An Energy Analysis Method for Aero-engines Based on the Thermodynamic Principles of Variable Mass Systems

Abstract

This invention discloses an energy analysis method for aero-engines based on the thermodynamic principles of variable mass systems, specifically including: (1) dividing the aero-engine into several components, taking it as the research object; (2) constructing an aero-thermodynamic model for each component; (3) constructing a set of control equations for the actual operation of the aero-engine, obtaining the operating parameters of the aero-engine during actual operation by solving the set of control equations, substituting the engine operating parameters into the aero-thermodynamic model of each component, and obtaining the inlet and outlet aero-thermodynamic parameter values ​​of each component; (4) calculating the total energy input to the engine, the energy dissipated by the engine, the energy stored by the engine, the available energy of the engine, and the energy lost by the engine during the actual operation of the aero-engine based on the inlet and outlet aero-thermodynamic parameter values ​​of each component. This invention can accurately obtain the energy transfer and conversion relationship during the operation of the aero-engine.

Description

Technical Field

[0001] This invention relates to the technical field of aero-engine energy management, specifically to an aero-engine energy analysis method based on the thermodynamic principles of variable mass systems. Background Technology

[0002] With the development of modern flight technology, future aircraft will place increasingly higher demands on engine performance. The next generation of aero engines requires high thrust-to-weight ratio, low fuel consumption, and high reliability. Increasing the engine's cycle pressure ratio, raising the turbine inlet gas temperature, and increasing shaft transmission power are the main measures to improve aero engine performance parameters, but this will introduce new energy management challenges. Since domestic research on aero engine energy management is still in its early stages, extensive testing is required during the development process, which increases research and development costs significantly. Therefore, establishing a reliable aero engine energy management analysis method is essential for conducting cost-effective research on engine energy management technology.

[0003] Current research on aero-engine energy management analysis methods is mostly based on the flow balance assumption. For example, the literature titled "Research on Modeling and Control Planning of Turbofan Engines" or the patent application with patent number "CN201910459624.2" are both based on the flow balance perspective, assuming that the flow rates at the inlet and outlet of each component are equal, neglecting the storage and release of mass within each component during actual engine operation. Therefore, models based on the flow balance assumption are difficult to accurately simulate the flow of matter and the transmission and conversion of energy within the aero-engine during actual operation. Therefore, it is necessary to establish a precise aero-engine energy acquisition method during engine operation, which will facilitate the management and analysis of energy throughout the entire aircraft operation process, revealing the energy transport and conversion patterns during the entire aircraft operation. This is of great significance for accurately predicting the heat transfer, collection, storage, comprehensive utilization, and dissipation mechanisms between aero-engine components. Summary of the Invention

[0004] Purpose of the invention: To address the above shortcomings, this invention provides an energy analysis method for aero-engines based on the thermodynamic principles of variable mass systems. It considers the storage and release of mass within each component of the engine during actual operation, and obtains the energy during engine operation more accurately, thereby enabling the analysis of energy transport and conversion laws during aero-engine operation.

[0005] Technical Solution: To solve the above problems, this invention discloses an energy analysis method for aero-engines based on the thermodynamic principles of variable mass systems, specifically including the following steps:

[0006] (1) Taking an actual twin-shaft turbofan aero-engine as an example, and combining the actual operating characteristics of the aero-engine, the aero-engine is divided into several components, namely, the air intake, fan, compressor, combustion chamber, high-pressure turbine, low-pressure turbine, outer bypass duct, mixing chamber, afterburner, and tail nozzle.

[0007] (2) Considering the changes in internal mass of each component caused by the compressibility of gas inside the aero-engine, an aero-thermodynamic model is constructed for each component; the aero-thermodynamic model includes the mass conservation equation, energy conservation equation and aero-thermodynamic parameter equation for each component.

[0008] (3) Based on the energy coupling relationship of each component of the aero-engine, construct a set of control equations for the actual operation of the aero-engine. The set of control equations includes flow balance equations and rotor dynamics equations between each component. Solve the set of control equations to obtain the operating parameters of the aero-engine during actual operation. Substitute the engine operating parameters into the aero-thermodynamic model of each component to obtain the inlet and outlet aero-thermodynamic parameter values ​​of each component.

[0009] (4) The total energy input to the engine, the energy dissipated by the engine, the energy stored by the engine, the available energy of the engine, and the energy lost by the engine during the actual operation of the aero-engine are calculated based on the aero-thermal parameters of each component.

[0010] Furthermore, (2.1) the basic assumptions for establishing the aerodynamic thermodynamic model:

[0011] (2.1.1) Ignore the effect of combustion delay;

[0012] (2.1.2) Ignore the effects of humidity and Reynolds number on the characteristics of each component;

[0013] (2.1.3) The influence of atmospheric humidity on engine performance parameters is not considered;

[0014] (2.1.4) The flow of gas, fuel and lubricating oil in aero engines shall be treated as quasi-one-dimensional flow;

[0015] (2.2) The specific aero-thermodynamic model of the air intake is as follows:

[0016] Inlet aerodynamic and thermodynamic parameter equations:

[0017] [T s0 ,P s0 ,T t1 ,P t1 ,T t2 ,P t2 ] = f1[H0,Ma0]

[0018] In the formula, T s0For incoming static temperature; P s0 For incoming static pressure; T t1 P is the total temperature of the airflow at the intake duct. t1 T is the total pressure of the airflow at the intake duct; t2 P is the total airflow temperature at the intake and outlet. t2 H0 is the total pressure of the airflow at the intake outlet; Ma0 is the aircraft's flight altitude; Ma0 is the Mach number; f1() is the intake characteristic curve;

[0019] Intake duct mass conservation equation and energy conservation equation:

[0020] W a1 -W a2 =0

[0021]

[0022] In the formula, W a1 Airflow rate at the intake duct; W a2 The airflow rate at the intake outlet; The total specific enthalpy at the intake of the air intake; The total specific enthalpy at the intake outlet;

[0023] (2.3) The aerodynamic thermodynamic model of the fan is as follows:

[0024] Fan aero-thermodynamic parameter equations:

[0025] [T t21 ,P t21 W a2 ]=f2[T t2 ,P t2 ,π F ,n L ]

[0026] In the formula, T t21 Total temperature at the fan outlet; P t21 Total pressure at the fan outlet; W a2 π represents the flow rate at the fan inlet. F n is the fan pressure ratio; L f2() represents the low-pressure shaft speed; f2() is the fan characteristic curve.

[0027] Fan mass conservation equation and energy conservation equation:

[0028]

[0029]

[0030] In the formula, W a21 m is the fan outlet flow rate. CV,F For the mass inside the fan; The total specific enthalpy at the fan outlet; The total specific enthalpy of the fan components;

[0031] (2.4) The specific aerodynamic thermodynamic model of the compressor is as follows:

[0032] Compressor aerodynamic and thermodynamic parameter equations:

[0033] [T t3 ,P t3 W a22 ]==f3[T t21 ,P t21 ,π C ,n H ]

[0034] In the formula, T t3 The total temperature at the compressor outlet; p t3 W is the total pressure at the compressor outlet. a22 π is the compressor inlet flow rate; C n is the pressure ratio of the press; H f3 is the high-pressure shaft speed; f3() is the compressor characteristic curve;

[0035] The mass conservation equation and energy conservation equation for the compressor are:

[0036]

[0037]

[0038] In the formula, W a22 N is the flow rate at the compressor inlet. C W is the compressor power. a3 The flow rate at the compressor outlet; m CV,C The mass inside the compressor; The total specific enthalpy of the compressor; The total specific enthalpy at the compressor outlet;

[0039] (2.5) The specific aerodynamic thermodynamic model of the combustion chamber is as follows:

[0040] Combustion chamber aero-thermodynamic parameter equations:

[0041] [P t4 ]=f4[P t3 W f ]

[0042] In the formula, P t4 W is the total pressure at the combustion chamber outlet. f f4() is the main fuel flow rate; f4() is the combustion chamber characteristic curve.

[0043] The mass conservation equation and energy conservation equation for the combustion chamber are as follows:

[0044]

[0045]

[0046] In the formula, W g4 airflow rate in the combustion chamber; m CV,combustor H represents the internal mass of the combustion chamber. μ For fuel with low calorific value; η b For the efficiency of the combustion chamber; The total specific enthalpy of the combustion chamber;

[0047] (2.6) The specific aerodynamic thermodynamic model of the high-pressure turbine is as follows:

[0048] High-pressure turbine aero-thermodynamic parameter equations:

[0049] [T t44 ,P t44 W g41 ]==f5[T t4 ,P t4 ,π HT ,n H ]

[0050] In the formula, T t4 T is the total temperature at the combustion chamber outlet. t44 P represents the total temperature at the high-pressure turbine outlet. t44 W is the total pressure at the turbine outlet. g41 π represents the flow rate at the high-pressure turbine inlet. HT The pressure drop ratio of the high-pressure turbine; n H f5() represents the rotational speed of the high-pressure turbine; f5() represents the characteristic curve of the high-pressure turbine.

[0051] The mass conservation equation and energy conservation equation for the high-pressure turbine are as follows:

[0052]

[0053]

[0054] In the formula, W g41 W is the flow rate at the high-pressure turbine inlet. g44 The flow rate at the high-pressure turbine outlet; m CV,HT The mass inside the high-pressure turbine; The total specific enthalpy at the high-pressure turbine inlet; N is the total specific enthalpy at the high-pressure turbine outlet. HT The power of the high-pressure turbine; This refers to the total specific enthalpy of the high-pressure turbine.

[0055] (2.7) The specific aero-thermodynamic model of the low-pressure turbine is as follows:

[0056] Low-pressure turbine aero-thermodynamic parameter equations:

[0057] [T t5 ,P t5 W g45 ]==f6[T t44 ,P t44 ,π LT ,n L ]

[0058] In the formula, T t5 P is the total temperature at the low-pressure turbine outlet. t5 W is the total pressure at the low-pressure turbine outlet. g45 The flow rate at the low-pressure turbine inlet; π LT The pressure drop ratio of the low-pressure turbine; n L f6() represents the rotational speed of the low-pressure turbine; f6() represents the characteristic curve of the low-pressure turbine.

[0059] The mass conservation equations and energy conservation equations for the low-pressure turbine are as follows:

[0060]

[0061]

[0062] In the formula, W g45 The flow rate at the low-pressure turbine inlet; W g5 The flow rate at the low-pressure turbine outlet; m CV,LT The mass inside the low-pressure turbine; The total specific enthalpy of the low-pressure turbine inlet; N is the total specific enthalpy at the low-pressure turbine outlet. LT The power of the low-pressure turbine; The total specific enthalpy of the low-pressure turbine;

[0063] (2.8) The specific aero-thermodynamic model of the outer bypass duct is as follows:

[0064] External bypass duct aero-thermodynamic parameter equations:

[0065] [T t16 ,P t16 ]==f7[T t13 ,P t13 ]

[0066] In the formula, T t16 P is the total temperature at the outlet of the duct. t16 T is the total pressure at the outlet of the bypass duct; t16 The total temperature at the outlet of the duct; T t13 f7() represents the total temperature at the inlet of the bypass duct; f7() represents the characteristic curve of the bypass duct.

[0067] The mass conservation equations and energy conservation equations for the bypass duct are as follows:

[0068]

[0069]

[0070] In the formula, W a13 The flow rate at the inlet of the bypass duct; W a16 The flow rate at the outlet of the duct; m CV,bypass For the internal mass of the outer bypass duct; The total specific enthalpy of the bypass duct inlet; The total specific enthalpy at the outlet of the bypass duct;

[0071] (2.9) The specific aerodynamic thermodynamic model of the mixing chamber is as follows:

[0072] The aero-thermodynamic parameter equations for the mixing chamber are as follows:

[0073] [T t6 ,P t6 ]==f8[T t16 ,P t16 W a16 ,T t5 ,P t5 W g5 ]

[0074] In the formula, T t6 P is the total temperature at the outlet of the mixing chamber. t6 f8 is the total pressure at the outlet of the mixing chamber; f8() is the characteristic curve of the mixing chamber;

[0075] The mass conservation equations and energy conservation equations for the mixing chamber are as follows:

[0076] W a16 +W g5 -W g6 =0

[0077]

[0078] In the formula, W g6 h6 is the flow rate at the mixing chamber outlet. * The total specific enthalpy at the outlet of the mixing chamber;

[0079] (2.10) The aerodynamic thermodynamic model of the afterburner is as follows:

[0080] Afterburner aerodynamic and thermodynamic parameter equations:

[0081] [P t7 ]=f9[P t6 W f,ab ]

[0082] In the formula, P t7 W is the total pressure at the outlet of the afterburner. f,ab f9() represents the afterburner fuel supply; f9() represents the characteristic curve of the afterburner combustion chamber.

[0083] The mass conservation equations and energy conservation equations for an afterburner are:

[0084]

[0085]

[0086] In the formula, W g7 The flow rate at the outlet of the afterburner; m CV,ab η is the mass inside the afterburner chamber. ab For the efficiency of the afterburner; The total specific enthalpy at the outlet of the afterburner; The total specific enthalpy of the afterburner; H μ It is a fuel with a low calorific value;

[0087] (2.11) The aerodynamic-thermodynamic model of the tail nozzle is as follows:

[0088] Equations for the aerodynamic and thermodynamic parameters of the tailpipe:

[0089] [T t9 ,P t9 W g9 ] = f 10 [T t7 ,P t7 ]

[0090] In the formula, T t7 T is the total airflow temperature at the nozzle inlet; t9 P is the total airflow temperature at the nozzle exit. t9 P is the total pressure of the airflow at the tailpipe exit. t7 W is the total airflow pressure at the nozzle inlet. g9 f is the exhaust flow rate at the tailpipe outlet. 10 () represents the tail nozzle characteristic curve;

[0091] The mass conservation equation and energy conservation equation for the tailpipe are as follows:

[0092] W g7 -W g9 =0

[0093]

[0094] In the formula, This is the total specific enthalpy at the tail nozzle exit.

[0095] Furthermore, the steady-state process dynamic equations for the high and low pressure shaft rotors are as follows:

[0096] η H N HT -|N C |=0

[0097] η L N LT -|N F |=0

[0098] Dynamic process high and low pressure shaft rotor dynamic equations:

[0099]

[0100]

[0101] The balance equation between the fan outlet flow rate and the inlet flow rates of the compressor and bypass:

[0102] W a21 -W a22 -W a13 =0

[0103] The balance equation between the high-pressure turbine inlet flow rate and the combustion chamber outlet flow rate is as follows:

[0104] W g41 -W g4 =0

[0105] The balance equation between the low-pressure turbine inlet flow rate and the high-pressure turbine outlet flow rate is as follows:

[0106] W g45 -W g44 =0

[0107] The balance equation between the exhaust nozzle outlet flow rate and the afterburner outlet flow rate is as follows:

[0108] W g9 -W g7 =0

[0109] Furthermore, the solution of the control equations in step (3) includes: setting the aircraft's flight altitude, Mach number, and combustion chamber fuel supply, and obtaining the independent variables of the control equations, namely the operating parameters of the aero-engine, by solving the control equations using numerical methods.

[0110] Further, step (4) specifically involves obtaining the corresponding enthalpy value through the aerodynamic and thermodynamic parameter values ​​of each component's inlet and outlet, and substituting the enthalpy value into the following formula to obtain the total energy input to the engine, the energy dissipated by the engine, the energy stored in the engine, the available energy of the engine, and the energy lost by the engine.

[0111] The total energy input to the engine is the lower calorific value of the fuel supplied:

[0112] E input =W f H u +W f，ab H u

[0113] Engine exhaust energy is defined as the heat carried away by the exhaust gases from the engine.

[0114] E dissipation =m9h9-m0h0

[0115] In the formula, h9 is the static specific enthalpy of the tail nozzle; h0 is the static specific enthalpy of the engine inlet;

[0116] The energy stored in the engine comes from the changes in the enthalpy of air and fuel in various components:

[0117] E storage =∑Δm i,CV h i *

[0118] In the formula, Δm i,CV h represents the change in the internal mass of each component per unit time. i * The total specific enthalpy of all components;

[0119] The usable energy of an engine is the effective power of its thermodynamic cycle.

[0120]

[0121] In the formula, m9 represents the air mass inside the tail nozzle; m0 represents the intake air mass at the engine inlet.

[0122] Engine energy loss is defined as the heat lost due to incomplete combustion of fuel:

[0123] E loss =(1-η b W f H u +(1-η ab W f,ab H u

[0124] In the formula, η b The efficiency of the combustion chamber; η ab This is for the efficiency of the afterburner.

[0125] Furthermore, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of any of the above-described methods. A computer-readable storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the steps of any of the above-described methods.

[0126] Beneficial Effects: The aero-engine energy analysis method based on the thermodynamic principles of variable mass systems described in this invention has significant advantages over existing technologies. Based on the fundamental principles of thermodynamics of variable mass systems, it constructs aero-thermodynamic models for each engine component, considering the internal mass storage and release caused by gas compressibility during actual operation. Furthermore, it designs a set of control equations based on the mass and energy coupling relationships between components to solve for the operating parameters during operation. This allows for the analysis of the changing characteristics of the inlet and outlet aero-thermodynamic parameters of each component during actual aero-engine operation, as well as the energy transport and conversion laws of the entire engine. Attached Figure Description

[0127] Figure 1 The diagram illustrates the process described in this invention.

[0128] Figure 2 The diagram shown is an overall structural diagram of the aero-engine described in this invention;

[0129] Figure 3 The diagram shown is a block diagram of the aero-engine components described in this invention.

[0130] Figure 4 The diagram illustrates the fuel supply pattern of the main combustion chamber as described in this invention.

[0131] Figure 5 The figure shows the pressure change at the main combustion chamber outlet as described in this invention;

[0132] Figure 6 The figure shows the temperature change at the main combustion chamber outlet as described in this invention;

[0133] Figure 7 The figure shows the change in the total flow rate at the nozzle outlet of the present invention;

[0134] Figure 8 The figure shows the energy changes at the engine inlet and outlet of the engine described in this invention;

[0135] Figure 9 The diagram illustrates the energy transfer and conversion relationship of the engine during a steady-state process according to the present invention.

[0136] Figure 10 The diagram illustrates the energy transfer and conversion relationship of the engine during a dynamic process. Detailed Implementation

[0137] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0138] like Figure 1 As shown, the present invention provides an energy analysis method for aero-engines based on the thermodynamic principles of variable mass systems, which specifically includes the following steps:

[0139] Step 1: Taking a real twin-shaft turbofan aero-engine as an example, analyze the transport paths and characteristics of various masses and energy within it, and determine the concepts and classifications of heat / mass flow. Based on the actual engine operating characteristics, disassemble the entire engine into several components. For example... Figure 2 and Figure 3 As shown, an aero engine is specifically divided into an air intake, fan, compressor, combustion chamber, high-pressure turbine, low-pressure turbine, bypass duct, mixing chamber, afterburner, and exhaust nozzle.

[0140] Step 2: Based on the working principles of each component of the aero-engine, each component is considered as a variable-mass thermodynamic system. Based on the mass conservation equation and energy conservation equation for variable-mass systems, considering the mass changes within each component caused by the compressibility of the gas, and combining the energy conversion and transfer within the components, an aerodynamic thermodynamic model is constructed for each component. The specific models are as follows:

[0141] (1) The following assumptions are made in establishing the aerodynamic thermodynamic model:

[0142] (1.1) Ignore the effect of combustion delay;

[0143] (1.2) Ignore the effects of humidity and Reynolds number on component characteristics;

[0144] (1.3) The influence of atmospheric humidity on engine performance parameters is not considered;

[0145] (1.4) The flow of gas, fuel and lubricating oil in the aero-engine is treated as a quasi-unidimensional flow.

[0146] like Figure 2 As shown, the cross-sections of each engine component are numbered accordingly, as detailed in Table 1 below:

[0147] Table 1 Definition of cross-sections of engine components

[0148]

[0149]

[0150] (2) The specific aero-thermodynamic model of the air intake is as follows:

[0151] The air intake uses the kinetic energy of the incoming airflow to compress the air flowing towards the engine. Given the flight altitude and Mach number, the airflow parameters of the inlet and outlet sections of the air intake can be calculated.

[0152] Inlet aerodynamic and thermodynamic parameter equations:

[0153] [T s0 ,P s0 ,T t1 ,P t1 ,T t2 ,P t2 ] = f1[H0,Ma0]

[0154] In the formula, T s0 For incoming static temperature; P s0 For incoming static pressure; T t1 P is the total temperature of the airflow at the intake duct. t1 T is the total pressure of the airflow at the intake duct; t2 P is the total airflow temperature at the intake and outlet. t2 H0 is the total pressure of the airflow at the intake outlet; Ma0 is the aircraft's flight altitude; Ma0 is the Mach number; f1() is the intake characteristic curve, that is, the corresponding aerodynamic and thermodynamic parameters are obtained from the intake characteristic data through H0 and Ma0.

[0155] Assuming the mass at the inlet and outlet of the air intake remains constant, and neglecting heat dissipation from the gas, the mass conservation equation and energy conservation equation for the air intake are as follows:

[0156] W a1 -W a2 =0

[0157]

[0158] In the formula, W a1 Airflow rate at the intake duct; W a2 The airflow rate at the intake outlet; The total specific enthalpy at the intake of the air intake; The total specific enthalpy at the intake outlet;

[0159] (3) The aerodynamic thermodynamic model of the fan is as follows:

[0160] The fan assembly is located on the low-pressure rotor of the engine. The fan compresses the air coming in from the intake device. The compressed air is divided into two streams: the airflow at the blade root enters the compressor assembly for further compression, while the airflow at the blade tip enters the bypass duct.

[0161] Fan aero-thermodynamic parameter equations:

[0162] [T t21 ,P t21 Wa2 ]=f2[T t2 ,P t2 ,π F ,n L ]

[0163] In the formula, T t21 Total temperature at the fan outlet; P t21 Total pressure at the fan outlet; W a2 π represents the flow rate at the fan inlet. F n is the fan pressure ratio; L f2() represents the low-pressure shaft speed; f2() is the fan characteristic curve, i.e., through T t2 P t2 π F n L The corresponding aerodynamic and thermodynamic parameters are obtained from the fan characteristic data.

[0164] Fan mass conservation equation and energy conservation equation:

[0165]

[0166]

[0167] In the formula, W a21 m is the fan outlet flow rate. CV,F For the mass inside the fan; The total specific enthalpy at the fan outlet; This refers to the total specific enthalpy of the fan components.

[0168] (4) The specific aerodynamic thermodynamic model of the compressor is as follows:

[0169] Compressor aerodynamic and thermodynamic parameter equations:

[0170] [T t3 ,P t3 W a22 ]==f3[T t21 ,P t21 ,π C ,n H ]

[0171] In the formula, T t3 The total temperature at the compressor outlet; p t3 W is the total pressure at the compressor outlet. a22 π is the compressor inlet flow rate; C n is the pressure ratio of the press; H f3 is the high-pressure shaft speed; f3() is the compressor characteristic curve, i.e., through T t21 P t21 π C n HThe corresponding aerodynamic and thermodynamic parameters are obtained from the compressor characteristic data;

[0172] The mass conservation equation and energy conservation equation for the compressor are:

[0173]

[0174]

[0175] In the formula, W a22 N is the flow rate at the compressor inlet. C W is the compressor power. a3 The flow rate at the compressor outlet; m CV,C The mass inside the compressor; The total specific enthalpy of the compressor; The total specific enthalpy at the compressor outlet;

[0176] (5) The specific aero-thermodynamic model of the combustion chamber is as follows:

[0177] Combustion chamber aero-thermodynamic parameter equations:

[0178] [P t4 ]=f4[P t3 W f ]

[0179] In the formula, P t4 W is the total pressure at the combustion chamber outlet. f The main fuel flow rate; f4() is the combustion chamber characteristic curve, i.e., through P t3 W f The corresponding aerodynamic and thermodynamic parameters are obtained from the combustion chamber characteristic data;

[0180] The mass conservation equation and energy conservation equation for the combustion chamber are as follows:

[0181]

[0182]

[0183] In the formula, W g4 airflow rate in the combustion chamber; m CV,combustor H represents the internal mass of the combustion chamber. μ For fuel with low calorific value; η b For the efficiency of the combustion chamber; The total specific enthalpy of the combustion chamber;

[0184] (6) The specific aero-thermodynamic model of the high-pressure turbine is as follows:

[0185] The function of the turbine is to expand the combustion gases, which have absorbed heat energy in the combustion chamber, to generate mechanical energy. The aerodynamic and thermodynamic parameter equations for a high-pressure turbine are as follows:

[0186] [T t44 ,P t44 W g41 ]==f5[T t4 ,P t4 ,π HT ,n H ]

[0187] In the formula, T t4 T is the total temperature at the combustion chamber outlet. t44 P represents the total temperature at the high-pressure turbine outlet. t44 W is the total pressure at the turbine outlet. g41 π represents the flow rate at the high-pressure turbine inlet. HT The pressure drop ratio of the high-pressure turbine; n H f5() represents the rotational speed of the high-pressure turbine; f5() is the characteristic curve of the high-pressure turbine, i.e., the curve passing through T. t4 ,P t4 ,π HT ,n H The corresponding aerodynamic and thermodynamic parameters are obtained from the high-pressure turbine characteristic data;

[0188] The mass conservation equation and energy conservation equation for the high-pressure turbine are as follows:

[0189]

[0190]

[0191] In the formula, W g41 W is the flow rate at the high-pressure turbine inlet. g44 The flow rate at the high-pressure turbine outlet; m CV,HT The mass inside the high-pressure turbine; The total specific enthalpy at the high-pressure turbine inlet; N is the total specific enthalpy at the high-pressure turbine outlet. HT The power of the high-pressure turbine; This refers to the total specific enthalpy of the high-pressure turbine.

[0192] (7) The specific aero-thermodynamic model of the low-pressure turbine is as follows:

[0193] Low-pressure turbine aero-thermodynamic parameter equations:

[0194] [T t5 ,P t5 W g45 ]==f6[T t44 ,P t44 ,π LT ,n L ]

[0195] In the formula, T t5P represents the total temperature at the low-pressure turbine outlet. t5 W is the total pressure at the low-pressure turbine outlet. g45 The flow rate at the low-pressure turbine inlet; π LT The pressure drop ratio of the low-pressure turbine; n L f6() represents the rotational speed of the low-pressure turbine; f6() is the characteristic curve of the low-pressure turbine, i.e., the curve obtained through T. t44 ,P t44 ,π LT ,n L The corresponding aerodynamic and thermodynamic parameters are obtained from the low-pressure turbine characteristic data;

[0196] The mass conservation equations and energy conservation equations for the low-pressure turbine are as follows:

[0197]

[0198]

[0199] In the formula, W g45 The flow rate at the low-pressure turbine inlet; W g5 The flow rate at the low-pressure turbine outlet; m CV,LT The mass inside the low-pressure turbine; The total specific enthalpy of the low-pressure turbine inlet; N is the total specific enthalpy at the low-pressure turbine outlet. LT The power of the low-pressure turbine; This refers to the total specific enthalpy of the low-pressure turbine.

[0200] (8) The aero-thermodynamic model of the outer bypass duct is as follows:

[0201] External bypass duct aerodynamic and thermodynamic parameter equations:

[0202] [T t16 ,P t16 ]==f7[T t13 ,P t13 ]

[0203] In the formula, T t16 P is the total temperature at the outlet of the duct. t16 T is the total pressure at the outlet of the bypass duct; t16 The total temperature at the outlet of the duct; T t13 f7() represents the total temperature at the inlet of the bypass duct; f7() is the characteristic curve of the bypass duct, i.e., the temperature through T. t13 ,P t13 Obtain the corresponding aerodynamic and thermodynamic parameters from the characteristic data of the outer bypass duct;

[0204] The mass conservation equations and energy conservation equations for the bypass duct are as follows:

[0205]

[0206]

[0207] In the formula, W a13 The flow rate at the inlet of the bypass duct; W a16 The flow rate at the outlet of the duct; m CV,bypass For the internal mass of the outer bypass duct; The total specific enthalpy of the bypass duct inlet; The total specific enthalpy at the outlet of the bypass duct;

[0208] (9) The specific aero-thermodynamic model of the mixing chamber is as follows:

[0209] The aero-thermodynamic parameter equations for the mixing chamber are as follows:

[0210] [T t6 ,P t6 ]==f8[T t16 ,P t16 W a16 ,T t5 ,P t5 W g5 ]

[0211] In the formula, T t6 P is the total temperature at the outlet of the mixing chamber. t6 f8() represents the total pressure at the outlet of the mixing chamber; f8() is the characteristic curve of the mixing chamber, i.e., the pressure through T. t16 ,P t16 W a16 ,T t5 ,P t5 W g5 Obtain the corresponding aerodynamic and thermodynamic parameters from the mixing chamber characteristic data;

[0212] The mass conservation equations and energy conservation equations for the mixing chamber are as follows:

[0213] W a16 +W g5 -W g6 =0

[0214]

[0215] In the formula, W g6 h6 is the flow rate at the mixing chamber outlet. * The total specific enthalpy at the outlet of the mixing chamber;

[0216] (10) The aero-thermodynamic model of the afterburner is as follows:

[0217] Afterburner aerodynamic and thermodynamic parameter equations:

[0218] [P t7 ]=f9[P t6 Wf,ab ]

[0219] In the formula, P t7 W is the total pressure at the outlet of the afterburner. f,ab f9() represents the afterburner fuel supply; f9() is the characteristic curve of the afterburner combustion chamber, i.e., through P t6 W f,ab Obtain the corresponding aerodynamic and thermodynamic parameters from the characteristic data of the afterburner;

[0220] The mass conservation equations and energy conservation equations for an afterburner are:

[0221]

[0222]

[0223] In the formula, W g7 The flow rate at the outlet of the afterburner; m CV,ab η is the mass inside the afterburner chamber. ab For the efficiency of the afterburner; The total specific enthalpy at the outlet of the afterburner; The total specific enthalpy of the afterburner; H μ It is a fuel with a low calorific value;

[0224] (2.11) The aerodynamic-thermodynamic model of the tail nozzle is as follows:

[0225] aerodynamic and thermodynamic parameter equations for the tailpipe:

[0226] [T t9 ,P t9 W g9 ] = f 10 [T t7 ,P t7 ]

[0227] In the formula, T t7 T is the total airflow temperature at the nozzle inlet; t9 P is the total airflow temperature at the nozzle exit. t9 P is the total pressure of the airflow at the tailpipe exit. t7 W is the total airflow pressure at the nozzle inlet. g9 f is the exhaust flow rate at the tailpipe outlet. 10 () represents the tail nozzle characteristic curve, passed through T t7 ,P t7 Obtain the corresponding aerodynamic and thermodynamic parameters from tail nozzle characteristic data;

[0228] The mass conservation equation and energy conservation equation for the tailpipe are as follows:

[0229] W g7 -W g9 =0

[0230]

[0231] In the formula, This represents the total specific enthalpy at the nozzle exit. The interpretations of the variables in the specific models of each component are shown in Tables 2 and 3 below:

[0232] Table 2: Explanation of Meanings and Units

[0233]

[0234] Table 3 Explanation of Subscript Meanings and Units

[0235]

[0236]

[0237] Step 3: Based on the material and energy coupling, matching, and cooperative relationships of various components during the operation of the aero-engine, establish and solve the control equations for the actual process of the aero-engine. The specific equations are as follows:

[0238] Steady-state process high and low pressure shaft rotor dynamic equations:

[0239] η H N HT -|N C |=0

[0240] η L N LT -|N F |=0

[0241] Dynamic process high and low pressure shaft rotor dynamic equations:

[0242]

[0243]

[0244] The balance equation between the fan outlet flow rate and the inlet flow rates of the compressor and bypass:

[0245] W a21 -W a22 -W a13 =0

[0246] The balance equation between the high-pressure turbine inlet flow rate and the combustion chamber outlet flow rate is as follows:

[0247] W g41 -W g4 =0

[0248] The balance equation between the low-pressure turbine inlet flow rate and the high-pressure turbine outlet flow rate is as follows:

[0249] W g45 -W g44 =0

[0250] The balance equation between the exhaust nozzle outlet flow rate and the afterburner outlet flow rate is as follows:

[0251] W g9 -W g7 =0

[0252] Initially, the model operates as a steady-state model, followed by a dynamic model. Given flight altitude, Mach number, and combustion chamber fuel supply, the model's independent variables are defined as follows: The independent equations are the aforementioned set of governing equations, with the number of independent variables equal to the number of independent equations, both being six; the model is closed. The independent variables can be solved numerically, and these independent variables represent the actual operating parameters of the engine.

[0253] The engine operating parameters [n] are obtained through iterative solution. L ,n H ,π F ,π C ,π TH ,π TL By inputting the aerodynamic and thermodynamic models of each component, the aerodynamic and thermodynamic parameter values ​​of the inlet and outlet sections of each engine component are obtained, and the engine energy transfer and conversion analysis is performed.

[0254] Step 4: Calculate the total energy input to the engine, the energy dissipated by the engine, the energy stored by the engine, the available energy of the engine, and the energy lost by the engine during the actual operation of the aero-engine based on the aero-thermal parameters of each component inlet and outlet.

[0255] Specifically, by using the pressure and temperature values ​​in the aerodynamic and thermodynamic parameters of each component's inlet and outlet, and according to the corresponding relationship table between pressure, temperature and enthalpy, the corresponding enthalpy value is obtained. The enthalpy value is then substituted into the following formula to obtain the total energy input to the engine, the energy dissipated by the engine, the energy stored by the engine, the available energy of the engine, and the energy lost by the engine.

[0256] The total energy input to the engine is the lower calorific value of the fuel supplied:

[0257] E input =W f H u +W f，ab H u

[0258] Engine exhaust energy is defined as the heat carried away by the exhaust gases from the engine.

[0259] E dissipation =m9h9-m0h0

[0260] In the formula, h9 is the static specific enthalpy of the tail nozzle; h0 is the static specific enthalpy of the engine inlet;

[0261] The energy stored in the engine comes from the changes in the enthalpy of air and fuel in various components:

[0262] E storage =∑Δm i,CV h i *

[0263] In the formula, Δm i,CV h represents the change in the internal mass of each component per unit time. i * The total specific enthalpy of all components;

[0264] The usable energy of an engine is the effective power of its thermodynamic cycle.

[0265]

[0266] In the formula, m9 represents the air mass inside the tail nozzle; m0 represents the intake air mass at the engine inlet.

[0267] Engine energy loss is defined as the heat lost due to incomplete combustion of fuel:

[0268] E loss =(1-η b W f H u +(1-η ab W f,ab H u

[0269] In the formula, η b The efficiency of the combustion chamber; η ab This is for the efficiency of the afterburner.

[0270] For each component, an aero-thermodynamic model, control equations and their solution process are constructed to construct a corresponding simulation model, and the aero-thermodynamic parameters and energy of the aero-engine are simulated and calculated during actual operation.

[0271] Specifically, a parameter input module is established to set flight mission parameters, engine-related parameters, and simulation calculation parameters. Flight mission parameters include current engine flight altitude, Mach number, and other flight parameters. Engine-related parameters include engine fuel supply and adjustable mechanism parameters that determine the engine operating mode. By providing different flight mission parameters and engine-related parameters, the engine operating state is determined, simulation results are obtained, and the aerodynamic and thermodynamic parameter variation characteristics of each section during the actual operation of the aero-engine and the energy transfer and conversion relationships within the system are analyzed.

[0272] In the specific implementation process, a ground test mode is selected, the aircraft's flight altitude H = 0m and flight Mach number Ma = 0 are set, the acceleration process of the aircraft engine is taken as the actual operation process, and the fuel supply pattern of the main combustion chamber in the engine is set as follows: Figure 4 As shown, the fuel supply to the main combustion chamber is 1 kg / s within 0-5 seconds, increases uniformly within 5-15 seconds, and reaches 2.4 kg / s after 15 seconds, while the afterburner remains closed. The simulation time step is set to 0.01 s. The simulation comparison results obtained using the model described in this application and existing models based on the flow balance assumption are shown below. Figures 5 to 8 As shown.

[0273] like Figure 5 As shown in Figure 2, the pressure change at the main combustion chamber inlet obtained by the simulation method of the present invention is as shown in Figure 2. Compared with Figure 1 obtained by the simulation of the prior art, during the acceleration process, the pressure increase is somewhat delayed due to the consideration of the variable mass system (i.e., the internal mass change of components caused by the compressibility of the gas), resulting in a more accurate pressure change curve. Figure 6 As shown in Figure 2, the temperature change at the main combustion chamber outlet obtained by the simulation method of the present invention is shown in curve 1. Compared with curve 1 obtained by the prior art simulation, the temperature change at the main combustion chamber outlet during acceleration can be observed. The temperature rises during acceleration, and the temperature rise is anticipated earlier when considering the variable mass system, resulting in a more accurate temperature change curve characteristic. Figure 7 As shown in Figure 2, the change in the total flow rate at the engine exhaust nozzle outlet during the acceleration process, simulated by the method described in this invention, is compared to curve 1 obtained from prior art simulations. During acceleration, the flow rate increases, while during deceleration, it decreases. Considering the variable mass system, the flow rate exhibits a significant lag, resulting in a more accurate curve characteristic. Figure 8 As shown, curve 1 represents energy input, and curve 2 represents energy loss and output. The curves coincide, indicating overall energy conservation. During acceleration, the total energy input to the engine increases with the increase in fuel flow, resulting in increased input energy. The absolute value of the energy difference between input and output throughout the entire process is less than 0.032%.

[0274] according to Figures 5 to 8 As shown, during engine acceleration, the process reaches a steady state after 0-5s and 15s; from 5-15s, it is in a dynamic change process. Figure 9 As shown, at time 2.5s, the engine's available energy during this steady-state process accounts for 21.60%, energy loss accounts for 2.00%, dissipation accounts for 76.40%, and storage accounts for 0.00%. Figure 10 As shown, at time 10s, the engine has 19.17% of its available energy, 2.00% of its energy loss, 78.15% of its energy dissipation, and 0.68% of its energy storage during this dynamic process.

Claims

1. A method for energy analysis of aero-engines based on the thermodynamic principles of variable mass systems, characterized in that, Includes the following steps: (1) Taking aero-engine as the research object and combining the actual operating characteristics of aero-engine, aero-engine is divided into several components, namely, air intake, fan, compressor, combustion chamber, high-pressure turbine, low-pressure turbine, bypass duct, mixing chamber, afterburner, and tail nozzle; (2) Considering the changes in internal mass of each component caused by the compressibility of the gas inside the aero-engine, an aerodynamic thermodynamic model is constructed for each component; the aerodynamic thermodynamic model includes the mass conservation equation, energy conservation equation, and aerodynamic thermodynamic parameter equation for each component; Step (2) is as follows: (2.1) Basic assumptions for establishing the aerodynamic thermodynamic model: (2.1.1) The effect of combustion delay is ignored; (2.1.2) Ignore the effects of humidity and Reynolds number on the characteristics of each component; (2.1.3) The influence of atmospheric humidity on engine performance parameters is not considered; (2.1.4) The flow of gases, fuels and lubricating oil in aero engines shall be treated as quasi-one-dimensional flow. (2.2) The aerodynamic and thermodynamic model of the air intake is as follows: Inlet aerodynamic and thermodynamic parameter equations: ； In the formula, For incoming static temperature; For incoming static pressure; The total temperature of the airflow at the intake duct; The total pressure of the airflow at the intake duct; The total temperature of the airflow at the intake and outlet. The total pressure of the airflow at the intake outlet; The flight altitude of the aircraft; It is the Mach number; The characteristic curve of the intake duct; Intake duct mass conservation equation and energy conservation equation: ； ； In the formula, The airflow rate at the air intake; The airflow rate at the intake outlet; The total specific enthalpy at the intake of the air intake; The total specific enthalpy at the intake outlet; (2.3) The aerodynamic thermodynamic model of the fan is as follows: Fan aero-thermodynamic parameter equations: ； In the formula, Total temperature at the fan outlet; Total pressure at the fan outlet; The flow rate at the fan inlet; This refers to the fan pressure ratio; For low pressure shaft speed; This is the fan characteristic curve; Fan mass conservation equation and energy conservation equation: ； ； In the formula, This refers to the fan outlet flow rate; For the mass inside the fan; The total specific enthalpy at the fan outlet; The total specific enthalpy of the fan components; (2.4) The specific aerodynamic and thermodynamic model of the compressor is as follows: Compressor aerodynamic and thermodynamic parameter equations: ； In the formula, Total temperature at the compressor outlet; The total pressure at the compressor outlet; This refers to the compressor inlet flow rate; The pressure ratio of the press; This refers to the high-pressure shaft speed; The compressor characteristic curve; The mass conservation equation and energy conservation equation for the compressor are: ； ； In the formula, This refers to the flow rate at the compressor inlet; Compressor power; This is the flow rate at the compressor outlet; The mass inside the compressor; The total specific enthalpy of the compressor; The total specific enthalpy at the compressor outlet; (2.5) The specific aerodynamic and thermodynamic model of the combustion chamber is as follows: Combustion chamber aero-thermodynamic parameter equations: ； In the formula, Total pressure at the combustion chamber outlet; Main fuel flow; The combustion chamber characteristic curve; The mass conservation equations and energy conservation equations for the combustion chamber are as follows: ； ； In the formula, This refers to the airflow rate inside the combustion chamber. Mass inside the combustion chamber; It is a fuel with a low calorific value; For the efficiency of the combustion chamber; The total specific enthalpy of the combustion chamber; (2.6) The specific aerodynamic thermodynamic model of the high-pressure turbine is as follows: High-pressure turbine aero-thermodynamic parameter equations: ； In the formula, The total temperature at the combustion chamber outlet; This refers to the total temperature at the high-pressure turbine outlet. The total pressure at the turbine outlet; This refers to the flow rate at the high-pressure turbine inlet. This refers to the pressure drop ratio of the high-pressure turbine. This refers to the rotational speed of the high-pressure turbine. The characteristic curve of the high-pressure turbine; The mass conservation equation and energy conservation equation for the high-pressure turbine are as follows: ； ； In the formula, This refers to the flow rate at the high-pressure turbine inlet. This represents the flow rate at the high-pressure turbine outlet. The mass inside the high-pressure turbine; The total specific enthalpy at the high-pressure turbine inlet; The total specific enthalpy at the high-pressure turbine outlet; The power of the high-pressure turbine; This refers to the total specific enthalpy of the high-pressure turbine. (2.7) The specific aerodynamic thermodynamic model of the low-pressure turbine is as follows: Low-pressure turbine aero-thermodynamic parameter equations: ； In the formula, This refers to the total temperature at the low-pressure turbine outlet. The total pressure at the low-pressure turbine outlet; The flow rate at the low-pressure turbine inlet; The pressure drop ratio of the low-pressure turbine; The rotational speed of the low-pressure turbine; The characteristic curve of a low-pressure turbine; The mass conservation equations and energy conservation equations for the low-pressure turbine are as follows: ； ； In the formula, The flow rate at the low-pressure turbine inlet; This refers to the flow rate at the low-pressure turbine outlet. The mass inside the low-pressure turbine; The total specific enthalpy of the low-pressure turbine inlet; The total specific enthalpy at the low-pressure turbine outlet; The power of the low-pressure turbine; The total specific enthalpy of the low-pressure turbine; (2.8) The specific aerodynamic and thermodynamic model of the outer bypass duct is as follows: External bypass duct aerodynamic and thermodynamic parameter equations: ； In the formula, The total temperature at the outlet of the outer duct; The total pressure at the outlet of the bypass duct; The total temperature at the inlet of the bypass duct; The characteristic curve of the bypass duct; The mass conservation equations and energy conservation equations for the bypass duct are as follows: ； ； In the formula, The flow rate at the inlet of the bypass duct; The flow rate at the outlet of the duct; For the internal mass of the outer bypass duct; The total specific enthalpy of the bypass duct inlet; The total specific enthalpy at the outlet of the bypass duct; (2.9) The specific aerodynamic thermodynamic model of the mixing chamber is as follows: The aero-thermodynamic parameter equations for the mixing chamber are as follows: ； In the formula, The total temperature at the outlet of the mixing chamber; The total pressure at the outlet of the mixing chamber; The characteristic curve of the mixing chamber; The mass conservation equations and energy conservation equations for the mixing chamber are as follows: ； ； In the formula, The flow rate at the mixing chamber outlet; The total specific enthalpy at the outlet of the mixing chamber; (2.10) The aerodynamic-thermodynamic model of the afterburner is as follows: Afterburner aerodynamic and thermodynamic parameter equations: ； In the formula, This refers to the total pressure at the outlet of the afterburner. To increase fuel supply; The characteristic curve of the afterburner; The mass conservation equations and energy conservation equations for an afterburner are: ； ； In the formula, The flow rate at the outlet of the afterburner; The mass inside the afterburner chamber; For the efficiency of the afterburner; The total specific enthalpy at the outlet of the afterburner; The total specific enthalpy of the afterburner; It is a fuel with a low calorific value; (2.11) The aerodynamic-thermodynamic model of the tail nozzle is as follows: Equations for the aerodynamic and thermodynamic parameters of the tailpipe: ； In the formula, The total temperature of the airflow at the tail nozzle inlet; This refers to the total temperature of the airflow at the tail nozzle exit. The total pressure of the airflow at the tail nozzle exit; The total pressure of the airflow at the tail nozzle inlet; This refers to the outlet flow rate of the tail nozzle. The tail nozzle characteristic curve; The mass conservation equation and energy conservation equation for the tailpipe are as follows: ； ； In the formula, The total specific enthalpy at the tail nozzle exit; (3) Based on the energy coupling relationship of each component of the aero-engine, construct a set of control equations for the actual operation of the aero-engine. The set of control equations includes the flow balance equations between each component and the rotor dynamics equations. By solving the control equations, the operating parameters of the aero-engine during actual operation are obtained. The engine operating parameters are then substituted into the aero-thermodynamic model of each component to obtain the inlet and outlet aero-thermodynamic parameter values ​​of each component. (4) The total energy input to the engine, the energy dissipated by the engine, the energy stored in the engine, the available energy of the engine and the energy lost by the engine during the actual operation of the aero-engine are calculated based on the aero-thermal parameters of each component.

2. The aero-engine energy analysis method based on the thermodynamic principles of a variable mass system according to claim 1, characterized in that, The governing equations for step (3) are as follows: Steady-state process high and low pressure shaft rotor dynamics equations: ； ； Dynamic process high and low pressure shaft rotor dynamic equations: ； ； The balance equation between the fan outlet flow rate and the inlet flow rates of the compressor and bypass: ； The balance equation between the high-pressure turbine inlet flow rate and the combustion chamber outlet flow rate is as follows: ； The balance equation between the low-pressure turbine inlet flow rate and the high-pressure turbine outlet flow rate is as follows: ； The balance equation between the exhaust nozzle outlet flow rate and the afterburner outlet flow rate is as follows: 。 3. The aero-engine energy analysis method based on the thermodynamic principles of a variable mass system according to claim 2, characterized in that, The solution of the control equations in step (3) includes: setting the aircraft flight altitude, Mach number, and combustion chamber fuel supply, and obtaining the independent variables of the control equations, namely the operating parameters of the aero-engine, by solving the control equations using numerical methods. .

4. The aero-engine energy analysis method based on the thermodynamic principles of a variable mass system according to claim 1, characterized in that, Step (4) specifically involves obtaining the corresponding enthalpy value through the aerodynamic and thermodynamic parameter values ​​of each component's inlet and outlet, and substituting the enthalpy value into the following formula to obtain the total energy input to the engine, the energy dissipated by the engine, the energy stored in the engine, the available energy of the engine, and the energy lost by the engine. The total energy input to the engine is the lower calorific value of the fuel supplied: ； Engine exhaust energy is defined as the heat carried away by the exhaust gases from the engine. ； In the formula, The static specific enthalpy of the tail nozzle; The static specific enthalpy of the engine inlet; The energy stored in the engine comes from the changes in the enthalpy of air and fuel in various components: ； In the formula, This represents the change in the internal mass of each component per unit time. The total specific enthalpy of all components; The usable energy of an engine is the effective power of its thermodynamic cycle. ； In the formula, Air quality inside the tailpipe; The quality of the air intake at the engine inlet; Engine energy loss is defined as the heat lost due to incomplete combustion of fuel: ； In the formula, For the efficiency of the combustion chamber; This is for the efficiency of the afterburner.

5. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 4.

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