Unducted propulsion system
Apparatuses and systems are provided herein for unducted propulsion systems. The system includes a forward housing for high efficiency for high subsonic sustained flight. A plurality of blades are affixed to the forward housing, wherein the forward housing defines a flowpath curve extending from the forward-most end of the forward housing through the axial extent of a forward blade root. The flowpath curve is described by an axial direction parallel to an axis of rotation and a radius from the axis of rotation. The flowpath curve includes a first point having a first radius where the radius reaches a maximum forward of the forward blade root and a second point aft of the first point having a second radius where the radius stops decreasing. The ratio of the first radius to the second radius is greater than or equal to 1.029.
1. An unducted propulsion system comprising:
a forward blade assembly comprised of a plurality of forward blades;
an aft blade assembly comprised of a plurality of aft blades;
a forward housing having an external surface;
an aft housing;
wherein for each forward blade and each aft blade comprises a blade root proximal to an axis of rotation and a blade tip distal from the axis of rotation;
wherein a flowpath curve corresponds to an intersection of the external surface of the forward housing with a plane containing the axis of rotation and a forward-most point of a forward blade root;
wherein, for the flowpath curve, radius, r, is a first perpendicular distance from the axis of rotation;
wherein a bulge location with radius r 1 on the flowpath curve is located by proceeding forward from the forward-most point on the forward blade root to a location where a first radius reaches a maximum;
wherein a local minimum with radius r 2 on the flowpath curve is located by proceeding aft from the bulge location to a nearest point where a second radius stops decreasing within an axial extent of the forward blade root;
wherein ratio r 1 /r 2 >1.029;
wherein the forward blade assembly and the forward housing rotate about the axis of rotation, wherein the aft blade assembly and the aft housing are stationary, and wherein the radius r 1 and the radius r 2 are effective radii, each corresponding to a circle that has the same cross-sectional area as the forward housing in a plane normal to the axis of rotation; and
wherein, for the flowpath curve, an axial direction, z, is parallel to the axis of rotation;
and wherein an axial distance z 1 is between the bulge location and the local minimum; and wherein
z
1
r
2
<
1.522
.
2. The unducted propulsion system of claim 1 , wherein an axial distance Z 2 is between a forward-most end of the forward housing and the local minimum, and
wherein ratio z 2 /r 2 <4.115.
3. The unducted propulsion system of claim 2 , wherein an aircraft is configured for cruise flight Mach number 0.74<M 0 <0.86; wherein
r
1
r
2
=
(
A
2
-
1
)
M
0
-
0.6
0.19
+
1
,
where 1.04<A 2 <1.14.
4. The unducted propulsion system of claim 3 , wherein an axial distance Z 1 is between the bulge location and the local minimum; and wherein
z
1
r
2
=
B
2
(
M
0
0
.
7
9
)
3
,
where 0.78<B2<1.18.
5. The unducted propulsion system of claim 4 , wherein
z
2
r
2
=
C
2
(
M
0
0.79
)
3
,
where 2.19<C2<3.19.
6. The unducted propulsion system of claim 5 , wherein 1.06<A2<1.14.
7. The unducted propulsion system of claim 6 , wherein 0.78<B2<1.08.
8. The unducted propulsion system of claim 7 , wherein 2.19<C2 <2.99.
9. The unducted propulsion system of claim 8 , wherein 1.06<A2<1.12.
10. The unducted propulsion system of claim 9 , wherein 0.88<B2<1.08.
11. The unducted propulsion system of claim 10 , wherein 2.39<C2<2.99.
12. The unducted propulsion system of claim 2 , wherein an aircraft is configured for dimensionless cruise thrust parameter,
F
net
ρ
0
V
0
2
A
an
,
where at cruise operation
i. F net is fan net thrust,
ii. ρ 0 is ambient air density,
iii. V 0 is flight velocity,
iv. A an is fan stream tube annular area entering a fan, and
F
net
ρ
0
V
0
2
A
an
>
0.06
.
13. The unducted propulsion system of claim 12 , wherein
F
net
ρ
0
V
0
2
A
an
>
0.08
.
14. The unducted propulsion system of claim 2 , wherein a number of blades in the forward blade assembly is greater than 4, wherein a number of blades in the aft blade assembly is greater than 4, and wherein a ratio of the number of blades in the forward blade assembly to the number of blades in the aft blade assembly is between 2:5 and 2:1.
15. The unducted propulsion system of claim 14 , wherein the number of blades in the forward blade assembly is between 8 and 18.
16. The unducted propulsion system of claim 15 , wherein a difference between the number of blades in the forward blade assembly to the number of blades in the aft blade assembly is between 2 and −2.
17. The unducted propulsion system of claim 2 , wherein a flowpath curve (z, r) coordinate system has origin at axial location of the local minimum with axial coordinate, z, increasing in a forward direction, wherein a curve forward of bulge (z>Z 1 ) wherein a lower bound lies within lower and upper bounds defined by
(
z
-
z
1
z
2
-
z
1
)
p
+
(
r
r
2
)
q
=
1
,
has exponents 1.5<p<2.0 and 2.0<q<3.0, and wherein an upper bound has exponents 2.0<p<3.0 and 3.0<q<3.5.
18. The unducted propulsion system of claim 17 , wherein the lower bound has exponents 1 .7<p<2.0 and 2.3<q<3.0, and wherein the upper bound has exponents 2.0<p<2.5 and 3.0<q<3.3.
19. An unducted propulsion system comprising:
a forward blade assembly comprised of a plurality of forward blades;
an aft blade assembly comprised of a plurality of aft blades;
a forward housing having an external surface;
an aft housing;
wherein for each forward blade and each aft blade comprises a blade root proximal to an axis of rotation and a blade tip distal from the axis of rotation;
wherein a flowpath curve corresponds to an intersection of the external surface of the forward housing with a plane containing the axis of rotation and a forward-most point of a forward blade root;
wherein, for the flowpath curve, radius, r, is a first perpendicular distance from the axis of rotation;
wherein a bulge location with radius r 1 on the flowpath curve is located by proceeding forward from the forward-most point on the forward blade root to a location where a first radius reaches a maximum;
wherein a local minimum with radius r 2 on the flowpath curve is located by proceeding aft from the bulge location to a nearest point where a second radius stops decreasing within an axial extent of the forward blade root;
wherein ratio r 1 /r 2 >1.029;
wherein the forward blade assembly and the forward housing are stationary, and wherein the aft blade assembly and a portion of the aft housing to which the plurality of aft blades are attached rotate about the axis of rotation; and
wherein, for the flowpath curve, an axial direction, z, is parallel to the axis of rotation;
and wherein an axial distance z 1 is between the bulge location and the local minimum; and whereir
z
1
r
2
<
1.522
.
20. The unducted propulsion system of claim 19 , wherein the flowpath curve further corresponds to respective forward-most points of two or more forward blade roots.
21. The unducted propulsion system of claim 19 , wherein the flowpath curve further corresponds to respective forward-most points of at least half of forward blade roots.