Device to aid in the regulation of aeronautical turbomachinery propellers

Abstract

This control device for a propulsion system, comprising means for calculating a pitch setpoint for at least one propeller of the propulsion system, the calculation means using a predictive propeller performance model that takes into account at least one flight speed to adapt a pitch angle setpoint, is characterized in that the predictive propeller performance model is configured to use polars implemented as a mathematical law. Figure for the abstract: Fig 1

Description

Title of the invention: Device for assisting in the regulation of aeronautical turbomachinery propellers technical field

[0001] The invention relates to the field of control devices for aeronautical turbomachinery, which may have a single propeller or a double propeller configuration. Prior art

[0002] "Open Rotor" fan engines are a type of turbomachinery in which the fan is outside the casing, unlike conventional turbojet engines (of the "Turbofan" type in Anglo-Saxon terminology).

[0003] Open rotor architectures include, in particular, conventional single-propeller turboprops, UDFs (“Unducted Dual Fan” also known as “Contra-Rotating Open Rotor” or CROR or contra-rotating open rotor in French) as well as USFs (acronym for the English term “Unducted Single Fan” for single non-ducted fan in French).

[0004] In the case of a CROR architecture, the propulsion system consists of two rotors, namely, a mobile upstream propeller which drives the flow and a downstream propeller, counter-rotating with respect to the upstream propeller, which aims to straighten the flow.

[0005] In the case of a USF architecture, the upstream propeller is mobile (i.e. rotor) while the downstream propeller is fixed (i.e. stator) and plays the role of a rectifier.

[0006] These different Open rotor architectures require pitch angle control.

[0007] The regulation of the operation of the propeller or propellers is classically based on two main modes of regulation.

[0008] A constant rotational speed regulation method is known, in which the propeller pitch, i.e., its angle of attack, is adjusted using a feedback loop to maintain a set rotational speed, the actual speed being measured by a dedicated sensor. This regulation method is used for all flight phases during which the forward speed is sufficiently high to obtain stable aerodynamic operation of the propeller.

[0009] Constant pitch angle control is also known, in which the pitch angle is controlled by the control stick position given by the pilot and the propeller rotation speed. This mode is used for all phases where the aircraft's forward speed is too low for the propeller's aerodynamic characteristics to provide sufficient thrust response to a change in rotational speed.

[0010] During a transition from one control mode to another, it is desirable to minimize thrust variations observed for a given value of the power transmitted by the shaft, as such variations are detrimental to the pilot's perception of healthy engine behavior. It is also desirable to limit variations in propeller speed(s), due to the impact of these variations on the overall engine dynamics, vibrations, and noise emitted. Furthermore, it is desirable to maintain continuity of overall engine operation in all situations involving a transition between operating modes, such as acceleration, deceleration, unexpected changes in aircraft altitude, or engine failures.

[0011] Current architectures of control systems rely mainly on the measurement of pitch angles and propeller rotation speeds, and do not allow for preventive action.

[0012] A solution for obtaining anticipatory regulation of pitch angle requirements, for Open rotor architectures with single propeller or doublet of counter-rotating propellers is presented in FR2 998 866, using iterative calculations of second-order polynomials whose coefficients are determined by interpolation of predefined tabular values.

[0013] This solution has drawbacks related to the interpolation and iterations required, particularly in terms of computational accuracy and response time, which have consequences for the convergence time of the angle control system. Furthermore, this solution does not take into account USF architectures. Description of the invention

[0014] To overcome the aforementioned drawbacks, a control device for a propulsion system is proposed, comprising means for calculating a pitch setpoint for at least one propeller of the propulsion system, the calculation means using a predictive model of propeller performance taking into account at least one flight speed to adapt a pitch angle setpoint.

[0015] This control device is characterized in that the predictive model of propeller performance is configured to use polars implemented in the form of a mathematical law.

[0016] For example, the propulsion system includes at least one element selected from a rotor, a stator, an upstream rotor and a downstream rotor counter-rotating with respect to the upstream rotor, and a rotor and stator assembly, the rotor being located upstream of the stator.

[0017] Advantageously, the predictive model of propeller performance takes into account a measurement of the propeller speed and a measurement of the mechanical torque of the propeller shaft.

[0018] According to an advantageous feature, the predictive model of propeller performance uses a mathematical optimization law to define a timing setpoint for at least one stator.

[0019] For example, the calculation means include an iteration loop whose stopping criterion is the convergence of a lift coefficient from a calculated value to a value obtained by using polars.

[0020] Advantageously, the calculation means include an iteration loop having a stopping criterion determined from a convergence of a calculated value of the mechanical torque to the measured mechanical torque.

[0021] For example, the polars are obtained by using a calibration of the mathematical formulation with respect to target results obtained by three-dimensional numerical simulation or by wind tunnel tests.

[0022] For example, said control device constitutes a module for a full authority control computer.

[0023] The invention also relates to a full authority control computer comprising a control device as mentioned.

[0024] The invention also relates to a turboprop engine comprising a control device as mentioned, as well as an aircraft equipped with such a turboprop engine.

[0025] According to another aspect, the invention relates to a control method for a propulsion system, comprising a step of calculating a pitch setpoint for at least one propeller of the propulsion system, during which a propeller performance prediction step is performed, taking into account at least one flight speed to adapt a pitch angle setpoint. This propeller performance prediction step is characterized by the use of polar curves implemented in the form of a mathematical law. Brief description of the drawings

[0026] Other objects, features and advantages of the invention will become apparent from the following description, given solely by way of non-limiting example, and made with reference to the accompanying drawings in which:

[0027] [Fig-1] illustrates the general principles of an embodiment of the invention;

[0028] [Fig.2] illustrates a flowchart of the input and output data used in a calculation code associated with a rotor;

[0029] [Fig.3] illustrates a flowchart of the input and output data used to estimate the required pitch angle in a calculation code associated with a rotor;

[0030] [Fig.4] illustrates a flowchart of the input and output data used in a calculation code associated with a stator;

[0031] [Fig.5] illustrates a flowchart of the input and output data used to estimate the required angle of adjustment in a calculation code associated with a stator;

[0032] [Fig.6] illustrates a flowchart of the architecture of the calculation code associated with a rotor;

[0033] [Fig.7] illustrates the typical shape of a polar curve relating the lift coefficient and the angle of incidence;

[0034] [Fig.8] illustrates the typical shape of a polar curve relating the drag coefficient and the co efficient of lift;

[0035] [Fig.9] qualitatively illustrates the influence of the recalibration parameters in the determination mination of a polar associated with a rotor;

[0036] [Fig. 10] qualitatively illustrates the influence of the recalibration parameters in the determination of a polar associated with a rotor or a stator;

[0037] [Fig. 11] illustrates a flowchart of the architecture of the calculation code associated with a stator;

[0038] [Fig. 12] illustrates the variation of the thrust delivered by a stator as a function of the stator pitch angle for three different types of operation;

[0039] [Fig. 13] illustrates the variation in efficiency of the rotor / stator module as a function of the stator pitch angle for three different operating types;

[0040] [Fig. 14] illustrates the calibration coefficients of the mathematical formulation of the polar Cl 125 vs AoA127;

[0041] [Fig. 15] illustrates the calibration coefficients of the mathematical formulation of the polar Cdl25 vs C1125;

[0042] [Fig. 16] illustrates the calibration coefficients of the mathematical formulation of the polar Cl 120 vs AoA122; and

[0043] [Fig. 17] illustrates the calibration coefficients of the mathematical formulation of the polar Cdl20 vs C1120; Detailed description of at least one embodiment

[0044] Figure 1 illustrates the general operation of an embodiment of the invention relating to a control loop for the pitch angle of a propeller or propellers, for regulation at constant rotational speed.

[0045] A setpoint 20 for the propeller speed 21 is given by the pilot or an autopilot or servo system. A propeller speed sensor 22 calculates the difference 23 between the setpoint and the instantaneous speed.

[0046] This difference 23 is transmitted to the FADEC 24 (full authority control computer) which calculates, using a measurement of the propeller rotation speed 25 and a measurement of the mechanical torque 26 of the propeller shaft, the power supplied to the propeller, as well as a pitch setpoint 27. The FADEC 24 also takes into account a measurement of the aircraft's flight speed 28. The FADEC 24 is configured and able to use for the calculation of the pitch setpoint 27 a pre-programmed predictive model of propeller performance 29 contained in its memory.

[0047] An angular pitch angle sensor 30 allows the difference 31 between the instantaneous pitch angle value and the setpoint 27 to be calculated, which is transmitted to the actuator 32, consisting of a cylinder which acts on the pitch angle of the propeller 21.

[0048] The predictive performance model of the propeller 29 is based on a one-dimensional calculation code of the lifting line type, allowing estimation of the aerodynamic performance of a rotor (applicable for a conventional propeller and for the CROR type architecture) or of a stator (applicable in a USF type configuration).

[0049] Figure 2 shows a flowchart of the input and output data used in the calculation code associated with a rotor. Thus, for given flight conditions 33 and for a given rotor geometry 34, it is possible, using a model 35 of the rotor, to estimate the thrust 36 delivered by the rotor, as well as the mechanical torque 37 consumed by the rotor for a given rotational speed 38 and for a given pitch angle 39.

[0050] From the calculation code presented in [Fig.2], the reverse procedure can be used to estimate the required pitch angle, as illustrated in [Fig.3]. Thus, the required pitch angle 40 can be estimated using the rotor model 41 from the parameters 42 representative of the flight conditions and measured by probes, from the known geometric parameters 43 of the rotor, and from the measured parameters of rotational speed 44 and mechanical torque 45 of the rotor.

[0051] It should be noted that in order to obtain the pitch angles in the case of the contra-rotating propeller doublet such as encountered in CROR type architectures, the calculation code of [Fig.3] is applied to each upstream and downstream rotor.

[0052] In the case of a USF architecture, the calculation code of [Fig.3] is used for the rotor and is complemented by a calculation code specific to the stator.

[0053] Figure 4 presents a flowchart of the input and output data used in the calculation code associated with a stator.

[0054] Thus, for given operating conditions 46 of the stator and for a given geometry 47 of the stator, it is possible, using a model 48 of the stator, to estimate the thrust 49 delivered by the stator, as well as the mechanical torque 50 generated by the stator for a given pitch angle 51.

[0055] Using the calculation code presented in [Fig. 4], the required pitch angle can be estimated in reverse, as illustrated in [Fig. 5]. Thus, the required pitch angle 52 can be estimated using the stator model 53 based on the stator operating conditions 54, the known geometric parameters 55 of the stator, and a mathematical optimization law 56 that maximizes the efficiency of the propeller module. Mathematical law 56 allows the required stator pitch angle to be automatically adjusted to maximize the efficiency of the rotor and stator assembly for a given propeller operating point.

[0056] The following describes the flowchart of [Fig.6] which summarizes the architecture of the calculation code associated with a rotor 60 and implemented by the FADEC 24 for any propulsion configuration of the Open rotor type.

[0057] The input values ​​61 consist of known geometric parameters for a given rotor, atmospheric parameters measured by probes, mechanical parameters measured by sensors present on the engine and calculated parameters specified below.

[0058] For example, the geometry of a given rotor is characterized by geometric parameters such as the diameter, the hub ratio, the number of blades, the activity factor, and a reference height to the rotor plane. From these initial geometric parameters, other geometric parameters are calculated, such as the external radius (Rtip), the internal radius (Rhubl20), the rotor cross-section (Areal20), the mean rotor chord, or the chord / diameter ratio of the rotor.

[0059] For example, atmospheric parameters measured by probes and representative of a given flight condition are the flight speed (V0), the speed of sound (Vson) and the ambient density (RhoAmb).

[0060] For example, the mechanical parameters measured by sensors and representative of a given operating point are the rotor speed (Nmechl20), the rotor pitch angle (Calagel20), and the mechanical torque on the rotor shaft (Trql20). From these initial mechanical parameters, other parameters are calculated, such as the rotor peripheral speed (Utipl20) and the ratio between the flight speed and the rotor peripheral speed (V0qUtipl20).

[0061] After determining the input data by measurement or calculation in step 61, the FADEC 24 proceeds to the calculation step 62 of the wake velocity field at infinity downstream of the rotor, assuming conservation of flow rate and using the transposition of the reference height to the rotor plane at infinity downstream (RqRtipWakel80), the induced axial velocity of the rotor wake at infinity (VizWakel80), the contraction of the fluid stream between the rotor plane and infinity downstream (Rtip 180qRtip 120) and the ratio between the axial velocity and the tangential velocity at infinity downstream (VzWakel8OqUtipl8O) as specified in the following formulas.

[0062] RqRtipWakelSO = ]RqRtipCalcQdl202 - RhubQtipl202 (1) 1 - RhubQtip\2Q

[0065] vizwake\80 = + (Uüpl2Q*RqRtipCalc0dl2Q)2 (2)

[0064] RPn^OnRtin 1 70 - J1 ' RhubQtip 1202 RtiplWqRtip 120 - V718()^1 / 712.()

[0065] VzWaM SOqWp 180 = (4)

[0066] In which:

[0067] RqRtipWakel80 is the transposition of the reference height to the rotor plane at infinity downstream;

[0068] RqRtipCalc0dl20 represents the reference height to the rotor plane for model calculations;

[0069] RhubQtipl20 represents the rotor hub ratio;

[0070] VizWakel80 is the induced axial velocity of the rotor wake at infinity;

[0071] VizWakel80qV120 is an iterative parameter representing the induced axial velocity of the wake reduced to the relative velocity of the rotor plane;

[0072] V0 is the flight speed;

[0073] Utipl20 is the peripheral speed of the rotor;

[0074] Rtipl80qRtipl20 represents the contraction of the fluid stream between the rotor plane and infinity downstream; and

[0075] Vzl80qVzl20 is an iterative parameter representing the ratio between the axial velocity at infinity downstream and the axial velocity at the level of the rotor plane.

[0076] At this stage the FADEC 24 initializes the two iterative parameters VizWakel80qV 120 and Vzl80qVzl20, which will take convergent values ​​during subsequent iterations (step 69).

[0077] The FADEC 24 then performs the calculation step 63 of the velocity field at the level of the rotor plane expressed by the following equations:

[0078] 1„ 1 *________VizWakelSQ________(5) " - 2 / VzWakelSüqUtipI^ RqRtipWakeVW /

[0079] Vnd97 - 1 * WzWa?180__* (V0 +VfeW^180)__ Utipï2Q*RqRtipCalc$d\2$ / VzWakelSOqUtipW)\2 1 + \ RqRtipWakelM / (6)

[0080] y 122 = y / (V0 + Vûl 22)2 + (Utip 120*RqRtipCalc0dl20 - Via 122)2 (7)

[0081] ^ / «122-^22(8) Vson

[0082] Phi A— a ta n [____V0 + Vizl22__) -.-.-180 (9) rniizz - atan utipl2V*RqRtipCalcM12Q - Viu\22)

[0083] AoA 122 = Calagel20 - PhiA22 (10)

[0084] In which,

[0085] Vizl22 represents the induced axial velocity at the level of the rotor plane;

[0086] Viul22 represents the induced tangential velocity of the frame relative to the level of the rotor plane;

[0087] V122 represents the relative speed at the level of the rotor plane;

[0088] Mnl22 represents the associated Mach number; and

[0089] AoA122 is the angle of incidence.

[0090] Next, FADEC 24 performs step 64 of the calculation of aerodynamic coefficients using the following equations:

[0091] FunCPrmdlll20 = %*acos(exp ( ( - 1 ) W,FaZel20*( 1 -RqRlipCalc0dl2û ) ) ''\1\■z2xj. t VZjyÜKeiQuqUtlpiMJ! (11)

[0092] FuncGoldsteinl20 = FuncPrandtll2Q* ___________RqRti pCalcQd1202_________ RqRtipCalc0dl2Q^ + VzWakel80qUtipl802 (12)

[0093] ri^o- ^VizWakel8Q*(VQ+VizWakel80)*FuncGoldsteinl2Q - ^bpay}2(}FCqDiam\2G Vn2*Utipï2{) (13)

[0094] In which,

[0095] FuncPrandtll20 represents the Prandtl approximation;

[0096] FuncGoldsteinl20 represents the Goldstein function; and

[0097] C1120 is the lift coefficient of the rotor blade.

[0098] At this stage, the FADEC 24 uses pre-programmed calculation functions stored in its memory, called polars, which relate, in the form of mathematical laws, the drag and lift coefficients determined experimentally or by 3D calculation for different angles of attack. The methods used for calculation step 65 of a polar expressing the lift coefficient (C1120AoA) as a function of the angle of attack (AoA122) and for calculation step 66 of a polar expressing the drag coefficient (Cdl20) as a function of the lift coefficient (C1120AoA) will be explained later with reference to Figures 7 to 10.

[0099] The FADEC then performs a comparison (step 67) between the value of the lift coefficient from the analytical calculation (C1120) and the value of the lift coefficient from the polar (C1120AoA).

[0100] If the two compared values ​​are equal, convergence has been achieved and the FADEC 24 uses the determined velocity field at the level of the rotor plane and the aerodynamic coefficients obtained, to calculate the thrust delivered by the rotor and the mechanical torque consumed by the rotor (step 68), with the following equations:

[0101] Fnï20 = NhPaleï20*^*RhoAmb*Corde}20-nm22*p:il20\^[Phin2^^ - Cdl20*sin(Phn22*^ - RtubQtipnO) (14)

[0102] Tnp20 = NbPalel20'>pRlioAmh'>Corclel20-Vn2!'s[Cll20-sin[Phil22*i^j ) + Cdnf^eosfPhini*^ ) ) *Rtipl20*( 1 -RhubQtipnO ) 'Rtipl20-RqRbpCalc0dl20 (15)

[0103] In which,

[0104] Fnl20 represents the thrust delivered by the rotor; and

[0105] Trql20 is the mechanical torque consumed by the rotor.

[0106] If the two compared values ​​are not equal, the FADEC 24 proceeds to a new step 69 of iteration of the calculation of iterative parameters VizWakel80qV120 (step 70) and Vzl80qVzl20 (step 71).

[0107] For the calculation of the iterative parameter Vzl80qVzl20 (step 71), the FADEC 24 first performs a step 72 of evaluation of the dimensionless invariants representative of the performance of a rotor as expressed in the following equations:

[0108] ja on _V0(16)

[0109] Q120 =F / 1120 (17) RhoAmb*( i *Diaml204 \ Or /

[0110] Trql20 *Nmedil20* & (18) C / ?120 =_________-_______________3___211______ RhoAmb* ( bLm^hA2Q ) \ 60 / [YES] In which,

[0112] J120 is the rotor advance coefficient;

[0113] Ctl20 is the rotor traction coefficient; and

[0114] Cpl20 is the rotor power coefficient.

[0115] After the evaluation step 72 of the dimensionless invariants, the FADEC 24 performs the calculation of the iterative parameter Vzl80qVz 120 (step 71) with the following equations: [01161 Mi202 + —z---8*0120---- _ / 120 (19) Y æ*( 1 - RhiibQtip 120 ) 2*TT

[0117] Vz>120 = Vizl20qUtipl20*Utipl20 (20)

[0118] Vzl20 = VO + Vzzl20 (21)

[0119] Vsl 80 = VO + 2*Vzzl20 (22) [°120] vOigo^nO = ​​^|80 (23)

[0121] In which,

[0122] Vizl20qUtipl20 represents the induced axial velocity reduced to the peripheral velocity at the level of the rotor plane;

[0123] Vizl20 is the axial velocity induced at the plane of the rotor;

[0124] Vzl20 is the axial speed at the level of the rotor plane; and

[0125] Vzl80 is the axial velocity at the wake at infinity downstream.

[0126] The calculation code presented above is based on the direct path theory of a calculation code associated with a rotor, as presented in [Fig.2], according to which the performance of the rotor (thrust delivered, mechanical torque consumed) is obtained as a function of its control (rotation speed and pitch angle).

[0127] Conversely, following the principle presented in [Fig. 3], the FADEC 24 uses the torque sensor available on the rotor's mechanical shaft to determine the angle of calibration knowing the measured mechanical torque, using for example a servo loop which iterates on the calibration angle to obtain equality between the mechanical torque from the model and the measured mechanical torque.

[0128] The following presents the mathematical formulation of the polar of a rotor as well as the method for obtaining it.

[0129] The mathematical formulation of the polar curve depends on its shape. To identify this shape, it is first necessary to obtain target results in terms of the performance to be achieved. These target results are derived from three-dimensional (3D) numerical simulations and / or physical tests in a wind tunnel, for example.

[0130] The [Fig.7] shows the typical shape of a polar relating the lift coefficient (C1120) and the angle of incidence (AoA122).

[0131] The [Fig.8] shows the typical shape of a polar relating the drag coefficient (Cdl20) and the lift coefficient (Cl 120).

[0132] The points shown in the graphs of Figures 7 and 8 were obtained by 3D numerical simulation calculations of a propeller with known geometry. These calculations were driven according to the Mach number, rotation speed, and pitch angle obtained from the target results. The lift coefficient (C1120) and drag coefficient (Cdl20) were identified to determine the thrust coefficient (Ctl20) and power coefficient (Cpl20) values ​​from the target results.

[0133] The mathematical formulation of the polars aims to establish a mathematical model that minimizes deviations from the set of points. To build this mathematical model, certain dependence parameters are selected.

[0134] The polar curve (C1120 vs AoA122) giving the lift coefficient as a function of the angle of incidence depends on the following parameters: the angle of incidence, the relative Mach number (Mnl22) to take into account the compressibility effects, and the ratio between the flight speed and the peripheral speed of the propeller (V0qUtipl20) to take into account the 3D effects of variation in the distribution of the load over the height of the blade.

[0135] The polar curve (Cdl20 vs C1120) giving the drag coefficient as a function of the lift coefficient depends on the following parameters: the lift coefficient, the relative Mach number (Mnl22) to take into account the compressibility effects, and the ratio between the flight speed and the peripheral speed of the propeller (V0qUtipl20) to take into account the 3D effects of variation of the load distribution over the height of the blade.

[0136] The ratio (VOqUtipQdes) between the parameter V0qUtipl20 and the value of this parameter at the helix drawing point (V0qUtipl20des) is defined by the following equation:

[0137] VOt / U ti p Qdes = VOg 120 (24) V0qUtipl20des

[0138] This report allows modeling the 3D effects of variation in load distribution over the height of the blade.

[0139] The slope coefficient klCl of the polar (C1120 vs AoA122) is then defined by the following equation:

[0140] H CZ = kiClBASE (25) 3.1 - k2compKCl*Mnl222

[0141] In which,

[0142] klClBASE represents the slope coefficient when the compressibility effect is zero; And

[0143] k2compKCl is a correction coefficient.

[0144] The angle of incidence when the lift coefficient is zero, depending on the compressibility effects and the 3D load distribution effects, is then defined by the following equation:

[0145] AoACIO - AoAC10base + (kïcorrAoACl0*V0qUtipQdes + k2compAoACl0*Mnl222) (26)

[0146] In which,

[0147] AoACIObase represents the zero-lift angle of incidence when the compressibility effect and 3D effects are negative;

[0148] klcorrAoAQO is a first-order coefficient that takes into account 3D effects and corrects the angle of incidence at zero lift; and

[0149] k2comp AoACIO is a second-order coefficient that takes into account the effects of com pressibility and correcting the angle of incidence at zero lift.

[0150] The mathematical formulation of the polar (C1120 vs AoA122) giving the lift coefficient as a function of the angle of attack is defined by the following equation: [°151] Cl 120 = H Cl *sin ((AoA 122 - AoA CZO) *1) (27)

[0152] Equation (27) is used by FADEC 24 during calculation step 65 of the polar expressing the lift coefficient (C1120AoA) as a function of the angle of incidence (AoA122).

[0153] Figure 9 qualitatively illustrates the influence of the parameters klCl and AoACIO in determining a curve whose plot must minimize deviations from the given points MXCR, MXCL, and TKOF. The parameter AoACIO represents the point of intersection of this curve with the axis AoA corresponding to zero lift, and the parameter klCl defines the slope of this curve.

[0154] For the mathematical formulation of the polar (Cdl20 vs C1120) giving the co Efficient drag as a function of the lift coefficient: we first define the upper limit of the 3D load distribution effects along the propeller height, since it is observed that the 3D effect becomes negligible for high values ​​of VOqUtipQdes. This limit is given by the following equation:

[0155] VQqUtipQdesCorr = mmÇVQqUtipQdes, VQqUtipQdesMax} (28)

[0156] In which,

[0157] VOqUtipQdesMax represents the maximum value of VOqUtipQdes from which the 3D effects become negligible.

[0158] For the mathematical definition of the polar (Cdl20 vs C1120) we base ourselves on a bi-parabolic type curve in hyperbolic cosine as expressed by the following equations:

[0159] DeltaClLow = abs(min{Cll2G - CLml, 0))(29)

[0160] DeltaClHigh — max (0, C7120 - CLml) (30)

[0161] Cd\2iï = CDml+kL* (cash (DeltaCILow)ExpL - +kR*(cosh{DeÀtaClHigh^^ (31)

[0162] Figure 10 qualitatively illustrates the influence of the calibration parameters kL, ExpL, CDml, CLml, ExpR, and kR on the curve whose plot must minimize deviations from the given points MXCR, MXCL, and TKOF. The parameters CLml and CDml define the position of the point corresponding to the minimum drag coefficient. The parameters kL and ExpL define the slope of the curve on the under-angle side. The parameters kR and ExpR define the slope of the curve on the over-angle side.

[0163] Corrections are then defined on the different coefficients, to take into account the 3D effects of load distribution over the height of the propeller, by the following equations:

[0164] CLml = CLmlBASE + klcorrCLml*VQqUtipQdesCorr (32)

[0165] CDml — CDmlBASE + kïcorrCDml*VQqUtipQdesCorr (33)

[0166] kL — kLBASE + klcorrKL^VOqUtipQdesCorr (34)

[0167] kR = kRBASE + k 1 corrKR *VOqUtipQdesCorr (35)

[0168] ExpL = ExpLBASE + klcorrExpL^VGqUtipQdesCorr (36)

[0169] ExpR = ^XP^BASE + klcorrExpR*VQqUîipQdesCorr (37)

[0170] In which,

[0171] CLmlBASE is the lift coefficient corresponding to the minimum drag coefficient when the 3D effect becomes negligible;

[0172] CDuiIbase is the minimum drag coefficient when the 3D effect becomes negligible;

[0173] kLBAsE is the slope coefficient on the under-incidence side when the 3D effect becomes negligible;

[0174] kRBAsE is the slope coefficient on the over-incidence side when the 3D effect becomes negligible;

[0175] ExpLBASE is the slope exponent on the under-incidence side when the 3D effect becomes negligible;

[0176] ExpRBAsE is the slope exponent on the over-incidence side when the 3D effect becomes negligible;

[0177] klcorrCLml is the first-order coefficient which takes into account 3D effects and corrects the lift coefficient corresponding to the minimum drag coefficient;

[0178] klcorrCDml is the first-order coefficient which takes into account 3D effects and corrects the minimum drag coefficient;

[0179] klcorrKL is the first-order coefficient which takes into account 3D effects and corrects the slope coefficient on the under-incidence side;

[0180] klcorrKR is the first-order coefficient which takes into account 3D effects and corrects the slope coefficient on the over-incidence side;

[0181] klcorrExpL is the first-order coefficient that takes into account 3D effects and corrects the slope exponent on the under-incidence side; and

[0182] klcorrExpR is the first-order coefficient which takes into account 3D effects and corrects the slope exponent on the over-incidence side.

[0183] Finally, the correction to be applied to model the compressibility effect is defined by the following equations:

[0184] MNdd = MNddcuy + kClMNdd*CH20 (38)

[0185] DeltaMNdd — max(Q, Mni22-MNdd) (39) [°186] AdderCdComp = k'2.compCd*DeltaMNdd2 <4°)

[0187] In which,

[0188] MNddcLoest is the divergence Mach number corresponding to the zero lift coefficient from which compressibility effects are taken into account;

[0189] kCIMNdd is the correction coefficient of the divergence Mach number as a function of the lift coefficient;

[0190] k2compCd is the second-order coefficient which takes into account the effects of compressibility and corrects the drag coefficient.

[0191] The mathematical formulation of the polar (Cdl20 vs Cl 120) giving the drag coefficient as a function of the lift coefficient is defined by the following equation:

[0192] Cdl20 = CDml + kL*(cosh(DeltaClLow) K'pL -1) + kR*(cosh(DellaClHigh)Exp'i - 1) + AdderCdComp (41)

[0193] Equation (41) is used by FADEC 24 during calculation step 66 of the polar expressing the drag coefficient (Cdl20) as a function of the lift coefficient from of the polar (C1120AoA).

[0194] The calibration coefficients of the mathematical formulation of the polar C1120 vs AoA122 and of the polar Cdl20 vs C1120 are specified in the tables of figures 16 and 17, respectively.

[0195] The following describes the flowchart of [Fig.1 1] which summarizes the architecture of the calculation code associated with a stator 80 and implemented by the FADEC 24 within the framework of a USF type propulsion architecture.

[0196] The input values ​​81 consist of known geometric parameters for a given stator, atmospheric parameters measured by probes, a mechanical parameter measured by sensors present on the motor and calculated parameters specified below.

[0197] For example, the geometry of a given stator is characterized by geometric parameters such as the diameter, the hub ratio, the number of blades, the activity factor, and a reference height to the propeller plane. From these initial geometric parameters, other geometric parameters are calculated, such as the external radius (Rtipl25), the internal radius (Rhubl25), the stator cross-section (Areal25), the mean chord of the stator, or the stator elongation.

[0198] For example, atmospheric parameters measured by probes and representative of a given flight condition are the flight speed (V0), the speed of sound (Vson) and the ambient density (RhoAmb).

[0199] For example, the mechanical parameter measured by sensors and representative of a given operating point is the stator pitch angle (Calagel25).

[0200] The FADEC 24 uses the calculation code associated with the upstream rotor 60 to complete the input parameters (step 81) with the rotor hub ratio (RhubQtipl20), the reference height to the rotor plane for model calculations (RqRtipCalc0dl20), the induced axial velocity at the rotor plane (Vizl20), the axial velocity at the rotor plane (Vzl20), and the tangential velocity at the immediate downstream end of the rotor (Vu 124). The Vul24 velocity is calculated using the following equations:

[0201] Whell20 = RhoAmb*Vzl20*Areal20 (42)

[0202] Trql20 '^mechY2Q* (43)

[0203] Vm124 = Wheel2Q dHtl2Q (44) Uiip 120 *RqRti p Calculation 120

[0204] In which,

[0205] Whell20 represents the flow rate through the rotor plane; and

[0206] dHtl20 represents the increase in enthalpy across the rotor disk.

[0207] The FADEC 24 then performs a calculation step 82 of the velocity field at the upstream level of the stator. To transpose the magnitudes of the velocity field to the immediate

[0208]

[0209]

[0210]

[0211]

[0212]

[0213]

[0214]

[0215] downstream of the rotor at the upstream end of the stator, the FADEC 24 uses a coefficient (CoeffVzl25) regulating the induced axial speed of the rotor current tube at the upstream end of the stator by the following equation: Wd 25 = (1 + Coeff VH25) *VÛ12O (45) According to equation (42), if CoeffVzl25 is zero, then the axial velocity induced at the upstream of the rectifier (Vizl25) is equal to the axial velocity induced at the immediate downstream of the rotor and the rectifier is considered to be located very close to the propeller. According to equation (42), if CoeffVzl25 is equal to 1, then the axial velocity induced at the upstream of the rectifier (Vizl25) is equal to twice the axial velocity induced at the immediate downstream of the rotor, and the stator is considered to be located in the infinite downstream wake of the rotor. To calculate the velocity field at the upstream end of the stator, the FADEC 24 uses the following equations: Vzl25 = VO + V^125 (46) Vzl25^Vzl20 = K43S (47) there is, -*- 'J .2 Rtipl25qRtipl20Aero = -------1 -120-------- \(l-RhubQtipl252)^Vzl25qVzl20 (48) RqRtip 125 = J RqRtipCalc0dl20 -RhubQtipl20 \Vzl25qVzl20^Rtipl25qRtipl20Aero2 (49)

[0216]

[0217]

[0218]

[0219]

[0220]

[0221]

[0222]

[0223]

[0224]

[0225] v |9S_ Vul24*RqRtipCalc0dl20 (50) vwt^ - RqRtipi25*Rtipl^^^ VI25 = ^VH252 +Vwl252 (51) In which, Vzl25 is the axial velocity at the upstream end of the stator; Vzl25qVzl20 represents the ratio between the axial speed at the upstream end of the stator and the speed at the rotor plane; Rtipl25qRtipl20Aero represents the external aerodynamic radius ratio between the stator plane and the rotor plane; RqRtipl25 represents the projection of the reference height of the propeller plane onto the upstream plane of the stator; Vu 125 is the tangential velocity at the upstream end of the stator; and V125 is the absolute speed at the upstream end of the stator; The FADEC 24 calculates the absolute velocity setting angle (Phil25) using the following equations: Phü 25 = atan (for atan I) *180 > 0 (52) \Vwl25 / 77' *\Vm125 / TC

[0227] Phii25 = atan (180, for atan (vf t9~Z) < o (53)

[0228] It can be considered that the stator generates an induced velocity perpendicular to the absolute velocity upstream of the stator and in the opposite direction to the thrust generated by the stator. Taking this induced velocity (Vil27) into account then makes it possible to determine the absolute velocity used in calculating the definition of the generated thrust and the resistive torque of the stator.

[0229] The FADEC 24 then performs a calculation step 83 of the velocity field at the level of the stator plane, corrected for induced effects.

[0230] The induced axial (Vizl27) and tangential (Viul27) velocities at the stator calculation plane are expressed by the following equations:

[0231] Vzzl27 = V125*W127qV125*cvs^^ (54)

[0232] Vitd27 = 7125 *Vi 127q7125*sin (Phi 125) (55)

[0233] Equations 54 and 55 contain the iterative parameter that expresses the ratio between the induced velocity at the plane of the stator and the absolute velocity upstream of the stator. At this stage, the FADEC 24 initializes the iterative parameter Vil27qV 125, which will take convergent values ​​during subsequent iterations (step 89).

[0234] The FADEC 24 calculates the velocity field at the level of the stator plane corrected for induced effects, using the following equations:

[0235] VH27 = VH25 + Vrzl27 (56)

[0236] Vu 127 = 7m 125 - 7zm 127 (57)

[0237] 7127 = VVzl272 + W1272 (58)

[0238] ^27 = -7122(59) Vson

[0239] In which,

[0240] Vzl27 is the axial velocity at the stator corrected for induced effects;

[0241] Vul27 is the tangential velocity at the stator, corrected for induced effects;

[0242] V127 is the absolute speed at the stator, corrected for induced effects; and

[0243] Mnl27 is the Mach number associated with the absolute speed.

[0244] The FADEC 24 calculates the pitch angle associated with the absolute speed (Phil27) and the angle of attack (AoA127) using the following equations:

[0245] Phi\27 = atan (for atan (> 0

[0246] Phiï27 = atan () *2^ + jgg, for atan (vfl77) - $ \ V II 1Z / / ' \ V II 1Z / / (61)

[0247] AoA 127 = Calibration 125 - Phi 127 (62)

[0248] Then the FADEC 24 performs the calculation 84 of the aerodynamic coefficient by the following equation:

[0249] nn'_ VH27t / V125AspRati(A25 (63) CoeffKJV25

[0250] Equation (63) contains a calibration coefficient CoeffKJ125 which allows the Kutta-Joukowski theorem to be adapted to geometries of the stator type located downstream of a rotor.

[0251] At this stage, the FADEC 24 uses pre-programmed calculation functions stored in its memory, called polars, which relate, in the form of mathematical laws, the drag and lift coefficients determined experimentally or by 3D calculation for different angles of attack. The methods used in the case of a stator for calculating a polar expressing the lift coefficient (C1125AoA) as a function of the angle of attack (AoA127) (step 85) and for calculating a polar expressing the drag coefficient (Cdl25) as a function of the lift coefficient (C1125AoA) (step 86) will be explained later.

[0252] The FADEC 24 then performs a comparison step 87 between the value of the lift coefficient from the analytical calculation (C1125) and the value of the lift coefficient from the polar (C1125AoA).

[0253] If the two compared values ​​are equal, convergence has been achieved and the FADEC 24 uses the determined velocity field at the level of the stator plane and the aerodynamic coefficients obtained, to perform the calculation of the thrust delivered by the propeller and the mechanical torque consumed by the propeller (step 88), with the following equations:

[0254] Fn 125 = NhPale 125*1 *RhoAmb*CorcM 25 *V12T* (CO25*cos (Phi 127 *) - Cd 125*sin (Phi 127 *)) *Rtip 125 » (1 - RhubQtip 125) (64)

[0255] Trql25 = NbPali-125*pRhoAmb*Cordel25*V1271*{Cll25*xm(Plul27*$0)+ 01125*00x^^127* ^0]) *Rlipl25*(l -RlwbQtipl25)*Rlipl25*R < / RtipOilc0dl25 (65)

[0256] If the two compared values ​​are not equal, the FADEC 24 proceeds to a new iteration (step 89) of the calculation of the iterative parameter Vil27qVI25 (step 90).

[0257] The FADEC 24 performs the evaluation of dimensionless invariants representative of stator performance using the following equations:

[0258] . / 125 = -<'47'""

[0259] Ct ! 25 =£M25 (67) Rho Amb * V1252 ^Diam 12 5 2

[0260] c p5 =77^125(68) RhoAmb * VI25" *Diam 125''

[0261] In which,

[0262] J125 is the stator advance coefficient;

[0263] Ctl25 is the stator traction coefficient; and

[0264] Cpl25 is the stator power coefficient.

[0265] It is necessary to associate a control objective with the calculation code 80 in order to use it to predict variations in the stator pitch angle. For the rotor, the measurement of the mechanical torque constitutes the control objective, but in the case of the stator, an alternative solution must be found because this type of measurement is not available.

[0266] The stator timing is determined to maximize the thrust generated by this stator in order to maximize the efficiency of the rotor / stator module, thereby minimizing fuel consumption.

[0267] Figures 12 and 13 present graphs showing that the maximization of the overall rotor / stator efficiency is achieved when the thrust on the stator is maximum.

[0268] Fig. 12 illustrates the variation of the thrust delivered (Fnl25) by the stator as a function of the stator pitch angle (Pitch 125) for three different operating types, namely hovering (CRUISE), climb point (MXCL) and takeoff (TKOF).

[0269] Fig. 13 illustrates the variation in efficiency of the rotor / stator module (Etatot) as a function of the stator pitch angle (Pitch 125) for three different operating types, namely hovering (CRUISE), climb point (MXCL) and takeoff (TKOF).

[0270] It is observed that the stator setting maximizing the stator thrust is the same as that which also maximizes the overall efficiency.

[0271] Therefore, it is proposed to define an analytical control equation which automatically adjusts the stator timing in order to maximize the thrust of this stator.

[0272] To this end, the FADEC 24 first calculates a series of derivatives using the following equations:

[0273] dCll25QdVa21qV125 = (69) v—- L / t- J / jv J. »2

[0274] Equation (69) expresses the derivative (dC1125QdVil27qV 125) of the lift coefficient of the Kutta-Joukowsky theorem;

[0275] dVzmQdVil21qV125 = V125*cos(Phi 125*^) (70)

[0276] Equation (70) gives the expression for the derivative (dVzl27QdVil27qV125) of the axial component of the absolute velocity of the stator;

[0277] dVul21QdVH21qV125 = ( - 1 ) *V125*sin (P / wT25) (71)

[0278] Equation (71) expresses the derivative (dVul27QdVil27qV125) of the tangential component of the absolute velocity of the stator;

[0279] dV125QdViï27qVn5=dVzl27QdVil27qV125*dn(Plùl27*^ + dVul27QdViï27qV125'\:os(Ph^

[0280]

[0281]

[0282]

[0283]

[0284]

[0285]

[0286]

[0287]

[0288]

[0289]

[0290]

[0291]

[0292]

[0293]

[0294] Equation (72) expresses the derivative (dV125QdVH27qV125) of the absolute speed of the stator; dCosPhil27QdVil27qVi25 = ÿ^fdVuVriQdVinTqVnS - ^^*dV\25QdVin7qV\25 (73) Equation (73) gives the value (dCosPhil27QdVil27qV125) of the derivative of the cosine of the angle of pitch of the absolute speed of the stator; dSiriPhimQdVH22qVÏ25 = y^*dVzl27QdVil27qVï25 -^^*dV125QdViï27qVl25 (74) Equation (74) gives the value (dSinPhil27QdVil27qV125) of the derivative of the sine of the pitch angle of the absolute speed of the stator; dCdr25QdCU25 = ( -1 , 'kL'E\pL\i*h\MiaC!LowŸ'^ + kRExpR\<*h(DehaCllJixh)^ + ( - D (75) Equation (75) expresses the derivative (dCdl25QdC1125) of the drag coefficient with respect to the lift coefficient using the parametric formulation of the polar. The function ceil() is a function that returns the smallest integer value greater than or equal to its argument; and <.V<.W,y>r25(M' 2 (VI27M,W'M272<.'17^ - 2 ■{WI252,A7I257V12.5-1(2(125^,,., (76) Equation (76) expresses the derivative (dCtMapl25QdVil27qV125) of the stator thrust using the definition of the thrust coefficient Ctl25. The FADEC 24 obtains the control equation by imposing that the value of the derivative (dCtMapl25QdVil27qV125) expressed by equation (76) is zero, namely the following equation (77): (77) Equation (77) then allows us to define the pitch angle that the stator should have, thus guiding the regulation system and corresponds to the mathematical law (56) of [Fig.4], The following presents the mathematical formulation of the polar of a stator as well as the method for obtaining it. The mathematical formulation of the polar of a stator is identical to the mathematical formulation of a rotor already presented, with the sole difference that the shape of the polar (Cl 125 vs AoA127) expressing the lift coefficient as a function of the angle of incidence is no longer linearly inclined as in the case of a rotor, but tends to be of order 3. Therefore, the lift coefficient (C1125) for a stator is expressed using the following equations:

[0295] H a = klClBASE (78) 5 / 1 - k2compKCl*Mn!2'l2

[0296] k?a = k2ClBASE (79) - klcompKCl^Mnm2

[0297] k2CJ = k2aBASE (80) - k2compKCl*Mn\212

[0298] Cl 125 = kl Cl*sin ((AoA 127 - A oACIO)) + kïCl*sin ((AoA 127 - AoA CIO) ~ + k3Cl*sin ((AoA 1 Tl - AM CIO))1 (81)

[0299] The mathematical formulation of the polar (Cdl25 vs C1125) giving the drag coefficient as a function of the lift coefficient is defined by the following equation (82), identical to equation 41 used in the case of a rotor:

[0300] Cdl25 = CDinl + kL*(cosh(Drt^^) + kR*(cosh(.DeltaClHigh)^ 1) + AdderCdComp (82)

[0301] The calibration coefficients of the mathematical formulation of the polar C1125 vs AoA127 and of the polar Cdl25 vs C1125 are specified in the tables of figures 14 and 15, respectively.

Claims

Demands

1. Control device for a propulsion system, comprising means for calculating (24) a pitch setpoint (27) of at least one propeller (21) of the propulsion system, the calculation means (24) using a predictive propeller performance model (29) taking into account at least one flight speed (28) to adapt a pitch angle setpoint (27), characterized in that the predictive propeller performance model (29) is configured to use polars implemented in the form of a mathematical law.

2. Control device according to claim 1, wherein the propulsion system comprises at least one element selected from a rotor, a stator, an upstream rotor and a downstream rotor counter-rotating with respect to the upstream rotor, and a rotor and stator assembly, the rotor being located upstream of the stator.

3. Control device according to any one of claims 1 and 2, wherein the predictive model of propeller performance (29) takes into account a measurement of the propeller speed (25) and a measurement of the mechanical torque (26) of the propeller shaft.

4. Control device according to any one of claims 1 to 3, wherein the predictive propeller performance model (29) uses a mathematical optimization law to define a pitch setpoint (27) of at least one stator.

5. Control device according to any one of claims 1 to 4, wherein the computing means (24) comprise an iteration loop of which a stopping criterion is the convergence of a lift coefficient from a calculated value to a value obtained by using polars.

6. Control device according to any one of claims 1 to 5, wherein the computing means (24) comprise an iteration loop having a stopping criterion determined from a convergence of a calculated value of the mechanical torque to the measured mechanical torque.

7. Control device according to any one of claims 1 to 6, wherein the polars are obtained by using a calibration of the mathematical formulation with respect to target results obtained by three-dimensional numerical simulation or by wind tunnel testing.

8. Control device according to any one of claims 1 to 7, wherein said device constitutes a module for a full authority control computer (24).

9. Full authority control calculator (24) comprising a device according to any one of claims 1 to 8.

10. Turboprop comprising a control device according to any one of claims 1 to 9.

11.

12. Aircraft comprising a turboprop according to claim 10. Control method for a propulsion system, comprising a step of calculating a pitch setpoint (27) of at least one propeller (21) of the propulsion system, during which a propeller performance prediction step is carried out taking into account at least one flight speed (28) to adapt a pitch angle setpoint (27), said prediction step being characterized by the use of polars implemented in the form of a mathematical law.

Images