A method and processor for predicting overpressure of combustible gas explosion in a square confined space

Abstract

This invention discloses a method and processor for predicting overpressure in a square confined space flammable gas explosion, relating to the field of flammable gas explosion overpressure prediction technology. The method includes: first, assuming relevant parameters during the explosion process in a square confined space; establishing a simplified physical model based on the flame development characteristics of flammable gas explosions in experiments; then, deriving a mathematical model for predicting explosion pressure based on the simplified physical model and the governing equations; finally, substituting the actual initial parameters from engineering predictions into the mathematical model for calculating explosion pressure, thus obtaining the predicted values ​​of overpressure at different stages of the explosion in the square confined space. The explosion overpressure prediction model established by this invention using a segmented method shows high agreement with experimental results; it can quickly predict the overpressure in a square confined space explosion, providing a reliable reference for assessing the hazard effects and consequences of flammable gas explosions.

Description

Technical Field

[0001] This invention relates to the field of overpressure prediction technology for combustible gas explosions, and specifically to a method and processor for predicting overpressure in combustible gas explosions in a square enclosed space. Background Technology

[0002] Currently, combustible gases such as natural gas and hydrogen are widely used due to their advantages of high calorific value, wide availability, and low pollution. They serve as industrial raw materials and fuels to provide energy for people's production and daily life. However, during their use, storage, and transportation, leaks of these combustible gases, when mixed with air, can easily trigger explosions upon contact with heat sources or sparks. This is especially true in confined spaces, where the pressure rises rapidly after an explosion due to wall constraints, creating shock waves that lead to structural damage, fragment scattering, and thermal radiation, resulting in severe property damage and casualties. To prevent accidents from occurring or escalating, improving the accuracy of explosion overpressure prediction is crucial for blast-resistant structural design and daily safety management. In particular, the peak overpressure generated during a confined space explosion is one of the most important parameters in blast-resistant design and daily safety management.

[0003] Currently, scholars in this field have conducted relevant research on explosion overpressure in confined spaces, gaining a relatively comprehensive understanding of explosion overpressure and its influencing factors. Due to experimental safety and economic constraints, the current approach primarily combines small-scale experiments, theoretical analysis, and numerical simulation to study explosion flame propagation and overpressure. In terms of experimental research and numerical simulation, the analysis of explosion flame propagation and explosion overpressure in pipelines is currently the most extensive research area. This research mainly focuses on the acceleration mechanism and overpressure caused by obstacles, shapes, and aspect ratios within the pipeline on explosion flame propagation. For the analysis of explosion flame propagation and overpressure in other containers, a 20L sphere is used as the background, and the effects of different gases, concentrations, ignition methods, and ignition energies on explosion overpressure and pressure rise rate are investigated. In terms of theoretical analysis, the acceleration mechanism of the explosion flame, the instability during explosion flame propagation, and the critical conditions for deflagration to detonation are analyzed. Combustible gas explosions occur frequently in industry and daily life, often inside factories, warehouses, and residential buildings, with extremely serious consequences. Existing research mainly focuses on pipes and spherical containers, but the study of the explosion characteristics of flammable gases occurring in square spaces is insufficient. Since explosions in square spaces such as factories and warehouses can have very serious consequences, research on explosions in square spaces is particularly important.

[0004] Guo Qiang et al. proposed "Experimental Study on Explosion and Detonation of Combustible Gas in a Square Space and Three-Dimensional Numerical Simulation," which analyzed a 1.21m... 3The study investigated the impact of pressure relief area and gas volume fraction within a square space on the explosion relief pressure, but neglected to consider the time parameter 't'. Its primary focus was on calculating the explosion relief pressure, lacking prediction of pressure changes over a specific time interval during an explosion in a square confined space. Time-pressure prediction would provide significant guidance for selecting the explosion relief pressure. This lack of prediction hinders the rapid and efficient development of explosion relief design schemes for square confined spaces. Hu Sheng et al.'s "A Review of Research on Combustible Gas Explosion Hazards and Pressure Relief Dimensions in Class A Warehouses" primarily utilized numerical simulation software for modeling, setting conditions, and calculations, without innovatively deriving or improving the formulas. Furthermore, the calculation formulas in the simulation software are not applicable to square confined spaces.

[0005] Therefore, further improvements are needed in the research on predicting flammable gas explosions in square enclosed spaces. Summary of the Invention

[0006] One of the objectives of this invention is to provide a method for predicting overpressure in a square confined space flammable gas explosion. This method is applicable to the study of flammable gas explosions in square confined spaces, and it is simple to operate and can be widely used in engineering applications. The prediction method of this invention provides a reliable reference for assessing the hazard effects and consequences of flammable gas explosions.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for predicting overpressure in a square confined space during a flammable gas explosion includes the following steps:

[0009] a. Assumptions are made regarding the relevant parameters during the explosion process in a square confined space;

[0010] b. Based on the characteristics of the flame development in a flammable gas explosion during the experiment, a simplified physical model is established. Assume the length, width, and height of the square enclosed space are x, y, and z, respectively, where x = a, y = b, and z = c. The explosion in the square confined space can be divided into three stages:

[0011] b1. Stage I: The reaction time is 0→t1. Assume that the flame development in this stage is a spherical laminar flame expansion, and the flame radius r1 in this stage satisfies 0. <r1≤a / 2;

[0012] b2. Stage II: The reaction time is t1→t2. Assume the flame in this stage is cylindrical, and the flame radius r2 in this stage satisfies a / 2 <r2≤b / 2;

[0013] b3. Stage III: The reaction time is t2→t3. Assume the flame shape in this stage is rectangular, and the flame radius r3 in this stage satisfies b / 2. <r3≤c / 2;

[0014] c. Based on the simplified physical model established in step b, and combined with the governing equations, derive the mathematical model for predicting explosion pressure.

[0015] The explosion pressure calculation formula for the first stage of the combustible gas reaction process in the aforementioned explosion pressure prediction mathematical model is shown in equation (1):

[0016]

[0017] In equation (1): P1 is the explosion pressure when the combustible gas reaches the corresponding flame area in stage I; P0 is the initial pressure of the square confined space; α is the turbulence factor; K r The combustion rate was measured at a reference temperature and pressure; t1 is the reaction time of stage I; V is the total volume of the square enclosed space; P m The final pressure of a square, enclosed space;

[0018] The explosion pressure calculation formula for the combustible gas reaction process in the second stage of the explosion pressure prediction mathematical model is shown in equation (2):

[0019]

[0020] In equation (2): P2 is the explosion pressure during the combustible gas reaction process in stage II; C1 is a constant coefficient; e is the natural constant; r2 is the flame radius in stage II; t2 is the reaction time in stage II;

[0021] The explosion pressure calculation formula for the combustible gas reaction process in the third stage of the explosion pressure prediction mathematical model is shown in equation (3):

[0022]

[0023] In equation (3): P3 is the explosion pressure during the combustible gas reaction process in stage III; C2 is a constant coefficient; r3 is the flame radius in stage III; R2 is the maximum flame radius in stage II; t3 is the reaction time in stage III;

[0024] d. Substitute the actual measured parameters into equations (1), (2), and (3) to obtain the explosion pressure of the explosive gas in the square confined space at different stages.

[0025] In the above-mentioned method for predicting overpressure of combustible gas explosion in a square confined space, the calculation of C1 in equation (2) is shown in equation (4):

[0026]

[0027] In equation (4): P1 is the explosion pressure when the combustible gas in stage I reaches the corresponding flame area; P0 is the initial pressure of the square confined space; e is the natural constant; α is the turbulence factor; K r The combustion rate measured at a certain reference temperature and reference pressure; P m t1 is the final pressure of the square enclosed space; r2 is the flame radius of stage II; t1 is the reaction time of stage I.

[0028] The above-mentioned method for predicting overpressure of combustible gas explosion in a square confined space is characterized in that: in equation (3), the calculation formula for C2 is as shown in equation (5):

[0029]

[0030] In equation (5): P3 is the explosion pressure during the combustible gas reaction process in stage III; P0 is the initial pressure of the square confined space; α is the turbulence factor; K r The combustion rate measured at a certain reference temperature and reference pressure; P m R2 represents the final pressure of the square enclosed space; R2 represents the maximum flame radius in stage II; and t2 represents the reaction time in stage II.

[0031] In the above-mentioned method for predicting overpressure in a square confined space combustible gas explosion, the relevant parameters in step a are assumed as follows: the explosion process is assumed to occur under insulated wall conditions; the combustible gas is uniformly distributed in the square confined space and ignited at the very center of the square confined space; in the initial reaction, the temperature of the combustible gas and the temperature of the combustion products remain constant throughout the explosion development process; in the initial reaction, both the combustible gas and the combustion products conform to the ideal gas law; and the effect of pressure rise on flame propagation speed within the square confined space is negligible.

[0032] In the above-mentioned method for predicting overpressure of combustible gas explosion in a square confined space, in step b, r1 is the distance from the explosion center to the spherical flame surface; r2 is the distance from the explosion center to the side of the cylindrical flame; and r3 is the distance from the explosion center to the side of the rectangular flame whose area no longer changes.

[0033] In the above-mentioned method for predicting overpressure of combustible gas explosion in a square confined space, in step c, during the combustible gas explosion process in the square confined space, it is assumed that the square confined space is an isothermal system and that the combustible gas satisfies the law of conservation of mass during the explosion process; the equations of state and the mass conservation equations of the unreacted and reacted substances are obtained.

[0034] Based on the equation of state and the mass conservation equation, the rate of change of the mass of the combusted gas per unit time is transformed into the pressure rise rate equation, as shown in equation (6):

[0035]

[0036] In equation (6): α is the turbulence factor; K r The combustion rate was measured at a reference temperature and reference pressure; A is the flame front area; V is the volume of the square enclosed space; P m P0 is the final pressure of the square confined space; P0 is the initial pressure of the square confined space; P is the explosion pressure.

[0037] For the first stage, the explosion pressure calculation formula for the combustible gas reaction process in the first stage is derived by combining formulas (7), (8) and (9) with formula (6);

[0038]

[0039] In equation (7): V b1 r1 represents the volume occupied by the reactants in stage I; r1 is the distance from the explosion center to the spherical flame surface.

[0040]

[0041] In equation (8): A1 is the area of ​​the flame front in stage I; r1 is the distance from the explosion center to the spherical flame front;

[0042]

[0043] In equation (9): A1 is the area of ​​the flame front in stage I; V is the volume of the square enclosed space; P m P0 is the final pressure of the square confined space; P1 is the initial pressure of the square confined space; P2 is the explosion pressure when the combustible gas in stage I reaches the corresponding flame area.

[0044] In the above-mentioned method for predicting the overpressure of combustible gas explosion in a square enclosed space, in step c, for stage II, the calculation formula for the explosion pressure in the combustible gas reaction process of stage II is derived by combining formulas (10), (11), and (12).

[0045]

[0046] In equation (10): V b2 R1 represents the volume occupied by the reactants in stage II; r2 represents the distance from the explosion center to the side of the cylindrical flame; R1 represents the maximum radius of the flame in stage I.

[0047] A2=4πR1r2 (11);

[0048] In equation (11): A2 is the flame front area in stage II; R1 is the maximum flame radius in stage I; r2 is the distance from the explosion center to the side of the cylindrical flame;

[0049]

[0050] In equation (12): A2 is the area of ​​the flame front in stage II; V is the volume of the square confined space; r2 is the distance from the explosion center to the side of the cylindrical flame; P m P0 is the final pressure of the square confined space; P2 is the initial pressure of the square confined space; P2 is the explosion pressure when the combustible gas in stage II reaches the corresponding flame area; R1 is the maximum flame radius in stage I.

[0051] In the above-mentioned method for predicting the overpressure of combustible gas explosion in a square confined space, in step c, for stage III, the calculation formula for the explosion pressure during the combustible gas reaction process in stage III is derived by combining formulas (13), (14), and (15):

[0052] V b3 =8R1R2(r3-r i3 (13);

[0053] In equation (13): V b3 R1 is the volume of reactants in stage III; R2 is the maximum flame radius in stage I; R3 is the flame radius in stage III; r i3 The initial flame radius for stage III;

[0054] A3 = 8R1R2 (14);

[0055] In equation (14): A3 is the flame front area in stage III; R1 is the maximum flame radius in stage I; R2 is the maximum flame radius in stage II;

[0056]

[0057] In equation (15); A3 is the flame front area of ​​stage III; V is the volume of the square enclosed space; r3 is the flame radius of stage III; r i3 P represents the initial flame radius for stage III. m P0 is the final pressure of the square confined space; P3 is the initial pressure of the square confined space; P4 is the explosion pressure when the combustible gas in stage III reaches the corresponding flame area.

[0058] Another object of the present invention is to provide a processor configured to execute the above-described method for predicting overpressure of combustible gas explosion in a square confined space.

[0059] Compared with the prior art, the present invention brings the following beneficial technical effects:

[0060] This invention conducts predictive research on flammable gas explosions within a square confined space. Through innovative derivation of the formula, it is made suitable for a square confined space. This invention is based on a square confined space where x = a, y = b, and z = c. The explosion overpressure prediction model is divided into three stages under certain conditions, with the flame radius of each stage being limited. By making assumptions about various conditions, the aspect ratio of the square space is limited, and the segmentation method is used to establish a model that has a high degree of agreement with the experimental results.

[0061] This invention approximates some parameters in a complex explosion process by simplifying the mathematical model and performing rapid calculations. A simplified physical model is established based on the flame development characteristics of combustible gas explosions in experiments. Based on this simplified physical model, the governing equations yield a mathematical model for predicting explosion pressure. By substituting the actual initial parameters from engineering calculations into the resulting mathematical model, the predicted overpressure values ​​for a square confined space at different stages of the explosion can be obtained. This enables rapid and accurate prediction and assessment of the overpressure in a square confined space combustible gas explosion, filling the gap in traditional simulations that only include spherical and various pipe models. Attached Figure Description

[0062] The invention will now be further described with reference to the accompanying drawings.

[0063] Figure 1 This is a flowchart of the overpressure prediction process for combustible gas explosion in a square enclosed space according to the present invention.

[0064] Figure 2 The three stages of simplifying the physical model of this invention are as follows: Figure 2 (a) represents stage I, (b) represents stage II, and (c) represents stage III.

[0065] Figure 3 This is a time history curve of acetylene explosion overpressure in a square enclosed space according to the present invention;

[0066] Figure 4 This is a time history curve of the overpressure of hydrogen and methane explosion in a square enclosed space according to the present invention.

[0067] Figure 5 This is a time history curve of overpressure in a square enclosed space for an oil and gas explosion according to the present invention. Detailed Implementation

[0068] This invention proposes a method and processor for predicting overpressure of combustible gas explosion in a square enclosed space. To make the advantages and technical solutions of this invention clearer and more explicit, the invention will be further described below with reference to specific embodiments.

[0069] The state equation and mass conservation equation mentioned in this invention are the basic equations for solving such problems. However, the basic equations are not applicable to square confined spaces. Therefore, this invention innovates the derivation of the existing equations to make them more suitable for square confined spaces. Through the verification of the embodiments, the method of this invention can achieve rapid and accurate prediction of the overpressure of combustible gas explosion in square confined spaces.

[0070] In addition, for faster calculation, the prediction method proposed in this invention can be imported into a processor, making its calculation speed faster and suitable for quickly assessing the explosion pressure range and pressure changes in a square confined space.

[0071] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.

[0072] The flowchart for predicting overpressure of combustible gas explosion in a square confined space according to this invention is as follows: Figure 1 As shown, the operation process is as follows:

[0073] The first step is to make approximate assumptions about some parameters in the complex explosion process; the specific assumptions are: the explosion process takes place under the condition of an insulated wall; the combustible gas is evenly distributed in the square confined space and ignites at the very center of the square confined space;

[0074] Initial reaction combustible gas temperature (T) u ) and combustion product temperature (T b The value of T remains constant throughout the explosion's development. u =T i = constant, T b =T f = constant; the initial reaction combustible gas and combustion products both conform to the ideal gas law; the effect of pressure rise on flame propagation speed is ignored.

[0075] The second step is to establish a simplified physical model based on the characteristics of the flame development of combustible gas explosions in the experiment.

[0076] like Figure 2 As shown, a physical model is established. Let the length, width, and height of the rectangular enclosed space be x, y, and z, respectively, where y = a, y = b, z = c, and a ≤ 1 / 3 b ≤ 1 / 3 c. Then, the explosion of this rectangular enclosed space can be divided into three stages:

[0077] like Figure 2 As shown in (a), in stage I, the reaction time is 0→t1. It is assumed that the flame development in this stage is almost a spherical laminar flame expansion, and the flame radius at this time satisfies 0. <r1≤a / 2。

[0078] like Figure 2As shown in (b), in stage II, the reaction time is t1→t2. When the spherical flame develops to a certain stage, the flame front encounters a narrower xy wall and cannot continue to develop, but is continuously compressed. This causes the flame to develop uniformly towards the wider wall. To simplify the calculation process, the flame development shape in this stage is approximated as cylindrical, and the flame radius at this time satisfies a / 2 <r2≤b / 2。

[0079] like Figure 2 As shown in (c), in stage III, the reaction time is t2→t3. At this time, the columnar flame cannot continue to develop after its side contacts the xz wall and is continuously compressed. This causes the flame to develop uniformly in the direction of the wider wall. To simplify the calculation process, the flame development shape in this stage is approximated as a rectangle. At this time, the flame radius satisfies b / 2. <r3≤c / 2。

[0080] In the simplified physical model, the flame radius is defined as the distance from the explosion center to the interface between the unburned and burned zones of the flame. Specifically, in stage I, the flame radius r1 refers to the distance from the explosion center to the spherical flame surface; in stage II, the flame radius r2 refers to the distance from the explosion center to the side of the cylindrical flame. In stage III, the flame radius r3 refers to the distance from the explosion center to the side of the rectangular flame with a constant area. This constant side can be further understood as the side of the rectangular flame whose area remains unchanged.

[0081] The third step involves establishing a simplified physical model and combining it with the governing equations to derive a mathematical model for predicting explosion pressure.

[0082] Establish the governing equations, assuming an isothermal system and that the combustible gas always satisfies mass conservation during the explosion:

[0083] For an isothermal system, the equations of state for the unreacted and reacted substances are as follows:

[0084]

[0085] The mass conservation equation is:

[0086] m = m u +m b =n u M u +n b M b (3);

[0087] V = V u +V b (4); In equations (1), (2), (3), and (4), m is the initial total mass of the premixed gas; m b The mass of the premixed gas that has been burned; m u The mass of unburned premixed gas; n u n is the number of moles of unburned premixed gas.b M represents the number of moles of the burned products. u M is the molar mass of the unburned premixed gas; b V represents the molar mass of the combustion products. u V is the volume of the unburned premixed gas. b V is the volume of combustion products; P is the total volume of the square confined space; R is the explosion pressure; T is the ideal gas constant. u T represents the initial temperature of the combustible gas in the reaction. b Temperature of the combustion products;

[0088] Throughout the explosion, for the isothermal system:

[0089]

[0090] In equation (5), P0 is the initial pressure; P m This refers to the final pressure, i.e., the maximum pressure; n i and n f The masses of the initial and final states are n, respectively. i ≈n f V0 is the initial gas volume;

[0091] After the combustible gas is ignited in the confined space, the reacting gas flows into the flame surface without turbulence at a velocity v. The mass flowing into the flame surface per unit time is:

[0092]

[0093] In equation (6), ρ u Where A is the density of the combustible gas; A is the flame front area; v is the velocity of the reacting gas;

[0094] If expressed in terms of moles, then:

[0095]

[0096] Using equation (1), the rate of change of combustion mass is expressed in terms of burned gas. Substituting this into equation (7), the rate of change of burned gas mass per unit time can be expressed as:

[0097]

[0098] In the formula, K r The combustion rate is measured at a certain reference temperature and reference pressure; α is the turbulence factor, which is 1 under laminar flow conditions.

[0099] Combining the equation of state and the mass conservation equations (2) to (5), the mass change rate form of equation (8) can be replaced with the pressure rise rate form:

[0100]

[0101] The mathematical model of overpressure in a square confined space explosion corresponds to a physical model divided into three stages. If heat loss from the container is ignored, the maximum pressure P of the gas explosion in the confined container... m The reaction is independent of the size and shape of the container, and depends only on the final state of the reaction. Therefore, it is assumed here that the maximum pressure P of the combustible gas reaction is... m Consistent with the reaction state equation (1) and equation (5), the reactant volumes for stages I, II, and III are:

[0102]

[0103] In the formula, P1, P2, and P3 represent the explosion pressures at the corresponding flame areas in stages I, II, and III, respectively; V b1 V b2 and V b3 n1, n2, and n3 represent the volumes occupied by reactants in stages I, II, and III, respectively; n1, n2, and n2 represent the molar numbers of combusted products in stages I, II, and III, respectively.

[0104] Based on the formulas for flame volume and flame front area in different stages of the explosion model, combined with equations (13)-(15), the formulas for the pressure rise rate in the three stages of an explosion in a square sealed container can be obtained as follows:

[0105] For Phase I: Combining equation (13), we get:

[0106]

[0107] Substituting this into formula (9), we obtain the formula for the rate of pressure rise during the explosion in the closed container in stage I:

[0108]

[0109] make Equation (17) can be written as:

[0110]

[0111] The explosion pressure during the first stage of the combustible gas explosion reaction was then obtained:

[0112]

[0113] For Phase II: A2 = 4πR1r2, when the flame develops to the shortest wall surface in the first stage, the flame volume V is... e1 for:

[0114]

[0115] Flame volume V at the initial stage of flame development in stage II i2 It can be calculated that:

[0116]

[0117] Assume that the flame volume at the end of stage I and the beginning of stage II are approximately equal:

[0118] V e1 ≈V i2 (twenty two);

[0119] By combining equations (20-22), the initial radius r of the cylindrical flame at the beginning of stage II is obtained. i2 :

[0120]

[0121] Then, combining equation (13), we get:

[0122]

[0123] Similarly, the formula for the rate of pressure rise during an explosion in a closed container in stage II is obtained as follows:

[0124]

[0125] During this stage, the flame radius r2 exhibits a certain functional change with the reaction time t2. Differentiating equation (14) with respect to t2 yields...

[0126]

[0127] and

[0128]

[0129] This is how the flame speed is obtained:

[0130]

[0131] Integrating both sides of equation (29), we can solve the equation to obtain the relationship between r2 and t2 in this stage.

[0132] Then, by rearranging and transforming equation (25), the explosion pressure during the second stage of the combustible gas explosion reaction process was obtained:

[0133]

[0134] In the formula, C1 is a constant coefficient, which varies under different reaction gas and reaction vessel conditions. It can be obtained by substituting the explosion pressure value P1 and reaction time t1 obtained in stage I and then back-calculating.

[0135]

[0136] For Phase III: V b3 =8R1R2(r3-r i3 A3 = 8R1R2, when the flame develops to the shortest wall surface in stage II, the flame volume V e2 for:

[0137]

[0138] Flame volume V at the initial stage of flame development in stage III i3 It can be calculated that:

[0139]

[0140] Similarly, assuming that the flame volume at the end of stage II and the beginning of stage III is approximately equal,

[0141] V e2 ≈V i3 (34);

[0142] The initial radius r of the cylindrical flame shape at the beginning of stage II is calculated using equations (32-34). i3 :

[0143]

[0144] Then, combining equation (13), we get:

[0145]

[0146] The flame radius r3 in this stage also changes as a function of the reaction time t3. Similarly, the derivative of equation (15) with respect to t3 is obtained.

[0147] Similarly, the formula for the rate of pressure rise during an explosion in a closed container in stage III is obtained as follows:

[0148]

[0149] By rearranging and transforming equation (37), the explosion pressure during the third stage of the combustible gas explosion reaction process is obtained:

[0150]

[0151] In the formula, C2 is a constant coefficient, which varies under different reaction gas and reaction vessel conditions. C2 can be obtained by substituting the explosion pressure value P2 obtained in stage I and the reaction time t2 and then back-calculating:

[0152]

[0153] Determine the initial parameter K r P m P0 and the lengths of flame radii r1, r2, and r3 at each stage determined according to the size of the square confined space, can be substituted into equations (19), (30), and (37) to calculate the predicted values ​​of the explosion overpressure in the square confined space at different stages of the explosion.

[0154] As can be seen from the above explosion pressure model, for a cube-shaped container, when min(x,y,z) = mid(x,y,z) = max(x,y,z), the model in stage I can directly perform the calculation. For mid(x,y,z) = max(x,y,z) > min(x,y,z), the calculation can be performed using the models in stages I and II respectively. In other cases, the explosion pressure of each stage needs to be solved according to the models in stages I, II, and III.

[0155] The fourth step involves substituting the actual predicted initial parameters of the project into the mathematical model obtained in the fourth step to calculate the predicted values ​​of the overpressure in the square confined space at different stages of the explosion.

[0156] To make the calculation of the method of the present invention faster, a corresponding processor can also be configured to execute the method for predicting the overpressure of a combustible gas explosion in a square confined space according to the present invention. The specific configuration can be implemented by those skilled in the art by referring to the existing technology.

[0157] Example 1:

[0158] The above-mentioned method for predicting the overpressure of combustible gas explosion in a square confined space is verified below with specific embodiments. Related experiments were selected where the reaction vessels were all square containers with a length-to-diameter ratio max(x,y,z) / min(x,y,z)≤3. Their pressure data were compared and verified with the above model. The experimental conditions are shown in Table 1. The overpressure results of combustible gas explosion obtained from the experiments were compared with the overpressure results calculated using equations (19), (30), and (37). The results are as follows: Figure 3 , Figure 4 , Figure 5 As shown.

[0159] Table 1

[0160]

[0161] from Figure 3 It can be seen that when max(x,y,z) / min(x,y,z) = 1 in the square confined space, the explosion overpressure calculated using the model theory for the combustible gas acetylene is almost completely consistent with the experimental results. Figure 4 and Figure 5 It can be seen that when max(x,y,z) / min(x,y,z)=2 and max(x,y,z) / min(x,y,z)=2.5, for combustible gases, in the initial stage of explosion, the trend of the explosion overpressure calculated by this model is basically consistent with that obtained by the experiment; in the later period, the results obtained by theoretical calculation deviate slightly from the experimental results.

[0162] Therefore, when the aspect ratio of the square confined space is small, the mathematical model for predicting explosion pressure established using the segmented method shows a higher degree of agreement with the experimental results. The main reason is that when the aspect ratio of the confined space is small, the explosion flame develops from the ignition center and, as the flame radius continues to expand, it almost always develops as a smooth, spherical laminar flame. However, in a confined space with a larger aspect ratio, the combustion reaction develops as a smooth, spherical laminar flame in the early stage, but in the middle stage, the spherical flame is gradually compressed, accelerating the time of flame instability, and eventually evolving into a folded or even turbulent flame that propagates outward.

[0163] At this point, the flame front will spread to the unburned area more quickly, prompting a new combustion reaction. This results in a significant reduction in the mass of combustible premixed gas per unit time compared to a smooth laminar flow flame, leading to a marked change in the explosion overpressure process.

[0164] Comparative analysis revealed that when the ratio of the maximum to minimum side length of the confined space was 1, 2, and 2.5, the relative errors between the experimental results and the theoretical calculations using the theoretically established mathematical model for predicting explosion pressure under the three working conditions were 6.09%, 8.7%, and 9.75%, respectively. All three relative errors were less than 10%, especially under the condition of a small aspect ratio. Therefore, when the aspect ratio of the confined space max(x,y,z) / min(x,y,z) ≤ 3, the established mathematical model for predicting explosion pressure can provide support to a certain extent for the explosion-proof design and daily safety management of confined spaces.

[0165] In summary, the method of this invention can achieve rapid and accurate prediction and assessment of overpressure in a square enclosed space due to flammable gas explosions, filling the gap in traditional simulation methods that only have spherical and various pipe models, and improving the ability to prevent and control indoor gas explosion disasters.

[0166] Any parts not mentioned in this invention can be achieved by referring to existing technologies.

[0167] It should be noted that those skilled in the art should recognize that the above embodiments are only used to illustrate this application and are not intended to limit this application. Any appropriate changes and variations made to the above embodiments within the essential spirit and scope of this application should fall within the scope of protection of the claims of this application.

Claims

1. A method for predicting overpressure in a square confined space during a combustible gas explosion, characterized in that, Includes the following steps: a. Assumptions are made regarding the relevant parameters during the explosion process in a square confined space; b. Based on the characteristics of the flame development in a flammable gas explosion during the experiment, a simplified physical model is established. Assume the length, width, and height of the square enclosed space are x, y, and z, respectively, where x = a, y = b, and z = c. The explosion in the square confined space can be divided into three stages: b1. Stage I: The reaction time is 0→t1. Assume that the flame development in this stage is a spherical laminar flame expansion, and the flame radius r1 in this stage satisfies 0. <r1≤a / 2; b2. Stage II: The reaction time is t1→t2. Assume the flame in this stage is cylindrical, and the flame radius r2 in this stage satisfies a / 2 <r2≤b / 2 b3. Stage III: The reaction time is t2→t3. Assume the flame shape in this stage is rectangular, and the flame radius r3 in this stage satisfies b / 2. <r3≤c / 2; c. Based on the simplified physical model established in step b, and combined with the governing equations, derive the mathematical model for predicting explosion pressure. The explosion pressure calculation formula for the first stage of the combustible gas reaction process in the aforementioned explosion pressure prediction mathematical model is shown in equation (1): In equation (1): P1 is the explosion pressure when the combustible gas in stage I reaches the corresponding flame area; P0 is the initial pressure of the square confined space; α is the turbulence factor; K r The combustion rate was measured at a reference temperature and reference pressure; t1 is the reaction time of stage I; V is the total volume of the square enclosed space; P m The final pressure of a square, enclosed space; The explosion pressure calculation formula for the combustible gas reaction process in the second stage of the explosion pressure prediction mathematical model is shown in equation (2): In equation (2): P2 is the explosion pressure during the combustible gas reaction process in stage II; C1 is a constant coefficient; e is the natural constant; r2 is the flame radius in stage II; t2 is the reaction time in stage II; The explosion pressure calculation formula for the combustible gas reaction process in the third stage of the explosion pressure prediction mathematical model is shown in equation (3): In equation (3): P3 is the explosion pressure during the combustible gas reaction process in stage III; C2 is a constant coefficient; r3 is the flame radius in stage III; R2 is the maximum flame radius in stage II; t3 is the reaction time in stage III; d. Substitute the actual measured parameters into equations (1), (2), and (3) to obtain the explosion pressure of the explosive gas in the square confined space at different stages.

2. The method for predicting overpressure of combustible gas explosion in a square confined space according to claim 1, characterized in that: In equation (2), the calculation of C1 is shown in equation (4): In equation (4): P1 is the explosion pressure when the combustible gas in stage I reaches the corresponding flame area; P0 is the initial pressure of the square confined space; e is the natural constant; α is the turbulence factor; K r The combustion rate measured at a certain reference temperature and reference pressure; P m t1 is the final pressure of the square enclosed space; r2 is the flame radius of stage II; t1 is the reaction time of stage I.

3. The method for predicting overpressure of combustible gas explosion in a square confined space according to claim 2, characterized in that: In equation (3), the calculation formula for C2 is shown in equation (5): In equation (5): P3 is the explosion pressure during the combustible gas reaction process in stage III; P0 is the initial pressure of the square confined space; α is the turbulence factor; K r The combustion rate measured at a certain reference temperature and reference pressure; P m R2 represents the final pressure of the square enclosed space; R2 represents the maximum flame radius in stage II; and t2 represents the reaction time in stage II.

4. The method for predicting overpressure of combustible gas explosion in a square confined space according to claim 1, characterized in that: In step a, the relevant parameters are assumed to be as follows: the explosion process is assumed to take place under insulated wall conditions; the combustible gas is uniformly distributed in the square confined space and ignited at the very center of the square confined space; in the initial reaction, the temperature of the combustible gas and the temperature of the combustion products remain constant throughout the explosion development process; in the initial reaction, both the combustible gas and the combustion products conform to the ideal gas law; and the effect of pressure rise on the flame propagation speed in the square confined space is negligible.

5. The method for predicting overpressure of combustible gas explosion in a square confined space according to claim 1, characterized in that: In step b, r1 is the distance from the explosion center to the spherical flame surface; r2 is the distance from the explosion center to the side of the cylindrical flame; and r3 is the distance from the explosion center to the side of the rectangular flame whose area no longer changes.

6. The method for predicting overpressure of combustible gas explosion in a square confined space according to claim 1, characterized in that: In step c, during the explosion of combustible gas in a square confined space, it is assumed that the square confined space is an isothermal system and that the combustible gas satisfies the law of conservation of mass during the explosion; the equations of state and the mass conservation equations for the unreacted and reacted substances are obtained. Based on the equation of state and the mass conservation equation, the rate of change of the mass of the combusted gas per unit time is transformed into the pressure rise rate equation, as shown in equation (6): In equation (6): α is the turbulence factor; K r The combustion rate was measured at a reference temperature and reference pressure; A is the flame front area; V is the volume of the square enclosed space; P m P0 is the final pressure of the square confined space; P0 is the initial pressure of the square confined space; P is the explosion pressure. For the first stage, the explosion pressure calculation formula for the combustible gas reaction process in the first stage is derived by combining formulas (7), (8) and (9) with formula (6); In equation (7): V b1 r1 represents the volume occupied by the reactants in stage I; r1 is the distance from the explosion center to the spherical flame surface. In equation (8): A1 is the area of ​​the flame front in stage I; r1 is the distance from the explosion center to the spherical flame front; In equation (9): A1 is the area of ​​the flame front in stage I; V is the volume of the square enclosed space; P m P0 is the final pressure of the square confined space; P1 is the initial pressure of the square confined space; P2 is the explosion pressure when the combustible gas in stage I reaches the corresponding flame area.

7. The method for predicting overpressure of combustible gas explosion in a square confined space according to claim 6, characterized in that: In step c, for stage II, the explosion pressure calculation formula for the combustible gas reaction process in stage II is derived by combining formulas (10), (11), and (12); In equation (10): V b2 R1 represents the volume occupied by the reactants in stage II; r2 represents the distance from the explosion center to the side of the cylindrical flame; R1 represents the maximum radius of the flame in stage I. A2=4πR1r2 (11); In equation (11): A2 is the flame front area in stage II; R1 is the maximum flame radius in stage I; r2 is the distance from the explosion center to the side of the cylindrical flame; In equation (12): A2 is the area of ​​the flame front in stage II; V is the volume of the square confined space; r2 is the distance from the explosion center to the side of the cylindrical flame; P m P0 is the final pressure of the square confined space; P2 is the initial pressure of the square confined space; P2 is the explosion pressure when the combustible gas in stage II reaches the corresponding flame area; R1 is the maximum flame radius in stage I.

8. The method for predicting overpressure of combustible gas explosion in a square confined space according to claim 6, characterized in that: In step c, for stage III, the explosion pressure calculation formula for the combustible gas reaction process in stage III is derived by combining formulas (13), (14), and (15): In b3 =8R1R2(r3-r i3 ) (13); In equation (13): V b3 R1 is the volume of reactants in stage III; R2 is the maximum flame radius in stage I; R3 is the flame radius in stage III; r i3 The initial flame radius for stage III; A3 = 8R1R2 (14); In equation (14): A3 is the flame front area in stage III; R1 is the maximum flame radius in stage I; R2 is the maximum flame radius in stage II; In equation (15); A3 is the flame front area of ​​stage III; V is the volume of the square enclosed space; r3 is the flame radius of stage III; r i3 P represents the initial flame radius for stage III. m P0 is the final pressure of the square confined space; P3 is the initial pressure of the square confined space; P4 is the explosion pressure when the combustible gas in stage III reaches the corresponding flame area.

9. A processor, characterized in that: It is configured to perform the method for predicting overpressure of combustible gas explosion in a square confined space as described in any one of claims 1 to 8.

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