Finite element numerical simulation method for detecting furfural in insulating oil based on photo-thermal lens spectrum

Abstract

The invention provides a finite element numerical simulation method based on photo-thermal lens spectrum insulating oil furfural detection, and relates to the field of numerical analysis of an insulating oil detection technology. The method comprises the following steps: constructing a geometric model comprising insulating oil containing trace furfural, an optical window and a detection plane to obtain a pump beam and a probe beam; the refractive index in the pump beam propagation process is solved; presetting extinction coefficients corresponding to the furfural with different concentrations, and obtaining photothermal effect data of the multi-concentration furfural; calculating the temperature distribution after the insulating oil absorbs energy, and describing the change relation of the refractive index along with the temperature through a thermo-optical coefficient; insulating oil temperature distribution and pump beam propagation characteristics in a steady state are obtained; solving the thermal stress of the insulating oil to the optical window sheet under the excitation of the pumping light beam; non-isothermal flowing and fluid-solid coupling behaviors of the insulating oil under the thermal lens effect are simulated, and fluid solving is carried out; the influence of the thermal lens effect on probe beam propagation is solved; and light spot distribution of the detection probe light beam is obtained.

Description

Technical Field

[0001] This invention relates to the field of numerical analysis of insulating oil testing technology, and in particular to a finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy. Background Technology

[0002] Power transformers are indispensable key equipment in power systems. Their internal oil-paper insulation material gradually ages under long-term electro-thermal stress, directly threatening the reliability and safety of power transmission. The degree of polymerization (DP) of the insulation paper is the most direct indicator of its aging degree; however, measuring the DP requires disassembling the transformer and sampling it, which is difficult to achieve under normal operating conditions. Therefore, indirectly assessing the insulation condition by detecting the content of characteristic aging products in the transformer insulating oil becomes an effective and feasible alternative method.

[0003] Furfural, a specific product of cellulose insulating paper degradation, exhibits a strong correlation between its concentration and the degree of aging of the insulating paper, and is widely recognized as an important indicator for assessing insulation condition. With the development of optical sensing technology, various spectroscopic detection methods have emerged.

[0004] Existing technologies have the following drawbacks: 1. Current methods for detecting dissolved furfural in insulating oil mainly include high-performance liquid chromatography (HPLC), electrochemical methods, and spectrophotometry. Among these, HPLC has become the mainstream method due to its high precision and accuracy. However, this method is complex to operate and requires frequent column replacements, limiting its application to laboratory environments and failing to meet the needs of long-term or online monitoring of transformers. 2. Spectroscopic detection technologies are widely used, with photothermal lens spectroscopy possessing numerous advantages. However, its application in the detection of trace furfural in insulating oil is still in its early stages. A finite element numerical simulation-based approach has not yet been developed, hindering the theoretical support for the design and optimization of detection systems and restricting practical implementation and performance improvement. 3. The issue of multi-physics fields is not fully considered, and the correlation between microscopic and macroscopic characteristics is not established, resulting in limited detection precision and accuracy. Summary of the Invention

[0005] The main objective of this invention is to provide a finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy, thereby solving the technical problems of insufficient reliability, low detection accuracy and precision, and limited applicability of furfural detection in insulating oil.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy, comprising the following steps: S1: Preset beam waist radius, optical power and wavelength parameters to obtain pump beam and probe beam; S2: Preset the insulating oil with a trace amount of furfural, the initial temperature of the optical window, and the initial refractive index to obtain the propagation trajectory of the pump beam: S3: The pump beam propagation is excited by the photothermal effect through insulating oil. The absorption of pump beam energy by trace amounts of furfural is quantified by the extinction coefficient. The extinction coefficients corresponding to different concentrations of furfural are preset to obtain photothermal lensing effect data of multiple concentrations of furfural. S4: Based on the fluid heat conduction equation and combined with the physical properties of insulating oil, calculate the temperature distribution of insulating oil after absorbing energy, and establish the relationship between temperature and refractive index through the thermo-optic coefficient to obtain the refractive index distribution of insulating oil after temperature change. S5: Iteratively feed back the refractive index distribution of the insulating oil obtained in S4, and repeat S2-S4 to obtain the temperature distribution of the insulating oil and the propagation characteristics of the pump beam under steady state. S6: Based on the control equations of continuum mechanics, combined with Young's modulus and Poisson's ratio of the optical window, the thermal stress of the insulating oil on the optical window under the excitation of the pump beam is solved to obtain the deformation of the optical window. S7: Obtain the dynamic viscosity of the insulating oil, combine it with the temperature distribution data of the insulating oil obtained in S5, simulate the non-isothermal flow behavior caused by the photothermal lensing effect through the Navis-Stokes equation, set up a dynamic mesh to realize the fluid solution, and obtain the flow data of the insulating oil under the pump beam. S8: Using data on the photothermal lensing effect of furfural excited by the pump beam, including the temperature distribution and refractive index distribution data of the insulating oil, and combining the ray equation, the probe beam under the photothermal lensing effect was solved, and the spot distribution of the probe light on the detection plane was obtained as the simulation result.

[0007] In the preferred embodiment, step S2 specifically involves: solving the wave vector k and position vector x according to the ray equation in the micro-Hamiltonian form, as shown in the formula: ; ; Where ω is the angular frequency and t is time.

[0008] In the preferred embodiment, in step S4, the physical properties include the density, thermal conductivity, and constant-pressure heat capacity of the insulating oil, and the relationship between the refractive index and temperature is as follows: ; Where n0 is the initial value of the refractive index, dn / dT is the thermo-optic coefficient, and ΔT is the temperature difference.

[0009] In the preferred embodiment, the extinction coefficient k is the imaginary part of the refractive index, which, together with the absorption coefficient... a The relationship between them is: ; in,λ The wavelength of light; Absorption coefficient of insulating oil a The results were obtained by Fourier transform infrared spectroscopy experiments on insulating oil containing trace amounts of furfural.

[0010] In the preferred embodiment, the thermo-optic coefficient in step S4 is derived theoretically using the Lorentz-Lorentz formula, and the derived expression for the thermo-optic coefficient is as follows: ; in, The coefficient of thermal expansion is p Polarizability; The relationship between the change in the refractive index of insulating oil and temperature change is described by the thermo-optic coefficient, which indicates the change in the refractive index of insulating oil when the temperature rises by 1 K.

[0011] In the preferred embodiment, in step S6, the thermal expansion process of the insulating oil is solved based on the control equations of continuum mechanics, thereby obtaining the thermal stress.

[0012] In the preferred embodiment, the non-isothermal flow state of the insulating oil after the thermal lensing effect in S7 is obtained by solving the Navis-Stokes equations. When solving the flow, the insulating oil region needs to be set as a moving grid to achieve fluid solution.

[0013] The preferred embodiment includes: establishing a geometric model, which includes insulating oil containing trace amounts of furfural, an optical window, and a detection plane; the geometric model can be established as a two-dimensional axisymmetric structure or a three-dimensional complete model; wherein, the three-dimensional complete model is established based on the actual liquid pool, and a metal pressure plate or set bolt is added outside the optical window.

[0014] In the preferred embodiment, the thickness of the insulating oil between the optical windows and the position of the detection plane can be set according to the actual thickness of the liquid pool and the optical path conditions.

[0015] In a preferred embodiment, the optical parameters of the pump beam and the probe beam include the beam waist radius, beam waist position, power, and wavelength, which are set according to the actual laser parameters.

[0016] This invention provides a finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy. The method involves acquiring a pump beam and a probe beam; pre-setting the initial temperature and initial refractive index of the insulating oil with trace amounts of furfural and the optical window to obtain the propagation trajectory of the pump beam; pre-setting the extinction coefficients corresponding to different concentrations of furfural to obtain photothermal lens effect data for multiple concentrations of furfural; calculating the temperature distribution of the insulating oil after energy absorption based on the fluid thermal balance equation and the physical properties of the insulating oil; establishing a correlation between temperature and refractive index through the thermo-optic coefficient to obtain the refractive index distribution of the insulating oil after temperature changes; iteratively feeding back the obtained refractive index distribution of the insulating oil and repeating the process to obtain the steady-state temperature distribution. The temperature distribution of insulating oil and the propagation characteristics of the pump beam were investigated. Based on the governing equations of continuum mechanics, and combined with Young's modulus and Poisson's ratio of the optical window, the thermal stress of the insulating oil on the optical window under pump beam excitation was solved. The dynamic viscosity of the insulating oil was obtained, and the non-isothermal flow behavior caused by the photothermal lensing effect was simulated by the Navis-Stokes equations. A dynamic mesh was set to realize the fluid solution and obtain the flow data of the insulating oil under the pump beam. Using the data of the furfural photothermal lensing effect excited by the pump beam, including the temperature distribution and refractive index distribution data of the insulating oil, and combined with the propagation trajectory of the pump beam, the probe beam solution under the photothermal lensing effect was realized, and the spot distribution of the probe beam on the detection plane was obtained.

[0017] This invention enables the optimization of key parameters of the detection system in advance through numerical simulation, reducing the difficulty of on-site system development and trial and error costs, realizing quantitative simulation and prediction of multi-concentration furfural, improving detection accuracy, perfecting physical field coupling, optimizing the entire detection process, reducing R&D costs, shortening the development cycle of the detection system, and improving the adaptability and practicality of the simulation method. Attached Figure Description

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a schematic diagram of the geometric model of the finite element numerical simulation method of the present invention; Figure 2 This is the temperature distribution of insulating oil under the two-dimensional axisymmetric model of the present invention; Figure 3 This is the radial refractive index distribution at the center of the insulating oil under the two-dimensional axisymmetric model of this invention; Figure 4 This is the thermal stress distribution of insulating oil under the two-dimensional axisymmetric model of this invention; Figure 5 This is the propagation trajectory of the probe beam calculated by this invention; Figure 6 This is the probe beam spot distribution at the detection plane calculated by this invention.

[0019] In the figure: 1. Insulating oil containing trace amounts of furfural; 2. Optical window; 3. Detection plane; 4. Three-dimensional optical window; 5. Metal bolt; 6. Detection plane; 7. Insulating oil containing trace amounts of furfural. Detailed Implementation

[0020] Example 1 like Figure 1-6 As shown, a finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy includes the following steps: S1: Establish a geometric model, which includes insulating oil containing trace amounts of furfural, an optical window, and a detection plane; preset the beam waist radius, optical power, and wavelength parameters to obtain the pump beam and probe beam; both the pump beam and probe beam adopt a Gaussian beam model.

[0021] S2: Preset the insulating oil with a trace amount of furfural, the initial temperature and initial refractive index of the optical window, and solve the wave vector k and position vector x according to the following Hamiltonian form of the ray equation, thereby obtaining the propagation trajectory of the pump beam.

[0022] ; ; in, ω Angular frequency, t It's time.

[0023] S3: After the pump beam propagates through the insulating oil, the insulating oil absorbs the energy of the pump beam and excites the photothermal effect. During this process, the absorption of pump beam energy by trace amounts of furfural is quantified by the extinction coefficient. The extinction coefficients corresponding to different concentrations of furfural are preset to obtain photothermal lensing effect data of multiple concentrations of furfural.

[0024] S4: Solve for the refractive index during the propagation of the pump beam through the geometric optics interface.

[0025] Based on the fluid heat balance equation and the physical properties of the insulating oil, the temperature distribution of the insulating oil after absorbing energy is calculated. A correlation between temperature and refractive index is established using the thermo-optic coefficient to obtain the refractive index distribution of the insulating oil after temperature changes. The physical properties include the density, thermal conductivity, and constant-pressure heat capacity of the insulating oil. The relationship between refractive index and temperature is as follows: ; Where n0 is the initial value of the refractive index, dn / dT is the thermo-optic coefficient, and ΔT is the temperature difference.

[0026] The simulation calculates the refractive index distribution by calculating the temperature distribution under pump beam excitation.

[0027] S5: Changes in the temperature of the insulating oil will alter its refractive index distribution through the thermo-optic coefficient, thereby affecting the propagation of the pump beam. Therefore, the refractive index distribution of the insulating oil obtained in S4 is substituted back into the differential equation in S2 for feedback calculation to obtain the propagation trajectory of the pump beam again. Through iterative calculation, S2 to S5 are repeatedly executed to obtain the temperature distribution of the insulating oil and the propagation characteristics of the pump beam under steady state.

[0028] S6: Based on the governing equations of continuum mechanics, combined with Young's modulus and Poisson's ratio of the optical window, the thermal stress of the insulating oil on the optical window under the excitation of the pump beam is solved, and the deformation of the optical window is obtained.

[0029] S7: Obtain the dynamic viscosity of the insulating oil, combine it with the temperature distribution data of the insulating oil obtained in S5, simulate the non-isothermal flow behavior caused by the photothermal lensing effect through the Navis-Stokes equation, set up a dynamic mesh to realize the fluid solution, and obtain the flow data of the insulating oil under the pump beam. S8: Using the data of the photothermal lensing effect of furfural excited by the pump beam, including the temperature distribution and refractive index distribution data of the insulating oil, and combined with the differential equation in S2, the probe beam transmission trajectory was obtained, that is, the probe beam was calculated after the pump beam irradiated the oil sample; the probe beam under the photothermal lensing effect was solved by combining the ray equation, the spot distribution of the probe light on the detection plane was obtained, and the current furfural detection result was obtained.

[0030] In this embodiment, the flow velocity field of the insulating oil under the photothermal lensing effect was obtained by using the spatial power distribution of the pump beam, thermal stress, thermal properties of the insulating oil (density, specific heat capacity, thermal conductivity, viscosity) and a moving mesh, thus realizing the fluid solution.

[0031] A detection plane is set along the propagation path of the probe beam, and the spot distribution of the probe beam is detected by an accumulator in geometric optics.

[0032] Figure 1 This is a schematic diagram of the geometric model of the finite element numerical simulation method of the present invention. (a) is a two-dimensional axisymmetric model, and (b) is a three-dimensional model.

[0033] In this embodiment, the optical parameters of the pump beam and probe beam include beam waist radius, beam waist position, power and wavelength, which are set according to the actual laser parameters.

[0034] By coupling geometric optics, solid-fluid heat transfer, solid mechanics, and laminar flow interfaces into a multi-physics field, the entire chain of physical processes from light absorption, heat generation, thermally induced refractive index change (thermal lensing effect), thermal expansion stress to fluid motion is fully reproduced. Absorbance data is converted into the core simulation parameter—the extinction coefficient, which links the microscopic spectral absorption characteristics of furfural with the macroscopic photothermal effect, building a bridge from microscopic spectral characteristics to macroscopic optical response, and realizing the quantification and prediction of furfural at multiple concentrations; thus reducing R&D costs and shortening the development cycle.

[0035] In the preferred scheme, the extinction coefficient k is the imaginary part of the refractive index, which, along with the absorption coefficient, represents the sum of the two components. a The relationship between them is: ; in, λ λ is the wavelength of light.

[0036] Absorption coefficient of insulating oil a The results were obtained by Fourier transform infrared spectroscopy experiments on insulating oil containing trace amounts of furfural.

[0037] In this embodiment, interface coupling specifically refers to the internal construction of coupling relationships within the software, allowing the temperature data output from the heat transfer interface to be simultaneously output to the geometric optics interface for solving the propagation of the pump beam, thus involving data transmission.

[0038] By constructing a multi-physics coupling model of light, heat, force, and fluid, a precise and comprehensive digital simulation of the spectral detection process of photothermal lenses was achieved.

[0039] like Figure 1 As shown, the two-dimensional axisymmetric model includes: 1 insulating oil containing trace amounts of furfural, 2 optical window, and 3 detection plane; the three-dimensional model includes: 4 three-dimensional optical window, 5 metal bolt, 6 detection plane, and 7 insulating oil containing trace amounts of furfural.

[0040] like Figure 1 As shown, Figure 1 The left image shows a two-dimensional axisymmetric model, and the right image shows a complete three-dimensional model.

[0041] In the preferred embodiment, the geometric model can be established as a two-dimensional axisymmetric structure or a three-dimensional complete model; wherein, the three-dimensional complete model is established based on the actual liquid pool, with the addition of metal pressure plates or set bolts outside the optical window.

[0042] The two-dimensional axisymmetric model is obtained by abstracting the actual cuboid liquid pool into an axisymmetric cylinder and then reducing its dimensions. The two-dimensional axisymmetric model consists of two optical windows, an insulating oil in the center, and a detection plane below. The detection plane is a circle in three-dimensional space, and a line segment below the two-dimensional axisymmetric model.

[0043] The complete three-dimensional model is built based on the actual structure of the liquid pool: the insulating oil is held between two rectangular optical windows, which are fixed by set bolts around their perimeter. A circular detection plane is located at a certain distance from the liquid pool.

[0044] Since the beam spot diameter is much smaller than the cross-sectional area of ​​the oil sample in practical applications, a two-dimensional axisymmetric geometric model can save computational resources unless there are special requirements. The following will use a two-dimensional axisymmetric geometric model as an example to illustrate the implementation. The operation method and parameter settings of the three-dimensional model are the same.

[0045] By defining and constructing a geometric model of "insulating oil containing trace amounts of furfural, optical windows, and detection planes," the core objects of the simulation are clearly identified, improving the consistency between the simulated scenario and the core structure of the actual detection system.

[0046] In this embodiment, the propagation process of the pump beam and probe beam is simulated through a geometric optics interface, where both the pump beam and probe beam employ a Gaussian beam model. The beam definition parameters include the beam waist radius, optical power, and wavelength, which can be adjusted according to the characteristics of the actual laser. Furthermore, the geometric optics interface is also used to solve for the refractive index, a key parameter for pump beam propagation. The real part of the refractive index determines the propagation path of the light, while the imaginary part reflects the interaction between the beam and the matter.

[0047] To simulate the process of insulating oil absorbing pump beam energy, this invention couples a solid-fluid heat transfer interface with a geometric optics interface. In this process, the absorption of pump beam energy by trace amounts of furfural is quantified using the extinction coefficient (imaginary part of the refractive index). The value of the extinction coefficient can be derived by performing Fourier transform infrared spectroscopy on insulating oil containing trace amounts of furfural and combining it with absorbance data. Since different concentrations of furfural have different extinction coefficients, this method can simulate the photothermal effect of multiple concentrations of furfural.

[0048] When the energy of the pump beam is absorbed by furfural in the insulating oil, the temperature of the insulating oil changes, and its distribution can be calculated using the heat transfer equation. Key parameters that need to be set during the calculation include the density, thermal conductivity, and constant-pressure heat capacity of the insulating oil.

[0049] Temperature changes further alter the refractive index of the insulating oil, which in turn affects the optical field distribution of the pump beam, thus creating a feedback effect on temperature. Based on this mechanism, by performing feedback calculations on the light propagation process solved through the geometric optics interface and the temperature distribution solved through the solid-fluid heat transfer interface, the steady-state temperature and refractive index distributions of the insulating oil are finally obtained. The results are as follows: Figure 2 , 3 As shown.

[0050] In the preferred embodiment, the thermo-optic coefficient mentioned in step S4 is derived theoretically using the Lorentz-Lorentz formula, and the derived expression for the thermo-optic coefficient is as follows: ; in, The coefficient of thermal expansion is p denoted as polarizability.

[0051] The relationship between the change in the refractive index of insulating oil and temperature change is described by the thermo-optic coefficient, which indicates the change in the refractive index of insulating oil when the temperature rises by 1 K.

[0052] The relationship between the refractive index of insulating oil and temperature is described by the thermo-optic coefficient, which represents the change in the refractive index of the insulating oil for every 1 K increase in temperature. The thermo-optic coefficient of insulating oil can be approximately calculated using the Lorentz-Lorentz formula, and its value is approximately 3.5 × 10⁻⁶. -4 1 / K.

[0053] To simulate the thermal expansion process, the solid-fluid heat transfer interface was coupled with a solid-mechanical interface to calculate the thermal stress exerted by the insulating oil on the optical window under pump beam excitation. The results are as follows: Figure 4 As shown. During this process, it is necessary to set material parameters such as Young's modulus and Poisson's ratio for the optical window.

[0054] The flow behavior of insulating oil under the thermal lensing effect can be solved by coupling the laminar flow interface with the heat transfer interface and the solid mechanics interface, respectively. Among them, the solution of non-isothermal flow and fluid-structure interaction requires setting the insulating oil region as a dynamic mesh to realize the dynamic simulation of the fluid.

[0055] By importing the calculated results of the thermal lensing effect excited by the pump beam into the geometric optics interface of the probe beam and using it as initial conditions, the influence of the thermal lensing effect on the propagation of the probe beam can be further solved. The propagation trajectory of the probe beam is as follows: Figure 5 As shown.

[0056] Along the propagation path of the probe beam, a detection plane is constructed using geometric components to detect the beam's spot distribution. The detection process is achieved by setting up an accumulator in geometric optics, and the result is as follows: Figure 6 .

[0057] The optical parameters of the pump beam and probe beam (such as beam waist radius, beam waist position, power, wavelength, etc.) can be flexibly set according to the parameters of the laser actually used.

[0058] The parameters used in this embodiment are set as follows: the thickness of the insulating oil and the position of the detection plane can be set according to the actual thickness of the liquid pool and the optical path conditions: the insulating oil thickness is 0.05 mm and the detection plane is located 1030 mm away from the waist of the detection beam, the liquid pool is located 30 mm away from the waist of the detection beam, the waist radius of the detection beam is 80 μm and the wavelength is 632.8 nm, the waist radius of the pump beam is 1 mm, the waist position is the same as that of the liquid pool, located 30 mm away from the waist of the detection beam, the power is 0.1 W and the wavelength is 5.87 μm.

[0059] In addition, the thickness of the insulating oil between the optical windows and the position of the detection plane can be adjusted according to the actual thickness of the liquid pool and the optical path conditions.

[0060] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy, characterized in that, Includes the following steps: S1: Preset beam waist radius, optical power and wavelength parameters to obtain pump beam and probe beam; S2: Preset the insulating oil with a trace amount of furfural, the initial temperature of the optical window, and the initial refractive index to obtain the propagation trajectory of the pump beam: S3: The pump beam propagation is excited by the photothermal effect through insulating oil. The absorption of pump beam energy by trace amounts of furfural is quantified by the extinction coefficient. The extinction coefficients corresponding to different concentrations of furfural are preset to obtain photothermal lensing effect data of multiple concentrations of furfural. S4: Based on the fluid heat conduction equation and combined with the physical properties of insulating oil, calculate the temperature distribution of insulating oil after absorbing energy, and establish the relationship between temperature and refractive index through the thermo-optic coefficient to obtain the refractive index distribution of insulating oil after temperature change. S5: Iteratively feed back the refractive index distribution of the insulating oil obtained in S4, and repeat S2-S4 to obtain the temperature distribution of the insulating oil and the propagation characteristics of the pump beam under steady state. S6: Based on the control equations of continuum mechanics, combined with Young's modulus and Poisson's ratio of the optical window, the thermal stress of the insulating oil on the optical window under the excitation of the pump beam is solved to obtain the deformation of the optical window. S7: Obtain the dynamic viscosity of the insulating oil, combine it with the temperature distribution data of the insulating oil obtained in S5, simulate the non-isothermal flow behavior caused by the photothermal lensing effect through the Navis-Stokes equation, set up a dynamic mesh to realize the fluid solution, and obtain the flow data of the insulating oil under the pump beam. S8: Using data on the photothermal lensing effect of furfural excited by the pump beam, including the temperature distribution and refractive index distribution data of the insulating oil, and combining the ray equation, the probe beam under the photothermal lensing effect was solved, and the spot distribution of the probe light on the detection plane was obtained as the simulation result.

2. The finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy according to claim 1, characterized in that, Specifically, in S2, the wave vector k and position vector x are obtained by solving the ray equation in the form of the micro-Hamiltonian, as shown in the formula: ； ； Where ω is the angular frequency and t is time.

3. The finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy according to claim 1, characterized in that, In S4, the physical properties include the density, thermal conductivity, and constant-pressure heat capacity of the insulating oil. The relationship between the refractive index and temperature is as follows: ； Where n0 is the initial value of the refractive index, dn / dT is the thermo-optic coefficient, and ΔT is the temperature difference.

4. The finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy according to claim 1, characterized in that, The extinction coefficient k is the imaginary part of the refractive index, which, along with the absorption coefficient, represents the sum of the two parts. a The relationship between them is: ； in, λ The wavelength of light; Absorption coefficient of insulating oil a The results were obtained by Fourier transform infrared spectroscopy experiments on insulating oil containing trace amounts of furfural.

5. The finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy according to claim 1, characterized in that, The thermo-optic coefficient mentioned in S4 is derived theoretically using the Lorentz-Lorentz formula, and the derived expression for the thermo-optic coefficient is as follows: ； in, The coefficient of thermal expansion is p Polarizability; The relationship between the change in the refractive index of insulating oil and temperature change is described by the thermo-optic coefficient, which indicates the change in the refractive index of insulating oil when the temperature rises by 1 K.

6. The finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy according to claim 1, characterized in that, In step S6, the thermal expansion process of the insulating oil is solved based on the control equations of continuum mechanics, thereby obtaining the thermal stress.

7. The finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy according to claim 1, characterized in that, In S7, the non-isothermal flow state of the insulating oil after the thermal lensing effect is obtained by solving the Navis-Stokes equations. When solving the flow, the insulating oil region needs to be set as a moving grid to achieve fluid solution.

8. The finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy according to claim 1, characterized in that, include: A geometric model is established, which includes insulating oil containing trace amounts of furfural, an optical window, and a detection plane. The geometric model can be established as a two-dimensional axisymmetric structure or a three-dimensional complete model. The three-dimensional complete model is established based on the actual liquid pool, with the addition of metal pressure plates or set bolts outside the optical window.

9. The finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy according to claim 1, characterized in that, The thickness of the insulating oil between the optical windows and the position of the detection plane can be set according to the actual thickness of the liquid pool and the optical path conditions.

10. The finite element numerical simulation method for detecting furfural in insulating oil based on photothermal lens spectroscopy according to claim 1, characterized in that, The optical parameters of the pump beam and probe beam include beam waist radius, beam waist position, power, and wavelength, which are set according to the actual laser parameters.

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