Abradable coating for turbine

Abstract

The present invention relates to an aeronautical propulsion system (1) comprising: a primary body (3); and a blower section (2).

Description

Title of the invention: Abradable coating for turbine technical field

[0001] The present exposition falls within the aeronautical field. More specifically, the present exposition relates to abradable coatings for a turbine section of an aircraft engine. STATE OF THE ART

[0002] A turbine section of an aircraft engine may include abradable elements arranged directly and radially opposite the rotor parts of the turbine section. These abradable elements allow, in particular, for improved sealing of the exhaust stream through which the exhaust gases are expanded within the turbine section. To maintain good sealing performance, it is particularly important to maintain a small operating clearance between these abradable elements and the rotor parts, the rotor elements generally being equipped with flaps that, together with the abradable elements, form a labyrinth seal.

[0003] Due to the high temperatures of these exhaust gases, the service life of these abradable components and / or the housings to which they are attached may be reduced. GENERAL STATEMENT

[0004] One object of the present exposition is to improve the thermal resistance of a turbine section of an aircraft engine.

[0005] To this end, an aeronautical propulsion system is proposed, according to one aspect of this presentation, comprising: a primary body delimiting a primary vein; and a blower section comprising a stator and a rotor centered on a longitudinal axis, the rotor being configured to be driven in rotation relative to the stator around the longitudinal axis so as to draw in a flow dividing into a primary flow intended to circulate within the primary vein and a secondary flow intended to circulate around the primary body; in which the primary body comprises: a shaft extending along the longitudinal axis; and a turbine comprising: a rotor configured to drive the shaft in rotation about the longitudinal axis, and comprising a disk centered on the longitudinal axis, and a blade comprising a foot connected to the disk and a vertex radially opposite to the foot; and a stator comprising a housing and an abradable element fixed to the housing, the abradable element being arranged directly above and at a distance from the apex of the blade, the abradable element presenting an upstream end edge and a downstream end edge, the abradable element being made up of a plurality of identical cells, each cell of the plurality of cells comprising a wall having an inner face delimiting a tubular space and an outer face opposite to the inner face, the tubular space having a first end opening onto the primary vein and a second end closed by the casing, the tubular space extending in a principal direction from the first end to the second end and having a plurality of sections taken in a plane orthogonal to the principal direction, each section of the plurality of sections being of regular hexagonal shape, the plurality of cells being arranged in a honeycomb pattern in which two adjacent cells of the plurality of cells are fixed to each other via their respective outer faces; in which: (T4OO)xJo.O23x,..x«°' x!2wx30x8«e 'OR: ---------;--------< 8.0 x Iff8 xC^x(T-600J is a temperature ® <Z+Mx3a-lfeo 0,00157 --7--x—i—i ) intended to be achieved in operation by a fluid entering a low-pressure turbine of the turbine, when the aeronautical propulsion system is operating at constant maximum power, T being expressed in degrees Celsius, and T being greater than or equal to 1100°C and less than or equal to 1250°C; 2(T) = C x T3 - x T2 + 0 x T - k, with Σ = 1.5207 x 10'1 7 = 4.857 x 10A 0 — 1.0184 x 10⁴⁰ K = 3.9333 x 10⁴, being expressed in degrees Kelvin, 4(T) being greater than or equal to 1.0.10³ Wm⁻¹.K⁻¹ and less than or equal to 2.0.10² Wm⁻¹.K⁻¹; e is a wall thickness of a cell in the plurality of cells, e being defined as a distance separating the inner face from the outer face of the wall, e being greater than or equal to 0.02 millimeter and less than or equal to 0.15 millimeter; a — + 3^2, being a radius circumscribed to a section of the plurality of sections of the tubular space of the cell of the plurality of cells, eta being greater than or equal to 0.25 millimeter and less than or equal to 1.0 millimeter; 1= 2xr^ ri being the radius inscribed in the section of the plurality of sections of the tubular space of the cell of the plurality of cells, 1 being greater than or equal to 0.5 millimeter and less than or equal to 3.0 millimeters; U is a diameter of the rotor of the blower section, being greater than or equal to 1.0 meter and less than or equal to 5.0 meters; Cp(T) =fixT4-vxT3 + ^xT2-pxT + a, with= 1.9327x 10'10, v = 7.999x 10*7, £ = 1.1407 x 10p = 4.489 x 10'1.17 ~ 1958, T being expressed in degrees Kelvin, and Cp( T) being greater than or equal to 500 J.kg *.K1 and less than or equal to 1500 J.kg *.K1 ; BPR is a dilution ratio of the aeronautical propulsion system, BPR being defined as a ratio between a mass flow rate of the secondary flow and a mass flow rate of the primary flow, and BPR being greater than or equal to 1 and less than or equal to 100; R is a radius of the top of the dawn, R being defined as a distance between the longitudinal axis and the top of the dawn, and R being greater than or equal to 0.25 meters and less than or equal to 0.40 meters; L is a length of the blade, L being defined as a distance between the foot and the top of the blade, and L being greater than or equal to 0.04 meters and less than or equal to 0.09 meters; Sa being an area of ​​an axial section of the abradable element comprising the upstream end edge and downstream end edge of the abradable element, La being a distance separating the upstream end edge from the downstream end edge of the abradable element, and H being greater than or equal to 5.5 millimeters and less than or equal to 14.0 millimeters; and ta-5 / TV 273.15^0.4 >withrexPrimeddegree^^ T) — l ,715 X 10 ^(273.15 / T+110.4 mu(T) being greater than or equal to 3.0 x 10⁵ Pa.s and less than or equal to 6.0 x 10⁵ Pa.s.

[0006] The wall of each cell in the plurality of cells can be made of a metallic alloy comprising iron, chromium, and aluminum.

[0007] The housing may be metallic and comprise nickel and chromium, preferably wherein the nickel is present in the housing in a mass ratio greater than or equal to 55%, and the chromium is present in the housing in a mass ratio greater than or equal to 5% and less than or equal to 10%.

[0008] The abradable element can be fixed to the housing by brazing using a filler alloy consisting of nickel, chromium and silicon.

[0009] The main direction of the tubular space can be inclined with respect to the longitudinal axis by an angle greater than or equal to 40° and less than or equal to 90°, preferably by an angle greater than or equal to 40° and less than or equal to 55°.

[0010] Each cell of the plurality of cells may include a heat shield arranged between the first and second ends of the tubular space, the heat shield extending from the second end of the tubular space over a distance that is greater than or equal to 5% and less than or equal to 20% of a distance separating the first end from the second end.

[0011] The primary body may include a compressor section, a combustion chamber, a turbine section, and a high-pressure shaft, wherein the turbine may be a low-pressure turbine of the turbine section, wherein the shaft may be a low-pressure shaft configured to drive the rotor relative to the stator of the blower section about the longitudinal axis, wherein the turbine section may further include a high-pressure turbine comprising a rotor and a stator, wherein the rotor of the high-pressure turbine may be configured to drive the high-pressure shaft about the longitudinal axis, wherein the compressor section may include a low-pressure compressor and a high-pressure compressor, wherein the low-pressure shaft may further be configured to drive a rotor relative to a stator of the low-pressure compressor about the longitudinal axis,in which the high-pressure shaft can be configured to drive a rotor relative to a stator of the high-pressure compressor around the longitudinal axis, and in which the combustion chamber can be configured to supply energy to an airflow from the compressor section so as to cause rotation of the rotor relative to the stator of the high-pressure turbine around the longitudinal axis, and of the rotor relative to the stator of the low-pressure turbine around the longitudinal axis.

[0012] According to another aspect of the present exposition, an aircraft comprising a cell and an aeronautical propulsion system according to the present exposition is proposed, wherein the aeronautical propulsion system is fixed to the cell.

[0013] According to another aspect of the present exposition, a method for manufacturing a turbine stator of a primary body of an aeronautical propulsion system is proposed, the stator comprising a housing and an abradable element fixed to the housing, the abradable element having an upstream end edge and a downstream end edge, the abradable element being made up of a plurality of identical cells, each cell of the plurality of cells comprising a wall having an inner face delimiting a tubular space and an outer face opposite to the inner face, the tubular space having a first end intended to open onto a primary flow delimited by the primary body and a second end closed by the housing, the tubular space extending in a principal direction from the first end to the second end and having a plurality of sections taken in a plane orthogonal to the principal direction,each section of the plurality of sections being of , regular hexagonal shape, the plurality of cells being arranged in a honeycomb pattern in which two adjacent cells of the plurality of cells are fixed to each other via their respective outer faces; in which the process includes dimensioning the abradable element such that: IJ / 'T', * (T^OO)xuO.O23x———.xa xl2ax30x^ae ' ---------;--------< 8.0 x Iff8 xC^x(T-600J Or : 0.0034xexp(l 084x / jx^^x4^x0.9x ' ® — <7+2e)x3«-8ca 0.00157 ---4---x—j— xmu( 1 ) T is a temperature intended to be reached during operation by a fluid entering a low-pressure turbine of the turbine, when the aeronautical propulsion system is operating at constant maximum power, T being expressed in degrees Celsius, and T being greater than or equal to 1100°C and less than or equal to 1250°C; 2(T) = CxT3-VxT2 + dxT-^ with Σ = 1.5207x 101 = 4.857x 10'8, Q — 1.0184 x 104- k = 3.9333 x 10^ being expressed in degrees Kelvin, A(T) being greater than or equal to 1.0.103 Wm *.K1 and less than or equal to 2.0.102 Wm *.K1 ; e is a wall thickness of a cell of the plurality of cells, e being defined as a distance separating the inner face from the outer face of the wall, and being greater than or equal to 0.02 millimeter and less than or equal to 0.15 millimeter; — r, rc being a radius circumscribed about a section of the plurality of sections of the tubular space of the cell of the plurality of cells, eta being greater than or equal to 0.25 millimeter and less than or equal to 1.0 millimeter; l = 2 x ri being the radius inscribed in the section of the plurality of sections of the tubular space of the cell of the plurality of cells, 1 being greater than or equal to 0.5 millimeter and less than or equal to 3.0 millimeters; is a diameter of a rotor of a blower section of the aeronautical propulsion system, 7) being greater than or equal to 1.0 meter and less than or equal to 5.0 meters; Cp(T) = / / x T4 - vx T3 + fx T1 - px T + a, with = 1.9327 x 10⁻¹⁰, v = 7.999 x 10⁷, Σ = 1.1407 x 10⁻¹ - p - 4.489 x 10⁻¹, 1058, T being expressed in degrees Kelvin, and Cp{T) being greater than or equal to 500 J.kg*.K1 and less than or equal to 1500 J.kg*.K1; BPR is a dilution ratio of the aeronautical propulsion system, BPR being defined as a ratio between a mass flow rate of a secondary flow and a mass flow rate of a primary flow, the primary and secondary flows being derived from a division of a flow drawn in by the rotor of the operating fan section, the primary flow being intended to circulate within the primary duct and the secondary flow being intended to circulate around the primary body, and BPR being greater than or equal to 1 and less or equal to 100; R is a radius of a turbine rotor blade apex, the abradable element being intended to be arranged at and near the blade apex, and R being defined like a distance between a longitudinal axis along which a tree of the body extends primary and the tip of the blade, the turbine rotor being configured to drive the shaft in rotation around the longitudinal axis, and R being greater than or equal to 0.25 meters and less than or equal to 0.40 meters; L is a length of the blade, L being defined as a distance between one foot of the blade and the blade apex, the blade foot being connected to a turbine disk, the disk being centered on the longitudinal axis, and L being greater than or equal to 0.04 meters and less than or equal to 0.09 meters; jj _ , $a being an area of ​​an axial section of the abradable element comprising the upstream end edge and downstream end edge of the abradable element, La being a distance separating the upstream end edge from the downstream end edge of the abradable element, and H being greater than or equal to 5.5 millimeters and less than or equal to 14.0 millimeters; and / TV 273.15rl 10.4 ' avCC T expressed in degrees Kelvin, mu(T) — l,715x 10 ^(273.15) t+ho,4 mu(T) being greater than or equal to 3.0.105 Pa.s and less than or equal to 6.0.105 Pa.s.

[0014] The method may include fixing the abradable element to the housing by brazing using a filler alloy consisting of nickel, chromium and silicon.

[0015] The method may include forming a heat shield between the first and second ends of the tubular space such that the heat shield extends from the second end of the tubular space over a distance that is greater than or equal to 5% and less than or equal to 20% of a distance separating the first end from the second end. DESCRIPTION OF THE FIGURES

[0016] Fig. 1 illustrates an example of an aircraft that may include an aeronautical propulsion system.

[0017] Fig. 2 is a schematic, partial, cross-sectional view of an example of an aeronautical propulsion system in which the fan section is enclosed.

[0018] Fig. 3 is a schematic, partial, cross-sectional view of an example of an aeronautical propulsion system in which the fan section is unfaired.

[0019] Fig. 4 is a schematic cross-sectional view of an example of a planetary reduction mechanism.

[0020] Fig. 5 is a schematic cross-sectional view of an example of an epicycloidal reduction mechanism.

[0021] The [Fig.6] is a schematic perspective view of an example of a rotor stage of the turbine section of an aeronautical propulsion system.

[0022] Fig. 7 is a schematic perspective view of an example of a single-stage rotor blade of the turbine section of an aeronautical propulsion system.

[0023] [Fig.8] is a side view of [Fig.7].

[0024] Figure 9 is a schematic cross-sectional view of an example of a rotor stage of the turbine section of an aeronautical propulsion system.

[0025] The [Fig. 10] is a schematic cross-sectional view of part of a stator of the turbine section of an aeronautical propulsion system.

[0026] The [Fig. 11] is a schematic cross-sectional view of a part of an abradable element along a plane orthogonal to the principal direction of the tubular space of each of the cells of the abradable element.

[0027] The [Fig. 12] is a flowchart illustrating steps in a method of implementing a process for manufacturing a stator of a turbine of a primary body of an aeronautical propulsion system. DETAILED DESCRIPTION

[0028] A propulsion system 1 has a principal direction extending along a longitudinal axis X and comprises, from upstream to downstream in the direction of the fluid flow in the propulsion system 1 when in operation, a blower section 2 and a primary body 3, often called a "gas generator", comprising a compressor section 4, 5, a combustion chamber 6 and a turbine section 7, 8. The propulsion system 1 here is an aeronautical propulsion system 1 configured to be fixed to the airframe of an aircraft 100 by means of a pylon (or mast).

[0029] The compressor section 4, 5 comprises a series of stages, each including a rotating blade wheel (rotor) 4a, 5a in front of a fixed blade wheel (stator) 4b, 5b. The turbine section 7, 8 also comprises a series of stages, each including a fixed blade wheel (stator) 7b, 8b behind which a rotating blade wheel (rotor) 7a, 8a rotates.

[0030] In the present description, the axial direction corresponds to the direction of the longitudinal axis X, corresponding to the rotation of the shafts 10, 11 of the primary body 3, and a radial direction is a direction perpendicular to and passing through this longitudinal axis X. Furthermore, the circumferential (or lateral, or tangential) direction corresponds to a direction perpendicular to and not passing through the longitudinal axis X. Unless otherwise specified, internal (respectively, inside) and external (respectively, outside), respectively, are used with reference to a radial direction such that the inner part or face of an element is closer to the longitudinal axis X than the outer part or face of the same element.

[0031] In operation, a flow F entering the propulsion system 1 is divided between a primary flow Fl and a secondary flow F2, which circulate from upstream to downstream in the propulsion system 1.

[0032] The secondary flow F2, also called the "bypass flow", flows around the primary body 3. The secondary flow F2 cools the periphery of the primary body 3 and is used to generate most of the thrust provided by the propulsion system 1.

[0033] The primary flow Fl flows in a primary channel 29 delimited by the primary body 3, inside and along the latter following the longitudinal axis X, passing successively through the compressor section 4, 5, the combustion chamber 6 where it is mixed with fuel to serve as an oxidizer, and the turbine section 7, 8. The passage of the primary flow Fl through the turbine section 7, 8 receiving energy from the combustion chamber 6 causes a rotation of the rotor stages 7a, 8a of the turbine section 7, 8, which in turn drives the rotation of the rotor stages 4a, 5a of the compressor section 4, 5 as well as a rotor 9 of the blower section 2.

[0034] In a twin-spool propulsion system 1, the compressor section 4, 5 may include a low-pressure compressor 4 and a high-pressure compressor 5. The turbine section 7, 8 may include a high-pressure turbine 7 and a low-pressure turbine 8. The rotor stages 5a of the high-pressure compressor 5 are driven in rotation by the rotor stages 7a of the high-pressure turbine 7 via a high-pressure shaft 10, which extends along the longitudinal axis X. The rotor stages 4a of the low-pressure compressor 4 and the rotor 9 of the fan section 2 are driven in rotation by the rotor stages 8a of the low-pressure turbine 8 via a low-pressure shaft 11, which also extends along the longitudinal axis X.Thus, the primary unit 3 comprises a high-pressure unit including the high-pressure compressor 5, the high-pressure turbine 7, and the high-pressure shaft 10, and a low-pressure unit including the blower section 2, the low-pressure compressor 4, the low-pressure turbine 8, and the low-pressure shaft 11. The rotational speed of the high-pressure unit is greater than the rotational speed of the low-pressure unit. In a three-segment propulsion system 1, the turbine section 7, 8 further comprises an intermediate turbine, positioned between the high-pressure turbine 7 and the low-pressure turbine 8, and whose rotor stages are configured to drive the rotor stages of the low-pressure compressor 4 via an intermediate shaft. The rotor 9 of the blower section 2 and the rotor stages of the... high pressure compressor 5 remain driven by the low pressure shaft 11 and the high pressure shaft 10, respectively.

[0035] The low-pressure shaft 11 is generally housed, along a portion of its length, within the high-pressure shaft 10 and is coaxial with the high-pressure shaft 10. The low-pressure shaft 11 and the high-pressure shaft 10 may be co-rotating, that is, driven in the same direction around the longitudinal axis X. Alternatively, the low-pressure shaft 11 and the high-pressure shaft 10 may be counter-rotating, that is, driven in opposite directions around the longitudinal axis X. If applicable, the intermediate shaft is housed between the high-pressure shaft 10 and the low-pressure shaft 11. The intermediate shaft and the low-pressure shaft 11 may be co-rotating or counter-rotating.

[0036] The fan section 2 comprises at least the rotor 9, which is driven in rotation relative to a stator portion 19e of the propulsion system 1, about the longitudinal axis X on which the rotor 9 is centered, by at least one rotor portion of the turbine section 7, 8, so as to draw in the flow F entering the propulsion system 1. Each rotor 9 of the fan section 2 comprises a hub 13 and blades 14 extending radially from the hub 13. The blades 14 of each rotor 9 may be fixed relative to the hub 13 or have variable pitch. In this case, the root of the blades 14 of each rotor 9 is pivotally mounted about a pitch axis and is connected to a pitch-changing mechanism 15 mounted in the propulsion system 1, the pitch being adjusted according to the flight phases by the pitch-changing mechanism 15.The rotor 9 of the blower section 2 also comprises at least fourteen blades 14 and at most twenty-four blades 14, preferably at least sixteen blades 14 and at most twenty-two blades 14.

[0037] The fan section 2 may further include a stator 16, or rectifier, which comprises blades 17 mounted on a stator hub 16 and whose function is to rectify the secondary flow F2 exiting the rotor 9. The stator blades 17 may be fixed relative to the stator hub 16 or have variable pitch. If so, and similarly to the rotor blades 14 of the rotor 9, the base of the stator blades 17 is pivotally mounted about a pitch axis and is connected to a pitch-changing mechanism 15a, which is generally separate from that of the rotor 9, the pitch being adjusted according to the flight phases by the pitch-changing mechanism 15a. The number of blades 17 in the stator 16 depends on the acoustic criteria defined for the propulsion system 1 and is at least equal to the number of blades 14 in the rotor 9.

[0038] In order to improve the propulsive efficiency of the propulsion system 1 and to reduce its specific fuel consumption as well as the noise emitted by the fan section 2, the propulsion system 1 has a bypass ratio in the (Anglo-Saxon terminology) high. A "high" dilution ratio is defined as a ratio greater than or equal to 1 and less than or equal to 100, for example, between 10 and 80 inclusive. To calculate the dilution ratio, the mass flow rate of the secondary flow F2 and the mass flow rate of the primary flow Fl are related to each other, measured when the propulsion system 1 is stationary, uninstalled, in takeoff mode in a standard atmosphere (as defined by the International Civil Aviation Organization (ICAO) Manual, Doc 7488 / 3, 3rd edition) and at sea level. In this presentation, the parameters (pressure, flow rate, thrust, speed, etc.) are systematically determined under these conditions. "Uninstalled" means that the measurements are taken when the propulsion system 1 is on a test bench (and not installed on an aircraft 100), as the measurements are then simpler to perform.Distances, or dimensions (length, width, radius, diameter, etc.), are measured at ambient temperature (approximately 20°C) when propulsion system 1 is cold, i.e., when propulsion system 1 has been at rest for a sufficient period for the parts of propulsion system 1 to be at ambient temperature, it being understood that these dimensions vary little with respect to the conditions in which propulsion system 1 is in takeoff mode.

[0039] The rotor 9 of the blower section 2 can be decoupled from the low-pressure shaft 11 by means of a reduction mechanism 19, placed between an upstream end of the low-pressure shaft 11 and the rotor 9, in order to independently control their respective rotational speeds. In this case, the propulsion system 1 further comprises an additional shaft, referred to as the "blower shaft 20". The low-pressure shaft 11 connects the rotor stages 8a of the low-pressure turbine 8 to an inlet of the reduction mechanism 19, while the blower shaft 20 connects the output of the reduction mechanism 19 to the rotor 9 of the blower section 2. The rotor 9 of the blower section 2 is therefore driven by the low-pressure shaft 11 via the reduction mechanism 19 and the blower shaft 20 at a rotational speed lower than the rotational speed of the low-pressure turbine 8.

[0040] This decoupling makes it possible to reduce the rotational speed and pressure ratio of the rotor 9 from the fan section 2 and to increase the power extracted by the low-pressure turbine 8. Indeed, the overall efficiency of the propulsion systems is primarily determined by the propulsion efficiency, which is favorably influenced by minimizing the variation in the kinetic energy of the fluid as it passes through the propulsion system 1. In a propulsion system 1 with a high dilution ratio, the majority of the flow generating the propulsive force consists of the secondary flow F2 of the propulsion system 1, the kinetic energy of the secondary flow F2 being mainly affected by the compression that the secondary flow F2 undergoes as it passes through the fan section 2. The propulsion efficiency and the pressure ratio of the section The pressure ratios of fan section 2 and fan section 2 are therefore linked: the lower the pressure ratio of fan section 2, the better the propulsive efficiency. To improve the propulsive efficiency of the propulsion system 1, the pressure ratio of fan section 2, which corresponds to the ratio between the average pressure at the outlet of the stator 16 of fan section 2 (or, in the absence of a stator 16, of the rotor 9) and the average pressure at the inlet of the rotor 9 of fan section 2, is less than or equal to 1.70, preferably less than or equal to 1.50, for example, between 0.90 and 1.45. The average pressures are measured here over the height of at least one of the blades 14 of the rotor 9, that is, from the surface that radially delimits the flow stream inside the inlet of the rotor 9 to the tip 21 of the blade 14.

[0041] The rotor 9 of the blower section 1 can alternatively be directly coupled to the low-pressure shaft 11 (or "direct-drive" in Anglo-Saxon terminology), i.e., without a reduction mechanism. The low-pressure shaft 11 is then combined with the blower shaft 20 so that the rotor 9 is driven by the low-pressure shaft 11 at the same rotational speed as that of the rotor stages 8a of the low-pressure turbine 8.

[0042] The propulsion system 1 is configured to provide a thrust of between 18,000 Lbf (80,068 N) and 51,000 Lbf (226,859 N), preferably between 20,000 Lbf (88,964 N) and 35,000 Lbf (155,688 N).

[0043] The blower section 2 can be shrouded or unshrouded.

[0044] In the case of a shrouded fan section 2, the fan section 2 comprises a fan housing 12 and the rotor 9 is housed in the fan housing 12. A shrouded fan section 2 comprises a rotor 9 extending upstream of a stator 16. The blades 17 of the stator 16 are then generally called "outlet blades" (or "OGV", for "Outlet Guide Vane" in Anglo-Saxon terminology) and have a fixed pitch relative to the hub of the stator 16. Furthermore, the dilution ratio of the propulsion system 1 is preferably greater than or equal to 1 and less than or equal to 100, typically greater than or equal to 10, for example between 10 and 35 inclusive, preferably between 10 and 18 inclusive. The peripheral speed at the tip 21 of the rotor blades 14 can also be between 260 m / s and 400 m / s inclusive. The blower pressure ratio can then be between 1.20 and 1.45.

[0045] In an unducted fan section 2, the fan section 2, which may also be referred to as the "propeller," is not enclosed by a fan casing. Since the fan section 2 is unducted, the blades 14 of the rotor 9 have variable pitch. Propulsion systems comprising at least one unducted rotor 9 are known, in Anglo-Saxon terminology, as "open rotor" or "unducted fan." The propulsion system 1 may comprise two unducted, counter-rotating rotors 9. Such a propulsion system 1 is known, in the In Anglo-Saxon terminology, this is known by the acronym "CROR" for "Contra-Rotating Open Rotor" (in French terminology) or "UDF" for "Unducted Double Fan" (in French terminology). The rotors 9 can be positioned downstream of the primary casing 3 to create a pusher type or upstream of the primary casing 3 to create a tractor type. Alternatively, the propulsion system 1 can comprise a single unducted rotor 9 and an unducted stator 16 (rectifier). Such a propulsion system 1 is known, in Anglo-Saxon terminology, by the acronym "USF" for "Unducted Single Fan". In the case of a USF-type propulsion system 1, the blades 17 of the stator 16 are fixed in rotation relative to the X-axis of rotation of the rotor 9 and, consequently, do not experience centrifugal force. The blades 17 of the stator 16 also have variable pitch.

[0046] Removing the fairing around the fan section 2 significantly increases the bypass ratio without the propulsion system 1 being negatively impacted by the mass of the housings 12 or nacelles intended to surround the fan section 2. The bypass ratio of the propulsion system 1, including an unfaired fan section 2, is thus greater than or equal to 1 and less than or equal to 100, typically greater than or equal to 40, for example, between 40 and 80 inclusive. The peripheral speed at the tip 21 of the blades 14 of the rotor(s) 9 can also be between 210 m / s and 260 m / s inclusive. The fan pressure ratio can then preferably be between 0.90 and 1.20 inclusive.

[0047] The diameter D of the rotor 9 of the fan section 2 is greater than or equal to 1.0 meter and less than or equal to 5.0 meters, and can typically be between 80 inches (203.2 cm) and 185 inches (469.9 cm) inclusive. When the rotor 9 is shrouded, the diameter D is preferably between 85 inches (215.9 cm) and 120 inches (304.8 cm) inclusive, for example on the order of 90 inches (228.6 cm), which allows the propulsion system 1 to be integrated in a conventional manner, in particular under a wing of the airframe of an aircraft 1. When the rotor 9 is unshrouded, the diameter D is preferably greater than or equal to 100 inches (254 cm), for example between 120 inches (304.8 cm) and 156 inches (396.2 cm). The diameter of the rotor 9 is measured here in a plane normal to the X axis of rotation of the rotor 9, at the level of an intersection between a vertex 21 and a leading edge 22 of the blades 14 of the rotor 9. It should be noted that, [Fig.2] and [Fig.3] being partial views, the diameter D is only partially visible.

[0048] The reduction mechanism 19 may comprise an epicyclic or planetary, single-stage or two-stage reduction mechanism. For example, the reduction mechanism 19 may be of the planetary type (or "star," in Anglo-Saxon terminology, as seen in [Fig. 4]) and comprise a sun pinion 19a (input of the reduction mechanism 19), centered on an axis of rotation of the mechanism. reduction 19 generally confused with the longitudinal axis X and configured to be driven in rotation by the low pressure shaft 11, a ring 19b (output of the reduction mechanism 19) coaxial with the solar pinion 19a and configured to drive in rotation the blower shaft 20 around its axis X of rotation, and a series of satellites 19c distributed circumferentially around the axis X of rotation of the rotor 9 of the blower section 2, between the solar pinion 19a and the ring 19b, each satellite 19c being internally meshed with the solar pinion 19a and externally with the ring 19b. The series of satellites 19c is mounted on a satellite carrier 19d which is fixed relative to the stator part 19e of the propulsion system 1, for example relative to a housing of the compressor section 4, 5. Alternatively, the reduction mechanism 19 can be epicycloidal (or "planetary", in Anglo-Saxon terminology, as seen in the [Fig.5]), in which case the ring 19b is fixedly mounted on the stator part 19e of the propulsion system 1 and the blower shaft 20 is driven in rotation by the planet carrier 19d. .

[0049] Regardless of the configuration of the reduction mechanism 19, the diameter of the ring gear 19b and the satellite carrier 19d are greater than the diameter of the solar pinion 19a, so that the rotational speed of the rotor 9 of the blower section 2 is less than the rotational speed of the low pressure shaft 11.

[0050] The reduction ratio of the reduction mechanism 19 is greater than or equal to 2.5 and less than or equal to 11. In the case of a propulsion system 1 comprising a rotor 9 of fan section 2 which is shrouded, the reduction ratio may be greater than or equal to 2.7 and less than or equal to 3.5, typically around 3.0. In the case of a propulsion system 1 comprising a rotor 9 of fan section 2 which is unshrouded, the reduction ratio may be between 9.0 and 11.0.

[0051] The twin-body propulsion system 1 may in particular include a single-stage high-pressure turbine 7, i.e. comprising exactly one stage, or a two-stage high-pressure turbine 7, i.e. comprising exactly two stages, a high-pressure compressor 5 comprising at least eight stages and at most eleven stages, a low-pressure turbine 8 comprising at least three stages and at most seven stages and a low-pressure compressor 4 comprising at least two stages and at most four stages.

[0052] The limit speed œ (or “redline speed”, in Anglo-Saxon terminology) of the low-pressure shaft 11, which corresponds to the absolute maximum speed likely to be encountered by the low-pressure shaft 11, and therefore by the rotor stages 4a, 8a of the low-pressure body, during the entire flight (according to the European certification regulation EASA CS-E 740 or according to the American certification regulation 14-CFR Part 33.87), is between 2,000 revolutions per minute (209 radians per second) and 30,000 revolutions per minute (3,142 radians per second) inclusive, for example between 8,500 revolutions per minute (890 radians per second) and 12,000 revolutions per minute (1,267 radians per second). included, preferably between 9,000 rpm (942 radians per second) and 11,000 rpm (1152 radians per second). The speed limit corresponds to the maximum rotational speed when the propulsion system 1 is in good working order, i.e., not at the end of its service life. It is therefore likely to be reached by the low-pressure shaft 11 under flight conditions. This speed limit is part of the data declared in the engine certification (or "type certificate data sheet," in Anglo-Saxon terminology). Indeed, this rotational speed is usually used as a reference speed for the sizing of propulsion systems and in certain certification tests, such as blade loss or rotor integrity tests. Of course, the high-pressure shaft 10, and therefore the rotor stages 5a, 7a of the high-pressure body, also has a speed limit, defined in the same way as for the low-pressure shaft 11, but higher than that of the low-pressure shaft, for example between 8,000 revolutions per minute and 30,000 revolutions per minute inclusive.

[0053] The exhaust gas temperature (or EGT temperature, or "EGT redline") is the temperature of the fluid exiting the combustion chamber 6 when the aircraft propulsion system 1 is operating at maximum continuous power or maximum stabilized power ("Maximum Continuous Power"), according to the European certification regulation EASA CS-E 740 (or according to the American certification regulation 14-CFR Part 33). The EGT temperature is part of the data declared in the aircraft propulsion system's certification manual (or "type certificate data sheet").To estimate it, it is necessary to use the maximum permissible Indicated Low Pressure Turbine Temperature (T) at maximum continuous power or maximum continuous power, which is measured at the inlet of the low pressure turbine 8, more precisely in a plane orthogonal to the longitudinal axis positioned between the stator part 8b and the rotor part 8a of the first stage of the low pressure turbine in the direction of the gas flow within the propulsion system 1. In the aeronautical propulsion system 1, this maximum permissible Indicated Low Pressure Turbine Temperature (T) at maximum power is greater than or equal to 1100°C and less than or equal to 1250°C.

[0054] The stator 16 of the blower section, the stator stages 4b, 5b of the compressor section 4, 5, the stator stages 7b, 8b of the turbine section 7, 8 and the stator part 19e of the propulsion system 1 are fixed relative to each other and relative to the mast for fixing the propulsion system 1 to the aircraft cell.

[0055] Although the remainder of this exposition is described with reference to the low pressure turbine 8, its content nevertheless applies similarly to the high pressure turbine 7.

[0056] Each rotor stage 8a of the low-pressure turbine 8 comprises a disk 30 and a plurality of blades 31. In addition, the rotor stages 8a of the low-pressure turbine 8 are connected to each other by means of a plurality of ferrules 32 connecting the disks 30 of the rotor stages 8a in pairs.

[0057] The disc 30 is bored. More precisely, the disc 30 has an internal surface 33 defining a bore 34 that passes axially through the disc 30. The bore 34 is circular and centered on the longitudinal axis X when the disc 30 is mounted in the propulsion system 1. The low-pressure shaft 11 extends through the bores 34 of the discs 30 of the low-pressure turbine 8 by being fixed to at least one of the discs 30 of the low-pressure turbine 8, so that it can be driven into rotation by the rotor stages 8a during the expansion of the hot fluid circulating from the high-pressure turbine 7.

[0058] Furthermore, the disc 30 has an external surface 37 delimiting a plurality of recesses 38 distributed around the longitudinal axis X and extending axially. Each of the recesses 38 is configured to ensure the attachment, removably or not, of one of the blades 31 to the disc 30. In this respect, each recess 38 is open to the primary vein 29 when the disc 30 is mounted in the propulsion system 1, and can have any shape suitable for the attachment of the blades 31, typically a dovetail or fir-tree shape, with at least one, or even several, lobe(s).

[0059] Each of the blades 31 comprises a foot 40 fixed to the disk 30 by cooperation with one of the recesses 38, a strut 41 connected to the foot 40 and comprising a platform 42 delimiting a radially internal portion of the primary flow 29, and a blade 43 connected to the platform 42 and extending within the primary flow 29. The blade 43 has an aerodynamic profile and, in this respect, presents a leading edge 44 on which the hot fluid first strikes upon encountering the rotor stage 8a, a trailing edge 45 axially opposite the leading edge 44, and a tip (or apex) 46 radially opposite the platform 42. The blade 43 interacts with the hot fluid flowing from the low-pressure turbine 8 to drive the disk 30 in rotation about the longitudinal axis X. To do this, the blade 43 extends to within the primary vein 29 with a certain incidence relative to the main direction of fluid flow.The blade 31 may further include a heel 47, extending from the end 46 of the blade 43, being attached there removably, or not, or being integral with the blade 43. The heel 47 ensures the sealing of the primary flow 29 by limiting hot fluid leakage at the interface between each rotor stage 8a and a housing 50 of the low-pressure turbine 8, to which the stator stages 8b are attached. In this respect, the heel 47 carries sealing flaps intended to cooperate with an abradable element 51 extending from the housing 50 of the low-pressure turbine 8. If applicable, the tip 46 of the blade 31 corresponds to the radially external end of the blade 43. sealing strips. More specifically, the abradable element 51 is configured to be consumed upon contact with the tip 46 of the blade 31 during the operation of the propulsion system 1, without risking damage to the casing 50. This eliminates the need for clearance between the tip 46 of the blade 31, thus limiting leakage at the interface between the casing 50 and the rotor stages 8a, and thereby improving the performance of the low-pressure turbine 8. Furthermore, the abradable element 41 provides thermal protection for the casing 50 against the high temperatures of the fluid circulating within the primary stream 29. The tip 46 of the blade 31 has a radius R defined as the distance between the longitudinal axis X and the tip 46 of the blade 31. The radius R of the tip 46 of the blade 31 is greater than or equal to 0.25 meters and less than or equal to 0.40 meters. meter. In addition, the blade 31 has a length L which is defined as the distance between foot 40 and apex 46 of the blade 31.The length L of the blade 31 is greater than or equal to 0.04 meters and less than or equal to 0.09 meters. The blade may comprise a ceramic matrix composite material and / or a metal alloy.

[0060] The housing 50 is a rotating element extending around the longitudinal axis X and may comprise a plurality of sections fixed to one another. The housing 50 may include frustoconical and / or annular portions. The housing 50 is fixed relative to the stator portion 19e of the propulsion system 1. Preferably, the housing 50 is metallic. Typically, the housing 50 comprises nickel and chromium. For example, nickel is present in the housing 50 in a mass ratio greater than or equal to 55%, and chromium is present in the housing 50 in a mass ratio greater than or equal to 5% and less than or equal to 10%. The housing 50 thus exhibits increased resistance to oxidation, which improves the thermal resistance of the low-pressure turbine 8 and therefore extends its service life.To further improve the thermal performance of the low-pressure turbine 8, a cooling system for the casing 50 can be provided, typically by drawing fluid from within the compressor section 4, 5. The material constituting the casing 50 can be single-crystal or the casing 50 can be forged, depending on the time and cost constraints of manufacturing the low-pressure turbine 8.

[0061] The abradable element 51 is fixed to the housing 50. Preferably, the abradable element 51 is fixed to the housing 50 by brazing with a filler alloy consisting of nickel, chromium, and silicon. Indeed, such brazing exhibits high thermal resistance, which improves the thermal resistance of the low-pressure turbine 8 and thus extends its service life. The abradable element 51 is also arranged directly above and at a distance from the tip 46 of at least one of the blades 31. Preferably, the abradable element 51 is a rotary element, typically annular, and extends all around the longitudinal axis X, being arranged directly above and at a distance from each of the blades 31. The abradable element 51 has an upstream end edge and an end edge downstream in the direction of the longitudinal axis X, the upstream end edge being a distance La from the downstream end edge along the longitudinal axis X. Furthermore, the abradable element 51 has an axial cross-section comprising the longitudinal axis X, the upstream end edge, and the downstream end edge of the abradable element. The axial cross-section of the abradable element 51 has an area Sa. The area Sa of the axial cross-section and the distance La separating the upstream end edge from the downstream end edge of the abradable element 51 define an average height H of the abradable element 51, which average height H is defined as the ratio of the area Sa of the axial cross-section to the distance La. In this respect, the average height H of the abradable element 51 is greater than or equal to 5.5 millimeters and less than or equal to 14.0 millimeters.

[0062] The abradable element 51 consists of a plurality of identical cells 52. In other words, the abradable element 51 has a hollow structure that allows it to be consumed during contact with the apex 46 of the blade 31

[0063] Each cell 52 comprises a wall 520 having an inner face 5201 delimiting a tubular space 5200, and an outer face opposite the inner face 5201. Preferably, the wall 520 of each cell 52 is made of a metallic alloy comprising iron, chromium, and aluminum. Thus, when the abradable element 51 is subjected to the secondary flux F2, a protective layer of alumina forms on the surface of the walls 520 of the cells 52 of the abradable element 51, which allows the abradable element 51 to withstand higher temperatures, typically temperatures above 1100°C, improving the thermal resistance of the low-pressure turbine 8 and thus extending its service life. The wall 520 has a thickness e defined as a distance separating the inner face 5201 from the outer face 5202 along a direction orthogonal to the inner face 5201 and the outer face 5202.The wall thickness e of the 520 is greater than or equal to 0.02 millimeters and less than or equal to 0.15 millimeters, which improves the abradability of the abradable element 51 and simplifies the manufacture of the housing 50. The plurality of cells 52 is arranged in a honeycomb pattern in which two adjacent cells 52 are fixed to each other via their respective outer face 5202, or at least a portion of their respective outer face 5202. In other words, the plurality of cells 52 is arranged in a staggered network similar to a honeycomb, notably to minimize the amount of material used in the manufacture of the abradable element 51, while maximizing its mechanical strength.

[0064] The tubular space 5200 has a first open end, i.e., opening onto the primary vein 29, and a second end closed by the casing 50, the second end thus forming the bottom of the cell 52. The tubular space

[0065]

[0066]

[0067] 5200 thus extends from the first end to the second end along a principal direction Y, the principal direction Y of the tubular space 5200 of each of the cells 52 being parallel to the principal direction Y of the tubular space 5200 of the other cells 52. Preferably, the principal direction Y is inclined with respect to the longitudinal axis X at an angle greater than or equal to 40° and less than or equal to 90°, for example, at an angle greater than or equal to 40° and less than or equal to 55°, the angle being taken from upstream to downstream. In this way, the penetration of fluid into the tubular space 5200, from the primary stream 29, is reduced, which in turn limits the heating of the abradable element 51 and, consequently, the heat flux passing through it towards the casing 50. Thus, the thermal resistance of the low-pressure turbine 8 is improved and its service life extended.Depending on the general shape of the abradable element 51, the first ends of adjacent cells 52 can be positioned at the same distance from the longitudinal axis X, or at different distances from each other. The same applies to the second ends of adjacent cells 52, depending on the shape of the housing 50. Thus, the general shape of the abradable element 51 is adapted to the shape of the housing 50 and to that of the apex 46 of the blade 31, including the sealing elements of the heel 47, if applicable. The tubular space 5200 further presents a plurality of sections orthogonal to the principal direction Y, that is, taken in a plane orthogonal to the principal direction Y, each section being of regular hexagonal shape, i.e., forming a convex polygon with six vertices and six sides, all six sides having the same length and the internal angles of the polygon all being 120°.The regular hexagonal shape allows, in particular, that the cells 52 form a regular tiling within the abradable element 51. Each hexagon of a section has a circumscribed radius rc, defined as a distance between the center and the vertices of the hexagon, and an inscribed radius r, defined as a distance between the center and the sides of the hexagon. The abradable element 51 is further such that relation (A) below is verified: r itT'i 77 (ÎMOOixi 0.023x—^xh xl2«x30x8«e 150wxD' ,, <8.0x10 Or : 0.0(B4xexp[l 084xïp^x^x0.9x^^^ ' & ' 0.00157 z_ ----4---x—jT) A(T) ^CxT3-^xT2 + 0xT-^ with £ = [,5207x 104= 4,857x 10'8> 9 = 1,0184 x ! 04- k = 3,9333 X 104 T being expressed in degrees Kelvin; a , a being greater than or equal to 0.25 millimeter and less than or equal to 1.0 millimeter; 1 = being greater than or equal to 0.5 millimeters and less than or equal to 3.0 millimeters; Cp(T) = / / x T4 - vx T3 + fx T1 - px T + a, with = 1.9327 x 10⁻¹⁰, v = 7.999 x Uf⁷ - 1.1407 x 10⁻³, p = 4.489 x 10⁻¹, a = 1058, T being expressed in degrees Kelvin; and , ^-5. / T 273.15+110.4' with r expressed in degrees Kelvin. mu(T) — l.715x 10 x [.273.15 / x r+110.4

[0068] In equation (A) above, the temperature T is the maximum permissible low-pressure turbine temperature prescribed at constant maximum power. Furthermore, the term A(T) represents the thermal conductivity of the fluid circulating within the primary channel 29, and is greater than or equal to 1.0 × 10³ Wm⁻¹·K⁻¹ and less than or equal to 2.0 × 10² Wm⁻¹·K⁻¹. In addition, the term Cp(T) represents the specific heat capacity of the fluid circulating within the primary channel 29, and is greater than or equal to 500 J·kg⁻¹·K⁻¹ and less than or equal to 1500 J·kg⁻¹·K⁻¹. Finally, the term μ{T} represents the dynamic viscosity of the fluid circulating within the primary channel 29, and is greater than or equal to 3.0 × 10⁵ Pa·s and less than or equal to 6.0 × 10⁵ Pa·s.

[0069] Thanks to a configuration conforming to equation (A), the heat flux passing through the abradable element 51 is significantly reduced. Indeed, this heat flux becomes particularly low compared to the power transmitted by the fluid from the primary stream 29 to the low-pressure turbine 8. In this way, the thermal resistance of the low-pressure turbine 8 is improved and its service life extended. Furthermore, the seal provided by the abradable element 51 can be maintained at higher temperatures, typically exceeding 1100°C. Equation (A) also makes it possible to ensure a compromise between, on the one hand, fluid leakage at the interface between the abradable element 51 and the tip 46 of the blade 31, and, on the other hand, the heat flux transmitted from the fluid in the primary stream 29 to the casing 50.

[0070] Preferably, each of the cells 52 comprises a heat shield 53 configured to reduce the heat flow from the primary vein 29 to the housing 50, through the abradable element 51. Preferably, the heat shield 53 comprises zirconia, or is even made of zirconia. More specifically, the heat shield 53 is arranged at the bottom of the cell 52, that is, between the first end and the second end of the tubular space 5200. In other words, the heat shield 53 extends from the second end of the tubular space 5200 over a distance that is greater than or equal to 5% and less than or equal to 20% of the distance separating the first end from the second end. With a filling rate of each cell 52 by the heat shield 53 that is between 5% and 20%, the efficiency thermal protection of the housing 50 by the abradable element 51 is improved, without reducing the abradability of the abradable element 51.

[0071] Ultimately, the abradable element 51 exhibits greater resistance to high temperatures, typically exceeding 1100°C, and this resistance is maintained for a longer operating time of the propulsion system 1. Furthermore, the abradable element 51 provides improved thermal protection for the housing 50. This is achieved without reducing the abradability of the abradable element 51, i.e., its capacity to be consumed upon contact with the tip 46 of the blade 31. Moreover, the overall performance and manufacturing cost of the aeronautical propulsion system 1 are not affected.

[0072] During a manufacturing process E for the stator 8b of the low-pressure turbine 8, a dimensioning E1 of the abradable element 51 is implemented such that relation (A) is satisfied. The manufacturing process E may also include the attachment E2 of the abradable element 51 to the housing 50, typically by brazing with a filler alloy consisting of nickel, chromium, and silicon. Finally, the manufacturing process E may include the formation E3 of the heat shield 53 within the tubular space such that the heat shield 53 extends from the second end to a point in the tubular space 5200 located at a distance from the second end of the tubular space 5200 that is greater than or equal to 5% and less than or equal to 20% of a distance separating the first end from the second end.

[0073] The E3 formation of the heat shield 53 is preferably achieved by thermal spraying. If necessary, thermal spraying can be achieved by injecting a powdered material into a plasma flame. In this way, the heated powder is accelerated and compacts at the bottom of the tubular space 5200, so that the heat shield 53 is formed by successive stacking of powder particles. Other implementations of the E3 formation of the heat shield 53 are, however, conceivable, such as impregnation with slurry and / or the use of a ceramic adhesive.

[0074] The table below details the properties of a propulsion system known from the prior art, on the one hand, and of an aeronautical propulsion system 1 conforming to this description, in particular to relation (A), on the other hand. The maximum permissible low-pressure turbine temperature prescribed at constant maximum power (T) for the propulsion system known from the prior art is 1060°C, while the maximum permissible low-pressure turbine temperature prescribed at constant maximum power (T) for the aeronautical propulsion system 1 conforming to this description exceeds 1150°C. Properties Propulsive system known from the prior art Propulsive system 1 conforming to the present presentation T 1060°C 1150°C UT) 0.086 Wm *.K1 0.09 Wm *.K1 Term “e” of relation (A) 0.1.10 3 m 0.08.103 m Term “a” of relation (A) 1.11.103 m 0.58.103 m Term “1” of relation (A) 3.14.10 3 m 1.59.103 m Term “D” of relation (A) 2.0 m 4.0 m CP(T) 1214 J.kg *.K1 1224 J.kg *.K1 BPR 10 50 Term “R” of relation (A) 0.40 m 0.30 m Term “ L of relation (A) 1.0 x 10⁻³ m 5.0 x 10² m Term "H" of relation (A) 5.0 x 10³ m 1.0 x 10² m μ(T) 5.04 kg.m⁻¹.s⁻¹ 5.26 kg.m⁻¹.s⁻¹ Wall alloy Includes Nickel Does not include Iron Includes Iron Does not include Nickel Casing material Includes Cobalt Does not include Nickel Includes Nickel Does not include Cobalt Brazing alloy Nickel Chromium Silicon Nickel Chromium Silicon Tube space inclination 90° 50° Heat shield None Zirconia

Claims

1. Demands Aeronautical propulsion system (1) comprising: a primary body (3) delimiting a primary vein (29); and a blower section (2) comprising a stator (19e) and a rotor (9) centered on a longitudinal axis (X), the rotor (9) being configured to be driven in rotation relative to the stator (19e) around the longitudinal axis (X) so as to draw in a flow (F) dividing between a primary flow (F1) intended to circulate within the primary vein (29) and a secondary flow (F2) intended to circulate around the primary body (3); in which the primary body (3) comprises: a shaft (10, 11) extending along the longitudinal axis (X); and a turbine (7, 8) comprising: a rotor (7a, 8a) configured to drive the shaft (10, 11) in rotation about the longitudinal axis (X), and comprising a disk (30) centered on the longitudinal axis (X), and a blade (31) comprising a foot (40) connected to the disk (30) and a vertex (46, 47) radially opposite the foot (40); and a stator (7b, 8b) comprising a housing (50) and an abradable element (51) fixed to the housing (50), the abradable element (51) being arranged to the right and at a distance from the apex (46, 47) of the blade (31), the abradable element (51) having an upstream end edge and a downstream end edge, the abradable element (51) being made up of a plurality of identical cells (52), each cell (52) of the plurality of cells (52) comprising a wall (520) having an inner face (5201) delimiting a tubular space (5200) and an outer face (5202) opposite the inner face (5201), the tubular space (5200) having a first end opening onto the primary vein (29) and a second end closed by the housing (50), the tubular space (5200) extending along a principal direction (Y) from the first end to the second end and presenting a plurality of sections taken in a plane orthogonal to the principal direction (Y),each section of the plurality of sections being of regular hexagonal shape, the plurality of cells (52) being arranged in a honeycomb pattern in which two adjacent cells (52) of the plurality of cells (52) are fixed to each other via their respective outer face (5202); in which: m 0.8 0.023x7-—— x.' xl2«x30x&w (+2^5 el) ^^xcp(r)x(T-6oo) ;Or : <8.0xHT8 nnnu J, no i 2 ”“1^) 0-002 A n l50xro<D2 -, ,8 \ 0.008 ‘T est 0,00.-> 4xexp| 1084xZ x—-—x——x^(Z+2e)--eJx—' 0.00157 "— --x—— xnui( 7 ) a temperature intended to be reached in operation by a fluid entering a low-pressure turbine (8) of the turbine (7, 8), when the aeronautical propulsion system (1) is operating at constant maximum power, T being expressed in degrees Celsius, and T being greater than or equal to 1100°C and less than or equal to 1250°C; 2(7) =CxT3-nxT2+0xT-K^ with = l,5207x 104I> = 4.857 x lOA 0 = 1.0184 x 104 K = 3.9333 x 104 T being expressed in degrees Kelvin, 2(7 ) being greater than or equal to 1.0.10 3 Wm *.K1 and less than or equal to 2.0.10 2 Wm *.K1; e is a wall thickness (520) of a cell (52) of the plurality of cells (52), e being defined as a distance separating the inner face (5201) from the outer face (5202) of the wall (520), ete being greater than or equal to 0.02 millimeter and less than or equal to 0.15 millimeter; a — + ,rc being a radius circumscribed about a section of the plurality of tubular space sections (5200) of cell (52) of plurality of cells (52), eta being greater than or equal to 0.25 millimeter and less than or equal to 1.0 millimeter; l = 2 x ri being the radius inscribed in the section of the plurality of sections of the tubular space (5200) of the cell (52) of the plurality of cells (52),? being greater than or equal to 0.5 millimeter and less than or equal to 3.0 millimeters; Æ is a diameter of the rotor (9) of the blower section (2), being greater than or equal to 1.0 meter and less than or equal to 5.0 meters; G(7) =^x74-vx73 + fx72-px7 + o-, with 1.9327 x 10'10, v = 7.999 x 104 f = 1.1407 x 10A p = 4.489 x 104 = 1058, T being expressed in degrees Kelvin, and Cp{T) being greater than or equal to 500 J.kg *.K1 and less than or equal to 1500 J.kg *.K1; BPR is a dilution ratio of the aeronautical propulsion system (1), BPR being defined as the ratio between a mass flow rate of the flow secondary (F2) and a mass flow rate of the primary flow (Fl), and BPR being greater than or equal to 1 and less than or equal to 100; R is a radius of the apex (46, 47) of the blade (31), R being defined as a distance between the longitudinal axis (X) and the apex (46, 47) of the blade (31), and R being greater than or equal to 0.25 meters and less than or equal to 0.40 meters; L is a length of the blade (31), L being defined as a distance between the foot (40) and the apex (46, 47) of the blade (31), and L being greater than or equal to 0.04 meters and less than or equal to 0.09 meters; H _ , Sa being an area of ​​an axial section of the abradable element l'a (51) comprising the upstream end edge and the downstream end edge of the abradable element (51), La being a distance separating the upstream end edge from the downstream end edge of the abradable element (51), and H being greater than or equal to 5.5 millimeters and less than or equal to 14.0 millimeters;and ,^5 / TV 273.15M 10.4, with T expressed mu(T) — 1.715x 10' x (273.15) x r+110.4 in degrees Kelvin, mu(T) being greater than or equal to 3.0.105 Pa.s and less than or equal to 6.0.105 Pa.s.;

2. Aeronautical propulsion system (1) according to claim 1, wherein the wall (520) of each cell (52) of the plurality of cells (52) is made of a metallic alloy comprising iron, chromium, and aluminum.

3. Aeronautical propulsion system (1) according to claim 1 or 2, wherein the casing (50) is metallic and comprises nickel and chromium, preferably wherein the nickel is present in the casing (50) in a mass ratio greater than or equal to 55%, and the chromium is present in the casing (50) in a mass ratio greater than or equal to 5% and less than or equal to 10%.

4. Aeronautical propulsion system (1) according to any one of claims 1 to 3, wherein the abradable element (51) is fixed to the housing (50) by brazing using a filler alloy consisting of nickel, chromium and silicon.

5. Aeronautical propulsion system (1) according to any one of claims 1 to 4, wherein the principal direction (Y) of the tubular space (5200) is inclined with respect to the longitudinal axis (X) at an angle greater than or equal to 40° and less than or equal to 90°, preferably at an angle greater than or equal to 40° and less than or equal to 55°

6. JJ. Aeronautical propulsion system (1) according to any one of claims 1 to 5, wherein each cell (52) of the plurality of cells (52) comprises a heat shield (53) arranged between the first and second end of the tubular space (5200), the heat shield (53) extending from the second end of the tubular space (5200) over a distance that is greater than or equal to 5% and less than or equal to 20% of a distance separating the first end from the second end.

7. An aircraft propulsion system (1) according to any one of claims 1 to 6, wherein the primary body (3) comprises a compressor section (4, 5), a combustion chamber (6), a turbine section (7, 8), and a high-pressure shaft (10), wherein the turbine (7, 8) is a low-pressure turbine (8) of the turbine section (7, 8), wherein the shaft (10, 11) is a low-pressure shaft (11) configured to drive the rotor (9) relative to the stator (19e) of the fan section (2) about the longitudinal axis (X), wherein the turbine section (7, 8) further comprises a high-pressure turbine (7) comprising a rotor (7a) and a stator (7b), wherein the rotor (7a) of the high-pressure turbine (7) is configured to drive the high-pressure shaft (10) about the longitudinal axis (X), wherein the compressor section (4, 5) includes a low-pressure compressor (4) and a high-pressure compressor (5),in which the low-pressure shaft (11) is further configured to drive a rotor (4a) relative to a stator (4b) of the low-pressure compressor (4) around the longitudinal axis (X), in which the high-pressure shaft (10) is configured to drive a rotor (5a) relative to a stator (5b) of the high-pressure compressor (5) around the longitudinal axis (X), and in which the combustion chamber (6) is configured to supply energy to an airflow from the compressor section (4, 5) so as to cause a rotation of the rotor (7a) relative to the stator (7b) of the high-pressure turbine (7) around the axis, longitudinal (X), and of the rotor (8a) relative to the stator (8b) of the low pressure turbine (8) around the longitudinal axis (X).

8. Aircraft (100) comprising a fuselage (52) and an aeronautical propulsion system (1) according to any one of claims 1 to 7, wherein the aeronautical propulsion system (1) is fixed to the fuselage (52).

9. A method (E) for manufacturing a stator (7b, 8b) of a turbine (7, 8) of a primary body (3) of an aeronautical propulsion system (1), the stator comprising a housing (50) and an abradable element (51) fixed to the housing (50), the abradable element (51) having an upstream end edge and a downstream end edge, the abradable element (51) being made up of a plurality of identical cells (52), each cell (52) of the plurality of cells (52) comprising a wall (520) having an inner face (5201) delimiting a tubular space (5200) and an outer face (5202) opposite the inner face (5201), the tubular space (5200) having a first end intended to open onto a primary flow (29) delimited by the primary body (3) and a second end sealed by the casing (50),the tubular space (5200) extending along a principal direction (Y) from the first end to the second end and having a plurality of sections taken in a plane orthogonal to the principal direction (Y), each section of the plurality of sections being of regular hexagonal shape, the plurality of cells (52) being arranged in a honeycomb pattern in which two adjacent cells (52) of the plurality of cells (52) are fixed to each other via their respective external face (5202); wherein the method (E) comprises a dimensioning (E1) of the abradable element (51) such that: / 0.8 (r-400)xJ0.023x. t. x« x 12«x30x&»e ' ----------ï------< 8'° x where: 0.0034xexp^l084x / jx iT x L x0,9x ^gp^x^J+Tey^Jx H ' ® (f+2e>d«-8«» O.OOJ57 4 xz ) T is a temperature intended to be reached during operation by a fluid entering a low-pressure turbine (8) of the turbine (7, 8), when the aeronautical propulsion system (1) is operating at constant maximum power, T being expressed in degrees Celsius, and T being greater than or equal to 1100°C and less than or equal to 1250°C; 2(T) = £ x T3-yx T2 + Bx Tk, with f = ],5207 x KF1 l> = 4.857 xJOA B = 1.0184 x HA k = 3.9333 x 10'4, T being expressed in degrees Kelvin, 4( T) being greater than or equal to 1.0.103 Wm *.K1 and less than or equal to 2.0.10 2 Wm *.K1; e is a wall thickness (520) of a cell (52) of the plurality of cells (52), e being defined as a distance separating the inner face (5201) from the outer face (5202) of the wall (520), ete being greater than or equal to 0.02 millimeter and less than or equal to 0.15 millimeter; + , rc being a radius circumscribed about a section of the plurality of tubular space sections (5200) of cell (52) of plurality of cells (52), eta being greater than or equal to 0.25 millimeter and less than or equal to 1.0 millimeter; l - 2 x ri being the radius inscribed in the section of the plurality of sections of the tubular space (5200) of the cell (52) of the plurality of cells (52),1 being greater than or equal to 0.5 millimeter and less than or equal to 3.0 millimeters; D is a diameter of a rotor (9) of a blower section (2) of the aeronautical propulsion system (1), D being greater than or equal to 1.0 meter and less than or equal to 5.0 meters; CP(T) ^x^-vxF^xf-pxî + ff, with 1.9327 x 10'1 °, v = 7.999 x 10^ £ = 1.1407 x 10 ^ p = 4.489 x 101,a = l058, T being expressed in degrees Kelvin, and Cp( T) being greater than or equal to 500 J.kg *.K1 and less than or equal to 1500 J.kg *.K1; BPR is a dilution ratio of the aeronautical propulsion system (1), BPR being defined as a ratio between a mass flow rate of a secondary flow (F2) and a mass flow rate of a primary flow (Fl), the primary flow (Fl) and the secondary flow (F2) being derived from a division of a flow (F) drawn in by the rotor of the fan section (2) in operation, the primary flow (Fl) being intended to circulate within the primary duct (29) and the secondary flow (F2) being intended to circulate around the primary body (3), and BPR being greater than or equal to 1 and less than or equal to 100; R is a radius of a vertex (46, 47) of a blade (31) of a turbine rotor (7, 8), the abradable element (51) being intended to be arranged at the right and at a distance from the vertex (46, 47) of the blade (31) and R being defined as a distance between a longitudinal axis (X) along which extends a shaft (10, 11) of the primary body (3) and the vertex (46, 47) of the blade (31), the turbine rotor (7, 8) being configured to drive the shaft (10, 11) in rotation around the longitudinal axis (X), and R being greater than or equal to 0.25 meters and less than or equal to 0.40 meters; L is a length of the blade (31), L being defined as a distance between a foot (40) of the blade (31) and the top (46, 47) of the blade (31), the foot (40) of the blade (31) being connected to a disk (30) of the turbine (7, 8), the disk (30) being centered on the longitudinal axis (X), and L being greater than or equal to 0.04 meters and less than or equal to 0.09 meters;H Sa being an area of ​​an axial section of the abradable element (51) comprising the upstream end edge and the downstream end edge of the abradable element (51), La being a distance separating the upstream end edge from the downstream end edge of the abradable element (51), and H being greater than or equal to 5.5 millimeters and less than or equal to 14.0 millimeters; and 10-5 / TV 273.15MlO,4^vecr expressed nuiÇTy — l,715x 10 R(273.157 r+im,4 in degrees Kelvin, mit Cl) being greater than or equal to 3.0.105 Pa.s and less than or equal to 6.0.105 Pa.s.;

10. Method (E) of manufacturing according to claim 9, comprising a fixing (E2) of the abradable element (51) to the housing (50) by brazing using a filler alloy consisting of nickel, chromium and silicon.

11. A manufacturing method (E) according to any one of claims 9 and 10, comprising forming a heat shield (53) between the first and second ends of the tubular space (5200) such that the heat shield (53) extends from the second end of the tubular space (5200) over a distance that is greater than or equal to 5% and less than or equal to 20% of a distance separating the first end from the second end.

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