Airfoils for gas turbine engines

A gas turbine engine, comprising:

• a turbomachine comprising a compressor section, a combustion section, and a turbine section arranged in serial flow order along a centerline axis, the compressor section comprising an airfoil, the airfoil including a leading edge, a trailing edge opposite the leading edge, a first sidewall extending between the leading edge and the trailing edge, a second sidewall extending between the leading edge and the trailing edge opposite the first sidewall, an airfoil root, and an airfoil tip opposite the airfoil root;
• wherein the airfoil is configured to rotate at a rotational speed (Ω) in radians per second;
• wherein the airfoil defines:
• an airfoil radius (R) in feet between the centerline axis and the airfoil tip,
• a span height (H) in feet between the airfoil root and the airfoil tip, a ratio of the span height (H) divided by the airfoil radius (R) is greater than or equal to 0.178 and less than or equal to 0.624,
• a leading edge thickness (TL) in feet between the first sidewall and the second sidewall, a ratio of the leading edge thickness (TL) divided by the airfoil radius (R) is greater than or equal to 0.002 and less than or equal to 0.006,
• an airfoil length (Lairfoil) in feet extending between the leading edge and the trailing edge, a ratio of the airfoil length (Lairfoil) divided by the airfoil radius (R) is greater than or equal to 0.170 and less than or equal to 0.452,
• a maximum thickness (Tmax) in feet between the first sidewall and the second sidewall, a ratio of the maximum thickness (Tmax) divided by the airfoil radius (R) is greater than or equal to 0.006 and less than or equal to 0.012,
• a tip speed (Utip) equal to Ω×R, the tip speed (Utip) greater than or equal to 1,267 feet/second and less than or equal to 1,800 feet/second, and
• an airfoil thickness parameter (ATP) determined as follows:
• H
• *
• T
• L
• L
• airfoil
• *
• T
• max
• ;
• wherein the airfoil thickness parameter (ATP) is greater than or equal to a lower bound of 0.3 and less than or equal to an upper bound of 1.4;
• wherein the lower bound and the upper bound are defined by a Beta Distribution (B) based on a ratio (x), a first constant (α), and a second constant (β), the Beta Distribution defined as:
• f
• ⁡
• (
• x
• ;
• α
• ,
• β
• )
• =
• 1
• B
• ⁡
• (
• α
• ,
• β
• )
• ⁢
• x
• α
• -
• 1
• (
• 1
• -
• x
• )
• β
• -
• 1
• ;
• wherein the ratio (x) is based on the tip speed (Utip) and the lower bound is defined by:
• 0
• .
• 7
• ⁢
• 9
• *
• [
• 1
• B
• ⁡
• (
• 1.9
• ,
• 2.4
• )
• ⁢
• (
• U
• t
• ⁢
• i
• ⁢
• p
• -
• 910
• 8
• ⁢
• 9
• ⁢
• 0
• )
• 0
• .
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• ⁢
• (
• 1
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• (
• U
• t
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• i
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• p
• -
• 910
• 8
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• 9
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• 0
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• )
• 1
• .
• 4
• ]
• ;
• and
• wherein the upper bound is defined by:
• 1
• .
• 4
• *
• [
• 1
• B
• ⁡
• (
• 1
• ⁢
• 8
• .5
• ,
• 43.5
• )
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• 0
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• 5
• 7
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• 6
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• 5
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• 7
• .
• 5
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• 42.5
• ]
• .