Computer simulation methods for boiling water reactors (BWRs).

Abstract

A computer-implemented simulation method for predicting local concentrations of constituents in coolant water at any location along a fuel rod in a boiling water reactor (BWR) fuel bundle mechanical design, where crud deposition may occur on the fuel rod. The method is based on a subchannel approach that predicts local mass fluxes of vapor and liquid in the coolant water for given steady-state or transient boundary conditions at any location along a fuel rod in a boiling water reactor (BWR) fuel bundle mechanical design. The subchannel approach is based on solving mass, momentum, and energy conservation equations for the vapor and liquid phases, where the liquid phase is represented by multiple field variables, specifically, three fields: liquid droplets, liquid base film, and disturbance waves, with the vapor phase added as a fourth field.

Description

[Technical field]

[0001] The present disclosure relates to a method for nuclear reactors, specifically boiling water reactors (BWRs), intended to characterize disturbance waves and base films in the coolant water, particularly when induced by transients such as inlet flow rate fluctuations in a BWR fuel assembly, in an annular two-phase flow regime, and in particular to characterize the formation of ZnO and Zn 2 SiO 4 This invention relates to one method that can be adapted to predict crud deposition of relatively highly soluble compounds such as uranium and arsenic in fuel assemblies. [Background technology]

[0002] Very dense crud deposits have been observed in the upper layers of fuel assemblies in BWRs in recent years. Crud is a colloquial term for corrosion and wear products (e.g. rust particles), some of which become activated (activated) when exposed to radiation. The mechanisms leading to crud deposition may lead to fuel performance issues such as spalling, reduced thermal conductivity, and even fuel failure, and therefore may be a safety concern. The dense crud deposits in the upper layers of the fuel assemblies were observed at specific fuel assembly locations, and no previous cycles or other similar plants have experienced crud this dense.

[0003] The background art is described in Non-Patent Document 1, which discloses a computer-implemented simulation method used in the mechanical design of fuel assemblies for BWRs, based on the sub-channel approach. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] SAXENA ABHISHEK ET AL: “A study of two-phase numerical flow using unsteady computations”, INTERNATIONAL JOURNAL OF MULTIPHASE FLOW, vol.126, May 8, 2019, XP086128222, ISSN:0301-9322, DOI: 10.1016 / J.IJMULTIPHASEFLOW.2019.05.003 Summary of the Invention [Problem to be solved by the invention]

[0005] It is therefore an object of the present invention to provide a method for simulating and predicting the impurity concentration in the annular two-phase flow region and associated margin to the crud deposition threshold in a BWR fuel assembly.

[0006] A more general objective is to develop a method to simulate and predict the local mass fluxes and local properties of disturbance waves and substrates in the coolant water of a BWR fuel assembly.

[0007] A further object is to design a BWR fuel assembly comprising fuel rods having fuel pellets with an enrichment level determined depending on the results of the simulation method in order to avoid crud. [Means for solving the problem]

[0008] The above mentioned objects are achieved according to the present invention according to the independent claims.

[0009] Preferred embodiments are set forth in the dependent claims.

[0010] According to a first aspect, the invention relates to a computer-implemented simulation method for predicting local concentrations of constituents in the coolant water at any location along a fuel rod in a fuel bundle mechanical design of a boiling water reactor (BWR), where crud deposits may occur. The simulation method is based on a sub-channel approach for predicting local mass fluxes of steam and liquid in the coolant water for given steady-state or transient boundary conditions at any location along a fuel rod in a fuel bundle mechanical design of a boiling water reactor (BWR). The sub-channel approach is based on the solution of mass, momentum and energy conservation equations for the steam and liquid phases. The liquid phase is represented by several field variables, specifically three fields consisting of droplets, liquid base film and disturbance waves, with the addition of the steam phase as a fourth field. The method includes solving individual mass, momentum, and energy conservation equations for the four fields and solving the necessary closure relations describing mass transfer between the fields, completed with mass conservation equations for components dissolved in the liquid phase and carried by each of the fields individually. simulating steady-state or transient boundary conditions for conditions of interest in the fuel assembly, such as inlet coolant flow to the sub-channels (wherein the coolant flow may have a predetermined flow rate variation), temperature, pressure, fuel rod power distribution, and assembly power; - analyzing predetermined parameters of the disturbance wave and the basement membrane, including the wave speed and frequency, and the basement membrane thickness; Analyzing the liquid base film between successively passing disturbance waves to calculate local instantaneous impurity concentrations between the disturbance waves during a simulated steady-state or transient operation; Includes.

[0011] A calculation is performed for each fuel rod of the fuel assembly, and for each fuel rod, the method further includes the step of comparing the calculated local instantaneous impurity concentration with a precipitation limit of the cladding compound, and deeming crud deposition to have occurred while the concentration is higher than the precipitation limit.

[0012] According to a second aspect, the invention relates to a computer-implemented simulation method. The method is based on a sub-channel approach to predict the local mass fluxes of steam and liquid in the coolant for given steady-state or transient boundary conditions at any location along a fuel rod in a fuel bundle mechanical design of a boiling water reactor (BWR). The sub-channel approach is based on the solution of mass, momentum and energy conservation equations for the steam and liquid phases. The liquid phase is represented by several field variables, specifically three fields consisting of droplets, liquid base film, disturbance waves, and the steam phase as a fourth field. The method comprises the steps of solving the individual mass, momentum and energy conservation equations for said four fields and solving the necessary closure relations describing the mass transfer between said fields, completed by models describing local phenomena such as base film dryout, crud temperature rise or droplet entrainment from waves. The method comprises: Simulating steady-state or transient boundary conditions, such as assumed scenarios associated with BWR operation (for transient simulations, the boundary conditions include input parameters having predetermined variations over time); - analyzing predetermined parameters of the disturbance wave and the liquid base film, including wave speed and frequency, and base film thickness; Includes.

[0013] In one embodiment, analyzing the predetermined parameters includes analyzing a liquid base film between successive passing disturbance waves to calculate local instantaneous dry patch formation and associated cladding temperature rise between the disturbance waves during said simulated steady-state or transient operation, the calculation being performed for each fuel rod of the fuel assembly.

[0014] In another embodiment, analyzing the predetermined parameters includes analyzing disturbance wave characteristics of a liquid to calculate entrainment of liquid droplets from said waves during said simulated steady-state or transient operation, the calculation being performed for each fuel rod of a fuel assembly.

[0015] According to a third aspect, the present invention provides a method for producing ... composition comprising the steps of: 235 It relates to a boiling water reactor (BWR) comprising a fuel assembly including fuel rods provided with fuel pellets having a U enrichment level, the enrichment level being determined depending on the results of a simulation carried out by the simulation method defined above, in particular such that no crud deposition occurs under given boundary conditions.

[0016] The present invention is based on an extensive root cause analysis which establishes that the crud deposition problem is related to significant variations in fuel assembly inlet coolant flow rates, and that these variations cause thermal-hydraulic propagation through the fuel assembly, resulting in high impurity concentrations above specific precipitation limits at certain fuel assembly locations. These new phenomena have not previously been directly addressed.

[0017] The method according to the first aspect of the present invention provides a strategy for solving the problem of crud deposition.

[0018] The aim of this strategy is therefore to assess the risk of crud deposition. Currently, there are no tools available to take into account the effects of disturbance waves, especially under conditions of fast varying fuel assembly inlet flows. The application of the above mentioned method is proposed because it is consistent with root cause analysis and allows the nuclear design to be modified, for example by reducing the amount of fissile material in the fuel available at a specific location of an individual fuel rod (e.g. 235 This is because the risk of crud deposition can be reduced by changing the fuel assembly's U enrichment. Measures to reduce the risk of crud deposition include limiting the power generated by each fuel assembly (e.g., adjusting the core loading pattern, such as loading more new fuel assemblies), reducing the total core power, or reducing the reactor water impurity concentration at the fuel assembly inlet (e.g., reducing zinc injection). However, 235 Adjusting the U enrichment is the preferred approach as it has the least impact on reactor operation and fuel economy.

[0019] Therefore, new computational tools have been developed that are based on known thermal-hydraulic models of BWR fuel, which are extended with new physics models that include a four-field approach and potential simplifying assumptions.

[0020] The following are well-known thermal hydraulic calculation tools for BWR fuel analysis: Reactor physics codes that use one dimension per assembly (e.g. POLCA, Westinghouse's state-of-the-art code for BWR core design and safety analysis). These core design codes do not take into account the thermal-hydraulic differences of the individual fuel rods, so due to their global approach they are not appropriate here. Subchannel analysis codes that use one dimension at the subchannel level (e.g., MEFISTO-T, the Westinghouse transient three-field subchannel analysis code). These thermal-hydraulic subchannel analysis codes are appropriate here since they apply a local approach. Computational Fluid Dynamics codes (CFD) are increasingly being used in reactor safety analysis as a tool to analyze safety-related phenomena occurring in the reactor coolant system. CFD codes provide full (high resolution) 3D, but are not appropriate here as they have a limited state-of-the-art for BWR fuel applications.

[0021] In thermal-hydraulic analysis, the term subchannel is traditionally defined by the space between the fuel rods in a fuel assembly. Often the space between three or four adjacent fuel rods defines a subchannel. Boundary conditions (such as inlet coolant flow) are applied to the subchannel thus defined. Interactions between the subchannels are also considered.

[0022] Furthermore, the code simulates the thermal flow of the BWR fuel assemblies, with the basic assumption that the coolant water carries heat away from the core, is subcooled at the inlet, and typically forms an annular two-phase (steam and liquid) flow at the outlet.

[0023] The standard subchannel analysis approach applies a one-dimensional, two-phase, three-field approach, which analyses the vapor, droplets and liquid film with separate conservation equations for all fields, including the mass, momentum and energy exchanges between the fields. To simulate the radial interactions between the fuel lattices, the mass, momentum and energy exchanges between the subchannels are also calculated.

[0024] The above can be calculated by applying state-of-the-art models, which are well documented in published disclosures and implemented, for example, in the above-mentioned Westinghouse code MEFISTO-T, or in several other codes from industry and academia (e.g. COBRA-TF).

[0025] According to a first aspect of the present invention, a set of models for dealing with the crud deposition problem is defined, which models are further developments of the state-of-the-art models mentioned above.

[0026] A disturbance wave model has thereby been developed and implemented in the subchannel analysis code based on the extension of the three-field model to a four-field model, making it possible to calculate the detailed distribution of impurity concentrations in each liquid base film flowing along the fuel rods of a fuel assembly under the operating conditions of interest, e.g., pressure, flow rate, power and fuel rod power distribution, including during transient operation.

[0027] Also, a local instantaneous impurity model is further developed and added to the first model to calculate the local instantaneous impurity concentration in the liquid base film during steady-state and transient operation during disturbance waves, e.g., inlet flow rate fluctuations, etc. It is believed that crud deposition occurs while the local instantaneous impurity concentration is higher than a predetermined crud compound precipitation threshold value.

[0028] The above two models are based on physical phenomena consistent with root cause analysis. Effect of the Invention

[0029] With this new tool, we can calculate the shape of the grid ( 235 By locally adjusting the fuel rod power (due to U enrichment), it became possible to avoid undesirable crud deposition in BWR fuel assemblies in annular two-phase flow under expected plant operating conditions. [Brief description of the drawings]

[0030] [Figure 1] FIG. 2 is a schematic diagram of cross-sectional steam / liquid annular two-phase flow along a fuel rod. [Diagram 2] FIG. 2 is a schematic diagram of a cross-sectional steam / liquid annular two-phase flow along a fuel rod illustrating some embodiments of the present invention. [Diagram 3] 1 is a schematic perspective view of a fuel assembly to which the method according to the invention is applied; [Figure 4] FIG. 2 is a schematic cross-sectional view of a fuel assembly including representations of various sub-channels. [Diagram 5] 13 shows a graph illustrating the results of a local instantaneous impurity concentration simulation. [Figure 6] 13 shows a graph illustrating the results of a local instantaneous impurity concentration simulation. [Figure 7] FIG. 1 is a flow diagram illustrating a method according to a first aspect of the present invention. [Figure 8] FIG. 4 is a flow diagram illustrating a method according to a second aspect of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0031] The computer-based simulation method will now be described in detail with reference to the accompanying figures, in which like or similar items are designated with the same reference numerals throughout the figures, and in which the items and figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.

[0032] First, a background on available computational tools and models is provided.

[0033] Two-phase modelling and validation using three-field subchannel analysis codes (e.g., MEFISTO-T) to predict two-phase flow in BWR fuel assemblies up to the critical power at which so-called dryout occurs has been known for some time, is publicly available and has been developed and applied by the applicant.

[0034] Westinghouse has developed the MEFISTO-T code with the primary goal of achieving fast, robust, practical and reliable predictions of steady-state and transient dryout power of boiling water reactor (BWR) fuel assemblies based on a dynamical approach. To achieve this goal, a computationally efficient simulation scheme is used. The code solves all relevant field (droplet, vapor, multi-film) mass balance equations in the circulating flow region at the subchannel level, while relying on fast and robust two-phase (liquid / vapor) subchannel solutions to provide cross-flow information. Thus, the MEFISTO-T code can provide a highly detailed solution of multi-film flow in BWR fuel assemblies, while increasing flexibility and reducing computational time by more than an order of magnitude compared to the standard three-field subchannel analysis approach. Models for the numerical computation of one-dimensional field flow distributions in open channels (subchannels), including field cross-flow, partial-length rods, spacer grids and numerical treatment of post-dryout conditions, are included in the code. The MEFISTO-T code is then applied to dryout prediction of a BWR fuel assembly using the VIPRE-W code as a fast and robust two-phase subchannel drive code. The dryout power is numerically predicted by iterating the assembly power such that the minimum film flow rate in the assembly reaches a pre-set dryout criterion. The predicted dryout power (including flow rate, pressure, inlet subcooling conditions, and power distribution trends) and predicted dryout location (both axial and radial) are compared with experimental results using the available dryout database and found to yield superior results.

[0035] The MEFISTO-T code applied to dryout prediction is described, for example, in "Modeling and validation of a mechanistic tool (MEFISTO) for the prediction of critical power in BWR fuel assemblies" by Adamsson, Carl; Le Corre, Jean-Marie, Nuclear Engineering and Design, 2011, ISSN 0029-5493; Worldcat; CODEN NEDEAU; v.241(8); p.2843-2858.

[0036] The MEFISTO-T code is based on a simplified approach to the analysis of subchannel liquid film flow by decoupling the transport equations of the liquid film in the subchannels from each other. This approach allows fast and robust simulation of steady-state operation and realistic transient phenomena of BWRs with high axial resolution. The code has been successfully validated against experimental data for both steady-state and transient conditions, including realistic variations in flow rate and power and three different axial power distributions, under conditions typical of BWR operation.

[0037] Semi-empirical dryout correlations are commonly used to predict the dryout power of BWR fuel rod assemblies under both steady-state and transient conditions. Although these correlations can be based on mechanical characteristics, they are empirical in nature and require the use of extensive fuel-specific critical power databases to be developed. In contrast, mechanical methods based on subchannel annular two-phase flow modeling, such as the MEFISTO-T code, have the potential to have accurate dryout prediction capabilities outside of the correlation development database.

[0038] In summary, MEFISTO-T is a subchannel analysis code developed at Westinghouse with the primary objective of predicting the film flow distribution on each fuel rod during steady-state and transient operation. The code is based on a one-dimensional three-field approach, where liquid films, droplets and vapor are considered in each subchannel. MEFISTO-T uses a simplified two-phase flow model (VIPREW) to calculate the time-dependent distribution of flow rate and enthalpy in all subchannels, and then applies the three-field approach to all or some of the subchannels, from the onset of the annular flow to the assembly exit.

[0039] In general, the simulation method according to the invention consists of extending the three-field approach to a four-field approach, in which the base film on each fuel rod is divided into a fast moving disturbance wave on a slow moving liquid base film. This is shown diagrammatically in figures 1 and 2. The simulation method is based on a subchannel mechanical model using a transient three-field (vapor, droplet, liquid film) approach including coupling between subchannels defined between the fuel rods. This mechanical model is for example the above mentioned MEFISTO-T code. A cross-section of a fuel assembly is shown in figure 4, where some of the subchannels are shown.

[0040] The present invention relates to a first computer-implemented simulation method for predicting local concentrations of constituents in coolant water anywhere along a fuel rod within the mechanical design of any fuel assembly of a boiling water reactor (BWR) on which crud deposits may occur. The first method will now be described in detail, and with particular reference to the flow diagram shown in FIG.

[0041] The method is based on a subchannel approach to predict the local mass fluxes of steam and liquid in the coolant at any location along the fuel rod within the mechanical design of any fuel assembly in a boiling water reactor (BWR) for given steady-state or transient boundary conditions. The subchannel method is based on the solution of mass, momentum and energy conservation equations for the vapor and liquid phases, where the liquid phase is represented by multiple field variables, specifically, three fields consisting of droplets, liquid base film and disturbance waves, and the vapor phase is added as a fourth field.

[0042] The method involves solving individual mass, momentum and energy conservation equations for the four fields and the necessary closure relations describing the mass transfer between said fields, completed by mass conservation equations for the components dissolved in the liquid phase and transported by each of said fields individually.

[0043] This method is simulating steady-state or transient boundary conditions for conditions of interest in the fuel assembly, such as inlet coolant flow to the sub-channels (wherein the coolant flow may have a predetermined flow rate variation), temperature, pressure, fuel rod power distribution, and assembly power; Analyzing certain parameters of the disturbance wave and the substrate, including wave speed and frequency, substrate thickness, etc., based on the interactions between the disturbance wave, the liquid substrate, the droplets, and the vapor; - calculating a local instantaneous impurity concentration by analyzing a liquid base film thickness between successively passing disturbance waves based on the simulated boundary conditions; Includes.

[0044] The calculation is performed for each fuel rod of the fuel assembly and includes thermal-hydraulic coupling between the subchannels. For each fuel rod, the method further includes comparing the calculated local instantaneous impurity concentration with a precipitation limit for the cladding compound, and considering crud to have occurred while the concentration is higher than the precipitation limit.

[0045] FIG. 6 shows a graph showing how the impurity concentration changes between passing disturbance waves.

[0046] Figure 3 shows a fuel assembly made up of fuel rods. It shows two fuel rods with high impurity concentrations. The different shades of grey indicate the impurity concentration, with black indicating the highest concentration. Also shown is a so-called partial length fuel rod.

[0047] According to one embodiment, the method step of analyzing certain parameters of the disturbance wave comprises solving mass and momentum conservation equations in all considered subchannels using a four-field approach (also called disturbance wave model) in which the wave and the substrate are considered separately. This model is coupled to a subchannel analysis code for cross-flow calculations, and some components of the momentum balance (such as pressure gradients and inertial terms) may be neglected.

[0048] According to another embodiment, the method includes applying an impurity mass conservation equation that is consistent with the four-field conservation equations described above. Based on the interaction between the waves and the liquid base film, the model calculates the detailed distribution of impurity concentrations axially and azimuthally (i.e., along the circumference of a given fuel rod) in each liquid base film flowing along the fuel rods of a fuel assembly under the operating conditions of interest.

[0049] According to yet another embodiment, the method further includes applying a local instantaneous impurity concentration model used as a post-processing of the base film impurity concentration model and configured to calculate, for each fuel rod, said local instantaneous impurity concentration in the slow moving liquid base film during any transients such as disturbance waves and predetermined inlet flow rate variations during nominal operation.

[0050] According to another embodiment, the method includes adjusting the fissile material content (e.g., 235The method further includes simulating operating conditions of interest by varying the concentration of uranium (U) in the mixture.

[0051] The present invention also relates to a second computer-implemented simulation method, which is illustrated generally by the flow diagram shown in FIG.

[0052] The second simulation method is based on a subchannel approach that predicts the local mass fluxes of steam and liquid in the coolant anywhere along the fuel rod within the mechanical design of any fuel assembly of a boiling water reactor (BWR) for given steady-state or transient boundary conditions. The subchannel approach is based on the solution of mass, momentum and energy conservation equations for the vapor and liquid phases, where the liquid phase is represented by multiple field variables, in particular three fields consisting of droplets, liquid base film and disturbance waves, and the vapor phase is added as a fourth field.

[0053] The method includes solving the individual mass, momentum and energy conservation equations for the four fields and the necessary closure relations describing the mass transfer between the fields, completed with a model describing the local phenomena. simulating steady-state or transient boundary conditions, such as scenarios associated with BWR operation; - analyzing predetermined parameters of the disturbance wave and the liquid base film, including wave speed and frequency, and base film thickness; Includes.

[0054] In one embodiment, the method step of analyzing the predetermined parameters includes analyzing the liquid base film between successive passing disturbance waves to calculate, for each fuel rod of the fuel assembly, the local instantaneous dry patch formation and associated cladding temperature rise between the disturbance waves during said simulated steady-state or transient operation.

[0055] In another embodiment, the method step of analyzing the predetermined parameters includes analyzing liquid disturbance wave characteristics to calculate, for each fuel rod of the fuel assembly, droplet entrainment from waves during said simulated steady-state or transient operation.

[0056] According to yet another embodiment, when simulating transient boundary conditions, the boundary conditions include input parameters having a predetermined time variation.

[0057] Preferably, the local phenomenon is drying out of the substrate, an increase in cladding temperature, and / or entrainment of droplets from the wave.

[0058] Therefore, the second simulation method can be applied to any steady, transient and hypothetical scenarios relevant for BWR operation with regard to the potential appearance of dry patches and rewetting (between waves), associated drying times and cladding temperature rise. The appearance of dry patches is derived from the local instantaneous consideration of the liquid base film between two successive disturbance waves, including exchange terms with the steam and droplet fields. Moreover, the second method can be further extended to calculate the amount of droplets entrained from the liquid film. Droplet entrainment is closely related to the wave properties and can be calculated from the consideration of the wave geometric dimensions, mass and momentum derived from the four-field approach.

[0059] The present invention also provides a method for producing a method for manufacturing a semiconductor device comprising the steps of: 235 The present invention relates to a boiling water reactor (BWR) having a fuel assembly including fuel rods provided with fuel pellets having a U enrichment level, the enrichment level being determined depending on the results of a simulation performed by the above-mentioned simulation method.

[0060] For example, simulation methods can be applied to determine the enrichment level required to make a fuel rod adjacent a corner similar in susceptibility to crud deposition to all other fuel rods in the fuel assembly.

[0061] The general application of the present invention allows for the design of a system that can be used to reduce the amount of material in the system, including localized concentrations of crud components, in a manner similar to existing design criteria. 235 U-optimization can be achieved in the nuclear design process.

[0062] As described above, the present invention is based on new advanced features and is implemented by two newly developed models, the disturbance wave model and the impurity concentration model.

[0063] The disturbance wave model applies a one-dimensional, two-phase, four-field approach. In the general three-field approach, the fields consist of vapor, droplets, and liquid film. In the four-field approach, the liquid film is further divided into liquid disturbance wave and liquid base film. That is, the four fields are vapor, droplets, liquid wave, and liquid base film. This is shown diagrammatically in Figure 1. Since there is an exchange of mass, momentum, and energy between the disturbance wave and the base film, a new constitutive model and field exchange terms are required.

[0064] The impurity concentration model is calculated by additionally applying the impurity conservation equation for all fields considered, which is similar to the mass conservation equation already used in the subchannel code, but with a different exchange term between the fields (since no impurities are transported in the vapor field).

[0065] These newly developed models are now described in more detail.

[0066] The disturbance wave model is based on the following assumptions and is shown in Figure 2.

[0067] The four fields consist of very fast moving vapor, droplets, fast moving waves that tend to be coherent and transport most of the film mass, and a slow moving liquid base film that is very thin and does not contribute much to the liquid film mass transport.

[0068] Solve the conservation equations for the transient fields:

number

[0069] The left side of the equation represents the inertial terms, and the right side of the equation represents (respectively) droplet deposition, entrainment, evaporation, and momentum carried by the crossflow, pressure gradient, gravity, and interfacial forces (from the vapor and wall).

[0070] Taking a similar approach in the new four-field formulation, and referring to Figure 2 where the various parameters are shown, we can establish the equations that represent the wave momentum conservation and the basement momentum conservation. The wave momentum conservation is as follows:

number

[0071] In practice, some simplifications can be made, as long as they are justified. For example, if mass exchange, pressure gradients, and momentum transfer of the vapor / droplet / wave / substrate due to inertia terms can be neglected, then:

number

[0072] Below is a list of what the parameters in the above equation represent: W: Mass flow rate w: Mass flow rate during cross flow u:speed D: deposition mass flux of droplets (to the film) E: Droplet entrained mass flux (from the membrane) Γ: Evaporative mass flux (from the film) Ψ: Wave / substrate mass flux Π: Wall perimeter p: pressure ρ: Density h: thickness τ: Interfacial force (per unit area) t: time z: Axial height Subscript: w:wave f: membrane d: droplet l:Liquid v:steam b:Base membrane

[0073] The resulting forces on the wave for the simple case given by the previous equation are shown diagrammatically by arrows in Figure 2. A balance of forces is achieved due to gravity, steam drag, and momentum transfer from the wave to the substrate ("friction"). F Gravity +F Drag +F Friction =0 This is solved in terms of wave velocity.

[0074] To complete the system of equations, for example, constitutive models are needed for the interfacial forces between the fields, in particular the wave drag and the wave-to-substrate forces. These constitutive modes can be based on physical considerations or on empirical phases (if a suitable experimental database is available).

[0075] Additional inputs are also required to adequately represent the average wave and substrate geometric properties locally. Although the choices may vary depending on the method, these inputs typically include the wave amplitude (h w ), width (l w ), and liquid base film thickness (h b ) These may also be derived from physical considerations and / or from calibrated empirical correlations (when an appropriate experimental database is available).

[0076] The equations are then solved for the wave mass flow and wave speed. The wave frequency is determined by consistency with the wave mass and momentum conservation equations.

[0077] Below are four examples of calibrated empirical correlations. Different correlations can be developed as more relevant data become available. These were determined using data from publicly available experimental databases at relevant BWR core conditions. The correlations were derived by regression analysis, which was specifically performed on the four-field model. Regression analysis is a powerful statistical method that can examine the relationship between two or more variables. There are many types of regression analysis, but at its core it is about examining the effect of one or more independent variables on a dependent variable. Equilibrium base film thickness:

number

number

number

number

[0078] Below is a list of what the parameters in the above equation represent: h b : Base film thickness h w : Wave amplitude l w :Wave (axis) width C w : Wave drag coefficient d H :Equivalent hydraulic diameter (4A / P) d A : equivalent circular area diameter (sqrt(4A / π)) Re v : Steam Reynolds number (ρ v *u v *dA / μ v ) Re vw : Steam Reynolds number for wave velocity (ρ v *(u v -uw )*dA / μ v ) Re f : Film Reynolds number (4*M f / Π / μ f ) Re w : Wave Reynolds number (4*M w / Π / μ f )

[0079] The Reynolds number (Re) is an important dimensionless quantity in fluid mechanics and is typically used to help predict flow patterns in various fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at higher Reynolds numbers, turbulent flow occurs due to differences in fluid speed and direction.

[0080] Because the calibrated correlations were derived from equilibrium (thermal and mechanical) data, a relaxation of the model was applied that allows the wave geometric properties to transition smoothly from one state to another. This relaxation characterizes the rate at which the wave can exchange mass with the substrate and the rate at which the wave properties can change, and is consistent with experimental observations.

[0081] The model has been implemented on MEFISTO-T and the correlation between the wave and basement geometric properties has been calibrated against the RISO database. It has been tested against simple flow transients such as the Fukano transient.

[0082] The RISO database is a high-pressure steam / water database published in 1978 by the Reactor Technology Department of the Riso National Laboratory in Denmark, entitled "An experimental and theoretical investigation of annular steam-water flow in tubes and annuli at 30 to 90 bar" by Wurtz, J. (1978) (Denmark, Forskningscenter Risoe. Risoe-R; No. 372).

[0083] Measurements are presented for membrane flow rate, pressure gradient, membrane thickness, wave frequency and velocity, and burnout (dryout) heat flux in one annular and two tubular geometries. More than 250 experiments were performed in both adiabatic and radiative conditions, using steam and water at pressures from 30 to 90 bar.

[0084] The results of the transient experiments performed by Fukano are available in "Fluctuation characteristics of heating surface temperature near an obstacle in transient boiling two-phase flow in a vertical annular channel" by T. Fukano, S. Mori, T. Nakagawa (2003), Nuclear Engineering and Design 219 (2003) 47-60.

[0085] In these low-pressure steam-water tests in a heated annulus, fast variations in input power, inlet enthalpy and inlet flow rate were performed and the dynamic behavior of disturbance waves was visually observed near the test section outlet. Long suppression (delay) of disturbance waves was observed under certain transients accompanied by large wall temperature changes corresponding to complete dryout of the base film between disturbance waves.

[0086] Here, the impurity concentration model is explained using the concept of impurity mass conservation in all fields. It is considered that steam is generated in the evaporation process and does not transport impurities.

[0087] As an example of impurity concentration calculation, we show one that can be applied to the three-field approach. film:

number

number

[0088] In the above formula, C is the impurity concentration, the superscript CF is the crossflow between the subchannels, and the subscripts f and d represent the film and droplet, respectively.

[0089] The same concept applies to the four-field approach, where the impurity concentrations are described consistently with mass conservation including mass exchange between the considered fields.

[0090] In the second step, we calculate the local instantaneous concentration of the basement membrane between waves using the input parameters (Δt, δ 0 ,C 0 5 and 6 show the basement membrane thickness and basement membrane concentration, respectively.

[0091] Figure 5 shows the time evolution of basement membrane thickness at a specific location between disturbance waves. At t = 0 (immediately after the wave), the basement membrane thickness is at its maximum value δ 0 At t=Δt (corresponding to the wave period), the base film thickness is at its minimum value δ Min The line defining the base film thickness change is primarily governed by the evaporation process. δ: Instantaneous basement membrane thickness Δt: wave period Subscripts: 0: initial value, LIM: limit value for impurity precipitation

[0092] Figure 6 shows the change in basement membrane concentration over time. At t = 0, the concentration is at its minimum, C 0 At t=Δt, the hypothetical maximum concentration C Max (When precipitation is ignored), and is mainly governed by the thinning of the base film. Lim is determined to be the value at which the cladding deposition begins.

[0093] Crud accumulation limit C Lim Plant-specific information is needed to determine C Inlet = 15.6 ppb, and C LIM =10*C Inlet It is.

[0094] The solubility limit is used as a threshold to convert local concentrations in the fuel rod cooling film to crud deposition mass flux, allowing crud deposition to be modeled as a simple threshold phenomenon. Using a subchannel analysis approach, this new modeling capability is able to accurately predict the relative levels of axial and azimuthal local film concentrations and crud deposition mass flux for different fuel rods without significant reliance on modeling assumptions.

[0095] The model was validated against inspection data from an operating BWR.

[0096] The main parameters that affect the margin of the cladding deposition are: These are the local heat flux, the local wave frequency, the local substrate thickness, and the bulk concentration of the components. The first three parameters can be controlled by optimizing the nuclear design, i.e. optimizing the enrichment variation along the axial direction of the fuel rod, which is expected to be most susceptible to the effects of crud.

[0097] The present invention is not limited to the preferred embodiments described above. Various alternatives, modifications and equivalents can be used. Therefore, the above embodiments should not be taken as limiting the scope of the present invention, which is defined by the appended claims.

Claims

1. 1. A computer implemented simulation method for predicting local concentrations of constituents in coolant water at any location along a fuel rod in a fuel bundle mechanical design of a boiling water reactor (BWR) where crud deposits may occur, the simulation method being based on a sub-channel approach for predicting local mass fluxes of steam and liquid in the coolant water for given steady-state or transient boundary conditions at any location along a fuel rod in a fuel bundle mechanical design of a boiling water reactor (BWR), the sub-channel approach being based on solving mass, momentum and energy conservation equations for the vapor and liquid phases, the liquid phase being represented by a number of field variables, specifically three fields consisting of liquid droplets, liquid base film, disturbance waves, and a fourth field for the vapor phase, the simulation method being completed by the steps of solving individual mass, momentum and energy conservation equations for the four fields, solving the necessary closure relations describing the mass transfer between the fields, and mass conservation equations for the constituents dissolved in the liquid phase and carried separately by each of the fields, the simulation method being completed by - simulating steady-state or transient boundary conditions for a condition of interest of a fuel assembly, the cooling water flow possibly having a predetermined flow rate variation; - analyzing predetermined parameters of the disturbance wave and substrate, including wave speed, wave frequency, and substrate thickness; - calculating a local instantaneous impurity concentration by analyzing the liquid base film thickness between successively passing disturbance waves based on the simulated boundary conditions, said calculation being performed for each fuel rod of the fuel assembly; Including, The simulation method further includes a step of comparing, for each fuel rod, the calculated local instantaneous impurity concentration with a crud compound precipitation limit, and considering crud to have occurred for a time during which the concentration is higher than the precipitation limit.

2. 2. The simulation method of claim 1, wherein the step of analyzing predetermined parameters of the disturbance wave and the liquid base film includes the steps of solving a disturbance wave momentum balance and a liquid base film momentum balance, and simplifying the calculations by ignoring momentum exchange from pressure gradients and inertial terms, which have limited impact on the results.

3. 3. The simulation method of claim 1 or 2, further comprising a step of applying a sub-channel disturbance wave model configured to calculate detailed distribution of impurity concentration in the axial and azimuthal directions, i.e., along the circumference of the fuel rod, in each liquid base film flowing along the fuel rod of the fuel assembly under operating conditions of interest based on the interaction of the wave with the liquid base film, the operating conditions consisting of pressure, flow velocity, power, and fuel rod power distribution.

4. 4. The simulation method of claim 3, further comprising applying an impurity concentration model used as a post-processing of the disturbance wave model to calculate, for each fuel rod, the local instantaneous impurity concentration in the slowly moving liquid base film during a disturbance wave during an imposed operating condition.

5. The simulation method according to any one of claims 1 to 4, further comprising simulating local concentrations of crud components when varying the enrichment of one or a number of fuel pellets of one or a number of fuel rods to reduce crud.

6. A computer implemented simulation method based on a sub-channel approach for predicting local mass fluxes of steam and liquid in coolant for given steady-state or transient boundary conditions at any location along a fuel rod in a fuel assembly mechanical design of a boiling water reactor (BWR), said sub-channel approach being based on the solution of mass, momentum and energy conservation equations for the steam and liquid phases, said liquid phase being represented by a number of field variables, specifically three fields consisting of droplets, liquid base film, disturbance waves, and a fourth field, the steam phase, said simulation method being completed by the steps of solving the individual mass, momentum and energy conservation equations for said four fields, solving the necessary closure relations describing the mass transfer between said fields, and models describing the local phenomena being base film dryout, crud temperature rise or droplet entrainment from waves, said simulation method further comprising: - simulating steady-state or transient boundary conditions; - analyzing selected parameters of the disturbance wave and the liquid base film, including wave speed and frequency, and base film thickness; A simulation method comprising:

7. 7. The method of claim 6, wherein analyzing the predetermined parameters includes analyzing a liquid base film between successively passing disturbance waves to calculate local instantaneous dry patch formation and associated cladding temperature increase between the disturbance waves during the simulated steady-state or transient operation, the calculation being performed for each fuel rod of a fuel assembly.

8. 8. The simulation method of claim 6 or 7, wherein the step of analyzing predetermined parameters comprises analyzing disturbance wave characteristics of a liquid to calculate entrainment of liquid droplets from the waves during the simulated steady-state or transient operation, the calculation being performed for each fuel rod of a fuel assembly.

9. A simulation method according to any one of claims 6 to 8, wherein, when simulating transient boundary conditions, the boundary conditions comprise input parameters having a predetermined time variation.

10. 10. A boiling water reactor (BWR) comprising a fuel assembly including fuel rods provided with fuel pellets having a fissile material concentration, i.e. enrichment level, the enrichment level being determined in dependence on the results of a simulation performed by the simulation method according to any one of claims 1 to 9.

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