A fast calculation method for the flow field in a rod bundle sub-channel under fully developed single-phase flow

Abstract

The present invention discloses a method for rapidly calculating the flow field in a fully developed state of single-phase flow within a rod bundle subchannel. Based on the fully developed flow characteristics, the method ignores the convection term and the axial diffusion term, simplifies the time-averaged Navier-Stokes equation into a diffusion equation that is easily solvable, and treats the friction pressure drop as a source term. The radial momentum diffusion caused by transient flow under turbulent conditions is calculated using a turbulence model and the eddy viscosity assumption. This calculation method can predict the flow field in a fully developed state within a rod bundle subchannel within 1 second and can serve as the basis for a next-generation reactor core subchannel analysis program.

Description

Technical Field

[0001] The present invention relates to the field of thermal hydraulic safety analysis of nuclear power reactor cores, and in particular to a method for quickly calculating the flow field in a fully developed single-phase flow in a rod bundle sub-channel. Background Art

[0002] In nuclear power systems, fuel rods in reactors are usually installed in the reactor core in the form of rod bundles;

[0003] The rod bundle sub-channels are very narrow and long, and the coolant reaches a fully developed state at the front end of the sub-channel. The flow field in this fully developed state determines the channel's heat transfer and resistance characteristics, particle deposition, and cladding corrosion characteristics, which are key information for nuclear reactor core safety analysis.

[0004] The current subchannel analysis program lumps a single subchannel, ignoring the flow field distribution within the cross section of each subchannel, which hinders the further development of the subchannel analysis program.

[0005] Conventional CFD requires drawing a large number of grids for long and narrow flow channels, which takes a long time to calculate and cannot meet the time requirements of core analysis programs.

[0006] For fully developed pipe flow, the flow parameters do not change with axial position, and the time-averaged radial velocity is equal to 0. Therefore, the convection term and axial diffusion term in the time-averaged NS equation can be ignored, and the time-averaged NS equation can be simplified to the form of a diffusion equation, which can reduce the calculation time.

[0007] In view of the development requirements of the next generation of core sub-channel thermal-hydraulic analysis programs, the present invention proposes a fast calculation method for the single-phase flow field in the rod bundle sub-channel by combining the fully developed flow characteristics of the pipeline flow. Summary of the Invention

[0008] In order to overcome the deficiencies in the prior art, the present invention provides a method for quickly calculating the flow field in a fully developed single-phase flow in a rod bundle sub-channel.

[0009] In order to achieve the above-mentioned purpose of the invention, the technical solutions adopted to solve the technical problems are as follows:

[0010] A method for rapidly calculating the flow field in a fully developed single-phase flow in a rod bundle sub-channel comprises the following steps:

[0011] Step 1: Divide the cross section of the rod bundle sub-channel into a grid, discretize the flow channel cross section into several grid areas, and use the numerical solution method to solve the following differential equation to obtain the axial velocity distribution u z :

[0012]

[0013] The boundary conditions of the above formula are:

[0014] (1) The rod bundle surface is a no-slip wall boundary, u z =0m / s;

[0015] (2) The non-wall boundary is a symmetric boundary,

[0016] Where η eff is the effective dynamic viscosity of the coolant, P is the friction pressure drop;

[0017] Step 2: For laminar flow conditions, the effective dynamic viscosity η eff Equal to the coolant molecular viscosity η; for turbulent conditions, the effective dynamic viscosity η eff Equal to coolant molecular viscosity η + turbulent viscosity ηt;

[0018] Step 3: For turbulent flow conditions, use the turbulent viscosity to calculate using the following formula:

[0019] η t =c μ ρk 2 / ε

[0020] Where k is the turbulent kinetic energy, ε is the turbulent kinetic energy dissipation rate, ρ is the liquid phase density, and c μ are constants, and k and ε are calculated using a turbulence model associated with the time-averaged flow field.

[0021] Furthermore, in step 3, the standard k-ε model is used to calculate the turbulent kinetic energy and dissipation rate, ignoring the convection term and axial diffusion term in the turbulent kinetic energy and dissipation rate. The governing equations are:

[0022]

[0023]

[0024] Where:

[0025]

[0026] Where η t is the turbulent viscosity, ρ is the liquid density, u z is the axial velocity distribution, and x and y are the directional components of the flow channel cross section.

[0027] Furthermore, in step 1, the effective dynamic viscosity between the center of the first layer of grid and the wall is calculated using the standard wall function.

[0028] Furthermore, for the turbulent kinetic energy field, the rod bundle wall is set as a symmetric boundary; for the dissipation rate field, the dissipation rate at the center of the first layer of grid is set to a constant value:

[0029]

[0030] Where C μ is the empirical constant, k p is the turbulent kinetic energy at the center of the first grid layer, y p is the distance between the center of the first layer of grid and the wall.

[0031] Furthermore, the values ​​of the undetermined parameters in the model, C μ The value is 0.09, the C1 value is 1.44, the C2 value is 1.92, and σ k The value is 1.0, σ ε The value is 1.3.

[0032] Due to the adoption of the above technical solution, the present invention has the following advantages and positive effects compared with the prior art:

[0033] This paper proposes a method for rapidly calculating the flow field in a fully developed state of single-phase flow within a rod bundle subchannel. Based on the fully developed flow characteristics, this method neglects convection and axial diffusion terms, simplifies the time-averaged Navier-Stokes equations into a more easily solvable diffusion equation, and treats frictional pressure drop as a source term. The radial momentum diffusion caused by transient flow under turbulent conditions is calculated using a turbulence model and eddy viscosity assumption. This method can predict the flow field in a fully developed state within a rod bundle subchannel within 1 second and could serve as the basis for next-generation reactor core subchannel analysis programs. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following is a brief introduction to the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without inventive work. In the drawings:

[0035] Figure 1 Schematic diagram of the cross section of the rod bundle sub-channel in an embodiment of the present invention;

[0036] Figure 2 Schematic diagram of a 1 / 8 sub-channel grid in an embodiment of the present invention;

[0037] Figure 3 Schematic diagram comparing the velocity distribution calculated in the embodiment of the present invention and the results of commercial software. DETAILED DESCRIPTION

[0038] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0039] In nuclear power systems, fuel rods are typically installed in the reactor core in bundles. Coolant flows through the bundle subchannels, removing fission heat and cooling the core. These subchannels are very narrow, with a hydraulic diameter of approximately 1 cm and a length of up to 5 meters. The coolant flow field reaches a fully developed state at the front of the subchannels. The fully developed flow field characteristics within the subchannels are crucial for core thermal-hydraulic analysis. Conventional CFD time-averaged Reynolds simulations require solving the entire set of time-averaged Navier-Stokes equations (NS equations), resulting in lengthy computational times.

[0040] This embodiment discloses a method for quickly calculating the flow field in a fully developed state of a single-phase flow in a rod bundle sub-channel. The method ignores the convection term and the axial diffusion term based on the fully developed flow characteristics, simplifies the time-averaged NS equations into a diffusion equation that is easy to solve, and treats the friction pressure drop as a source term. The radial momentum diffusion caused by transient flow under turbulent conditions is calculated using a turbulence model and an eddy viscosity assumption. The calculation method can achieve flow field prediction in a fully developed state in a rod bundle sub-channel within 1 second, and can serve as the basis for a new generation of reactor core sub-channel analysis programs. Specifically, it includes the following steps:

[0041] Step 1: Divide the cross section of the rod bundle sub-channel into a grid, discretize the flow channel cross section into several grid areas, and use the numerical solution method to solve the following differential equation to obtain the axial velocity distribution u z :

[0042]

[0043] The boundary conditions of the above formula are:

[0044] (1) The rod bundle surface is a no-slip wall boundary, u z =0m / s;

[0045] (2) The non-wall boundary is a symmetric boundary,

[0046] Where η eff is the effective dynamic viscosity of the coolant, P is the friction pressure drop;

[0047] Step 2: For laminar flow conditions, the effective dynamic viscosity η eff Equal to the coolant molecular viscosity η; for turbulent conditions, the effective dynamic viscosity η effEqual to coolant molecular viscosity η + turbulent viscosity η t ;

[0048] Step 3: For turbulent flow conditions, use the turbulent viscosity to calculate using the following formula:

[0049] η t =c μ ρk 2 / ε

[0050] Where k is the turbulent kinetic energy, ε is the turbulent kinetic energy dissipation rate, ρ is the liquid phase density, and c μ is a constant, and k and ε are calculated using the turbulence model associated with the time-averaged flow field.

[0051] Furthermore, in step 3, the standard k-ε model is used to calculate the turbulent kinetic energy and dissipation rate, ignoring the convection term and axial diffusion term in the turbulent kinetic energy and dissipation rate. The governing equations are:

[0052]

[0053]

[0054] Where:

[0055]

[0056] Where η t is the turbulent viscosity, ρ is the liquid density, u z is the axial velocity distribution, and x and y are the directional components of the flow channel cross section.

[0057] Furthermore, in step 1, the effective dynamic viscosity between the center of the first layer of grid and the wall is calculated using the standard wall function.

[0058] Furthermore, for the turbulent kinetic energy field, the rod bundle wall is set as a symmetric boundary; for the dissipation rate field, the dissipation rate at the center of the first layer of grid is set to a constant value:

[0059]

[0060] Where C μ is the empirical constant, k p is the turbulent kinetic energy at the center of the first grid layer, y p is the distance between the center of the first layer of grid and the wall.

[0061] Optional, undetermined parameter values ​​in the model:

[0062] <![CDATA[C m ]]> <![CDATA[C1]]> <![CDATA[C2]]> <![CDATA[σ k ]]> <![CDATA[σ ε ]]> 0.09 1.44 1.92 1.0 1.3

[0063] Figure 1Schematic diagram of a cross-section of a rod bundle subchannel, with a rod diameter of 9.5 mm and a rod spacing of 12.6 mm. For geometric symmetry, only 1 / 8 of the subchannel is calculated. Figure 2 This is the meshing of the 1 / 8 subchannel. For turbulent flow conditions, the Y+ range of the center of the first layer of mesh is 33-41, which meets the requirements for using wall functions. Figure 3 The comparison between the calculation method proposed in the present invention and the calculation results of the commercial CFD software Fluent is shown. The calculation results of the two are consistent, but the calculation time of the present invention is less than 1s, which greatly reduces the calculation time while ensuring the calculation accuracy.

[0064] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for rapid calculation of the flow field in a fully developed single-phase flow in a rod bundle sub-channel, characterized in that: The following steps are involved: Step 1: Divide the cross section of the rod bundle sub-channel into a grid, discretize the flow channel cross section into several grid areas, and use the numerical solution method to solve the following differential equation to obtain the axial velocity distribution u z : The boundary conditions of the above formula are: (1) The rod bundle surface is a no-slip wall boundary, u z =0m / s; (2) The non-wall boundary is a symmetric boundary, Where η eff is the effective dynamic viscosity of the coolant, P is the friction pressure drop; Step 2: For laminar flow conditions, the effective dynamic viscosity η eff Equal to the coolant molecular viscosity η; for turbulent conditions, the effective dynamic viscosity η eff Equal to coolant molecular viscosity η + turbulent viscosity η t ; Step 3: For turbulent flow conditions, use the turbulent viscosity to calculate using the following formula: or t =c μ pk 2 / e Where k is the turbulent kinetic energy, ε is the turbulent kinetic energy dissipation rate, ρ is the liquid phase density, and c μ are constants, and k and ε are calculated using a turbulence model associated with the time-averaged flow field.

2. The method for rapid flow field calculation in a fully developed single-phase flow in a rod bundle sub-channel according to claim 1, characterized in that: In step 3, the standard k-ε model is used to calculate the turbulent kinetic energy and dissipation rate, ignoring the convection term and axial diffusion term in the turbulent kinetic energy and dissipation rate. The governing equations are: Where: Where η t is the turbulent viscosity, ρ is the liquid density, u z is the axial velocity distribution, and x and y are the directional components of the flow channel cross section.

3. The method for rapid flow field calculation in a fully developed single-phase flow in a rod bundle sub-channel according to claim 1, characterized in that: In step 1, the effective dynamic viscosity between the center of the first layer of mesh and the wall is calculated using the standard wall function.

4. The method for rapid flow field calculation in a fully developed single-phase flow in a rod bundle sub-channel according to claim 1, characterized in that: For the turbulent kinetic energy field, the rod bundle wall is set as the symmetric boundary; for the dissipation rate field, the dissipation rate ε at the center of the first layer of grid is P Set to a fixed value: Where C μ is the empirical constant, k p is the turbulent kinetic energy at the center of the first grid layer, y p is the distance between the center of the first layer of grid and the wall.

5. The method for rapid flow field calculation in a fully developed single-phase flow in a rod bundle sub-channel according to claim 1, characterized in that: The values ​​of the undetermined parameters in the model, C μ The value is 0.09, the C1 value is 1.44, the C2 value is 1.92, and σ k The value is 1.0, σ ε The value is 1.3.

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