Civil aviation turbofan engine fuel control simulation method and system

Abstract

The invention provides a civil aviation turbofan engine fuel control simulation method and system, and the method comprises the steps: building a fuel pipeline flow equation which comprises a continuous equation and a momentum equation and is used for representing the dynamic change of the fuel pressure in a pipeline along the axial direction; establishing a fuel nozzle atomization equation based on a K-H instability model; establishing a pressure-flow characteristic equation of the fuel pump; a fuel oil system equation set describing the performance of the civil aviation turbofan engine fuel oil system is formed simultaneously and used for solving pressure distribution, flow and nozzle atomization characteristics of the fuel oil system under different working conditions; the method comprises the following steps of: axially dividing a fuel oil pipeline into a plurality of control volumes at equal intervals, and discretizing each control volume; and iteratively solving the discretized fuel system equation set.

Description

Technical Field

[0001] The present invention relates to the field of simulation technology, in particular to civil aviation turbofan engine simulation, and specifically to a civil aviation turbofan engine fuel control simulation method and system. Background Art

[0002] The fuel control of turbofan engines involves the entire flight process of the aircraft. The normal operation of the fuel system is crucial to flight safety. Accurate fuel control simulation can help predict and analyze the performance of the fuel system under various normal and fault conditions. Through fuel control simulation, it can help optimize the design and operation strategy of the engine fuel control system, accurately control the fuel supply, and enable the engine to operate at the best fuel-air mixture ratio under different operating conditions (such as takeoff, cruising, landing, etc.), thereby improving fuel combustion efficiency, reducing fuel consumption, and reducing operating costs.

[0003] Modern civil aviation turbofan engines are constantly developing towards high bypass ratio, high thrust and low fuel consumption. These performance improvements have put forward higher requirements for the fuel control system. At the same time, with the application of digital electronic control (FADEC-Full Authority Digital Engine Control) technology, accurate and flexible control of fuel can be achieved. The complex control algorithms in the FADEC system (such as adaptive control, model predictive control, etc.) are tested and verified in a simulation environment to ensure their reliability and effectiveness in actual operation. Simulation can help to more fully understand and optimize the performance of the fuel control system.

[0004] At present, the existing turbofan engine fuel performance simulation methods are implemented through component simulation, data-driven simulation, and machine learning or data mining algorithm models. For example, a large amount of actual turbofan engine operation data, including fuel flow, engine speed, pressure, temperature and other parameters, is collected, and machine learning or data mining algorithms, such as neural networks, support vector machines, regression analysis, etc., are used to establish a fuel control model. Taking neural networks as an example, the engine operating parameters are used as input, and the fuel flow or other control parameters are used as output. The mapping relationship between input and output is learned by training a large amount of data, thereby realizing the prediction and simulation of fuel control. The established data-driven model is verified using a part of the data that is not involved in the training to evaluate the accuracy and generalization ability of the model. The model is adjusted and optimized according to the verification results, such as adjusting the structure and hyperparameters of the model, to improve the performance of the model. However, data-driven simulation is highly dependent on data quality, which directly affects the accuracy and reliability of the model. In addition, data-driven models, such as deep neural networks, are usually regarded as "black box" models. Their internal decision-making process and logic are difficult to intuitively understand and explain. For the complex control strategies of turbofan engines, it is difficult to determine whether the model's decisions are reasonable and whether there are potential risks. It is also not conducive to targeted optimization and adjustment of the model. Summary of the invention

[0005] In view of the defects and shortcomings of the prior art, the purpose of the present invention is to provide a fuel control simulation method based on a civil aviation turbofan engine, establish a fuel system physical model based on the fuel pipeline flow equation, the fuel nozzle atomization equation and the fuel pump characteristic equation, consider the dynamic change of the fuel pressure along the axial direction, accurately simulate the mass conservation and momentum change of the fuel in the pipeline, and use the fuel nozzle atomization equation of the KH instability model to accurately simulate the mixing effect and combustion efficiency of the fuel and air, finally, combine the pressure-flow characteristic equation of the fuel pump to accurately simulate the driving condition of the fuel in the system, the comprehensive physical model thus established can accurately reflect the working process of the fuel system, and provide a reliable theoretical basis for the design, optimization and fault diagnosis of the engine.

[0006] According to the first aspect of the present invention, a civil aviation turbofan engine fuel control simulation method comprises the following steps:

[0007] Based on the dynamic changes of fuel in the micro-element section of the fuel pipeline, the fluid movement of fuel in the fuel pipeline is equivalent to the flow of compressible fluid in a one-dimensional pipeline. Combining the inner diameter of the pipeline with the viscosity of the fuel, the fuel pipeline flow equation is established, including the continuity equation and the momentum equation, which are used to characterize the dynamic changes of the fuel pressure in the pipeline along the axial direction.

[0008] The fuel nozzle atomization equation based on the KH instability model is established to describe the breakup and atomization of fuel droplets.

[0009] The pressure-flow characteristic equation of the fuel pump is established based on quadratic polynomial fitting;

[0010] The fuel pipeline flow equation, the pressure-flow characteristic equation of the fuel pump and the fuel nozzle atomization equation are combined to form a fuel system equation group describing the performance of the fuel system of a civil aviation turbofan engine, which is used to solve the pressure distribution, flow rate and nozzle atomization characteristics of the fuel system under different working conditions;

[0011] The fuel pipeline is divided into equally spaced control volumes along the axial direction, and the flow equation of the fuel pipeline is integrated in each control volume to achieve spatial discretization;

[0012] Time discretization of time terms;

[0013] Iteratively solve the discretized fuel system equations.

[0014] As an optional embodiment, the fuel pipeline flow equation establishment process includes:

[0015] Based on the dynamic changes of fuel in the micro-element section of the fuel pipeline, the relationship between the pressure difference, friction and the mass of the fuel is described as follows:

[0016]

[0017] Among them, ΔL represents the length of the infinitesimal segment, ρ is the fuel density, v is the flow velocity, and A is the cross-sectional area of ​​the fuel pipe;

[0018] For steady flow, the above relationship is simplified to a momentum equation that includes dynamic pressure loss and resistance loss along the way, expressed as follows:

[0019]

[0020] Where x is the coordinate along the pipeline direction, D is the inner diameter of the pipeline, and μ is the viscosity of the fuel;

[0021] The fluid motion of fuel in the fuel pipeline is equivalent to the flow of compressible fluid in a one-dimensional pipeline, and the flow control equation of compressible fluid is established, which is expressed as:

[0022]

[0023] Further simplification, the continuous equation for fuel flow control is obtained, which is expressed as:

[0024]

[0025] As an optional embodiment, the process of establishing the fuel nozzle atomization equation based on the KH instability model includes:

[0026] Assume that there are tiny fluctuations on the surface of the fuel droplet, with a wavelength of λ; when the difference between the fluctuation speed on the surface of the fuel droplet and the flow velocity inside the droplet reaches a certain level, the droplet will break.

[0027] According to linear stability analysis, there is a critical wavelength λ c , when the wave wavelength is greater than the critical wavelength λ c When , the fluctuations will grow and cause the droplets to break;

[0028] Based on the critical wavelength λ c The fuel nozzle atomization equation is established with the radius R of the droplet, the surface tension σ, and the density difference Δρ between the liquid and the gas:

[0029]

[0030] Where v represents the relative velocity between the fuel droplet and the surrounding gas;

[0031] When the fluctuation wavelength on the surface of the fuel droplets meets the breakup conditions, the droplets split and the atomization process is realized.

[0032] As an optional embodiment, the process of establishing the pressure-flow characteristic equation of the fuel pump based on quadratic polynomial fitting includes:

[0033] By fitting the experimental data with a quadratic polynomial, the pressure-flow characteristic equation of the fuel pump is obtained, which is expressed as:

[0034] ΔP pump =aQ 2 ++bQ+c

[0035] Among them, ΔP pump represents the pressure rise provided by the fuel pump, Q represents the flow rate through the fuel pump, and a, b, and c are fitting coefficients, which are obtained by fitting the experimental test data of the fuel pump under different working conditions.

[0036] As an optional embodiment, the integration of the fuel pipeline flow equation on each control volume includes spatial discretization of the continuity equation, including the following process:

[0037] First, the fuel pipeline with a total length of L is divided into N control volumes with equal spacing along the axial direction. The length of each control volume is denoted as Δx i , i=1,2,3,…,N,

[0038] Determine the node position corresponding to each control volume, take the center position of the control volume as the node, and the physical quantity on the node will be used as the unknown quantity for solving the subsequent discrete equations;

[0039] For the continuity equation Integrating over each control volume i, according to the Gaussian divergence theorem, we get:

[0040]

[0041] Among them, V i is the volume of the control volume, A i is the surface area of ​​the control volume, is the surface normal vector;

[0042] The density in the control volume is approximately equivalent to the value ρ at the central node of the control volume i , then the mass in the control volume Approximately expressed as ρ i V i ;

[0043] Derivative with respect to time It is further described as

[0044] If the volume of the control volume is considered to be a fixed value that does not change with time, it can be further simplified to:

[0045]

[0046] This achieves the discretization of density terms;

[0047] for represents the mass flow through the control volume surface; in the case of one-dimensional flow in a pipeline, the control volume includes two surfaces, namely the inlet surface and the outlet surface. The flow term is decomposed into the difference between the flow through the inlet surface and the outlet surface, and the flow velocity and density at the interface are approximated by the central difference format to realize the discretization of the flow term, which is expressed as:

[0048] (ρ i+1 / 2v i+1 / 2 -ρ i-1 / 2 v i-1 / 2 )A;

[0049] Among them, ρ i+1 / 2 and ρ i-1 / 2 They represent the density at the interface at i+1 / 2 and i-1 / 2 of the control volume interface, respectively, and v i+1 / 2 With v i-1 / 2 They represent the values ​​of the density at the interface at i+1 / 2 and i-1 / 2 of the control volume interface respectively;

[0050] Finally, the discretized form of the continuous equation is:

[0051]

[0052] Further sorting can be obtained:

[0053]

[0054] Among them, V i =AΔx i ;

[0055] Thus, the discrete continuous equation expression is obtained, which is equivalent to:

[0056]

[0057] Furthermore, the integration of the fuel pipeline flow equations on each control volume includes spatial discretization of the momentum equation, including the following process:

[0058] For the momentum equation The integration is performed on each control volume i, including the discretization of the pressure gradient term, the dynamic pressure loss term, and the resistance loss term along the way, respectively:

[0059] (1) Using the central difference format, the pressure P at the control volume interface i+1 / 2 is i+1 / 2 Approximately:

[0060]

[0061] The pressure P at the control volume interface i-1 / 2 i-1 / 2 Approximately:

[0062]

[0063] Then the pressure gradient term After discretization, it is expressed as:

[0064]

[0065] (2) Using the central difference format, the flow velocity v at the control volume interface i+1 / 2 is i+1 / 2 Approximately:

[0066]

[0067] The flow velocity v at the control volume interface i-1 / 2 i-1 / 2 Approximately:

[0068]

[0069] Then in the control volume i, the dynamic pressure loss term After discretization, it is expressed as:

[0070] Expand further The discretized expression is:

[0071] (3) In the control volume i, the drag loss term along the way After discretization, it is expressed as:

[0072] Expand further i+1 / 2 , can be obtained

[0073] (4) Combining the discrete expressions of the pressure gradient term, the dynamic pressure loss term, and the drag loss term along the path, the discrete momentum equation within the control volume i is obtained, which is expressed as:

[0074]

[0075] Therefore, the momentum equation is converted into an equation about the node pressure and flow velocity through spatial discretization, which is equivalently expressed as.

[0076] In a further embodiment, the process of iteratively solving the discretized fuel system equations includes:

[0077] Representing vectors as vectors N represents the total number of control volumes, i.e. the number of nodes, ρ i 、v i , P i denote the density, flow velocity and pressure at the i-th control volume node respectively;

[0078] The system of simultaneous equations is described as

[0079] First calculate the Jacobian matrix

[0080] In each iteration, assuming the current number of iterations is k, it is known that calculate and

[0081] Then solve the linear equations Get the increment

[0082] Update variables

[0083] Check the convergence criterion by calculating the isorm If it is less than the set convergence threshold ∈, the iteration is considered to have converged and a solution is obtained; otherwise, continue to the next iteration, i.e. set k = k + 1, and repeat the above steps until the convergence condition is met.

[0084] In a further embodiment, the fuel pump characteristic equation is solved by successive approximation, first assuming an initial flow rate, and then by iterative formula Where b≠0, gradually approaching the actual flow value.

[0085] A computer system according to a second aspect of the present invention comprises:

[0086] one or more processors; and

[0087] Memory, storing instructions that can be operated;

[0088] Wherein, when the instruction is executed by one or more processors, the one or more processors are caused to perform operations, and the operations include the process of executing the aforementioned civil aviation turbofan engine fuel control simulation method.

[0089] Compared with the prior art, the significant advantages of the civil aviation turbofan engine fuel control simulation method proposed in the present invention are:

[0090] (1) Based on the fuel system design and conservation of mass and momentum, a comprehensive fuel system physical model is constructed, which can accurately reflect the working process of the fuel system, provide a reliable theoretical basis for engine design, optimization and fault diagnosis, and provide strong support for the design and optimization of civil aviation turbofan engines;

[0091] (2) Through spatial discretization, the fuel pipeline is divided into equally spaced control volumes along the axial direction, and discretization is performed on each control volume. The continuous fuel flow process can be converted into a discrete form that is easy for computer processing, and the changes in fuel parameters at different locations can be flexibly handled. By applying physical equations to each control volume, the flow details of the fuel in the pipeline can be captured more finely, such as the changes in pressure and flow rate at different locations. In addition, the fuel system problems under different working conditions can be adaptively handled. Whether the engine is in different working conditions such as takeoff, cruising or landing, by adjusting the boundary conditions and initial conditions, combined with the discretized equation group, the performance of the fuel system under the corresponding working conditions can be accurately simulated;

[0092] (3) The fuel control simulation method designed by the present invention can provide strong support for the design and optimization of civil aviation turbofan engines. By simulating the fuel system performance under different design parameters (such as pipeline size, nozzle structure, fuel pump parameters, etc.), the design scheme can be optimized to improve the fuel efficiency of the engine and reduce emissions. For example, by changing parameters such as the aperture of the fuel nozzle, the changes in the nozzle atomization characteristics are observed in the simulation model, and then the nozzle design is optimized so that the fuel can be more fully burned in the combustion chamber, thereby improving the overall performance of the engine.

[0093] It should be understood that all combinations of the aforementioned concepts and the additional concepts described in more detail below can be considered as part of the inventive subject matter of the present disclosure as long as such concepts are not mutually inconsistent. In addition, all combinations of the claimed subject matter are considered as part of the inventive subject matter of the present disclosure.

[0094] The foregoing and other aspects, embodiments and features of the present invention can be more fully understood from the following description in conjunction with the accompanying drawings. Other additional aspects of the present invention, such as the features and / or beneficial effects of the exemplary embodiments, will be apparent from the following description or learned from the practice of the specific embodiments according to the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] The accompanying drawings are not intended to be drawn to scale. In the accompanying drawings, each identical or nearly identical component shown in each figure may be represented by the same reference numeral. For clarity, not every component is labeled in each figure. Embodiments of various aspects of the present invention will now be described by way of example and with reference to the accompanying drawings.

[0096] Figure 1 Schematic diagram of a fuel control simulation method for a civil aviation turbofan engine according to an embodiment of the present invention.

[0097] Figure 2 It is a schematic diagram of the process of spatial discretization of continuous equations according to an embodiment of the present invention.

[0098] Figure 3 3 is a schematic diagram of a process of spatial discretization of the momentum equation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0099] In order to better understand the technical content of the present invention, specific embodiments are given and described as follows in conjunction with the accompanying drawings.

[0100] Various aspects of the present invention are described in this disclosure with reference to the accompanying drawings, in which many illustrative embodiments are shown. The embodiments of the present disclosure are not necessarily intended to include all aspects of the present invention. It should be understood that the various concepts and embodiments introduced above, as well as those described in more detail below, can be implemented in any of many ways, because the concepts and embodiments disclosed by the present invention are not limited to any implementation. In addition, some aspects disclosed by the present invention can be used alone or in any appropriate combination with other aspects disclosed by the present invention.

[0101] {Example 1}

[0102] Combination Figure 1 , Figure 2 , Figure 3As shown, the civil aviation turbofan engine fuel control simulation method according to an embodiment of the present invention belongs to a method for constructing a physical model, which includes the following steps:

[0103] Based on the dynamic changes of fuel in the micro-element section of the fuel pipeline, the fluid movement of fuel in the fuel pipeline is equivalent to the flow of compressible fluid in a one-dimensional pipeline. Combining the inner diameter of the pipeline with the viscosity of the fuel, the fuel pipeline flow equation is established, including the continuity equation and the momentum equation, which are used to characterize the dynamic changes of the fuel pressure in the pipeline along the axial direction.

[0104] The fuel nozzle atomization equation based on the KH instability model is established to describe the breakup and atomization of fuel droplets.

[0105] The pressure-flow characteristic equation of the fuel pump is established based on quadratic polynomial fitting;

[0106] The fuel pipeline flow equation, the pressure-flow characteristic equation of the fuel pump and the fuel nozzle atomization equation are combined to form a fuel system equation group describing the performance of the fuel system of a civil aviation turbofan engine, which is used to solve the pressure distribution, flow rate and nozzle atomization characteristics of the fuel system under different working conditions;

[0107] The fuel pipeline is divided into equally spaced control volumes along the axial direction, and the flow equation of the fuel pipeline is integrated in each control volume to achieve spatial discretization;

[0108] Time discretization of time terms;

[0109] Iteratively solve the discretized fuel system equations.

[0110]

Construction of physical model

[0111] It should be understood that the fuel system of a civil aviation turbofan engine mainly includes fuel pumps, fuel nozzles and other components. For fuel performance simulation, it is considered as a fluid system. A basic physical model is established based on the laws of conservation of mass, energy and momentum. For example, for the flow of fuel in a pipeline, the Bernoulli equation is used to describe the energy state of the fuel.

[0112] Considering the atomization process of the fuel nozzle, a droplet breakup model, such as the KH (Kelvin-Helmholtz) instability model, can be used to describe the breakup and atomization of fuel droplets. It is assumed that there is an unstable wave caused by the velocity difference on the droplet surface. When the wave grows to a certain extent, the droplet will break.

[0113] Furthermore, after the physical model is determined, the physical model describing these processes is established based on the analysis of the actual physical processes of the fuel system, such as the flow of fuel in the pipeline and the atomization of the fuel nozzle, according to the basic physical laws (conservation of mass, conservation of energy, conservation of momentum).

[0114] Furthermore, the established mathematical model is solved through the physical model's geometric parameters (fuel pipeline size, nozzle aperture, etc.), physical parameters (fuel density, surface, etc.), boundary conditions and initial conditions, and the continuous mathematical model is discretized to facilitate numerical calculations on a computer. Through discretization methods (such as the finite volume method) and solution algorithms (such as the Newton-Raphson iteration method), solutions that meet the convergence criteria are obtained through iterative calculations to determine the performance parameters of the fuel system under various operating conditions.

[0115]

Construction of mathematical model

[0116] In an embodiment of the present invention, establishing a fuel pipeline flow equation according to a physical model includes the following steps:

[0117] Based on the law of conservation of momentum, the relationship between the force and acceleration of the fuel in the pipeline is analyzed. Considering the dynamic changes of the fuel in the micro-element section of the fuel pipeline, the relationship between the pressure difference, friction and the mass of the fuel can be described as follows:

[0118]

[0119] Among them, ΔL represents the length of the infinitesimal segment, ρ is the fuel density, v is the flow velocity, and A is the cross-sectional area of ​​the fuel pipe;

[0120] For steady flow, the above relationship is simplified to a momentum equation that includes dynamic pressure loss and resistance loss along the way, expressed as follows:

[0121]

[0122] Where x is the coordinate along the pipeline direction, D is the inner diameter of the pipeline, and μ is the viscosity of the fuel;

[0123] As shown in the above equation, the pressure change in the pipeline along the axial direction, the first term represents the pressure loss (dynamic pressure loss) caused by the change in flow velocity, and the second term represents the pressure loss (along-the-way resistance loss) caused by viscous friction;

[0124] The fluid motion of fuel in the fuel pipeline is equivalent to the flow of compressible fluid in a one-dimensional pipeline, and the flow control equation of compressible fluid is established, which is expressed as:

[0125]

[0126] Further simplification, the continuous equation for fuel flow control is obtained, which is expressed as:

[0127]

[0128] Therefore, the conservation of fuel mass in the pipeline is described by the continuity equation, that is, the difference in the mass of fuel flowing into and out of a certain control volume per unit time is equal to the rate of change of the fuel mass in the control volume.

[0129] As an optional embodiment, the process of establishing the fuel nozzle atomization equation based on the KH instability model includes:

[0130] Assume that there are tiny fluctuations on the surface of the fuel droplet, with a wavelength of λ; when the difference between the fluctuation speed on the surface of the fuel droplet and the flow velocity inside the droplet reaches a certain level, the droplet will break.

[0131] According to linear stability analysis, there is a critical wavelength λ c , when the wave wavelength is greater than the critical wavelength λ c When , the fluctuations will grow and cause the droplets to break;

[0132] Based on the critical wavelength λ c The fuel nozzle atomization equation is established with the radius R of the droplet, the surface tension σ, and the density difference Δρ between the liquid and the gas:

[0133]

[0134] Where v represents the relative velocity between the fuel droplet and the surrounding gas;

[0135] When the fluctuation wavelength on the surface of the fuel droplets meets the breakup conditions, the droplets split and the atomization process is realized.

[0136] In an embodiment of the present invention, the process of establishing the pressure-flow characteristic equation of the fuel pump based on quadratic polynomial fitting includes:

[0137] By fitting the experimental data with a quadratic polynomial, the pressure-flow characteristic equation of the fuel pump is obtained, which is expressed as:

[0138] ΔP pump =aQ 2 +bQ+c;

[0139] Among them, ΔP pump represents the pressure rise provided by the fuel pump, Q represents the flow rate through the fuel pump, and a, b, and c are fitting coefficients, which are obtained by fitting the experimental test data of the fuel pump under different working conditions.

[0140] As an optional implementation, the inlet and outlet pressure differences of the fuel pump can be measured at a series of different rotation speeds and flow rates, and then the value of the fitting coefficient can be determined using a fitting method such as the least squares method, so that the error between the fitting equation and the experimental data is minimized.

[0141] It should be understood that in the embodiment of the present invention, when combined with the entire fuel system, the fuel flow rate Q at the nozzle nozzle and nozzle front pressure P nozzle It is related to the nozzle characteristics (such as aperture, spray cone angle, etc.) and can be described by empirical formulas or formulas derived based on the nozzle atomization model, such as Where g is a coefficient related to the nozzle structure.

[0142] In an embodiment of the present invention, Figure 2 As shown, the fuel pipeline flow equations are integrated over each control volume, including the spatial discretization of the continuity equations, including the following process:

[0143] First, the fuel pipeline with a total length of L is divided into N control volumes with equal spacing along the axial direction. The length of each control volume is denoted as Δx i , i=1,2,3,…,N,

[0144] Determine the node position corresponding to each control volume, take the center position of the control volume as the node, and the physical quantity on the node will be used as the unknown quantity for solving the subsequent discrete equations;

[0145] For the continuity equation Integrating over each control volume i, according to the Gaussian divergence theorem, we get:

[0146]

[0147] Among them, V i is the volume of the control volume, A i is the surface area of ​​the control volume, is the surface normal vector;

[0148] The density in the control volume is approximately equivalent to the value ρ at the central node of the control volume i , then the mass in the control volume Approximately expressed as ρ i V i ;

[0149] Derivative with respect to time It is further described as

[0150] If the volume of the control volume is considered to be a fixed value that does not change with time, it can be further simplified to:

[0151]

[0152] This realizes the discrete process of density term;

[0153] for represents the mass flow through the control volume surface; in the case of one-dimensional flow in a pipeline, the control volume includes two surfaces, namely the inlet surface and the outlet surface. The flow term is decomposed into the difference between the flow through the inlet surface and the outlet surface, and the flow velocity and density at the interface are approximated by the central difference format to realize the discretization of the flow term, which is expressed as:

[0154] (ρ i+1 / 2 v i+1 / 2 -ρ i-1 / 2 v i-1 / 2 )A;

[0155] Among them, ρ i+1 / 2 and ρ i-1 / 2 They represent the density at the interface at i+1 / 2 and i-1 / 2 of the control volume interface, respectively, and v i+1 / 2 With v i-1 / 2 They represent the values ​​of the density at the interface at i+1 / 2 and i-1 / 2 of the control volume interface respectively;

[0156] Finally, the discretized form of the continuous equation is:

[0157]

[0158] Further sorting can be obtained:

[0159]

[0160] Among them, V i =AΔx i ;

[0161] Thus, the discrete continuous equation expression is obtained, which is equivalent to:

[0162]

[0163] As an optional implementation, combining Figure 3 As shown, the fuel pipeline flow equations are integrated on each control volume, including the spatial discretization of the momentum equation, including the following process:

[0164] For the momentum equation The integration is performed on each control volume i, including the discretization of the pressure gradient term, the dynamic pressure loss term, and the resistance loss term along the way, respectively:

[0165] (1) Using the central difference format, the pressure P at the control volume interface i+1 / 2 is i+1 / 2 Approximately:

[0166]

[0167] The pressure P at the control volume interface i-1 / 2 i-1 / 2Approximately:

[0168]

[0169] Then the pressure gradient term After discretization, it is expressed as:

[0170]

[0171] (2) Using the central difference format, the flow velocity v at the control volume interface i+1 / 2 is i+1 / 2 Approximately:

[0172]

[0173] The flow velocity v at the control volume interface i-1 / 2 i-1 / 2 Approximately:

[0174]

[0175] Then in the control volume i, the dynamic pressure loss term After discretization, it is expressed as:

[0176] Expand further The discretized expression is:

[0177] (3) In the control volume i, the drag loss term along the way is After discretization, it is expressed as:

[0178] Expand further i+1 / 2 , can be obtained

[0179] (4) Combining the discrete expressions of the pressure gradient term, the dynamic pressure loss term, and the drag loss term along the path, the discrete momentum equation within the control volume i is obtained, which is expressed as:

[0180]

[0181] Therefore, the momentum equation is converted into an equation about the node pressure and flow velocity through spatial discretization, which is equivalently expressed as.

[0182] As an optional implementation, the equivalent expression of the continuous equation is obtained after spatial discretization: It is a semi-discrete equation about density and flow velocity. By time discretizing the time derivative term, the density variation with time is solved.

[0183] As an optional implementation, time discretization is performed by an explicit Euler method, or by an implicit Crank-Nicholson method.

[0184] Taking the explicit Euler method for time discretization as an example, the continuous equation obtained after spatial discretization is The process of time discretization for the equations of the time derivative of density and the density and velocity related functions includes:

[0185] First, determine the discrete formula, that is, the time discrete formula of the explicit Euler method, which is expressed as:

[0186]

[0187] Where n is the time step number and h is the time step length.

[0188] Then, according to the known density at the nth time step and flow rate Calculation Function The value of

[0189] Then calculate the density of the next time step n+1 based on the total That is, through Add the time step h and The product of is obtained.

[0190] In this embodiment, the explicit Euler method needs to consider the stability condition. Generally speaking, for equations with convection characteristics, the time step h should satisfy the Courant condition, for example where Δx i represents the spatial step length, that is, the length of each control volume, and v represents the flow velocity. If this condition is not met, the numerical calculation will be unstable and non-physical oscillation will occur.

[0191] [Iterative solution of the joint system of equations]

[0192] Combination Figure 1 As an optional implementation, the process of iteratively solving the discretized fuel system equations includes the following steps:

[0193] Representing vectors as vectors N represents the total number of control volumes, i.e. the number of nodes, ρ i 、v i , P i denote the density, flow velocity and pressure at the i-th control volume node respectively;

[0194] The system of simultaneous equations is described as is a function vector that includes all equations such as the above pipeline flow equation, fuel pump characteristic equation and fuel nozzle atomization equation;

[0195] First calculate the Jacobian matrix

[0196] In each iteration, assuming the current number of iterations is k, it is known that calculate and

[0197] Then solve the linear equations Get the increment

[0198] Update variables

[0199] Check the convergence criterion by calculating the isorm If it is less than the set convergence threshold ∈, for example, the value is 10 -6 , the iteration is considered to have converged and a solution is obtained; otherwise, continue to the next iteration, i.e. set k = k + 1, and repeat the above steps until the convergence condition is met.

[0200] In this embodiment, the fuel pump characteristic equation is solved by successive approximation. First, an initial flow rate is assumed, and then the iterative formula is used. Where b≠0, gradually approaching the actual flow value.

[0201]

Computer System

[0202] In conjunction with the implementation of the civil aviation turbofan engine fuel control simulation method of the above embodiment, a computer system is also proposed according to the present invention, including: one or more processors; and a memory.

[0203] The aforementioned memory can be used to store operable instructions.

[0204] Among them, when these instructions are executed by one or more processors, the one or more processors are caused to perform operations, and the operations include the process of executing the civil aviation turbofan engine fuel control simulation method of the aforementioned embodiment.

[0205] Although the present invention has been disclosed as above with preferred embodiments, it is not intended to limit the present invention. A person with ordinary knowledge in the technical field to which the present invention belongs may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention shall be determined by the definition of the claims.

Claims

1. A civil aviation turbofan engine fuel control simulation method, characterized in that: include: Based on the dynamic changes of fuel in the micro-element section of the fuel pipeline, the fluid movement of fuel in the fuel pipeline is equivalent to the flow of compressible fluid in a one-dimensional pipeline. Combining the inner diameter of the pipeline with the viscosity of the fuel, the fuel pipeline flow equation is established, including the continuity equation and the momentum equation, which are used to characterize the dynamic changes of the fuel pressure in the pipeline along the axial direction. The fuel nozzle atomization equation based on the KH instability model is established to describe the breakup and atomization of fuel droplets. The pressure-flow characteristic equation of the fuel pump is established based on quadratic polynomial fitting; The fuel pipeline flow equation, the pressure-flow characteristic equation of the fuel pump and the fuel nozzle atomization equation are combined to form a fuel system equation group describing the performance of the fuel system of a civil aviation turbofan engine, which is used to solve the pressure distribution, flow rate and nozzle atomization characteristics of the fuel system under different working conditions; The fuel pipeline is divided into equally spaced control volumes along the axial direction, and the flow equation of the fuel pipeline is integrated in each control volume to achieve spatial discretization; Discretize the time term in time; Iteratively solve the discretized fuel system equations.

2. The civil aviation turbofan engine fuel control simulation method according to claim 1, characterized in that: The fuel pipeline flow equation establishment process includes: Based on the dynamic changes of fuel in the micro-element section of the fuel pipeline, the relationship between the pressure difference, friction and the mass of the fuel is described as follows: Among them, ΔL represents the length of the infinitesimal segment, ρ is the fuel density, v is the flow velocity, and A is the cross-sectional area of ​​the fuel pipe; For steady flow, the above relationship is simplified to a momentum equation that includes dynamic pressure loss and resistance loss along the way, expressed as follows: Where x is the coordinate along the pipeline direction, D is the inner diameter of the pipeline, and μ is the viscosity of the fuel; The fluid motion of fuel in the fuel pipeline is equivalent to the flow of compressible fluid in a one-dimensional pipeline, and the flow control equation of compressible fluid is established, which is expressed as: Further simplification, the continuous equation for fuel flow control is obtained, which is expressed as:

3. The civil aviation turbofan engine fuel control simulation method according to claim 1, characterized in that: The process of establishing the fuel nozzle atomization equation based on the KH instability model includes: Assume that there are tiny fluctuations on the surface of the fuel droplet, with a wavelength of λ; when the difference between the fluctuation speed on the surface of the fuel droplet and the flow velocity inside the droplet reaches a certain level, the droplet will break. According to linear stability analysis, there is a critical wavelength λ c , when the wave wavelength is greater than the critical wavelength λ c When , the fluctuations will grow and cause the droplets to break; Based on the critical wavelength λ c The fuel nozzle atomization equation is established with the radius R of the droplet, the surface tension σ, and the density difference Δρ between the liquid and the gas: Where v represents the relative velocity between the fuel droplet and the surrounding gas; When the fluctuation wavelength on the surface of the fuel droplets meets the breakup conditions, the droplets split and the atomization process is realized.

4. The civil aviation turbofan engine fuel control simulation method according to claim 1, characterized in that: The process of establishing the pressure-flow characteristic equation of the fuel pump based on quadratic polynomial fitting includes: By fitting the experimental data with a quadratic polynomial, the pressure-flow characteristic equation of the fuel pump is obtained, which is expressed as: △P pump =aQ 2 +bQ+c; Among them, ΔP pump represents the pressure rise provided by the fuel pump, Q represents the flow rate through the fuel pump, and a, b, and c are fitting coefficients, which are obtained by fitting the experimental test data of the fuel pump under different working conditions.

5. The civil aviation turbofan engine fuel control simulation method according to claim 1, characterized in that: The integration of the fuel pipeline flow equation on each control volume, including the spatial discretization of the continuity equation, includes the following process: First, the fuel pipeline with a total length of L is divided into N control volumes with equal spacing along the axial direction. The length of each control volume is denoted as Δx i , i=1,2,3,…,N, Determine the node position corresponding to each control volume, take the center position of the control volume as the node, and the physical quantity on the node will be used as the unknown quantity for solving the subsequent discrete equations; For the continuity equation Integrating over each control volume i, according to the Gaussian divergence theorem, we get: Among them, V i is the volume of the control volume, A i is the surface area of ​​the control volume, is the surface normal vector; The density in the control volume is approximately equivalent to the value ρ at the central node of the control volume i , then the mass in the control volume Approximately expressed as ρ i V i ; Derivative with respect to time It is further described as If the volume of the control volume is considered to be a fixed value that does not change with time, it can be further simplified to: This achieves the discretization of density terms; for represents the mass flow through the control volume surface; in the case of one-dimensional flow in a pipeline, the control volume includes two surfaces, namely the inlet surface and the outlet surface. The flow term is decomposed into the difference between the flow through the inlet surface and the outlet surface, and the flow velocity and density at the interface are approximated by the central difference format to realize the discretization of the flow term, which is expressed as: (r i+1 / 2 u i+1 / 2 -r i-1 / 2 v i-1 / 2 )A; Among them, ρ i+1 / 2 and ρ i-1 / 2 They represent the density at the interface at i+1 / 2 and i-1 / 2 of the control volume interface, respectively, and v i+1 / 2 With v i-1 / 2 They represent the values ​​of the density at the interface at i+1 / 2 and i-1 / 2 of the control volume interface respectively; Finally, the discretized form of the continuous equation is: Further sorting can be obtained: Among them, V i =AΔx i ; Thus, the discrete continuous equation expression is obtained, which is equivalent to:

6. The civil aviation turbofan engine fuel control simulation method according to claim 5, characterized in that: The integration of the fuel pipeline flow equation on each control volume, including the spatial discretization of the momentum equation, includes the following process: For the momentum equation The integration is performed on each control volume i, including the discretization of the pressure gradient term, the dynamic pressure loss term, and the resistance loss term along the way, respectively: (1) Using the central difference format, the pressure P at the control volume interface i+1 / 2 is i+1 / 2 Approximately: The pressure P at the control volume interface i-1 / 2 i-1 / 2 Approximately: Then the pressure gradient term After discretization, it is expressed as: (2) Using the central difference format, the flow velocity v at the control volume interface i+1 / 2 is i+1 / 2 Approximately: The flow velocity v at the control volume interface i-1 / 2 i-1 / 2 Approximately: Then in the control volume i, the dynamic pressure loss term After discretization, it is expressed as: Expand further The discretized expression is: (3) In the control volume i, the drag loss term along the way is After discretization, it is expressed as: Expand further i+1 / 2 , can be obtained (4) Combining the discrete expressions of the pressure gradient term, the dynamic pressure loss term, and the drag loss term along the path, the discrete momentum equation within the control volume i is obtained, which is expressed as: Therefore, the momentum equation is converted into an equation about the node pressure and flow velocity through spatial discretization, which is equivalently expressed as.

7. The civil aviation turbofan engine fuel control simulation method according to claim 6, characterized in that: After spatial discretization, the equivalent expression of the continuous equation is obtained It is a semi-discrete equation about density and flow velocity. By time discretizing the time derivative term, the density variation with time is solved.

8. The civil aviation turbofan engine fuel control simulation method according to claim 7, characterized in that: Time discretization is performed by explicit Euler method or implicit Crank-Nicholson method.

9. The civil aviation turbofan engine fuel control simulation method according to any one of claims 1 to 8, characterized in that: The iterative solution of the discretized fuel system equations includes: Representing vectors as vectors N represents the total number of control volumes, i.e. the number of nodes, ρ i 、v i , P i denote the density, flow velocity and pressure at the i-th control volume node respectively; The system of simultaneous equations is described as First calculate the Jacobian matrix In each iteration, assuming the current number of iterations is k, it is known that calculate and Then solve the linear equations Get the increment Update variables Check the convergence criterion by calculating the isorm If it is less than the set convergence threshold ∈, the iteration is considered to have converged and a solution is obtained; otherwise, continue to the next iteration, that is, set k = k + 1, and repeat the above steps until the convergence condition is met.

10. The civil aviation turbofan engine fuel control simulation method according to any one of claims 1 to 8, characterized in that: The fuel pump characteristic equation is solved by successive approximation. First, an initial flow rate is assumed, and then the iterative formula is used. Where b≠0, gradually approaching the actual flow value.

11. A computer system, characterized in that: include: one or more processors; as well as Memory, storing instructions that can be operated; Wherein, when the instruction is executed by one or more processors, the one or more processors are caused to perform operations, wherein the operations include the process of executing the civil aviation turbofan engine fuel control simulation method as described in any one of claims 1-10.

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