Method for calculating temperature of turbine rotor and stator in transition state of aero-engine

Abstract

The invention relates to the technical field of aero-engine transition state characteristics and control process temperature calculation, in particular to a cooling-considered aero-engine transition state turbine rotor and stator temperature calculation method. An independent differential equation is established by introducing a hot side fuel gas and cold side cooling air double-heat-source model, and the method is suitable for an aero-engine scene with a complex cooling structure; a lumped parameter method is adopted to reasonably simplify a three-dimensional heat conduction equation, on the premise that the engineering precision of a component with the small Bi number is guaranteed, temperature distribution is simplified into a uniform field, the calculation dimension is remarkably reduced, in combination with an explicit Euler method numerical integration method, rapid discrete solving of a differential equation is achieved, the real-time requirement of an airborne model for transition state calculation is met, and the calculation efficiency is improved. And the time step length is adaptively adjusted to guarantee the numerical stability. By outputting the rotor / stator temperature of the turbine in real time, the dynamic heat exchange effect of the metal component and the airflow in the transition state can be accurately evaluated, and engine control law design and stability optimization are supported.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of transition state characteristics of an aero-engine and its control process temperature calculation, and particularly relates to a transition state turbine rotor and stator temperature calculation method of an aero-engine considering cooling. BACKGROUND

[0002] In the engine transition state working process, a large amount of heat exchange will be generated between the engine metal components and the primary flow or the secondary flow due to the temperature difference. First of all, the temperature of the turbine rotor and stator has a great influence on the dynamic characteristics of the engine and its control process. For a multi-state engine, most of the work is carried out in the transition state, and in many cases, the component temperature may become a factor that determines the main characteristics of the engine. On the one hand, the heat absorption and release of the primary flow and the components in the transition state process affect the temperature, cycle power and pressure of the engine thermodynamic cycle, causing changes in the performance of the engine in the transition state; on the other hand, the influence of the tip clearance, the inconsistent thermal deformation of the casing and the wheel disc and other factors in the transition state process cause the change of the rotor blade tip clearance, thereby causing the deviation of the component characteristics from the nominal rated characteristics, resulting in changes in the component efficiency, flow and aerodynamic stability boundary. Due to the existence of solid heat capacity, the response frequency of the engine heat exchange is lower than that of the high and low pressure rotating speed, so the transition state calculation precision of the on-board model will be reduced.

[0003] In the past heat exchange model, a single heat source is mostly used, and the final steady state temperature of the heat exchange model is the same as the temperature of the heat source. However, in the actual working environment of the aero-engine, due to the gas flow path design or the component cooling design, the working environment of each component is not a single heat source, but a double heat source environment with cooling.

[0004] The thermal state calculation of the structure element with complex configuration is very complicated and requires a large amount of machine time. In order to solve the control task, a relatively simple model must be developed on the basis of the complex model. For the studied task, under the condition that the influence of the transition state component temperature on the transition process characteristics is estimated relatively accurately, these models should be simple enough, and will not make the dynamic mathematical model considering other factors become complex. The calculation time on the digital computer is also maintained at an acceptable level. Therefore, the fast and accurate calculation of the base temperature of each component is the key technology to realize the evaluation of the heat exchange and the influence of the tip clearance change. SUMMARY

[0005] The purpose of the present application is to avoid the shortcomings of the prior art and provide a transition state turbine rotor and stator temperature calculation method of an aero-engine. By introducing a double heat source model, a temperature mathematical model of the transition state component of the aero-engine is constructed, the dynamic heat exchange effect of the metal turbine rotor and stator and the airflow in the transition state can be accurately evaluated, and the engine control law design and stability optimization are supported.

[0006] To achieve the above object, the technical scheme adopted by the present application is as follows: the turbine rotor and stator temperature calculation method for aero-engine transition state, characterized by comprising the following steps:

[0007] Step one, determining initial conditions,

[0008] obtaining the initial average temperature of turbine stator (Ts, 0) and the initial average temperature of turbine rotor (Tr, 0) before the start of engine transition state process;

[0009] Further, the initial average temperature of turbine stator (Ts, 0) and the initial average temperature of turbine rotor (Tr, 0) are calculated by the disclosed component-level mathematical model under steady state condition;

[0010] Step two, obtaining heat source parameters and flow parameters,

[0011] obtaining the heat source parameters and flow parameters in each time step of the engine according to the engine component-level mathematical model in real time;

[0012] The parameters obtained by the engine component-level mathematical model in real time are as follows:

[0013] Heat source parameters: high-pressure turbine inlet gas temperature T4; turbine stator cold side temperature, i.e. outer duct air temperature T 13 ; turbine rotor cold side temperature, i.e. cooling air temperature T3;

[0014] Flow parameters: high-pressure turbine inlet gas flow W4; outer duct air flow W 13 ; cooling air flow W3';

[0015] Step three, constructing turbine rotor and turbine stator temperature differential equations,

[0016] Turbine stator temperature equation:

[0017]

[0018] Turbine rotor temperature equation:

[0019]

[0020] Further, the construction process of the turbine rotor and turbine stator temperature differential equations includes,

[0021] Firstly, the heat conduction differential equation reveals the internal relationship of continuous temperature field in space and time field, and the mathematical model of heat transfer problem is established depending on the concept of control body; defining a control body as a spatial region whose mass, momentum and energy can pass through its surface, for any control body, the law of conservation of energy is described as:

[0022] All forms of energy entering the control body + energy generated within the control body itself

[0023] = All forms of energy flowing out of the control body + changes in energy stored within the control body.

[0024] Its mathematical expression is:

[0025] Q in +Q generate =Q out +Q change (1-1)

[0026] In the formula: Q in All forms of energy, Q, enter the control body. generate It controls the energy released or absorbed by the body itself, Q out All forms of energy, Q, flow out of the control body change All forms of energy flowing out of the control body, measured in joules; the energy generated within the control body itself is called the internal heat source.

[0027] Regarding the energy balance of the control volume per unit time, we have:

[0028] Φ in +Φ generate =Φ out +Φ change (1-2),

[0029] Where: Φ in The form of energy entering the control body per unit time, Φ generate It refers to the energy released or absorbed by the body within a unit of time. out All forms of energy flowing out of the control volume per unit time, Φ change All forms of energy flowing out of the control volume per unit time;

[0030] For a micro-element control volume, the heat flow rate entering and exiting the control volume through heat conduction is:

[0031]

[0032] In the formula dΦ λ,x ,dΦ λ,y ,dΦ λ,z dΦ represents the heat flowing into the x-section, y-section, and z-section, respectively; λ,x+dx dΦ λ,y+dy dΦ λ,z+dz These represent the heat flowing out of cross sections x, y, and z, respectively; q λ,x q λ,y q λ,zHeat flux density flowing into the microelement control body along the x-axis, y-axis and z-axis directions through heat conduction respectively; Heat flux density flowing out of the microelement control body along the x-axis, y-axis and z-axis directions through heat conduction respectively; the microelement control body is an arbitrary micro parallelepiped taken from the turbine rotor and stator; the x-axis, y-axis and z-axis are the coordinate axes of a global coordinate system, the global coordinate system is that the direction of the engine gas main flow is the x-axis, the vertical direction of the x-axis cross section is the Z-axis, and the horizontal direction is the y-axis; the x cross section is the cross section perpendicular to the x-axis in the microelement control body, the y cross section is the cross section perpendicular to the y-axis in the microelement control body, and the z cross section is the cross section perpendicular to the z-axis in the microelement control body;

[0033] Then the heat absorbed by the microelement body due to heat conduction in unit time is,

[0034]

[0035] Considering that the density and specific heat of the object are approximately constant in general heat transfer problems, the energy increment in the microelement body in a unit time interval is represented as:

[0036]

[0037] In the formula, ρ is the density, c p is the heat capacity;

[0038] The heat generated by the object per unit volume in unit time is denoted as q v Then the heat generated by the internal heat source of the microelement body in a unit time interval is,

[0039] dΦ v = q v dxdydz (1-6),

[0040] According to the energy conservation theorem,

[0041] dΦ λ +dΦ v = dΦ τ (1-7),

[0042] Then the general form of the three-dimensional non-steady-state heat conduction differential equation in the Cartesian coordinate system is,

[0043]

[0044] Further, the present application simplifies the three-dimensional heat conduction differential equation and proposes the following assumptions:

[0045] (1) The heat conduction coefficient λ of the turbine rotor and the turbine stator is assumed to be constant;

[0046] (2) Assume that the internal temperature of each turbine rotor and turbine stator is uniform at all times and independent of spatial coordinates;

[0047] (3) Assume that the density p and heat capacity c of the turbine rotor and turbine stator are constants;

[0048] (4) Assume that there is no heat transfer between the turbine rotor and turbine stator;

[0049] (5) Ignore radiative heat transfer in the compressor components;

[0050] (6) Assume that the surface heat exchange related parameters of the turbine rotor and turbine stator are uniformly distributed;

[0051] According to the assumption that the thermal conductivity λ of the turbine rotor and turbine stator is constant, the three-dimensional unsteady heat conduction differential equation (1-8) in the Cartesian coordinate system is simplified as,

[0052]

[0053] In the formula, a = λ / pc, which is called the thermal diffusion coefficient;

[0054] According to the assumption that the internal temperature of the turbine rotor and turbine stator is uniform at all times, the temperature is independent of the spatial coordinates, which meets the conditions of the lumped parameter method, formula (1-9) is simplified as,

[0055]

[0056] According to the lumped parameter method, the heat source Φ v It is believed that,

[0057] q v V = hA (T f -T) (1-11),

[0058] Where T f is the fluid temperature, V is the volume of the turbine rotor and stator, h is the heat transfer coefficient, and A is the arbitrary cross-sectional area of the turbine rotor and stator perpendicular to the heat flow direction; formula (1-10) is brought into formula (1-11) to obtain,

[0059]

[0060] Formula (1-12) is the simplified differential equation of the transition state heat transfer of the turbine rotor and turbine stator based on the assumption conditions, that is, the heat flow absorbed by the object is balanced with the convective heat transfer heat flow on the surface;

[0061] In the case of relatively accurate estimation of the influence of the transition state turbine rotor and turbine stator temperature on the transition process characteristics, formula (1-12) is transformed into,

[0062]

[0063] The two differential equations of the average temperature T r and T s of the turbine rotor and stator are given below, in which the heat transfer coefficient correction is considered and the real-time is ensured:

[0064]

[0065] In the equations, T s is the average temperature of the turbine stator, T r is the average temperature of the turbine stator, T4 is the gas temperature; T 13 is the temperature of the outer duct air, T3 is the cooling air temperature; τ sT , τ rT are the time constants of the turbine stator and rotor;

[0066] a s1 , a s2 , a r1 , a r1 , B s1 , B s2 , B r1 , B r2 are the heat transfer correction coefficients;

[0067] In the turbine stator differential equation, the heat exchange of the hot gas and the outer duct air with the temperature of T 13 is calculated, while in the turbine rotor differential equation, the heat exchange with the hot gas and the cooling air with the temperature of T3 is calculated; the above equations are solved to obtain the turbine rotor and turbine stator temperatures of the aero-engine in transition state considering the cooling;

[0068] The relationship between the heat transfer coefficient and the engine state when calculating the air and hot gas exchange is considered by the functional relationship of equation (1-16),

[0069] α i = K i (W i ) 0.8 (1-16),

[0070] Therefore,

[0071]

[0072] In which, W4 is the high-pressure turbine inlet gas flow; W 13 is the outer duct air flow; W3' is the air flow for cooling the high-pressure turbine; C s1 , C s2 , C r1 , C r2 are the coefficients;

[0073] The time constant τST and τ rT The value is given as a function of the reduced time.

[0074]

[0075] In the formula: t is time, b p1 b p2 W is a coefficient. 4max This represents the maximum gas flow rate at the high-pressure turbine inlet.

[0076] Step 4: Perform model recognition.

[0077] Model identification of heat transfer coefficient (a) in Equations 1-14 and 1-15 s1 a s2 a r1 a r1 ), time constant (τ) sT ,τ rT The parameter (C) in ) s1 C s2 C r1 C r2 ,bp1,bp2,) and heat transfer coefficient (B s1 B s2 B r1 B r2 Model identification relies on accurate calculations of the unsteady temperature fields of structural components performed by turbine designers.

[0078] Step 5: Numerical solution of the differential equation.

[0079] Discrete solution is performed using the explicit Euler method:

[0080] Selection of time step: The step size is determined based on the time constant, and it must be smaller than the time constants of the rotor and stator to ensure stability;

[0081] Iterative temperature update:

[0082]

[0083] Step 6: Output the temperature results.

[0084] The average turbine rotor temperature T at each time step s and turbine stator average temperature T r As a real-time temperature output.

[0085] The beneficial effects of the present application are: the present application provides an aero-engine transition state turbine rotor and stator temperature calculation method, which introduces a hot side gas and a cold side cooling air double heat source model, more truly reflects the actual working environment of the engine combined with the differentiated heat exchange characteristics of the turbine rotor and stator, establishes an independent differential equation, accurately captures the temperature dynamic response of different components, and is especially suitable for aero-engine scenes with complex cooling structures; the lumped parameter method is used to reasonably simplify the three-dimensional heat conduction equation, the temperature distribution is simplified to a uniform field under the premise of ensuring the engineering precision of the Bi number of small components, the calculation dimension is significantly reduced, combined with the explicit Euler method numerical integration method, the differential equation is quickly dispersed and solved, the real-time requirement of the airborne model for transition state calculation is met, and the numerical stability is ensured by self-adaptive adjustment of the time step. The present application can accurately evaluate the dynamic heat exchange effect of the metal component and the airflow under the transition state by outputting the turbine rotor / stator temperature in real time, and supports the design of engine control law and stability optimization. BRIEF DESCRIPTION OF DRAWINGS

[0086] Figure 1 is a flowchart of the present application;

[0087] Figure 2 is a microelement heat conduction analysis diagram when the present application is implemented;

[0088] Figure 3 is a schematic diagram of the transition state heat exchange process of the component when the present application is implemented;

[0089] Figure 4 is a schematic diagram of the component-level model of the aero-engine when the present application is implemented. DETAILED DESCRIPTION

[0090] The principles and characteristics of the present application are described below in conjunction with the drawings, and the examples are only used to explain the present application and are not used to limit the scope of the present application.

[0091] In order to achieve the above-mentioned purpose, the present application provides the following specific embodiments: as shown in Figure 1 The aero-engine transition state turbine rotor and stator temperature calculation method, characterized by comprising the following steps:

[0092] Step one, determine the initial condition,

[0093] The initial average temperature of the turbine stator (Ts, 0) and the initial average temperature of the turbine rotor (Tr, 0) before the start of the engine transition state process are obtained;

[0094] Further, the turbine stator initial average temperature (Ts, 0) and the turbine rotor initial average temperature (Tr, 0) are calculated by the disclosed component-level mathematical model (such as Gasturb) under steady state working condition;

[0095] Step two, obtain heat source parameters and flow parameters,

[0096] Obtaining heat source parameters and flow parameters in each time step of the engine is obtained in real time according to the engine component level mathematical model;

[0097] The parameters obtained by the engine component level mathematical model in real time are as follows:

[0098] Heat source parameters: high pressure turbine inlet gas temperature T4; turbine stator cold side temperature, i.e. outer duct air temperature T 13 ; Turbine rotor cold side temperature, i.e. cooling air temperature T3;

[0099] Flow parameters: high pressure turbine inlet gas flow W4; outer duct air flow W 13 ; Cooling air flow W3';

[0100] Step three, constructing turbine rotor and turbine stator temperature differential equation,

[0101] Turbine stator temperature equation:

[0102]

[0103] Turbine rotor temperature equation:

[0104]

[0105] Further, the construction process of the turbine rotor and turbine stator temperature differential equation includes,

[0106] Firstly, the heat conduction differential equation reveals the internal relationship of continuous temperature field in space and time field, and the mathematical model of heat transfer problem is established depending on the concept of control body; defining control body is a spatial region whose mass, momentum and energy can pass through its surface, for any control body, the law of conservation of energy is described as:

[0107] All forms of energy entering the control body + energy generated in the control body

[0108] = all forms of energy flowing out of the control body + change of energy stored in the control body

[0109] Its mathematical expression is:

[0110] Q in +Q generate =Q out +Q change (1-1),

[0111] In the formula: Q in All forms of energy entering the control body, Q generate is the energy released or absorbed in the control body, Qout All forms of energy flowing out of the control volume, Q change All forms of energy flowing out of the control volume, in joules, the term generated internally by the control volume is called the internal heat source; in joules, the term generated internally by the control volume is called the internal heat source;

[0112] For the energy balance of the control volume per unit time, we have,

[0113] Φ in + Φ generate = Φ out + Φ change (1-2),

[0114] In the formula: Φ in All forms of energy entering the control volume per unit time, Φ generate is the energy released or absorbed by the control volume per unit time, Φ out All forms of energy flowing out of the control volume per unit time, Φ change All forms of energy flowing out of the control volume per unit time;

[0115] For the micro-element control volume, as shown in Figure 2 Heat transfer analysis is carried out on the micro-element body, and when the temperature differential equation of the turbine rotor and stator is constructed, the heat flow into and out of the control volume through heat conduction is,

[0116]

[0117] In the formula dΦ λ,x , dΦ λ,y , dΦ λ,z , respectively, the heat flowing into the x-section, y-section, and z-section; dΦ λ,x+dx , dΦ λ,y+dy , dΦ λ,z+dz respectively, the heat flowing out of the x-section, y-section, and z-section; q λ,x , q λ,y , q λ,z respectively, the heat flow density along the x-axis, y-axis, and z-axis direction into the micro-element control volume through heat conduction; respectively, the heat flow density along the x-axis, y-axis, and z-axis direction out of the micro-element control volume through heat conduction; the micro-element control volume is an arbitrary small parallelepiped taken from the turbine rotor and stator; the x-axis, y-axis, and z-axis are the coordinate axes of the global coordinate system, which takes the direction of the engine gas main flow as the x-axis, the vertical direction of the x-axis cross section as the Z-axis, and the horizontal direction as the y-axis; the x-section is the section perpendicular to the x-axis in the micro-element control volume, the y-section is the section perpendicular to the y-axis in the micro-element control volume, and the z-section is the section perpendicular to the z-axis in the micro-element control volume;

[0118] The heat absorbed by the micro-element due to heat conduction in unit time is,

[0119]

[0120] Considering that the density and specific heat of the object are approximately constant in heat transfer problems, the increment of the energy in the micro-element in unit time interval is expressed as:

[0121]

[0122] wherein ρ is the density, c p is the heat capacity;

[0123] The heat generated by the object in unit volume in unit time is denoted as q v The heat generated by the internal heat source of the micro-element in unit time interval is,

[0124] dΦ v = q v dxdydz(1-6),

[0125] According to the energy conservation theorem, it is obtained that,

[0126] dΦ λ +dΦ v = dΦ τ (1-7),

[0127] The general form of the three-dimensional unsteady heat conduction differential equation in the Cartesian coordinate system is,

[0128]

[0129] Further, the present application simplifies the three-dimensional heat conduction differential equation and proposes the following assumptions:

[0130] (1) The heat conduction coefficient λ of the turbine rotor and the turbine stator is assumed to be constant;

[0131] (2) The internal temperature of each turbine rotor and turbine stator is assumed to be uniform at all times, i.e., the Biot number Bi is small and is independent of the spatial coordinates;

[0132] (3) The density ρ and the heat capacity c of the turbine rotor and the turbine stator are assumed to be constant;

[0133] (4) There is no heat transfer between the turbine rotor and the turbine stator;

[0134] (5) The radiation heat transfer of the compressor components is ignored;

[0135] (6) The surface heat exchange related (convective heat transfer coefficient) parameters of the turbine rotor and the turbine stator are assumed to be uniformly distributed;

[0136] According to the assumption that the heat conductivity coefficient λ of the turbine rotor and the turbine stator is constant, the three-dimensional unsteady heat conduction differential equation (1-8) in the Cartesian coordinate system is simplified as,

[0137]

[0138] In the formula, a = λ / ρc, which is called the thermal diffusion coefficient;

[0139] Generally, in engineering applications, when Bi < 0.1, it can be approximately considered that the internal thermal resistance of the object is negligible compared with the surface convective heat transfer resistance; such a heat conduction body in which any instantaneous internal temperature gradient is small enough to be neglected is called a lumped capacitance body, and such an analysis method that ignores the internal thermal resistance of the object is called the lumped capacitance method;

[0140] According to the assumption that the internal temperature of the turbine rotor and the turbine stator is uniform at any time, the temperature is independent of the spatial coordinate, and the lumped parameter method condition is met, formula (1-9) is simplified as,

[0141]

[0142] According to the lumped parameter method, the heat source Φ v It is considered that,

[0143] q v V = hA (T f -T) (1-11),

[0144] Wherein, T f is the fluid temperature, V is the volume of the turbine rotor and stator, h is the heat transfer coefficient, and A is the arbitrary cross-sectional area of the turbine rotor and stator perpendicular to the heat flow direction; formula (1-10) is brought into formula (1-11) to obtain,

[0145]

[0146] Formula (1-12) is the simplified differential equation of the turbine rotor and the turbine stator in the transient state heat exchange based on the assumption condition, that is, the heat flow absorbed by the object is balanced with the convective heat flow on the surface;

[0147] The transient state heat exchange process of the engine turbine rotor and stator is shown in Figure 3 Taking the acceleration process as an example: the hot side gas temperature Tg and the cold side gas temperature Tc of the engine turbine rotor and stator are increased to Tg and Tc in the time interval Δt with the improvement of the engine state, the hot side wall surface temperature Tw1 and the cold side wall surface temperature Tw2 of the turbine rotor and stator are increased to Tw1 and Tw2 in the time interval Δt with the improvement of the engine state, and the metal average temperature determined by the convective heat exchange on both sides of the turbine rotor and stator is increased to Tw - in the time interval Δt with the improvement of the engine state.+ where h1 and h2 are the heat transfer coefficients of the hot side and the cold side, and p, c, V, λ are the physical properties of the turbine rotor and stator.

[0148] After the influence of the turbine rotor and stator temperatures on the transient process characteristics is estimated relatively accurately, the model is simplified, and equation (1-12) is transformed into

[0149]

[0150] Two differential equations containing the average temperatures T r and T s of the turbine rotor and stator are given in the case of considering turbine cooling and ensuring real-time and using heat transfer coefficient correction:

[0151]

[0152] In the equations, T s is the average temperature of the turbine stator, T r is the average temperature of the turbine stator, T4 is the gas temperature; T 13 is the temperature of the outer air duct air, T3 is the cooling air temperature; τ sT , τ rT are the time constants of the turbine stator and rotor;

[0153] a s1 , a s2 , a r1 , a r1 , B s1 , B s2 , B r1 , B r2 are heat transfer correction coefficients;

[0154] In the turbine stator differential equation, the heat exchange of the hot gas and the outer air duct air with a temperature of T 13 is calculated, while in the turbine rotor differential equation, the heat exchange with the hot gas and the cooling air with a temperature of T3 is calculated; solving the above equations gives the turbine rotor and stator temperatures of the aero-engine in the transient state considering cooling.

[0155] The relationship between the heat transfer coefficient and the engine state when calculating the heat exchange between the air and the hot gas is considered through the functional relationship of equation (1-16),

[0156] α i = K i (W i ) 0.8 (1-16),

[0157] Therefore,

[0158]

[0159] Where W4 is the inlet gas flow rate of the high-pressure turbine; W 13 W3' is the airflow rate of the bypass duct; W3' is the airflow rate used to cool the high-pressure turbine; C s1 C s2 C r1 C r2 For coefficients;

[0160] Time constant τ ST and τ rT The value of is given as a function of the reduced time.

[0161]

[0162] In the formula: t is time, b p1 b p2 W is a coefficient. 4max This represents the maximum gas flow rate at the high-pressure turbine inlet.

[0163] Step 4: Perform model recognition.

[0164] Model identification of heat transfer coefficient (a) in Equations 1-14 and 1-15 s1 a s2 a r1 a r1 ), time constant (τ) sT ,τ rT The parameter (C) in ) s1 C s2 C r1 C r2 ,bp1,bp2,) and heat transfer coefficient (B s1 B s2 B r1 B r2 Model identification relies on accurate calculations of the unsteady temperature fields of structural components performed by turbine designers.

[0165] Step 5: Numerical solution of the differential equation.

[0166] Discrete solution is performed using the explicit Euler method:

[0167] Selection of time step: The step size is determined based on the time constant, and it must be smaller than the time constants of the rotor and stator to ensure stability;

[0168] Iterative temperature update:

[0169]

[0170] Step 6: Output the temperature results.

[0171] The turbine rotor average temperature T s and turbine stator average temperature T r as a real-time temperature output.

[0172] As Figure 4 is an engine schematic diagram, including engine components and interface parameters. The component-level model is established from the inlet duct to the tail nozzle under the condition that the characteristics of each component of the engine are known and the engine regulation law is given. The gas flow equation, the thermodynamic equation and the engine common working equation are established one by one, the common working equation is composed into a nonlinear equation system and is solved simultaneously, the common working point of the engine is determined, and the aerodynamic and thermodynamic parameters of each section of the engine are calculated. The method calculates the initial temperature and heat source parameters of the turbine rotor and stator through the component-level model: high-pressure turbine inlet gas temperature T4; turbine stator cold side temperature, i.e. outer duct air temperature T 13 ; turbine rotor cold side temperature, i.e. cooling air temperature T3; flow parameters: high-pressure turbine inlet gas flow W4; outer duct air flow W 13 ; cooling air flow W3'.

[0173] Compared with the prior art, the technical scheme of the present application has the advantages that

[0174] (1) The calculation accuracy and engineering applicability are improved. The limitations of the traditional single heat source model are overcome by introducing a double heat source model (hot side gas and cold side cooling air), and the actual working environment of the engine is more truly reflected. Independent differential equations are established in combination with the differentiated heat exchange characteristics of the turbine rotor and stator, and the temperature dynamic response of the turbine rotor and stator is accurately captured, which is especially suitable for the aviation engine environment with complex cooling structure.

[0175] (2) High-efficiency real-time calculation capability. The three-dimensional heat conduction equation is reasonably simplified by using the lumped parameter method, the temperature distribution is simplified to a uniform field under the premise of ensuring the engineering accuracy of the turbine rotor and stator with small Bi number, and the calculation dimension is significantly reduced. In combination with the explicit Euler method numerical integration method, the differential equation is quickly discretely solved, the real-time requirement of the airborne model for transient state calculation is met, and the time step is adaptively adjusted to ensure numerical stability.

[0176] (3) Optimization of thermodynamic and aerodynamic performance evaluation. The dynamic heat exchange effect of the metal turbine rotor and stator and the airflow under the transient state is accurately evaluated by outputting the turbine rotor / stator temperature in real time, and the influence of the dynamic heat exchange effect on the engine cycle parameters (such as power and efficiency) is quantified. At the same time, the key temperature input is provided for the change of the tip clearance, the prediction accuracy of the component characteristics (flow, efficiency and stability boundary) is indirectly improved, and the engine control law design and stability optimization are supported.

[0177] (4) Model simplification and engineering usability, based on heat balance equation and experimental data to calibrate model parameters, avoid the need for complex structure heat transfer fine modeling. Modular design, seamless integration with existing component-level mathematical model, only need to obtain real-time gas temperature, cooling air flow and other conventional parameters, reduce the engineering implementation threshold, suitable for rapid simulation and control system development of multi-state engine.

[0178] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for calculating the transition state turbine rotor and stator temperatures of an aero-engine, characterized in that, Includes the following steps: Step 1: Determine the initial conditions. Obtain the initial average temperature of the turbine stator (Ts, 0) and the initial average temperature of the turbine rotor (Tr, 0) before the start of the engine transient process; Step 2: Obtain heat source parameters and flow rate parameters. The heat source parameters and flow parameters of the engine are obtained in real time based on the mathematical model of the engine components. The parameters obtained in real time from the engine component-level mathematical model are as follows: Heat source parameters: High-pressure turbine inlet gas temperature T4; Turbine stator cold side temperature, i.e., bypass air temperature T. 13 The turbine rotor cold side temperature is the cooling air temperature T3. Flow parameters: High-pressure turbine inlet gas flow rate W4; Bypass duct air flow rate W 13 Cooling airflow W3'; Step 3: Construct the differential equations for the turbine rotor and turbine stator temperatures. Turbine stator temperature equation: Turbine rotor temperature equation: Step 4: Perform model recognition. The model identifies the heat transfer coefficient (a) in the differential equations of turbine rotor and turbine stator temperatures. s1 a s2 a r1 a r1 ), time constant (τ) sT ,τ rT The parameter (C) in ) s1 C s2 C r1 C r2 ,bp1,bp2,) and heat transfer coefficient (B s1 B s2 B r1 B r2 Model identification relies on accurate calculations of the unsteady temperature fields of structural components performed by turbine designers. Step 5: Numerical solution of the differential equation. Discrete solution is performed using the explicit Euler method: Selection of time step: The step size is determined based on the time constant, and it must be smaller than the time constants of the rotor and stator to ensure stability; Iterative temperature update: Step 6: Output the temperature results. The average turbine rotor temperature T at each time step s and turbine stator average temperature T r As a real-time temperature output.

2. The method for calculating the transient temperature of the turbine rotor and stator of an aero-engine as described in claim 1, characterized in that: In step one, the initial average temperature of the turbine stator (Ts, 0) and the initial average temperature of the turbine rotor (Tr, 0) are calculated under steady-state conditions using a publicly available component-level mathematical model.

3. The method for calculating the transient turbine rotor and stator temperatures of an aero-engine as described in claim 1, characterized in that: The process of constructing the differential temperature equations for the turbine rotor and turbine stator in step three includes, First, the heat conduction differential equation reveals the intrinsic connection between the continuous temperature field in the spatial and temporal domains. The mathematical model of the heat transfer problem relies on the concept of a control volume. A control volume is defined as a spatial region on its surface through which mass, momentum, and energy can pass. For any control volume, the law of conservation of energy is described as follows: All forms of energy entering the control body + energy generated within the control body itself = All forms of energy flowing out of the control body + changes in energy stored within the control body. Its mathematical expression is: Q in +Q generate =Q out +Q change (1-1), In the formula: Q in All forms of energy, Q, enter the control body. generate It controls the energy released or absorbed by the body itself, Q out All forms of energy, Q, flow out of the control body change All forms of energy flowing out of the control body, measured in joules; the energy generated within the control body itself is called the internal heat source. The unit is joule, and the energy that controls the body's own energy production is called the internal heat source; Regarding the energy balance of the control volume per unit time, we have: F in +F generate =Φ out +F change (1-2), Where: Φ in The form of energy entering the control body per unit time, Φ generate It refers to the energy released or absorbed by the body within a unit of time. out All forms of energy flowing out of the control volume per unit time, Φ change All forms of energy flowing out of the control volume per unit time; For a micro-element control volume, the heat flow rate entering and exiting the control volume through heat conduction is: In the formula dΦ λ,x ,dΦ λ,y ,dΦ λ,z dΦ represents the heat flowing into the x-section, y-section, and z-section, respectively; λ,x+dx ,dΦ λ,y+dy ,dΦ λ,z+dz These represent the heat flowing out of cross sections x, y, and z, respectively; q λ,x q λ,y q λ,z These represent the heat flux densities flowing into the micro-element control volume along the x-axis, y-axis, and z-axis directions through thermal conduction, respectively. These represent the heat flux densities flowing out of the micro-element control volume along the x-axis, y-axis, and z-axis directions, respectively, through thermal conduction. The amount of heat absorbed by the infinitesimal element per unit time due to thermal conduction is: Considering that the density and specific heat of an object are approximately constant in general heat transfer problems, the increase in the internal energy of the infinitesimal element per unit time interval can be expressed as: In the formula, ρ is density, and c p Heat capacity; The amount of heat generated per unit volume of an object per unit time is denoted as q. v Then, the heat generated by the internal heat source of the infinitesimal element within a unit time interval is, dΦ v =q v dxdydz(1-6), According to the law of conservation of energy, dΦ λ +dΦ v =dΦ τ (1-7), The general form of the three-dimensional unsteady heat conduction differential equation in Cartesian coordinates is:

4. The method for calculating the transition state turbine rotor and stator temperature of an aero-engine as described in claim 3, characterized in that: The three-dimensional unsteady heat conduction differential equation is simplified, and the following assumptions are proposed: (1) Assume that the thermal conductivity λ of the turbine rotor and turbine stator is constant; (2) Assume that the internal temperature of each turbine rotor and turbine stator is uniform at all times and is independent of spatial coordinates; (3) Assume that the turbine rotor and turbine stator density ρ and heat capacity c are constants; (4) Assume there is no heat transfer between the turbine rotor and the turbine stator; (5) Radiative heat transfer is ignored in compressor components; (6) Assume that the heat transfer parameters on the turbine rotor and turbine stator surfaces are uniformly distributed; Based on the assumption that the thermal conductivity λ of the turbine rotor and turbine stator is constant, the three-dimensional unsteady heat conduction differential equation (1-8) in Cartesian coordinates simplifies to: In the formula, a = λ / ρc, which is called the thermal diffusivity; Based on the assumption that the internal temperature of the turbine rotor and turbine stator is uniform at all times, and that the temperature is independent of spatial coordinates, satisfying the conditions of the lumped parameter method, equation (1-9) simplifies to: According to the lumped parameter method, the heat source Φ v think, q v V=hA(T f -T)(1-11), Among them, T f Let V be the fluid temperature, V be the volume of the turbine rotor and stator, h be the heat transfer coefficient, and A be any cross-sectional area of ​​the turbine rotor and stator perpendicular to the heat flow direction; substituting equation (1-10) into equation (1-11) yields... Equation (1-12) is the simplified heat transfer differential equation for the turbine rotor and turbine stator in the transition state based on the assumptions, that is, the heat flow absorbed by the object is in balance with the convective heat transfer flow on the surface. Having relatively accurately estimated the influence of the transient turbine rotor and turbine stator temperatures on the transient process characteristics, the model is simplified, and equation (1-12) is transformed into: The average temperature T, including the turbine rotor and stator, is given after considering turbine cooling, ensuring real-time performance, and applying heat transfer coefficient correction. r and T s Two differential equations: In the formula, T s T is the average temperature of the turbine stator. r T is the average temperature of the turbine stator, and T4 is the combustion gas temperature; T 13 T1 is the outside bypass air temperature, T2 is the cooling air temperature; τ sT ,τ rT a is the time constant of the turbine stator and rotor; s1 a s2 a r1 a r1 B s1 B s2 B r1 B r2 , is the heat transfer correction factor; The temperature of the hot combustion gas and the bypass duct is calculated as T in the turbine stator differential equation. 13 The heat exchange with the air is calculated in the differential equation of the turbine rotor, while the heat exchange with the hot combustion gas and the cooling air with temperature T3 is calculated in the differential equation of the turbine rotor. Solving the above equation yields the transient turbine rotor and turbine stator temperatures of the aero-engine considering cooling. The relationship between the heat transfer coefficient and engine conditions during air-fuel exchange is considered using the functional relationship of equation (1-16). a i =K i (W i ) 0.8 (1-16), Therefore, there is. Where W4 is the inlet gas flow rate of the high-pressure turbine; W 13 W3' is the airflow rate of the bypass duct; W3' is the airflow rate used to cool the high-pressure turbine; C s1 C s2 C r1 C r2 For coefficients; Time constant τ ST and τ rT The value is given as a function of the reduced time. In the formula: t is time, b p1 b p2 W is a coefficient. 4max This represents the maximum gas flow rate at the inlet of the high-pressure turbine.

5. A method for calculating the transition state turbine rotor and stator temperature of an aero-engine as described in any one of claims 1-4, characterized in that: The aforementioned micro-element control body is an arbitrary tiny parallelepiped extracted from the turbine rotor and stator; the aforementioned x-axis, y-axis, and z-axis are the coordinate axes of the global coordinate system, with the mainstream direction of engine gas as the x-axis, the vertical direction of the cross-section of the x-axis as the z-axis, and the horizontal direction as the y-axis; the aforementioned x-section is the cross-section of the micro-element control body perpendicular to the x-axis, the y-section is the cross-section of the micro-element control body perpendicular to the y-axis, and the z-section is the cross-section of the micro-element control body perpendicular to the z-axis.

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