Lightweight parameterized design method for large-size thick-wall F92 steel tee joint

Abstract

The application discloses a lightweight parameterized design method for a large-size thick-wall F92 steel tee joint, and belongs to the technical field of pipeline component optimization design. The method comprises the following steps: obtaining initial geometric parameters and allowable stress threshold values and creep damage threshold values, constructing a tee parameterized benchmark model and importing a creep constitutive relation; performing flow-heat-solid coupling simulation under an ultra-supercritical working condition, and extracting global stress and stress gradient; constructing a nonlinear mapping function, bidirectionally adjusting wall thickness and transition fillet radius at each position according to the stress level, and outputting intermediate values; generating discrete size driving factors through traversal and applying feasible region constraints; driving and controlling vertex adaptive deformation, generating a non-uniformly distributed lightweight tee intermediate model, and performing fairing processing; performing creep life checking by using Robinson linear damage accumulation theory; and iteratively correcting sensitivity factors until safety requirements are met. The application can realize minimization of the weight of the tee joint under the premise of ensuring the creep life.

Description

Technical Field

[0001] This invention relates to the field of pipeline component optimization design technology, specifically to a lightweight parametric design method for large-size thick-walled F92 steel tees. Background Technology

[0002] The main steam piping system of ultra-supercritical thermal power generating units typically employs large-size, thick-walled tees, mostly made of F92 steel. These tees must withstand pressures exceeding 25 MPa and temperatures above 600°C for extended periods during service, making creep damage their primary failure mechanism. Traditional tee designs are often based on the assumption of uniform wall thickness and determine the dimensions of the intersection area according to standard-specified local reinforcement rules. To ensure structural safety, designers often increase the overall wall thickness or the radius of transition fillets; however, this approach significantly increases structural weight, reduces material utilization, and increases the supporting load and construction costs of the piping system.

[0003] In low-stress regions, uniform thick-walled designs lead to material redundancy. However, near intersections where high stress concentrations occur, relying solely on empirical formulas and uniform thickening cannot accurately match the stress distribution for targeted strengthening. Existing optimization design methods often adjust dimensions based on a single stress index, failing to effectively utilize stress gradient information to differentiate the load-bearing characteristics of different regions. This results in optimization results that struggle to simultaneously meet weight reduction and creep life requirements. Furthermore, existing methods generally lack a complete process combining bidirectional adjustment of geometric parameters, creep damage evaluation, and iterative closed-loop control, making it impossible to reliably guarantee design life while achieving lightweighting.

[0004] Therefore, the traditional uniform wall thickness design leads to material redundancy and excessive weight in the low-stress zone of the tee. Existing optimization methods fail to incorporate stress gradient information into the mapping function to distinguish regional characteristics and lack deep coupling with creep damage evaluation and non-uniform rational B-spline NURBS parametric surface reconstruction, making it impossible to achieve lightweighting while ensuring the creep life of F92 steel tees in ultra-supercritical units. Summary of the Invention

[0005] The purpose of this invention is to provide a lightweight parametric design method for large-size thick-walled F92 steel tees to solve the above-mentioned problems in the prior art, and to minimize the weight of the tees while meeting the requirements of high temperature and high pressure creep life.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A lightweight parametric design method for large-size thick-walled F92 steel tees, used to determine the spatially non-uniformly distributed wall thickness and transition fillet geometry of the tees, includes the following steps: S1. Obtain the initial geometric parameters of the tee to be designed, the preset allowable stress threshold of F92 steel, and the preset creep damage threshold. The initial geometric parameters include the outer diameter of the main pipe, the inner diameter of the branch pipe, the initial wall thickness, and the initial transition fillet radius. Using the initial wall thickness and the initial transition fillet radius as the initial benchmark values ​​for optimization, establish minimizing the weight of the tee as the optimization objective, construct a parameterized benchmark model of the tee based on non-uniform rational B-splines, and import the preset creep constitutive relation corresponding to F92 steel. The preset creep constitutive relation is a mathematical model used to describe the high-temperature creep behavior of the material and is used for subsequent creep life assessment. S2. Based on the preset ultra-supercritical working conditions, perform fluid-thermal-structure interaction simulation calculations on the parameterized benchmark model of the three-way valve, extract continuous equivalent stress data and stress gradient data of the entire three-way valve, and define the values ​​at each spatial location in the continuous equivalent stress data as the stress values ​​at that location. S3. Based on the stress value, the stress gradient data, and the allowable stress threshold, a nonlinear mapping function between the stress value and the geometric dimensions is constructed. The nonlinear mapping function uses the stress value as the independent variable and the wall thickness and transition fillet radius at each position of the tee as the dependent variable, and includes a sensitivity factor for adjusting the rate of change of the wall thickness and fillet radius. The mapping function is configured to: based on the initial reference value, adjust the wall thickness and transition fillet radius at each position according to the magnitude of the stress value at each position relative to the allowable stress threshold, and output the intermediate wall thickness and intermediate transition fillet radius corresponding to each position. S4. Call the nonlinear mapping function to perform traversal calculations based on the stress value and the stress gradient data to obtain the intermediate wall thickness value and intermediate transition fillet radius value at each position, and restrict the intermediate value within a preset feasible domain to generate a discrete size driving factor that varies with spatial position. The discrete size driving factor includes the target wall thickness value and target transition fillet radius value at the corresponding position, i.e., the target geometric parameters of the tee. S5. Using the discrete size driving factor, the control vertices of the parameterized reference model of the tee are driven to undergo adaptive deformation to generate a lightweight intermediate model of the tee with non-uniform distribution of wall thickness and fillet. The reconstructed surface is then smoothed. S6. Based on the preset creep constitutive relation, the lightweight tee intermediate model is verified by finite element method using Robinson linear damage accumulation theory; the verification conditions are whether the equivalent stress is lower than the allowable stress threshold and whether the creep damage factor is less than the creep damage threshold. S7. If the verification conditions are met, the discrete size driving factor is output as the target geometric parameter of the tee to complete the lightweight design of the tee; if the verification conditions are not met, the sensitivity factor in the nonlinear mapping function is adjusted, and S4-S6 are executed again to iteratively update the intermediate model of the lightweight tee until the conditions are met.

[0007] Furthermore, the construction of the parameterized benchmark model for the tee based on non-uniform rational B-splines described in S1 specifically includes: The outer diameter of the main pipe, the inner diameter of the branch pipe, the initial wall thickness, and the initial transition fillet radius are mapped to the control vertex parameters of a non-uniform rational B-spline surface. Configure the non-uniform degrees of freedom of the control vertex to allow the control vertex to perform independent three-dimensional coordinate offsets according to the discrete size driving factor; Based on the control vertex parameters, non-uniform degrees of freedom, and the topology of the tee, the parameterized benchmark model of the tee is generated by fitting a non-uniform rational B-spline surface.

[0008] Furthermore, the extraction of continuous equivalent stress data and stress gradient data across the entire tee region as described in S2 specifically includes: The ultra-supercritical operating conditions are set to a main steam pressure greater than 25 MPa and a steam temperature greater than 600 °C. The transient flow field is solved iteratively using a pre-defined turbulence model, which is the standard k-type turbulence model. Turbulence model; During the fluid-thermal-structure interaction simulation calculation, the fluid pressure and temperature loads calculated based on the ultra-supercritical working conditions are applied to the finite element mesh nodes on the surface of the three-way parameterized reference model, and bidirectional iteration is performed until convergence. After convergence, the continuous equivalent stress data on the global finite element nodes of the tee are extracted, and the derivatives of each node along the wall thickness normal direction are calculated to generate the stress gradient data.

[0009] Furthermore, the nonlinear mapping function between stress values ​​and geometric dimensions described in S3 specifically includes: A mapping framework is established with the stress value as input and the wall thickness and transition fillet radius at each position of the tee as output. The stress gradient data is introduced into the mapping framework as a regional weighting coefficient to enhance the adjustment range of the transition fillet radius in the high gradient region of the intersection line. The stress value is mapped to a first stress function σ(x,y,z) that varies with spatial coordinates; The stress gradient data is mapped to a first gradient function that varies with spatial coordinates. and to Normalization is performed to obtain the dimensionless normalized gradient function. Its value range is [0,1]; Set the sensitivity factor that varies with spatial coordinates Satisfying the relation: ; in, The baseline sensitivity factor has a length / stress dimension; This is a preset non-negative proportionality coefficient; Define the preset minimum allowable wall thickness and maximum allowable wall thickness and minimum allowable transition fillet radius and maximum allowable transition fillet radius ,in Less than the initial wall thickness; The nonlinear mapping function is specifically configured with the following calculation steps: Calculate wall thickness offset ;in The preset allowable stress threshold for F92 steel; Calculate the intermediate wall thickness value related to the location. To compare the initial wall thickness with sum; Calculate fillet offset Where β is a preset non-negative fillet shape coefficient; Calculate the radius of the intermediate transition fillet at the corresponding position. The initial transition fillet radius and sum.

[0010] Furthermore, the generation of the discrete size driving factor that varies with spatial location as described in S4 specifically includes: The continuous equivalent stress data is discretized into several spatial grid points; For each spatial grid point, extract its stress value σ(x,y,z) and stress gradient value; The stress value and stress gradient value are input into the nonlinear mapping function for calculation, and the corresponding intermediate wall thickness value and intermediate transition fillet radius value are output. The intermediate wall thickness is forcibly constrained to be no less than [amount missing]. and not higher than Within the range, the intermediate transition fillet radius value is forcibly constrained to be no less than and not higher than Within the range, the constrained values ​​are used as the target wall thickness and target transition fillet radius values ​​at that point, forming a discrete dimension driving factor.

[0011] Furthermore, the lightweight tee intermediate model described in S5, which generates both wall thickness and fillet radius with non-uniform distribution, specifically includes: Based on the target wall thickness and target transition fillet radius values ​​in the discrete size driving factors of each spatial grid point, calculate the three-dimensional coordinate offset of the non-uniform rational B-spline control vertex. The control vertex is driven to move adaptively according to the coordinate offset using the discrete size driving factor. The control vertices after movement are reconstructed using non-uniform rational B-spline surfaces and then smoothed to generate a lightweight intermediate tee model with non-uniform distribution of wall thickness and fillet radius.

[0012] Furthermore, S6 specifically includes: Using Robinson's linear damage accumulation theory and the preset creep constitutive relation, the creep damage factor of the tee within the preset design time is calculated; The maximum stress value is extracted based on the stress value of the entire tee area. It is then determined whether the maximum stress value is lower than the allowable stress threshold of F92 steel, and whether the creep damage factor is lower than the creep damage threshold. If the maximum stress value is lower than the allowable stress threshold of F92 steel and the creep damage factor is less than the creep damage threshold, then the verification condition is satisfied.

[0013] Furthermore, the adjustment of the sensitivity factor in the nonlinear mapping function as described in S7 specifically includes: If the maximum stress value is higher than the allowable stress threshold of F92 steel or the creep damage factor is greater than the creep damage threshold, then the local area exceeding the threshold is extracted, and the reference sensitivity factor is increased. Or the non-negative proportionality coefficient The value of this value enhances the wall thickness compensation rate in this local area; If the maximum stress value is lower than 90% of the allowable stress threshold of F92 steel and the creep damage factor is less than 50% of the creep damage threshold, then the reference sensitivity factor is increased. Or the non-negative proportionality coefficient The value of [value] is increased to increase the thinning rate of this local area, thereby further achieving lightweighting; If the direction adjustment is still not satisfied, then... and Perform collaborative corrections until a lightweight model that meets the verification conditions is obtained.

[0014] Furthermore, if the verification conditions described in S7 are met, the target geometric parameters of the tee are output to complete the lightweight design of the tee, specifically including: When the lightweight tee intermediate model meets the verification conditions, it is identified as the final optimal tee geometry model; Extract the target wall thickness and target transition fillet radius values ​​corresponding to each spatial coordinate point in the optimal tee geometric model, and output them as the target geometric parameters of the tee to complete the lightweight design of the tee.

[0015] Furthermore, the preset creep constitutive relation is the Norton-Arrhenius coupled creep model: ; in, The steady-state creep strain rate; The stress value is mentioned. Absolute temperature; is the universal gas constant; B is the material creep coefficient; n is the creep stress exponent; Q is the creep activation energy; its parameters are calibrated based on the creep strength data of Grade 92 steel in ASME BPVC.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention fundamentally changes the traditional design concept of uniform wall thickness for tees. By obtaining the actual stress distribution through fluid-thermal-structure interaction simulation and using stress gradient information to distinguish between high-gradient and low-gradient regions, it enables bidirectional adjustment of the wall thickness and transition fillet radius in a spatially non-uniform manner. This allows for sufficient reinforcement of high-stress areas and reasonable thinning of low-stress areas. This mapping mechanism ensures that the material distribution is precisely matched with actual load-bearing requirements, minimizing the overall weight of the tee while ensuring that the equivalent stress and creep life meet safety requirements.

[0017] 2. The combination of parameterized non-uniform rational B-spline NURBS model and discrete size driving factor ensures the flexible controllability of complex surface morphology and the smoothness of reconstructed surface.

[0018] 3. The entire method integrates an iterative verification closed loop for creep damage accumulation. Through automatic correction of the sensitivity factor, it can stably converge to the lightest geometric configuration that meets the creep life requirements, providing an efficient and reliable engineering implementation approach for the design of key components of ultra-supercritical units. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0021] This invention provides a lightweight parametric design method for large-size, thick-walled F92 steel tees. The method involves constructing a parametric baseline model, performing fluid-thermo-structural coupling simulation, establishing a nonlinear mapping between stress and geometric dimensions, generating discrete dimension driving factors, driving model deformation, and performing an iterative closed loop for creep damage verification. The final output is a tee geometric parameter that meets both lightweight and safety requirements. This method fundamentally changes the traditional design concept of uniform wall thickness. By distributing the material non-uniformly in space, it achieves a precise match between load-bearing requirements and material distribution, maximizing lightweight performance while ensuring structural safety.

[0022] This embodiment provides a lightweight parametric design method for large-size, thick-walled F92 steel tees, such as... Figure 1 As shown, it includes the following steps: S1. Obtain the initial geometric parameters of the tee to be designed, the preset allowable stress threshold of F92 steel, and the preset creep damage threshold. The initial geometric parameters include the outer diameter of the main pipe, the inner diameter of the branch pipe, the initial wall thickness, and the initial transition fillet radius. Using the initial wall thickness and the initial transition fillet radius as the initial benchmark values ​​for optimization, establish minimizing the weight of the tee as the optimization objective, construct a parameterized benchmark model of the tee based on non-uniform rational B-splines, and import the preset creep constitutive relation corresponding to F92 steel. The preset creep constitutive relation is a mathematical model used to describe the high-temperature creep behavior of the material and is used for subsequent creep life assessment. S2. Based on the preset ultra-supercritical working conditions, perform fluid-thermal-structure interaction simulation calculations on the parameterized benchmark model of the three-way valve, extract continuous equivalent stress data and stress gradient data of the entire three-way valve, and define the values ​​at each spatial location in the continuous equivalent stress data as the stress values ​​at that location. S3. Based on the stress value, the stress gradient data, and the allowable stress threshold, a nonlinear mapping function between the stress value and the geometric dimensions is constructed. The nonlinear mapping function uses the stress value as the independent variable and the wall thickness and transition fillet radius at each position of the tee as the dependent variable, and includes a sensitivity factor for adjusting the rate of change of the wall thickness and fillet radius. The mapping function is configured to: based on the initial reference value, adjust the wall thickness and transition fillet radius at each position according to the magnitude of the stress value at each position relative to the allowable stress threshold, and output the intermediate wall thickness and intermediate transition fillet radius corresponding to each position. S4. Call the nonlinear mapping function to perform traversal calculations based on the stress value and the stress gradient data to obtain the intermediate wall thickness value and intermediate transition fillet radius value at each position, and restrict the intermediate value within a preset feasible domain to generate a discrete size driving factor that varies with spatial position. The discrete size driving factor includes the target wall thickness value and target transition fillet radius value at the corresponding position. S5. Using the discrete size driving factor, the control vertices of the parameterized reference model of the tee are driven to undergo adaptive deformation to generate a lightweight intermediate model of the tee with non-uniform distribution of wall thickness and fillet. The reconstructed surface is then smoothed. S6. Based on the preset creep constitutive relation, the lightweight tee intermediate model is verified by finite element method using Robinson linear damage accumulation theory; the verification conditions are whether the equivalent stress is lower than the allowable stress threshold and whether the creep damage factor is less than the creep damage threshold. S7. If the verification conditions are met, output the target geometric parameters of the tee to complete the lightweight design of the tee; if the verification conditions are not met, adjust the sensitivity factor in the nonlinear mapping function and return to execute S4-S6 to iteratively update the intermediate model of the lightweight tee until the conditions are met.

[0023] The following example uses a specific F92 steel equal-diameter tee for the main steam pipeline of an ultra-supercritical unit to illustrate the specific process of the above method. The outer diameter of the main pipe of the tee to be designed is 600mm, the inner diameter of the branch pipe is 500mm, the initial wall thickness is 80mm, and the initial transition fillet radius is 40mm.

[0024] Step S1 is executed to obtain the initial geometric parameters of the tee, namely, the main pipe outer diameter of 600mm, the branch pipe inner diameter of 500mm, the initial wall thickness of 80mm, and the initial transition fillet radius of 40mm. Preset allowable stress thresholds and creep damage thresholds for F92 steel are obtained. Based on the allowable stress data for Grade 92 steel at 620℃ in the ASME BPVC standard, the allowable stress threshold is set to 85MPa, and the creep damage threshold is set to 1.0. These two thresholds are used for stress comparison and creep life determination in subsequent mapping functions, respectively. The initial wall thickness of 80mm and the initial transition fillet radius of 40mm are set as the initial baseline values ​​for the entire optimization process, and minimizing the tee's weight is explicitly defined as the optimization objective.

[0025] Based on this, a parameterized benchmark model for a tee is constructed using non-uniform rational B-spline technology. Specifically, the outer diameter of the main pipe, the inner diameter of the branch pipe, and the initial wall thickness are included. and initial transition fillet radius The control vertex parameters are mapped to a non-uniform rational B-spline NURBS surface, and non-uniform degrees of freedom are configured for each control vertex. This allows each control vertex to perform independent three-dimensional coordinate offsets based on the subsequently calculated discrete size driving factors. This non-uniform degree of freedom configuration means that vertices in the main pipe region, branch pipe region, and intersection transition region can move according to different offset directions and amplitudes, so as to achieve a completely non-uniform wall thickness and fillet distribution in space in subsequent steps. Based on the topology of the tee, the intersection region of the main pipe and branch pipe adopts a continuous surface transition, and a fully parameterized tee reference model is generated by NURBS surface fitting. In step S1, the preset creep constitutive relation corresponding to F92 steel is also imported. This constitutive relation is a Norton-Arrhenius coupled creep model describing the creep behavior of the material at high temperature. Its specific expression is described later and is used for subsequent creep life assessment.

[0026] After completing the baseline model construction, the process proceeds to step S2, where fluid-thermal-structure interaction (FTH) simulation calculations are performed under preset ultra-supercritical operating conditions. These conditions are specifically set with a main steam pressure of 28 MPa and a steam temperature of 620°C, consistent with typical operating parameters for ultra-supercritical units. Standard... The turbulence model is used to solve the internal flow field of the tee through transient iteration, and the empirical constants in the turbulence model are taken from the standard recommended values.

[0027] In the coupled simulation, the fluid domain mesh is first generated based on the internal flow channel geometry of the tee. The fluid domain mesh is refined in the near-wall region to ensure boundary layer solution accuracy. Then, the flow field is solved to obtain the pressure and temperature distributions on the inner wall of the tee. Next, the calculated fluid pressure and temperature fields are used as loads and accurately transferred and applied to the finite element mesh nodes on the surface of the parameterized reference model through the fluid-structure interaction interface. The solid domain mesh is divided into at least four layers in the wall thickness direction to ensure the accuracy of stress calculation. Bidirectional data transfer and iteration between the fluid and solid domains are performed. In each iteration, the fluid solver transfers pressure and temperature to the solid solver. The solid solver calculates the deformation and then feeds the displacement back to the fluid solver to update the flow channel shape. This process is repeated until the residual of the entire coupled field is less than the preset convergence tolerance. After convergence, continuous equivalent stress data on each finite element node of the entire tee domain is extracted, and the derivatives of each node along the wall thickness normal direction are calculated to generate stress gradient data. Taking a representative node in the shoulder region of the intersection line as an example, the stress value at this location may reach 105 MPa, while the stress value in the straight section of the main pipe far from the intersection line may only be 55 MPa. Correspondingly, the stress variation along the wall thickness normal is drastic in the shoulder region of the intersection line, with a stress gradient of up to 2.5 MPa / mm, while the stress gradient in the straight section of the main pipe is only 0.3 MPa / mm. These stress values ​​and stress gradient data together constitute complete information reflecting the mechanical response of the tee under actual working conditions, and the equivalent stress value at each spatial location is defined as the stress value at that location.

[0028] In step S3, based on the previously obtained stress values, stress gradient data, and allowable stress threshold of 85 MPa, a nonlinear mapping function between stress values ​​and geometric dimensions is constructed. The input to this mapping function is the stress value, and the output is the wall thickness and transition fillet radius at each spatial location of the tee. It also includes a built-in sensitivity factor. The sensitivity factor is an adjustable parameter in the mapping function that controls the rate of change of wall thickness and fillet offset with stress. In this embodiment, the sensitivity factor is specifically a reference sensitivity factor. Non-negative proportionality coefficient The configuration principle of the mapping function is as follows: starting from the initial reference values, namely the initial wall thickness of 80mm and the initial transition fillet radius of 40mm, the wall thickness and transition fillet radius are adjusted bidirectionally based on the stress values ​​at each location relative to the allowable stress threshold, and the corresponding intermediate wall thickness value is output. and the radius value of the intermediate transition fillet The output logic of this mapping function is as follows: when the stress value at a certain location is higher than the allowable stress threshold, the intermediate wall thickness and intermediate transition fillet radius at that location are increased based on the initial reference values; when the stress value is lower than the allowable stress threshold, the intermediate wall thickness and intermediate transition fillet radius at that location are decreased based on the initial reference values; when the stress value is equal to the allowable stress threshold, the intermediate wall thickness and intermediate transition fillet radius remain unchanged from the initial reference values.

[0029] The specific construction process of this mapping function is as follows: A mapping framework is established with the stress value as input and the wall thickness and transition fillet radius at each position of the tee as output. Within this framework, stress gradient data is introduced as a regional weighting coefficient. Its function is to enhance the adjustment range of the transition fillet radius for areas with significantly higher stress gradients, such as the intersection line. By introducing stress gradient data as a regional weighting coefficient, the fillet offset... By wall thickness offset Normalized gradient Coefficient of linkage between fillet radius and wall thickness Joint decision, and Same sign. In the region of equal gradient at the intersection line, When it is close to 1, To reduce stress concentration, the transition fillet radius is increased accordingly. When the gradient is negative, the transition fillet radius shrinks accordingly to further reduce weight; in the low gradient region, As the radius approaches zero, the variation in fillet radius decreases accordingly. At this point, load-bearing capacity is primarily adjusted through variations in wall thickness. The stress values ​​are then mapped to a first stress function that varies with spatial coordinates. The stress gradient data is then mapped to a first gradient function that varies with spatial coordinates. Then, G(x,y,z) is normalized using the global maximum stress gradient as the benchmark, resulting in a dimensionless normalized gradient function with values ​​ranging from 0 to 1. In the high gradient region of the intersection line, Approaching 1; in low gradient regions such as the straight sections of main pipes and branch pipes, Approximately 0. Subsequently, a sensitivity factor that varies with spatial coordinates is set. Satisfying the relation: ; in The reference sensitivity factor, which has the dimension of length / stress, is initially set to 1.0 mm / MPa in this embodiment; This is a preset non-negative scaling factor, initially set to 0.5 in this embodiment, used to control the degree of enhancement of gradient sensitivity.

[0030] Meanwhile, based on the minimum wall thickness requirements for this specification of tee according to the ASME BPVC standard, and the feasibility of the manufacturing process in terms of wall thickness and fillet radius, the minimum permissible wall thickness is determined. 55mm, maximum permissible wall thickness The minimum allowable transition fillet radius is 110mm. The maximum allowable transition fillet radius is 20mm. It is 80mm. Among them... A wall thickness less than 80mm from the initial thickness provides feasible space for wall thickness reduction in low-stress areas. The above boundary values ​​are merely exemplary values ​​for the tee specification of this embodiment. For tees of different specifications, applicable boundary values ​​can be determined according to the corresponding standards and process conditions.

[0031] The specific calculation steps for the nonlinear mapping function are as follows: (1) First, calculate the wall thickness offset: ; in The preset allowable stress threshold for F92 steel is 85 MPa in this embodiment.

[0032] Under this calculation formula, when the stress at a certain location When the pressure is above 85 MPa, It is a positive value; when the stress is below 85 MPa, It is a negative value.

[0033] In this embodiment, taking the intersection shoulder node of the aforementioned tee as an example, the stress at this location is 105 MPa, the normalized gradient is 0.9, and the calculated stress is... , This means that the wall thickness needs to be increased by 29mm from the initial thickness.

[0034] Taking the aforementioned main pipe straight section node as an example, the stress at that location is 55 MPa, the normalized gradient is 0.1, and the calculated values ​​are... , This indicates that the wall thickness can be reduced by 31.5 mm from the initial thickness.

[0035] (2) Calculate the intermediate wall thickness: The initial wall thickness is... With wall thickness offset Add them together to get the intermediate wall thickness at that location. In this embodiment, for the shoulder node of the intersection line, the intermediate wall thickness value is... For the main straight section node, the intermediate wall thickness value .

[0036] (3) Calculate the fillet offset: ; Where β is a preset non-negative fillet shape coefficient, which is set to 0.8 in this embodiment, used to adjust the non-linearity of the fillet variation with wall thickness and gradient. In this embodiment, for the intersection line shoulder node, .

[0037] (4) Add the initial transition fillet radius to the fillet offset to obtain the intermediate transition fillet radius value. Specifically, the initial transition fillet radius is 40mm and... Add them together to get the radius of the intermediate transition fillet at the corresponding position. that place For the straight sections of the main pipe and branches, since there are no geometric abrupt changes, their normalized gradients are... Approaching 0, fillet offset It is also close to 0. Within this region, the intermediate transition fillet radius value... Numerically, the initial setting of 40mm remains unchanged, but the actual geometry still exhibits a cylindrical surface.

[0038] In step S4, the aforementioned nonlinear mapping function is invoked to perform traversal calculations based on the stress values ​​and stress gradient data across the entire domain. To achieve spatial discretization, the continuous equivalent stress field data is transformed into several spatial grid points. In this embodiment, approximately 50,000 spatial grid points are divided along the circumferential, axial, and wall thickness directions of the main pipe. Grid refinement is performed in the intersection region to ensure accurate capture of dimensional changes.

[0039] For each spatial grid point, extract its stress value. The stress value and stress gradient value are input into the nonlinear mapping function for calculation to obtain the intermediate wall thickness value at that point. and the radius value of the intermediate transition fillet Subsequently, in step S4, a preset feasible region constraint is applied to the above output value: the intermediate wall thickness value is forcibly constrained to be no less than... and not higher than Within the range, the intermediate transition fillet radius value is forcibly constrained to be no less than and not higher than Within the range, the constrained values ​​form the discrete size driving factor of that point, which is the final target wall thickness value and the target transition fillet radius value.

[0040] In this embodiment, the intermediate wall thickness value for the shoulder node of the intersection line has been calculated above. The value is within the range of [55, 110], so the target wall thickness is taken as 109 mm; for the main pipe straight section node, the intermediate wall thickness is... lower than Due to constraints, it was forcibly adjusted to 55mm as the target wall thickness value.

[0041] The value after the above constraints is used as the discrete dimension driving factor for that point. This generated discrete dimension driving factor includes the final target wall thickness and target transition fillet radius at each spatial location. Through feasible region constraints, in the intersection region with high stress gradient, the transition fillet is significantly enhanced to reduce stress concentration; in the straight sections of the main and branch pipes, since there is no intersection structure, the transition fillet parameter only serves as a reference for local surface smoothing, and weight reduction is mainly achieved through wall thickness reduction. This mechanism achieves a high degree of matching between material distribution and stress field, satisfying both the basic requirements of structural strength and ensuring the feasibility of the manufacturing process.

[0042] Proceeding to step S5, the aforementioned discrete size driving factor is used to drive the control vertices of the tee parameterized reference model to undergo adaptive deformation. Based on the target wall thickness and target transition fillet radius of each spatial grid point, the three-dimensional coordinate offset to be generated by each NURBS control vertex is calculated through inverse mapping. Specifically, for a non-uniform rational B-spline surface, let the initial inner wall control vertex be... The corresponding vertex of the outer wall is When the target wall thickness With initial wall thickness There is a difference At that time, by calculating the surface in The unit normal vector n at the parameter (directing towards the side with increased wall thickness) drives the control vertex to offset along the normal. For double-sided offset (simultaneous movement of the inner and outer walls), the formula for calculating the offset of the control vertex is: ; Where (u,v) are the surface parameter coordinates. Let be the unit normal vector at that point. For a single-face offset (inner wall stationary, only outer wall moving), the offset of the outer wall control vertex is... By updating the control vertex matrix Reconstruct the NURBS surface.

[0043] For changes in wall thickness, the control vertex shifts along the normal direction of the surface at that vertex, with the shift amount being the difference between the target wall thickness and the initial wall thickness at that position. For changes in the transition fillet radius, the control vertex in the intersection region shifts along the normal direction of the intersection surface, with the shift amount determined based on the difference between the target transition fillet radius and the initial transition fillet radius. The positive direction of the shift is defined as the normal direction from the inner wall surface to the outer wall surface. When the target wall thickness is greater than the initial wall thickness, the shift is positive, and the control vertex moves outward; when the target wall thickness is less than the initial wall thickness, the shift is negative, and the control vertex moves inward, thereby achieving both wall thickness increase and thinning. In the intersection region, the control vertex needs to coordinate the shifts in both the wall thickness increase and fillet radius increase directions simultaneously; in the main pipe straight section region, the control vertex mainly performs the inward shift in the wall thickness direction to achieve thinning. The non-uniform degrees of freedom of each control vertex have been configured in step S1, therefore the control vertices in the intersection region and the straight section region can move independently according to their respective shift amounts without interfering with each other. Then, these control vertices are driven to move along the calculated offset direction. After the control vertices are in place, the new control vertex network is reconstructed using NURBS surface modeling, generating a lightweight tee intermediate model where the wall thickness and transition fillet radius are non-uniformly distributed with spatial position. At this point, the model has a wall thickness of approximately 109 mm and a transition fillet radius of approximately 61 mm in the intersection region, and a wall thickness of approximately 55 mm in the straight sections of the main pipe and branch pipe. In the transition region where the stress is between the two, the wall thickness exhibits a smooth, gradual distribution. After reconstruction, mesh smoothing is performed on the surface, using the Laplace smoothing algorithm to eliminate local irregular fluctuations. The smoothing process uses the target wall thickness and target transition fillet radius at each spatial mesh point as constraints, ensuring that the displacement of the control vertex during the smoothing process does not exceed the allowable deviation range of the target size at its location. This maintains the determined non-uniform wall thickness and fillet radius distribution while ensuring a smooth and continuous geometric shape, resulting in a smooth and edgeless transition between the outer surfaces of the main pipe and branch pipe, and between regions of different thicknesses. This meets manufacturing process requirements and is beneficial to the mesh quality of subsequent finite element analysis.

[0044] In step S6, the lightweight tee intermediate model is verified using finite element analysis based on the theory of creep damage accumulation. Based on the Norton-Arrhenius coupled creep model imported in step S1, the steady-state creep strain rate expression of this model is: ; in, The steady-state creep strain rate; The stress value is mentioned. Absolute temperature; is the universal gas constant; B is the material creep coefficient; n is the creep stress exponent; Q is the creep activation energy; its parameters are calibrated based on the creep strength data of Grade 92 steel in ASME BPVC.

[0045] In this embodiment, the creep parameters of F92 steel at 620℃ are: n=5.0, Q=510kJ / mol =8.314 J / (mol·K), these parameters were all obtained by least squares fitting calibration based on the creep strength data of Grade 92 steel in the ASME BPVC standard. The Robinson linear damage accumulation theory was used to calculate the creep damage factor of the tee within a preset design time period, which was taken as 200,000 hours based on the design life of the ultra-supercritical unit. The Robinson linear damage accumulation theory discretizes time into several time intervals, calculates the creep damage increment based on the current stress level in each time interval, and linearly accumulates the damage increments in all time intervals to obtain the final creep damage factor. The specific calculation process is as follows: the design life L (200,000 hours in this embodiment) is discretized into m time steps. At each time step, based on the current stress level and temperature Steady-state creep strain rate was calculated using the Norton-Arrhenius model. Then, by integration, the creep damage increment at that time step can be obtained. ,in This represents the endurance strength time fitted based on ASME data. Total creep damage factor. Simultaneously, during the verification process, the stress distribution across the entire tee area was extracted again to identify the maximum stress value, and two checks were performed: whether the maximum stress value was lower than the allowable stress threshold of 85 MPa for F92 steel, and whether the creep damage factor was less than the creep damage threshold of 1.0. The intermediate model was deemed to meet the verification conditions if and only if the maximum stress value was lower than 85 MPa and the creep damage factor was less than 1.0.

[0046] Step S7 determines the subsequent operations based on the verification results. If the intermediate model meets the verification conditions, it is identified as the final optimal tee geometry model. The target wall thickness and target transition fillet radius values ​​corresponding to each spatial coordinate point of the model are extracted as target geometric parameters for output, completing the lightweight design of the tee. At this time, the output tee wall thickness is spatially non-uniformly distributed, with a thicker intersecting line region to ensure sufficient creep life and a thinner straight section region to achieve weight reduction. The overall weight is significantly reduced compared to the initial uniform wall thickness design. If the model does not meet the verification conditions, the sensitivity factor adjustment process is initiated. The specific adjustment strategy is as follows: If the maximum stress value is higher than 85 MPa or the creep damage factor is greater than 1.0, it indicates that the local area has insufficient bearing capacity. Therefore, the local area exceeding the threshold is extracted, and the benchmark sensitivity factor is increased. The value can be increased, for example, from 1.0 to 1.3, or the non-negative proportionality coefficient can be increased. For example, increasing the value from 0.5 to 0.8 strengthens the wall thickness compensation rate in these regions, resulting in a greater increase in wall thickness in the next iteration. If the maximum stress value is already below 90% of the allowable stress threshold (76.5 MPa), and the creep damage factor is also less than 50% of the creep damage threshold (0.5), it indicates that the structure still has significant weight reduction potential. Therefore, by increasing... or To increase the thinning rate in these high-safety-margin areas, further lightweighting can be achieved; this is because in areas where stress is below the allowable threshold, It is inherently negative, increasing or This will increase the absolute value of ΔT, that is, the negative offset will be larger, thus outputting a smaller target wall thickness and achieving a stronger thinning effect.

[0047] In adjustment and During the process, if adjusting a single parameter cannot meet the directional requirements, for example, simply increasing the value of the parameter... If the stress requirement is met but the weight reduction is insufficient, then... and A coordinated correction is performed, adjusting both values ​​simultaneously to balance stress safety margin and weight reduction effect. Specifically, adjustments are made proportionally and synchronously based on the distribution of stress over-limit areas and lightweight areas. and The value: If the stress over-limit region is dominant, then the value should be increased preferentially. If lightweighting potential dominates, then priority should be given to increasing [the area]. ; until a lightweight model that meets the verification conditions is obtained.

[0048] After each adjustment of the sensitivity factor, return to step S4 to regenerate the discrete size driving factor and drive the model deformation. Then, repeat steps S5 and S6 for verification. This process is iterated until a lightweight model that meets the verification conditions is obtained. Through the automatic correction and iterative closed-loop of the sensitivity factor described above, a lightweight model that meets the verification conditions is finally obtained. In this embodiment, after iterative adjustment, the baseline sensitivity factor... It eventually converges to 1.15, a non-negative proportionality coefficient. The model eventually converges to 0.65, at which point it meets the validation criteria.

[0049] Following the complete design process described above, the final tee model has a wall thickness of 110mm and a transition fillet radius of 65mm in the high-stress region of the intersection line, and a wall thickness of 55mm in the low-stress region of the straight sections of the main pipe and branch pipes. The overall wall thickness distribution exhibits a smooth, gradual transition along both the circumferential and axial directions. Compared to the initial design with a uniform wall thickness of 80mm, the total weight is reduced by 18%. Simultaneously, its maximum equivalent stress is 82MPa, lower than the allowable stress threshold of 85MPa, and its creep damage factor is 0.72, less than the creep damage threshold of 1.0, meeting safety requirements. This result demonstrates the effectiveness of the method of this invention in achieving lightweight design while ensuring creep life.

[0050] The NURBS modeling, fluid-thermal-structure interaction simulation, turbulence model solving, and damage accumulation calculation used in the above specific embodiments, combined with the stress gradient-driven non-uniform mapping function and sensitivity factor iterative correction mechanism of the present invention, can complete the automatic lightweight design of large-size thick-walled tees under creep conditions.

[0051] Embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0052] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0053] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0054] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0055] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A lightweight parametric design method for large-size thick-walled F92 steel tees, used to determine the spatially non-uniformly distributed wall thickness and transition fillet geometry of the tees, characterized in that, Includes the following steps: S1. Obtain the initial geometric parameters of the tee to be designed, the preset allowable stress threshold of F92 steel, and the preset creep damage threshold. The initial geometric parameters include the outer diameter of the main pipe, the inner diameter of the branch pipe, the initial wall thickness, and the initial transition fillet radius. Using the initial wall thickness and the initial transition fillet radius as the initial benchmark values ​​for optimization, establish minimizing the weight of the tee as the optimization objective, construct a parameterized benchmark model of the tee based on non-uniform rational B-splines, and import the preset creep constitutive relation corresponding to F92 steel. The preset creep constitutive relation is a mathematical model used to describe the high-temperature creep behavior of the material and is used for subsequent creep life assessment. S2. Based on the preset ultra-supercritical working conditions, perform fluid-thermal-structure interaction simulation calculations on the parameterized benchmark model of the three-way valve, extract continuous equivalent stress data and stress gradient data of the entire three-way valve, and define the values ​​at each spatial location in the continuous equivalent stress data as the stress values ​​at that location. S3. Based on the stress value, the stress gradient data, and the allowable stress threshold, a nonlinear mapping function between the stress value and the geometric dimensions is constructed. The nonlinear mapping function uses the stress value as the independent variable and the wall thickness and transition fillet radius at each position of the tee as the dependent variable, and includes a sensitivity factor for adjusting the rate of change of the wall thickness and fillet radius. The mapping function is configured to: based on the initial reference value, adjust the wall thickness and transition fillet radius at each position according to the magnitude of the stress value at each position relative to the allowable stress threshold, and output the intermediate wall thickness and intermediate transition fillet radius corresponding to each position. S4. Call the nonlinear mapping function to perform traversal calculations based on the stress value and the stress gradient data to obtain the intermediate wall thickness value and intermediate transition fillet radius value at each position, and restrict the intermediate value within a preset feasible domain to generate a discrete size driving factor that varies with spatial position. The discrete size driving factor includes the target wall thickness value and target transition fillet radius value at the corresponding position, i.e., the target geometric parameters of the tee. S5. Using the discrete size driving factor, the control vertices of the parameterized reference model of the tee are driven to undergo adaptive deformation to generate a lightweight intermediate model of the tee with non-uniform distribution of wall thickness and fillet. The reconstructed surface is then smoothed. S6. Based on the preset creep constitutive relation, the lightweight tee intermediate model is verified by finite element method using Robinson linear damage accumulation theory; the verification conditions are whether the equivalent stress is lower than the allowable stress threshold and whether the creep damage factor is less than the creep damage threshold. S7. If the verification conditions are met, the discrete size driving factor is output as the target geometric parameter of the tee to complete the lightweight design of the tee. If the verification conditions are not met, the sensitivity factor in the nonlinear mapping function is adjusted, and execution returns to steps S4-S6 to iteratively update the lightweight tee intermediate model until the conditions are met.

2. The lightweight parametric design method for large-size thick-walled F92 steel tees according to claim 1, characterized in that, The construction of the tee parameterized benchmark model based on non-uniform rational B-splines as described in S1 specifically includes: The outer diameter of the main pipe, the inner diameter of the branch pipe, the initial wall thickness, and the initial transition fillet radius are mapped to the control vertex parameters of a non-uniform rational B-spline surface. Configure the non-uniform degrees of freedom of the control vertex to allow the control vertex to perform independent three-dimensional coordinate offsets according to the discrete size driving factor; Based on the control vertex parameters, non-uniform degrees of freedom, and the topology of the tee, the parameterized benchmark model of the tee is generated by fitting a non-uniform rational B-spline surface.

3. The lightweight parametric design method for large-size thick-walled F92 steel tees according to claim 1, characterized in that, The extraction of continuous equivalent stress data and stress gradient data across the entire tee region as described in S2 specifically includes: The ultra-supercritical operating conditions are set to a main steam pressure greater than 25 MPa and a steam temperature greater than 600 °C. The transient flow field is solved iteratively using a pre-defined turbulence model, which is the standard k-type turbulence model. Turbulence model; During the fluid-thermal-structure interaction simulation calculation, the fluid pressure and temperature loads calculated based on the ultra-supercritical working conditions are applied to the finite element mesh nodes on the surface of the three-way parameterized reference model, and bidirectional iteration is performed until convergence. After convergence, the continuous equivalent stress data on the global finite element nodes of the tee are extracted, and the derivatives of each node along the wall thickness normal direction are calculated to generate the stress gradient data.

4. The lightweight parametric design method for large-size thick-walled F92 steel tees according to claim 1, characterized in that, The nonlinear mapping function between stress values ​​and geometric dimensions described in S3 specifically includes: A mapping framework is established with the stress value as input and the wall thickness and transition fillet radius at each position of the tee as output. The stress gradient data is introduced into the mapping framework as a regional weighting coefficient to enhance the adjustment range of the transition fillet radius in the high gradient region of the intersection line. The stress value is mapped to a first stress function σ(x,y,z) that varies with spatial coordinates; The stress gradient data is mapped to a first gradient function that varies with spatial coordinates. and to Normalization is performed to obtain the dimensionless normalized gradient function. Its value range is [0,1]; Set the sensitivity factor that varies with spatial coordinates Satisfying the relation: ； in, The baseline sensitivity factor has a length / stress dimension; This is a preset non-negative proportionality coefficient; Define the preset minimum allowable wall thickness and maximum allowable wall thickness and minimum allowable transition fillet radius and maximum allowable transition fillet radius ,in Less than the initial wall thickness; The nonlinear mapping function is specifically configured with the following calculation steps: Calculate wall thickness offset ;in The preset allowable stress threshold for F92 steel; Calculate the intermediate wall thickness value related to the location. To compare the initial wall thickness with sum; Calculate fillet offset Where β is a preset non-negative fillet shape coefficient; Calculate the radius of the intermediate transition fillet at the corresponding position. The initial transition fillet radius and sum.

5. The lightweight parametric design method for large-size thick-walled F92 steel tees according to claim 4, characterized in that, The generation of discrete size driving factors that vary with spatial location as described in S4 specifically includes: The continuous equivalent stress data is discretized into several spatial grid points; For each spatial grid point, extract its stress value σ(x,y,z) and stress gradient value; The stress value and stress gradient value are input into the nonlinear mapping function for calculation, and the corresponding intermediate wall thickness value and intermediate transition fillet radius value are output. The intermediate wall thickness is forcibly constrained to be no less than [amount missing]. and not higher than Within the range, the intermediate transition fillet radius value is forcibly constrained to be no less than and not higher than Within the range, the constrained values ​​are used as the target wall thickness and target transition fillet radius values ​​at that point, forming a discrete dimension driving factor.

6. The lightweight parametric design method for large-size thick-walled F92 steel tees according to claim 5, characterized in that, The lightweight tee intermediate model described in S5, which generates wall thickness and fillet radius with non-uniform distribution, specifically includes: Based on the target wall thickness and target transition fillet radius values ​​in the discrete size driving factors of each spatial grid point, calculate the three-dimensional coordinate offset of the non-uniform rational B-spline control vertex. The control vertex is driven to move adaptively according to the coordinate offset using the discrete size driving factor. The control vertices after movement are reconstructed using non-uniform rational B-spline surfaces and then smoothed to generate a lightweight intermediate tee model with non-uniform distribution of wall thickness and fillet radius.

7. A lightweight parametric design method for large-size thick-walled F92 steel tees according to claim 6, characterized in that, S6 specifically includes: Using Robinson's linear damage accumulation theory and the preset creep constitutive relation, the creep damage factor of the tee within the preset design time is calculated; The maximum stress value is extracted based on the stress value of the entire tee area. It is then determined whether the maximum stress value is lower than the allowable stress threshold of F92 steel, and whether the creep damage factor is lower than the creep damage threshold. If the maximum stress value is lower than the allowable stress threshold of the F92 steel and the creep damage factor is less than the creep damage threshold, then the verification condition is satisfied.

8. A lightweight parametric design method for large-size thick-walled F92 steel tees according to claim 7, characterized in that, S7 describes adjusting the sensitivity factor in the nonlinear mapping function, specifically including: If the maximum stress value is higher than the allowable stress threshold of F92 steel or the creep damage factor is greater than the creep damage threshold, then the local area exceeding the threshold is extracted, and the reference sensitivity factor is increased. Or the non-negative proportionality coefficient The value of this value enhances the wall thickness compensation rate in this local area; If the maximum stress value is lower than 90% of the allowable stress threshold of F92 steel and the creep damage factor is less than 50% of the creep damage threshold, then the reference sensitivity factor is increased. Or the non-negative proportionality coefficient The value of [value] is increased to increase the thinning rate of this local area, thereby further achieving lightweighting; If the direction adjustment is still not satisfied, then... and Perform collaborative corrections until a lightweight model that meets the verification conditions is obtained.

9. A lightweight parametric design method for large-size thick-walled F92 steel tees according to claim 1, characterized in that, If the verification conditions described in S7 are met, the target geometric parameters of the tee are output to complete the lightweight design of the tee, specifically including: When the lightweight tee intermediate model meets the verification conditions, it is identified as the final optimal tee geometry model; Extract the target wall thickness and target transition fillet radius values ​​corresponding to each spatial coordinate point in the optimal tee geometric model, and output them as the target geometric parameters of the tee to complete the lightweight design of the tee.

10. A lightweight parametric design method for large-size thick-walled F92 steel tees according to claim 1, characterized in that, The preset creep constitutive relation is the Norton-Arrhenius coupled creep model: ； in, The steady-state creep strain rate; The stress value is mentioned. Absolute temperature; is the universal gas constant; B is the material creep coefficient; n is the creep stress exponent; Q is the creep activation energy; its parameters are calibrated based on the creep strength data of Grade 92 steel in ASME BPVC.

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