Unducted propulsion system
Apparatuses and systems are provided herein for unducted propulsion systems. The system includes an aft housing for low drag for high subsonic sustained flight. A plurality of blades are affixed to the aft housing, wherein the housing defines a flowpath curve extending from the axial extent of the aft blade root to the aft end of the aft housing. 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 first point having a first radius where the radius reaches a maximum aft of the aft blade root and a second point forward 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 1.081.
1. An unducted propulsion system for an aircraft configured for high subsonic cruise comprising:
an axis of rotation;
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;
an aft housing;
wherein each forward blade comprises a forward blade root proximal to the axis of rotation and a forward blade tip distal from the axis of rotation;
wherein each aft blade comprises an aft blade root proximal to the axis of rotation and an aft blade tip distal from the axis of rotation;
wherein a flowpath curve corresponds to an intersection of an external surface of the aft housing with a plane containing the axis of rotation and an aft-most point of the aft blade root;
wherein for the flowpath curve, an axial direction, z, is parallel to the axis of rotation and radius, r, is distance from the axis of rotation;
wherein a bulge location with radius r b on the flowpath curve is found by proceeding aft from the aft-most point on the aft blade root to where a first radius reaches a maximum;
wherein a local minimum with radius r h on the flowpath curve is found by proceeding forward from the bulge location to a nearest point where a second radius stops decreasing within an axial extent of the aft blade root; and
wherein ratio r b /r h >1.081;
wherein ratio r b /r h <1.424; and
wherein the forward blade assembly and the forward housing rotate about the axis of rotation, and wherein the aft blade assembly and the aft housing are stationary when the unducted propulsion system is in operation.
2. The unducted propulsion system of claim 1 , wherein the aircraft is configured for cruise flight Mach number 0.74<M 0 <0.86, and wherein
r
b
r
h
=
(
A
1
-
1
)
M
0
-
0.6
0.19
+
1
,
where 1.11<A1<1.31.
3. The unducted propulsion system of claim 2 , wherein 1.16<A1<1.31.
4. The unducted propulsion system of claim 3 , wherein 1.16<A1<1.26.
5. The unducted propulsion system of claim 1 ,
wherein an axial distance z, is between the bulge location and the local minimum, and wherein ratio z b /r h <2.103.
6. The unducted propulsion system of claim 5 , wherein a location with radius r m is axially halfway between the bulge location and the local minimum, and wherein ratio
r
m
/
r
h
-
1
r
b
/
r
h
-
1
=
C
1
,
where 0.59<C1<0.79.
7. The unducted propulsion system of claim 6 ,
wherein axial distance z b is between the bulge location and the local minimum, and wherein ratio z b /r h <1.974, and wherein a location with radius r m is axially halfway between the bulge location and the local minimum, and wherein ratio
r
m
/
r
h
-
1
r
b
/
r
h
-
1
>
0.64
.
8. The unducted propulsion system of claim 6 , wherein the ratio z b /r h >1.011.
9. The unducted propulsion system of claim 8 , wherein 0.64<C1<0.79.
10. The unducted propulsion system of claim 9 , wherein 0.64<C1<0.74.
11. The unducted propulsion system of claim 10 , wherein the aircraft is configured for cruise flight Mach number 0.74<M 0 <0.86, and wherein
r
b
r
h
=
(
A
1
-
1
)
M
0
-
0.6
0.19
+
1
,
where 1.11<A1<1.31.
12. The unducted propulsion system of claim 11 , wherein
z
b
r
h
=
B
1
(
M
0
0.79
)
3
,
where 1.23<B1<1.63.
13. The unducted propulsion system of claim 8 , wherein 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
(
v
)
F
net
ρ
0
V
0
2
A
an
>
0.06
.
14. The unducted propulsion system of claim 13 , wherein
F
net
ρ
0
V
0
2
A
an
>
0.08
.
15. The unducted propulsion system of claim 8 , wherein one of: the flowpath curve further corresponds to respective aft-most points of two or more aft blade roots; or the flowpath curve further corresponds to respective aft-most points of at least half of the two or more aft blade roots.
16. The unducted propulsion system of claim 8 , 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.
17. The unducted propulsion system of claim 16 , wherein the number of blades in the forward blade assembly is between 8 and 18.
18. The unducted propulsion system of claim 17 , 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.
19. The unducted propulsion system of claim 5 , wherein the ratio z b /r h >1.011.
20. The unducted propulsion system of claim 19 , wherein the aircraft is configured for cruise flight Mach number 0.74<M 0 <0.86, and wherein
r
b
r
h
=
(
A
1
-
1
)
M
0
-
0.6
0.19
+
1
,
where 1.11<A1<1.31.
21. The unducted propulsion system of claim 20 , wherein
z
b
r
h
=
B
1
(
M
0
0.79
)
3
,
where 1.23<B1<1.63.
22. The unducted propulsion system of claim 21 , wherein 1.16<A1<1.31, and wherein 1.23<B1<1.53.
23. The unducted propulsion system of claim 22 , wherein 1.16<A1<1.26, and wherein 1.33<B1<1.53.