CN110909501A - Method for calculating load amplification factor in system dynamic analysis - Google Patents
Method for calculating load amplification factor in system dynamic analysis Download PDFInfo
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Abstract
The invention discloses a method for calculating a load amplification factor in system dynamic analysis, which comprises the following steps: the method comprises the steps of establishing a system model power analysis model by using a finite element calculation program, determining key input and output parameters by combining the contact relation between components according to the mechanical analysis result of a nominal model, establishing a probability density function describing the key input parameters of the system model by using the distribution interval and the uniform distribution hypothesis of the key input parameters, obtaining the probability density function and the distribution interval thereof, carrying out numerical sampling on the key input parameters of the system by using a Latin hypercube sampling algorithm and verifying the rationality of the key input parameters, establishing a key input-output large database by using finite element transient calculation, carrying out database result analysis, obtaining the ratio of an upper limit value of a 99% confidence interval to a nominal model calculated value, and quantitatively giving the influence degree of input uncertainty on the power response, namely a load amplification factor.
Description
Technical Field
The invention belongs to the field of reactor structure mechanical analysis, and particularly relates to power analysis and calculation of main equipment, pipelines and auxiliary systems in a reactor coolant system.
Background
In the structural mechanical analysis and safety evaluation of the reactor coolant system, a system dynamic analysis model (hereinafter referred to as a system model) may be a main device (such as a reactor system, a reactor coolant pump, a steam generator, and a voltage stabilizer), a pipeline system (such as a main pipeline and an auxiliary pipeline) or an auxiliary system (such as a waste heat removal system, a purification system, and the like) in the reactor coolant system. The model is generally used for calculating the dynamic response and load distribution among main components of an analysis object under the action of external dynamic loads (such as earthquake, LOCA, impact and the like), and provides calculation input for further carrying out stress evaluation on each component in a detailed mode.
Because of the influence of factors such as model simplification, manufacturing deviation, field assembly and calculation errors, input parameters of a system model often have a certain degree of uncertainty, and in order to reflect the influence of the uncertainty on dynamic response, load distribution and subsequent stress evaluation, engineering generally multiplies a calculation load between components obtained by dynamic response calculation by an amplification factor (the design load is the calculation load multiplied by the amplification factor) to serve as the input of subsequent refined stress evaluation so as to ensure the reliability of design. The essence of this approach is to translate the uncertainty problem of the dynamic response into a given problem of the envelope parameters in the deterministic analysis. How to determine the numerical value of the load amplification factor becomes an important link for the mechanical analysis of the reactor structure.
Theoretically, the load amplification factor of the system model can be determined by reference, experimental fitting, theoretical analytical solution or numerical simulation. Because publicly published documents and data lack quantitative research of load amplification factors, the mechanical design of the reactor structure of the domestic in-service nuclear power station generally refers to the load amplification factors (single values) of foreign prototype reactors (or approximate reactor types), and the reference values are applied to all substructures and components, and the most severe condition is considered during selection, so that the design load of part of the structures or components is excessively conserved, the design margin is low, and even the false appearance that the result cannot meet the design requirement occurs. Under the real condition, because different output parameters have different sensitivity degrees to input parameters, the values of the load amplification factors have larger differences according to different analysis objects, analysis parts and physical quantities. Therefore, the quantitative influence rule of the uncertainty of the system parameters on different components and physical quantities is researched, the determination method and the calculation process of the load amplification factor are mastered, the real allowances of different loads are obtained, and data support is provided for design margin mining and optimal design. .
Along with the improvement of the performance requirement of the reactor, the structural arrangement and the functions of the independent new reactor are greatly changed, the load amplification factor of the traditional reactor has the problems of applicability (failure by using a reference method), long test period and high cost (low feasibility of a test fitting method), the system model has multiple degrees of freedom and complex connection relation, the nonlinear problems of gaps, friction, fluid-solid coupling, materials and the like generally exist, and the input-output relation is difficult to obtain explicitly (the difficulty of a theoretical analysis method is large). Therefore, numerical simulation becomes the most feasible method.
In summary, in the process of implementing the technical solution of the embodiments of the present application, the inventors of the present application find that at least the following problems exist in the current technology:
(1) the prior published literature and data lack quantitative research on the influence of input uncertainty on the dynamic response of a system model.
(2) In the mechanical design of each in-service reactor type, the load amplification factor value of the foreign similar reactor type (or prototype reactor) is used for reference, and the value is conservative, so that the design load of a part of structure is higher than the real condition, and the design margin is reduced.
(3) The determination of the load amplification factor of the new reactor type has the difficulties of low empirical applicability, high test cost, high analytic solution difficulty and the like, and numerical calculation needs to be carried out by means of a statistical method.
Disclosure of Invention
The invention provides a numerical calculation method of a load amplification factor in dynamic analysis of a reactor coolant system and an auxiliary system, and solves the numerical determination problem caused by lack of experience, high test cost and difficult theoretical derivation. The method can quantitatively examine the influence of the uncertainty of the input parameters on the response confidence interval and the statistical property, and provides a quantitative basis for the margin mining of the non-conforming items. Meanwhile, load amplification factors with differentiation can be determined according to the influence degree of input parameters on different responses in the system model, so that the problem of over-conservative calculation in the traditional method is solved.
The method comprises the following steps:
1) and establishing a dynamic analysis finite element model of the analysis object, wherein the model can reflect the vibration characteristics of the related main structure or component.
2) And (3) carrying out transient dynamic response analysis on the nominal model by adopting a finite element calculation program to obtain nominal contact load among the components, and further carrying out stress evaluation on the components, wherein the nominal model is a model with all analysis parameters taking nominal values (ideal design values), and the nominal contact load is the contact load obtained by taking nominal values of the input parameters.
3) Finding out the contact load related to the weak part as a key output parameter according to the stress evaluation result; according to design experience or sensitivity analysis, contact rigidity and gaps between components which have obvious influence on key output parameters are selected as key input parameters.
4) And (3) deriving a probability density function meeting uniform distribution and a distribution interval thereof according to the upper and lower boundaries of the distribution of the key input parameters, as shown in a formula (1).
5) And (4) completing spatial sampling of key input parameters according to the derived probability density function by utilizing a Latin hypercube algorithm, and carrying out sampling verification.
6) And carrying out finite element transient dynamic analysis of the system according to the samples of the key input parameters to obtain a big data pool of the key input-output parameters.
7) And obtaining a 99% confidence interval of the key output parameter according to the data pool of the output parameter.
8) The ratio of the upper limit of the 99% confidence interval to the nominal calculated value is used as the load magnification factor.
Wherein:
wherein the key input parameter w is a random variable, PW(w) is the probability density function of w, alAnd auThe lower and upper bounds of w, respectively.
Further, when data sampling is performed by using the Latin hypercube algorithm, different parameters can be assumed to be independent of each other because no correlation exists between key input parameters.
One or more technical schemes provided by the invention at least have the following technical effects or advantages:
1) by utilizing the calculation method provided by the invention, the influence degree of the uncertainty of the input parameter on the dynamic response of the system model can be researched and examined, and a load amplification factor, which is a parameter required by deterministic analysis, is obtained.
2) The method provided by the invention can be used for mining design margins and providing data support for engineering decisions.
3) The dynamic response statistical characteristics of the analysis object can be mastered by only adopting a Monte Carlo numerical simulation method without adopting a complex mode of test data fitting, approximate heap type reference or theoretical solution.
4) All the processes are realized by computer programs, the calculation result is reliable, and the analysis process can be integrated in the mechanical standard analysis process of the reactor structure.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention;
FIG. 1 is a schematic flow diagram of the process;
FIG. 2 is a schematic diagram of a finite element model of a reactor system according to the present invention;
FIG. 3 is a schematic diagram of a reaction spectrum corresponding to the X-direction seismic acceleration time course of the reactor pressure vessel supporting position in the embodiment of the application;
FIG. 4 is a schematic diagram illustrating statistical distribution of contact stiffness sampling results of 3 locations in an embodiment of the present application;
FIG. 5 is a schematic diagram of a statistical distribution of CB-RPV contact load extremes in an embodiment of the present application;
FIG. 6 is a schematic diagram of a probability density function of an extreme CB-RPV contact load in an embodiment of the present application.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflicting with each other.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described and thus the scope of the present invention is not limited by the specific embodiments disclosed below.
Referring to fig. 1-6, the present embodiment illustrates a method for calculating a load amplification factor of a pressurized water reactor system for a dynamic response analysis of the pressurized water reactor system under a seismic load. Reactor system key components include: fuel Assemblies (FA), core hangers (CB), upper internals (UVI), core barrels (CS), Control Rod Drive Mechanisms (CRDM), Reactor Pressure Vessels (RPV), integrated reactor dome structures (UVI), and the like. The finite element model of the reactor system is shown in figure 2, the input of the seismic analysis of the reactor system is three horizontal direction manual fitting seismic displacement time courses, wherein, the seismic response spectrum corresponding to the X direction fitting time course is shown in figure 3, and the action position is the intersection point position of the central axis of the reactor pressure vessel and the inlet connecting pipe nozzle.
In order to better understand the technical solution, the technical solution will be described in detail with reference to the drawings and the specific embodiments.
S10, establishing a reactor system dynamic analysis finite element model through finite analysis software or programs, developing transient dynamic response analysis of a nominal model, obtaining contact loads among all parts in the reactor system, and further developing stress evaluation of all parts.
After step S10, the method of the embodiment of the present application proceeds to step S20, i.e.: according to the contact relationship among components of the reactor system and the nominal model stress evaluation result, the contact rigidity and the gap of 3 parts (a hanging basket-upper core plate CB-UCP, a hanging basket-surrounding cylinder CB-CS and a hanging basket-pressure container CB-RPV) which have large influence on the result are selected as key input parameters for uncertainty research, and the nominal contact load of the parts is used as key output parameters.
After step S20, the method of the embodiment of the present application proceeds to step S30, i.e.: and (3) constructing a Probability Density Function (PDF) of contact rigidity and gaps by using the upper and lower boundaries of key input parameters and adopting a uniform distribution model to obtain the probability density function and a distribution interval thereof, wherein the expression of the function is shown in a formula (1).
After step S30, the method of the embodiment of the present application proceeds to step S40, i.e.: and (4) finishing the spatial sampling of the input parameters by utilizing a Latin hypercube algorithm according to the PDF derived in the step S30.
After step S40, the method of the embodiment of the present application proceeds to step S50, i.e.: the PDF of the collected sample is matched against the PDF derived in step S30 to examine the sample' S plausibility. The PDF of the 3 site contact stiffness samples is shown in fig. 4, where the black line is the target PDF and fig. 4 is the non-dimensionalized sample distribution range.
After step S50, the method of the embodiment of the present application proceeds to step S60, i.e.: and (4) bringing the samples of the key input parameters collected in the step S40 into the reactor system power analysis finite element model established in the step S10, carrying out transient power analysis, and obtaining a large database of the key output parameters.
After step S60, the method of the embodiment of the present application proceeds to step S70, i.e.: calculating a 99% confidence interval of the key output parameters and the like. The Voilin graph of the statistical distribution of the CB-RPV contact load extreme values is shown in FIG. 5, and the probability density curve is shown in FIG. 6.
After step S70, the method of the embodiment of the present application proceeds to step S80, i.e.: upper limit of 99% confidence interval of load (130.7X 10)4N) and nominal model calculation (114.1X 10)4N) as a load amplification factor, the value was 1.145.
In practical application, the commercial finite element software comprises: ANSYS, ABAQUS, etc., numerical calculation software and programming languages include: MATLAB, FORTRAN, C/C + +, PYTHON, and the like.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (6)
1. A method for calculating a load amplification factor in system dynamic analysis is characterized by comprising the following steps:
step 1: establishing a dynamic analysis finite element model of an analysis object;
step 2: carrying out finite element transient dynamic analysis on a nominal model of an analysis object to obtain nominal contact loads among components in the system, and carrying out stress evaluation on the components in the system to obtain a stress evaluation result;
and step 3: according to the stress evaluation result, finding out the contact load related to the weak component of the analysis object as a key output parameter, and selecting an input parameter which has obvious influence on the key output as a key input parameter;
and 4, step 4: obtaining a probability density function and a distribution interval thereof according to the upper and lower bounds of key input parameters;
and 5: carrying out spatial sampling on the key input parameters, and establishing a key input-output parameter database by means of finite element transient analysis;
step 6: obtaining a confidence interval according to a database of the key output parameters;
and 7: and taking the ratio of the upper limit value of the confidence interval to the nominal contact load as a load amplification factor.
2. The method for calculating the load amplification factor in the system dynamic analysis according to claim 1, wherein the analysis object of the method is a reactor coolant system and an auxiliary system thereof.
3. The method for calculating the load amplification factor in the system dynamic analysis according to claim 1, wherein key input parameters of the method are contact stiffness and clearance between components to be analyzed, and key output parameters are contact load between the components.
4. The method for calculating the load amplification factor in the system dynamic analysis according to claim 1, wherein the probability density function of the key input parameters in the step 4 satisfies a uniform distribution, as shown in formula (1):
wherein the key input parameter w is a random variable, PW(w) is the probability density function of w, alAnd auLower and upper bounds of w, respectively。
5. The method for calculating the load amplification factor in the system dynamic analysis according to claim 1, wherein the step 5 performs spatial sampling on the key input parameters by using a Latin hypercube algorithm.
6. The method for calculating a load amplification factor in system dynamic analysis according to claim 1, wherein the confidence interval in step 6 has a confidence of 99%.
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Application publication date: 20200324 |