Non-piped propulsion system

Abstract

Apparatuses and systems are provided herein for non-tubular propulsion systems. The system includes an efficient front housing for high subsonic sustained flight. A plurality of blades are secured to the front housing, wherein the front housing defines a flow path curve extending from a forward-most end of the front housing through an axial extent of the front blade root. The flow path curve is described by an axial direction parallel to an axis of rotation and a radius from the axis of rotation. The flow path curve includes a first point having a first radius, wherein the radius reaches a maximum value forward of the front blade root, and a second point aft of the first point having a second radius, wherein the radius ceases to decrease. A ratio of the first radius to the second radius is greater than or equal to 1.029.

Description

TECHNICAL FIELD

[0001] The technology relates generally to un-ducted propulsion systems. BACKGROUND

[0002] Generally, a fan of an aircraft propulsion system produces thrust by accelerating air passing through the fan. Factors that are not conducive to thrust production efficiency include energy losses as air enters and passes through the fan, speed contributions that do not contribute to thrust (e.g., swirl and vortex in air exiting the fan), frictional drag on the outer surface of the aircraft propulsion system, and shock wave related drag (e.g., wave drag) on the outer surface of the aircraft propulsion system. Thus, for an aircraft propulsion system, a goal is to generate a given amount of thrust without requiring excessive input power to the fan. Thus, it is desirable to minimize inefficiencies in thrust production. SUMMARY

[0003] According to one aspect of the disclosure, an un-ducted propulsion system for an aircraft configured for high subsonic cruise includes: a rotational axis; a front vane assembly consisting of a plurality of front vanes; a rear vane assembly consisting of a plurality of rear vanes; a front casing; a rear casing; wherein, for each front vane and each rear vane, includes a vane root proximate to the rotational axis and a vane tip distal to the rotational axis; wherein, a flow path curve corresponds to a line of intersection of an outer surface of the front casing and a plane containing the rotational axis and a forward-most point of the vane root; wherein, for the flow path curve, an axial direction z is parallel to the rotational axis and a radius r is a first distance from the rotational axis; wherein, a convex location on the flow path curve having a radius r1 is found by proceeding forward from the forward-most point on the vane root to a location where the first radius reaches a maximum; wherein, a local minimum on the flow path curve having a radius r2 is found by proceeding backward from the convex location to a nearest point where the second radius stops decreasing within an axial range of the vane root, and wherein, a ratio r1 / r2 > 1.029; wherein, an axial distance z1 is between the convex location and the local minimum, and wherein, a ratio z1 / r2 < 1.522; and wherein, an axial distance z2 is between a forward-most end of the front casing and the local minimum, and wherein, a ratio z2 / r2 < 4.115.

[0004] According to another aspect of the disclosure, there is provided a non-ducted propulsion system for an aircraft configured for high subsonic cruise, comprising: a rotational axis; a forward vane assembly, the forward vane assembly consisting of a plurality of forward vanes; a forward casing; wherein, for each forward vane, comprising a forward vane root proximate to the rotational axis and a forward vane tip distal to the rotational axis; wherein, a flow path curve corresponds to an intersection of an outer surface of the forward casing and a plane containing the rotational axis and a forward-most point of the forward vane root; wherein, for the flow path curve, an axial direction z is parallel to the rotational axis, and a radius r is a distance from the rotational axis; wherein, a convex position on the flow path curve having a radius r1 is found by proceeding forward from the forward-most point on the forward vane root to a position where a first radius reaches a maximum; wherein, a local minimum on the flow path curve having a radius r2 is found by proceeding backward from the convex position to a nearest point where a second radius stops decreasing, and wherein, a ratio r1 / r2 > 1.066; wherein, an axial distance z1 is between the convex position and the local minimum, and wherein, a ratio z1 / r2 < 1.522; and wherein, an axial distance z2 is between a forward-most end of the forward casing and the local minimum, and wherein, a ratio z2 / r2 < 4.115. BRIEF DESCRIPTION OF DRAWINGS

[0005] Embodiments of systems and apparatuses related to non-ducted propulsion systems are disclosed herein. The specification includes drawings, wherein:

[0006] Figure 1 A front cross-sectional view of an exemplary non-ducted propulsion system having a rotational axis, forward and aft vane assemblies, forward and aft casings, an engine inlet, and an engine outlet is shown according to some embodiments;

[0007] Figure 2 A schematic perspective view of an exemplary gas turbine engine attached to a wing of an aircraft is shown according to some embodiments;

[0008] Figure 3 A cross-section of an exemplary non-ducted propulsion system is shown according to some embodiments, showing curvature along a flow path curve;

[0009] Figure 4 Air flow through a vane assembly of a non-ducted propulsion system is shown according to some embodiments;

[0010] Figure 5 Effects on air when air moves over a non-linear solid surface are shown;

[0011] Figure 6 A schematic diagram showing three surface positions defining an exemplary flow path curve for an aft casing is shown according to some embodiments;

[0012] Figure 7 An example of flow path curves for a rear housing is shown in accordance with some embodiments;

[0013] Figure 8 An example of flow path curves for a front housing is shown in accordance with some embodiments; Figure 7 An example plot of the first derivative of the same three flow path curves in FIG. 2 with respect to axial distance is shown in FIG. 3 in accordance with some embodiments;

[0014] Figure 9 Curvature is illustrated by showing the second derivative of the three curves in FIG. 2 with respect to axial distance in FIG. 4 in accordance with some embodiments; Figure 7

[0015] Figure 10 An example of flow path curves for a front housing is shown in FIG. 5 in accordance with some embodiments; Figure 1 The same front elevation cross-sectional view of the un-tubulated propulsion system of FIG. 5, but with element numbering specifically referencing the front housing or spinner portion, is shown in FIG. 6 in accordance with some embodiments;

[0016] Figure 11 is a plot 200 depicting the shape of a front housing of an un-tubulated propulsion system in accordance with some embodiments;

[0017] Figure 12 is a plot 1200 depicting the shape bounds of a front housing of an un-tubulated propulsion system in accordance with some embodiments; and

[0018] Figure 13 is a flowchart of a method of operating an un-tubulated propulsion system in accordance with some embodiments.

[0019] ​The elements in the drawings are shown for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions and / or relative positioning of some of the elements in the drawings can be exaggerated relative to other elements to help improve the understanding of various embodiments of the present disclosure. Furthermore, common but well-understood elements that are useful or necessary in a commercially feasible embodiment are often not depicted in order to facilitate a less obstructed view of these various embodiments of the present disclosure. The front cross-sectional view of the non-ducted propulsion system in the drawing depicts the external flow path curvature formed by the intersection of the outer surface of the housing with a plane that includes the axis of rotation. Such cross-sectional views also indicate structures that are helpful in understanding embodiments of the present disclosure, such as the vanes. Limiting the cross-sectional view to a single side of the axis of rotation does not imply that the system is axisymmetric about the axis of rotation. The cross-sectional view is used to illustrate certain characteristics, such as the shape of the housing associated with the vane assembly. Furthermore, the drawings omit certain details of the system that are not needed for a complete understanding of certain aspects of the system. Certain acts and / or steps can be described or depicted in a particular order or sequence, but it is not necessarily meant to imply that the specific order or sequence was required, required to achieve particular results, or is the only order or sequence that works. Unless otherwise specified herein, the terms and expressions used herein have the ordinary technical meaning as is accorded to such terms and expressions by those skilled in the technical field as set forth above. DETAILED DESCRIPTION

[0020] Aspects and advantages of the present disclosure will be set forth in part in the following description, or can be apparent from the description, or can be learned through practice of the present disclosure.

[0021] Reference will now be made in detail to the presently preferred embodiments of the application, one or more examples of which are illustrated in the drawings. The detailed description uses numerical and letter designations to refer to various features of the application. Like or similar designations in the drawings and description have been used to refer to like or similar parts of the application.

[0022] The word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any implementation described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other implementations.

[0023] As used herein, the terms "first", "second", and "third" can be used interchangeably to distinguish one component from another and are not intended to signify location or importance of the individual components.

[0024] The terms "forward" and "aft" refer to relative positions within a gas turbine engine or vehicle and refer to the normal operating attitude of the gas turbine engine or vehicle. For example, for a gas turbine engine, forward refers to a position closer to the engine inlet and aft refers to a position closer to the engine outlet or exhaust.

[0025] The terms "upstream" and "downstream" refer to the relative direction with respect to the flow of fluid in a fluid path. For example, "upstream" refers to the direction from which fluid flows, and "downstream" refers to the direction to which fluid flows.

[0026] Unless otherwise indicated herein, the terms "coupled," "fixed," "attached to," and the like, mean either directly coupled, fixed, or attached by one or more intermediate components or features.

[0027] The term "propulsion system" refers generally to a system that generates a thrust force, which is generated by a propulsor, and the propulsor provides the thrust force using an electric motor, a heat engine such as a turbine, or a combination of an electric motor and a turbine.

[0028] The term "casing" refers to a shell that encloses the propulsion system and provides an aerodynamic exterior. The casing can be composed of or include a hub, spinner, and nacelle. Further, the casing can rotate about a rotating or stationary axis, or be axially segmented such that one portion rotates while another portion is stationary.

[0029] The singular forms "a," "an," and "the" include plural referents unless the context clearly dictates otherwise.

[0030] For a flow path curve that corresponds to a casing outer surface, the axial direction "z" is parallel to the axis of rotation, and the radius "r" is the distance from the axis of rotation. The z-r plane is positioned by an angular coordinate theta (i.e., a cylindrical coordinate system is employed in which the coordinate theta precisely positions the orientation of the z-r plane in 3D space). Because the casing outer surface can not be axially symmetric about the axis of rotation, the shape of the flow path curve can depend on the z-r plane used to define it. In the specification and claims, the z-r plane used to define the flow path curve includes, in addition to specifying that it includes the axis of rotation, a point on the casing or on a blade root within a blade assembly associated with the casing that the curve describes that is closest to the curve. Further, for any axial position z of the curve along the casing rotation about the axis of rotation, rather than referring to the radius on the flow path curve at the specified z-r position relative to the axis of rotation, the radius r is the "effective" radius of the casing cross-sectional area that is perpendicular to the axis of rotation at that axial z position. Thus, for an axial position of the casing rotation, the radius r is the radius of a circle that has the same casing cross-sectional area in a planar cross-section that is perpendicular to the axis of rotation.

[0031] The term "bulge" refers to a location on the flow path curve where the radius reaches a maximum value along the curve away from the nearest / associated blade assembly (i.e., forward of a forward blade assembly for a forward casing and aft of an aft blade assembly for an aft casing).

[0032] The term“local minimum” refers to a first position on a segment of the flow path curve from the convexity towards and through the axial extent of the associated blade root at which the radius stops decreasing. If the radius monotonically decreases from the convexity through the axial extent of the associated blade root, the local minimum is at the position on the segment of the flow path curve furthest from the convexity. Thus, the local minimum is the smallest radius position closest to the maximum radius position, which is also within the axial extent of the blade root or between the blade root and the maximum radius position. It will be appreciated that any gaps or steps in the flow path curve caused by connections, fits or relative motion between components of the casing will be ignored when determining the local minimum.

[0033] As used throughout the specification and claims, approximate language is applied to modify any quantitative representation that can permit variations without resulting in a change in the basic function to which it is related. Accordingly, a value modified by a term or terms, such as“about,”“approximately,” and“substantially,” is not limited to the precise value specified. In at least some instances, the approximate language can correspond to the precision of an instrument used to measure the value, or the precision of a method or machine used to construct or manufacture the component and / or system. For example, the approximate language can refer to within a margin of 1%, 2%, 4%, 10%, 15%, or 20%.

[0034] Herein and throughout the specification and claims, range limitations are combined and interchanged, such ranges are identified and include all the sub-ranges included therein unless context or language indicates otherwise. For example, all ranges disclosed herein are inclusive of the endpoints, and the endpoints are independently combinable with each other.

[0035] The technology described herein relates to un-ducted propulsion systems, in particular the shape of the outer surface of one or more casings surrounding the propulsion system, for which the casings can comprise a spinner, a hub and / or a nacelle.

[0036] The operating principle of a turbofan engine is that a central gas turbine core drives a bypass fan located at a radial position between the fan duct and the engine core. Conversely, the operating principle of an un-ducted propulsion system is that the bypass fan is located outside the engine nacelle. This allows the use of larger fan blades capable of acting on a larger amount of air than a turbofan engine, thereby increasing the propulsion efficiency compared to traditional engine designs.

[0037] Non-ducted propulsion systems can take the form of a propeller system as used on a wide range of aircraft, such as radio-controlled model airplanes, drones, piston engine propeller aircraft, turbo-prop regional aircraft, and large turbo-prop military transport aircraft. Another type of non-ducted propulsion system, sometimes referred to as an “open rotor,” consists of two blade assemblies, one located in a forward position and one located in an aft position, with at least one of them rotating about an axis to impart power to a propulsion flow that generates thrust. Such a two-blade assembly system offers some advantages, but also presents some challenges, and is far less common than single-blade row systems. As used herein, the term “propeller” can refer to a single blade assembly of a non-ducted propulsion system or to a forward blade assembly of a non-ducted propulsion system consisting of two blade assemblies. The term “fan” can refer to a propeller or to two blade assemblies of a non-ducted propulsion system.

[0038] According to the present disclosure, a non-ducted propulsion system is capable of achieving high subsonic cruise flight speeds. Cruise is a phase of flight that occurs when an aircraft is flying level at a set altitude after it has climbed and before it begins to descend. Thus, as used herein, cruise represents a continuous, high-speed, and steady flight condition in which an aircraft is intended to operate. This description is to distinguish cruise from certain abnormal or transient conditions, such as a dive, in which an aircraft can reach high flight speeds, but the aircraft is not intended to experience such conditions for most of its mission from takeoff to landing.

[0039] A non-ducted propulsion system capable of achieving high subsonic cruise flight can have two blade assemblies positioned in an aerodynamic relationship to each other. As used herein, “aerodynamic relationship” means that they are positioned such that one is downstream of the other, so that at least a portion of the air acted upon by the forward blade assembly is subsequently acted upon by the aft blade assembly. This allows the tangential velocity (also referred to as swirl) imparted to the air by the forward blade assembly to be neutralized, i.e., at least partially canceled out, in the change in tangential velocity imparted by the aft blade assembly. At least one of the blade assemblies is a rotating assembly that carries an array of airfoils that rotate about a rotation axis and that are located outside of the engine nacelle. The other blade assembly can be another rotating blade assembly (a rotor), or it can be a stationary blade assembly (a stator). Without the aft blade assembly to cancel out the swirl of the forward blade assembly, the high power per frontal or annular fan area required for high-speed flight would cause excessive swirl in the air passing through the non-ducted propulsion system, resulting in an inefficient production of thrust. For this reason, single-propeller propulsion systems, such as the propellers on turbo-prop engines, typically power aircraft that do not cruise at Mach numbers exceeding 0.72.

[0040] If the unstreamlined propulsion system includes two vane assemblies that are both rotors, the vanes of the forward vane assembly and the aft vane assembly are arranged to rotate in opposite directions about a common axis and are axially spaced along the axis. For example, the respective vanes of the forward rotor assembly and the aft rotor assembly can be coaxially mounted and spaced apart, with the vanes of the forward rotor assembly configured to rotate clockwise about the axis and the vanes of the aft rotor assembly configured to rotate counterclockwise about the axis (or vice versa).

[0041] If one of the two vane assemblies is a stator, that vane assembly does not rotate about the axis and is aerodynamically positioned either upstream or downstream of the rotating vane assembly, the forward vane assembly or the aft vane assembly, respectively. If aerodynamically positioned upstream of the rotating vane assembly, the stationary vane assembly imparts a tangential velocity to the air in a direction opposite the direction of rotation of the rotor, referred to as counter-rotation. Due to the direction of rotation, the aft rotating vane assembly imparts a tangential velocity change to the air to reduce the magnitude of the tangential velocity of the air passing through it. If aerodynamically positioned downstream of the rotating vane assembly, the stationary vane assembly imparts a tangential velocity change opposite the direction of the tangential velocity imparted by the rotor, referred to as de-rotation. By de-rotating the air it receives from the rotating vane assembly, the aft vane assembly reduces the magnitude of the tangential velocity of the air passing through it. The vanes in a stator are often referred to as “buckets.” However, the general terms “vanes” and “vane assembly” as used herein are used for either a rotating vane assembly or a stationary vane assembly.

[0042] For the stationary vane assembly, aircraft structure can mix, integrate, or merge with the vane assembly. For example, pylons used to mount the engine to the aircraft can occupy some of the same axial extent in the rotating axis of the rotating vane assembly as at least some of the vanes in the stationary vane assembly. Further, portions of the aircraft structure can be designed for the purpose of counter-rotation for the forward vane assembly or de-rotation for the aft vane assembly. As a result, the aircraft structure can add or even replace some of the vanes in the stationary vane assembly.

[0043] As used herein, distances parallel to the axis of rotation and perpendicular to the axis of rotation indicate positions or coordinates that define external flowpath surfaces of the indicated structure. The external flowpath surfaces work with the vane assembly to influence the flow of working fluid (typically air) through the fan. The external flowpath surfaces, formed by one or more casings, separate the airflow accelerated by the fan from internal mechanisms, machinery, or equipment associated with the propulsion system. As the flight Mach number and the acceleration of air through the fan increase, the shape of these external flowpath surfaces becomes increasingly important to avoid high pressure losses or drag. Further, these external flowpath surfaces can bulge (i.e., increase in size) axially away from the vicinity of the vane assembly to accommodate the aforementioned internal items.

[0044] For a non-ducted propulsion system, high-speed flight requires even higher speeds through the fan and through the flow path surface formed by one or more housings. As used herein, "fan flow" is the fluid flow accelerated by the fan to produce thrust. Such speeds can reach or exceed the speed of sound, or Mach 1. Under certain conditions, high Mach flow can lead to a sharp increase in pressure loss and drag, thereby impairing the thrust generation performance or efficiency of the system. This can result in low fuel efficiency. Additionally, it may be desirable to limit the diameter of the fan to avoid the disadvantages associated with weight, drag, and installation on the aircraft. However, a compact fan results in a higher thrust per unit frontal or annulus area of the fan, and thus a higher acceleration compared to a situation where the fan diameter is not so restricted. Additionally, the axial length of the system, and thus the length of the flow path surface defining the fan flow, affects drag and weight. At the same time, reducing the axial length can also impair the performance of the non-ducted propulsion system by causing a higher magnitude of curvature of the flow path surface, thereby resulting in high Mach number regions. Accordingly, it is desirable to provide a non-ducted propulsion system having an external flow path shape of a housing located upstream and axially within the range of a front blade assembly, enabling the aircraft to fly at high subsonic speeds with good efficiency and having transonic flow within the fan. It is also desirable to provide a non-ducted propulsion system having an external flow path shape of a housing located downstream and axially within the range of a rear blade assembly, enabling the aircraft to fly at high subsonic speeds with low losses and low drag.

[0045] According to the present disclosure, a non-ducted propulsion system for a subsonic aircraft having a cruise Mach number M0 of 0.74 or greater (e.g., 0.74 < M0 < 0.86) or between a cruise Mach number of 0.78 and 0.84 has a rotational axis, a front blade assembly, a rear blade assembly, a front housing, and a rear housing. The front blade assembly and the rear blade assembly each include a plurality of blades, each blade having a root near the rotational axis and a tip remote from the rotational axis. The flow path curve corresponds to the intersection line of the outer surface of the rear housing and a plane containing the rotational axis and the last point of the rear blade root. For the flow path curve, the axial direction z is parallel to the rotational axis and increases in the rearward or downstream direction. For the flow path curve, the radial coordinate r is the distance from the rotational axis.

[0046] The flow path curve has a bulge and a local minimum. The position of the bulge at a radius of r b is found by traveling rearward from the last point of the rear blade root to the position where the radius reaches a maximum value. The position of the local minimum at a radius of r h is found by traveling axially forward from the bulge to the position where the radius stops decreasing. The ratio r b / r h of the flow path curve > 1.08. Additionally, the axial distance z b between the bulge and the local minimum can conform to the ratio zb / r h <2.41. In addition, the flow path curve can have a radius r m at a location axially midway between the protrusion and the local minimum such that (r m / r h -1) / (r b / r h -1)>0.59. The above ratios can be adjusted according to a predetermined cruise Mach number M0, as shown in EQS. 1, 2, and 3, presented in the following order:

[0047]

[0048] In the above equations, 0.74 < M0 < 0.86, and the constants Al, Bl, and Cl range from 1.11 < Al < 1.31, 1.23 < Bl < 1.63, and 0.59 < Cl < 0.79. The above relationships for the flow path curve corresponding to the aft blade root can apply to the flow path curve associated with multiple aft blade roots, or to the flow path curve associated with all aft blade roots.

[0049] According to the present disclosure, a non-ducted propulsion system for a subsonic aircraft having a cruise Mach number M0 of 0.74 or greater (e.g., 0.74 < M0 < 0.86) has a rotational axis, a forward vane assembly, an aft vane assembly, a forward housing, and an aft housing. The forward vane assembly and the aft vane assembly each include a plurality of vanes, each vane having a root proximate the rotational axis and a tip distal from the rotational axis. A flow path curve corresponds to a line of intersection of an outer surface of the forward housing and a plane containing the rotational axis and a forward-most point of the forward vane roots. For the flow path curve, an axial direction z is parallel to the rotational axis, increasing in a forward or upstream direction. For the flow path curve, a radius r is a distance from the rotational axis. At an axial location of the forward housing rotating about the rotational axis (e.g., a spinner), the radius r is an effective radius, i.e., a radius of a circle having the same cross-sectional area as the forward housing normal to the rotational axis.

[0050] The flow path curve has a convexity and a local minimum. The convexity with a radius of r1 is found by proceeding forward from the forward-most point of the forward vane root to the location where the radius reaches a maximum. The local minimum with a radius of r2 is found by proceeding aft from the convexity to the location where the radius stops decreasing within the axial extent of the forward vane root. The ratio of r1 / r2 of the flow path curve > 1.029. Further, the axial distance z1 between the convexity and the local minimum can comply with the ratio z1 / r2 < 1.522. Further, the forward housing can have a forward-most point where the axial distance z2 between the local minimum and the forward-most end of the flow path curve can comply with the ratio z2 / r2 < 4.115. The above ratios can be adjusted to suit a predetermined cruise Mach number M0 as shown in EQS. 4, 5, and 6 presented in the following order:

[0051]

[0052] where 0.74 < M0 < 0.86, 1.04 < A2 < 1.14, 0.78 < B2 < 1.18, and 2.19 < C2 < 3.19.

[0053] Further in accordance with the present disclosure, a non-ducted propulsion system for a subsonic aircraft having a cruise Mach number M0 of 0.74 or greater (e.g., 0.74 < M0 < 0.86) includes a rotating element comprised of a rotational axis, a forward vane assembly, and a forward housing. The forward housing or spinner rotates with the forward vane assembly about the rotational axis. The forward vane assembly includes a plurality of vanes, each vane having a root proximate the rotational axis and a tip distal from the rotational axis. The axial direction z of the spinner is parallel to the rotational axis, increasing in a forward or upstream direction. The radius r of the spinner shape is the distance from the rotational axis. The radial coordinate r is the effective radius, i.e., the radius of a circle having the same cross-sectional area as the spinner perpendicular to the rotational axis. The spinner has a convexity location with a radius of r1 at the maximum radius forward of the forward vane assembly. Proceeding axially aft from the convexity, the spinner has a local minimum with a radius of r2 where the radius stops decreasing within the axial extent of the forward vane root. The shape of the spinner is such that the ratio of r1 / r2 > 1.066. Further, the axial distance z1 between the convexity and the local minimum can comply with the ratio z1 / r2 < 1.522. Further, the forward housing can have a forward-most point where the axial distance z2 between the local minimum and the forward-most end of the flow path curve can comply with the ratio z2 / r2 < 4.115. The above ratios can be adjusted to suit a predetermined cruise Mach number M0 using EQS. 4, 5, and 6 where 0.74 < M0 < 0.86, 1.09 < A2 < 1.14, 0.78 < B2 < 1.18, and 2.19 < C2 < 3.19.

[0054] These and other features, aspects, and advantages of the present disclosure and / or embodiments will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the present disclosure and serve to explain the principles of the present disclosure.

[0055] Throughout this document and in the claims, range limitations are combined and interchanged, such ranges are identified and include all the sub-ranges included therein unless context or language indicates otherwise. For example, all ranges disclosed herein are inclusive of the endpoints, and the endpoints are independently combinable with each other.

[0056] In the drawings, like reference numerals refer to like elements throughout the various embodiments described herein.

[0057] Figure 1 A front cross-sectional view of an example un-tubulated propulsion system 100 is shown. As Figure 1 shown, the un-tubulated propulsion system 100 takes the form of an open-rotor propulsion system and has a rotating element 138, depicted as a propeller assembly, that includes an array of blades 102 fixed to a forward housing 106 and configured to rotate about a rotational axis 120 of the un-tubulated propulsion system 100. The un-tubulated propulsion system 100 also includes, in the example embodiment, a non-rotating stationary element 142 that includes an array of vanes 104 (also referred to as buckets) disposed about the rotational axis 120. These vanes can be arranged such that they are not all equidistant from the propeller. These vanes are mounted to a stationary frame and do not rotate relative to the central axis 120. The non-rotating stationary element 142 includes a stationary aft housing 126. The forward housing 106 and the aft housing 126 have three-dimensional outer surfaces. To explain the surface shaping guidelines disclosed herein, parameters are defined along a flow path curve that corresponds to the intersection of the outer surface with a plane that includes the rotational axis. Thus, the flow path curve 105 corresponds to the intersection of the forward housing 106 with a z-r plane that includes the rotational axis. Similarly, the flow path curve 125 corresponds to the intersection of the aft housing 126 with a z-r plane that includes the rotational axis. For reference purposes, Figure 1 A forward direction is also depicted with arrow 118.

[0058] As Figure 1As shown, the example un-tubulated propulsion system 100 also includes a drive mechanism 128 that provides torque and power to the rotating element 138 through a transmission (not shown). In various embodiments, the drive mechanism 128 (also referred to as an engine) can be a gas turbine engine, an electric motor, an internal combustion engine, or any other suitable source of torque and power, and can be positioned proximate to the rotating element 138, or can be remotely positioned through a suitably configured transmission. The transmission transmits power and torque from the drive mechanism 128 to the rotating element 138, and can include one or more shafts, gearboxes, or other mechanical or hydraulic drive systems. In Figure 1 In various embodiments, the drive mechanism 128 is schematically depicted as including a gas generator 130 and a power turbine 132. Examples of turbomachinery comprising a gas generator (e.g., a compressor, a combustor, and a high-speed turbine) and a power turbine of a gas turbine engine are shown and described in US20210108597, the entirety of which is hereby incorporated by reference for all purposes. Examples of turbomachinery comprising a gas generator (e.g., a compressor, a combustor, and a high-speed turbine) and a power turbine of a gas turbine engine are also depicted in US10704410, US5190441, US9340277, and US10358926, the entirety of each of which is hereby incorporated by reference for all purposes. Figure 1 Alternative configurations to the configuration shown are contemplated, the entirety of each of which is hereby incorporated by reference for all purposes.

[0059] As the rotating element 138 rotates about the rotational axis 120 in a given direction, the size, shape, and configuration of the airfoil blades 102 of the rotating element 138 are designed to generate thrust by moving the working fluid (e.g., air) in a direction 144. Figure 1 As it does so, the blades 102 impart a degree of swirl to the fluid as it moves in the direction 144. The size, shape, and configuration of the blades 104 of the stationary element are designed to reduce the size of the swirl of the fluid, thereby increasing the kinetic energy that generates thrust for a given shaft power input to the rotating element. Each rotating blade 102 has a blade root 122 and a blade tip 124. Each stationary blade 104 has a blade root 136 and a blade tip 134. For both the rotating blades 102 and the stationary blades 104, the span is defined as the distance between the root and the tip. The stationary blades 104 can have a shorter span than the rotating blades 102 (e.g., 50% of the span of the blades 102), or can have a longer span than the blades 102 or the same span as the blades 102 as desired. Figure 1In some embodiments, the stationary vanes 104 are shown fixed to the casing 126 at their respective vane roots 136. In some embodiments, some or all of the stationary vanes 104 can be fixed to or integrated with an aircraft structure (e.g., a wing, a pylon, or a fuselage). The number of vanes 104 of the stationary element can be less than or greater than or equal to the number of vanes 102 of the rotating element, and is typically greater than two or greater than four. In some embodiments, the ratio of the number of rotating vanes 102 to the number of stationary vanes 104 is between 2:5 and 2:1. In some embodiments, the difference between the number of rotating vanes 102 and the number of stationary vanes 104 is between 2 and -2.

[0060] The vanes 104 of the stationary element 142 can be aerodynamically positioned upstream of the rotating vanes 102 to act as anti-swirl vanes, i.e., to impart a tangential velocity opposite to the direction of rotation of the rotating element 138. Alternatively, as shown, the vanes 104 can be aerodynamically positioned upstream of the rotating vanes 102 to act as de-swirl vanes, i.e., to impart a tangential velocity change opposite to the rotating element 138. Any swirl remaining in the airflow downstream of the un-ducted propulsion system 100 is equivalent to a loss of thrust producing kinetic energy. Figure 1

[0061] It can be desirable for either or both of the sets of rotating vanes 102 and the sets of stationary vanes 104 to incorporate a pitch change mechanism, such that the vanes can be rotated independently or in combination with each other relative to a pitch rotation axis. Such pitch changes can be used to vary the thrust and / or swirl effects under various operating conditions, including to provide a thrust reversing feature that can be useful under certain operating conditions, such as when the aircraft is landing.

[0062] The inlet 127 is axially located between the vanes 104 and the vanes 102. Alternatively, the inlet 127 can be located elsewhere, e.g., forward of the vanes 102. The ratio of the mass of air accelerated by the rotating vanes 102 and bypassed around the inlet 127 to the mass of air accelerated by the rotating vanes and entering an engine core (not shown) via the inlet 127 is referred to as the bypass ratio. In some embodiments, the ratio of the swept area of the vanes (calculated as π x [(vane tip radius) 2 – (vane root radius) 2 ]) to the cross-sectional area of the inlet (measured in the z-r plane) is greater than 20:1 or greater than 30:1, and less than 80:1.

[0063] Notably, Figure 1 ​The illustrated example un-ducted propulsion system 100 is provided by way of example only. In other example embodiments, it can have other suitable configurations. For example, instead of being a forward rotating vane assembly and a rear stationary vane assembly as illustrated, the two vane assemblies can be counter-rotating relative to each other. As another example, the forward vane assembly can be stationary and the rear vane assembly can be rotating. As another example, the un-ducted propulsion system can consist of only a rotating vane assembly (i.e., a propeller).

[0064] Figure 2 is a perspective view of an example gas turbine engine attached to a wing of an aircraft in accordance with certain aspects of the present disclosure. Figure 2 The un-ducted propulsion system 100 is described as being mounted to the wing 218 via a pylon 220 to facilitate mounting to or containment by a pylon structure. Further, the spacing between each vane can not all be equal from each other and / or at the same axial z position. These are examples where the casing 126 can not be axisymmetric.

[0065] The un-ducted propulsion system 100 includes a turbomachine contained substantially within a forward casing or spinner 106 and a rear casing 126. In some configurations, both the forward casing 106 and the rear casing 126 include rotating hubs associated with rotating vanes 102 and 104, respectively. In other configurations, one of the forward casing 106 and the rear casing 126 is entirely rotating or includes a rotating structure (e.g., a rotating hub), while the other is a stationary casing associated with the respective rotating and stationary vanes. In some embodiments, the forward casing 106 can be considered a spinner and the rear casing 126 can be considered a nacelle. The rear casing 126 can contain a compressor, a combustor, and a turbine of the turbomachine, followed by an engine exit 121.

[0066] In Figure 2 In the illustrated example non-limiting example, the un-ducted propulsion system 100 includes a rotating assembly (or rotor) that includes a forward casing 106 and an airfoil-shaped assembly of vanes 102 (also referred to as fans, rotors, or propellers) associated with the forward casing 106. In this example, the forward casing 106 is a spinner that rotates about an axis of rotation 120. In other configurations, the forward casing can not rotate as the system consists of a stationary forward vane assembly and a rotating rear vane assembly. The un-ducted propulsion system 100 also includes a stationary assembly that can include an engine inlet 127 and an airfoil-shaped stationary assembly of vanes 104 associated with the rear casing 126. In this configuration, the casing 126 and vanes 104 do not rotate about the axis 120, although the vanes can individually articulate to modify a pitch angle, a skew angle, or a sweep angle, for example, via mechanisms contained within the casing 126. At least one function of the stationary vane 104 assembly is to remove swirl in the airflow exiting the rotor.

[0067] The aft casing 126 extends in the axial direction from an engine inlet 127 to an engine outlet 121. The aft casing 126 contains internal machinery that produces torque for the vane 102 assembly and defines surfaces that are shaped to provide aerodynamic efficiency (reduced drag) for air that passes through the vanes 102 and 104 and continues to travel downstream. The flow that exits the engine outlet 121 produces some thrust that propels and / or pushes the aircraft forward. The majority of the thrust produced by the engine of the un-ducted propulsive system 100 comes from accelerated air that passes through the casing 126, or air that passes through the vanes 104 and bypasses the inlet 127. In some embodiments, the engine can also include a third flow (the first and second flows are the bypass and turbine core airflows defined by the compressor, combustor, and turbine).

[0068] To simplify Figure 2 the explanation in FIG. 1, the forward casing 106 is shown as a continuous spinner. However, each casing can be composed of separate parts with various mechanical components to allow for variable pitch angles of the forward vane 102 assembly and / or the aft vane 104 assembly. The axial extent of such dedicated parts of each casing can be approximately the same as the corresponding axial extent of the vane 102 assembly and / or the vane 104 assembly, or the axial extent of the casing can be shorter or longer (in axial extent) than the span of the vanes or the respective axial extent of the vane assemblies. Figure 2 The dashed line in FIG. 1 indicates the axis of rotation 120 of the vanes 102. The dashed curves 105 and 125 represent the flow path curves corresponding to the intersection of the casings 106 and 126, respectively, with a plane that includes the axis of rotation 120. In the example example where the forward casing 106 and the associated forward vane 102 assembly rotate about the axis of rotation 120, the shape of the flow path curve can be defined by an effective radius and an axial distance parallel to the axis of rotation 120. However, in this example where the aft casing 126 and the associated aft vane 104 assembly do not rotate about the axis of rotation 120, the flow path curve shape of the radius versus axial position depends on the orientation of the z-r plane about the axis of rotation, i.e., the curve can have different shapes for different positions of the plane that intersects the aft casing 126.

[0069] Referring to Figure 1 and Figure 2Because the vane 102 assemblies and / or the stationary vane 104 assemblies have thickness, flow restrictions, referred to as choking, can occur to the air flow through the vane 102 and / or vane 104 rows. Thus, the air flow is accelerated not only through the rows due to the generated thrust, but also due to choking, the air flow must be accelerated further. In high subsonic cruise, for example when the flight Mach number (M0) is greater than about 0.74, these combined effects of generated thrust and choking can cause the axial component of the velocity of the air flow through the rows to approach the speed of sound (i.e., Mach number of 1), referred to as choking, which can result in high pressure losses within the vane 102 or vane 104 passages. Higher vane 102 or vane 104 counts (e.g., 8 to 18) can make choking a major issue because increasing the count increases the overall choking of the vane material for the air flow to accelerate through the vane 102 assemblies.

[0070] A strategy called area ruling can reduce the Mach number in the passages within the vane 102 or vane 104. To visualize area ruling, Figure 3 A cross-sectional view of the non-tube propulsion system 100 is shown. The flow path curve 125 corresponds to Figure 1 and Figure 2 the intersection of the outer surface of the housing 126 with a cross-sectional plane that includes the rotation axis 120 and the last point of the vane 104 rear vane root 136 in the rear vane assembly. Thus, the points on the outer surface of the housing 126 are determined by choosing the vane root 136 and the upstream or downstream distance parallel to the rotation axis 120 from the last point of the vane root 136. By forming a rear housing surface recess 404, the Mach number within the passages of the vane 104 can be reduced. The rear housing recessed area 404 corresponds to a valley and is located at a local minimum radius of the surface of the housing. Referring to the corresponding air flow through the vane 104 and past the housing (i.e., the flow path curve 125), it can be seen that due to the concave shape of the housing at the location of the vane 104, the velocity is appropriately reduced. To achieve this recessed area 404 that produces the desired result (reducing the Mach number at the vane 104 to avoid choking), the radial distance of the curve 125 from the rotation axis 120 must increase away from the vane 104, resulting in a downstream convex curvature 406 and possibly an upstream convex curvature 402. Thus, the housing 126 not only needs to bulge outwards to accommodate the internal components of the propulsion system, but also needs to bulge outwards to avoid choking in the passages between the vane 104.

[0071] On the surface of the housing upstream of the blade 104, a convex portion 402 may also be formed on the housing. Thus, the housing 126 can bulge outwards to accommodate the internal components of the ducted propulsion system and bulge upstream to accommodate, for example, components or an inlet 127. It may also be desirable to minimize the axial length of the ducted propulsion system. The goal of avoiding blockage while restricting the axial length may lead to an increase in the surface curvature of the housing 126, resulting in local acceleration of the air along the flow path curve 125 (especially at the convex portion). As described below, at high subsonic flight, there may be challenges in the curvature near the convex portion of the surface of the flow path curve 125.

[0072] Figure 4 The airflow through the Figure 1 fan of the ducted propulsion system 100 is shown. It has a velocity V0 (e.g., corresponding to 0.74 < M0 < 0.86) relative to the airspeed at the far upstream 502 of the ducted propulsion system 100 and the ducted propulsion system 100, which is the flight speed of the aircraft. Closer to the fan, the effect of the fan is to cause a higher airspeed when the air enters the fan. As the air passes through the fan, the fan powers the airflow passing through it to accelerate (i.e., further increase the speed) the air passing through the rest of the propulsion system. In the region far downstream 506 in the axial direction, the airflow reaches the exhaust velocity V e .

[0073] The airflow through the blade 104 assembly, from the far upstream to the far downstream, can be regarded as an air tube (or fan flow tube) 508. The radial and axial extents of the fan flow tube 508 (slipstream airflow) are indicated by the hash region. The outer boundary 510 of the fan flow tube 508 intersects the radially outermost section (or tip) 124 of the blade 102 assembly. The inner boundary 514 of the fan flow tube 508 intersects the blade 104 assembly near the flow path curve 125 and follows the shape of the flow path curve 125 immediately downstream of the blade 104 assembly. Since in this exemplary example, the engine inlet 127 sucks air from the innermost radial region between the blades 102 and 104, the fan flow tube 508 does not include the portion of the air that enters the engine inlet 127 through the blade 102 and is discharged through the engine outlet 121. The average axial velocity of the air at any axial position within the fan flow tube 508 can be visualized by the annular cross-sectional area 516 of the fan flow tube 508 at that position. For selected positions along the fan flow tube 508, examples of the annular cross-sectional area 516 of the fan flow tube 508 are the far upstream 502, the nacelle bulge 504, and the far downstream 506.

[0074] Since the mass flow rate of air through the annular region downstream of the inlet 127 and within the fan flow tube 508 is the same, and the air density in the entire fan flow tube 508 is approximately constant, the average axial velocity of the air is approximately inversely proportional to the annular area 516. Thus, at a far upstream 502, the velocity of the fan flow tube 508 into the fan has not yet been increased by the fan, and the annular area 516 is largest. At a far downstream 506, the fan flow tube 508 includes energized air having a higher velocity relative to the air velocity in the far upstream 502, and thus the annular area 516 is smaller than at 502. The smallest annular area relative to the annular area of the flow path curve 125 occurs on the housing 126 proximate to the protrusion 504. At the nacelle protrusion 504, the air has been energized by the blade 104 assembly, the radial distance from the axis of rotation is the maximum radius, and the annular area 516 is the smallest relative to the other mentioned annular areas of the flow path curve 125. Thus, the average axial velocity of the air flow on the housing 126 (the surface defining the flow path curve 125) is higher, and due to the protrusion in the flow path curve 125.

[0075] Figure 5 Further explanation of the problems caused by the high average axial velocity of the air flow over the nacelle, Figure 5 The effects are depicted when air flows frictionless from left to right over a wavy solid surface 604. Streamlines 602 indicate the paths of fluid particles starting at different distances from the surface 604. Concave surfaces 606 or valleys increase static pressure and decrease the velocity of the air. Conversely, convex surfaces 608 or peaks decrease static pressure and increase the velocity of the air. Thus, for Figure 1 The variation in static pressure and the relative variation in air velocity for the flow over the housing 126 in

[0076] The curvature of a surface can be expressed in terms of a corresponding radius of curvature. For example, at an arbitrary point along the surface 604, a radius of curvature r c and a center of curvature 610 can be defined. To illustrate, Figure 5 Two radii of curvature 612, 614 and their corresponding centers (shown as "+") 610 are shown, which correspond to two surface positions. At a distance to the left of the peak of the convex surface 608, the curvature is low, corresponding to a larger r c 614. Closer to the peak of the convex surface 608, the curvature is high, corresponding to a smaller r c 612. Positions within the concave surface 606 also have low and high curvatures. However, for points within the concave surface 606, the center of curvature is above the curve 604, and the radius of curvature points toward the surface 604.

[0077] As mentioned above, the air flow over the housing 126 can have an average velocity Ve This effect can cause problems for high subsonic flight. In particular, when the air speed on the flow path surface 125 approaches the speed of sound or Mach number = 1.0, the drag starts to increase dramatically. Generally, the increase in friction drag is roughly proportional to the square of the air speed. However, as the Mach number increases, the wave drag contributes more to the increase in drag. Wave drag is the drag that results from the formation of shock waves when the air flow near the shell surface 126 becomes supersonic (e.g., Mach number > 1.0).

[0078] The above explanation shows three factors that contribute to high drag. The first factor is a high cruise flight Mach number M0, such as 0.74 < M0 < 0.86. The second factor is a high non-dimensional cruise fan net thrust based on the fan annulus area and the flight speed. The same acceleration of the airflow by the fan that produces thrust also increases the drag on the shell 126 (e.g., fuselage). The thrust is expressed non-dimensionally in a way that accounts for the flight speed, the ambient conditions, and the fan annulus area, resulting in a thrust parameter where F net is the cruise fan net thrust, p0 is the ambient air density, V0 is the cruise flight speed, and A an is the fan flow tube cross-sectional area at the fan inlet. The fan annulus area A an is calculated using the maximum radius as the tip radius of the forward-most rotor blade and the minimum radius as the minimum radius of the fan flow tube entering the fan.

[0079] A solution to the wave drag problem at high subsonic flight (e.g., 0.74 < M0 < 0.86) is based on a non-conventional surface curvature strategy to design the shape of the flow path curve 125 on the shell 126. Figure 6 A schematic diagram showing three surface locations 702, 704, and 706 on the flow path curve 125 is shown. For Figure 3 and Figure 4 , the flow path curve 125 corresponds to Figure 1 and Figure 2The outer surface of the housing 126 shown intersects the plane including the axis of rotation 120 and the last point of the rear blade root 136 in the rear blade assembly. Therefore, curve 125 corresponds to traveling axially forward and backward along the surface of housing 126 from the last point on the rear blade root 136. If the rear blade used to define the flow path curve 125 has a variable orientation (e.g., actuated by a pitch-changing mechanism), the most relevant rear blade orientation for locating the flow path curve is when the last point of the rear blade root 136 is at the very end. If the last point of the rear blade root 136 is not attached to housing 126, for example, if there is a gap between the rear blade root 137 and housing 126 to allow pitch variation, or if the rear blade 104 is attached to a frame and suspended on housing 126, then curve 125 passes through the nearest point on the surface of housing 126 to the last point of the rear blade root 136. Each surface position along the flow path curve 125 can be defined based on the (z,r) coordinate system 708, where the z-axis is the rotation axis 120 and r is the distance from the rotation axis 120.

[0080] Flow path curve 125 has a (z,r) coordinate system 708 corresponding to the (z,r) coordinate system. b ,r b The protrusion or maximum radius position 704, and has a maximum radius r b The flow path curve 125 has a (0,r) coordinate system corresponding to the (z,r) coordinate system 708 ahead of the convex position at 704. h The local minimum position of ) is 702, and it has a radius r. h (0,r) h ) and (z b ,r b The surface location at ) determines the axial and radial extent of the segment of flow path curve 125, the shape of which is designed as described herein to address the high wave drag problem of high subsonic flight.

[0081] Flow path curve 125 has a (z,r) coordinate system 708 corresponding to (z) b / 2,r m The third position 706 of the curve 125 is located at the midway point between the first surface position 702 and the second surface position 704. For the fixed endpoints 702 and 704 of the segment of curve 125, specifying the position of 706 has a significant impact on the curvature distribution. Radius r h 113, r m 117, r b 111 and axial distance z b 115 is also like Figure 1 As shown.

[0082] For high subsonic cruise, achieving low drag without adding unnecessary length to the shell 126 at high subsonic cruise Mach numbers (i.e., M0> 0.74) depends on proper positioning of the points / endpoints / locations 702, 704, and 706. For example, for sufficient bulge to suppress Mach numbers within the aft vane assembly, limited length to avoid excessive friction drag and weight, and limited convex curvature near the bulge, it can be desirable that r b / r h > 1.081, z b / r h < 2.103 and (r m / r h -1) / (r b / r h -1) > 0.59. With slightly larger radius increase and smaller axial distance, so that r b / r h > 1.118, z b / r h < 1.974 and (r m / r h -1) / (r b / r h -1) > 0.64, better results can be obtained. Furthermore, imposing an upper limit on the bulge so that r b / r h < 1.424 can be beneficial.

[0083] Furthermore, the above ratios can be tailored to accommodate a predetermined cruise flight Mach number M0, with constants A1, B1, and C1 as shown in EQs. 1, 2, and 3

[0084]

[0085] where M0> 0.74, A1> 1.11, B1< 1.63, and C1> 0.59. Additional restrictions on each parameter can yield more optimized configurations, such as 0.74 < M0< 0.86, 1.11 < A1< 1.31, 1.23 < B1< 1.63, and 0.59 < C1< 0.79. An example of further constraints on the constants used to configure the aft shell 126 include 1.16 < A1< 1.31, 1.23 < B1< 1.53, and 0.64 < C1< 0.79. As another example of constant constraints, 1.16 < A1< 1.26, 1.33 < B1< 1.53, and 0.64 < C1< 0.74.

[0086] Table 1 provides the bulge radius (r b ) 111 versus the local minimum radius (r hExamples of the ratio of 113, where 1.11 < A1 < 1.31 (bold) and 0.74 < M0 < 0.86.

[0087]

[0088] Table 1

[0089] Table 2 provides the axial distance 115 between the local minimum and the bulge position and the ratio to the local minimum radius (r h ) Examples of the ratio of 113, where 1.23 < B1 < 1.63 (bold) and 0.74 < M0 < 0.86.

[0090]

[0091] Table 2

[0092] Table 3 provides the ratio (r m / r h -1) / (r b / r h ) Examples, where 0.59 < C1 < 0.79 (bold) and 0.74 < M0 < 0.86.

[0093]

[0094] Table 3

[0095] In addition to being applicable to the range of the cruise flight Mach number M0, the above constraints on the curve 125 may be particularly advantageous for the range of the dimensionless cruise fan net thrust parameter <​​​​​​​​​​​​​​​The unconventional surface curvature strategy described above for solving the wave drag problem of sustained high-subsonic flight (e.g., 0.74 < M0 < 0.86) is applicable to the ducted propulsion system described herein. In some configurations, the unconventional surface curvature strategy can be applied to a ducted propulsion system without an engine inlet (omitting inlet 127); for example, the rotor is not driven by a ramjet engine but by another type of machine (e.g., an electric motor). Figure 7 depicts three exemplary flow path curves 125 that can be used to define Figure 1 and Figure 2 the surface of the housing 126 shown in. The flow path curves 125 are adjacent to the rear housing 126 and are between the surface positions at (0, r h ) and (z b , r b ) in the (z, r) coordinate system 708, as Figure 6 shown.

[0098] To explain how the points 702, 704, and 706 in Figure 6 define the shape of the rear housing 126 to reduce drag during high-speed flight, in the graph 800 of Figure 7 , three exemplary flow path curves 125 between the point 702 and the point 704 are plotted, where z and r are dimensionless by the local minimum radius r h . For ease of comparison, these three curves conform to EQS.1, 2, and 3, where M0 = 0.79, A1 = 1.21, and B1 = 1.43, with only a difference in the parameter C1. The flow path curve 802 corresponds to C1 = 0.50 and is described by a cubic polynomial shape, labeled "cubic". The flow path curve 802 gives a smoothly varying curvature relative to the curves 804 and 806. The flow path curve 804 corresponds to C1 = 0.61 and is labeled "ex1". The flow path curve 806 corresponds to C1 = 0.69 and is labeled "ex2". Over the first third of its length, the flow path curve 804 (designated "ex1") has a faster increase in radius with axial distance than the curve 802. The flow path curve 806 (designated "ex2") also has a faster increase in radius than the curve 802, but has a smaller radius change near the peak radius of the housing (the position of the flow path curve 125 with the maximum radius r b ) compared to the curve 802 or 804. Figure 8 shows a graph 900 of the first derivative of r with respect to z for the curves in Figure 7 . All curves start and end with a first derivative of zero because the ends are at local minimum and maximum radii. Figures 902, 904, and 906 correspond to the first derivatives of the cubic, ex1, and ex2 curves in Figure 7 .

[0099] Figure 9 It shows Figure 7 The graph 1000 shows the second derivatives of the three curves (r, z) with respect to z. The second derivative indicates curvature, with a positive second derivative indicating concave curvature and a negative second derivative indicating convex curvature. The absolute value of the second derivative indicates the magnitude of the curvature. Curves 1002, 1004, and 1006 are respectively... Figure 7 The second derivatives of the flow path curves “cubic”, “ex1”, and “ex2” are shown. The cubic polynomial flow path curve has the smoothest curvature change (linear with axial distance). Flow path curve “ex1” also has a monotonically changing curvature; however, its curvature 1004 starts high near the rear blade root 136 and decreases towards the maximum radius. This “pre-loading” curvature results in a smaller convex curvature at the maximum radius than curvature 1002. Flow path curve “ex2” has a larger change at the third curvature 1006, which suppresses the Mach number within the channel of blade 104 and avoids a high convex curvature immediately upstream of the maximum radius. Since curve “ex2” has a relatively low convex curvature, where the combined effect of fan tube acceleration and the increased radius of the flow path curve could otherwise lead to an excessively high Mach number, the third curvature 1006 (“ex2”) is preferred.

[0100] As mentioned earlier, the flight speed of an aircraft is limited by many factors. For propeller-driven aircraft, the propeller plays a crucial role in the speed at which the aircraft can fly. At a high level, the larger the propeller and / or the more blades it has, the faster the aircraft can fly. Unfortunately, while speed is generally proportional to propeller size and the number of blades, so is weight, and larger sizes can pose problems for the installation and feasibility of the propulsion system. For example, as propeller size and / or the number of blades increases, propeller weight typically increases, and larger propellers may struggle to accommodate maintaining ground or fuselage clearance for a given fuselage configuration. Furthermore, at high subsonic flight speeds, a larger number of blades increases congestion in the flow areas of the propeller blade array, a problem given the transonic flow around the blades. In particular, excessive congestion reduces propeller efficiency and the range of maneuverability. Therefore, creating an acceptable aircraft capable of flying at higher sustained speeds (e.g., cruise speed) requires more than just increasing propeller size and / or the number of propeller blades.

[0101] Figure 10 It shows the relationship with Figure 1The same cross-sectional view is shown, but the front portion of the non-ducted propulsion system 100 (specifically, the rotating element 138) is annotated. The rotating element 138 includes a front housing depicted as a rotator 106 and a plurality of blades 102. Each blade 102 has a blade root 122 and a blade tip 124. The blades 102 are attached to the rotator 106 at the blade root 122. The rotating element 138 may have any suitable number of blades 102. For example, in one embodiment, the rotating element 138 includes 8 to 18 blades. As part of the rotating element 138, the rotator 106 and the blades 102 rotate about a rotation axis 120. The rotator 106 has a foremost point / end / position 108 relative to the arrow 118 indicating the direction of travel of the non-ducted propulsion system 100, and therefore the aircraft.

[0102] The front housing 106 is shaped such that it has a different radius along its axial length, and its shape is observed along a flow path curve 105 formed by the intersection of the rotator surface and a plane including the rotation axis 120 and the foremost point of the front blade root 122. As previously mentioned, the flow path curve is defined by the effective radius at the axial position of the housing's rotation. Therefore, in Figure 10 In the example shown, selecting the front blade root 122 for constructing the plane does not affect the flow path curve 105. However, in some embodiments, the front housing 106 may be stationary. Therefore, the convention of specifying the front blade root 122 to define the plane, and thus define the flow path curve 105, applies to other embodiments, as this helps to define the curve for embodiments where the front housing 106 is stationary. The flow path curve 105 of the rotator 106 has a convex position in the axial location, where the radius reaches the maximum axial front of the foremost point of the front blade root 122 of the blade 102, thereby determining the first radius 110 (in Figure 10 (represented as "r1" in the original text). The flow path curve 105 of the rotator 106 has a local minimum position, where the radius reaches a local minimum near the blade 102 as it travels rearward from the convex axis, thus determining the second radius 112 (in...). Figure 10The axial position of the first radius 110 is forward of the axial position of the second radius 112 (i.e., between the axial position of the second radius 112 and the forward-most position 108 of the rotor 106). The span of the blade 102 is defined as the distance between the blade root 122 and the blade tip 124. In one embodiment, the blade 102 has a maximum axial distance / width 140 near the mid-span (i.e., 50% of the blade height from the blade root to the blade tip). In one embodiment, the blade 102 is fixed to the rotor 106 such that when oriented or configured for cruise operation, the forward-most point of the blade root 122 is proximate to the local minimum with the second radius 112, and such that 0% to 40% of the maximum width 140 is forward of the forward-most point of the blade root 122. In another embodiment, 20% to 40% of the maximum width 140 is forward of the forward-most point of the blade root 122.

[0103] In one embodiment, the first radius 110 is greater than the second radius 112, and thus defines a convexity of the rotor 106, the location on the rotor progressing axially forward from the forward blade root 122 where the radius reaches a maximum. The first distance 114 (denoted by “zl” in Figure 10 the local minimum with the second radius 112. The second distance (denoted by “z2” in Figure 10 the local minimum with the second radius 112. The various parameters (i.e., the first radius 110, the second radius 112, the first distance 114, and the second distance 116) can be specified based on a predetermined speed of the aircraft. That is, suitable values for the various parameters depend on a predetermined speed range of the aircraft. In some embodiments, the predetermined speed of the aircraft is based on a desired airspeed of the aircraft. For example, the predetermined speed of the aircraft can be a speed or speed range at which the aircraft is designed to operate at cruise. The predetermined speed of the aircraft can be any suitable value, and may, for example, be between 0.74 Mach and 0.86 Mach (also referred to herein as a high subsonic cruise speed). Although the example predetermined speed range of the aircraft is between 0.74 Mach and 0.86 Mach, it should be noted that this range can be greater than or less than the provided range, and have higher and / or lower maximum and minimum values. For example, the predetermined flight Mach number can be between 0.78 and 0.84.

[0104] At a high level, as the predetermined speed of the aircraft increases, the size of the bulge (i.e., the ratio of the first radius 110 to the second radius 112) that favors low pressure losses on the spinner and within the blade 102 assembly increases. Simply put, for a particular flight speed, the larger the bulge, the lower the flow velocity through the blade 102 row. However, as the size of the bulge increases, the length required for the spinner 106 increases, and the weight of the rotating element 138 increases. Thus, the size of the bulge is determined by a number of factors based on the predetermined speed of the aircraft. Further, the minimum size of the second radius 112 is generally dictated by the equipment required for the rotating element 138 (e.g., blade retention hardware, pitch change mechanisms, counterweight systems, gearboxes, gearbox cooling systems, lubrication systems, bearings, and drive shafts).

[0105] In one embodiment, composed of a forward blade assembly and an aft blade assembly, the dimensionless bulge radius is r1 / r2 > 1.029. In other embodiments, the size of the bulge is described by the ratio of the first radius 110 to the second radius 112 and is defined by EQ. 4:

[0106]

[0107] where r1 is the first radius 110, r2 is the second radius 112 associated with the housing 106, M0 is the Mach number of the sustained high-speed flight (e.g., cruise) of the aircraft, and A2 is a constant. In one embodiment, the value of A2 is in the range of 1.04 to 1.14. As shown in EQ. 4, for each A2 value in this range, the size of the bulge (i.e., the ratio of the first radius 110 to the second radius 112) increases as the predetermined speed of the aircraft increases. Specifically, for the minimum value A2 = 1.04, the ratio of the first radius 110 to the second radius 112 is 1.029 at M0 = 0.74, 1.040 at M0 = 0.79, 1.051 at M0 = 0.84, and 1.055 at M0 = 0.86. For the maximum value A2 = 1.14, the ratio of the first radius 110 to the second radius 112 is 1.103 at M0 = 0.74, 1.140 at M0 = 0.79, 1.177 at M0 = 0.84, and 1.192 at M0 = 0.86. Table 4 provides examples of the ratio of the first radius 110 to the second radius 112 where 1.04 < A2 < 1.14 (bolded) and 0.74 < M0 < 0.86.

[0108]

[0109] Table 4

[0110] As previously mentioned, the geometry of the spinner 106 can also be described based on the first distance 114 (i.e., the axial distance between the protrusion having the first radius 110 and the local minimum having the second radius 112). In one embodiment consisting of a front vane assembly and a rear vane assembly, the dimensionless axial distance z1 / r2<1.522. In another embodiment, the first distance 114 is described in terms of a ratio of the first distance 114 to the second radius 112 and is defined by EQ. 5:

[0111]

[0112] where z1 is the first distance 114, r2 is the second radius 112, M0 is the Mach number of a sustained high-speed flight (e.g., cruise) of the aircraft, and B2 is a value. In one embodiment, the value of B2 is in the range of 0.78 to 1.18. As shown in EQ. 5, for each B2 value in this range, the first distance 114 increases with an increase in the predetermined speed of the aircraft. Simply put, the length of the spinner 106 increases with an increase in the predetermined speed of the aircraft. Specifically, for the minimum value B2=0.78, the ratio of the first distance 114 to the second radius 112 is 0.641 at M0=0.74, 0.780 at M0=0.79, 0.938 at M0=0.84, and 1.006 at M0=0.86. For the maximum value B2=1.18, the ratio of the first distance 114 to the second radius 112 is 0.970 at M0=0.74, 1.180 at M0=0.79, 1.419 at M0=0.84, and 1.522 at M0=0.86. Table 5 provides examples of the ratio of the first distance 114 to the second radius 112 where 0.78<B2<1.18 (bold) and 0.74<M0<0.86.

[0113]

[0114] Table 5

[0115] As previously mentioned, the geometry of the spinner 106 can also be described based on the second distance 116 (i.e., the distance between the forward-most position 108 of the spinner 106 and the local minimum having the second radius 112). In one embodiment consisting of a front vane assembly and a rear vane assembly, the dimensionless axial distance z2 / r2<4.115. In one embodiment, the second distance 116 is described in terms of a ratio between the second distance 116 and the second radius 112 and is defined by EQ. 6:

[0116]

[0117] where z2 is the second distance 116, r2 is the second radius 112, M0 is the Mach number of the aircraft's sustained high-speed flight (e.g., cruising), and C2 is a value. In one embodiment, C2 has a value in the range of 2.19 to 3.19. As shown in EQ. 6, the second distance 116 increases as the predetermined speed of the aircraft increases. Simply put, the length of the spinner 106 increases as the predetermined speed of the aircraft increases. Specifically, for a minimum value of C2 = 2.19, the ratio of the second distance 116 to the second radius 112 is 1.800 at M0 = 0.74, 2.190 at M0 = 0.79, 2.633 at M0 = 0.84, and 2.825 at M0 = 0.86. For a maximum value of C2 = 3.19, the ratio of the second distance 116 to the second radius 112 is 2.622 at M0 = 0.74, 3.190 at M0 = 0.79, 3.835 at M0 = 0.84, and 4.115 at M0 = 0.86. Table 6 provides examples of the ratio of the second distance 216 to the second radius 112, where 2.19 < C2 < 3.19 (bolded) and 0.74 < M0 < 0.86.

[0118]

[0119] Table 6

[0120] While Figure 10 the discussion of the non-piped propulsion system for propelling an aircraft consistent with the teachings herein, the discussion of Figure 11 provides more details of plots of values of geometric dimensions of the spinner of such non-piped propulsion systems.

[0121] Figure 11 is a plot 200 depicting the shape of the outer flow path of the spinner of a non-piped propulsion system in accordance with some embodiments. The Y-axis 204 represents the spinner radius r / r2 normalized by the second radius 112, which is at a local minimum in the axial extent closest to the blade 102 having the first radius 110. The X-axis 202 represents the axial distance z / r2 from the axial location of the second radius 112 (i.e., the local minimum) normalized by the second radius 112.

[0122] FIG. 200 shows forebody or spinner 106 shapes for different cruise Mach numbers M0. Specifically, FIG. 200 includes a first graph 206, a second graph 208, a third graph 210, and a fourth graph 212. Each of the first graph 206, the second graph 208, the third graph 210, and the fourth graph 212 is from the same values A2= 1.09, B2= 0.98, and C2= 2.69, but for different cruise Mach numbers M0. The first graph 206 corresponds to M0= 0.70, the second graph 208 corresponds to M0= 0.74, the third graph 210 corresponds to M0= 0.79, and the fourth graph 212 corresponds to M0= 0.84. As can be seen from FIG. 200, which depicts the general shape and relative dimensions of the spinner, the ratio of the first radius to the second radius and the ratio of the second distance to the second radius increase with increasing predetermined velocity.

[0123] In addition to specifying the forebody size ratios, further constraints on the shape of the flowpath curve are described herein. The following super-elliptic equation can provide an appropriate curvature distribution along the flowpath curve 105 to avoid excessive Mach numbers along the forebody portion forward of the protuberance. The super-elliptic expression provides an optional boundary on the flowpath curve 105 forward of the protuberance when specifying the shape of the spinner using the obtained r1, z1, and z2. EQ. 7 below gives the super-elliptic in terms of the axial coordinate z and the radius r.

[0124] or, equivalently,

[0125] In EQ. 7, the exponents p and q define the shape of the curve forward of the protuberance via the ratios r1 / r2, z1 / r2, and z2 / r2 determined via EQS. 4, 5, and 6 above. Figure 12 Provided are shapes of the flowpath curve 105 that are Figure 11FIG. 1200 is similar to FIG. 200. Thus, the X-axis 202 and Y-axis 204 and curve 210 in FIG. 1200 are the same as in FIG. 200. Curves 1208 and 1212 conform to the same ratios as curve 210, determined by EQS 4, 5, and 6. However, curves 1208 and 1212 define the range of suitable points of flowpath curve 105 by using EQ. 7 to determine the values of exponents p and q. Curve 1208, where exponent p = 1.5 and q = 2.0, forms a lower limit on suitable points of flowpath curve 105 forward of the bump. Curve 1212, where exponent p = 3.0 and q = 3.5, forms an upper limit on suitable points of flowpath curve 105 forward of the bump. Thus, within the axial range from the bump to the forward-most end 108 of forward case 106, EQ. 7 with a range of exponents p and q provides a band or range of points to limit the shape of forward case 106. Curve 210 fits EQ. 7 very well using exponents p = 2.0 and q = 3.0. Thus, the lower limit is chosen to conform to the range of exponents 1.5 < p < 2.0 and 2.0 < q < 3.0, while the upper limit is chosen to conform to the range of exponents 2.0 < p < 3.0 and 3.0 < q < 3.5. For at least some cruise Mach numbers M0, such as 0.79 shown in FIG. 210, a low-loss flowpath curve can be obtained within more limited bounds, such that the lower limit on the flowpath curve is constrained to the range 1.7 < p < 2.0 and 2.5 < q < 3.0, while the upper limit on the flowpath curve is constrained to the range 2.0 < p < 2.5 and 3.0 < q < 3.3.

[0126] In some configurations, the above-mentioned spinner shape parameters associated with a predetermined flight speed can be particularly advantageous in designing a spinner shape. The thrust parameter is the same as defined above: The thrust parameter can be greater than or equal to 0.060 (e.g., greater than 0.080 or greater than 0.084).

[0127] It is recognized that the front housing 106 or spinner need not be axisymmetric about the axis of rotation of the propeller. For example, at an axial location proximate a second radius of the plurality of blades, the distance of the spinner or hub surface can vary in the circumferential direction to accommodate blade attachment or variable pitch mechanisms. As previously noted, for axial locations along the front housing 106 that rotate about the axis of rotation 120, as is the case with a spinner, the radius (e.g., the second radius) is defined as the “effective” radius of a circle having the same cross-sectional area of the spinner normal to the axis of rotation. Thus, the term “radius” as used in the specification and claims refers to the radius of a circle having the cross-sectional area of the spinner at that axial location. However, for a stationary front housing 106, as is the case for a non-ducted propulsion system in which the front blade assembly is stationary and the rear blade assembly rotates, the flow path curve 105 corresponds to the intersection of the front housing with a plane that includes the axis of rotation and the forward-most point of the front blade roots 122. If the front blades 102 have variable pitch, the forward-most point corresponds to the blade orientation that positions the forward-most point in its forward-most position, which can approximate cruise or design point conditions. In this case, the flow path curve 105 disclosed herein can correspond to one, more than one, or all of the blade roots 122. In cases where the forward-most point of the front blade roots 122 is not attached to the front housing 106, e.g., there is a gap spacing between the front blade roots 122 and the front housing 106 to allow for pitch variation, or the front blades 102 are attached to a pylon and suspended from the front housing 106, then the curve 105 passes through the forward-most point of the front blade roots 122 to the nearest point on the surface of the front housing 106.

[0128] In some embodiments, a rotating element for a non-ducted propulsion system for propelling an aircraft includes a plurality of blades fixed to a spinner, wherein the spinner is configured to rotate about an axis of rotation, wherein the spinner includes a first radius and a second radius, wherein the second radius is proximate the plurality of blades, and the first radius is forward from the second radius, wherein a ratio of the first radius to the second radius is in a range of 1.029 to 1.192, and wherein the aircraft is configured to travel at a predetermined speed.

[0129] In some embodiments, a rotating element of a non-piped propulsion system for propelling an aircraft includes a plurality of blades fixed to a spinner, wherein the spinner is configured to rotate about an axis of rotation, wherein a flow path curve on the spinner includes a first radius and a second radius, wherein the first radius is at a convexity or maximum radius in front of the associated plurality of blades, wherein the second radius is at a local minimum behind the convexity, wherein a first distance is defined between an axial location of the convexity and the local minimum, and wherein a second distance is defined between a forward-most end of the spinner and an axial location of the local minimum, wherein a ratio of the first radius to the second radius is in a range of 1.029 to 1.192, wherein a ratio of the first distance to the second radius is in a range of 0.641 to 1.522, wherein a ratio of the second distance to the second radius is in a range of 1.800 to 4.115, and wherein the aircraft is configured to travel at a predetermined speed. Figure 13 is a flowchart of a method 1300 of operating a non-piped propulsion system for propelling an aircraft. The non-piped propulsion system includes a spinner and a plurality of blades fixed to the spinner. The method includes a step 1302 of rotating the spinner about an axis of rotation and a step 1304 of operating the aircraft at a predetermined speed greater than or equal to 0.74 Mach. The spinner can be rotated relative to the plurality of blades. Figure 1 and Figure 2 configured as described herein. For example, the spinner can include a first radius and a second radius, wherein the second radius is proximate to the plurality of blades and the first radius is forward from the second radius, wherein a ratio of the first radius to the second radius is greater than 1.029. Further, the ratio of the first radius to the second radius can be defined by EQ. 4:

[0130]

[0131] wherein rl is the first radius, r2 is the second radius, M0 corresponds to a predetermined sustained speed of the aircraft (e.g., cruise), and A2 is a value in a range of 1.04 to 1.14.

[0132] Further, a first distance is defined between an axial location corresponding to the first radius and an axial location corresponding to the second radius, and a ratio of the first distance to the second radius is less than 1.522. Further, the ratio of the first distance to the second radius can be defined by EQ. 5:

[0133]

[0134] wherein zl is the first distance, r2 is the second radius, M0 corresponds to a predetermined sustained speed of the aircraft (e.g., cruise), and B2 is a value in a range of 0.78 to 1.18.

[0135] Further, a second distance is defined between a forward-most end of the spinner and an axial location corresponding to the second radius, and a ratio of the second distance to the second radius is less than 4.115. Further, the ratio of the second distance to the second radius can be defined by EQ. 6:

[0136]

[0137] where z2 is the second distance, r2 is the second radius, M0 corresponds to a predetermined sustained high speed of the aircraft (such as cruise), and C2 is a value in the range of 2.19 to 3.19.

[0138] A non-ducted propulsion system for an aircraft configured for high subsonic cruise, comprising: a rotational axis; a forward vane assembly, the forward vane assembly consisting of a plurality of forward vanes; an aft vane assembly, the aft vane assembly consisting of a plurality of aft vanes; a forward housing; an aft housing; wherein, for each forward vane and each aft vane, comprises a vane root proximate to the rotational axis and a vane tip distal to the rotational axis; wherein, a flowpath curve corresponds to an intersection of an outer surface of the forward housing and a plane containing the rotational axis and a forward-most point of the vane root; wherein, for the flowpath curve, an axial direction z is parallel to the rotational axis and a radius r is a first distance from the rotational axis; wherein, a convex position on the flowpath curve having a radius r1 is found by proceeding forward from the forward-most point on the vane root to a location where the first radius reaches a maximum; wherein, a local minimum on the flowpath curve having a radius r2 is found by proceeding aft from the convex position to a nearest point where the second radius stops decreasing within an axial extent of the vane root, and wherein a ratio r1 / r2 > 1.029.

[0139] The non-ducted propulsion system according to any preceding clause, wherein an axial distance z1 is between the convex position and the local minimum, and wherein a ratio z1 / r2 < 1.522.

[0140] The non-ducted propulsion system according to any preceding clause, wherein an axial distance z2 is between a forward-most end of the forward housing and the local minimum, and wherein a ratio z2 / r2 < 4.115.

[0141] The non-ducted propulsion system according to any preceding clause, wherein the aircraft is configured to cruise at a Mach number of 0.74 < M0 < 0.86, and wherein where 1.04 < A2 < 1.14.

[0142] The non-ducted propulsion system according to any preceding clause, wherein, where 0.78 < B2 < 1.18.

[0143] The un-tubulated propulsion system of any preceding clause, wherein wherein 2.19 < C2< 3.19.

[0144] The un-tubulated propulsion system of any preceding clause, wherein 1.06 < A2< 1.14.

[0145] The un-tubulated propulsion system of any preceding clause, wherein 0.78 < B2< 1.08.

[0146] The un-tubulated propulsion system of any preceding clause, wherein 2.19 < C2< 2.99.

[0147] The un-tubulated propulsion system of any preceding clause, wherein 1.06 < A2< 1.12.

[0148] The un-tubulated propulsion system of any preceding clause, wherein 0.88 < B2< 1.08.

[0149] The un-tubulated propulsion system of any preceding clause, wherein 2.39 < C2< 2.99.

[0150] The un-tubulated propulsion system of any preceding clause, wherein the aircraft is configured to have a dimensionless cruise thrust parameter wherein at cruise operation:

[0151] (i) F net is the fan net thrust,

[0152] (ii) p0 is the ambient air density,

[0153] (iii) V0 is the flight speed,

[0154] (iv) A an is the fan flow tube annulus area into the fan, and

[0155] (v)

[0156] The un-tubulated propulsion system of any preceding clause, wherein

[0157] The un-tubulated propulsion system of any preceding clause, wherein the forward vane assembly and the forward housing are stationary, and wherein the aft vane assembly and a portion of the aft housing to which the plurality of aft vanes are attached rotate about the axis of rotation.

[0158] The un-ducted propulsion system according to any preceding clause, wherein the flow path curve further corresponds to respective forward-most points of two or more forward vane roots.

[0159] The un-ducted propulsion system according to any preceding clause, wherein the flow path curve further corresponds to respective forward-most points of at least half of the forward vane roots.

[0160] The un-ducted propulsion system according to any preceding clause, wherein the forward vane assembly and the forward casing rotate about the rotation axis, wherein a portion of the aft casing to which the aft vane assembly and the plurality of aft vanes are fixed rotate about the rotation axis, and wherein a third radius at a given axial position of the forward casing rotation is an effective radius that is a fourth radius of a circle having the same cross-sectional area perpendicular to the rotation axis at that axial position.

[0161] The un-ducted propulsion system according to any preceding clause, wherein the forward vane assembly and the forward casing rotate about the rotation axis, wherein the aft vane assembly and the aft casing are stationary, and wherein a third radius at a given axial position of the forward casing rotation is an effective radius that is a fourth radius of a circle having the same cross-sectional area perpendicular to the rotation axis at that axial position.

[0162] The un-ducted propulsion system according to any preceding clause, wherein a number of vanes in the forward vane assembly is greater than 4, wherein a number of vanes in the aft vane assembly is greater than 4, and wherein a ratio of the number of vanes in the forward vane assembly to the number of vanes in the aft vane assembly is between 2:5 and 2:1.

[0163] The un-ducted propulsion system according to any preceding clause, wherein the number of vanes in the forward vane assembly is between 8 and 18.

[0164] The un-ducted propulsion system according to any preceding clause, wherein a difference between the number of vanes in the forward vane assembly and the number of vanes in the aft vane assembly is between 2 and -2.

[0165] The un-ducted propulsion system according to any preceding clause, wherein a ratio r1 / r2 > 1.044.

[0166] The un-ducted propulsion system according to any preceding clause, wherein an axial distance z1 is between the convex position and the local minimum, and wherein a ratio z1 / r2 < 1.393.

[0167] The un-ducted propulsion system according to any preceding clause, wherein an axial distance z2 is between a forward-most end of the forward housing and the local minimum, and wherein z2 / r2 < 3.857.

[0168] The un-ducted propulsion system according to any preceding clause, wherein a span is a second distance between the blade root and the blade tip, wherein the plurality of forward blades in the forward blade assembly are oriented for cruise operation, wherein the plurality of forward blades in the forward blade assembly have a maximum axial width near the intermediate span, and wherein 0% to 40% of the maximum axial width is forward of the forward-most point of the forward blade root.

[0169] The un-ducted propulsion system according to any preceding clause, wherein an origin of a flow path curve (z, r) coordinate system is at an axial location of the local minimum, wherein an axial coordinate z increases in a forward direction, wherein a curve forward of the convexity (z > zl) lies within lower and upper bounds defined by wherein the lower bound has exponents 1.5 < p < 2.0 and 2.0 < q < 3.0, and wherein the upper bound has exponents 2.0 < p < 3.0 and 3.0 < q < 3.5.

[0170] The un-ducted propulsion system according to any preceding clause, 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.

[0171] An un-ducted propulsion system for an aircraft configured for high subsonic cruise, comprising: a rotational axis; a forward blade assembly, the forward blade assembly consisting of a plurality of forward blades; a forward housing; wherein, for each blade, comprising a blade root proximate the rotational axis and a blade tip distal from the rotational axis; wherein a flow path curve corresponds to an intersection of an outer surface of the forward housing and a plane containing the rotational axis and a forward-most point of the forward blade root; wherein, for the flow path curve, an axial direction z is parallel to the rotational axis and a radius r is a distance from the rotational axis; wherein a convex position on the flow path curve having a radius rl is found by proceeding forward from the forward-most point on the forward blade root to a location where the first radius reaches a maximum; wherein a local minimum on the flow path curve having a radius r2 is found by proceeding backward from the convex position to a nearest point where the second radius stops decreasing, and wherein r1 / r2 > 1.066.

[0172] The un-ducted propulsion system according to any preceding clause, wherein an axial distance zl is between the convex position and the local minimum, and wherein zl / r2 < 1.522.

[0173] The un-ducted propulsive system according to any preceding clause, wherein an axial distance z2 is between a forward-most end of the forward housing and the local minimum, and wherein z2 / r2<4.115.

[0174] An un-ducted propulsive system for an aircraft configured for high subsonic cruise, comprising: a rotational axis; a forward vane assembly, the forward vane assembly consisting of a plurality of forward vanes; an aft vane assembly, the aft vane assembly consisting of a plurality of aft vanes; a forward housing; an aft housing; wherein each forward vane and each aft vane comprises a vane root proximal to the rotational axis and a vane tip distal to the rotational axis; wherein a flowpath curve corresponds to an intersection of an outer surface of the aft housing with a plane containing the rotational axis and a last point on the aft vane root; wherein, for the flowpath curve, an axial direction z is parallel to the rotational axis, and a radius r is a distance from the rotational axis; wherein a convex position on the flowpath curve having a radius r b is found by proceeding aft from the last point on the aft vane root to a first radius where a maximum is reached; wherein a local minimum on the flowpath curve having a radius r h is found by proceeding forward from the convex position to a second radius where a nearest point is reached where the decrease stops within an axial extent of the aft vane root; and wherein r b / r h >1.081.

[0175] The un-ducted propulsive system according to any preceding clause, wherein an axial distance z b is between the convex position and the local minimum, and wherein z b / r h <2.103.

[0176] The un-ducted propulsive system according to any preceding clause, wherein a position having a radius r m is located axially halfway between the convex position and the local minimum, and wherein r

[0177] The un-ducted propulsive system according to any preceding clause, wherein the aircraft is configured to cruise at a Mach number of 0.74 wherein 1.11

[0178] The un-ducted propulsive system according to any preceding clause, wherein wherein 1.23

[0179] The un-ducted propulsion system of any preceding clause, wherein wherein 0.59 < C1 < 0.79.

[0180] The un-ducted propulsion system of any preceding clause, wherein 1.16 < A1 < 1.31.

[0181] The un-ducted propulsion system of any preceding clause, wherein 1.23 < B1 < 1.53.

[0182] The un-ducted propulsion system of any preceding clause, wherein 0.64 < C1 < 0.79.

[0183] The un-ducted propulsion system of any preceding clause, wherein 1.16 < A1 < 1.26.

[0184] The un-ducted propulsion system of any preceding clause, wherein 1.33 < B1 < 1.53.

[0185] The un-ducted propulsion system of any preceding clause, wherein 0.64 < C1 < 0.74.

[0186] The un-ducted propulsion system of any preceding clause, wherein the aircraft is configured to have a dimensionless cruise thrust parameter wherein at cruise operation:

[0187] (i) F net is the fan net thrust,

[0188] (ii) p0 is the ambient air density,

[0189] (iii) V0 is the flight speed,

[0190] (iv) A an is the fan flow tube annulus area into the fan, and

[0191] (v)

[0192] The un-ducted propulsion system of any preceding clause, wherein

[0193] The un-ducted propulsion system of any preceding clause, wherein the forward vane assembly and the forward housing rotate about the axis of rotation, and wherein the aft vane assembly and the aft housing are stationary.

[0194] The un-ducted propulsion system of any preceding clause, wherein the flow path curve further corresponds to respective last points of two or more aft vane roots.

[0195] The un-ducted propulsion system according to any preceding clause, wherein the flow path curve further corresponds to a respective last point of at least half of the rear vane roots.

[0196] The un-ducted propulsion system according to any preceding clause, wherein the front vane assembly and the front housing rotate about the rotation axis, wherein a portion of the rear housing to which the rear vane assembly and the plurality of rear vanes are fixed rotate about the rotation axis, and wherein a third radius at a given axial position of the rear housing rotation is an effective radius, the effective radius being a fourth radius of a circle having the same cross-sectional area perpendicular to the rotation axis at that axial position.

[0197] The un-ducted propulsion system according to any preceding clause, wherein the front vane assembly and the front housing are stationary, wherein a portion of the rear housing to which the rear vane assembly and the plurality of rear vanes are fixed rotate about the rotation axis, and wherein a third radius at a given axial position of the rear housing rotation is an effective radius, the effective radius being a fourth radius of a circle having the same cross-sectional area perpendicular to the rotation axis at that axial position.

[0198] The un-ducted propulsion system according to any preceding clause, wherein a number of vanes in the front vane assembly is greater than 4, wherein a number of vanes in the rear vane assembly is greater than 4, and wherein a ratio of the number of vanes in the front vane assembly to the number of vanes in the rear vane assembly is between 2:5 and 2:1.

[0199] The un-ducted propulsion system according to any preceding clause, wherein a number of vanes in the front vane assembly is between 8 and 18.

[0200] The un-ducted propulsion system according to any preceding clause, wherein a difference between the number of vanes in the front vane assembly and the number of vanes in the rear vane assembly is between 2 and -2.

[0201] The un-ducted propulsion system according to any preceding clause, wherein a ratio r b / r h > 1.118.

[0202] The un-ducted propulsion system according to any preceding clause, wherein an axial distance z b between the convex position and the local minimum, and wherein a ratio z b / r h < 1.974.

[0203] The un-ducted propulsion system according to any preceding clause, wherein a radius is rm the position of the local minimum, and wherein the ratio

[0204] The non-piped propulsion system according to any preceding clause, wherein the ratio b / r h <1.424.

Claims

1. A non-piped propulsion system for an aircraft configured for high subsonic cruise, characterized in that, Comprising: a rotation axis; a front vane assembly consisting of a plurality of front vanes; a rear vane assembly consisting of a plurality of rear vanes; a front casing; a rear casing; wherein, for each front vane and each rear vane, a vane root close to the rotation axis and a vane tip away from the rotation axis are comprised; wherein a flow path curve corresponds to the intersection of the outer surface of the front casing with a plane containing the rotation axis and the most forward point of the front vane root; wherein, for the flow path curve, an axial direction z is parallel to the rotation axis and a radius r is a first distance from the rotation axis; wherein a convex position on the flow path curve with a radius r1 is found by proceeding forward from the most forward point on the front vane root to a position where the first radius reaches a maximum; wherein a local minimum on the flow path curve with a radius r2 is found by proceeding backward from the convex position to the nearest point where the second radius stops decreasing within the axial extent of the front vane root, and wherein the ratio r1 / r2 > 1.029; wherein an axial distance z1 is between the convex position and the local minimum, and wherein the ratio z1 / r2 < 1.522; and wherein an axial distance z2 is between the most forward end of the front casing and the local minimum, and wherein the ratio z2 / r2 < 4.

115.

2. The un-tubulated propulsion system of claim 1, wherein, wherein, The aircraft is configured for cruise Mach number 0.74 < M0< 0.86, and wherein, wherein A2 is a constant, with 1.04 < A2 < 1.

14.

3. The un-tubulated propulsion system of claim 2, wherein, wherein, wherein B2 is a constant, with 0.78 < B2 < 1.

18.

4. The un-tubulated propulsion system of claim 3, wherein, wherein, wherein C2 is a constant, with 2.19 < C2 < 3.

19.

5. The un-tubulated propulsion system of claim 4, wherein, wherein, 1.06<A2<1.14。 6. The un-tubulated propulsion system of claim 5, wherein, wherein, 0.78<B2<1.08。 7. The un-tubulated propulsion system of claim 6, wherein, wherein, 2.19<C2<2.99。 8. The un-tubulated propulsion system of claim 7, wherein, wherein, 1.06<A2<1.12。 9. The un-tubulated propulsion system of claim 8, wherein, wherein, 0.88<B2<1.08。 10. The un-tubulated propulsion system of claim 9, wherein, wherein, 2.39<C2<2.99。 11. The un-tubulated propulsion system of claim 4, wherein, wherein, The aircraft is configured to have a dimensionless cruise thrust parameter wherein at cruise operation i.F net is the net thrust of the fan, wherein, ii. p0 is the ambient air density, iv.A an is the fan flow tube annular area of the incoming fan, and 12. The un-tubulated propulsion system of claim 11, wherein, iii. V0 is the flight speed, 13. The un-tubulated propulsion system of claim 4, wherein, wherein, wherein, 14. The un-tubulated propulsion system of claim 13, wherein, the front vane assembly and the front casing are stationary, and wherein the rear vane assembly and a portion of the rear casing to which the plurality of rear vanes is attached rotate around the rotation axis. wherein, 15. The un-tubulated propulsion system of claim 13, wherein, the flow path curve further corresponds to the respective most forward points of two or more front vane roots. wherein, 16. The un-tubulated propulsion system of claim 4, wherein, the flow path curve further corresponds to the respective most forward points of at least half of the front vane roots. wherein, 17. The un-tubulated propulsion system of claim 4, wherein, the front vane assembly and the front casing rotate around the rotation axis, wherein the rear vane assembly and a portion of the rear casing to which the plurality of rear vanes is fixed rotate around the rotation axis, and wherein a third radius at a given axial position of the rotation of the front casing is an effective radius, the effective radius being a fourth radius of a circle having the same cross-sectional area perpendicular to the rotation axis at that axial position. wherein, 18. The un-tubulated propulsion system of claim 4, wherein, the front vane assembly and the front casing rotate around the rotation axis, wherein the rear vane assembly and the rear casing are stationary, and wherein a third radius at a given axial position of the rotation of the front casing is an effective radius, the effective radius being a fourth radius of a circle having the same cross-sectional area perpendicular to the rotation axis at that axial position. wherein, The number of blades in the front blade assembly is greater than 4, wherein the number of blades in the rear blade assembly is greater than 4, and wherein the ratio of the number of blades in the front blade assembly to the number of blades in the rear blade assembly is between 2:5 and 2:

1.

19. The un-tubulated propulsion system of claim 18, wherein, wherein, The number of blades in the front blade assembly is between 8 and 18.

20. The un-tubulated propulsion system of claim 19, wherein, wherein, The difference between the number of blades in the front blade assembly and the number of blades in the rear blade assembly is between 2 and -2.

21. The un-tubulated propulsion system of claim 1, wherein, wherein, The ratio r1 / r2 is > 1.

044.

22. The un-tubulated propulsion system of claim 21, wherein, wherein, The axial distance z1 is between the convex position and the local minimum, and wherein the ratio z1 / r2 is < 1.

393.

23. The un-tubulated propulsion system of claim 22, wherein, wherein, The axial distance z2 is between the forward-most end of the front casing and the local minimum, and wherein The ratio z2 / r2 is < 3.

857.

24. The un-tubulated propulsion system of claim 18, wherein, wherein, The span is a second distance between the blade root and the blade tip, wherein the plurality of front blades in the front blade assembly are oriented for cruise operation, wherein the plurality of front blades in the front blade assembly have a maximum axial width near the intermediate span, and wherein 0% to 40% of the maximum axial width is forward of the forward-most point of the front blade root.

25. The un-tubulated propulsion system of claim 4, wherein, wherein, The origin of the flow path curve (z, r) coordinate system is at the axial position of the local minimum, wherein the axial coordinate z increases in the forward direction, wherein the curve in front of the convexity (z > zl) lies within the lower and upper limits defined by wherein p and q are exponents, wherein the exponents of the lower limits are 1.5 < p < 2.0 and 2.0 < q < 3.0, and wherein the exponents of the upper limits are 2.0 < p < 3.0 and 3.0 < q < 3.

5.

26. The un-tubulated propulsion system of claim 25, wherein, wherein, The exponents of the lower bound are 1.7 < p < 2.0 and 2.3 < q < 3.0, and wherein the exponents of the upper bound are 2.0 < p < 2.5 and 3.0 < q < 3.

3.

27. A non-piped propulsion system for an aircraft configured for high subsonic cruise, characterized in that, comprising: a rotational axis; a front blade assembly, the front blade assembly consisting of a plurality of front blades; a front casing; wherein, for each front blade, comprising a front blade root proximate the rotational axis and a front blade tip distal from the rotational axis; wherein, a flow path curve corresponds to an intersection of an outer surface of the front casing and a plane containing the rotational axis and a forward-most point of the front blade root; wherein, for the flow path curve, an axial direction z is parallel to the rotational axis and a radius r is a distance from the rotational axis; wherein, a convex position on the flow path curve having a radius r1 is found by proceeding forward from the forward-most point on the front blade root to a location where a first radius reaches a maximum; wherein, a local minimum on the flow path curve having a radius r2 is found by proceeding backward from the convex position to a nearest point where a second radius stops decreasing, and wherein, the ratio r1 / r2 is > 1.066; wherein, an axial distance z1 is between the convex position and the local minimum, and wherein the ratio z1 / r2 is < 1.522; and wherein, an axial distance z2 is between a forward-most end of the front casing and the local minimum, and wherein the ratio z2 / r2 is < 4.115.

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