Airfoil profile for gas turbine engines
An airfoil assembly for a gas turbine engine includes at least two airfoils. Each airfoil of the at least two airfoils includes a leading edge, a trailing edge, a pressure side extending between the leading edge and the trailing edge, and a suction side opposite the pressure side. Each airfoil defines a chord line extending from the leading edge to the trailing edge along the pressure side, a suction side tangency point, a first reference line extending from the leading edge perpendicular to the chord line, a second reference line extending from the leading edge to the suction side tangency point, a camber line angle defined between the first reference line and the second reference line, and a solidity based on an axial width of the at least two airfoils and a pitch between adjacent ones of the at least two airfoils.
1 . A gas turbine engine defining a longitudinal centerline axis, comprising:
a compressor section;
a combustion section defining a combustion chamber; and
a turbine section, the turbine section comprising a plurality of stator vanes and a plurality of rotor blades, the plurality of stator vanes and the plurality of rotor blades each including a plurality of airfoils, each airfoil of the plurality of airfoils comprising a leading edge, a trailing edge, a pressure side, and a suction side opposite the pressure side;
wherein the plurality of airfoils define an airfoil type R, wherein the airfoil type R is equal to 1 for the plurality of airfoils forming the plurality of stator vanes of a first stage of the turbine section, and wherein the airfoil type R is equal to 2 for the plurality of airfoils forming the plurality of rotor blades of the first stage of the turbine section and the plurality of airfoils forming the plurality of stator vanes and the plurality of rotor blades of remaining stages of the turbine section;
wherein an airfoil of the plurality of airfoils defines:
a chord line extending from the leading edge to the trailing edge along the pressure side,
a suction side tangency point,
a first reference line extending from the leading edge perpendicular to the chord line,
a second reference line extending from the leading edge to the suction side tangency point,
a third reference line extending through the leading edge parallel to the longitudinal centerline axis,
a leading edge angle (μ LE ) between the third reference line and the second reference line,
a trailing edge reference circle centered on the trailing edge, the trailing edge reference circle intersecting the pressure side at a first point, intersecting the suction side at a second point, and defining a midpoint between the first point and the second point,
a fourth reference line extending from the midpoint to the trailing edge,
a fifth reference line extending through the trailing edge parallel to the longitudinal centerline axis,
a trailing edge angle (μ TE ) between the fourth reference line and the fifth reference line,
an arc length defined by a first length (a) and a second length (b), the second length (b) perpendicular to the first length (a), and
a camber line angle (λ) defined between the first reference line and the second reference line;
wherein the turbine section defines:
a solidity (σ) of the plurality of airfoils, the solidity (σ) is defined by an axial width (AW) of each of the plurality of airfoils and a pitch (P) of the plurality of airfoils, the solidity (σ) equal to
AW
P
,
an airfoil lift factor (Z) equal to:
(
2
σ
)
·
[
(
cos
μ
TE
2
)
·
(
tan
μ
LE
+
tan
μ
TE
)
]
,
a reference airfoil lift factor (Z ref ) based on the airfoil lift factor Z where the solidity σ is equal to 1, the reference airfoil lift factor (Z ref ) equal to:
2
cos
u
TE
2
(
tan
μ
LE
-
tan
μ
TE
)
,
an induced leading edge air angle (χ ind ) based on a reference airfoil lift factor (Z ref ) where the solidity (σ) is equal to 1, the induced leading edge air angle (χ ind ) equal to:
{
tan
-
1
[
z
ref
/
σ
2
cos
μ
TE
2
]
-
tan
μ
TE
}
-
μ
LE
,
an optimal leading edge droop factor (λ′), wherein λ=λ·χ ind ,
a first heat transfer factor (Nnd r ) based on a second heat transfer factor (Nnd c ) and a constant (b), the induced leading edge air angle (χ ind ), the second heat transfer factor (Nnd c d) equal to:
80.54
cos
(
χ
ind
)
0.612
)
2
+
(
193.64
·
b
·
sin
(
χ
ind
)
0.804
)
2
,
the first heat transfer factor (Nnd r ) equal to:
Nnd
c
Nnd
c
(
χ
ind
=
0
)
,
wherein the constant (b) is equal to 3 when the airfoil type R is equal to 1 and the constant (b) is equal to 4 when the airfoil type R is equal to 2, and
a leading edge droop effect (LEDE), the LEDE equal to:
Nnd
r
+
0.075
(
0.05
(
1
+
Rb
πλ
a
0.5
1
+
b
2
)
6
)
;
and
wherein
1
≤
LEDE
(
λ
′
=
1
)
LEDE
<
1
.332
.
2 . The gas turbine engine of claim 1 , wherein the solidity (σ) is greater than or equal to 0.3 and less than or equal to 0.85.
3 . The gas turbine engine of claim 1 , wherein the leading edge angle (μ LE ) is greater than or equal to 0° and less than or equal to 55°.
4 . The gas turbine engine of claim 1 , wherein the trailing edge angle (μ TE ) is greater than or equal to 40° and less than or equal to 80°.
5 . The gas turbine engine of claim 1 , wherein the optimal leading edge droop factor (λ′) is greater than or equal to 0.315 and less than or equal to 1.
6 . The gas turbine engine of claim 1 , wherein camber line angle (λ) is greater than or equal to 13.4 degrees and less than or equal to 83.45 degrees.
7 . The gas turbine engine of claim 1 , wherein a normalized camber line angle (nλ) is equal to: λ′·Z 0.25 .
8 . The gas turbine engine of claim 7 , wherein the normalized camber line angle (nλ) is greater than or equal to 0.358 and less than or equal to 1.189.
9 . The gas turbine engine of claim 1 , wherein:
the plurality of stator vanes and the plurality of rotor blades comprise a first plurality of stator vanes and a first plurality of rotor blades;
the turbine section comprises a first turbine stage including the first plurality of stator vanes and the first plurality of rotor blades and a second turbine second stage including a second plurality of stator vanes and a second plurality of rotor blades; and
the first plurality of stator vanes, the first plurality of rotor blades, the second plurality of stator vanes, and the second plurality of rotor blades include the plurality of airfoils.
10 . The gas turbine engine of claim 1 , wherein:
the turbine section comprises a first turbine stage including the plurality of stator vanes and the plurality of rotor blades;
the plurality of airfoils form the plurality of stator vanes of the first turbine stage such that the airfoil type R is equal to 1; and
the LEDE is equal to:
Nnd
r
+
0.075
(
0.05
(
1
+
1
·
3
·
πλa
0
.
5
1
+
3
2
)
6
)
.
11 . The gas turbine engine of claim 1 , wherein:
the plurality of stator vanes and the plurality of rotor blades comprise a first plurality of stator vanes and a first plurality of rotor blades;
the turbine section comprises a first turbine stage including the first plurality of stator vanes and the first plurality of rotor blades and a second turbine second stage including a second plurality of stator vanes and a second plurality of rotor blades; and
the plurality of airfoils form one or more of the first plurality of rotor blades, the second plurality of stator vanes, and the second plurality of rotor blades such that the airfoil type is equal to 2; and
the LEDE is equal to:
Nnd
r
+
0.075
(
0.05
(
1
+
2
·
4
·
πλa
0
.
5
1
+
4
2
)
6
)
.