Prediction method for XPS time of ignition of thermal insulation material by fire spread of electric wire under limitation of single-side outer wall

Abstract

The invention discloses a method for predicting the XPS time of ignition of a thermal insulation material by fire spread of an electric wire under a limited single-side outer wall, and belongs to the technical field of ignition time prediction. The method comprises the following steps: data acquisition: acquiring various parameters in the ignition process of ignition of XPS by fire spread of a wire under the condition that a single-side outer wall is limited; and time prediction: inputting the acquired data into a prediction model to predict the time t of igniting the XPS by the fire spread of the electric wire, and dividing the process of igniting the XPS by the fire spread of the electric wire into two stages: a contraction stage and an ignition stage of the XPS, so that the calculation formula of the ignition time t is as follows: t = tig + tsh. By adopting the technical scheme of the invention, the time for igniting the XPS material by the electric wire under the condition that the single-side outer wall is limited can be accurately predicted, so that a scientific basis is provided for the safety design of a building, and the occurrence of fire accidents is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of prediction of ignition time, and more specifically, relates to a method for predicting the time when a wire fire spreads and ignites the thermal insulation material XPS under the limitation of a single-sided exterior wall. Background Technique

[0002] With the increasing requirements for heat insulation performance in modern buildings, extruded polystyrene (XPS), as a widely used thermal insulation material, is widely used due to its excellent thermal insulation performance. However, the performance of XPS materials under fire conditions remains an important safety hazard. Especially in fires caused by wire short circuits or other electrical faults, the spread of wire flames may lead to the ignition of XPS, thus triggering a larger-scale fire.

[0003] In practical applications, the interaction between wires and thermal insulation materials is often affected by building design, material properties, and environmental conditions. Through research and analysis, wires are often connected to thermal insulation materials, and in building exterior walls, wires usually penetrate directly inside the thermal insulation materials. Once a wire catches fire, the flame will spread rapidly, thus igniting the thermal insulation material. If not handled properly, it will lead to an expansion of the fire range and cause significant losses. Especially under the condition of a single-sided exterior wall limitation, the propagation of wire flames is restricted by the wall and surrounding materials, which may cause the flame to be more concentrated and the temperature to be higher, thus affecting the ignition time of XPS. Therefore, the coupling factors between wire fire spread and ignition of thermal insulation materials under the structure of a single-sided exterior wall limitation must be emphasized.

[0004] Currently, there are still relatively few methods for predicting the ignition time of wires igniting XPS under specific limited conditions, mainly relying on experience and qualitative analysis, lacking systematic quantitative research and model support, and existing research often ignores the influence of material thickness, heat conduction characteristics, and the surrounding environment, making it difficult to effectively evaluate fire risks and take corresponding protective measures in practical engineering. Therefore, there is an urgent need for a scientific and accurate prediction method to better understand the influence of wire fire spread on the ignition time of XPS, so as to improve the fire safety of buildings. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for predicting the time when a wire fire spreads and ignites the thermal insulation material XPS under the limitation of a single-sided exterior wall, so as to solve the technical problem in the prior art that it is difficult to accurately predict the ignition time of a wire fire spreading and igniting XPS. Adopting the technical solution of the present invention can accurately predict the time when a wire ignites the XPS material under the condition of a single-sided exterior wall limitation, thus providing a scientific basis for the safety design of buildings and reducing the occurrence of fire accidents.

[0006] To achieve the above object, the technical solution provided by the present invention is as follows:

[0007] The present invention provides a prediction method for the time when a wire fire spreads and ignites the thermal insulation material XPS under the limitation of a single-sided exterior wall. Under the condition of a single-sided exterior wall limitation, the preheating zone when the wire fire spreads to the XPS is selected as the control volume, and the wire penetration position is taken as the ignition point. The prediction method includes:

[0008] Data collection, collecting various parameters during the process of a wire fire spreading and igniting XPS under the condition of a single-sided exterior wall limitation. The parameters include, but are not limited to, the physical property parameters of the wire metal core and XPS, the thickness in the direction of the wire penetrating the XPS, the width and height of the wire flame, the shrinkage distance of the XPS, the temperatures of the flame and the gypsum board, and the internal temperature of the XPS; and

[0009] Time prediction, inputting the collected data into a prediction model to predict the time t when the wire fire spreads and ignites the XPS. Among them, the process of the wire fire spreading and igniting the XPS is divided into two stages: the shrinkage stage of the XPS and the ignition stage. Therefore, the calculation formula for the ignition time t is as follows: t = t ig + t sh ;

[0010] In the above formula, t ig is the ignition time of the XPS; t sh is the shrinkage time of the XPS.

[0011] According to any one of the technical solutions of the present invention, the ignition time t of the XPS is determined by selecting according to the thickness of the XPS ig calculation model:

[0012]

[0013] In the above formula, ρ is the density of the XPS, kg / m 3 ; c is the specific heat capacity of the XPS, J / (kg·K); d is the thickness in the direction of the wire penetrating the XPS, m; k is the thermal conductivity of the XPS, W / (m·K); T ∞ is the room temperature, K; T ig,XPS is the ignition temperature of the XPS; is the heat flux received at the ignition point, and its calculation is as follows:

[0014]

[0015] Among them, is the heat flux of the ignition flame, W / m 2 ; is the external heat flux, W / m 2 ; is the heat loss caused by the re-radiation and convection on the surface of the XPS, W / m 2 .

[0016] Furthermore, the heat flux of the ignition flame is calculated according to the following method:

[0017]

[0018] In the above formula, is the heat conduction heat flow of the wire metal core to the unit area of the preheating zone, W / m 2 ; is the convective heat transfer heat flow of the flame to the unit area of the preheating zone, W / m 2 ; is the thermal radiation heat flow of the flame to the unit area of the preheating zone, W / m 2 .

[0019] More preferably, when calculating , the heat conduction model is transformed from the general cylindrical wall heat conduction to the composite cylindrical wall heat conduction, and its calculation formula is as follows:

[0020]

[0021]

[0022] T c is the temperature of the metal core, K; T p，XPS is the pyrolysis temperature of XPS, K; r c is the radius of the metal core, m; r o is the radius of the whole wire, m; r XPS is the radius of the surface covered with XPS, m; λ p is the thermal conductivity of the insulating material PE, W / (m·K); λ p,XPS is the thermal conductivity of the thermal insulation material XPS, W / (m·K); h c is the heat transfer coefficient of the metal core, W / (㎡·K); T f is the temperature of the flame, K; W f is the flame width, m; L p，XPS is the pyrolysis length of XPS, m; λ c is the thermal conductivity of the metal core, W / (m·K).

[0023] More preferably, the calculation method of the convective heat transfer heat flow of the flame to the unit area of the preheating zone is as follows:

[0024]

[0025] h pf is the convective heat transfer coefficient from the flame to XPS, and is calculated according to the following formula:

[0026]

[0027] In the above formula, k g is the heat transfer coefficient in the gas phase, L is the characteristic length, Nu is the Nusselt number, and is calculated according to the following formula:

[0028]

[0029] Both C and n are constants, and the Rayleigh number R a is calculated through the following formula:

[0030]

[0031] Gr is the Grashof number; Pr is the Prandtl number; where g is the acceleration due to gravity, m / s 2 ; β is the coefficient of gas expansion, K -1 ; υ is the kinematic viscosity, m 2 / s; α is the thermal diffusivity of air, m 2 / s.

[0032] Even more preferably, the heat radiation heat flux of the flame to the unit area of the preheating zone is calculated as follows:

[0033]

[0034] In the above formula, ε f is the emissivity of the flame; σ is the Stefan-Boltzmann constant, is the view factor of the flame to the preheating zone; where:

[0035]

[0036] κ is the radiation absorption coefficient of the hot flue gas particles; l m is the average beam length, m, d o is the diameter of the entire wire, m.

[0037] Even more preferably, the flame radiation plane is regarded as an isosceles triangle with the flame width as the base and the flame height as the height, and the origin is taken at the center position of the flame bottom to establish the calculation formula of the flame view factor, and the view factor from the flame surface to the preheating zone surface can be obtained as:

[0038]

[0039] According to any one of the technical solutions of the present invention, the external heat flux consists of the following parts:

[0040]

[0041] Among them, is the side exterior wall, that is, the heat conduction heat flux per unit area of the gypsum board to the preheating zone, W / m 2 ; is the convective heat transfer heat flux per unit area of the gypsum board to the preheating zone, W / m 2 ; is the thermal radiation heat flux per unit area of the gypsum board to the preheating zone, W / m 2 .

[0042] Further preferably, when calculating the heat conduction heat flux per unit area of the side exterior wall to the preheating zone , the heat conduction between the side exterior wall and the XPS at ignition is regarded as one-dimensional steady-state flat heat conduction, and the temperature of the side exterior wall and the pyrolysis temperature of the XPS are taken as the temperature difference to establish the Fourier heat conduction formula, that is:

[0043]

[0044] where R t is the thermal resistance of each part.

[0045] Further preferably, and are calculated with reference to and

[0046] According to any of the technical solutions described in the present invention, the shrinkage time t sh of the XPS is calculated as follows:

[0047]

[0048] L 0 is the original thickness of the XPS in the x-axis direction, unit m; L sh is the shrinkage distance of the XPS, unit m; α XPS is the linear expansion coefficient of the XPS; m is the mass of the XPS, kg; c XPS is the specific heat capacity of the XPS, J / (kg·K); A is the area receiving heat. When calculating the area receiving heat, the smaller value of the wire flame height and half of the height of the thermal insulation material is taken as the height of the receiving surface, and the thickness of the material is taken as the width of the receiving surface.

[0049] Adopting the technical solution provided by the present invention, compared with the prior art, the following beneficial effects can be achieved:

[0050] (1) The present invention proposes a prediction method for the time of wire fire spread to ignite XPS under the condition of limited unilateral exterior wall. Through this prediction model, the time of wire ignition of XPS material can be accurately predicted, which is beneficial to improving the fire safety of buildings, providing a scientific basis for the safety design of buildings, and reducing the occurrence of fire accidents.

[0051] (2) When predicting the time for the wire fire to spread and ignite XPS, the present invention fully considers the influence of the heat shrinkage of XPS itself on the ignition time, introduces the concept of shrinkage time for the first time, and relates it to the convective heat and radiative heat of the flame, thereby facilitating the improvement of the accuracy of the prediction results.

[0052] (3) When calculating the heat conduction heat flux of the wire metal core to the unit area of the preheating zone, the present invention considers the thermal conductivity parameter of the XPS adhesion layer, converts the heat conduction model from the general cylindrical wall heat conduction to the composite cylindrical wall heat conduction, thus being closer to the actual situation and further improving the prediction accuracy; at the same time, the copper core temperature that is not easily measured is converted into the easily measured wire flame temperature according to the pyrolysis length and the flame width, improving the simplicity of the prediction. Description of the Drawings

[0053] Figure 1 Schematic diagram of the wire fire spreading and igniting XPS;

[0054] Figure 2 Schematic diagram of XPS shrinkage and heat conduction model;

[0055] Figure 3 Flame and gypsum board radiation model;

[0056] Figure 4 Preheating length of the wire and preheating zone length under different restrictions when the restricted distance is 30 mm in the embodiment;

[0057] Figure 5 Comparison between the ignition time values of each component calculated in the embodiment of the present invention and the experimental statistical values;

[0058] Figure 6 Heat flux feedback of each component received by the XPS preheating zone under two types of wires in the embodiment of the present invention. Detailed Embodiment

[0059] The present invention provides a method for predicting the time for a wire fire to spread and ignite a thermal insulation material XPS under the restriction of a single-sided exterior wall. As Figure 1 shown in the schematic diagram of the wire fire spreading and igniting XPS, under the condition of being restricted by a single-sided exterior wall, the preheating zone when the wire fire spreads to XPS is selected as the control volume, and the wire penetration position is taken as the ignition point. The following assumptions are made to simplify the calculation process: the temperature distribution on the cross-section of the wire metal core and the insulation layer is uniform; the deformation caused by heat of the gypsum board is ignored, that is, there is no change at the place where it is in contact with the gypsum board; the heat loss caused by the wire is ignored; the burned part is adiabatic; the same position as the wire penetration is taken as the ignition point, and the change of the ignition point caused by the flame oscillation during the shrinkage process is ignored.

[0060] Due to the obvious shrinkage phenomenon of XPS, the ignition time cannot be predicted simply by the ignition time calculated from heat, so as Figure 2 shown, the present invention divides the overall process of wire fire spreading and igniting XPS into two stages: the shrinkage stage and the ignition stage, that is, fully considering the shrinkage time t sh of XPS. The shrinkage distance is taken as the distance from the starting surface of XPS to the ignition point; and the heat conduction caused by the gypsum board is approximately considered as one-dimensional steady-state heat conduction, and the temperature of the gypsum board is taken as the value at the starting section of XPS; when analyzing the flame view factor, as Figure 3 shown, the flame is approximately considered as an isosceles triangle; when considering the view factor of the gypsum board, it is also simplified to the flame projection (isosceles triangle).

[0061] The following will specifically describe the solution of the present invention in detail with reference to specific embodiments. The embodiments of the present invention use two different types of wires (Type Ⅰ: the copper core diameter is 6 mm and the insulation layer thickness is 2 mm; Type Ⅱ: the copper core diameter is 8 mm and the insulation layer thickness is 2 mm), and the size of XPS is 5 cm × 5 cm × 10 cm.

[0062] The prediction method of the embodiments of the present invention includes:

[0063] Data collection, collecting various parameters during the ignition process of wire fire spreading and igniting XPS under the condition of a single-sided exterior wall restriction. The parameters include the physical property parameters of the wire metal core and XPS, the thickness of the wire penetrating the XPS direction, the width and height of the wire flame, the fire spreading speed, the shrinkage distance of XPS, the temperatures of the flame and the gypsum board, and the internal temperature of XPS; and

[0064] Time prediction, inputting the collected data into the prediction model to predict the time t of wire fire spreading and igniting XPS; the calculation formula of the ignition time t in the present invention is as follows:

[0065] t = t ig + t sh (1)

[0066] Wherein, t ig is the ignition time of XPS; t sh is the shrinkage time of XPS.

[0067] Specifically, when collecting data, the process of flame spread is recorded by a camera to obtain the width and height of the wire flame, the fire spread speed, and the shrinkage distance of the XPS; the temperature of the flame and the gypsum board and the internal temperature of the XPS are measured by a K-type thermocouple and a data module; at the same time, the spread of the flame is also photographed by an infrared thermal imager, so that the temperature distribution of the gas phase and the solid phase during the wire combustion process can be more intuitively displayed, facilitating the observation of the heat changes of the flame, the copper core, and the XPS, and the change of the XPS preheating zone can be intuitively observed.

[0068] Furthermore, the ignition time t of the XPS is determined according to the thickness of the XPS. ig Whether the calculation model of is the thick thermal model or the thin thermal model is specifically calculated as follows:

[0069]

[0070] Among them, ρ is the density of the XPS, kg / m 3 ; c is the specific heat capacity of the XPS, J / (kg·K); d is the thickness in the direction of the wire penetrating the XPS, m; k is the thermal conductivity of the material, W / (m·K); is the heat flux received at the ignition point, W / m 2 .

[0071] Specifically, if the thickness L of the material is less than a certain critical thickness L c , it is the thin thermal model; if the thickness L is greater than the critical thickness L c , it is the thick thermal model. Usually, the estimation formula for the critical thickness L c is:

[0072]

[0073] Among them, k usually represents the thermal conductivity of the material, W / (m·K); h is the external convective heat transfer coefficient, W / (m 2 ·K); c p is the specific heat capacity of the material, J / (kg·K). In practical applications, usually, when the thickness of the material exceeds 0.05 m (50 mm), it is considered the thick thermal model. Since the thickness of the thermal insulation material in the embodiment of the present invention is 5 mm, the calculation model of the ignition time should be the thick thermal model, that is, the ignition time calculation formula is established by using the ignition temperature of the XPS and the total heat obtained at the ignition point.

[0074] The XPS in the preheating zone is heated from the room temperature T ∞ to the ignition temperature T ig,XPS . The energy conservation equation per unit area and per unit time at the ignition point in the preheating zone is:

[0075]

[0076] In the above formula, is the heat flux received at the ignition point, W / m 2 ; is the heat flux of the ignition flame, W / m 2 ; is the external heat flux, W / m 2 ; is the heat loss due to XPS surface re-radiation and convection, W / m 2 ; that is, the heat obtained at the ignition point is divided into the flame heat flux caused by the wire flame, the external heat flux caused by the gypsum board, and the heat loss caused by XPS surface re-radiation and heat flow.

[0077] Specifically, the heat flux of the ignition flame consists of the following parts:

[0078]

[0079] is the heat conduction heat flow of the wire metal core to the unit area of the preheating zone, W / m 2 ; is the convective heat transfer heat flow of the flame to the unit area of the preheating zone, W / m 2 ; is the thermal radiation heat flow of the flame to the unit area of the preheating zone, W / m 2 .

[0080] As a preferred implementation manner of the embodiment of the present invention, when calculating the heat conduction heat flow of the wire metal core to the unit area of the preheating zone, since the wire is inserted into the XPS, it can also be regarded as the heat conduction of the cylindrical wall, and the thickness of the XPS attached to the surface can be approximately estimated as the thickness of the insulating layer. Therefore, the calculation formula is as follows:

[0081]

[0082] In the above formula, T c is the temperature of the metal core, K; T p，XPS is the pyrolysis temperature of the XPS, K; r c is the radius of the metal core, m; r o is the radius of the entire wire, m; r XPS is the radius of the surface covered with XPS, m; λ p is the thermal conductivity of the insulating material PE, W / (m·K); λ p,XPS is the thermal conductivity of the thermal insulation material XPS, W / (m·K). Since the thermal conductivity parameters of the XPS attachment layer are considered and the thermal conductivity model is transformed from the general cylindrical wall thermal conductivity to the composite cylindrical wall thermal conductivity, it is closer to the actual situation and can improve the accuracy of prediction.

[0083]

[0084] In the above formula, h c is the heat transfer coefficient of the metal wire core, W / (㎡·K); T f is the temperature of the flame, K; W f is the width of the flame, m; L p，XPS is the pyrolysis length of XPS, m; λ c is the thermal conductivity of the metal wire core, W / (m·K). Through this calculation formula, the temperature of the copper core, which is not easy to measure, is converted into the temperature of the wire flame that is easy to measure according to the pyrolysis length and the flame width.

[0085] Therefore, the heat conduction heat flow of the metal wire core of the wire to the unit area of the preheating zone is:

[0086]

[0087] As a preferred implementation manner of the embodiment of the present invention, under the condition of no external conditions such as air flow, the convective heat transfer process can be calculated according to natural convection. Therefore, the convective heat transfer heat flow of the flame to the unit area of the preheating zone is calculated as follows:

[0088]

[0089] where h pf is the convective heat transfer coefficient from the flame to XPS and can be calculated according to the following formula:

[0090]

[0091] In the above formula, k g is the gas-phase heat transfer coefficient; Nu is the Nusselt number; L is the characteristic length and can be calculated by half of the XPS thickness.

[0092] The convective heat transfer coefficient is determined by Nu, and the relationship between Nu and the Rayleigh number R a is as follows:

[0093]

[0094] Both C and n are constants, and their specific values are related to the value range of R a ; Since the embodiment of the present invention can be approximately considered as vertical plate convection, Ra can be calculated by the following formula:

[0095]

[0096] Gr is the Grashof number; Pr is the Prandtl number; where g is the acceleration of gravity, m / s 2; β is the gas expansion coefficient, K -1 ; υ is the kinematic viscosity, m 2 / s; α is the thermal diffusivity of air, m 2 / s.

[0097] Therefore, the convective heat transfer flux per unit area of the preheating zone by the flame is:

[0098]

[0099] Specifically, in the embodiments of the present invention, it can be approximately considered as vertical plate convection, and Ra ≤ 10 9 , so Nu can be calculated by the following formula:

[0100]

[0101] Therefore, the convective heat transfer flux per unit area of the preheating zone by the flame is:

[0102]

[0103] Further preferably, the radiative heat transfer flux per unit area of the preheating zone by the flame is:

[0104]

[0105] In the above formula, ε f is the emissivity of the flame; σ is the Stefan-Boltzmann constant, and its value is approximately 5.67×10 -8 W / (㎡·K 4 ); is the view factor from the flame to the preheating zone; where:

[0106] ε f = 1 - exp(-κl m ) (16)

[0107] κ is the radiative absorption coefficient of the hot flue gas particles, l m is the mean beam length, m; considering the wire combustion as rectangular fuel combustion, so the equivalent diameter D e can be used to replace l m , that is:

[0108]

[0109] d o is the diameter of the whole wire, m.

[0110] The distance from the micro-element area of the preheating zone to the radiation plane is half of the length of the pyrolysis zone, that is:

[0111]

[0112] x is the distance from the differential area in the preheating zone to the radiation plane, m; L p is the length of the pyrolysis zone, m.

[0113] The differential area of the radiation plane on the wire flame surface is dA i , and the differential area of the XPS preheating zone surface is dA j , the length of the connecting line between the two differential elements is R, and the connecting line forms polar angles θ i and n j with the normal n i to the radiation plane respectively. j and θ i The values of R, θ j and θ i vary with the positions of the upper area of A j and A

[0114]

[0115] Specifically, as shown in Figure 3 (a), considering the flame radiation plane as an isosceles triangle with the flame width as the base and the flame height as the height, and taking the center position at the bottom of the flame as the origin to establish the calculation formula for the flame view factor, the view factor from the flame surface to the preheating zone surface in this embodiment can be obtained as:

[0116]

[0117] Therefore, the heat radiation heat flux of the flame to the unit area of the preheating zone is:

[0118]

[0119] In the embodiment of the present invention, under the condition of limited unilateral outer wall, the external heat flux consists of the following parts:

[0120]

[0121] Among them is the heat conduction heat flux of the gypsum board (side outer wall) to the unit area of the preheating zone, W / m 2 ; is the convective heat transfer heat flux of the gypsum board to the unit area of the preheating zone, W / m 2 ; is the heat radiation heat flux of the gypsum board to the unit area of the preheating zone, W / m 2 .

[0122] Further preferably, since this process generally belongs to a short-time ignition process and the temperature change of the gypsum board during the ignition process is ignored, it can be considered that the heat conduction between the gypsum board and the XPS during ignition belongs to one-dimensional steady-state flat heat conduction. Taking the temperature of the gypsum board and the pyrolysis temperature of the XPS as the temperature difference, the Fourier heat conduction formula is established, that is:

[0123]

[0124] In the above formula, R t is the thermal resistance of each part. From Figure 2 (b), it can be judged that the heat conduction in the embodiment of the present invention is divided into two sections, and the heat flow of the gypsum board conduction is:

[0125]

[0126] That is, the heat conduction process is divided into two sections, and the whole process is transformed into one-dimensional steady-state composite wall heat conduction affected by the restricted distance and the shrinkage distance. Then, according to the thermal conductivity of the gypsum board and the XPS, the total thermal resistance is determined, and finally the calculation formula for the gypsum board heat conduction is established. Specifically, in the embodiment of the present invention, the thermal conductivity λ g of the gypsum board is 0.25 W / (m·K), and the thermal conductivity λ XPS of the XPS is 0.040 W / (m·K); s is the side restricted distance, in m; L sh is the shrinkage distance of the XPS, in m.

[0127] Further preferably, to calculate the convective heat transfer heat flow per unit area of the gypsum board to the preheating zone, it can be calculated with reference to 's calculation formula:

[0128]

[0129] Specifically in this embodiment:

[0130]

[0131] Further preferably, when calculating the thermal radiation heat flow per unit area of the gypsum board to the preheating zone, it can be calculated with reference to 's calculation formula:

[0132]

[0133] Among them, ε g is the surface emissivity of the gypsum board, which is 0.93; is the view factor of the gypsum board to the preheating zone.

[0134] Specifically, in combination with Figure 3(b), in the embodiment of the present invention, the flame projection radiation plane is regarded as an isosceles triangle with the flame width as the base and the flame height as the height, and the center position at the bottom of the flame is taken as the origin. Since the restricted distance has a great influence on the radiation of the gypsum board, the restricted distance s is introduced on the original basis to establish an orthogonal coordinate system with the z-axis, and finally the calculation formula of the view factor for the radiation of the gypsum board to the preheating zone is established:

[0135]

[0136] Furthermore, in this embodiment, the heat loss caused by XPS surface re-radiation and convection is calculated as follows:

[0137]

[0138] h t，XPS is the total surface heat transfer coefficient of XPS heat loss to the surrounding environment, W / (㎡·K); h c，XPS is the convective heat transfer coefficient of the surface of XPS heat loss to the surrounding environment, W / (㎡·K); ε XPS is the emissivity of XPS to the surroundings; σ is the Stefan-Boltzmann constant; σ XPS is the Stefan-Boltzmann constant.

[0139] In the present invention, due to the obvious shrinkage phenomenon of XPS, the ignition time cannot be predicted simply by the ignition time obtained from heat calculation. The shrinkage time t sh should also be considered. Since the thermal insulation material is closely attached to the side gypsum board, compared with the influence of the wire flame, the shrinkage degree caused by the gypsum board can be ignored. Therefore, it can be considered that the heat flux causing material shrinkage is The shrinkage distance (L sh ) of XPS can be calculated by the linear thermal expansion formula:

[0140] L sh = L 0 α XPS ΔT (30)

[0141] where L 0 is the original thickness of XPS along the x-axis direction, in m; α XPS is the linear expansion coefficient of XPS, which is 60×10 -6 ; ΔT is the temperature change difference, in °C; combined with the definition of heat flux, it can be obtained that:

[0142]

[0143] m is the mass of XPS, in kg; c XPS is the specific heat capacity of XPS, in J / (kg·K); A is the area receiving heat, in m2 It can be seen from the above formula that the shrinkage distance is proportional to the sum of the convective heat and radiative heat from the flame. Therefore, the shrinkage time t sh can be expressed as:

[0144]

[0145] Due to the uncertainty of the wire flame height under different working conditions, sometimes the flame height will exceed the top of the thermal insulation material, and sometimes it will not reach it. Therefore, the smaller value of the wire flame height and half of the height of the thermal insulation material (XPS) is taken as the height of the acceptance surface, and the thickness of the XPS material is the width of the acceptance surface.

[0146] Specifically, in the embodiment of the present invention, the thickness and width of the selected thermal insulation material are both 5 cm. Therefore, A can be taken as the product of the flame height and the characteristic length of the material. When the flame height exceeds half of the original thermal insulation material height H 0 half, the height is taken as half of H 0 half. It can be seen from the above formula that the shrinkage distance is proportional to the sum of the convective heat and radiative heat from the flame. Therefore, the shrinkage time t sh is expressed as:

[0147]

[0148] The total ignition time for the wire fire to spread and ignite XPS in the embodiment of the present invention is:

[0149]

[0150] Converting the total ignition time into the sum of the ignition time and the shrinkage time, compared with the existing research, the introduction of the shrinkage time is conducive to better analyzing the ignition behavior of thermoplastic materials and is more in line with the actual situation.

[0151] The present invention can also calculate the shrinkage speed of XPS according to the shrinkage distance and shrinkage time of XPS, and thus can further calculate the length of the preheating zone of XPS:

[0152]

[0153] Since there is little research on how to calculate the length of the preheating zone of thermoplastic materials in the existing research, due to the different combustion behaviors of XPS and the wire fire spread behavior, when calculating the length of the preheating zone of XPS, the shrinkage speed is used to replace the fire spread speed of the material to estimate the preheating zone of XPS.

[0154] Such as Figure 6 shows the calculated values of the heat of each component of two wire models. Combining Figure 6 it can be seen that the flame convective heat flux It plays an important role in the flame propagation process, significantly greater than other parts. Different from the heat fluxes of other parts, the heat conduction flux of the gypsum board can be observed It is always in a downward trend. This is because the influencing factors include not only the temperature of the gypsum board but also the side limited distance s, and the thermal conductivity of XPS is much smaller than that of the gypsum board. Therefore, in this experiment, the influence of the limited distance is greater than that of the gypsum board temperature, and finally makes It also shows a downward trend in Region I. And according to Figure 6 The calculated values of the heat of each specific component shown, the heat flux of the flame gas required in Equation (34) can be obtained And the total heat received by the XPS preheating zone It provides convenience and basis for the subsequent calculation of the shrinkage time, ignition time and preheating zone length.

[0155] The calculated values obtained by using the prediction method of this embodiment are compared with the actual values. As Figure 4 shown, when the limited distance s is 30 mm, the experimental values of the XPS preheating zone length measured by infrared and thermocouple respectively are compared with the calculated values (the relevant calculation parameters are shown in Table 1, and the comparison results are shown in Table 2 below). Its ignition time is the synthesis of the preheating time, melting time and pyrolysis time, which is detailed in the experimental values measured by the thermocouple, and the experimental values and calculated values of each working condition are finally compared and fitted. As Figure 5 shown, the results show that the fitting error is within 20%, so the model is in good agreement with the experimental values.

[0156] Table 1 Specific calculated values for igniting XPS when the limited distance of Type I wire is 30 mm

[0157]

[0158] Table 2 Some key characteristic parameters for igniting XPS when the limited distance of Type I wire is 30 mm

[0159]

[0160] In summary, the present invention provides an effective prediction method for evaluating the ignition time of a wire igniting an XPS (extruded polystyrene) thermal insulation material under the condition of a unilateral outer wall constraint. Specifically, the present invention can accurately predict the ignition time, especially in the case where the heat transfer and fire spread characteristics between the wire and the XPS material are complex. A comprehensive prediction model is established, thereby improving the fire safety of buildings. By accurately predicting the time when the wire ignites the XPS material, it provides a scientific basis for the safe design of buildings and reduces the occurrence of fire accidents. At the same time, it can also provide tools and methods for building designers and engineers to conduct fire risk assessments and material selections during the design phase, and optimize the fire protection design of buildings.

Claims

1. A method for predicting the XPS time of electric wire fire spreading and igniting thermal insulation materials under a restricted single-side exterior wall, characterized in that: Under the condition of limited single-side exterior wall, the preheating area when the wire fire spreads to XPS is selected as the control body, and the wire insertion position is taken as the ignition point. The prediction method includes: Data collection: collect various parameters during the process of wire fire spreading and igniting XPS under the condition of limited external wall on one side, including but not limited to the physical characteristics of wire metal core and XPS, the thickness of wire in the direction of XPS insertion, the width and height of wire flame, the shrinkage distance of XPS, the temperature of flame and gypsum board, and the internal temperature of XPS; and Time prediction: The collected data is input into the prediction model to predict the time t of wire fire spreading and igniting XPS. The process of wire fire spreading and igniting XPS is divided into two stages: the contraction stage of XPS and the ignition stage. Therefore, the calculation formula of ignition time t is as follows: t = t ig +t sh ; In the above formula, t ig is the ignition time of XPS; t sh is the shrinkage time of XPS.

2. The prediction method according to claim 1, characterized in that: Determine the XPS ignition time t according to the XPS thickness selection ig Computational model: When judging thermally thick and thin models, the following conditions are usually used: Where ρ is the density of XPS, kg / m 3 ; c is the specific heat capacity of XPS, J / (kg·K); d is the thickness of the wire in the direction of XPS insertion, m; k is the thermal conductivity of XPS, W / (m·K); T ∞ is room temperature, K; T ig,XPS is the ignition temperature of XPS; is the heat flux received at the ignition point and is calculated as: in, is the heat flux of the pilot flame, W / m 2 ; is the external heat flux, W / m 2 ; is the heat loss due to re-radiation and convection on the XPS surface, W / m 2 .

3. The prediction method according to claim 2, characterized in that: The heat flux of the pilot flame Calculated according to the following method: In the above formula, The heat flux of the wire metal core to the unit area of ​​the preheating zone, W / m 2 ; is the convective heat transfer heat flux per unit area of ​​the flame in the preheating zone, W / m 2 ; is the heat flux of flame radiation per unit area of ​​preheating zone, W / m 2 .

4. The prediction method according to claim 3, characterized in that: In the right When performing calculations, the heat conduction model is transformed from general cylindrical wall heat conduction to composite cylindrical wall heat conduction, and the calculation formula is as follows: T c is the temperature of the metal wire core, K; T p，XPS is the pyrolysis temperature of XPS, K; r c is the radius of the metal wire core, m; r o is the radius of the entire conductor, m; r XPS is the radius of the surface covered by XPS, m; λ p is the thermal conductivity of the insulating material PE, W / (m·K); λ p,XPS is the thermal conductivity of the thermal insulation material XPS, W / (m·K); h c is the heat transfer coefficient of the metal core, W / (㎡·K); T f is the flame temperature, K; W f is the flame width, m; L p，XPS is the pyrolysis length of XPS, m; λ c is the thermal conductivity of the metal wire core, W / (m·K).

5. The prediction method according to claim 3, characterized in that: Convective heat transfer heat flow per unit area of ​​the flame preheating zone The calculation method is as follows: h pf is the convective heat transfer coefficient from flame to XPS, calculated according to the following formula: In the above formula, k g is the gas phase heat transfer coefficient, L is the characteristic length, and Nu is the Nusselt number, which can be calculated according to the following formula: C and n are constants, and the Rayleigh number R a The calculation is done by the following formula: Gr is the Grashof number; Pr is the Prandtl number; where g is the acceleration due to gravity, m / s 2 ; β is the gas expansion coefficient, K -1 ; υ is kinematic viscosity, m 2 / s; α is the thermal diffusion coefficient of air, m 2 / s.

6. The prediction method according to claim 3, characterized in that: Heat flux of flame radiation per unit area of ​​preheating zone The calculation process is as follows: In the above formula, ε f is the emissivity of the flame; σ is the Stefan-Boltzmann constant, is the viewing angle factor of the flame to the preheating zone; where: κ is the radiation absorption coefficient of hot flue gas particles; l m is the average beam length, m, d o is the diameter of the entire wire, m.

7. The prediction method according to claim 6, characterized in that: The flame radiation plane is regarded as an isosceles triangle with the flame width as the base and the flame height as the height, and the center of the flame bottom is taken as the origin to establish the calculation formula of the flame view factor. The view factor from the flame surface to the preheating zone surface can be obtained as:

8. The prediction method according to any one of claims 2 to 7, characterized in that: The external heat flux It consists of the following parts composition: in, is the heat conduction heat flux per unit area of ​​the preheating zone from the side exterior wall, i.e. the gypsum board, W / m 2 ; is the convection heat transfer heat flux per unit area of ​​the preheating zone of the gypsum board, W / m 2 ; is the heat flux per unit area of ​​the preheating zone from the gypsum board, W / m 2 .

9. The prediction method according to claim 8, characterized in that: Calculate the heat conduction heat flux per unit area of ​​the preheating zone from the side exterior wall When the heat conduction between the side outer wall and XPS during ignition is regarded as one-dimensional steady-state flat plate heat conduction, and the side outer wall temperature and the pyrolysis temperature of XPS are taken as the temperature difference, and the Fourier heat conduction formula is established, namely: Among them, R t is the thermal resistance of each part.

10. The prediction method according to any one of claims 2 to 7, characterized in that: XPS contraction time t sh The calculation is as follows: L0 is the original thickness of XPS along the x-axis, in m; L sh is the shrinkage distance of XPS, unit: m; α XPS is the linear expansion coefficient of XPS; m is the mass of XPS, kg; c XPS is the specific heat capacity of XPS, J / (kg·K); A is the area receiving heat. When calculating the area receiving heat, the smaller value between the flame height of the wire and half the height of the insulation material is taken as the height of the receiving surface, and the thickness of the material is taken as the width of the receiving surface.

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