Nonlinear state equation underwater explosion numerical calculation load correction method based on water

Abstract

The invention relates to an underwater explosion numerical calculation load correction method based on a water nonlinear state equation, and belongs to the technical field of underwater structure damage and protection. According to the method, a nonlinear fitting state equation of water is used as a correction object, an initial load curve under a typical three-dimensional underwater explosion working condition is obtained through an ALE numerical calculation method, a theoretical shock wave peak value is divided by an initial numerical shock wave peak value to obtain an initial correction coefficient, C1-C6 in the nonlinear fitting state equation of water is multiplied by the initial correction coefficient, and the initial load curve under the typical three-dimensional underwater explosion working condition is obtained. A corrected result is obtained; due to the fact that parameters of the corrected nonlinear fitting state equation of the water change, the compression ratio of the water at the measuring point changes, the shock wave peak pressure obtained after preliminary correction is lower than the theoretical shock wave peak pressure, repeated iteration correction is needed, and the pressure ratio and the compression ratio in iteration are utilized to calculate the pressure value of the water according to the mutual influence relation between the pressure ratio and the compression ratio in iteration. And a nonlinear fitting state equation parameter correction formula of water is obtained, so that the underwater explosion numerical calculation load meets the engineering application requirement.

Description

Technical Field

[0001] The invention relates to the technical field of underwater structure damage and protection, in particular to a load correction method for underwater explosion numerical calculation based on a nonlinear state equation of water. Background Art

[0002] With the development of numerical calculation technology for underwater explosions, the technology of three-dimensional numerical calculation using the ALE method has emerged. This technology suppresses the numerical oscillation before and after the shock wave interruption by adding artificial viscosity terms, thereby improving the stability of the calculation.

[0003] However, the above-mentioned method of adding artificial viscosity has the problem of introducing artificial interference and causing calculation errors, especially in the mid- and far-field calculation conditions, the shock wave peak clipping and smoothing caused by superimposed grid homogenization makes the calculation error more obvious. Although previous studies have attempted to increase the shock wave peak by increasing the mass of the explosive package, it will cause the bubble pulsation period and bubble radius to be inconsistent with the actual situation, affecting the structural load response of the bubble pulsation stage during the mid-field calculation, which has a major defect.

[0004] Therefore, it is urgent to provide a load correction method for numerical calculation of underwater explosion based on the nonlinear state equation of water. Summary of the invention

[0005] In view of the shortcomings in the above-mentioned existing production technology, the applicant provides a method for correcting the load of underwater explosion numerical calculation based on the nonlinear state equation of water, thereby compensating for the defect of insufficient numerical calculation accuracy by correcting the parameters of the nonlinear state equation of water, and provides an engineering correction coefficient calculation formula for easy use in actual engineering.

[0006] The technical solution adopted by the present invention is as follows: a method for correcting loads of underwater explosion numerical calculation based on nonlinear state equation of water, comprising the following steps:

[0007] Step 1, determine the nonlinear fitting state equation and parameters of water;

[0008] Step 2: Calculate the density of water at different depths. Assume that the water medium parameters change with depth in an isothermal process. Use the relationship between density and depth to solve the nonlinear state equation of water and obtain the density of water at different depths.

[0009] Step 3: Obtain parameter statistics table by iterative calculation under typical working conditions, carry out underwater explosion load calculation by ALE method, use nominal correction coefficient to make preliminary correction to nonlinear fitting state equation of water, and because the compression ratio of water decreases, the actual correction coefficient is less than the nominal correction coefficient, and obtain parameter statistics table consisting of nominal correction coefficient, actual correction coefficient and relative increment of water compression ratio through multiple iterative calculations;

[0010] Step 4: Establish the correction coefficient expression. According to the parameter statistical table, perform non-linear fitting on the actual correction coefficient and the relative increment of the water compression ratio to obtain the correction coefficient expression, and use this expression to calculate the actual correction coefficient;

[0011] Step 5: Define the application range of the correction coefficient expression to ensure that when calculating the underwater explosion load at different depths using the ALE method, the correction method is combined to obtain the explosion load.

[0012] In one embodiment, the non-linear fitting equation of state of water in Step 1 is as follows:

[0013]

[0014] where p is the measured point pressure; C 0 is the reference pressure; μ = ρ / ρ 0 -1, which is the compression ratio of water; C 1 is 2.2 GPa; C 2 is 9.54 GPa; C 3 is 14.57 GPa; C 4 is 0.28; C 5 is 0.28; C 6 is 0;

[0015] In the initial reference state, μ = 0, e V = 0, and C 0 at different depths is obtained.

[0016] In one embodiment, in Step 1, for the convenience of subsequent correction operations, let P = p - C 0 , and the non-linear fitting equation of state of water is changed to the following formula:

[0017]

[0018] In one embodiment, the condition for the isothermal process in Step 2 is dT = 0, and the water density at different depths is obtained by simultaneously solving the non-linear equation of state of water and the hydrostatic pressure formula.

[0019] In one embodiment, in Step 2, the following formula is specifically used:

[0020]

[0021] Simultaneously solve the non-linear equation of state of water to obtain the water density at different depths.

[0022] In one embodiment, during the iterative calculation in Step 3, the high-order terms in the equation of state of water are ignored, and the actual correction coefficient is simplified to the product of the nominal correction coefficient and the relative increment of the compression ratio of water.

[0023] In one embodiment, in Step 4, the correction coefficient expression is used to calculate the peak pressure and the theoretically calculated peak pressure based on the initial values, and the actual correction coefficient is obtained to improve the accuracy of the numerical calculation of the underwater explosion load.

[0024] In one embodiment, in Step 5, the correction method is applicable to the water depth range of 0 - 400 meters, and the number of grids on the charge radius is 2 - 10.

[0025] The beneficial effects of the present invention are as follows:

[0026] The present invention solves the problem of errors in the prior art, and proposes an effective load correction method for the calculation errors caused by artificial interference and grid homogenization introduced by the existing ALE method when calculating underwater explosions; by correcting the parameters of the nonlinear equation of state of water, the accuracy of the numerical calculation is significantly improved, especially in the mid - to - far - field calculation conditions;

[0027] The present invention provides an engineering correction coefficient formula, which is convenient for use in actual engineering; through multiple iterative corrections, by utilizing the mutual influence relationship between the pressure ratio and the compression ratio, an accurate correction coefficient is obtained, making the corrected numerical calculation results closer to the theoretical values;

[0028] The present invention improves the calculation accuracy and applicability. The correction method has a low impact on the first bubble pulsation period of the underwater explosion load, and can assist in the analysis and calculation of the dynamic response of the structure under the action of the mid - to - far - field underwater explosion load. It is applicable to the calculation of underwater explosion loads with different water depths and charges, and improves the calculation accuracy of the structural response. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic diagram for calculating the correction coefficient expression of the present invention.

[0030] Figure 2 It is a comparison chart of the peak pressures of each charge under different methods of the present invention.

[0031] Figure 3 It is a comparison chart of the first bubble pulsation periods of each charge under different methods of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0032] In order to make the above objects, features, and advantages of the present invention more obvious and understandable, the following will describe the specific embodiments of the present invention in detail with reference to the accompanying drawings. In the description of the present invention, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation of the present invention.

[0033] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include at least one of such features. In the description of the present invention, the meaning of "a plurality" is at least two, such as two, three, etc., unless otherwise specifically and clearly defined.

[0034] In the present invention, unless otherwise clearly specified and limited, the terms "mounted", "connected", "connected to", "fixed", etc. shall be construed in a broad sense. For example, it may be a fixed connection, a detachable connection, or integrated; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements or the interaction relationship between two elements, unless otherwise clearly limited. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0035] In the present invention, unless otherwise clearly specified and limited, the first feature being "on" or "under" the second feature may be that the first and second features are in direct contact, or the first and second features are indirectly in contact through an intermediate medium. Moreover, the first feature being "above", "over", and "on top of" the second feature may be that the first feature is directly above or obliquely above the second feature, or merely indicates that the first feature has a higher horizontal height than the second feature. The first feature being "under", "below", and "beneath" the second feature may be that the first feature is directly below or obliquely below the second feature, or merely indicates that the first feature has a lower horizontal height than the second feature.

[0036] It should be noted that when an element is referred to as being "fixed to" or "disposed on" another element, it may be directly on the other element or there may be a central element. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may be a central element at the same time. The terms "vertical", "horizontal", "upper", "lower", "left", "right" and similar expressions used herein are for illustrative purposes only and are not intended to be the only implementation method.

[0037] like Figure 1 As shown, the present invention provides a method for numerically calculating underwater explosion load correction based on a nonlinear state equation of water, comprising the following steps:

[0038] Step 1, determine the nonlinear fitting state equation and parameters of water;

[0039] Step 2: Calculate the density of water at different depths. Assume that the water medium parameters change with depth in an isothermal process. Use the relationship between density and depth to solve the nonlinear state equation of water and obtain the density of water at different depths.

[0040] Step 3: Obtain parameter statistics table by iterative calculation under typical working conditions, carry out underwater explosion load calculation by ALE method, use nominal correction coefficient to make preliminary correction to nonlinear fitting state equation of water, and because the compression ratio of water decreases, the actual correction coefficient is less than the nominal correction coefficient, and obtain parameter statistics table consisting of nominal correction coefficient, actual correction coefficient and relative increment of water compression ratio through multiple iterative calculations;

[0041] Step 4, establishing a correction coefficient expression, performing nonlinear fitting on the actual correction coefficient and the relative increment of the water compression ratio according to the parameter statistics table, obtaining a correction coefficient expression, and using the expression to calculate the actual correction coefficient;

[0042] Step five: clarify the scope of use of the correction coefficient expression to ensure that when the ALE method is used to calculate underwater explosion loads at different depths, the correction method is combined to obtain the explosion load.

[0043] In some embodiments, the nonlinear fitting state equation of water in step 1 is as follows:

[0044]

[0045] Where, p is the pressure at the measuring point; C 0 is the reference pressure; μ=ρ / ρ 0 -1, is the compression ratio of water; C 1 2.2GPa; C 2 9.54GPa; C 3 14.57GPa; C4 0.28; C 5 0.28; C 6 is 0;

[0046] In the initial reference state, μ=0, e V =0, find C at different depths 0 .

[0047] Furthermore, in step 1, to facilitate subsequent correction operations, P = pC 0 , the nonlinear fitting state equation of water is transformed into the following formula:

[0048]

[0049] In some embodiments, the condition of the isothermal process in step 2 is dT=0, and the water density at different depths is solved by using the nonlinear state equation of water and the hydrostatic pressure formula.

[0050] Furthermore, in step 2, the following formula is specifically used:

[0051]

[0052] The nonlinear state equations of water are solved simultaneously to obtain the density of water at different depths.

[0053] In some embodiments, during the iterative calculation process of step three, high-order terms in the state equation of water are ignored, and the actual correction coefficient is simplified to the product of the nominal correction coefficient and the relative increase of the compression ratio of water.

[0054] In some embodiments, in step four, the correction coefficient expression is used to calculate the actual correction coefficient based on the initial numerical calculation peak pressure and the theoretical calculation peak pressure to improve the accuracy of the underwater explosion numerical calculation load.

[0055] In some embodiments, in step five, the correction method is applicable to a water depth range of 0-400 meters, and the number of grids on the radius of the drug package is 2-10.

[0056] In a specific embodiment, in step 3, a parameter statistics table is obtained by iterative calculation using typical working conditions, and underwater explosion load calculation under the ALE method is carried out using typical working conditions. Because when the nonlinear fitting state equation of water is corrected using the nominal correction coefficient, the compression ratio of water will be reduced, so the actual correction coefficient is smaller than the nominal correction coefficient. In order to further ensure that the pressure at the measuring point after correction is close to the theoretical value, it is necessary to complete the correction iteration;

[0057] Since the maximum compression ratio of water at the measuring point is 10 -3, so the high-order terms in the equation of state of water can be ignored, and the actual correction coefficient can be simplified to the product of the nominal correction coefficient and the relative increment of the compression ratio of water.

[0058] Accordingly, a parameter table 1 composed of the nominal correction coefficient, the actual correction coefficient, and the relative increment of the compression ratio of water (the compression ratio of water at the measured point after correction divided by the compression ratio of water at the measured point without correction) can be obtained.

[0059] Table 1 Statistical Table of Iterative Statistics of Each Parameter

[0060]

[0061] In a specific embodiment, in step four, an expression for the correction coefficient is established. From the statistical table of iterative statistics of each parameter obtained in the previous step, a non-linear fitting is performed on the actual correction coefficient and the relative increment of the compression ratio of water, and the expression between the two is obtained as:

[0062] C = 1.83 - k + 0.17k 2

[0063] k = p c / p l

[0064] In the above formula, p c is the peak pressure of the initial numerical calculation, and p l is the peak pressure of the theoretical calculation

[0065] According to the relative relationship in the third step, the expression between the nominal correction coefficient and the actual correction coefficient is obtained as:

[0066]

[0067] In a specific embodiment, in step five, the application range of the correction coefficient expression is clarified. According to the underwater explosion pressure calculation formula, the peak pressure of the shock wave is not affected by the water depth under the same amount of explosive. In essence, the compression ratio of water at the corresponding measured point does not change with the depth. Therefore, when calculating the underwater explosion load at different depths using the ALE method, high-precision explosion loads can be obtained by combining this correction method. For the number of grids on the radius of the explosive charge, it is recommended to use 2 - 10 according to the calculation results.

[0068] In a specific embodiment, the underwater explosion load calculation is carried out at a water depth of 400m, a burst distance of 0.49m, and different amounts of explosives. The comparison diagram of the peak pressure of the shock wave obtained by using the theoretical formula, uncorrected numerical calculation, and this correction method's numerical calculation is obtained, and the specific results are as Figure 2 shown;

[0069] The comparison diagram of the first bubble pulsation period obtained by using the theoretical formula and this correction method's numerical calculation, and the specific results are as Figure 3as shown

[0070] The error between the calculated result after peak pressure correction and the theoretical settlement result is within 2.5%. Compared with the 30% calculation error without correction, the accuracy is higher. The error between the calculated result after the first bubble pulsation period correction and the theoretical settlement result is within 3.5%. Therefore, the engineering application requirements can be better met by using this correction method.

[0071] Starting from the non-linear equation of state of water, the present invention uses a correction formula to apply the corrected equation of state to the three-dimensional numerical calculation of underwater explosion loads, obtaining a load curve with higher accuracy. This method has a relatively low impact on the first bubble pulsation period of underwater explosion loads, and can contribute to the analysis and calculation of the dynamic response of structures under mid- and far-field underwater explosion loads, improving the calculation accuracy of structural responses.

[0072] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0073] The above-described embodiments only express the implementation manners of the present invention, and the description thereof is relatively specific and detailed, but it cannot be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention patent shall be subject to the appended claims.

Claims

1. A method for load correction of underwater explosion numerical calculation based on nonlinear state equation of water, characterized in that: The following steps are involved: Step 1, determine the nonlinear fitting state equation and parameters of water; Step 2: Calculate the density of water at different depths. Assume that the water medium parameters change with depth in an isothermal process. Use the relationship between density and depth to solve the nonlinear state equation of water and obtain the density of water at different depths. Step 3: Obtain parameter statistics table by iterative calculation under typical working conditions, carry out underwater explosion load calculation by ALE method, use nominal correction coefficient to make preliminary correction to nonlinear fitting state equation of water, and because the compression ratio of water decreases, the actual correction coefficient is less than the nominal correction coefficient, and obtain parameter statistics table consisting of nominal correction coefficient, actual correction coefficient and relative increment of water compression ratio through multiple iterative calculations; Step 4, establishing a correction coefficient expression, performing nonlinear fitting on the actual correction coefficient and the relative increment of the water compression ratio according to the parameter statistics table, obtaining a correction coefficient expression, and using the expression to calculate the actual correction coefficient; Step five: clarify the scope of use of the correction coefficient expression to ensure that when the ALE method is used to calculate underwater explosion loads at different depths, the correction method is combined to obtain the explosion load.

2. The method for correcting loads of underwater explosion numerical calculation based on nonlinear state equation of water according to claim 1, characterized in that: The nonlinear fitting state equation of water in step 1 is as follows: Among them, p is the pressure at the measuring point; C0 is the reference pressure; μ = ρ / ρ0-1, which is the compression ratio of water; C1 is 2.2 GPa; C2 is 9.54 GPa; C3 is 14.57 GPa; C4 is 0.28; C5 is 0.28; C6 is 0; In the initial reference state, μ=0, e V =0, and calculate C0 at different depths.

3. The method for correcting loads of underwater explosion numerical calculation based on nonlinear state equation of water according to claim 2, characterized in that: In step 1, to facilitate the subsequent correction operation, P = p-C0 is recorded, and the nonlinear fitting state equation of water is changed to the following formula:

4. The method for correcting loads of underwater explosion numerical calculation based on nonlinear state equation of water according to claim 1, characterized in that: The condition of the isothermal process in step 2 is dT=0, and the water density at different depths is solved by using the nonlinear state equation of water and the hydrostatic pressure formula.

5. The method for correcting loads of underwater explosion numerical calculation based on nonlinear state equation of water according to claim 4, characterized in that: In step 2, the following formula is used: The nonlinear state equations of water are solved simultaneously to obtain the density of water at different depths.

6. The method for correcting loads of underwater explosion numerical calculation based on nonlinear state equation of water according to claim 1, characterized in that: In the iterative calculation process of step three, the high-order terms in the state equation of water are ignored, and the actual correction coefficient is simplified to the product of the nominal correction coefficient and the relative increase of the compression ratio of water.

7. The method for correcting loads of underwater explosion numerical calculation based on nonlinear state equation of water according to claim 1, characterized in that: In step 4, the correction coefficient expression is used to calculate the peak pressure based on the initial numerical value and the theoretically calculated peak pressure to obtain the actual correction coefficient to improve the accuracy of the numerical calculation load of the underwater explosion.

8. The method for correcting loads of underwater explosion numerical calculation based on nonlinear state equation of water according to claim 1, characterized in that: In step five, the correction method is applicable to a water depth range of 0-400 meters, and the number of grids on the radius of the drug package is 2-10.

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