Patent Description:
Integrally bladed rotors (IBRs) are used in some gas turbine engine applications, and include a unitary structure that includes a hub from which a plurality of non-removable circumferentially arranged rotor blades radially extend. IBRs eliminate the need for individual blade attachments. IBRs have been used for both fan and compressor applications in (e.g., turbofan) gas turbine engines. The rotor blades of IBRs may be subjected to stresses during gas turbine engine operation. Because IBR rotor blades are integrally formed with the rotor hub, the stress field may extend into the rotor hub from which the blades extend.

A prior art integrated bladed rotor having the features of the preamble of claim <NUM> is disclosed in <CIT>. <CIT> also discloses a prior art integrated bladed rotor.

One aspect of the present invention provides an integrated bladed rotor of a gas turbine engine in accordance with claim <NUM>.

In an embodiment, a majority of the groove is parallel to an expected flow direction of a fluid interacting with the airfoil.

In an embodiment of any of the previous embodiments, an axial vector component of an orientation of the groove is greater than a radial vector component of the orientation of the groove.

In an embodiment of any of the previous embodiments, part of the groove is parallel to the runout of the root fillet at an intersection of the root fillet with the airfoil.

In an embodiment of any of the previous embodiments, a majority of the groove is parallel to the runout of the root fillet at an intersection of the root fillet with the airfoil.

In an embodiment of any of the previous embodiments, the airfoil has a pressure side and a suction side; the groove includes a first groove segment on the pressure side; the suction side includes a second groove segment; and a depth of the second groove segment on the suction side is smaller than a depth of the first groove segment on the pressure side. In some embodiments, the groove includes the second groove segment.

In an embodiment of any of the previous embodiments, the airfoil has a pressure side and a suction side; and the groove extends from the pressure side to the suction side of the airfoil.

In an embodiment of any of the previous embodiments, the groove extends completely around the airfoil; and the groove has a uniform depth.

In an embodiment of any of the previous embodiments, the airfoil has a leading edge; and the airfoil is devoid of the groove at the leading edge of the airfoil.

In an embodiment of any of the previous embodiments, the airfoil has a chord extending from a leading edge to a trailing edge of the airfoil; and the groove is interrupted in a mid-chord region of the airfoil.

In an embodiment of any of the previous embodiments, the root fillet has a radial height relative to the rotation axis; and the groove is disposed radially outward of the root fillet, and radially inward of a distance of two times the radial height of the root fillet from the root fillet.

In an embodiment of any of the previous embodiments, the groove has a depth measured from the outer surface of the airfoil and a width transverse to a longitudinal axis of the groove; and the depth of the groove is equal to or less than half of the width of the groove.

In an embodiment of any of the previous embodiments, a cross-sectional profile of the groove is a circular segment.

A further aspect of the present invention provides a gas turbine engine in accordance with claim <NUM>.

The present disclosure relates to mitigating crack propagation in integrated bladed rotors of gas turbine engines. In some embodiments, the mitigation of crack propagation in integrated bladed rotors may be achieved by way of a streamwise groove (e.g., depression, notch) formed on an outer surface of an airfoil of one or more blades of the integrated bladed rotor. The groove may be configured to influence crack propagation to reduce the risk of a large and uncontained fragment of the integrated bladed rotor being released from the integrated bladed rotor due to fracture during operation of the gas turbine engine.

Aspects of various embodiments are described below through reference to the drawings.

The term "connected" may include both direct connection in which two elements contact each other and indirect connection in which at least one additional element is located between the two elements. The term "substantially" as used herein may be applied to modify any quantitative representation which could permissibly vary without resulting in a change in the basic function to which it is related.

<FIG> illustrates gas turbine engine <NUM> (referred hereinafter as "engine <NUM>") of a type preferably provided for use in subsonic flight, generally comprising in serial flow communication, fan <NUM> through which ambient air is propelled, a (e.g., multistage) compressor <NUM> for compressing the air, combustor <NUM> in which the compressed air is mixed with fuel and ignited for generating a(n) (e.g., annular) stream of hot combustion gas, and turbine section <NUM> for extracting energy from the combustion gas.

In some embodiments, compressor <NUM> may include one or more integrated bladed rotors such as integrated bladed rotor <NUM> (referred herein after as "IBR <NUM>") as described herein. IBR <NUM> may be rotatable about rotation axis RA during operation of engine <NUM>. In some embodiments of engine <NUM>, rotation axis RA may correspond to a central axis of engine <NUM>. In various embodiments, IBR <NUM> may be part of a high-pressure spool, or may be part of a low-pressure spool of engine <NUM>. In some embodiments of engine <NUM>, fan <NUM> may instead or in addition also be an integrated bladed rotor as described herein. Even though <FIG> shows engine <NUM> being of the turbofan type, it is understood that aspects of the present disclosure are also applicable to other (e.g., turboshaft, turboprop) types of gas turbine engines.

Compressor <NUM> may define gas path <NUM> of the core of engine <NUM>. Gas path <NUM> may be defined by and be disposed between a radially inner shroud and a radially outer shroud of compressor <NUM>. Gas path <NUM> may have an annular configuration and may extend around rotation axis RA. Gas path <NUM> may extend principally axially at the location of IBR <NUM>. IBR <NUM> may be used as an airfoil-based axial compressor in engine <NUM> and may compress and convey the air toward combustor <NUM> during operation of engine <NUM>. The air being compressed through gas path <NUM> in the region of IBR <NUM> may flow principally parallel to rotation axis RA (i.e., axially). <FIG> shows an expected flow direction F of the air interacting with one or more blades of IBR <NUM> during operation of engine <NUM>.

<FIG> is a perspective view of an exemplary representation of IBR <NUM> of engine <NUM>. IBR <NUM> may be a monolithic component (i.e., unitary structure) that includes hub <NUM> from which one or more (i.e., a plurality) of non-removable circumferentially arranged rotor blades <NUM> radially extend. In other words, blades <NUM> may be integral (e.g., integrally formed) with hub <NUM> so that IBR <NUM> may be devoid of individual releasable blade attachments between blades <NUM> and hub <NUM>. IBR <NUM> may also be referred to as a bladed disk ("blisk"), or a bladed ring ("bling").

Hub <NUM> and the entire IBR <NUM> may have rotation axis RA. Hub <NUM> may have radially outer platform <NUM> (also referred to as a "rim" of IBR <NUM>) relative to rotation axis RA. Platform <NUM> may define part of gas path <NUM> shown in <FIG>. For example, platform <NUM> may define part of the radially inner shroud of gas path <NUM> defined by compressor <NUM>. Blades <NUM> may extend radially outwardly from platform <NUM>. It is understood that the term "radially outwardly" includes directions that are principally radially outward and not necessarily purely radially outward. For example, it is understood that blades <NUM> may be tilted and may not necessarily extend purely radially from hub <NUM>.

<FIG> also shows an exemplary airfoil stacking line S, which is a reference line commonly used to designate the position in space of planar cross sections of a rotor blade such as one of blades <NUM> where the rotor blade may generally lie along stacking line S. Airfoil stacking line S may extend radially from rotation axis RA and may provide a frame of reference for a corresponding one of blades <NUM>, and for other elements mentioned herein.

<FIG> is a side elevation view of an exemplary blade <NUM> of IBR <NUM>. The embodiment shown in <FIG> is outside the wording of the claims, but illustrates features of the invention as exemplified in <FIG>. Blade <NUM> is viewed in <FIG> along a direction normal to a plane containing both rotation axis RA and stacking line S. <FIG> also shows an axial cross-section of part of hub <NUM> from which blade <NUM> extends. Blade <NUM> includes airfoil <NUM> and root fillet <NUM> providing a smooth transition between platform <NUM> of hub <NUM> and airfoil <NUM>. Airfoil <NUM> is disposed radially outward of root fillet <NUM>. Root fillet <NUM> defines a concave outer surface extending from platform <NUM> of hub <NUM> to airfoil <NUM>. Root fillet <NUM> and airfoil <NUM> have a surface continuity so that an outer surface of airfoil <NUM> and an outer surface of root fillet <NUM> are touching at one or more locations. Root fillet <NUM> and airfoil <NUM> have a tangent (angular) surface continuity at one or more (e.g., all) locations where outer surfaces of root fillet <NUM> and airfoil <NUM> meet along a common edge and that the tangent plane at each point along the common edge is equal for both outer surfaces. The common edge between root fillet <NUM> and airfoil <NUM> also corresponds to runout <NUM> of root fillet <NUM>. In some embodiments, root fillet <NUM> may be a circular fillet and may be specified by one or more radii values. In various embodiments, root fillet <NUM> may have a uniform or a varied radius around blade <NUM>.

Airfoil <NUM> may include leading edge <NUM> and trailing edge <NUM>. Leading edge <NUM> may be disposed forward of trailing edge <NUM> relative to the general streamwise flow direction F of air interacting with airfoil <NUM>. Airfoil <NUM> may include pressure side <NUM> and an opposite suction side <NUM> (shown in <FIG>).

Airfoil <NUM> includes streamwise groove <NUM> formed into an exterior surface of airfoil <NUM>. Groove <NUM> is entirely disposed outside of root fillet <NUM>. In other words, groove <NUM> is not part of root fillet <NUM>. Groove <NUM> is disposed radially outward of root fillet <NUM> and spaced apart from root fillet <NUM>, as shown in <FIG>.

Groove <NUM> may have a longitudinal axis L and may extend substantially along the streamwise direction of the air being conveyed in gas path <NUM> and interacting with airfoil <NUM>. In some embodiments, some or at least a majority of longitudinal axis L may be substantially parallel to the expected flow direction F at corresponding axial locations along rotation axis RA. In some embodiments, the expected flow direction F of air interacting with airfoil <NUM> in the region of groove <NUM> may be related (e.g., parallel) to the axial cross-sectional profile of platform <NUM> shown in <FIG>. In some embodiments, the expected flow direction F of air interacting with airfoil <NUM> the region of groove <NUM> may be related (e.g., parallel) to runout <NUM> of root fillet <NUM>. For example, in some embodiments, some or a majority of groove <NUM> may be parallel to runout <NUM> of root fillet <NUM>.

The streamwise orientation of groove <NUM> may provide a desired influence on crack propagation while providing little or minimal influence on the flow of air interacting with airfoil <NUM>. In other words, at least part(s) of groove <NUM> may be oriented to be streamlined in order to offer low resistance to the flow of air through compressor <NUM>. For example, in some embodiments, some, a majority, or an entirety of groove <NUM> may be parallel to the expected flow direction F of air (or of another working fluid) interacting with airfoil <NUM>.

The expected flow direction F of air interacting with airfoil <NUM> may differ at different axial and/or radial locations of airfoil <NUM> depending on the geometric parameters of IBR <NUM>, and/or based on operating parameter(s). The expected flow direction F selected for the purpose of orienting groove <NUM> may be selected to obtain a desired performance at one or more operating conditions. In some embodiments, an axial vector component of longitudinal axis L of groove <NUM> may be greater than a radial vector component of longitudinal axis L of groove <NUM>. Longitudinal axis L of groove <NUM> may also have a lateral vector component (e.g., into or out of the page in <FIG>) that may be based on the stagger angle of blade <NUM>. Longitudinal axis L of groove <NUM> may be linear or non-linear.

In various embodiments, groove <NUM> may extend partially or completely around airfoil <NUM>. In other words, groove <NUM> may extend partially or completely around stacking line S. For example, groove <NUM> may extend on pressure side <NUM> and/or on suction side <NUM> of airfoil <NUM>. In some embodiments, groove <NUM> may wrap around leading edge <NUM> and/or trailing edge <NUM>. In some embodiments, groove <NUM> may extend continuously (e.g., be uninterrupted) around airfoil <NUM>.

IBR <NUM> may be made from a suitable metallic material. In various embodiments, IBR <NUM> may be made by casting, machining and/or using other suitable manufacturing process(es). For example, groove <NUM> may be cast with the remainder of IBR <NUM> or maybe formed a machining operation subsequent to casting. For example, IBR <NUM>, including groove <NUM> may be machined from a casting, forging or bar stock.

<FIG> is a cross-section view of part of the blade <NUM> and hub <NUM> of <FIG> taken along line <NUM>-<NUM> in <FIG>, but <FIG> shows groove <NUM> in accordance with the invention. Groove <NUM> may extend from pressure side <NUM> to suction side <NUM> of airfoil <NUM>. In some embodiments, groove <NUM> may extend completely around airfoil <NUM>. For example, pressure side <NUM> may include first groove segment 42A, and suction side <NUM> may include second groove segment 42B where both first groove segment 42A and second groove segment 42B are part of the same groove <NUM>. Alternatively, only one of pressure side <NUM> or suction side <NUM> may include groove <NUM>. Alternatively, both pressure side <NUM> and suction side <NUM> may include respective and separate groove segments 42A, 42B in cases where groove <NUM> does not continuously extend from pressure side <NUM> to suction side <NUM>. In some embodiments, airfoil <NUM> may include groove segments 42A, 42B that are at different spanwise (e.g., radial) locations along airfoil <NUM>.

Groove <NUM> may have any suitable cross-sectional profile and size to provide a desired stress concentration that provide the desired influence on crack propagation. In some embodiments, a cross-sectional profile of groove <NUM> transverse to longitudinal axis L (shown in <FIG>) of groove <NUM> may be a circular segment, or may be another suitable shape (e.g., U-shaped or V-shaped). Such circular segment may be a region (e.g., area A) of two-dimensional space that is bounded by an arc of a circle and by a chord connecting the endpoints of the arc. Groove <NUM> may have depth D measured from the outer surface of airfoil <NUM>, and width W measured transversely to longitudinal axis L of groove <NUM>. In some embodiments, depth D of groove <NUM> may be equal to or less than <NUM>% of width W of groove <NUM>. In some embodiments, depth D of groove <NUM> may be equal to or greater than <NUM>% of width W of groove <NUM>. In some embodiments, depth D of groove <NUM> may be between <NUM>% and <NUM>% of width W of groove <NUM>.

In various embodiments, groove <NUM> may have a uniform (constant) or a varied area along a length (longitudinal axis L) of groove <NUM>. For example, groove <NUM> may have area A on pressure side <NUM> that is different from area A of groove <NUM> on suction side <NUM>. In some embodiments, area A of groove <NUM> on suction side <NUM> may be smaller than area A of groove <NUM> on pressure side <NUM> for preferred aerodynamic performance.

In various embodiments, groove <NUM> may have a uniform (constant) or a varied depth D along a length (longitudinal axis L) of groove <NUM>. For example, groove <NUM> may have depth D on pressure side <NUM> that is different from depth D of groove <NUM> on suction side <NUM>. In some embodiments, depth D of groove <NUM> on suction side <NUM> may be smaller than depth D of groove <NUM> on pressure side <NUM>.

In various embodiments, groove <NUM> may have a uniform (constant) or a varied width W along a length (longitudinal axis L) of groove <NUM>. For example, groove <NUM> may have width W on pressure side <NUM> that is different from width W of groove <NUM> on suction side <NUM>. In some embodiments, width W of groove <NUM> on suction side <NUM> may be smaller than width W of groove <NUM> on pressure side <NUM>.

In some embodiments, airfoil <NUM> may include a plurality of groove segments 42A, 42B connected together and having different cross-sectional dimensions. In some embodiments, airfoil <NUM> may include a plurality of disconnected groove segments 42A, 42B that have the same or different cross-sectional dimensions.

Root fillet <NUM> provides a transition between outer platform <NUM> of hub <NUM> and airfoil <NUM>. Root fillet <NUM> and airfoil <NUM> have surface and tangent continuity. Root fillet <NUM> may have a radial height H from platform <NUM> measured radially relative to rotation axis RA. Radial height H may correspond to a maximum radial height of root fillet <NUM> from platform <NUM>. Radial height H may be measured from platform <NUM> to runout <NUM> of root fillet <NUM>. Depending on the geometry of blade <NUM>, runout <NUM> may not necessarily be at a uniform radial height H around airfoil <NUM>. Runout <NUM> defines a radially inner extremity of airfoil <NUM>. Accordingly, groove <NUM> is disposed radially outward of root fillet <NUM>. In some examples outside the wording of the claims, groove <NUM> and root fillet <NUM> may be adjoining as shown in <FIG>. Groove <NUM> is radially spaced apart from root fillet <NUM> as shown by non-zero dimension G in <FIG>. In various embodiments, groove <NUM> may be disposed anywhere along radial region RR of airfoil <NUM>, but spaced apart from runout <NUM>. Radial region RR may extend from radially outward from runout <NUM> of root fillet <NUM> to a distance of two or three times radial height H of root fillet <NUM>. In other words, groove <NUM> is disposed radially outwardly of root fillet <NUM> and may be radially inwardly of a distance of two or three times (i.e., <NUM> or <NUM>) radial height H of root fillet <NUM> from root fillet <NUM>.

In some embodiments, every blade <NUM> of IBR <NUM> may each include an identical groove <NUM> to facilitate balancing of IBR <NUM>. However, adequate balancing IBR <NUM> may also be achieved in other embodiments where not every blade <NUM> includes groove <NUM>, or where some blades <NUM> of the same IBR <NUM> include grooves of different configurations.

<FIG> is an axial cross-section view of part of another exemplary integrated bladed rotor, outside the wording of the claims, including one or more exemplary blades <NUM> and platform <NUM>. Blade <NUM> and platform <NUM> may include elements previously described above. Like elements have been identified using reference numerals incremented by <NUM>. Blade <NUM> may include airfoil <NUM> and root fillet <NUM> providing a smooth transition between platform <NUM> of hub <NUM> and airfoil <NUM>. Root fillet <NUM> may include runout <NUM> at the intersection of root fillet <NUM> and airfoil <NUM>. Airfoil <NUM> may be disposed radially outward of root fillet <NUM>. Airfoil <NUM> may include leading edge <NUM> and trailing edge <NUM>. Airfoil <NUM> may include pressure side <NUM> and opposite suction side <NUM>.

In some applications, the stresses at leading edge <NUM> of airfoil <NUM> may be relatively high, and may be higher than the stresses in other region(s) of airfoil <NUM>. Leading edge <NUM> may also be more susceptible to impact by foreign objects ingested by engine <NUM>. Accordingly, in some situations, it may be desirable to have reduced or no groove-associated stress concentrations at and/or near leading edge <NUM> of airfoil <NUM>. In some embodiments, the configuration of groove <NUM> may differ at and/or near leading edge <NUM> than in other regions of airfoil <NUM>. In some embodiments, groove <NUM> may be smaller (e.g., smaller area A shown in <FIG>) at and/or near leading edge <NUM> to provide a reduced stress concentration factor at and/or near leading edge <NUM> relative to other regions of airfoil <NUM>. In some embodiments, groove <NUM> may be interrupted at and/or near leading edge <NUM> of airfoil <NUM>. In other words, airfoil <NUM> may be devoid of groove <NUM> at and/or near leading edge <NUM> of airfoil <NUM>.

<FIG> is an axial cross-section view of part of another exemplary integrated bladed rotor, outside the wording of the claims, including one or more exemplary blades <NUM> and platform <NUM>. Blade <NUM> and platform <NUM> may include elements previously described above. Like elements have been identified using reference numerals incremented by <NUM>. Blade <NUM> may include airfoil <NUM> and root fillet <NUM> providing a smooth transition between platform <NUM> of hub <NUM> and airfoil <NUM>. Root fillet <NUM> may include runout <NUM> at the intersection of root fillet <NUM> and
airfoil <NUM>. Airfoil <NUM> may be disposed radially outward of root fillet <NUM>. Airfoil <NUM> may include leading edge <NUM> and trailing edge <NUM>. Airfoil <NUM> may include pressure side <NUM> and opposite suction side <NUM>. Airfoil <NUM> may also include exemplary chord C joining leading edge <NUM> and trailing edge <NUM> of airfoil <NUM>.

In some applications, the stresses at a mid-chord region MC of airfoil <NUM> may be relatively high, and may be higher than the stresses in other region(s) of airfoil <NUM>. Accordingly, in some situations, it may be desirable to have reduced or no groove-associated stress concentrations in mid-chord region MC of airfoil <NUM>. In some embodiments, the cross-sectional profile of groove <NUM> may vary as a function of a position along chord C or as a function of an axial position along rotation axis RA. In some embodiments, the configuration of groove <NUM> may differ in mid-chord region MC of airfoil <NUM> compared to other regions of airfoil <NUM>. In some embodiments, groove <NUM> may be smaller (e.g., smaller area A shown in <FIG>) in mid-chord region MC of airfoil <NUM> to provide a reduced stress concentration factor in mid-chord region MC of airfoil <NUM>. In some embodiments, groove <NUM> may be interrupted in mid-chord region MC of airfoil <NUM>. In other words, airfoil <NUM> may be devoid of groove <NUM> in mid-chord region MC of airfoil <NUM>.

<FIG> is a schematic axial cross-section view of part of an exemplary integrated bladed rotor 20A (referred hereinafter as "IBR 20A") without crack-mitigating groove <NUM>. <FIG> is a schematic axial cross-section view of part of IBR <NUM> with crack-mitigating groove <NUM>. In operation, compressor blades <NUM> may be subjected to a steady stress associated with low-cycle-fatigue (LCF) as a result of centrifugal and thermal loads. Compressor blades <NUM> may also be subjected to vibratory stresses associated with high-cycle-fatigue (HCF) occurring at resonance conditions for example. When the useful life of blade <NUM> is exhausted and a fatigue crack is initiated on airfoil <NUM> for example, damage tolerance methods and tools may be used to determine the remaining crack propagation life and trajectory of the crack leading up to failure. The trajectory of the propagating crack may be important for determining the potential size, shape, and mass of the fragment that will be released from IBR 20A, <NUM>. For a crack that originates from airfoil <NUM>, the resulting fragment upon failure can be classified either as either a relatively benign blade release which may be contained by the casing of engine <NUM> surrounding IBR 20A, or as a disc rupture (i.e., large fragment) which may be more troublesome and may not be contained by the casing.

The trajectory of a propagating crack may be a function of the combined LCF-HCF stress field. Mathematically, the combined LCF-HCF stress field may be represented as a vector summation of the individual LCF and HCF crack growth contributions (e.g., LCF + ΣHCF). In general, LCF loads dominated by radial centrifugal loading may tend to grow the crack parallel to gas path <NUM> (shown in <FIG> and <FIG>), thereby promoting a containable blade release failure mode.

On the other hand, HCF loads may exhibit more complex stress fields and may occur at resonance conditions. For resonance modes with significant airfoil-hub participation, there is potential for the resulting dynamic stress field to grow the crack into hub <NUM>. Even if the magnitude of the dynamic stresses are low in comparison to the steady stresses, the resulting modal frequency and accumulated HCF cycles may amplify the HCF vector (i.e., ΣHCF). In such case, the resulting failure mode may be an uncontained disc rupture.

The addition of groove <NUM> in airfoil <NUM> radially outward of root fillet <NUM> may influence crack propagation by discouraging the crack originating on airfoil <NUM> from growing into hub <NUM>. In other words, the presence of groove <NUM> may influence crack propagation to promote a contained blade release as opposed to a disc rupture.

Groove <NUM> may serve this function by introducing stress concentration factor K in the radial flow stress direction as well as an increase in the local nominal stresses. This helps in favouring the LCF contribution of crack growth, which is predominately caused by radial stresses. Groove <NUM> may also amplify the radial stress contribution of the HCF stress field. Both these changes to the stress field may favour a blade release as opposed to a disc rupture.

Groove <NUM> may be used on compressor IBR <NUM> where the resulting airfoil steady stresses are low in comparison to dynamic stresses and the corresponding LCF lives are high. Groove <NUM> may be designed and positioned such that it does not produce a new critical lifing location and the minimum life of the IBR <NUM> is not significantly altered. For example, groove <NUM> may be added to airfoil <NUM> without altering a typical or desired root fillet geometry.

Claim 1:
An integrated bladed rotor (<NUM>) for a gas turbine engine (<NUM>), the integrated bladed rotor (<NUM>) comprising:
a hub (<NUM>) having a rotation axis (RA) and a radially outer platform (<NUM>) relative to the rotation axis (RA); and
a plurality of blades (<NUM>) extending radially outwardly from the platform (<NUM>) of the hub (<NUM>), the blades (<NUM>) being integrally formed with the hub (<NUM>) to define a monolithic component with the hub (<NUM>), each blade (<NUM>) including:
an airfoil (<NUM>) including a groove (<NUM>) formed in an outer surface of the airfoil (<NUM>); and
a root fillet (<NUM>) providing a transition between the outer platform (<NUM>) of the hub (<NUM>) and the airfoil (<NUM>), the root fillet (<NUM>) defining a concave surface extending from the outer platform (<NUM>) of the hub (<NUM>) to the airfoil (<NUM>),
wherein the groove (<NUM>) is disposed radially outward of the root fillet (<NUM>), characterised in that:
the groove (<NUM>) is radially spaced apart from a runout (<NUM>) of the root fillet (<NUM>) where an outer surface of the root fillet (<NUM>) and the outer surface of the airfoil (<NUM>) meet along a common edge, and the root fillet (<NUM>) and the airfoil (<NUM>) have tangent surface continuity at one or more locations along the common edge.