CN111191382A - Method for calculating progressive crack propagation length of metal pipeline in front and back directions under internal explosion - Google Patents
Method for calculating progressive crack propagation length of metal pipeline in front and back directions under internal explosion Download PDFInfo
- Publication number
- CN111191382A CN111191382A CN202010023251.7A CN202010023251A CN111191382A CN 111191382 A CN111191382 A CN 111191382A CN 202010023251 A CN202010023251 A CN 202010023251A CN 111191382 A CN111191382 A CN 111191382A
- Authority
- CN
- China
- Prior art keywords
- pipeline
- crack
- explosion
- calculating
- length
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Abstract
The invention discloses a method for calculating the progressive expansion length of front and back cracks of a metal pipeline under internal explosion. The method can quickly obtain the progressive expansion length of the pipeline crack under the internal explosion, is simple and quick to calculate, solves the problem that the progressive expansion length of the crack is difficult to obtain through an experimental means, and has lower requirements on the knowledge and skill level of a calculator.
Description
Technical Field
The invention belongs to the field of pipeline explosion, and particularly relates to a method for calculating the progressive expansion length of front and back cracks of a metal pipeline under internal explosion.
Background
The pipeline is widely applied to the fields of chemical industry, nuclear power, storage and transportation and the like, and combustible and explosive dangerous liquid or gas is often conveyed inside the pipeline. In the case of a combustible gas pipeline, due to misoperation or other careless leakage, air or oxygen may be mixed in the combustible gas pipeline, and further, the pipeline explosion accident is caused. And from the microsecond time scale, the crack propagation of the pipeline under the action of the internal explosion is gradual or step-shaped, and the gradual crack propagation length in each period is referred to as the gradual crack propagation length. For some pipelines with certain wall thickness made of metal with better toughness, the gradual crack propagation distance can be obtained by measuring traces on the crack section; for the pipeline made of the material with thin wall thickness and poor toughness, the gradual crack propagation length cannot be obtained through an experimental means. Certainly, the crack progressive expansion distance can be obtained by constructing a numerical analysis model for crack expansion of the pipeline under the internal explosion, but the numerical model needs to consider the progressive damage and the evolution of the material and the fluid-solid coupling effect between the explosion shock wave and the pipeline, the model is complex, the construction difficulty is high, and the requirements on knowledge and skills of modeling personnel are high. At present, the mechanism of the gradual dynamic expansion of the pipeline crack under the internal explosion is not clear, so that no theoretical formula or method for calculating the gradual expansion length of the pipeline crack exists at present.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for calculating the progressive expansion length of the front and back cracks of a metal pipeline under internal explosion, which can quickly obtain the progressive expansion length of the cracks of the pipeline under internal explosion, is simple and quick to calculate, and has the following specific technical scheme:
a method for calculating the progressive propagation length of a front crack and a rear crack of a metal pipeline under internal explosion is characterized by comprising the following steps of:
s1: calculating the natural vibration frequency f of the pipeline0；
S2: determining axial movement rate D of explosive load in pipeline0；
S3: respectively calculating the average progressive expansion length of the forward crack and the backward crack of the pipeline according to the following formula
Wherein delta is the breaking elongation of the crack path material along the axial directionLength of length, f0In order to be the natural vibration frequency of the pipeline,
the average propagation speed of the crack is positive for forward cracks and negative for backward cracks.
Further, when the metal pipe is a pipe with two fixed ends, the natural vibration frequency f is0The calculation formula of (a) is as follows:
in the formula, R is the middle diameter of the pipeline, E is the elastic modulus of the pipeline material, rho is the density of the pipeline material, and nu is the Poisson ratio of the pipeline material.
Further, when the explosion in the pipeline is caused by the detonation of the combustible mixed gas, the axial movement rate D of the explosive load0Equal to the detonation velocity of the mixed gas, can be obtained by the following calculation formula according to the CJ detonation theory:
in the formula, Q is the heat released by the chemical reaction of the mixed gas with unit mass, and gamma is the polytropic index of the detonation product gas.
Further, when the explosion in the pipeline is caused by the detonation of the combustible mixed gas, the axial movement rate D of the explosive load0Equal to the mixed gas detonation velocity, the mixed gas detonation velocity can be obtained by inputting related information according to the prompt of a network station through the official network program https:// heart0。
Further, when the explosion in the pipeline is caused by the explosion of a linear explosive coaxial with the pipeline, the explosion velocity D of the explosive is found according to the type and the density of the explosive, and the explosion velocity D is the axial movement velocity D of the explosive load0。
Further, when the explosion in the pipeline is caused by the detonation of a point charge, the velocity of the axial movement of the detonation loadD0Equal to the propagation velocity of the shock wave in the pipe, and is calculated by the following formula:
D0＝(0.768+0.206L-0.10L2)-1×103
wherein, L is the length of the explosive core from the crack initiation position, and the unit is m.
Further, the average propagation speed of the crack
The time required for the crack to propagate over a given length is measured experimentally and is then obtained by dividing the given length by the time.
Furthermore, the value range of the elongation after fracture delta of the crack path material along the axial direction is 0-0.15, and the average propagation speed of the crack is
The value range of (A) is 200 m/s-300 m/s. .
The invention has the following beneficial effects:
(1) the method can conveniently and rapidly calculate the gradual expansion length of the pipeline crack under the internal explosion, and solves the problem that no theoretical calculation method for the gradual expansion length of the pipeline crack under the internal explosion exists at present;
(2) compared with a numerical modeling and simulation mode, the method is simpler, more convenient and faster in calculation, and has lower requirements on knowledge and skill level of a calculator;
(3) for the pipeline with poor material toughness and thin wall thickness, the method can directly obtain the gradual expansion length of the crack, and solves the problem that the gradual expansion length of the crack is difficult to obtain through an experimental means.
Detailed Description
The present invention will be described in detail below based on preferred embodiments, and objects and effects of the present invention will become more apparent, and it should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.
The invention discloses a method for calculating the progressive expansion length of a front crack and a rear crack of a metal pipeline under internal explosion, wherein the front crack is a crack with the crack expansion direction consistent with the direction of an internal explosion load, and the rear crack is a crack with the crack expansion direction opposite to the direction of the internal explosion load, and the method is characterized by comprising the following steps of:
s1: calculating the natural vibration frequency f of the pipeline0；
Wherein f is0There are various calculation methods:
for pipes fixed at both ends, the natural frequency f0Can be calculated from the following formula:
in the formula, R is the middle diameter of the pipeline, E is the elastic modulus of the pipeline material, rho is the density of the pipeline material, and nu is the Poisson ratio of the pipeline material.
For other cases, the calculation can be carried out through finite element modal analysis, scaling experiments and the like.
S2: determining axial movement rate D of explosive load in pipeline0；
(1) When the explosion in the pipeline is caused by the detonation of the combustible mixed gas, the axial movement rate D of the explosive load0Equal to the detonation velocity of the mixed gas, the value of which can be calculated by CJ detonation theory, NASA CEA (national space agency Chemical Equisibrium with Applications) program, if according to CJ detonation theory, the calculation formula is:
in the formula, Q is the heat released by the chemical reaction of unit mass of mixed gas; gamma is the polytropic index of detonation product gas and can be calculated by the type and volume percentage of chemical reaction products.
The NASA CEA program calculates the website as: https:// cearun. The detonation velocity of the mixed gas can be obtained by inputting related information according to the website prompt, namely the detonation velocityAxial rate of movement D of the explosive load0。
(2) When the explosion in the pipeline is caused by the explosion of a linear explosive coaxial with the pipeline, the explosion velocity D of the explosive is found according to the type and the density of the explosive, and the explosion velocity D is the axial movement velocity D of the explosive load0。
(3) When the explosion in the pipeline is caused by the explosion of the point explosive, the axial movement speed of the explosive load is equal to the propagation speed of the shock wave in the pipeline, and the axial movement speed is calculated by the length L (m) of the explosive core from the crack initiation position and the following empirical formula
D0＝(0.768+0.206L-0.01L2)-1×103
S3: respectively calculating the average progressive expansion length of the forward crack and the backward crack of the pipeline according to the following formula
And delta is the elongation after fracture of the crack path material along the axial direction, the value range is 0-0.15, and delta can be simply taken as 0 when no reliable data exist.
The method of the present invention is verified by experiments below.
A6061-T6 aluminum alloy pipeline with 914mm length, 41.28mm outer diameter and 0.89mm wall thickness is fixed at two ends, the middle part of the pipeline has the defect of 25.4mm length, 0.6mm width and 0.56mm depth, and the inside of the pipeline is provided with a pipeline with the molar ratio of 2: 1 mixed hydrogen and oxygen, the initial pressure of the mixed gas being 0.225MPa, 0.279MPa and 0.339MPa, respectively, and the initial temperature being 298K. The mixed gas is ignited at the center of the left end face of the pipeline and then detonates, under the high pressure action of detonation waves, the initial defect of the pipeline is initiated to penetrate through cracks, and the front and back cracks axially expand to cause the pipeline to break.
The calculation method of the invention is as follows:
(1) calculating natural vibration frequency of pipeline
The two ends of the pipeline are fixed, and the E, rho and v of 6061-T6 aluminum alloy are respectively 69GPa and 2780kg/m30.33. The natural vibration frequency is calculated by a theoretical formula as follows:
(2) determining axial movement rate of explosive load in pipeline
Calculating the detonation velocity of the mixed gas under 3 initial pressure conditions by adopting an NASA CEA program, inputting the types of the mixed gas into a webpage of the NASA CEA program, wherein the molar ratio is 2: 1, the initial pressure is 0.225MPa, 0.279MPa and 0.339MPa, the initial temperature is 298K, and the program can output the corresponding detonation velocity D0The settlement results were 2.75km/s, 2.76km/s and 2.77km/s, respectively.
(3) Calculating average progressive propagation length of pipeline crack
To simplify the calculation, the post-fracture elongation δ of the crack path material in the axial direction is taken to be 0. The average crack propagation speed is obtained by simulation of a simplified numerical model, pipelines in the numerical model are described by a Johnson-Cook material model, hexahedron first-order units are dispersed, simulation calculation is completed by LS-Dyna software, and then the average crack propagation speed under three initial pressure conditions is obtained through post-processing, and the average crack propagation speed is shown in table 1.
TABLE 1 average propagation velocity of pipe cracks at different initial pressures
And further calculating the average progressive crack propagation length by the following formula:
the theoretical calculation results and the actual average progressive propagation length of the crack are shown in table 2.
TABLE 2 comparison of theoretical calculation results of crack progressive propagation length with actual results
It can be seen from table 2 that the deviation between the theoretical calculation result and the actual result of the present invention is within 15%, and the calculation result of the present invention has better accuracy considering that the dynamic propagation of the crack under the internal explosion is a highly transient process, and the characteristic time scale is microsecond. The calculation deviation mainly comes from the fact that the elongation after fracture of the material of the crack path is not considered in the example (namely the plastic deformation of the material after fracture is not considered, and delta is 0), and if a reliable delta value is obtained, the calculation result of the method is more accurate.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and not intended to limit the invention, and although the invention has been described in detail with reference to the foregoing examples, it will be apparent to those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof. All modifications and equivalents may be resorted to as falling within the spirit and scope of the invention.
Claims (8)
1. A method for calculating the progressive propagation length of a front crack and a rear crack of a metal pipeline under internal explosion is characterized by comprising the following steps of:
s1: calculating the natural vibration frequency f of the pipeline0；
S2: determining axial movement rate D of explosive load in pipeline0；
S3: respectively calculating the average progressive expansion length of the forward crack and the backward crack of the pipeline according to the following formula
Wherein δ is the elongation after fracture of the crack path material in the axial direction, f0In order to be the natural vibration frequency of the pipeline,
the average propagation speed of the crack is positive for forward cracks and negative for backward cracks.
2. The method for calculating the progressive crack propagation length of the metal pipeline under the internal explosion according to claim 1, wherein when the metal pipeline is a pipeline with two fixed ends, the natural vibration frequency f of the metal pipeline is fixed0The calculation formula of (a) is as follows:
in the formula, R is the middle diameter of the pipeline, E is the elastic modulus of the pipeline material, rho is the density of the pipeline material, and nu is the Poisson ratio of the pipeline material.
3. The computational implosion of claim 1A method for progressively extending the length of a crack propagating forward and backward in a metal pipe after blasting, characterized in that the axial movement rate D of the explosive load is such that when the explosion in the pipe is caused by the detonation of a combustible gas mixture0Equal to the detonation velocity of the mixed gas, can be obtained by the following calculation formula according to the CJ detonation theory:
in the formula, Q is the heat released by the chemical reaction of the mixed gas with unit mass, and gamma is the polytropic index of the detonation product gas.
4. The method for calculating the progressive crack propagation length from front to back of the metal pipeline under internal explosion according to claim 1, wherein when the explosion in the pipeline is caused by the detonation of combustible mixed gas, the axial movement speed D of the explosive load is0Equal to the detonation velocity of the mixed gas, namely the axial movement velocity D of the explosive load can be obtained by inputting relevant information according to website prompts through an official network program https:// heart0。
5. The method for calculating the progressive crack propagation length of the metal pipeline under the internal explosion according to claim 1, wherein when the internal explosion of the pipeline is caused by the explosion of a linear explosive coaxial with the pipeline, the explosion velocity D of the explosive is found according to the type and the density of the explosive, and the explosion velocity D is the axial movement velocity D of the explosive load0。
6. The method for calculating the progressive crack propagation length of the metal pipeline under the internal explosion according to claim 1, wherein when the explosion in the pipeline is caused by the explosion of the point explosive, the axial movement rate D of the explosion load is0Equal to the propagation velocity of the shock wave in the pipe, and is calculated by the following formula:
D0＝(0.768+0.206L-0.01L2)-1×103
wherein, L is the length of the explosive core from the crack initiation position, and the unit is m.
7. The method for calculating the progressive crack propagation length under internal explosion of a metal pipeline according to claim 1, wherein the average crack propagation speed is
The time required for the crack to propagate over a given length is measured experimentally and is then obtained by dividing the given length by the time.
8. The method for calculating the progressive crack propagation length under the internal explosion according to claim 1, wherein the axial elongation at break delta of the crack path material ranges from 0 to 0.15, and the average crack propagation rate is 0 to 0.15
The value range of (A) is 200 m/s-300 m/s.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010023251.7A CN111191382A (en) | 2020-01-09 | 2020-01-09 | Method for calculating progressive crack propagation length of metal pipeline in front and back directions under internal explosion |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010023251.7A CN111191382A (en) | 2020-01-09 | 2020-01-09 | Method for calculating progressive crack propagation length of metal pipeline in front and back directions under internal explosion |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN111191382A true CN111191382A (en) | 2020-05-22 |
Family
ID=70708783
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010023251.7A Pending CN111191382A (en) | 2020-01-09 | 2020-01-09 | Method for calculating progressive crack propagation length of metal pipeline in front and back directions under internal explosion |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111191382A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113094908A (en) * | 2021-04-16 | 2021-07-09 | 中国石油大学(华东) | Combustible gas pipeline explosion intensity deduction method based on section trace measurement |
| CN113158489A (en) * | 2021-05-13 | 2021-07-23 | 中国石油大学(华东) | Equivalent load-based method for calculating wall thickness of anti-explosion pipeline |
| CN113190789A (en) * | 2021-04-29 | 2021-07-30 | 中国石油天然气集团有限公司 | Gas pipeline crack propagation speed calculation method |
-
2020
- 2020-01-09 CN CN202010023251.7A patent/CN111191382A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113094908A (en) * | 2021-04-16 | 2021-07-09 | 中国石油大学(华东) | Combustible gas pipeline explosion intensity deduction method based on section trace measurement |
| CN113190789A (en) * | 2021-04-29 | 2021-07-30 | 中国石油天然气集团有限公司 | Gas pipeline crack propagation speed calculation method |
| CN113190789B (en) * | 2021-04-29 | 2024-04-09 | 中国石油天然气集团有限公司 | Gas pipeline crack propagation speed calculation method |
| CN113158489A (en) * | 2021-05-13 | 2021-07-23 | 中国石油大学(华东) | Equivalent load-based method for calculating wall thickness of anti-explosion pipeline |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111191382A (en) | Method for calculating progressive crack propagation length of metal pipeline in front and back directions under internal explosion | |
| Turner et al. | Underwater implosion of cylindrical metal tubes | |
| Benselama et al. | A numerical study of the evolution of the blast wave shape in tunnels | |
| CN115221814B (en) | Hydrogen pipeline chemical explosion shock wave intensity prediction method | |
| Du et al. | Consequence analysis of premixed flammable gas explosion occurring in pipe using a coupled fluid-structure-fracture approach | |
| Rokhy et al. | 3D numerical simulation of the gas detonation forming of aluminum tubes considering fluid-structure interaction and chemical kinetic model | |
| Cheng et al. | Full-scale experimental investigation on the shock-wave characteristics of high-pressure natural gas pipeline physical explosions | |
| Du et al. | Incremental dynamic crack propagation of pipe subjected to internal gaseous detonation | |
| Kojima et al. | Numerical analysis of wave propagation across Solid–Fluid interface with Fluid–Structure interaction in circular tube | |
| Su et al. | Experimental and numerical evaluations on characteristics of vented methane explosion | |
| Du et al. | Propagation and intensity of blast wave from hydrogen pipe rupture due to internal detonation | |
| Wang et al. | Influence of ground impedance on explosive shock wave test accuracy | |
| CN107575265A (en) | A kind of analysis method for judging gas explosion of driving face in coal mine superpressure | |
| Chen et al. | Dynamic burst pressure of cylindrical explosion containment vessels | |
| WO2021138860A1 (en) | Method for calculating progressive expansion length of forward and backward cracks of metal pipe during internal explosion | |
| Wu et al. | Full‐scale experiments to study shock waves generated by the rupture of a high‐pressure pipeline | |
| CN110414822B (en) | Method for calculating internal explosion load rate according to pipeline crack progressive propagation distance | |
| Ligon et al. | Simplified Methodology for Analysis of Reflected Detonation and DDT: Part 1—Elastic Analysis | |
| Xuanneng Gao | Propagation law of shock waves in single layer spherical lattice shell under internal explosion | |
| WO2021012136A1 (en) | Method for calculating internal explosion load rate based on progressive extension distance of pipeline cracks | |
| Ma et al. | Experimental and numerical investigation of blast loads induced by moving charge explosion | |
| Kuang et al. | Study on the mesh size determination method of blast wave numerical simulation with strong applicability | |
| Chen et al. | Impact response of flowing-fluid filled square vessels | |
| Simoens et al. | Analysis of the dynamic response of a controlled detonation chamber | |
| Shepherd | Structural response to explosions |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |