Improving the dynamic behavior of the drive shaft of the fan rotor of an aeronautical propulsion system

Abstract

An aeronautical propulsion system (1) has a mean internal radius Rm_a of the high-pressure turbine (7) satisfying formula (I), where: FN is the thrust of the propulsion system (1); BPR is the dilution rate of the propulsion system (1); and I = 0.16 millimeters by Newton (mm / N) and J = 28 millimeters.

Description

[0001] DESCRIPTION

[0002] TITLE: Improvement of the dynamic behavior of the fan rotor drive shaft of an aeronautical propulsion system

[0003] TECHNICAL FIELD

[0004] This application generally concerns the field of propulsion systems, and more particularly aeronautical propulsion systems having a high, or even very high, dilution ratio.

[0005] STATE OF THE ART

[0006] A propulsion system generally comprises, from upstream to downstream in the direction of gas flow, a fan section, a compressor section which may include a low-pressure compressor and a high-pressure compressor, a combustion chamber and a turbine section which may include in particular a high-pressure turbine and a low-pressure turbine. The high-pressure compressor is rotated by the high-pressure turbine via a high-pressure shaft. The fan and, where appropriate, the low-pressure compressor are rotated by the low-pressure turbine via a low-pressure shaft.

[0007] Technological research efforts have already led to very significant improvements in the environmental performance of aircraft. The Applicant takes into consideration the impact factors in all phases of design and development to obtain less energy-intensive, more environmentally friendly aeronautical components and products whose integration and use in civil aviation have moderate environmental consequences with the aim of improving the energy efficiency of aircraft.

[0008] Thus, in order to improve the propulsive efficiency of the propulsion system and to reduce its specific consumption as well as the noise emitted by the fan section, propulsion systems have been proposed having a high bypass ratio (BPR, corresponding to the ratio between the flow rate of the secondary air flow and the flow rate of the primary air flow). To achieve such bypass ratios, the fan section can be decoupled from the low-pressure turbine, thus making it possible to independently optimize their respective rotation speeds. Generally, the decoupling is achieved using a reduction mechanism placed between the upstream end of the low-pressure shaft and a rotor of the fan section. The rotor of the fan section is then driven by the low-pressure shaft via the reduction mechanism at a rotation speed lower than that of the low-pressure shaft.

[0009] The current trend is to increase the overall compression ratio of the propulsion system, which corresponds to the ratio between the outlet pressure of the high-pressure compressor and the inlet pressure of the fan. This in fact makes it possible to increase the inlet pressure of the combustion chamber gases, and therefore to further improve the overall efficiency of the propulsion system. Increasing the overall compression ratio therefore requires increasing the compression ratio of the high-pressure compressor and / or the low-pressure compressor, especially since at the same time we are trying to reduce the compression ratio of the fan for the reasons explained above. One of the consequences is that the torque to be transmitted by the low-pressure shaft to the reduction mechanism is reduced in comparison with a direct-drive propulsion system.The low-pressure shaft can therefore have a smaller diameter, which facilitates the integration of the high-pressure body into the propulsion system. However, this reduction in the diameter of the low-pressure shaft has the effect of reducing the frequency of the natural modes, while the increase in the rotational speed of the low-pressure shaft increases the operating range of the low-pressure shaft. As a result, the low-pressure shaft can exceed a critical speed and can enter resonance. At resonance, which occurs when the low-pressure shaft passes the critical speed, it undergoes overvoltage phenomena which amplify the deformations and forces caused by the (inevitable) unbalances of the low-pressure shaft. Under these conditions, the low-pressure shaft is said to be supercritical.

[0010] Thus, changing the diameter of the low-pressure shaft has an impact on its dynamic behavior and modifies the positioning of its supercritical modes. However, a propulsion system rotating at a critical speed in steady state risks rapid degradation, which must be avoided.

[0011] EXPOSED

[0012] An aim of the present application is to optimize the propulsion system in order to increase its efficiency while controlling the dynamic behavior of the fan rotor drive shaft.

[0013] For this purpose, according to a first aspect, an aeronautical propulsion system is proposed comprising:

[0014] - a first turbine configured to drive a first compressor via a first shaft around an axis of rotation;

[0015] - a second turbine configured to drive a second compressor via a second shaft, the second shaft being configured to rotate at a higher speed than the first shaft around the axis of rotation;

[0016] - a fan rotor connected to a fan shaft;

[0017] - a reduction mechanism coupling the first shaft and the fan shaft to drive the fan shaft at a rotational speed lower than the rotational speed of the first shaft; wherein an average radius of a bore of the second turbine complies with the following formula:

[0018] R m a < I * FN * BPR * 10“ 4 + J where: R m _a is the mean radius of the bore of the second turbine in millimeters (mm);

[0019] FN is the thrust of the propulsion system measured when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in Newton (N);

[0020] BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; and

[0021] I = 0.16 millimeters per Newton (mm / N) and J = 28 millimeters.

[0022] Some preferred but non-limiting features of the propulsion system according to the first aspect are the following, taken individually or in combination: the mean radius of the bore of the second turbine further complies with the following formula: R m a > G * FN * BPR * 10“ 4 + H where G = 0.16 millimeters per Newton (mm / N) and H = 18 millimeters (mm); the average radius of the bore of the second turbine also respects the following formula: Rm a < E * L HP 2 * XN * 10“ 9 + Fi where: LHP is a distance between an inlet of the second compressor and an outlet of the second turbine in millimeters (mm); E = 3.15 (mm.rpm) -1 and Fi = 23 millimeters (mm); and XN is the limiting speed of the first shaft, in revolutions per minute (rpm); the average radius of a bore of the second turbine also respects the following formula: R m _a > EU Hf S XN * 10 9 + F2 where: LHP is a distance between an inlet of the second compressor (5) and an outlet of the second turbine in millimeters (mm); E = 3.15 (mm. rpm) -1 and F2 = 13 millimeters (mm); and XN is the limiting speed of the first shaft, in revolutions per minute (rpm); the average radius of a bore of the second turbine also respects the following formula: . 2

[0023] R m a < K * I * 10 3 * n + M ] * XN * 10“ 9 + N, where: D9 is the fan rotor diameter in millimeters (mm), measured in a plane normal to the axis of rotation at an intersection between a tip and a leading edge of the fan rotor blades; BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; T e is the maximum temperature at the inlet of the drive turbine when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius (°C); Tref = 273K; n is the number of stages in the second turbine and the second compressor; GAMMA is the adiabatic coefficient of air; XN is the limiting speed of the first shaft, in revolutions per minute (rpm); and K = 6.76, L = 153.6 m -1 .(°C) -1 / 2 . (rpm) -1 , M = 421 mm.(°C) 1 / 2 and Ni = -11 millimeters (mm);

[0024] - the average radius of a bore of the second turbine also respects the following formula: . 2

[0025] R m a > K * * 10 3 * n + M ] * XN * 10“ 9 + N, where: D9 is the fan rotor diameter in millimeters, measured in a plane normal to the axis of rotation at an intersection between a tip and a leading edge of the fan rotor blades; BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; T eis the maximum temperature at the inlet of the drive turbine when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius (°C); Tref = 273K; n is the number of stages in the second turbine and the second compressor; GAMMA is the adiabatic coefficient of air; XN is the limiting speed of the first shaft, in revolutions per minute (rpm); and K = 6.76, L = 153.6 m -1 .(°C) -1 / 2 . (rpm) -1 , M = 421 mm.(°C) 1 / 2 and N2 = - 21 millimeters (mm);

[0026] - a hub-to-head ratio of the second turbine is between 0.77 and 0.90;

[0027] - the propulsion system comprises a further bearings configured to center the first shaft relative to the axis of rotation, the bearings comprise a bearing mode damper;

[0028] - the propulsion system further comprises an inter-turbine casing extending between the first turbine and the second turbine and configured to support the second turbine through a bearing assembly;

[0029] - the inter-turbine casing comprises a plurality of guide vanes configured to straighten an air flow at the inlet of the first turbine;

[0030] - the propulsion system includes between twenty and thirty guide vanes

[0031] - an overall compression ratio of the propulsion system, corresponding to the ratio between a pressure at the outlet of the second compressor and a pressure at the inlet of the fan rotor, is greater than or equal to 40 and less than or equal to 70;

[0032] - the second turbine is two-stage;

[0033] - the second compressor comprises at least eight stages and at most eleven stages;

[0034] - the dilution ratio of the propulsion system is greater than or equal to 10, for example between 10 and 35 inclusive, for example between 10 and 18 inclusive, for example between 10 and 15 inclusive;

[0035] - the first turbine comprises at least three stages and at most five stages; and / or

[0036] - the first compressor comprises at least two stages and at most four stages.

[0037] According to a second aspect, there is provided an aircraft comprising at least one propulsion system according to the first aspect attached to the aircraft by means of a mast.

[0038] According to a third aspect there is provided a method of dimensioning or manufacturing a propulsion system comprising a reduction mechanism coupling a first turbine and a fan rotor to drive the fan rotor at a speed lower than a speed of the first turbine, and a second turbine configured to rotate at a higher speed than the first turbine, the second turbine being dimensioned such that an average radius of a bore of the second turbine complies with the following formula:

[0039] R m a < I * FN * BPR * 10“ 4 + J where: R m _a is the mean radius of the bore of the second turbine in millimeters;

[0040] FN is the thrust of the propulsion system measured when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in Newton (N);

[0041] BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; and

[0042] I = 0.16 millimeters per Newton (mm / N) and J = 28 millimeters.

[0043] Some preferred but non-limiting features of the sizing method according to the third aspect are the following, taken individually or in combination:

[0044] - the second turbine is dimensioned so that the mean radius of the bore of the second turbine is the mean radius of the bore of the second turbine also respects the following formula:

[0045] R m a > G * FN * BPR * 10“ 4 + H where G = 0.16 millimeters per Newton (mm / N) and H = 18 millimeters (mm); - the second turbine is dimensioned so that the mean radius of the bore of the second turbine also complies with the following formula:

[0046] R m a < E * L HP 2 * XN * 10“ 9 + F, where: LHP is a distance between an inlet of the second compressor (5) and an outlet of the second turbine in millimeters (mm); E = 3.15 (mm.rpm) -1 and Fi = 23 millimeters (mm); and XN is the limiting speed of the first shaft, in revolutions per minute (rpm);

[0047] - the second turbine is dimensioned so that the average radius of the bore of the second turbine also complies with the following formula:

[0048] R m _a > EU Hf S XN * 10 9 + F2where: LHP is a distance between an inlet of the second compressor and an outlet of the second turbine in millimeters (mm); E = 3.15 (mm. rpm) -1 and F2 = 13 millimeters (mm); and XN is the limiting speed of the first shaft, in revolutions per minute (rpm);

[0049] - the second turbine is dimensioned so that the average radius of the bore of the second turbine also complies with the following formula: . 2

[0050] R m a < K * I * 10 3 * n + M ] * XN * 10“ 9 + N, where: D9 is the fan rotor diameter in millimeters (mm), measured in a plane normal to the axis of rotation at an intersection between a tip and a leading edge of the fan rotor blades; BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; T eis the maximum temperature at the inlet of the drive turbine when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius (°C); Tref = 273K; n is the number of stages in the second turbine and the second compressor; GAMMA is the adiabatic coefficient of air; XN is the limiting speed of the first shaft, in revolutions per minute (rpm); and K = 6.76, L = 153.6 m -1 .(°C) -1 / 2 . (rpm) -1 , M = 421 mm.(°C) 1 / 2 and Ni = -11 millimeters (mm);

[0051] - the second turbine is dimensioned so that the average radius of the bore of the second turbine also complies with the following formula: . 2

[0052] R m a > K * * 10 3 * n + M ] * XN * 10“ 9 + N, where: D9 is the fan rotor diameter in millimeters (mm), measured in a plane normal to the axis of rotation at an intersection between a tip and a leading edge of the fan rotor blades; BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; T e is the maximum temperature at the inlet of the drive turbine when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius (°C); T re f = 273K; n is the number of stages in the second turbine and the second compressor; GAMMA is the adiabatic coefficient of air; XN is the limiting speed of the first shaft, in revolutions per minute (rpm); and K = 6.76, L = 153.6 m -1 .(°C) -1 / 2 . (rpm) -1 , M = 421 mm.(°C) 1 / 2and N2 = - 21 millimeters (mm). According to a fourth aspect, there is provided a method of manufacturing a propulsion system comprising the following steps:

[0053] - dimension the propulsion system in accordance with the method of the third aspect; and

[0054] - manufacture the propulsion system.

[0055] DESCRIPTION OF FIGURES

[0056] Other characteristics, aims and advantages of the invention will emerge from the following description, which is purely illustrative and non-limiting, and which must be read in conjunction with the appended drawings in which:

[0057] Figure 1 is a schematic, partial, sectional view of an example propulsion system according to one embodiment;

[0058] Figure 2 is a schematic sectional view of an example of a reduction mechanism according to a first variant;

[0059] Figure 3 is a schematic sectional view of an example of a reduction mechanism according to a second variant;

[0060] Figure 4 is an example of an aircraft that may include at least one propulsion system according to one embodiment; and

[0061] Figure 5 is a flowchart illustrating exemplary steps of a sizing or manufacturing method according to one embodiment.

[0062] Throughout the figures, similar elements have identical references.

[0063] DETAILED DESCRIPTION

[0064] A propulsion system 1 has a main direction extending along a longitudinal axis X and comprises, from upstream to downstream in the direction of flow of the gases in the propulsion system 1 when it is in operation, a fan 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 is here an aeronautical propulsion system 1 configured to be fixed to an aircraft 100 via a pylon (or mast).

[0065] The compressor section 4, 5 comprises a succession of stages each comprising a moving blade wheel (rotor) 4a, 5a rotating in front of a fixed blade wheel (stator) 4b, 5b. The turbine section 7, 8 also comprises a succession of stages each comprising a fixed blade wheel (stator) 7b, 8b behind which a moving blade wheel (rotor) 7a, 8a rotates.

[0066] In the present application, the axial direction corresponds to the direction of the longitudinal axis X, in correspondence with the rotation of the shafts of the gas generator, and a radial direction is a direction perpendicular to this axis X and passing through it. Furthermore, the circumferential (or lateral, or even tangential) direction corresponds to a direction perpendicular to the longitudinal axis X and not passing through it. Unless otherwise specified, internal (respectively, interior) and external (respectively, exterior), respectively, are used in reference to a radial direction so that the internal part or face of an element is closer to the axis X than the external part or face of the same element.

[0067] In operation, an air flow F entering the propulsion system 1 is divided between a primary air flow F1 and a secondary air flow F2, which circulate from upstream to downstream in the propulsion system 1.

[0068] The secondary airflow F2 (also called the "bypass airflow") flows around the primary body 3. The secondary airflow F2 cools the periphery of the primary body 3 and is used to generate most of the thrust provided by the propulsion system 1.

[0069] The primary air flow F1 flows in a primary vein inside the primary body 3, passing successively through the compressor section 4, 5, the combustion chamber 6 where it is mixed with fuel to serve as an oxidant, and the turbine section 7, 8. The passage of the primary air flow F1 through the turbine section 7, 8 receiving energy from the combustion chamber 6 causes rotation of the rotor of the turbine section 7, 8, which in turn drives rotation of the rotor of the compressor section 4, 5 as well as a rotor part 9 of the fan section 2.

[0070] In a twin-spool propulsion system 1, the compressor section 4, 5 may comprise a low-pressure compressor 4 and a high-pressure compressor 5. The turbine section 7, 8 may comprise a high-pressure turbine 7 and a low-pressure turbine 8. The rotor of the high-pressure compressor 5 is rotated by the rotor of the high-pressure turbine 7 via a high-pressure shaft 10. The rotor of the low-pressure compressor 4 and the rotor portion 9 of the fan section 2 are rotated by the rotor of the low-pressure turbine 8 via a low-pressure shaft 11. Thus, the primary body 3 comprises a high-pressure body comprising the high-pressure compressor 5, the high-pressure turbine 7 and the high-pressure shaft 10, and a low-pressure body comprising the fan 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 spool is greater than the rotational speed of the low-pressure spool. In a triple-spool 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 configured to drive the rotor of the low-pressure compressor 4 via an intermediate shaft. The fan rotor 9 and the rotor of the high-pressure compressor 5 remain driven by the low-pressure shaft 11 and the high-pressure shaft 10, respectively.

[0071] The low pressure shaft 11 is generally housed, over a section of its length, in 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, i.e. driven in the same direction around the longitudinal axis X. Alternatively, the low pressure shaft 11 and the high pressure shaft are counter-rotating, i.e. driven in opposite directions around the longitudinal axis X. Where appropriate, 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.

[0072] The fan section 2 comprises at least the fan rotor 9 adapted to be driven in rotation relative to a fan casing 12 by the turbine section 7, 8. Each fan rotor 9 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 12 or have a variable pitch. In this case, the root of the blades 14 of each rotor 9 is pivotally mounted along a pitch axis and is connected to a pitch change mechanism 15 mounted in the propulsion system 1, the pitch being adjusted according to the flight phases by a pitch change mechanism 15. The pitch change mechanism 15 is illustrated in broken lines in Figure 1 to show that this feature is optional.

[0073] The fan section 2 may further comprise a fan stator 16, or rectifier, which comprises blades 17 mounted on a hub 18 of the fan stator 16 and have the function of straightening the secondary air flow F2 which flows out of the fan rotor 9. The blades 17 of the fan stator 18 may be fixed relative to the hub 18 or have a variable pitch.

[0074] In order to improve the propulsive efficiency of the propulsion system 1 and to reduce its specific consumption as well as the noise emitted by the fan section 2, the propulsion system 1 has a high bypass ratio. By high bypass ratio, we mean here a bypass ratio greater than or equal to 10, for example between 10 and 80 inclusive. To calculate the bypass ratio, the mass flow rate of the secondary air flow F2 and the mass flow rate of the primary air flow F1 are 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, 3 eedition) and at sea level (conditions known as SLS, for Seal Level Standard). It should be noted that, in the present application, the parameters (pressure, flow rate, thrust, speed, etc.) are systematically determined under these conditions. By "not installed", it is understood here that the measurements are carried out when the propulsion system 1 is in a test bench (and not installed on an aircraft 100), the measurements then being simpler to carry out. The distances (length, radius, diameter) are, on the other hand, measured at ambient temperature (approximately 20°C) when the propulsion system 1 is cold, that is to say when the propulsion system has been stopped for a sufficient period for the parts of the propulsion system to be at ambient temperature.

[0075] The fan rotor 9 is 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 fan rotor 9, in order to independently optimize their respective rotational speed. In this case, the propulsion system 1 further comprises an additional shaft, called the fan shaft 20. The low-pressure shaft 11 connects the low-pressure turbine 8 to an inlet of the reduction mechanism 19 while the fan shaft 20 connects the outlet of the reduction mechanism 19 to the fan rotor 9. The fan rotor 9 is therefore driven by the low-pressure shaft 11 via the reduction mechanism 19 and the fan shaft 20 at a rotational speed lower than the rotational speed of the low-pressure turbine 8.

[0076] This decoupling makes it possible to reduce the rotational speed and the pressure ratio of the fan rotor 9 and to increase the power extracted by the low-pressure turbine 8. Indeed, the overall efficiency of the propulsion systems is conditioned to the first order by the propulsive efficiency, which is favorably influenced by a minimization of the variation in kinetic energy of the air when passing through the propulsion system 1. In a propulsion system 1 with a high bypass ratio, the majority of the flow generating the propulsive force is constituted by the secondary air flow F2 of the propulsion system 1, the kinetic energy of the secondary air flow F2 being mainly affected by the compression that the secondary air flow F2 undergoes when passing through the fan section 2. The propulsive efficiency and the pressure ratio of the fan section 2 are therefore linked: the lower the pressure ratio of the fan section 2, the better the propulsive efficiency will be.In order to optimize the propulsive efficiency of the propulsion system 1, the pressure ratio of the fan, which corresponds to the ratio between the average pressure at the outlet of the fan stator 17 (or, in the absence of a stator, of the fan rotor 9) and the average pressure at the inlet of the fan rotor 9, is less than or equal to 1.70, for example less than or equal to 1.50, for example between 1.05 and 1.45. The average pressures are measured here over the height of the blade 14 (from the surface which radially delimits the flow path at the inlet of the fan rotor 9 to the tip 21 of the fan blade 14).

[0077] The propulsion system 1 is configured to provide thrust between 18,000 Ibf (80,068 N) and 51,000 Ibf (22,2411 N), for example between 20,000 Ibf (88,964 N) and 35,000 Ibf (15,5688 N).

[0078] The fan section 2 is shrouded and for this purpose comprises a fan casing 12, the fan rotor 9 being housed in the fan casing 12.

[0079] The fan section 2 comprises in particular a fan rotor 9 extending upstream of a fan stator. The vanes of the fan stator are then generally called outlet vanes (“Outlet Guide Vane” or “OGV” in English) and have a fixed pitch relative to the hub of the fan stator. Furthermore, the bypass ratio of the propulsion system 1 is for example greater than or equal to 10, for example between 10 and 35 inclusive, for example between 10 and 18 inclusive, for example between 10 and 15 inclusive. Note that, when the bypass ratio is greater than or equal to 25, the fan rotor 9 is preferably of variable pitch. The peripheral speed at the tip 21 of the vanes of the fan rotor 9 may also be between 260 m / s and 400 m / s. The blades 14 of the fan rotor 9 may be fixed or have variable pitch. The fan pressure ratio may be between 1.20 and 1.45.

[0080] The reduction mechanism 19 may comprise a reduction mechanism 19, in this example a reduction mechanism with an epicyclic gear train, for example of the “epicyclic” or “planetary” type according to the terminology sometimes encountered by those skilled in the art, single-stage or two-stage.According to a first variant, the reduction mechanism 19 may be of the planetary type (“star” in English) (Figure 2) and comprise a sun gear 19a (input of the reduction mechanism 19), centered on an axis X of rotation of the reduction mechanism 19 (generally confused with the longitudinal axis X) and configured to be driven in rotation by the low pressure shaft 11, a ring gear 19b (output of the reduction mechanism 19) coaxial with the sun gear 19a and configured to drive the fan shaft 20 in rotation around the axis X of rotation, and a series of satellites 19c distributed circumferentially around the axis X of rotation between the sun gear 19a and the ring gear 19b, each satellite 19c being meshed internally with the sun gear 19a and externally with the ring gear 19b.The series of satellites 19c is mounted on a planet carrier 19d which is fixed relative to a stator part 19e of the propulsion system 1, for example relative to a casing of the compressor section 4, 5. According to a second variant, the reduction mechanism 19 may be of the epicyclic type (“planetary” in English) (Figure 3), in which case the crown 19b is fixedly mounted on the stator part 19e of the propulsion system 1 and the fan shaft 20 is driven in rotation by the planet carrier 19d which is therefore movable in rotation relative to a stator part 19. e of the propulsion system 1, for example in relation to a casing of the compressor section 4, 5).

[0081] Whatever the configuration of the reduction mechanism 19, the diameter of the crown 19b and the planet carrier 19d are greater than the diameter of the sun gear 19a, so that the rotation speed of the fan rotor 9 is lower than the rotation speed of the low pressure shaft 11.

[0082] The reduction rate of the reduction mechanism 19 is greater than or equal to 2.5 and less than or equal to 11, for example greater than or equal to 2.7 and less than or equal to 6.0, for example around 3.0.

[0083] Decoupling the low pressure shaft 11 and the fan rotor 9 by means of the reduction mechanism makes it possible to obtain an efficient propulsion system 1 whose fan pressure ratio is less than 1.45. Consequently, the amount of energy to drive the fan rotor 9 is reduced so that the inlet flow rate of the high pressure compressor 5 and therefore the inlet section of the high pressure compressor 5 can be reduced. This, however, has the consequence of limiting the space available for the low pressure shaft 11 (since the low pressure shaft 11 is housed within the high pressure shaft 10). In addition, the reduction in the flow rate in the high pressure compressor 5 also has the effect of reducing the flow rate in the low pressure turbine, which makes it possible to increase the rotational speed of the low pressure shaft 11 and to reduce the torque transmitted by the low pressure shaft 11 and its diameter.However, reducing the diameter of the low pressure shaft 1 requires optimizing the dynamic behavior of the low pressure shaft 11 to prevent it from becoming more supercritical.

[0084] In order to optimize the propulsion system 1 while controlling the dynamic behavior of the low pressure shaft 11, the propulsion system 11 is dimensioned so that the average radius R m _a of a bore of the high pressure turbine 7 is at most equal to:

[0085] R m a < / * F / V * BPR * 10“ 4 + J (1 ) where: R m _a is expressed in millimeters (mm);

[0086] FN is the thrust of the propulsion system, in Newton (N);

[0087] BPR is the bypass ratio of propulsion system 1; and

[0088] I = 0.16 millimeters per Newton (mm / N) and J = 28 millimeters (mm).

[0089] Indeed, the torque transmitted by the low pressure shaft 11 to the fan rotor 9 is linked to the thrust of the fan rotor 9 and to the BPR dilution ratio of the propulsion system 1. Furthermore, increasing the BPR dilution ratio of the propulsion system 1 makes it possible to reduce the diameter of the high pressure body, and therefore the average radius R m _a of the bore of the high pressure turbine 7. Thus, by dimensioning the propulsion system so that the average radius R m _a of the bore of the high pressure turbine 7 also respects the formula (2), we obtain a propulsion system 1 in which the size of the high pressure body and the diameter of the low pressure shaft 11 are dimensioned according to the thrust of the fan rotor 9 (which contributes mainly to the overall thrust of the propulsion system 1) and the BPR bypass ratio.

[0090] The average radius R m_a of the bore of the high-pressure turbine 7 corresponds to the distance, measured in a plane normal to the longitudinal axis X at the midpoint between the leading edge 7c and the trailing edge 7d of the moving blades of the rotor 7a furthest upstream of the high-pressure turbine 7 (i.e. of the rotor 7a of the first stage of the high-pressure turbine 7), between the bore of the rotor disc 7a of the high-pressure turbine 7 and the axis of rotation X. The bore here corresponds to the radially inner face of the rotor disc 7a.

[0091] For example, the average radius R m _a of the bore of each disc of the high pressure turbine 7 respects the formula (1).

[0092] For example, the average radius of the high-pressure turbine bore is at most 300 mm.

[0093] A propulsion system 1 with an average radius R m_a of the bore of the high pressure turbine 7 complies with formula (1) can then achieve an overall compression ratio, which corresponds to the pressure ratio between the pressure at the outlet of the high pressure compressor 5 and the pressure at the inlet of the fan rotor 9 (measured at the level of the foot of the fan rotor 9), to be greater than or equal to 40 and less than or equal to 70, for example greater than or equal to 44 and less than or equal to 55.

[0094] The rotational speed of the high-pressure turbine 7 can then be between 15,000 revolutions per minute and 27,000 revolutions per minute. When the rotational speed of the high-pressure turbine (and therefore of the high-pressure shaft 10) is within this interval and its average radius R m _a respects the formula (1), the mechanical loading of the rotors 7a is acceptable for the high pressure turbine 7.

[0095] For example, propulsion system 1 is further dimensioned so that the mean radius R m _a of the bore of the high pressure turbine 7 is at most equal to:

[0096] R m a < E * L HP 2 * XN * 10“ 9 + F, (2) where: LHP is the length of the high pressure body, in millimeters (mm);

[0097] E = 3.15 (mm.rpm)' 1 and Fi = 23 millimeters (mm); and

[0098] XN is the redline speed of the low pressure shaft 11, in revolutions per minute (rpm), which corresponds to the absolute maximum speed likely to be encountered by the low pressure shaft 11 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)). The redline speed corresponds to the maximum rotation speed when the propulsion system is healthy (and potentially at the end of its life). It is therefore likely to be reached by the low pressure shaft 11 in flight conditions. This redline speed is part of the data declared in the engine certification (type certificate data sheet). Indeed, this rotation speed is usually used as a reference speed for the dimensioning of propulsion systems 1 and in certain certification tests (such as blade loss or rotor integrity tests).The length LHP of the high-pressure body corresponds to the distance between an inlet of the high-pressure compressor 5 and an outlet of the high-pressure turbine 7. The inlet of the high-pressure compressor 5 corresponds to the most upstream part of the most upstream blade wheel 5b (rotor) of the high-pressure compressor 5 (i.e., generally, the leading edge 5c at the blade root of the first stage of the high-pressure compressor 5). The outlet of the high-pressure turbine 7 corresponds to the most downstream part of the blade wheel 7a (rotor) of the high-pressure turbine 7 (i.e., generally, the trailing edge 7d at the blade root of the last stage of the high-pressure turbine 7).

[0099] The length of the LHP high pressure body can, for example, be between 950 mm and 1450 mm for a high pressure body comprising between ten and thirteen compressor and turbine stages.

[0100] The average radius R m_a of a bore of the high pressure turbine 7 also respects the following formula, in particular when the fan section 2 is shrouded:

[0101] Rm_a > EU HP 2 * XN * 10 9 + F2(3) where: F2 = 13 millimeters (mm).

[0102] Sizing the mean bore radius to comply with formula (3) ensures a minimum radius for the high pressure turbine and therefore guarantees its ability to withstand centrifugal forces.

[0103] The low pressure shaft 11 being housed in the high pressure shaft 10, its diameter is constrained by the average radius R m_a of the bore of the high pressure turbine 7. However, the larger the diameter of the low pressure shaft 11, the more its natural modes appear at high rotational speeds (or, in other words, the more the shaft deformation modes are shifted towards high frequencies). Formula (1) thus makes it possible to obtain a compromise between a small diameter average bore radius of the high pressure turbine 7 - which makes it possible to improve the overall compression ratio of the propulsion system and its BPR bypass ratio - while controlling the dynamic situation of the low pressure shaft 11.

[0104] Indeed, the deformation frequency of the low pressure shaft 11 is proportional to the ratio between the diameter of the low pressure shaft 11 and the squared distance between the bearings 11a-11c of the low pressure shaft 11. Thus, the further apart the bearings 11a-11c supporting the low pressure shaft 11 are, the lower the deformation frequency (and therefore the deformation modes) of the low pressure shaft 11. However, the position of the bearings 11a-11c of the low pressure shaft 11 depends on the length LHP of the high pressure body. By defining the average radius R m _a of the bore of the high pressure turbine 7 as a function of the length LHP of the high pressure body (which is formed by the high pressure compressor 5 and the high pressure turbine 7), the dynamic behavior of the low pressure shaft 11 can therefore be better controlled.

[0105] Note that the limiting speed XN is between 8,500 rpm and 12,000 rpm, for example between 9,000 rpm and 11,000 rpm.

[0106] For example, the average radius R m _a of the bore of each disc of the high pressure turbine 7 respects the formula (2). In some cases, the average radius of the bore R m _a of the high pressure turbine 7 is dimensioned before the length of the high pressure body LHP can be determined. In this case, the mean bore radius can be determined from the fundamental dimensioning parameters of the diameter Dg of the fan rotor 9, the bypass ratio BPR of the propulsion system 1 or the limiting speed XN of the low pressure shaft 11, rather than the length of the high pressure body (as defined in formulas (5) and (6)):

[0107] / 2 Q 5

[0108] R m a < K * l L * J-^^ * Te + T ref ) ' CAMMA ~ 1 * 10 3 * n + MI * XN * 10 -9 + Ni (4) where: BPR is the dilution ratio of the propulsion system 1;

[0109] Dg is the diameter of the fan rotor 9 in millimeters (mm), measured in a plane normal to the axis of rotation (X) at an intersection between a tip 21 and a leading edge 22 of the blades 14 of the fan rotor (9); Note that since Figure 1 is a partial view, the diameter Dg is only partially visible;

[0110] Te is the maximum temperature at the inlet of the low pressure turbine 8, in degrees Celsius;

[0111] Tref = 273 K; n is the number of stages in the second turbine (7) and the second compressor (5);

[0112] GAMMA is the adiabatic coefficient of air; and

[0113] K = 6.76, L = 153.6 m- 1 .(°C)- 1 / 2 .(rpm)- 1 , M = 421 mm.(°C) 1 / 2and Ni = - 11 millimeters (mm).

[0114] As specified for formula (6), when the average bore radius R m _a of the high pressure turbine 7 respects the formula (7), the dynamic behavior of the low pressure shaft 11 can therefore be better controlled.

[0115] Preferably, the average radius R m _a of the bore of each disc of the high pressure turbine 7 respects the formula (4).

[0116] The temperature Te at the inlet of the low pressure turbine 8 can be between 950°C and 1230°C.

[0117] Additionally, the average bore radius also follows the following formula: where N2 = - 21 millimeters (mm).

[0118] Preferably, the average radius R m _a of the bore of each disc of the high pressure turbine 7 respects the formula (5).

[0119] In one embodiment, in order to maintain the possibility of introducing and passing the low pressure shaft 11 into the high pressure shaft 10, while ensuring the ability of the low pressure shaft 11 to transmit the torque necessary for the fan rotor 9 and the low pressure compressor 4, the average radius R m _a of the bore of the second turbine 7 is at least equal to:

[0120] R m a > G * FN * BPR * 10“ 4 + H (6) where: G = 0.16 millimeters per Newton (mm / N) and H = 18 millimeters (mm). For example, the average radius R m _a of the bore of each disc of the high pressure turbine 7 respects the formula (6).

[0121] The Applicant also noticed that the position of the bearings 11a-11c of the low pressure shaft 11 could also have an influence on the deformation modes of the low pressure shaft 11. In this case, the low pressure shaft 11 is supported by three or four bearings 11a, 11b and / or 11c, in order to better control the deformation modes of the low pressure shaft 1 and possibly shift the deformation modes of the low pressure shaft 11 in transient conditions of the propulsion system 1, with safety margins compared to the stabilized conditions.

[0122] The low pressure shaft can thus include one or two front bearings 11a and two rear bearings 11b, 11c. A first front bearing 11a is mounted on the one hand on the low pressure shaft 11 and on the other hand on an inlet casing 26 of the propulsion system 1, which extends between the fan rotor 9 and the low pressure compressor 4. If necessary, a second front bearing can be mounted on the one hand on the low pressure shaft 11 and on the other hand on an inter-compressor casing 23 (or intermediate casing) of the propulsion system 1, i.e. between the low pressure compressor 4 and the high pressure compressor 5. A first rear bearing 11b can be mounted on the one hand on the low pressure shaft 11 and on the other hand on the inter-turbine casing 24 (i.e. on the casing extending between the high pressure turbine 7 and the low pressure turbine 8), upstream of the low pressure turbine 8.Alternatively, the first rear bearing 11b may be mounted on the exhaust casing 27, which extends immediately downstream of the low-pressure turbine 8. The first rear bearing 11b extends downstream of the bearing 12b furthest downstream of the high-pressure shaft 10. The second rear bearing 11c may be mounted on the exhaust casing 27. Where appropriate, the first and second rear bearings 11b, 11c may be mounted on the same cylindrical shell, which is itself fixed to the exhaust casing 27.

[0123] The inlet casing 26, the intermediate casing 23, the exhaust casing 27 and, where appropriate, the inter-turbine casing 24 form structural casings of the propulsion system 1 through which the forces generated by the propulsion system 1 pass.

[0124] High pressure turbines 7 complying with formula (1) may then have a hub-to-head ratio, which corresponds to the ratio between an external radius R2 of the high pressure turbine 7 and an internal radius R1 of the rotor 7a (moving blade wheels) of the high pressure turbine 7, greater than 0.77 and less than 0.90. The external radius R2 of the high pressure turbine 7 and the internal radius R1 are measured here in a plane normal to the axis of rotation X at the midpoint between the leading edge 7c and the trailing edge 7d of the moving blades of the rotor 7a at the hub (i.e. at 50% of the chord at the blade root) of the rotor 7a furthest downstream of the high pressure turbine 7 (i.e., the last stage of the high pressure turbine 7). The external radius R2 of the high pressure turbine 7 corresponds to the distance, in this plane, between the tip 7e of the blades of the rotor 7a of the high pressure turbine 7 and the axis of rotation X of the high pressure turbine 7.The internal radius R1 of the rotor 7a corresponds to the distance, in a plane normal to the axis of rotation X of the high-pressure turbine 7, between the external radial surface of the hub of the rotor 7a (which radially delimits the flow path in the rotor 7a) and the axis of rotation X, midway between the leading edge 7c and the trailing edge 7d of the moving blades of the rotor 7a at the hub (at 50% of the chord at the blade root).

[0125] Such high-pressure turbines 7 then have an optimized outlet section Ss. Indeed, the smaller the hub-head ratio, the smaller the external diameter of the high-pressure turbine 7 (at iso-section). A hub-head ratio between 0.77 and 0.90, in combination with an average radius R m_a reduced bore (respecting formula (1)) and an optimized rotation speed as described above, thus makes it possible to obtain not only a more efficient high-pressure turbine 7 (due to its adapted rotation speed), in an adapted size, while optimizing the outlet surface which expands the gases at the outlet of the combustion chamber 5. The sizing of the high-pressure turbine 7 so as to obtain a hub-head ratio of between 0.77 and 0.90 therefore makes it possible to make the high-pressure turbine 7 more efficient, and therefore to reduce the specific consumption of the propulsion system 1, without penalizing the dynamic behavior of the low-pressure shaft 11.

[0126] In order to further improve the control of the supercriticality of the low pressure shaft 11, the bearings 11a-11c of the low pressure shaft 11 comprise a bearing mode damper comprising a pressurized oil film configured to dampen the mode transition (viscous damping). This type of damping is generally known by the English term "squeeze film".

[0127] In addition, the propulsion system 1 further comprises an inter-turbine casing 24 extending between the high-pressure turbine 7 and the low-pressure turbine 8. The inter-turbine casing delimits the flow path between the high-pressure turbine 7 and the low-pressure turbine 8 and comprises guide vanes 25 configured to straighten an air flow exiting the high-pressure turbine 7 and thus improve the supply of the low-pressure turbine 8 and therefore the efficiency of the low-pressure body. The guide vanes 25 therefore have an aerodynamic surface configured to redirect the air flow entering the low-pressure turbine 8. In one embodiment, the propulsion system 1 comprises between twenty and thirty guide vanes 25.

[0128] If necessary, the inter-turbine casing 24 forms a structural casing of the propulsion system 1 making it possible to improve the overall dynamics of the propulsion system 1. For this purpose, the inter-turbine casing comprises an inner shroud mounted on a set of bearings of the propulsion system 1, typically a rear bearing 26 of the high-pressure shaft, an outer shroud which can be configured to absorb the mechanical forces in the propulsion system 1, as well as a series of arms extending radially between the inner shroud and the outer shroud and configured to allow the passage of services and the absorption of mechanical forces between the inner shroud and the outer shroud. The guide vanes 25 can be separate from the arms and extend between the arms and the low-pressure turbine 8.

[0129] Comparative example: Engine 1 is a double-body propulsion system comprising a shrouded fan and corresponding to the current technical standard (at the date of filing of this application) which we are seeking to improve.

[0130] Engine 2 is a double-body propulsion system comprising a shrouded fan which conforms to the teaching of the present application and has an average bore radius which complies with formula (1).

[0131] The dynamic situation of the low pressure shaft of engine 1 is subcritical. Engine 1 also has an average bore radius R m _a less than the minimum average bore radius R m a _MiN as defined in formula (1), while engine 2 has a mean bore radius R m_a in accordance with formula (1). It follows that engine 2 is more compact than engine 1 with a higher bypass ratio, a reduced number of stages, and a dynamic situation of the low pressure shaft of engine 2 which is supercritical. This dynamic situation can however be controlled via the introduction of flexible cages and viscous vibration dampers on all or part of the bearings of the low pressure shaft (in particular the most upstream bearing). Furthermore, an optimization of the positioning of the vein of the high pressure body associated with an improvement in the cooling efficiency of the blades of the high pressure turbine and an improved active control of the clearances at the tip of the blades in the high pressure turbine allows in particular the transition from 10 to 9 stages in the high pressure compressor.

[0132] The reduction in the number of stages (from 4 to 3 stages) in the low-pressure turbine is also associated with an increase in the reduction ratio of the reduction mechanism and an increase in the rotational speed of the fan rotor. Maintaining the compactness of the reduction mechanism is made possible by improving materials, for example the use of ceramic rolling elements (bearings).

[0133] The expected gain for engine 2 compared to engine 1 is reduced consumption installed on aircraft due to reduced friction drag (reduced fan rotor diameter and reduced engine length) and reduced mass.

Claims

CLAIMS 1. Aeronautical propulsion system (1) comprising: - a first turbine (8) configured to drive a first compressor (4) via a first shaft (11) around an axis of rotation (X); - a second turbine (7) configured to drive a second compressor (5) via a second shaft (10), the second shaft (10) being configured to rotate at a higher speed than the first shaft (11) around the axis of rotation (X); - a fan rotor (9) connected to a fan shaft (20); - a reduction mechanism (19) coupling the first shaft (11) and the fan shaft (20) in order to drive the fan shaft (20) at a rotational speed lower than the rotational speed of the first shaft (11); wherein an average radius of a bore of the second turbine (7) complies with the following formula: G * FN * BPR * 10 -4 + H < R m a< I * FN * BPR * 10“ 4 + J where: R m _a is the mean radius of the bore of the second turbine (7) in millimeters (mm); FN is the thrust of the propulsion system measured when the propulsion system (1) is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in Newton (N); BPR is the bypass ratio of the propulsion system (1) and is measured when the propulsion system (1) is stationary in takeoff mode in a standard atmosphere and at sea level; and G = 0.16 millimeters per Newton (mm / N), H = 18 millimeters (mm), I = 0.16 millimeters per Newton (mm / N) and J = 28 millimeters.

2. Propulsion system (1) according to claim 1, wherein the average radius of the bore of the second turbine (7) further complies with the following formula: R m a < E * L HP 2 * XN * 10“ 9+ F, where: LHP is a distance between an inlet of the second compressor (5) and an outlet of the second turbine (7) in millimeters (mm); E = 3.15 (mm.rpm) -1 and Fi = 23 millimeters (mm); and XN is the limiting speed of the first shaft (1 1 ), in revolutions per minute (rpm).

3. Propulsion system (1) according to one of claims 1 and 2, in which the average radius of a bore of the second turbine (7) further complies with the following formula: R m _a > EU Hf S XN * 10 9 + F2where: LHP is a distance between an inlet of the second compressor (5) and an outlet of the second turbine (7) in millimeters (mm); E = 3.15 (mm.rpm) -1 and F2 = 13 millimeters (mm); and XN is the limiting speed of the first shaft (1 1 ), in revolutions per minute (rpm).

4. Propulsion system (1) according to one of claims 1 to 3, in which the average radius of a bore of the second turbine (7) further complies with the following formula: where: Dg is the diameter of the fan rotor (9) in millimeters, measured in a plane normal to the axis of rotation (X) at an intersection between a tip (21) and a leading edge (22) of the blades (14) of the fan rotor (9); BPR is the bypass ratio of the propulsion system (1) and is measured when the propulsion system (1) is stationary in takeoff mode in a standard atmosphere and at sea level; Te is the maximum temperature at the inlet of the drive turbine (8) when the propulsion system (1) is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius; Tref = 273K; n is the number of stages in the second turbine (7) and the second compressor (5); GAMMA is the adiabatic coefficient of air; XN is the limiting speed of the first shaft (11), in revolutions per minute (rpm); and K = 6.76, L = 153.6 m- 1 .(°C)- 1 / 2 .(rpm)- 1 , M = 421 mm.(°C) 1 / 2 and Ni = -11 millimeters (mm).

5. Propulsion system (1) according to one of claims 1 to 4, in which the average radius of a bore of the second turbine (7) further complies with the following formula: where: Dg is the diameter of the fan rotor (9) in millimeters, measured in a plane normal to the axis of rotation (X) at an intersection between a tip (21) and a leading edge (22) of the blades (14) of the fan rotor (9); BPR is the bypass ratio of the propulsion system (1) and is measured when the propulsion system (1) is stationary in takeoff mode in a standard atmosphere and at sea level; Te is the maximum temperature at the inlet of the drive turbine (8) when the propulsion system (1) is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius; Tref = 273K; n is the number of stages in the second turbine (7) and the second compressor (5); GAMMA is the adiabatic coefficient of air; XN is the limiting speed of the first shaft (11), in revolutions per minute (rpm); and K = 6.76, L = 153.6 m- 1 .(°C)- 1 / 2 .(rpm)- 1 , M = 421 mm.(°C) 1 / 2 and N2 = - 21 millimeters (mm).

6. Propulsion system (1) according to one of claims 1 to 5, in which a hub-head ratio of the second turbine (7) is between 0.77 and 0.

90.

7. Propulsion system (1) according to one of claims 1 to 6, comprising a further bearings (11a-11c) configured to center the first shaft (11) relative to the axis of rotation (X), the bearings (11a-11c) comprise a bearing mode damper.

8. Propulsion system (1) according to one of claims 1 to 7, further comprising an interturbine casing (24) extending between the first turbine (8) and the second turbine (7) and configured to support the second turbine (7) through a bearing assembly (11a).

9. Propulsion system (1) according to claim 8, wherein the inter-turbine casing (24) comprises a plurality of guide vanes (25) configured to straighten an air flow at the inlet of the first turbine (8).

10. Propulsion system (1) according to claim 9, comprising between twenty and thirty guide vanes (25).

11. Propulsion system (1) according to one of claims 1 to 10, in which an overall compression ratio of the propulsion system (1), corresponding to the ratio between a pressure at the outlet of the second compressor (5) and a pressure at the inlet of the fan rotor (9), is greater than or equal to 40 and less than or equal to 70.

12. Propulsion system (1) according to one of claims 1 to 11, in which the second turbine (7) is two-stage.

13. Propulsion system (1) according to one of claims 1 to 12, in which the second compressor (5) comprises at least eight stages and at most eleven stages.

14. Propulsion system (1) according to one of claims 1 to 13, in which the dilution ratio of the propulsion system (1) is greater than or equal to 10, for example between 10 and 35 inclusive, for example between 10 and 18 inclusive, for example between 10 and 15 inclusive.

15. Propulsion system (1) according to one of claims 1 to 14, in which the first turbine (8) comprises at least three floors and at most five floors.

16. Propulsion system (1) according to one of claims 1 to 15, in which the first compressor (4) comprises at least two stages and at most four stages.

17. Aircraft comprising at least one propulsion system (1) according to one of claims 1 to 16 fixed to the aircraft by means of a mast.

18. Method for dimensioning a propulsion system (1) comprising a reduction mechanism (19) coupling a first turbine (8) and a fan rotor (9) to drive the fan rotor (9) at a speed lower than a speed of the first turbine (8), and a second turbine (7) configured to rotate at a higher speed than the first turbine (8), the second turbine (7) being dimensioned such that an average radius of a bore of the second turbine complies with the following formula: G * FN * BPR * 10 -4 + H < R m a < I * FN * BPR * 10“ 4 + J where: R m _a is the mean radius of the bore of the second turbine (7) in millimeters (mm); FN is the thrust of the propulsion system measured when the propulsion system (1) is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in Newton (N); BPR is the bypass ratio of the propulsion system (1) and is measured when the propulsion system (1) is stationary in takeoff mode in a standard atmosphere and at sea level; and G = 0.16 millimeters per Newton (mm / N), H = 18 millimeters (mm), I = 0.16 millimeters per Newton (mm / N) and J = 28 millimeters.

19. A sizing method according to claim 18, wherein the second turbine (7) is sized such that the mean radius of the bore of the second turbine (7) further complies with the following formula: R m a < E * L HP 2 * XN * 10“ 9 + F, where: LHP is a distance between an inlet of the second compressor (5) and an outlet of the second turbine (7) in millimeters (mm); E = 3.15 (mm.rpm) -1 and Fi = 23 millimeters (mm); and XN is the limiting speed of the first shaft (1 1 ), in revolutions per minute (rpm).

20. A sizing method according to one of claims 18 and 19, wherein the second turbine (7) is sized such that the mean radius of the bore of the second turbine (7) further complies with the following formula: R m _a > EU Hf S XN * 10 9 + F2where: LHP is a distance between an inlet of the second compressor (5) and an outlet of the second turbine (7) in millimeters (mm); E = 3.15 (mm.rpm) -1 and F2 = 13 millimeters (mm); and XN is the limiting speed of the first shaft (1 1 ), in revolutions per minute (rpm).

21. A sizing method according to one of claims 18 to 20, wherein the second turbine (7) is sized such that the mean radius of the bore of the second turbine (7) further complies with the following formula: . 2 R m »»*_ a « < K * I 1 * 10 3 * n + M ] * XN * 10“ 9 + N, J where: D9 is the diameter of the fan rotor (9) in millimeters, measured in a plane normal to the axis of rotation (X) at an intersection between a vertex (21) and a leading edge (22) of the blades (14) of the fan rotor (9); BPR is the bypass ratio of the propulsion system (1) and is measured when the propulsion system (1) is stationary in takeoff mode in a standard atmosphere and at sea level; Te is the maximum temperature at the inlet of the drive turbine (8) when the propulsion system (1) is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius; Tref = 273K; n is the number of stages in the second turbine (7) and the second compressor (5); GAMMA is the adiabatic coefficient of air; XN is the limiting speed of the first shaft (1 1 ), in revolutions per minute (rpm); and K = 6.76, L = 153.6 m- 1 .(°C)- 1 / 2 .(rpm)- 1 , M = 421 mm.(°C) 1 / 2 and Ni = -11 millimeters (mm).

22. A sizing method according to one of claims 18 to 21, wherein the second turbine (7) is sized such that the mean radius of the bore of the second turbine (7) further complies with the following formula: where: Dg is the diameter of the fan rotor (9) in millimeters, measured in a plane normal to the axis of rotation (X) at an intersection between a tip (21) and a leading edge (22) of the blades (14) of the fan rotor (9); BPR is the bypass ratio of the propulsion system (1) and is measured when the propulsion system (1) is stationary in takeoff mode in a standard atmosphere and at sea level; Te is the maximum temperature at the inlet of the drive turbine (8) when the propulsion system (1) is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius; Tref = 273K; n is the number of stages in the second turbine (7) and the second compressor (5); GAMMA is the adiabatic coefficient of air; XN is the limiting speed of the first shaft (1 1 ), in revolutions per minute (rpm); and K = 6.76, L = 153.6 m- 1 .(°C)- 1 / 2 .(rpm)- 1 , M = 421 mm.(°C) 1 / 2 and N2 = - 21 millimeters (mm).

23. Method for manufacturing a propulsion system (1) comprising the following steps: dimensioning the propulsion system (1) in accordance with one of claims 18 to 22; and manufacturing the propulsion system (1).

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