  includes an airfoil body  440  having an aerodynamic shape for accelerating air through the gas turbine engine  110 . The airfoil body  440  further includes a blade tip (not shown due to cross section) spaced apart radially outward from a blade root  443 , a leading edge  445 , and a trailing edge  447  opposite the leading edge  445 . The airfoil body  440  further includes a pressure side external surface  451 , and a suction side external surface  453  opposite the pressure side  451  as shown  FIG.  11   . 
     The blade  436  is formed to include a first cavity  442  within the airfoil body  440  and a second cavity  444  within the airfoil body  440  that is spaced apart from the first cavity  442  in a direction of the blade thickness as shown in  FIG.  11   . Specifically, the airfoil body  440  defines a camber line  460  extending from the leading edge  445  to the trailing edge  447 . The first cavity  442  and the second cavity  444  are arranged on opposing sides of the camber line  460 . The at least one passageway  446  extends between the first cavity  442  and the second cavity  444  so as to intersect the camber line  460 . The damping fluid  450  is configured to move between the two cavities  442 ,  444  similar to the other embodiments described herein. 
     The cavities  442 ,  444  are formed similar to the cavities  42 ,  44 . The cavities  442 ,  444  are configured to be arranged at any location along the span of the blade  436 . In some embodiments, the cavities may be positioned at the mid-span position or at the tip for midspan or tip bending modes. The cavities  442 ,  444  may also be tailored for torsion in this way. In some embodiments, the cavities  442 ,  444  are arranged near the root  443  where there is a larger blade thicknesses available to accommodate the cavities  442 ,  444 . In some embodiments, the cavities  442 ,  444  are effective even if the cavities are formed in part of the blade, for example in the hub, to produce an effect. As discussed above, the cavities  442 ,  444  may be located within the blade  436  at any location that accommodates specific deflection, bending, and/or torsion of the blade  436 . 
     A method includes a first operation of forming an airfoil having a leading edge, a trailing edge opposite the leading edge, a pressure side, and a suction side opposite the pressure side. The method further includes a second operation of forming a first cavity within the airfoil and forming a second cavity within the airfoil, the second cavity being spaced apart from the first cavity. The method further includes a third operation of at least partially filling at least one of the first cavity and the second cavity with a damping fluid. 
     The method further includes a fourth operation of forming at least one passageway extending between and fluidly interconnecting the first cavity and the second cavity. The method further includes a fifth operation of inducing a modal response in the airfoil such that the damping fluid moves at least partially from one of (i) the first cavity to the second cavity and (ii) the second cavity to the first cavity so as to damp the airfoil and attenuate the modal response. 
     The present disclosure relates to reducing flutter effects induced into blades  16 ,  36 ,  136 ,  236 ,  336  during operation of the gas turbine engine  110 . Flutter is a common aeromechanic phenomenon that may lead to excessive airfoil vibratory stress and eventual airfoil failure. These flutter affects may be difficult to accommodate when combined with other airfoil requirements, and the frequency of the rotor may also be difficult to assess and verify until the overall designs are complete. 
     To combat the flutter affects, the illustrative embodiments include attenuating modal response of the blades  16 ,  36 ,  136 ,  236 ,  336  by forming cavities  22 ,  24 ,  42 ,  44 ,  122 ,  124 ,  242 ,  244 ,  342 ,  344  within the blades  16 ,  36 ,  136 ,  236 ,  336  such that damping fluid  30 ,  50 ,  130 ,  250 ,  3501   450  disposed within the cavities  22 ,  24 ,  42 ,  44 ,  122 ,  124 ,  242 ,  244 ,  342 ,  344  may flow therebetween. When the blade  16 ,  36 ,  136 ,  236 ,  336  deforms or vibrates, the mode shape motion drives the damping fluid  30 ,  50 ,  130 ,  250 ,  3501   450  to pass from one cavity to another cavity. This motion damps the blade  16 ,  36 ,  136 ,  236 ,  336  and thus attenuates the modal response. 
     Because the cavities  22 ,  24 ,  42 ,  44 ,  122 ,  124 ,  242 ,  244 ,  342 ,  344  are applied through the blade  16 ,  36 ,  136 ,  236 ,  336  thickness, the airfoil shape of the blade  16 ,  36 ,  136 ,  236 ,  336  may be maintained without affecting the aerodynamics of the blade  16 ,  36 ,  136 ,  236 ,  336 . An additional benefit of the present disclosure may include modifying an existing blade to include the described cavities with damping fluid that, when in operation, achieve the desired frequency without affecting the existing aerodynamic airfoil shape of the blades  16 ,  36 ,  136 ,  236 ,  336 . Moreover, the rotor  10  may be designed with a combination of blades  16 ,  36 ,  136 ,  236 ,  336  that generate mistuned blades and further reduce flutter effects. 
     While the disclosure has been illustrated and described in detail in the foregoing drawings and description, the same is to be considered as exemplary and not restrictive in character, it being understood that only illustrative embodiments thereof have been shown and described and that all changes and modifications that come within the spirit of the disclosure are desired to be protected