Method for predicting fire spreading speed of three parallel electric wires

Abstract

The invention discloses a method for predicting the fire spread speed of three parallel electric wires, and belongs to the technical field of fire spread prediction of multiple electric wires. The prediction method comprises the steps that various physical characteristic parameters of three parallel electric wires in the fire spreading process are collected; selecting any preheating zone of one of the three electric wires, and constructing an energy conservation equation of unit area and unit time in the preheating zone when the outer insulating material of the electric wire in the preheating zone is heated from room temperature to pyrolysis temperature; calculating heat conduction heat flow of the metal wire core of the electric wire to the unit area of the preheating area, and heat radiation heat flow and heat convection heat flow of flame to the unit area of the preheating area; and on the basis of the constructed energy conservation equation, a prediction result of the fire spreading speed of the three parallel electric wires can be calculated. Compared with the prior art, the method not only breaks through the limitation of single-wire prediction, but also reduces the prediction error of the fire spreading speed of the multi-wire system, and provides more reliable theoretical basis and technical support for electrical fire prevention.

Description

Technical Field

[0001] This invention belongs to the technical field of predicting the spread of fire in multiple electrical wires in electrical fires, and particularly relates to a method for predicting the spread speed of fire in three parallel electrical wires. Background Technology

[0002] With the booming development of the new energy industry, electrical wires, as an important carrier of electrical energy, have been widely used in various fields of daily life and industrial production. Whether it's household appliances, smart devices, new energy vehicles, or large-scale energy infrastructure such as photovoltaic power generation, wind power generation, and power transmission and distribution, electrical wires play an indispensable role. However, the insulation materials of electrical wires (such as polyvinyl chloride (PVC) and polyethylene (PE)) are usually flammable. Under improper use or operating conditions, wires may overheat due to overload or aging, or experience short circuits, causing the insulation materials to ignite and thus start a fire, resulting in casualties and huge property losses. In recent years, numerous fire accidents caused by electrical wires and cables have occurred both domestically and internationally. Therefore, accurate prediction of the spread rate of electrical wire fires is of great significance.

[0003] A search revealed that Chinese patent application No. 2022 10070874.9 discloses a multi-parameter continuously adjustable cable fire spread experimental device and method. This application establishes an experimental device that can adjust multiple factors such as heat jet flow, cable spacing, and tilt angle. Through this device, the geometric dimensions of the flame can be obtained, and the characteristics of cable fire spread under multiple factors can be clarified. However, it does not perform quantitative analysis on the fire spread rate.

[0004] For example, patent application No. 202110786948.4 discloses a method for determining the fire spread rate of parallel dual cables. It first determines the energy conservation equation for the preheating zone, then calculates the heat flux of each part, and finally predicts the fire spread rate using a fire spread calculation formula. This application can calculate the fire spread rate at any given time using a model, and by additionally considering the influence of the viewing angle factor on the radiative heat flux during fire spread, it can more accurately predict the fire spread rate of parallel dual cables.

[0005] However, existing technologies still have significant shortcomings in quantitative research, especially in the quantitative analysis of fire spread rate. Currently, they are limited to methods for determining the fire spread rate of parallel double wires, and fail to fully consider the complex effects of the interaction of multiple wires. Summary of the Invention

[0006] To address the limitation of existing technologies, which primarily predict the fire spread rate of two parallel electrical wires and fail to adequately consider the mutual influence between multiple different wires, this invention provides a method for predicting the fire spread rate of three parallel electrical wires. By establishing heat transfer and radiation models for the three wires, this invention can accurately predict the fire spread rate, thus providing a reliable theoretical basis and technical support for electrical fire safety assessment and fire prevention design.

[0007] To achieve the above objectives, the technical solution provided by the present invention is as follows: This invention provides a method for predicting the spread rate of a fire caused by three parallel electrical wires, comprising: Collect various physical characteristic parameters during the fire spread process of three parallel electric wires; Select any preheating zone of one of the three wires and construct the energy conservation equation per unit area per unit time in the preheating zone when the outer insulation material of the wire in the preheating zone is heated from room temperature to pyrolysis temperature. Calculate the heat transfer flux per unit area of ​​the preheating zone from the metal core of the wire. ; Calculate the heat flux per unit area of ​​the preheating zone from the flame. Meanwhile, based on the flame tilt and the coupling effect of the spacing between adjacent wires on radiative heat transfer, the viewing angle factor of the flame towards the preheating zone is corrected. Calculate the convective heat flux per unit area of ​​the preheating zone from the flame. ;as well as The collected physical property parameters are compared with the calculated heat conduction and heat flow. Thermal radiation and heat flow and convective heat transfer heat flow Substituting the obtained energy conservation equation, we can calculate the predicted spread rate of the fire across the three parallel electric wires.

[0008] According to any of the technical solutions described in this invention, the energy conservation equation per unit area per unit time in the preheating zone is: ; in, ρ p The density of the insulating material is expressed in kg / m³. c p Specific heat capacity of insulating material, kJ / kg·K; T p The pyrolysis temperature of the insulating material, in K; r c Let be the radius of the metal wire core, in meters (m). r 0 represents the radius of the entire conductor, in meters (m). v f The fire spread rate is expressed in m / s. Room temperature, K; The heat flux conducted per unit area of ​​the preheating zone by the metal core of the wire, in W / m 2 ; The heat flux radiated by the flame to a unit area of ​​the preheating zone, in W / m² 2 ; The heat flux from the flame to the preheating zone is the convective heat transfer flux, W / m³. 2 ; This is the length of the preheating zone.

[0009] According to any of the technical solutions described in this invention, the heat radiation flow per unit area of ​​the preheating zone from the flame. The calculation is as follows: ; in, The emissivity of the flame; σ It is the Stefan-Boltzmann constant; F f The perspective factor of the flame toward the preheating zone.

[0010] According to any of the technical solutions described in this invention, when calculating the heat flux radiated by the flame to a unit area of ​​the preheating zone, the viewing angle factor of the flame on its own wire preheating zone is calculated as follows, assuming the flame is not tilted: ; When the flame is tilted, the viewing angle factor for its own wire preheating zone is calculated as follows: ; The viewing angle factor of the flame on other wire preheating zones is calculated as follows: ; in, , , W f The width of the flame is in meters (m). H f R is the flame height, in meters; R is the length of the line connecting the flame radiation micro-element surface and the preheating zone micro-element surface, in meters. It is the angle between the flame and the vertical direction.

[0011] According to any of the technical solutions described in this invention, the angle between the flame and the vertical direction It is obtained through the probability of flame merging, specifically including: First, the test video was edited, and the flame merging video in the stable phase was selected. Then, the video was processed frame by frame to obtain a grayscale image of the flame merging. The grayscale image is then converted to a binary image, and then the binary image is converted into flame merged data text using a Matlab program; Finally, after processing the text in drawing software, a flame merging probability cloud map is obtained, and the merging probability value of different positions of the flame can be directly obtained.

[0012] According to any of the technical solutions described in this invention, the emissivity of the flame is calculated as follows: ; in, The radiation absorption coefficient of hot flue gas particles. l m Let the average beam length be m; considering wire combustion as rectangular fuel combustion, therefore the equivalent diameter can be used. D e to replace l m .

[0013] According to any of the technical solutions described in this invention, the length of the preheating zone is... The length of the preheating zone is determined using either thermocouple or infrared thermal imaging. For wires that can be directly photographed, the length is directly calculated using infrared thermal imaging. For obscured wires, the length is indirectly calculated using real-time thermocouple temperature data and the following formula: ; T ig The ignition temperature of the insulating material, in K; T s Let K be the surface temperature of the wire. t ph Preheating time, in seconds; v f The fire spread rate is expressed in m / s.

[0014] According to any of the technical solutions described in this invention, the convective heat flux per unit area of ​​the preheating zone from the flame is calculated as follows: ; in, r 0 represents the radius of the entire conductor, in meters (m). T f Let K be the temperature of the flame. T p The pyrolysis temperature of the insulating material, in K; h The convective heat transfer coefficient is W / (m²). 2 ·K).

[0015] According to any of the technical solutions described in this invention, when three wires burn in parallel, the flame fusion characteristics are divided into three stages: a complete fusion stage, an intermittent fusion stage, and a non-fusion stage; for the condition that the three wires are equidistant, when calculating the convective heat transfer flux per unit area of ​​the preheating zone, the calculation is performed in stages according to the above stages, wherein: During the complete merging phase, the convective heat flux is evenly distributed among the three wires, and the convective heat transfer flux per unit area of ​​the preheating zone from the flame is calculated according to the following formula: ; During the intermittent merging and non-merging phases, the convective heat flux per unit area of ​​the preheating zone from the flame is calculated using the following formula: ; in, d 0 represents the diameter of the entire conductor, in meters (m). is the thermal conductivity of air, W / (m·K); g The acceleration due to gravity is m / s². 2 ; β K is the gas expansion coefficient. -1 ; v For kinematic viscosity, m 2 / s; α m is the thermal diffusivity. 2 / s; The average temperature of the additional entrainment zone is given in K.

[0016] According to any of the technical solutions of the present invention, the calculation formula for convective heat transfer heat flux in the fully merged stage under the condition of unequal spacing of three wires is the same as the calculation formula under the condition of equal spacing of three wires. When calculating the convective heat transfer flux during intermittent merging and non-merging phases, a spacing correction factor is introduced based on the calculation formula for the three wires with equal spacing. The spacing correction factor for the wires on the left and right sides is: s is the distance between the corresponding wire and the middle wire; the distance correction factor for the middle wire is the geometric mean of the distance correction factors for the two wires on the left and right sides.

[0017] Compared with the prior art, the present invention can achieve the following beneficial effects: (1) This invention provides a method for predicting the fire spread rate of three parallel wires. When calculating radiative heat flow, when the spacing between the wires is small, the flames of adjacent wires will merge and cause the flames to tilt. This change in flame shape will significantly affect the viewing angle factor, thus introducing a large error in the calculation of fire spread rate. Therefore, in order to address this technical gap, this invention corrects the viewing angle factor of the flame towards the preheating zone based on the tilt of the flame and the coupling effect of the spacing between adjacent wires on radiative heat transfer, and additionally considers the heat transfer effect between different wires, so as to more accurately predict the fire spread rate when multiple wires are laid side by side in actual working conditions.

[0018] (2) In the calculation of convective heat flow, the present invention uses different formulas for different merging stages of the flame, which significantly improves the accuracy of heat transfer calculation of the three wire system under the conditions of equal spacing and unequal spacing.

[0019] (3) In summary, compared with the prior art, the present invention not only breaks through the limitations of single-wire prediction, but also reduces the prediction error of fire spread speed in multi-wire systems, providing a more reliable theoretical basis and technical support for electrical fire prevention. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of a heat transfer model using three parallel, equally spaced wires in an embodiment of the present invention. Figure 2 This is a schematic diagram of a heat transfer model for three parallel wires with unequal spacing in an embodiment of the present invention; Figure 3 This is a schematic diagram of the radiation model of three parallel wires with equal and unequal spacing in an embodiment of the present invention; Figure 4 This is the flame merging probability processing procedure in an embodiment of the present invention; Figure 5 This is a graph showing the variation of the flame tilt angle with the wire spacing under the condition of equal spacing in an embodiment of the present invention; Figure 6 This is a summary diagram of the tilt angles of two types of flames under unequal spacing conditions in the embodiments of the present invention; Figure 7 This is a schematic diagram of the method for determining the length of the preheating zone in an embodiment of the present invention; Figure 8 This is a schematic diagram illustrating the determination of the preheating zone length of the infrared thermal imager in an embodiment of the present invention; Figure 9 This invention provides heat feedback for four types of wires under equal spacing conditions in this embodiment. Figure 10 This invention provides heat feedback for two types of wires under unequal spacing conditions in this embodiment. Figure 11The flame front positions of four types of wires under equal spacing conditions in this embodiment of the invention; Figure 12 This is a comparison between the calculated fire spread rate and the experimental value in the embodiments of the present invention; Figure 13 This is a comparison of fire spread rates and fire spread zoning diagrams for single-line, double-line, and triple-line fire spread in embodiments of the present invention. Detailed Implementation

[0021] To further understand the present invention, specific embodiments are described in detail below. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of this disclosure. In the following detailed description, numerous specific details are set forth to provide a comprehensive understanding of the embodiments of this disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of this disclosure.

[0022] Meanwhile, the terms "comprising" and "including" in this application indicate the presence of the features, steps, operations and / or components, but do not exclude the presence or addition of one or more other features, steps, operations or components.

[0023] It should also be understood that, for clarity, certain features of this disclosure may be described herein in the context of individual embodiments, but may also be provided in combination with each other in individual embodiments. That is, unless obviously incompatible or specifically excluded, each individual embodiment is considered to be combinable with any other embodiment, and such combination is considered to represent another different embodiment. Conversely, for brevity, various features of this disclosure described in the context of individual embodiments may also be provided individually or in any sub-combination. Finally, while a particular embodiment may be described as part of a series of steps or part of a more general structure, each step or substructure may also be considered an independent embodiment in itself.

[0024] This invention provides a method for predicting the fire spread rate of three parallel electric wires. First, various physical characteristic parameters during the fire spread process are collected. Then, any preheating zone of the three electric wires is selected. By establishing a heat transfer model and a radiation model of the three electric wire system, the conductive heat flow of the core material, the radiative heat flow of the flame, and the convective heat flow are accurately calculated. Finally, an energy conservation equation is constructed to achieve a quantitative prediction of the fire spread rate.

[0025] Specifically, this invention incorporates merging probability and wire spacing correction perspective factors into the radiative heat flux calculation, additionally considering the heat transfer influence between different wires. In the convective heat flux calculation, different formulas are used for different flame merging stages, significantly improving the accuracy of heat transfer calculations for three-wire systems under both equidistant and unequal spacing conditions. Compared to existing technologies, this invention not only overcomes the limitations of single-wire prediction but also reduces the prediction error of fire spread velocity in multi-wire systems, providing a more reliable theoretical basis and technical support for electrical fire prevention.

[0026] Specifically, the method for predicting the fire spread rate of three parallel electric wires according to an embodiment of the present invention includes the following steps: Step 1: Data Collection Collect various parameters during the fire spread process of three parallel electric wires, including the physical properties of the wire core and insulation layer (density, specific heat capacity, thermal conductivity, etc.), flame width, flame height, flame and entrainment zone temperature, and preheating zone length. Step 2: Select any preheating zone of one of the three wires and construct the energy conservation equation per unit area per unit time for the outer insulation material of the wire in that preheating zone when it is heated from room temperature to the pyrolysis temperature (considering the wire as a cylindrical control body conductor): ; in, ρ p The density of the insulating material is expressed in kg / m³. c p Specific heat capacity of insulating material, kJ / kg·K; T p The pyrolysis temperature of the insulating material, in K; r c Let be the radius of the metal wire core, in meters (m). r 0 represents the radius of the entire conductor, in meters (m). v f The fire spread rate is expressed in m / s. Room temperature, K; The heat flux conducted per unit area of ​​the preheating zone by the metal core of the wire, in W / m 2 ; The heat flux radiated by the flame to a unit area of ​​the preheating zone, in W / m² 2 ; The heat flux from the flame to the preheating zone is the convective heat transfer flux, W / m³. 2 ; The length of the preheating zone; Step 3: Calculate the heat transfer flux per unit area of ​​the preheating zone from the metal core of the wire. ; The heat transfer between the metal core and insulation layer of an electric wire can be considered as a heat-conducting cylinder. According to Fourier's law, the heat conduction rate of the cylinder wall is: (1); Therefore, the heat flux conducted per unit area of ​​the preheating zone by the metal core of the wire is: (2); in, is the thermal conductivity coefficient of the insulating material, W / (m·K); L p The pyrolysis length of the insulating material, in meters (m). T c The temperature of the metal wire core in the preheating zone, in K; (3); in, T f Let K be the temperature of the flame. is the thermal conductivity coefficient of the metal wire core, W / (m·K); h c The heat transfer coefficient of the metal wire core is W / (m²). 2 ·K); W f The width of the flame is in meters (m). L p The pyrolysis length of the insulating material, in meters (m). Substituting equation (3) into equation (2), we obtain the heat transfer flow per unit area of ​​the preheating zone through the metal core of the wire: (4).

[0027] Step 4: Calculate the heat flux radiated by the flame per unit area to the preheating zone. : (5); in, The emissivity of the flame; σ This is the Stefan-Boltzmann constant, with a value of approximately 5.67 × 10⁻⁶. -8 W / (m 2 ·K 4 ); F f The perspective factor of the flame toward the preheating zone; (6); in, The radiation absorption coefficient of hot flue gas particles. l m Let be the average beam length, in meters (m).

[0028] Treating wire combustion as rectangular fuel combustion allows for the use of equivalent diameters. D e to replace l m : (7); in, d 0 represents the diameter of the entire conductor, in meters (m).

[0029] The areas of the radiating plane infinitesimal elements are respectively , , The surface area of ​​the preheating zone is The lengths of the lines connecting the radiating plane element and the preheating zone surface element are respectively R 1. R 2. R 3. The angles between the normal to the radiating plane and the line connecting them are respectively... β 1. β 2. β 3. Establish a coordinate system with the flame center as the origin, the X-axis along the flame width direction, and the Y-axis along the flame height direction. Then, the viewing angle factor of the radiating surface relative to the preheating zone is: (8); For R, the following relationship holds: (9); For cos β 1 can be represented as: (10); Therefore, the perspective factor can ultimately be expressed as: (11-1); in, , , W f The width of the flame is in meters (m). H f R is the flame height, in meters; R is the length of the line connecting the flame radiation micro-element surface and the preheating zone micro-element surface, in meters.

[0030] The above formula is applicable to calculating the radiation heat viewing angle factor of the flame on the preheating zone of the wire itself, such as calculating the radiation viewing angle factor of the middle wire among three equally spaced wires. However, in actual multi-wire combustion scenarios, due to the influence of flame tilting effect, direct calculation using the above formula will affect the accuracy of the calculation. Therefore, this embodiment further projects the flame surface onto a vertical plane for geometric correction. , The angle between the flame and the vertical direction; the viewpoint factor calculation correction is as follows: (11-2); To calculate the radiation viewing angle factor of the flame on the preheating zone of other wires, the coupling effect of the flame tilt and the spacing between adjacent wires on radiative heat transfer must be considered. Based on this, the formula for calculating the viewing angle factor is revised as follows: (11-3); in, R The calculated values ​​should be corrected accordingly: ; s This refers to the spacing between the wires.

[0031] Furthermore, the angle between the flame and the vertical direction It is obtained through the probability of flame merging, and such as Figure 3 As shown, the flame merging probability is obtained through the following steps: First, the test video is edited (e.g., using Adobe Premiere software), and the flame merging video in the stable phase is selected. Then, the video is processed frame by frame (in this embodiment, it is done in a Matlab program) to obtain a grayscale image of the flame merging. The grayscale image is then converted into a binary image (using the Otsu method in this embodiment), and then the binary image is converted into flame merged data text using a Matlab program; Finally, after processing the text in the Tecplot plotting software, a flame merging probability cloud map is obtained, and the merging probability values ​​at different positions of the flame can be directly obtained. Table 1 below shows the corresponding values ​​between the merging probability and the flame tilt angle obtained by the inventors of this applicant through extensive experimental research.

[0032] Table 1. Corresponding values ​​of merging probability and tilt angle

[0033] In summary, the heat flux radiated by the flame to a unit area of ​​the preheating zone is: (12); F f总 It is the sum of the viewpoint factors received by the preheating zone micro-element surface from all radiating micro-element surfaces.

[0034] Step 5: Calculate the convective heat transfer flux from the flame to the preheating zone. : (13); in, h The convective heat transfer coefficient is W / (m²). 2 ·K), which is calculated as follows: (14); In the above formula, is the thermal conductivity of air, W / (m·K); Nu For Nusselt numbers; L For the characteristic length, take the wire diameter. d 0, m.

[0035] The convective heat transfer coefficient is from Nu It is confirmed that for cylindrical wires, Nu With Rayleigh number Ra The relationship with Prandtl's number Pr is as follows: (15); in, Ra is the Rayleigh number; Pr is the Prandtl number.

[0036] Prandtl number: (16); Glaschov number: (17); Rayleigh number: (18); in, g The acceleration due to gravity is m / s². 2 ; β K is the gas expansion coefficient. -1 ; v For kinematic viscosity, m 2 / s; α m is the thermal diffusivity. 2 / s.

[0037] Therefore, the convective heat transfer flux per unit area of ​​the preheating zone from the flame is: (19); Furthermore, when the three wires burn in parallel, due to the different spacing, this embodiment preferably divides the flame fusion characteristics into three stages: (1) complete fusion stage; (2) intermittent fusion stage; and (3) non-fusion stage. Therefore, the convective heat transfer flux per unit area of ​​the preheating zone is calculated in stages.

[0038] For three wires with equal and unequal spacing, during the complete merging phase, the convective heat flux is uniformly distributed among the three wires, as expressed by the following formula: (20); During the intermittent merging and non-merging phases, the convective heat flux of the flames on both sides will be greatly reduced. For three parallel flames with equal spacing, the convective heat flux is calculated using the following formula: (twenty one); in, The average temperature of the entrainment zone is K; during the experiment, thermocouples were used to monitor the temperature of the entrainment zone in real time.

[0039] For three parallel roots with unequal spacing, a spacing correction factor is introduced for the convective heat flux. Calculations are performed, where n is an empirical exponent. The middle wire is affected by the combined action of the wires on both sides; therefore, the preferred spacing correction factor is the geometric mean. Therefore, the convective heat flux is calculated by the following formula: (twenty two); Where n is an empirical index, n≈0.1~0.3, and for natural convection of a horizontal cylinder, n is taken as 0.25.

[0040] Step Six: Combine the data collected in Step One with the calculations obtained in Steps Three through Five. , , Substituting the energy conservation equation from step two, the fire spread rate can be calculated. v f : .

[0041] Furthermore, the length of the preheating zone The preheating zone length can be determined using either the thermocouple method or infrared thermal imaging. For wires that can be directly photographed, the length can be directly calculated using an infrared thermal imager. For shielded wires, however, the preheating zone length must be indirectly calculated using real-time thermocouple temperature data and a formula. The specific formula for calculating the preheating zone length using the thermocouple method is as follows: (twenty three); in, T ig The ignition temperature of the insulating material, in K; T s Let K be the surface temperature of the wire. t ph The preheating time is in seconds (s).

[0042] Example This embodiment conducted two simulation experiments. The first experiment used four types of wires (Type I: copper core diameter 6mm, insulation layer thickness 2mm; Type II: copper core diameter 8mm, insulation layer thickness 2mm; Type III: copper core diameter 6mm, insulation layer thickness 1mm; Type IV: copper core diameter 8mm, insulation layer thickness 1mm) to simulate the fire spread of three equally spaced parallel wires under ten wire spacings (s=0, 2, 5, 8, 10, 12, 14, 16, 18, 20mm).

[0043] The second experiment used two types of wires (Type I: copper core diameter 6mm, insulation layer thickness 2mm; Type II: copper core diameter 8mm, insulation layer thickness 2mm) to simulate the spread of fire by controlling two spacing parameters (s1=0~18mm and s2=3~20mm, s1<s2).

[0044] like Figure 1 and Figure 2 The figures shown are schematic diagrams of heat transfer models for three parallel wires with equal and unequal spacing, respectively. To simplify the heat transfer model, the following assumptions are made: the change in insulation thickness during the melting process is ignored; the wires are considered to be thermally thin; heat loss and Marangoni convection heat during combustion are negligible; the temperature distribution on the cross-section of the wire core and insulation layer is uniform; and the ignition conditions of the three wires are the same.

[0045] The actual flame is simplified to a radiating plane, and the heat transferred from the flame to the preheating zone is equivalent to the heat transferred from this radiating surface to the preheating zone. When analyzing the radiative heat transfer of the flame to the preheating zone of the intermediate wire, the wire is simplified to a rectangular plate, and the flame is approximated as a triangle. The following steps will use the preheating zone of the intermediate wire as the research object for example calculations, such as... Figure 3 The diagrams shown are schematic representations of three parallel wires with equal spacing and three wires with unequal spacing, respectively. The left diagram shows parallel wires with equal spacing, and the right diagram shows parallel wires with unequal spacing.

[0046] Specifically, this embodiment includes the following steps: S1. Select the preheating zone of the middle wire among the three wires, and construct the energy conservation equation per unit area per unit time for the outer insulation material of the wire in the preheating zone as it is heated from room temperature to the pyrolysis temperature: ; S2. Calculate the heat transfer flow per unit area of ​​the preheating zone from the metal core of the wire according to formula (4); S3. Calculate the heat flux radiated by the flame to a unit area of ​​the preheating zone. ; Specifically, when three equally spaced wires are burning in parallel, the flame viewing factor of the middle wire is calculated according to formula (11-1); while the flame viewing factors of the left and right wires need to be corrected and calculated according to formula (11-3).

[0047] When three wires with unequal spacing are burning in parallel, the viewing angle factor of the middle wire is calculated according to formula (11-2); while the flame viewing angle factor correction method for the left and right wires is the same as that for the two wires with equal spacing.

[0048] When the flame tilts, the R in the formula is modified accordingly as follows: ; Considering the influence of wire spacing, R is further modified as follows: .

[0049] like Figure 4 The merging probabilities are obtained as shown, and their values ​​are taken from Table 1. Figure 4 Only the process of obtaining the flame merging probability for Type I wires with a spacing of 5mm was demonstrated. Figure 5 This is a summary of the flame tilt angles for four types of electrical wires under equal spacing conditions. Figure 6 This is a summary of the flame tilt angles for two types of wires (Type I and Type II) under unequal spacing conditions; s is the spacing between the wires.

[0050] S4. Calculate the convective heat flux per unit area of ​​the preheating zone from the flame. ; When three wires burn in parallel, the flame fusion characteristics are divided into three stages due to the different spacing: (1) complete fusion stage; (2) intermittent fusion stage; (3) non-fusion stage. Therefore, the convective heat transfer flux per unit area of ​​the preheating zone is calculated in stages, as detailed in formulas (20) to (22).

[0051] S5. Calculate the fire spread rate v f : .

[0052] Regarding the preheating zone length, the infrared thermal imager captures a frontal image of the wires. Under equidistant conditions, the preheating zone lengths of wires 1 and 3 can be statistically calculated. This is because when the three wires are placed parallel to each other with the same spacing, wires 1 and 3 exhibit symmetry, and the estimated preheating zone lengths are the same value. Figure 7 As shown in (a), this is the statistical method for calculating the preheating zone length using an infrared thermal imager when the spacing of Type I wires is 10mm under equidistant conditions. For unequal spacing conditions, the method for calculating the preheating zone using an infrared thermal imager only applies to wire 1. For wire 2 under equidistant conditions and wires 2 and 3 under unequal spacing conditions, thermocouples are used to measure their temperature, and the preheating zone length is calculated using a formula. Figure 7 (b) shows the statistical method for the preheating zone length of the thermocouple when the spacing of the Type I wire is 10mm under the condition of equal spacing. The preheating zone length is calculated by formula (23).

[0053] Figure 8The image shows short-time screenshots taken from the top of an infrared thermal imager under two conditions: equal spacing (s=10mm) and unequal spacing (s1=6mm, s2=10mm). The difference in the length of the preheating zone of the three wires is clearly visible. This phenomenon clearly indicates a significant difference in the amount of heat absorbed by the three wires during the preheating process.

[0054] Figure 9 The heat feedback values ​​for the three heat flows of flame 1 and flame 2 under the condition of equal spacing are given. Figure 10 The thermal feedback values ​​of three flames under six different s2 spacings when s1=3 are given. The calculated heat conduction flux, heat radiation flux, heat convection flux, and preheating zone length are then substituted into the fire spread calculation formula to obtain the fire spread rate.

[0055] Based on the above steps, the fire spread rate of wires 1 and 2 of type I and type II, as well as the fire spread rate of wire 1 of type III and type IV, was calculated under the condition of equal spacing. The change in the position of the flame front over time under the condition of equal spacing was statistically analyzed based on the experiments. Figure 11 As shown in the figure, the position of the flame front changes linearly, and the slope obtained from the fitting is the fire spread rate. The calculated fire spread rate was compared with the fire spread rate obtained from experiments. Figure 12 As shown in (a), the fire spread rate of three flames (Type I and Type II) under unequal spacing conditions was calculated and compared with the fire spread rate obtained from experiments, as shown in (a). Figure 12 As shown in (b), the error between the calculated and experimental values ​​in both experiments was within 20%, thus proving that the prediction method matches the actual situation well.

[0056] An investigation was conducted into existing research, comparing the average fire spread rates of the same type of single-line, double-line, and triple-line fires. Figure 13 As shown in (a), it is evident that multiple wires promote the spread of flames over electrical wires. A fire spread zoning map was constructed based on key parameters such as wire spacing, copper core diameter, and insulation thickness, as shown below. Figure 13 As shown in (b), it is divided into three regions: in region one, the fire spread is suppressed under the effect of small spacing; in region two, the fire spread is promoted under the effect of medium spacing; in region three, the fire spread gradually weakens under the effect of large spacing, and after the flame interaction disappears, it is the same as the burning of a single wire.

Claims

1. A method for predicting the spread rate of fire from three parallel electric wires, characterized in that, include: Collect various physical characteristic parameters during the fire spread process of three parallel electric wires; Select any preheating zone of one of the three wires and construct the energy conservation equation per unit area per unit time in the preheating zone when the outer insulation material of the wire in the preheating zone is heated from room temperature to pyrolysis temperature. Calculate the heat transfer flux per unit area of ​​the preheating zone from the metal core of the wire. ; Calculate the heat flux per unit area of ​​the preheating zone from the flame. Meanwhile, based on the flame tilt and the coupling effect of the spacing between adjacent wires on radiative heat transfer, the viewing angle factor of the flame towards the preheating zone is corrected. Calculate the convective heat flux per unit area of ​​the preheating zone from the flame. ; as well as The collected physical property parameters are compared with the calculated heat conduction and heat flow. Thermal radiation and heat flow and convective heat transfer heat flow Substituting the obtained energy conservation equation, we can calculate the predicted spread rate of the fire across the three parallel electric wires.

2. The prediction method according to claim 1, characterized in that, The energy conservation equation per unit area per unit time in the preheating zone is: ； in, ρ p The density of the insulating material is expressed in kg / m³. c p Specific heat capacity of insulating material, kJ / kg·K; T p The pyrolysis temperature of the insulating material, in K; r c Let be the radius of the metal wire core, in meters (m). r 0 represents the radius of the entire conductor, in meters (m). v f The fire spread rate is expressed in m / s. Room temperature, K; The heat flux conducted per unit area of ​​the preheating zone by the metal core of the wire, in W / m 2 ; The heat flux radiated by the flame to a unit area of ​​the preheating zone, in W / m² 2 ; The heat flux from the flame to the preheating zone is the convective heat transfer flux, W / m³. 2 ; This is the length of the preheating zone.

3. The prediction method according to claim 1, characterized in that, The heat radiation heat flow per unit area of ​​the preheating zone from the flame The calculation is as follows: ； in, The emissivity of the flame; σ It is the Stefan-Boltzmann constant; F f The perspective factor of the flame toward the preheating zone.

4. The prediction method according to claim 3, characterized in that, When calculating the heat flux radiated by the flame to a unit area of ​​the preheating zone, assuming the flame is not tilted and the viewing angle factor of its own wire preheating zone is calculated as follows: ； When the flame is tilted, the viewing angle factor for its own wire preheating zone is calculated as follows: ； The viewing angle factor of the flame on other wire preheating zones is calculated as follows: ； in, , , W f The width of the flame is in meters (m). H f R is the flame height, in meters; R is the length of the line connecting the flame radiation micro-element surface and the preheating zone micro-element surface, in meters. It is the angle between the flame and the vertical direction.

5. The prediction method according to claim 4, characterized in that, The angle between the flame and the vertical direction It is obtained through the probability of flame merging, specifically including: First, the test video was edited, and the flame merging video in the stable phase was selected. Then, the video was processed frame by frame to obtain a grayscale image of the flame merging. The grayscale image is then converted to a binary image, and then the binary image is converted into flame merged data text using a Matlab program; Finally, after processing the text in drawing software, a flame merging probability cloud map is obtained, and the merging probability value of different positions of the flame can be directly obtained.

6. The prediction method according to claim 3, characterized in that, The emissivity of the flame is calculated as follows: ； in, The radiation absorption coefficient of hot flue gas particles. l m Let the average beam length be m; considering wire combustion as rectangular fuel combustion, therefore the equivalent diameter can be used. D e to replace l m .

7. The prediction method according to any one of claims 2-6, characterized in that, The length of the preheating zone The length of the preheating zone is determined using either thermocouple or infrared thermal imaging. For wires that can be directly photographed, the length is directly calculated using infrared thermal imaging. For obscured wires, the length is indirectly calculated using real-time thermocouple temperature data and the following formula: ； T ig The ignition temperature of the insulating material, in K; T s Let K be the surface temperature of the wire. t ph Preheating time, in seconds; v f The fire spread rate is expressed in m / s.

8. The prediction method according to any one of claims 1-6, characterized in that, The convective heat flux per unit area of ​​the preheating zone from the flame is calculated as follows: ； in, r 0 represents the radius of the entire conductor, in meters (m). T f Let K be the temperature of the flame. T p The pyrolysis temperature of the insulating material, in K; h The convective heat transfer coefficient is W / (m²). 2 ·K).

9. The prediction method according to claim 8, characterized in that, When three wires burn in parallel, the flame fusion characteristics are divided into three stages: complete fusion, intermittent fusion, and no fusion. For the three wires with equal spacing, the convective heat flux per unit area of ​​the preheating zone is calculated in stages according to the above-mentioned stages, where: During the complete merging phase, the convective heat flux is evenly distributed among the three wires, and the convective heat transfer flux per unit area of ​​the preheating zone from the flame is calculated according to the following formula: ； During the intermittent merging and non-merging phases, the convective heat flux per unit area of ​​the preheating zone from the flame is calculated using the following formula: ； in, d 0 represents the diameter of the entire conductor, in meters (m). is the thermal conductivity of air, W / (m·K); g The acceleration due to gravity is m / s². 2 ; β K is the gas expansion coefficient. -1 ; v For kinematic viscosity, m 2 / s; α m is the thermal diffusivity. 2 / s; The average temperature of the additional entrainment zone is given in K.

10. The prediction method according to claim 9, characterized in that, For the three wires with unequal spacing, the calculation formula for convective heat transfer flux in the fully merged stage is the same as that for the three wires with equal spacing. When calculating the convective heat transfer flux during intermittent merging and non-merging phases, a spacing correction factor is introduced based on the calculation formula for the three wires with equal spacing. The spacing correction factor for the wires on the left and right sides is: s is the spacing between the corresponding wire and the intermediate wire; The spacing correction factor for the middle wire is the geometric mean of the spacing correction factors for the two wires on the left and right sides.

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