Method and system for internally cooling turbine blade of heavy gas turbine

Abstract

The invention relates to the technical field of internal cooling of turbine blades, in particular to a method and system for internal cooling of a turbine blade of a heavy gas turbine, and the method comprises the following steps: S1, correcting a Fourier heat transfer physical model by introducing relaxation parameters to obtain a corrected heat transfer physical model, and deducing to obtain a corresponding control equation; s2, discretizing the control equation, and converting the control equation into a discrete equation; s3, performing numerical simulation on internal cooling of the turbine blade of the heavy gas turbine according to the discrete equation; and S4, performing internal cooling on the turbine blade of the heavy gas turbine according to a numerical simulation result. By adopting the method, the turbine blade of the heavy-duty gas turbine can be internally cooled according to an accurate numerical simulation result.

Description

Technical Field

[0001] The present invention relates to the technical field of internal cooling of turbine blades, and in particular to a method and system for internal cooling of turbine blades of heavy-duty combustion engines. Background Art

[0002] In the field of power generation and drive, advanced heavy-duty gas turbines are undoubtedly the shining "crown jewel", which carries the core power of the industry. These high-performance gas turbine engines operate in extremely high temperature environments (between 1200 and 1500 degrees Celsius) in order to improve thermal efficiency and power output. With the rapid development of gas turbine technology, the inlet temperature of the turbine is also gradually rising, and with it the heat load on the turbine blades. In order to ensure the durability of the blades and extend their service life, strict control of the tolerance level and changes of the internal temperature of the blade material has become a crucial technical challenge. It cannot be ignored that the actual working temperature of the blades is far higher than the limit temperature that the metal can withstand. Therefore, how to efficiently and safely cool the blades has become the key to the stable operation of the gas turbine. Summary of the invention

[0003] The present invention provides a method and system for internal cooling of heavy-duty gas engine turbine blades to solve the problems existing in the above-mentioned prior art. The technical solution is as follows:

[0004] In one aspect, a method for internally cooling a heavy-duty gas engine turbine blade is provided, comprising:

[0005] S1. By introducing relaxation parameters, the Fourier heat transfer physical model is modified to obtain a modified heat transfer physical model, and the corresponding control equation is derived;

[0006] S2, discretizing the control equation and converting it into a discrete equation;

[0007] S3. performing numerical simulation on the internal cooling of the turbine blade of the heavy-duty gas engine according to the discrete equation;

[0008] S4. Based on the results of numerical simulation, the heavy-duty gas engine turbine blades are internally cooled.

[0009] Optionally, the modified heat transfer physical model is Among them, q represents tensor, t represents time, D represents thermal conductivity, T represents temperature, and λ is the introduced relaxation parameter. At this time, the propagation speed of the thermal signal is is a finite value, controlled by the relaxation parameter λ;

[0010] The control equation is: Where ρ represents the fluid density, represents the flow velocity vector of the fluid, k is the thermal conductivity, c p represents the specific heat capacity of the fluid, It is a new second-order time derivative term added to the control equation corresponding to the Fourier heat transfer physical model.

[0011] Optionally, the S2 specifically includes:

[0012] The control equation is expanded at the nth time layer, and the newly added second-order time derivative term in the control equation is Use the central difference of the previous time layer to approximate and add the newly added second-order time derivative The previous time layer is discretized as: and is regarded as the source term of the control equation, which is discretized as: Among them, the discretization method of the second-order time derivative term is: τ represents the time step.

[0013] Optionally, the S3 specifically includes:

[0014] Determine the internal cooling research area of ​​the heavy-duty gas turbine turbine blade, mesh the research area, and use Fluent-Meshing's latest Poly-Hexcore mesh technology to perform local encryption;

[0015] According to the discretized control equation, a source term UDF plug-in is written for the divided grid using Fluent software to perform numerical simulation.

[0016] Optionally, the method of discretizing the control equation in S2 can analyze the error, Using Taylor's formula in mathematics, we get:

[0017]

[0018] Where f'(ξ) represents the derivative of f(ξ) with respect to t, and ξ represents t n-1 With t n For any value in , it can be seen from the formula that: for the second-order time derivative term, the value of the n layer can be approximated by using the value of the n-1 layer, and the error is controllable.

[0019] In another aspect, a system for internally cooling a heavy-duty combustion engine turbine blade is provided, the system comprising:

[0020] A correction module is used to correct the Fourier heat transfer physical model by introducing relaxation parameters to obtain a corrected heat transfer physical model and derive the corresponding control equation;

[0021] A discretization module, used for discretizing the control equation and converting it into a discrete equation;

[0022] A numerical simulation module, used for numerically simulating the internal cooling of the turbine blade of the heavy-duty gas engine according to the discrete equation;

[0023] The internal cooling module is used to perform internal cooling on the turbine blades of the heavy-duty gas engine according to the results of numerical simulation.

[0024] Optionally, the modified heat transfer physical model is Among them, q represents tensor, t represents time, D represents thermal conductivity, T represents temperature, and λ is the introduced relaxation parameter. At this time, the propagation speed of the thermal signal is is a finite value, controlled by the relaxation parameter λ;

[0025] The control equation is: Where ρ represents the fluid density, represents the flow velocity vector of the fluid, k is the thermal conductivity, c p represents the specific heat capacity of the fluid, It is a new second-order time derivative term added to the control equation corresponding to the Fourier heat transfer physical model.

[0026] Optionally, the discretization module is specifically used to:

[0027] The control equation is expanded at the nth time layer, and the newly added second-order time derivative term in the control equation is Use the central difference of the previous time layer to approximate and add the newly added second-order time derivative The previous time layer is discretized as: and is regarded as the source term of the control equation, which is discretized as: Among them, the discretization method of the second-order time derivative term is: τ represents the time step.

[0028] Optionally, the numerical simulation module is specifically used to:

[0029] Determine the internal cooling research area of ​​the heavy-duty gas turbine turbine blade, mesh the research area, and use Fluent-Meshing's latest Poly-Hexcore mesh technology to perform local encryption;

[0030] According to the discretized control equation, a source term UDF plug-in is written for the divided grid using Fluent software to perform numerical simulation.

[0031] Optionally, the discretization module discretizes the control equation to analyze the error, Using Taylor's formula in mathematics, we get:

[0032]

[0033] Where f'(ξ) represents the derivative of f(ξ) with respect to t, and ξ represents t n-1 With t n For any value in , it can be seen from the formula that: for the second-order time derivative term, the value of the n layer can be approximated by using the value of the n-1 layer, and the error is controllable.

[0034] On the other hand, an electronic device is provided, comprising a processor and a memory, wherein the memory stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the above-mentioned method for internal cooling of heavy-duty gas engine turbine blades.

[0035] On the other hand, a computer-readable storage medium is provided, wherein at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement the above-mentioned method for internal cooling of a heavy-duty gas engine turbine blade.

[0036] The beneficial effects brought about by the technical solution provided by the present invention include at least:

[0037] By adopting the present invention, the internal cooling of the turbine blades of the heavy-duty gas engine can be performed according to the accurate numerical simulation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0039] Figure 1 This is a flow chart of a method for internally cooling a heavy-duty gas engine turbine blade provided by an embodiment of the present invention;

[0040] Figure 2 is a schematic diagram of mesh division for impingement cooling provided by an embodiment of the present invention;

[0041] Figure 3 is a schematic diagram of grid division for column rib cooling provided by an embodiment of the present invention;

[0042] Figure 4 is a schematic diagram of mesh division of a cooling grid with ribbed channels provided in an embodiment of the present invention;

[0043] Figure 5This is a block diagram of a system for internal cooling of a heavy-duty gas engine turbine blade provided by an embodiment of the present invention;

[0044] Figure 6 It is a structural schematic diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to make the technical problems, technical solutions and advantages to be solved by the present invention more clear, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0046] The embodiment of the present invention provides a method for internal cooling of a heavy-duty gas engine turbine blade, which can be implemented by an electronic device, which can be a terminal or a server. Figure 1 A flow chart of a method for internally cooling a heavy-duty gas engine turbine blade is shown, and the processing flow of the method may include the following steps:

[0047] S1. By introducing relaxation parameters, the Fourier heat transfer physical model is modified to obtain a modified heat transfer physical model, and the corresponding control equation is derived;

[0048] Conduction, convection and thermal radiation are three forms of heat transfer. In the study of heat transfer problems, the most classic heat transfer physical model is the Fourier heat transfer physical model based on Fourier's law: q = -D▽T, where q represents the tensor, D represents thermal conductivity, and T represents temperature. Many numerical simulations involving heat transfer problems are based on the Fourier heat transfer physical model, and the problem of internal cooling of blades is no exception. The corresponding control equation is: Where ρ represents the fluid density, t represents the time, and T represents the temperature. represents the flow velocity vector of the fluid, k is the thermal conductivity, c p Represents the specific heat capacity of the fluid. However, the study found that the governing equation derived from the classical Fourier law shows the paradox of infinite propagation speed of thermal signals, which is contrary to actual experience.

[0049] To this end, the embodiment of the present invention modifies the Fourier heat transfer physical model by introducing a relaxation parameter to obtain a modified heat transfer physical model, and derives the corresponding control equation. The modified heat transfer physical model is: Among them, q represents tensor, t represents time, D represents thermal conductivity, T represents temperature, and λ is the introduced relaxation parameter. At this time, the propagation speed of the thermal signal is is a finite value, controlled by the relaxation parameter λ;

[0050] The control equation is: Where ρ represents the fluid density, represents the flow velocity vector of the fluid, k is the thermal conductivity, c p represents the specific heat capacity of the fluid, It is a new second-order time derivative term added to the control equation corresponding to the Fourier heat transfer physical model.

[0051] S2, discretizing the control equation and converting it into a discrete equation;

[0052] The continuous control equations need to be converted into discrete equations through discretization methods. The choice of discretization method has a direct impact on the accuracy and efficiency of the simulation.

[0053] Optionally, the S2 specifically includes:

[0054] The control equation is expanded at the nth time layer, and the newly added second-order time derivative term in the control equation is Use the central difference of the previous time layer to approximate and add the newly added second-order time derivative The previous time layer is discretized as: and is regarded as the source term of the control equation, which is discretized as: Among them, the discretization method of the second-order time derivative term is: τ represents the time step.

[0055] The advantage of the above discretization method is that the newly added second-order time derivative term can be converted into a known source term, and the above method can analyze the error.

[0056] Optionally, the method of discretizing the control equation in S2 can analyze the error, Using Taylor's formula in mathematics, we get:

[0057]

[0058] Where f'(ξ) represents the derivative of f(ξ) with respect to t, and ξ represents t n-1 With t n For any value in , it can be seen from the formula that: for the second-order time derivative term, the value of the n layer can be approximated by using the value of the n-1 layer, and the error is controllable.

[0059] In the process of numerical simulation, the control equation corresponding to the modified heat transfer physical model cannot be directly obtained by Fluent commercial software at the current moment. The embodiment of the present invention uses Taylor series expansion to analyze the error, uses the second-order central difference at the previous moment to approximate the second-order derivative term at the current moment, and regards it as a known source term. In this way, the error can be effectively controlled to ensure the accuracy of the numerical simulation.

[0060] S3. performing numerical simulation on the internal cooling of the turbine blade of the heavy-duty gas engine according to the discrete equation;

[0061] Optionally, the S3 specifically includes:

[0062] Determine the internal cooling research area of ​​the heavy-duty gas turbine turbine blade, mesh the research area, and use Fluent-Meshing's latest Poly-Hexcore mesh technology to perform local encryption;

[0063] According to the discretized control equation, a source term UDF plug-in is written for the divided grid using Fluent software to perform numerical simulation.

[0064] At present, turbine blade cooling technology can be classified into external cooling and internal cooling according to the cooling position. External cooling mainly includes film cooling and divergent cooling. Internal cooling mainly includes impingement cooling, rib column cooling and fin turbulence cooling. In the design of internal cooling of blades, impingement cooling technology has been widely used for the leading edge area where the heat load is most concentrated. This method guides the cold air to a specific impingement hole through the duct inside the stationary blade or the flow channel design in the moving blade, so that it is directly shot to the inner surface (target surface) of the blade. This impingement jet method can significantly improve the local heat transfer coefficient and effectively cope with the high heat load in the leading edge area. However, since the trailing edge structure is relatively weak and cannot withstand the complex impingement cooling structure, a column-rib cooling scheme is usually adopted, namely rib column cooling and ribbed cooling. A series of column-rib structures perpendicular to the flow direction of the cold air are arranged in the limited space of the trailing edge of the blade to enhance the cooling effect. These columns-ribs not only optimize the flow path of the cold air, but also increase the contact area with the blade surface, thereby improving the cooling efficiency. In the middle part of the blade, fins are added to change the motion characteristics of the cold air. These fins transform the original laminar flow of cold air into turbulent flow, increasing the instability of the flow and thus improving the heat exchange efficiency. At the same time, the addition of fins also increases the fluid-solid heat exchange area, further enhancing the cooling effect. These carefully designed cooling solutions ensure that the blades can be fully cooled in different areas, ensuring their long-term stable operation.

[0065] The analysis of the internal cooling problem of turbine blades is often performed by numerical simulation using Fluent commercial software. However, the control equation corresponding to the modified heat transfer physical model becomes more complicated, changing from a parabolic type to a hyperbolic type. A key problem, which is also the focus and difficulty of solving the problem, is that the core program inside Fluent commercial software is not open to the public, and it becomes infeasible to directly discretize it. However, Fluent provides users with custom functions that can be written in C language to expand the functions of Fluent, including source term UDF. Therefore, the embodiment of the present invention uses Fluent software to write a source term UDF plug-in for the divided grid according to the discretized control equation to perform numerical simulation. This method not only optimizes the built-in control equation of Fluent, but also improves its applicability in specific application scenarios.

[0066] In the simulation of the internal cooling problem of turbine blades, mesh generation is a complex but crucial process, which directly affects the accuracy and computational efficiency of the simulation. In fluid simulation, there has always been a debate between hexahedron and tetrahedron meshes in various aspects of the simulation, but basically a consensus can be reached: that is, "hexahedron is better than tetrahedron in the solution process (although it is more difficult to divide)". The embodiment of the present invention prefers to use as many hexahedron meshes as possible in the calculation, which can not only effectively reduce the number of meshes, but also may reduce the impact of pseudo-diffusion. Therefore, the embodiment of the present invention does not use traditional structured meshes, but uses Fluent-Meshing's latest Poly-Hexcore mesh technology for local encryption. This mesh technology enables hexahedron meshes and polyhedron meshes to achieve common node connection (no interface surface). By increasing the proportion of hexahedral meshes, Poly-Hexcore technology not only improves the accuracy of the mesh, but also optimizes the number of meshes and reduces the consumption of computing resources. This technology also specifically supports the division of boundary layer meshes, so that the layered Poly mesh near the wall, the pure Poly mesh in the transition area, and the hexahedral mesh in the core area can work together to form an efficient calculation area filling strategy.

[0067] The following is a schematic diagram of the mesh generation for the three internal cooling methods:

[0068] like Figure 2 As shown in the figure, the impingement cooling grid is locally encrypted near the impingement hole, and three boundary layers are set on the relevant wall surfaces.

[0069] like Figure 3 As shown in the figure, the column-fin cooling grid is locally encrypted near the column-fin, and a boundary layer is also set on the relevant wall surface.

[0070] like Figure 4As shown in the figure, the mesh of the ribbed channel cooling grid is divided regularly near the ribs, the surface is mainly polygonal, and the internal grid is filled with hexahedral grids.

[0071] S4. Based on the results of numerical simulation, the heavy-duty gas engine turbine blades are internally cooled.

[0072] The embodiment of the present invention uses a modified heat transfer physical model to numerically simulate the heat transfer inside the turbine blade, which can better restore the actual heat transfer situation. Under steady-state research, the numerical calculation results of the three cooling methods calculated by the modified heat transfer physical model are within ±10% compared with the experimental results. Furthermore, the embodiment of the present invention uses the modified heat transfer physical model to conduct transient simulation experiments on the three cooling methods. The transient heat transfer data has a better fit effect than the Fourier heat transfer physical model and the experimental results.

[0073] like Figure 5 As shown, an embodiment of the present invention further provides a system for internally cooling a turbine blade of a heavy-duty gas engine, the system comprising:

[0074] A correction module 510 is used to correct the Fourier heat transfer physical model by introducing a relaxation parameter to obtain a corrected heat transfer physical model and derive a corresponding control equation;

[0075] A discretization module 520, used for discretizing the control equation and converting it into a discrete equation;

[0076] A numerical simulation module 530, for numerically simulating the internal cooling of the turbine blade of the heavy-duty gas engine according to the discrete equation;

[0077] The internal cooling module 540 is used to perform internal cooling on the turbine blades of the heavy-duty gas engine according to the results of the numerical simulation.

[0078] Optionally, the modified heat transfer physical model is Among them, q represents tensor, t represents time, D represents thermal conductivity, T represents temperature, and λ is the introduced relaxation parameter. At this time, the propagation speed of the thermal signal is is a finite value, controlled by the relaxation parameter λ;

[0079] The control equation is: Where ρ represents the fluid density, represents the flow velocity vector of the fluid, k is the thermal conductivity, c p represents the specific heat capacity of the fluid, It is a new second-order time derivative term added to the control equation corresponding to the relative Fourier heat transfer physical model.

[0080] Optionally, the discretization module is specifically used to:

[0081] The control equation is expanded at the nth time layer, and the newly added second-order time derivative term in the control equation is Use the central difference of the previous time layer to approximate and add the newly added second-order time derivative The previous time layer is discretized as: and is regarded as the source term of the control equation, which is discretized as: Among them, the discretization method of the second-order time derivative term is: τ represents the time step.

[0082] Optionally, the numerical simulation module is specifically used to:

[0083] Determine the internal cooling research area of ​​the heavy-duty gas turbine turbine blade, mesh the research area, and use Fluent-Meshing's latest Poly-Hexcore mesh technology to perform local encryption;

[0084] According to the discretized control equation, a source term UDF plug-in is written for the divided grid using Fluent software to perform numerical simulation.

[0085] Optionally, the discretization module discretizes the control equation to analyze the error, Using Taylor's formula in mathematics, we get:

[0086]

[0087] Where f'(ξ) represents the derivative of f(ξ) with respect to t, and ξ represents t n-1 With t n For any value in , it can be seen from the formula that: for the second-order time derivative term, the value of the n layer can be approximated by using the value of the n-1 layer, and the error is controllable.

[0088] An embodiment of the present invention provides a system for internally cooling a heavy-duty gas engine turbine blade. Its functional structure corresponds to a method for internally cooling a heavy-duty gas engine turbine blade provided by an embodiment of the present invention, and will not be described in detail here.

[0089] Figure 6It is a structural schematic diagram of an electronic device 600 provided in an embodiment of the present invention. The electronic device 600 may have relatively large differences due to different configurations or performances, and may include one or more processors (central processing units, CPU) 601 and one or more memories 602, wherein at least one instruction is stored in the memory 602, and the at least one instruction is loaded and executed by the processor 601 to implement the steps of the above-mentioned method for internal cooling of heavy-duty gas engine turbine blades.

[0090] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions, which can be executed by a processor in a terminal to perform the above method for internally cooling a heavy-duty gas engine turbine blade. For example, the computer-readable storage medium can be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, etc.

[0091] A person skilled in the art will understand that all or part of the steps to implement the above embodiments may be accomplished by hardware or by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a disk or an optical disk, etc.

[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for internal cooling of a heavy-duty gas engine turbine blade, characterized in that: The method comprises: S1. By introducing relaxation parameters, the Fourier heat transfer physical model is modified to obtain a modified heat transfer physical model, and the corresponding control equation is derived; S2, discretizing the control equation and converting it into a discrete equation; S3. performing numerical simulation on the internal cooling of the turbine blade of the heavy-duty gas engine according to the discrete equation; S4. Based on the results of numerical simulation, the heavy-duty gas engine turbine blades are internally cooled.

2. The method according to claim 1, characterized in that The modified heat transfer physical model is: Among them, q represents tensor, t represents time, D represents thermal conductivity, T represents temperature, and λ is the introduced relaxation parameter. At this time, the propagation speed of the thermal signal is is a finite value, controlled by the relaxation parameter λ; The control equation is: Where ρ represents the fluid density, represents the flow velocity vector of the fluid, k is the thermal conductivity, c p represents the specific heat capacity of the fluid, It is a new second-order time derivative term added to the control equation corresponding to the relative Fourier heat transfer physical model.

3. The method according to claim 2, characterized in that The S2 specifically includes: The control equation is expanded at the nth time layer, and the newly added second-order time derivative term in the control equation is Use the central difference of the previous time layer to approximate and add the newly added second-order time derivative The previous time layer is discretized as: and is regarded as the source term of the control equation, which is discretized as: Among them, the discretization method of the second-order time derivative term is: τ represents the time step.

4. The method according to claim 3, characterized in that The S3 specifically includes: Determine the internal cooling research area of ​​the heavy-duty gas turbine turbine blade, mesh the research area, and use Fluent-Meshing's latest Poly-Hexcore mesh technology to perform local encryption; According to the discretized control equation, a source term UDF plug-in is written for the divided grid using Fluent software to perform numerical simulation.

5. The method according to claim 3, characterized in that: The method of discretizing the control equation in S2 can analyze the error, Using Taylor's formula in mathematics, we get: Where f'(ξ) represents the derivative of f(ξ) with respect to t, and ξ represents t n-1 With t n For any value in , it can be seen from the formula that: for the second-order time derivative term, the value of the n layer can be approximated by using the value of the n-1 layer, and the error is controllable.

6. A system for internal cooling of a heavy-duty gas turbine blade, characterized in that: The system comprises: A correction module is used to correct the Fourier heat transfer physical model by introducing relaxation parameters to obtain a corrected heat transfer physical model and derive the corresponding control equation; A discretization module, used for discretizing the control equation and converting it into a discrete equation; A numerical simulation module, used for numerically simulating the internal cooling of the turbine blade of the heavy-duty gas engine according to the discrete equation; The internal cooling module is used to perform internal cooling on the turbine blades of the heavy-duty gas engine according to the results of numerical simulation.

7. The system according to claim 6, characterized in that The modified heat transfer physical model is: Among them, q represents tensor, t represents time, D represents thermal conductivity, T represents temperature, and λ is the introduced relaxation parameter. At this time, the propagation speed of the thermal signal is is a finite value, controlled by the relaxation parameter λ; The control equation is: Where ρ represents the fluid density, represents the flow velocity vector of the fluid, k is the thermal conductivity, c p represents the specific heat capacity of the fluid, It is a new second-order time derivative term added to the control equation corresponding to the relative Fourier heat transfer physical model.

8. The system according to claim 7, characterized in that The discretization module is specifically used for: The control equation is expanded at the nth time layer, and the newly added second-order time derivative term in the control equation is Use the central difference of the previous time layer to approximate and add the newly added second-order time derivative The previous time layer is discretized as: and is regarded as the source term of the control equation, which is discretized as: Among them, the discretization method of the second-order time derivative term is: τ represents the time step.

9. The system according to claim 8, characterized in that The numerical simulation module is specifically used for: Determine the internal cooling research area of ​​the heavy-duty gas turbine turbine blade, mesh the research area, and use Fluent-Meshing's latest Poly-Hexcore mesh technology to perform local encryption; According to the discretized control equation, a source term UDF plug-in is written for the divided grid using Fluent software to perform numerical simulation.

10. The system according to claim 8, characterized in that The discretization module discretizes the control equation to analyze the error. Using Taylor's formula in mathematics, we get: Where f'(ξ) represents the derivative of f(ξ) with respect to t, and ξ represents t n-1 With t n For any value in , we can know from the formula: For the second-order time derivative term, the value of the n-1 layer can be used to approximate the value of the n layer, and the error is controllable.

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