Method and device for determining equivalent additional mass of hanging basket

Abstract

The invention discloses a method and a device for determining the equivalent additional mass of a hanging basket, relates to the technical field of flow-induced vibration of reactor internals, and mainly aims to improve the determination accuracy of the equivalent additional mass of the hanging basket. Comprising the steps that the radius value, the wall thickness value, the height value and the first-order beam type modal additional mass of a target hanging basket, the density value of fluid where the target hanging basket is located and the radius value of a pressure container containing the fluid are obtained; based on the following formula, according to the radius value, the wall thickness value and the height value of the target hanging basket, the density value of fluid and the radius value of the pressure container, all the high-order shell mode additional masses of the target hanging basket are calculated respectively, # imgabs0 # conducts weighting processing on the first-order beam type mode additional masses and all the high-order shell mode additional masses based on the preset weight, and the first-order beam type mode additional masses and all the high-order shell mode additional masses of the target hanging basket are obtained. And obtaining the equivalent additional mass of the target hanging basket.

Description

Technical Field

[0001] The present application relates to the technical field of flow-induced vibration of pile internal components, and in particular to a method and device for determining the equivalent added mass of a hanging basket. Background Art

[0002] In nuclear reactions, the internals are highly complex integrated components in the reactor structure, which contain a large number of key structures. They play a key role in nuclear fuel support, thermal energy circulation and normal operation of the primary circuit. Therefore, their structural integrity needs to be paid special attention to. Under the excitation of the primary circuit fluid, the internals will inevitably vibrate. This structural vibration induced by the fluid is collectively referred to as flow-induced vibration, which is essentially a fluid-solid coupling phenomenon. Under operating conditions, it is necessary to conduct flow-induced vibration response analysis on the internals to evaluate their high-cycle fatigue characteristics to ensure safe operation. Among them, the hanging basket is a key component of the internals. Since it directly provides a support boundary for the fuel assembly, the flow-induced vibration response analysis of the hanging basket has always been the focus of engineers and designers.

[0003] At present, the method for analyzing the flow-induced vibration response of the suspended basket based on power spectrum density is widely used because it is based on the random vibration theory and has the characteristics of fast speed in obtaining the flow-induced vibration response of the suspended basket, easy implementation in engineering, and high execution efficiency. It should be noted that since the suspended basket is immersed in a primary fluid, the vibration characteristics of the suspended basket are very different from those in the air. In practice, the influence of the fluid on the vibration characteristics of the suspended basket is usually reflected in the form of equivalent added mass. Therefore, the accuracy of the equivalent added mass directly determines the accuracy of the vibration characteristics of the suspended basket. Accurate vibration characteristics of the suspended basket are the prerequisite for analyzing the flow-induced vibration response of the suspended basket.

[0004] However, since the equivalent added mass of the hanging basket changes with the change of its modal order, the accuracy of the equivalent added mass of the hanging basket calculated based on the existing calculation method of the first-order beam modal added mass of the hanging basket is low. Summary of the invention

[0005] In view of this, the present application provides a method and device for determining the equivalent added mass of a hanging basket, the main purpose of which is to solve the problem that the equivalent added mass of the hanging basket calculated based on the existing method for calculating the added mass of the hanging basket has low accuracy, because the equivalent added mass of the hanging basket changes with the change of its modal order.

[0006] According to one aspect of the present application, a method for determining an equivalent added mass of a hanging basket is provided, comprising:

[0007] Obtaining the radius value, wall thickness value, height value, first-order beam modal additional mass of the target hanging basket, the density value of the fluid in which the target hanging basket is located, and the radius value of the pressure vessel containing the fluid;

[0008] Based on the following formula, the additional mass of each high-order shell mode of the target hanging basket is calculated according to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel.

[0009]

[0010] Among them, ρ a represents the higher-order shell modal added mass, ρ f represents the density of the fluid, b represents the radius of the pressure vessel, ξ i represents the weighting coefficient, N represents a natural number, K m represents the m-order second-kind deformation Bessel function, a represents the radius of the hanging basket, Δ represents the wall thickness of the hanging basket, and ψ(z) represents the axial deflection function;

[0011] Based on preset weights, the first-order beam modal additional mass and each of the higher-order shell modal additional mass are weighted to obtain the equivalent additional mass of the target hanging basket.

[0012] Preferably, after performing weighted processing on the first-order beam modal additional mass and each of the higher-order shell modal additional mass based on preset weights to obtain the equivalent additional mass of the target hanging basket, the method further comprises:

[0013] Acquiring surface pulsating pressure power spectrum density data of the target hanging basket;

[0014] The equivalent added mass and the surface pulsating pressure power spectrum density data are input into a pre-constructed hanging basket finite element model to obtain the root mean square value of the flow-induced vibration stress response of the target hanging basket.

[0015] Preferably, after inputting the equivalent added mass and the surface pulsating pressure power spectrum density data into a pre-built hanging basket finite element model to obtain the root mean square value of the flow-induced vibration stress response of the target hanging basket, the method further comprises:

[0016] Performing peak value conversion processing on the root mean square value of the flow-induced vibration stress response to obtain the stress peak value of the target hanging basket;

[0017] According to the material of the target hanging basket, searching for the corresponding material high cycle fatigue stress threshold;

[0018] If the stress peak value is less than the high cycle fatigue stress threshold of the material, it is determined that the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life is a low risk level;

[0019] If the stress peak value is greater than the high cycle fatigue stress threshold of the material, it is determined that the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life is a high risk level.

[0020] Preferably, before respectively calculating each high-order shell modal additional mass of the target hanging basket based on the formula according to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel, the method further includes:

[0021] Obtain the shell radial vibration equation of the target hanging basket

[0022] u=Cψ(z)sinmθsinωt

[0023] Among them, u represents the radial vibration displacement of the hanging basket, C represents any real constant, θ represents the circumferential coordinate, and ω represents the shell frequency of the hanging basket;

[0024] The shell radial vibration equation is derived with respect to time to obtain the derived shell radial vibration equation:

[0025]

[0026] Based on the derived shell radial vibration equation, the radial velocity continuity condition expression is constructed.

[0027]

[0028] Where r represents the radial coordinate;

[0029] The potential function of the fluid is constructed based on the radial velocity continuity condition expression

[0030] φ=κ(r,z)sinmθcosωt

[0031] Where φ represents the fluid potential function, κ(r,z) represents the transition function, and z represents the axial coordinate;

[0032] Substitute the potential function into the pre-constructed potential flow control equation to obtain the constraint equation of the transition function. The potential flow control equation is expressed as the following formula:

[0033]

[0034] The constraint equation of the transition function is expressed as follows:

[0035]

[0036] The transition function is subjected to an infinite series expansion operation to obtain the transition function after infinite series expansion.

[0037]

[0038] Among them, c i represents the weighting coefficient, η i (r,z) represents an orthogonal function cluster, and n represents the number of cutoff terms in the series;

[0039] The transition function after the infinite series expansion is introduced into the constraint equation of the transition function, and the weighted coefficient is calculated based on the weighted residual method under the preset boundary conditions.

[0040]

[0041] Among them, the orthogonal function cluster

[0042] The orthogonal function cluster η i (r, z) and the weighting coefficient c i Substitute the transition function after the infinite series expansion into The infinite series expression of the transition function is obtained, and the infinite series expression of the transition function is substituted into the potential function of the fluid to obtain the explicit expression of the potential function of the fluid:

[0043]

[0044] The explicit expression of the fluid potential function is differentiated with respect to time to obtain the expression of the dynamic water pressure:

[0045]

[0046] Where p(θ,z,t) represents the dynamic water pressure;

[0047] Integrate the hydrodynamic pressure expression along the height direction to obtain the first expression of the resultant force per unit annular length:

[0048]

[0049] Among them, M p The first expression for the resultant force per unit circumferential length is:

[0050] Construct an expression for the inertial force caused by the additional mass of the high-order shell mode of the hanging basket, and integrate the inertial force expression along the height direction to obtain the second expression of the resultant force per unit circumferential length.

[0051]

[0052] Among them, M a The second expression for the resultant force per unit circumferential length is, represents the inertial force expression;

[0053] Let the first expression of the resultant force be equal to the second expression of the resultant force, and obtain the high-order shell modal additional mass calculation formula of the target hanging basket:

[0054]

[0055] Preferably, before obtaining the shell radial vibration equation of the target hanging basket, the method further includes:

[0056] A shell radial vibration equation is constructed according to the natural vibration characteristics of the cylindrical shell, and a potential flow control equation of the fluid in the annular cavity in a cylindrical coordinate system is constructed according to the classical potential flow theory, so as to construct a high-order shell modal added mass calculation formula based on the shell radial vibration equation and the potential flow control equation.

[0057] Preferably, the preset boundary conditions include:

[0058] It means that the surface of the basket is not separated from the fluid. Indicates that the velocity of the fluid in the pressure vessel is 0, Indicates that the velocity of the fluid at the bottom of the basket is 0, κ z＝0 =0 means that the free surface sloshing of the fluid is not considered.

[0059] According to another aspect of the present application, a device for determining an equivalent added mass of a hanging basket is provided, comprising:

[0060] A parameter acquisition module, used to acquire the radius value, wall thickness value, height value, first-order beam modal additional mass of the target hanging basket, the density value of the fluid in which the target hanging basket is located, and the radius value of the pressure vessel containing the fluid;

[0061] The high-order shell modal additional mass calculation module is used to calculate the high-order shell modal additional mass of the target hanging basket according to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel based on the following formula.

[0062]

[0063] Among them, ρ a represents the higher-order shell modal added mass, ρ f represents the density of the fluid, b represents the radius of the pressure vessel, ξ i represents the weighting coefficient, N represents a natural number, K m represents the m-order second-kind deformation Bessel function, a represents the radius of the hanging basket, Δ represents the wall thickness of the hanging basket, and ψ(z) represents the axial deflection function;

[0064] The hanging basket equivalent added mass determination module is used to perform weighted processing on the first-order beam modal added mass and each of the high-order shell modal added mass based on preset weights to obtain the equivalent added mass of the target hanging basket.

[0065] Preferably, after the hanging basket equivalent additional mass determination module, the device further includes a flow-induced vibration stress response root mean square value determination module, which is used to:

[0066] Acquiring surface pulsating pressure power spectrum density data of the target hanging basket;

[0067] The equivalent added mass and the surface pulsating pressure power spectrum density data are input into a pre-constructed hanging basket finite element model to obtain the root mean square value of the flow-induced vibration stress response of the target hanging basket.

[0068] Preferably, after the flow-induced vibration stress response root mean square value determination module, the device further includes a fatigue failure risk level determination module, which is used to:

[0069] Performing peak value conversion processing on the root mean square value of the flow-induced vibration stress response to obtain the stress peak value of the target hanging basket;

[0070] According to the material of the target hanging basket, searching for the corresponding material high cycle fatigue stress threshold;

[0071] If the stress peak value is less than the high cycle fatigue stress threshold of the material, it is determined that the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life is a low risk level;

[0072] If the stress peak value is greater than the high cycle fatigue stress threshold of the material, it is determined that the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life is a high risk level.

[0073] Preferably, before the high-order shell modal additional mass calculation module, the device further includes a high-order shell modal additional mass calculation formula construction module, which is used to:

[0074] Obtain the shell radial vibration equation of the target hanging basket

[0075] u=Cψ(z)sinmθsinωt

[0076] Among them, u represents the radial vibration displacement of the hanging basket, C represents any real constant, θ represents the circumferential coordinate, and ω represents the shell frequency of the hanging basket;

[0077] The shell radial vibration equation is derived with respect to time to obtain the derived shell radial vibration equation:

[0078]

[0079] Based on the derived shell radial vibration equation, the radial velocity continuity condition expression is constructed.

[0080]

[0081] Where r represents the radial coordinate;

[0082] The potential function of the fluid is constructed based on the radial velocity continuity condition expression

[0083] φ=κ(r,z)sinmθcosωt

[0084] Where φ represents the fluid potential function, κ(r,z) represents the transition function, and z represents the axial coordinate;

[0085] Substitute the potential function into the pre-constructed potential flow control equation to obtain the constraint equation of the transition function. The potential flow control equation is expressed as the following formula:

[0086]

[0087] The constraint equation of the transition function is expressed as follows:

[0088]

[0089] The transition function is subjected to an infinite series expansion operation to obtain the transition function after infinite series expansion.

[0090]

[0091] Among them, c i represents the weighting coefficient, η i (r,z) represents an orthogonal function cluster, and n represents the number of cutoff terms in the series;

[0092] The transition function after the infinite series expansion is introduced into the constraint equation of the transition function, and the weighted coefficient is calculated based on the weighted residual method under the preset boundary conditions.

[0093]

[0094] Among them, the orthogonal function cluster

[0095] The orthogonal function cluster η i (r, z) and the weighting coefficient c i Substitute the transition function after the infinite series expansion into The infinite series expression of the transition function is obtained, and the infinite series expression of the transition function is substituted into the potential function of the fluid to obtain the explicit expression of the potential function of the fluid:

[0096]

[0097] The explicit expression of the fluid potential function is differentiated with respect to time to obtain the expression of the dynamic water pressure:

[0098]

[0099] Where p(θ,z,t) represents the dynamic water pressure;

[0100] Integrate the hydrodynamic pressure expression along the height direction to obtain the first expression of the resultant force per unit annular length:

[0101]

[0102] Among them, M p The first expression for the resultant force per unit circumferential length is:

[0103] Construct an expression for the inertial force caused by the additional mass of the high-order shell mode of the hanging basket, and integrate the inertial force expression along the height direction to obtain the second expression of the resultant force per unit circumferential length.

[0104]

[0105] Among them, M a The second expression for the resultant force per unit circumferential length is, represents the inertial force expression;

[0106] Let the first expression of the resultant force be equal to the second expression of the resultant force, and obtain the high-order shell modal additional mass calculation formula of the target hanging basket:

[0107]

[0108] Preferably, the high-order shell modal added mass calculation formula construction module is also used for:

[0109] A shell radial vibration equation is constructed according to the natural vibration characteristics of the cylindrical shell, and a potential flow control equation of the fluid in the annular cavity in a cylindrical coordinate system is constructed according to the classical potential flow theory, so as to construct a high-order shell modal added mass calculation formula based on the shell radial vibration equation and the potential flow control equation.

[0110] Preferably, the preset boundary conditions include:

[0111] It means that the surface of the basket is not separated from the fluid. Indicates that the velocity of the fluid in the pressure vessel is 0, Indicates that the velocity of the fluid at the bottom of the basket is 0, κ z＝0=0 means that the free surface sloshing of the fluid is not considered.

[0112] By means of the above technical solution, the technical solution provided by the embodiment of the present application has at least the following advantages:

[0113] The present application provides a method and device for determining the equivalent added mass of a hanging basket. First, the radius value, wall thickness value, height value, first-order beam modal added mass, density value of the fluid in which the target hanging basket is located, and radius value of the pressure vessel containing the fluid are obtained. Secondly, based on the formula According to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel, the various high-order shell modal additional masses of the target hanging basket are calculated respectively, where ρ a represents the higher-order shell modal added mass, ρ f represents the density of the fluid, b represents the radius of the pressure vessel, ξ i represents the weighting coefficient, N represents a natural number, K m represents the m-order second-kind deformed Bessel function, a represents the radius value of the hanging basket, Δ represents the wall thickness value of the hanging basket, ψ(z) represents the axial deflection function; finally, based on the preset weight, the first-order beam modal added mass and each of the higher-order shell modal added mass are weighted to obtain the equivalent added mass of the target hanging basket. Compared with the prior art, the embodiment of the present application calculates the higher-order shell modal added mass of the target hanging basket at each modal order by constructing a higher-order shell modal added mass calculation formula, and then based on the preset weight, the weighted sum of the first-order beam modal added mass and each of the higher-order shell modal added mass is used as the equivalent added mass of the target hanging basket, which overcomes the problem of low calculation accuracy caused by the change of the equivalent added mass of the hanging basket due to the change of its modal order, and effectively improves the accuracy of determining the equivalent added mass of the hanging basket.

[0114] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present application. Also, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0116] Figure 1A flow chart of a method for determining an equivalent additional mass of a hanging basket provided in an embodiment of the present application is shown;

[0117] Figure 2 A flowchart for constructing a high-order shell modal added mass calculation formula provided in an embodiment of the present application is shown;

[0118] Figure 3 A flow chart showing the risk level determination of fatigue damage of a hanging basket provided in an embodiment of the present application is shown;

[0119] Figure 4 A block diagram of a device for determining the equivalent added mass of a hanging basket provided in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0120] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0121] At the same time, it should be understood that for the convenience of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship.

[0122] The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the present application, its application, or uses.

[0123] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0124] It should be noted that like reference numerals and letters refer to similar items in the following figures, and therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0125] The embodiments of the present application can be applied to computer systems / servers, which can operate with many other general or special computing system environments or configurations. Examples of well-known computing systems, environments and / or configurations suitable for use with computer systems / servers include, but are not limited to: personal computer systems, server computer systems, thin clients, thick clients, handheld or laptop devices, microprocessor-based systems, set-top boxes, programmable consumer electronics, network personal computers, small computer systems, large computer systems, and distributed cloud computing technology environments including any of the above systems, etc.

[0126] Computer systems / servers may be described in the general context of computer system executable instructions (such as program modules) executed by a computer system. In general, program modules may include routines, programs, object programs, components, logic, data structures, etc., which perform specific tasks or implement specific abstract data types. Computer systems / servers may be implemented in a distributed cloud computing environment where tasks are performed by remote processing devices linked through a communication network. In a distributed cloud computing environment, program modules may be located on local or remote computing system storage media including storage devices.

[0127] The present application embodiment provides a method for determining the equivalent additional mass of a hanging basket, such as Figure 1 As shown, the method includes:

[0128] 101. Obtain the radius value, wall thickness value, height value, first-order beam modal additional mass of the target hanging basket, the density value of the fluid in which the target hanging basket is located, and the radius value of the pressure vessel containing the fluid.

[0129] Among them, the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid in which the target hanging basket is located, and the radius value of the pressure vessel containing the fluid can all be directly obtained; the first-order beam modal added mass can be calculated based on the existing hanging basket first-order beam modal added mass calculation method. In the embodiment of the present application, the current execution end can be a hanging basket flow-induced vibration response analysis module.

[0130] 102. Based on the high-order shell modal additional mass calculation formula, according to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel, the various high-order shell modal additional masses of the target hanging basket are calculated respectively.

[0131] Among them, the calculation formula for the added mass of the high-order shell mode is as follows

[0132]

[0133] Among them, ρ a represents the higher-order shell modal added mass, ρ f represents the density of the fluid, b represents the radius of the pressure vessel, ξ i represents the weighting coefficient, N represents a natural number, K m represents the m-order second-kind deformation Bessel function, a represents the radius of the hanging basket, Δ represents the wall thickness of the hanging basket, ψ(z) represents the axial deflection function, which can be taken as In an embodiment of the present application, the modal order of the target hanging basket is usually first order, second order, third order, etc. When calculating the high-order shell modal added mass of the target hanging basket, the value of m in the high-order shell modal added mass calculation formula can be changed to calculate the various high-order shell modal added masses of the target hanging basket respectively. For example, when m is 2, the second-order shell modal added mass of the target hanging basket is calculated; when m is 3, the third-order shell modal added mass of the target hanging basket is calculated.

[0134] 103. Based on the preset weights, the first-order beam modal added mass and each high-order shell modal added mass are weighted to obtain the equivalent added mass of the target hanging basket.

[0135] The preset weights may be pre-configured based on engineering experience. In the embodiment of the present application, by taking the weighted sum of the first-order beam modal added mass and each higher-order shell modal added mass as the equivalent added mass of the target hanging basket, the situation that the equivalent added mass of the hanging basket will change with the change of its modal order is taken into account, thereby improving the accuracy of determining the equivalent added mass of the hanging basket.

[0136] Compared with the prior art, the embodiment of the present application calculates the high-order shell modal added mass of the target hanging basket at each modal order by constructing a high-order shell modal added mass calculation formula, and then takes the weighted sum of the first-order beam modal added mass and each high-order shell modal added mass as the equivalent added mass of the target hanging basket based on the preset weight, thereby overcoming the problem of low calculation accuracy caused by the change of the equivalent added mass of the hanging basket due to the change of its modal order, and effectively improving the determination accuracy of the equivalent added mass of the hanging basket.

[0137] In an embodiment of the present application, in order to further define and illustrate, Figure 2 As shown, in step 102 of the embodiment, based on the high-order shell modal additional mass calculation formula, according to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel, before calculating each high-order shell modal additional mass of the target hanging basket, the embodiment method also includes:

[0138] 201. Obtain the shell radial vibration equation of the target hanging basket

[0139] u=Cψ(z)sinmθsinωt.

[0140] Wherein, u represents the radial vibration displacement of the hanging basket, C represents any real constant, θ represents the circumferential coordinate, and ω represents the shell frequency of the hanging basket. In the embodiment of the present application, the shell radial vibration equation is pre-constructed according to the natural vibration characteristics of the cylindrical shell.

[0141] 202. Derivative the shell radial vibration equation with respect to time to obtain the derived shell radial vibration equation

[0142]

[0143] 203. Construct the radial velocity continuity condition expression based on the derived shell radial vibration equation

[0144]

[0145] Where r represents the radial coordinate.

[0146] 204. Constructing the potential function of the fluid based on the radial velocity continuity condition expression

[0147] φ=κ(r,z)sinmθcosωt.

[0148] Among them, φ represents the fluid potential function, κ(r,z) represents the transition function, and z represents the axial coordinate.

[0149] 205. Substitute the potential function into the pre-constructed potential flow control equation to obtain the constraint equation of the transition function.

[0150] Among them, the potential flow control equation is expressed as follows

[0151]

[0152] The constraint equation of the transition function is expressed as follows

[0153]

[0154] In the embodiment of the present application, the potential flow control equation is specifically the potential flow control equation of the fluid in the annular cavity in the cylindrical coordinate system, which can be constructed according to the classical potential flow theory.

[0155] 206. Perform infinite series expansion on the transition function to obtain the transition function after infinite series expansion

[0156]

[0157] Among them, c i represents the weighting coefficient, η i (r,z) represents an orthogonal function cluster, n represents the number of cutoff terms of the series, and n=2N-1, that is, n is an odd number.

[0158] 207. Substitute the transition function after infinite series expansion into the constraint equation of the transition function, and calculate the weighted coefficient based on the weighted residual method under the preset boundary conditions.

[0159]

[0160] Among them, the orthogonal function cluster

[0161] In the embodiment of the present application, the preset boundary conditions include: It means that the surface of the basket is not separated from the fluid. Indicates that the velocity of the fluid in the pressure vessel is 0, Indicates that the velocity of the fluid at the bottom of the basket is 0, κ z＝0 =0 means that the free surface sloshing of the fluid is not considered.

[0162] 208. Orthogonal function cluster η i (r,z) and weighting coefficient c i Substitute the transition function after infinite series expansion In the above equation, we get the infinite series expression of the transition function, and substitute the infinite series expression of the transition function into the potential function of the fluid to get the explicit expression of the potential function of the fluid:

[0163]

[0164] 209. Derivative the explicit expression of the fluid potential function with respect to time to obtain the expression of dynamic water pressure

[0165]

[0166] Where p(θ,z,t) represents the dynamic water pressure.

[0167] 210. Integrate the hydrodynamic pressure expression along the height direction to obtain the first expression of the resultant force per unit circumferential length:

[0168]

[0169] Among them, M p It represents the first expression of the resultant force per unit circumferential length.

[0170] 211. Construct the inertial force expression caused by the additional mass of the high-order shell mode of the hanging basket, and integrate the inertial force expression along the height direction to obtain the second expression of the resultant force on the unit circumferential length

[0171]

[0172] Among them, M a The second expression for the resultant force per unit circumferential length is, Represents the inertial force expression.

[0173] 212. Let the first expression of the resultant force be equal to the second expression of the resultant force, and obtain the high-order shell modal additional mass calculation formula of the target hanging basket:

[0174]

[0175] Steps 201 to 212 of the embodiment are detailed steps for constructing a calculation formula for the added mass of the hanging basket in high-order shell mode.

[0176] In an embodiment of the present application, in order to further define and illustrate, Figure 3 As shown, in step 103 of the embodiment, based on the preset weights, weighted processing is performed on the first-order beam modal additional mass and each high-order shell modal additional mass to obtain the equivalent additional mass of the target hanging basket. The embodiment method further includes:

[0177] 301. Obtain surface pulsating pressure power spectrum density data of the target hanging basket.

[0178] Among them, the surface pulsating pressure power spectrum density data of the target basket can be directly measured based on the instrument.

[0179] 302. The equivalent added mass and the surface pulsating pressure power spectrum density data are input into the pre-built hanging basket finite element model to obtain the root mean square value of the flow-induced vibration stress response of the target hanging basket.

[0180] Among them, the construction process of the finite element model of the hanging basket is an existing method in the field and will not be repeated here. In the embodiment of the present application, the equivalent added mass can be first input into the finite element model of the hanging basket to calculate the structural mode of the hanging basket; then the surface pulsating pressure power spectrum density data of the hanging basket measured in step 301 of the embodiment is input into the finite element model of the hanging basket as an excitation to calculate the root mean square value of the flow-induced vibration stress response of the target hanging basket.

[0181] 303. Perform peak value conversion processing on the root mean square value of the flow-induced vibration stress response to obtain the stress peak value of the target hanging basket.

[0182] In the embodiment of the present application, the root mean square value of the flow-induced vibration stress response is converted into a peak value, that is, the stress peak value of the target hanging basket, that is, the maximum stress that the target hanging basket may reach under the current working conditions.

[0183] 304. Find the corresponding material high cycle fatigue stress threshold according to the material of the target hanging basket.

[0184] In the embodiment of the present application, the stress limit value corresponding to the number of high-cycle fatigue cycles of the material in the material search standard is determined according to the material of the target hanging basket, that is, the high-cycle fatigue stress threshold of the material.

[0185] 305a. If the stress peak is less than the material high cycle fatigue stress threshold, the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life is determined to be a low risk level.

[0186] In the embodiment of the present application, if the stress peak is less than the high-cycle fatigue stress threshold of the material, it means that under the current working conditions, the stress peak that the target hanging basket may reach does not exceed the stress limit corresponding to the number of high-cycle fatigue cycles of the material in the standard, which is relatively safe. At this time, the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life can be judged as a low risk level.

[0187] 305b. If the stress peak value is greater than the high cycle fatigue stress threshold of the material, it is determined that the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life is a high risk level.

[0188] In the embodiment of the present application, if the stress peak is greater than the high-cycle fatigue stress threshold of the material, it means that under the current working conditions, the stress peak that the target hanging basket may reach has exceeded the stress limit corresponding to the number of high-cycle fatigue cycles of the material in the standard, and failure is prone to occur. At this time, the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life can be judged as a high risk level.

[0189] The present application provides a method for determining the equivalent added mass of a hanging basket. First, the radius value, wall thickness value, height value, first-order beam modal added mass, density value of the fluid in which the target hanging basket is located, and radius value of the pressure vessel containing the fluid are obtained. Secondly, based on the formula According to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel, the various high-order shell modal additional masses of the target hanging basket are calculated respectively, where ρ a represents the higher-order shell modal added mass, ρ f represents the density of the fluid, b represents the radius of the pressure vessel, ξ i represents the weighting coefficient, N represents a natural number, K m represents the m-order second-kind deformed Bessel function, a represents the radius value of the hanging basket, Δ represents the wall thickness value of the hanging basket, ψ(z) represents the axial deflection function; finally, based on the preset weight, the first-order beam modal added mass and each of the higher-order shell modal added mass are weighted to obtain the equivalent added mass of the target hanging basket. Compared with the prior art, the embodiment of the present application calculates the higher-order shell modal added mass of the target hanging basket at each modal order by constructing a higher-order shell modal added mass calculation formula, and then based on the preset weight, the weighted sum of the first-order beam modal added mass and each of the higher-order shell modal added mass is used as the equivalent added mass of the target hanging basket, which overcomes the problem of low calculation accuracy caused by the change of the equivalent added mass of the hanging basket due to the change of its modal order, and effectively improves the accuracy of determining the equivalent added mass of the hanging basket.

[0190] Furthermore, as a response to the above Figure 1In order to realize the method shown in the figure, the embodiment of the present application provides a device for determining the equivalent additional mass of a hanging basket, such as Figure 4 As shown, the device comprises:

[0191] Parameter acquisition module 41, high-order shell modal additional mass calculation module 42, hanging basket equivalent additional mass determination module 43;

[0192] The parameter acquisition module 41 is used to acquire the radius value, wall thickness value, height value, first-order beam modal additional mass of the target hanging basket, the density value of the fluid in which the target hanging basket is located, and the radius value of the pressure vessel containing the fluid;

[0193] The high-order shell modal additional mass calculation module 42 is used to calculate the high-order shell modal additional mass of the target hanging basket according to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel based on the following formula:

[0194]

[0195] Among them, ρ a represents the higher-order shell modal added mass, ρ f represents the density of the fluid, b represents the radius of the pressure vessel, ξ i represents the weighting coefficient, N represents a natural number, K m represents the m-order second-kind deformation Bessel function, a represents the radius of the hanging basket, Δ represents the wall thickness of the hanging basket, and ψ(z) represents the axial deflection function;

[0196] The hanging basket equivalent added mass determination module 43 is used to perform weighted processing on the first-order beam modal added mass and each of the higher-order shell modal added masses based on preset weights to obtain the equivalent added mass of the target hanging basket.

[0197] In a specific application scenario, after the hanging basket equivalent additional mass determination module, the device further includes a flow-induced vibration stress response root mean square value determination module, which is used to:

[0198] Acquiring surface pulsating pressure power spectrum density data of the target hanging basket;

[0199] The equivalent added mass and the surface pulsating pressure power spectrum density data are input into a pre-constructed hanging basket finite element model to obtain the root mean square value of the flow-induced vibration stress response of the target hanging basket.

[0200] In a specific application scenario, after the flow-induced vibration stress response root mean square value determination module, the device further includes a fatigue failure risk level determination module, which is used to:

[0201] Performing peak value conversion processing on the root mean square value of the flow-induced vibration stress response to obtain the stress peak value of the target hanging basket;

[0202] According to the material of the target hanging basket, searching for the corresponding material high cycle fatigue stress threshold;

[0203] If the stress peak value is less than the high cycle fatigue stress threshold of the material, it is determined that the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life is a low risk level;

[0204] If the stress peak value is greater than the high cycle fatigue stress threshold of the material, it is determined that the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life is a high risk level.

[0205] In a specific application scenario, before the high-order shell modal additional mass calculation module, the device further includes a high-order shell modal additional mass calculation formula construction module, which is used to:

[0206] Obtain the shell radial vibration equation of the target hanging basket

[0207] u=Cψ(z)sinmθsinωt

[0208] Among them, u represents the radial vibration displacement of the hanging basket, C represents any real constant, θ represents the circumferential coordinate, and ω represents the shell frequency of the hanging basket;

[0209] The shell radial vibration equation is derived with respect to time to obtain the derived shell radial vibration equation:

[0210]

[0211] Based on the derived shell radial vibration equation, the radial velocity continuity condition expression is constructed.

[0212]

[0213] Where r represents the radial coordinate;

[0214] The potential function of the fluid is constructed based on the radial velocity continuity condition expression

[0215] φ=κ(r,z)sinmθcosωt

[0216] Where φ represents the fluid potential function, κ(r,z) represents the transition function, and z represents the axial coordinate;

[0217] Substitute the potential function into the pre-constructed potential flow control equation to obtain the constraint equation of the transition function. The potential flow control equation is expressed as the following formula:

[0218]

[0219] The constraint equation of the transition function is expressed as follows:

[0220]

[0221] The transition function is subjected to an infinite series expansion operation to obtain the transition function after infinite series expansion.

[0222]

[0223] Among them, c i represents the weighting coefficient, η i (r,z) represents an orthogonal function cluster, and n represents the number of cutoff terms in the series;

[0224] The transition function after the infinite series expansion is introduced into the constraint equation of the transition function, and the weighted coefficient is calculated based on the weighted residual method under the preset boundary conditions.

[0225]

[0226] Among them, the orthogonal function cluster

[0227] The orthogonal function cluster η i (r, z) and the weighting coefficient c i Substitute the transition function after the infinite series expansion into The infinite series expression of the transition function is obtained, and the infinite series expression of the transition function is substituted into the potential function of the fluid to obtain the explicit expression of the potential function of the fluid:

[0228]

[0229] The explicit expression of the fluid potential function is differentiated with respect to time to obtain the expression of the dynamic water pressure:

[0230]

[0231] Where p(θ,z,t) represents the dynamic water pressure;

[0232] Integrate the hydrodynamic pressure expression along the height direction to obtain the first expression of the resultant force per unit annular length:

[0233]

[0234] Among them, M p The first expression for the resultant force per unit circumferential length is:

[0235] Construct an expression for the inertial force caused by the additional mass of the high-order shell mode of the hanging basket, and integrate the inertial force expression along the height direction to obtain the second expression of the resultant force per unit circumferential length.

[0236]

[0237] Among them, M a The second expression for the resultant force per unit circumferential length is, represents the inertial force expression;

[0238] Let the first expression of the resultant force be equal to the second expression of the resultant force, and obtain the high-order shell modal additional mass calculation formula of the target hanging basket:

[0239]

[0240] In a specific application scenario, the high-order shell modal added mass calculation formula building module is also used for:

[0241] A shell radial vibration equation is constructed according to the natural vibration characteristics of the cylindrical shell, and a potential flow control equation of the fluid in the annular cavity in a cylindrical coordinate system is constructed according to the classical potential flow theory, so as to construct a high-order shell modal added mass calculation formula based on the shell radial vibration equation and the potential flow control equation.

[0242] In a specific application scenario, the preset boundary conditions include:

[0243] It means that the surface of the basket is not separated from the fluid. Indicates that the velocity of the fluid in the pressure vessel is 0, Indicates that the velocity of the fluid at the bottom of the basket is 0, κ z＝0 =0 means that the free surface sloshing of the fluid is not considered.

[0244] The present application provides a device for determining the equivalent additional mass of a hanging basket. First, the radius value, wall thickness value, height value, first-order beam modal additional mass, density value of the fluid in which the target hanging basket is located, and radius value of the pressure vessel containing the fluid are obtained. Secondly, based on the formula According to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel, the various high-order shell modal additional masses of the target hanging basket are calculated respectively, where ρ a represents the higher-order shell modal added mass, ρ f represents the density of the fluid, b represents the radius of the pressure vessel, ξ i represents the weighting coefficient, N represents a natural number, K mrepresents the m-order second-kind deformed Bessel function, a represents the radius value of the hanging basket, Δ represents the wall thickness value of the hanging basket, ψ(z) represents the axial deflection function; finally, based on the preset weight, the first-order beam modal added mass and each of the higher-order shell modal added mass are weighted to obtain the equivalent added mass of the target hanging basket. Compared with the prior art, the embodiment of the present application calculates the higher-order shell modal added mass of the target hanging basket at each modal order by constructing a higher-order shell modal added mass calculation formula, and then based on the preset weight, the weighted sum of the first-order beam modal added mass and each of the higher-order shell modal added mass is used as the equivalent added mass of the target hanging basket, which overcomes the problem of low calculation accuracy caused by the change of the equivalent added mass of the hanging basket due to the change of its modal order, and effectively improves the accuracy of determining the equivalent added mass of the hanging basket.

[0245] Each embodiment in this specification is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system embodiment, since it basically corresponds to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0246] The method and system of the present application may be implemented in many ways. For example, the method and system of the present application may be implemented by software, hardware, firmware, or any combination of software, hardware, and firmware. The above order of steps for the method is for illustration only, and the steps of the method of the present application are not limited to the order specifically described above, unless otherwise specifically stated. In addition, in some embodiments, the present application may also be implemented as a program recorded in a recording medium, which includes machine-readable instructions for implementing the method according to the present application. Therefore, the present application also covers a recording medium storing a program for executing the method according to the present application.

[0247] Obviously, those skilled in the art should understand that the above modules or steps of the present application can be implemented by a general computing device, they can be concentrated on a single computing device, or distributed on a network composed of multiple computing devices, and optionally, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, and in some cases, the steps shown or described can be executed in a different order from that herein, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. Thus, the present application is not limited to any specific combination of hardware and software.

[0248] The above description is only the preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for determining the equivalent added mass of a hanging basket, characterized in that: include: Obtaining the radius value, wall thickness value, height value, first-order beam modal additional mass of the target hanging basket, the density value of the fluid in which the target hanging basket is located, and the radius value of the pressure vessel containing the fluid; Based on the following formula, the additional mass of each high-order shell mode of the target hanging basket is calculated according to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel. Among them, ρ a represents the higher-order shell modal added mass, ρ f represents the density of the fluid, b represents the radius of the pressure vessel, ξ i represents the weighting coefficient, N represents a natural number, K m represents the m-order second-kind deformation Bessel function, a represents the radius of the hanging basket, Δ represents the wall thickness of the hanging basket, and ψ(z) represents the axial deflection function; Based on preset weights, the first-order beam modal additional mass and each of the higher-order shell modal additional mass are weighted to obtain the equivalent additional mass of the target hanging basket.

2. The method according to claim 1, characterized in that After performing weighted processing on the first-order beam modal additional mass and each of the higher-order shell modal additional mass based on the preset weights to obtain the equivalent additional mass of the target hanging basket, the method further includes: Acquiring surface pulsating pressure power spectrum density data of the target hanging basket; The equivalent added mass and the surface pulsating pressure power spectrum density data are input into a pre-constructed hanging basket finite element model to obtain the root mean square value of the flow-induced vibration stress response of the target hanging basket.

3. The method according to claim 2, characterized in that After inputting the equivalent added mass and the surface pulsating pressure power spectrum density data into a pre-built hanging basket finite element model to obtain the root mean square value of the flow-induced vibration stress response of the target hanging basket, the method further includes: Performing peak value conversion processing on the root mean square value of the flow-induced vibration stress response to obtain the stress peak value of the target hanging basket; According to the material of the target hanging basket, searching for the corresponding material high cycle fatigue stress threshold; If the stress peak value is less than the high cycle fatigue stress threshold of the material, it is determined that the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life is a low risk level; If the stress peak value is greater than the high cycle fatigue stress threshold of the material, it is determined that the risk level of fatigue damage of the target hanging basket due to flow-induced vibration during its service life is a high risk level.

4. The method according to claim 1, characterized in that Before respectively calculating each high-order shell modal additional mass of the target hanging basket based on the formula according to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel, the method further includes: Obtain the shell radial vibration equation of the target hanging basket u=Cψ(z)sinmθsinωt Among them, u represents the radial vibration displacement of the hanging basket, C represents any real constant, θ represents the circumferential coordinate, and ω represents the shell frequency of the hanging basket; The shell radial vibration equation is derived with respect to time to obtain the derived shell radial vibration equation: Based on the derived shell radial vibration equation, the radial velocity continuity condition expression is constructed. Where r represents the radial coordinate; The potential function of the fluid is constructed based on the radial velocity continuity condition expression φ=κ(r,z)sinmθcosωt Where φ represents the fluid potential function, κ(r,z) represents the transition function, and z represents the axial coordinate; Substitute the potential function into the pre-constructed potential flow control equation to obtain the constraint equation of the transition function. The potential flow control equation is expressed as the following formula: The constraint equation of the transition function is expressed as follows: The transition function is subjected to an infinite series expansion operation to obtain the transition function after infinite series expansion. Among them, c i represents the weighting coefficient, η i (r,z) represents an orthogonal function cluster, and n represents the number of cutoff terms in the series; The transition function after the infinite series expansion is introduced into the constraint equation of the transition function, and the weighted coefficient is calculated based on the weighted residual method under the preset boundary conditions. Among them, the orthogonal function cluster The orthogonal function cluster η i (r, z) and the weighting coefficient c i Substitute the transition function after the infinite series expansion into The infinite series expression of the transition function is obtained, and the infinite series expression of the transition function is substituted into the potential function of the fluid to obtain the explicit expression of the potential function of the fluid: The explicit expression of the fluid potential function is differentiated with respect to time to obtain the expression of the dynamic water pressure: Where p(θ,z,t) represents the dynamic water pressure; Integrate the hydrodynamic pressure expression along the height direction to obtain the first expression of the resultant force per unit annular length: Among them, M p The first expression for the resultant force per unit circumferential length is: Construct an expression for the inertial force caused by the additional mass of the high-order shell mode of the hanging basket, and integrate the inertial force expression along the height direction to obtain the second expression of the resultant force per unit circumferential length. Among them, M a The second expression for the resultant force per unit circumferential length is, represents the inertial force expression; Let the first expression of the resultant force be equal to the second expression of the resultant force, and obtain the high-order shell modal additional mass calculation formula of the target hanging basket:

5. The method according to claim 4, characterized in that Before obtaining the shell radial vibration equation of the target hanging basket, the method further includes: A shell radial vibration equation is constructed according to the natural vibration characteristics of the cylindrical shell, and a potential flow control equation of the fluid in the annular cavity in a cylindrical coordinate system is constructed according to the classical potential flow theory, so as to construct a high-order shell modal added mass calculation formula based on the shell radial vibration equation and the potential flow control equation.

6. The method according to claim 4, characterized in that The preset boundary conditions include: It means that the surface of the basket is not separated from the fluid. Indicates that the velocity of the fluid in the pressure vessel is 0, Indicates that the velocity of the fluid at the bottom of the basket is 0, κ z＝0 =0 means that the free surface sloshing of the fluid is not considered.

7. A device for determining the equivalent added mass of a hanging basket, characterized in that: include: A parameter acquisition module, used to acquire the radius value, wall thickness value, height value, first-order beam modal additional mass of the target hanging basket, the density value of the fluid in which the target hanging basket is located, and the radius value of the pressure vessel containing the fluid; The high-order shell modal additional mass calculation module is used to calculate the high-order shell modal additional mass of the target hanging basket according to the radius value, wall thickness value, height value of the target hanging basket, the density value of the fluid, and the radius value of the pressure vessel based on the following formula. Among them, ρ a represents the higher-order shell modal added mass, ρ f represents the density of the fluid, b represents the radius of the pressure vessel, ξ i represents the weighting coefficient, N represents a natural number, K m represents the m-order second-kind deformation Bessel function, a represents the radius of the hanging basket, Δ represents the wall thickness of the hanging basket, and ψ(z) represents the axial deflection function; The hanging basket equivalent added mass determination module is used to perform weighted processing on the first-order beam modal added mass and each of the high-order shell modal added mass based on preset weights to obtain the equivalent added mass of the target hanging basket.

8. The device according to claim 7, characterized in that After the hanging basket equivalent additional mass determination module, the device further includes a flow-induced vibration stress response root mean square value determination module, which is used to: Acquiring surface pulsating pressure power spectrum density data of the target hanging basket; The equivalent added mass and the surface pulsating pressure power spectrum density data are input into a pre-constructed hanging basket finite element model to obtain the root mean square value of the flow-induced vibration stress response of the target hanging basket.

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