CN113095004A - Liquid metal flow heat transfer calculation method - Google Patents

Liquid metal flow heat transfer calculation method Download PDF

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CN113095004A
CN113095004A CN202110331441.XA CN202110331441A CN113095004A CN 113095004 A CN113095004 A CN 113095004A CN 202110331441 A CN202110331441 A CN 202110331441A CN 113095004 A CN113095004 A CN 113095004A
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王明军
何少鹏
章静
田文喜
秋穗正
苏光辉
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Xian Jiaotong University
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Abstract

The invention discloses a liquid metal flowing heat transfer calculation method, which comprises the following steps: 1. establishing physical fields required for solving in OpenFOAM; 2. applying boundary conditions to each physical field and marking wall meshes; 3. the mass and momentum conservation equation is solved by pressure-velocity coupling iteration, and the specific energy equation is solved; 4. judging whether the coupling iteration is converged, and determining to return to the step 3 or carry out the next step; 5. based on k-omega-kθ‑ΩθThe turbulent heat exchange model is used for updating momentum, effective viscosity and thermal diffusivity in a specific energy equation; 6. updating physical properties and variable source terms in each equation; 7. updating marked wall surface gridsMean square value k of the pulsating temperatureθAnd its specific dissipation factor omegaθJudging whether the external iteration converges or not, and determining to return to the step 3 to continue the calculation or finish the calculation; the invention solves the problems that the traditional constant value turbulence Plantt number vortex diffusion model has low precision and strong theoretical performance when calculating the liquid metal flow heat transfer phenomenon, but the advanced turbulence heat exchange model with complex solution is difficult to realize and apply in commercial CFD software.

Description

Liquid metal flow heat transfer calculation method
Technical Field
The invention belongs to the technical field of a nuclear reactor thermodynamic and hydraulic calculation method, and particularly relates to a liquid metal flow heat transfer calculation method.
Background
The liquid metal reactor is one of the first generation nuclear energy systems recommended by the fourth Generation International Forum (GIF) for the prior development of reactor types, and has the advantages of strong heat carrying capacity of a coolant, difficulty in boiling and the like, so that the liquid metal reactor has received extensive attention and research. In the traditional commercial CFD software, for the numerical simulation of liquid metal, a simple eddy diffusion model based on the reynolds simulation assumption, which is applicable to common working media such as water and air, is usually adopted, however, as the liquid metal has special thermophysical properties such as low prandtl number and high thermal conductivity, as shown in fig. 1, the flow heat exchange characteristics of the liquid metal are greatly different from those of the common working media, and the simple eddy diffusion model with weak theory and poor precision is no longer applicable to the liquid metal with the prandtl number far less than 1, which brings great difficulty to the numerical simulation of the thermal engineering design and safety analysis of the liquid metal reactor.
To solve this problem, some methods are available: using user-defined function (UDF) to assign turbulent Plantt number Pr in commercial CFD software such as FluenttWriting some global/local turbulence variables (e.g. turbulence viscosity v)t) The method can correct the simulation result to a certain extent, but the turbulent heat exchange behavior at the position close to the wall surface is difficult to capture; in addition, the researchers utilize the large vortex simulation data to fit out turbulence Prandtl number correlation suitable for different geometric flow channels and implant the turbulence Prandtl number correlation into commercial CFD software, and the method can achieve better simulation precision in specific and limited geometric flow channels, but cannot meet the increasing complex liquid metal reactor core structure. In recent years, a method of considering liquid gold Belongs to the difference between a temperature boundary layer and a flow boundary layer, and is established from theoretical analysis as an advanced turbulent flow heat exchange model-k-omega-
Figure BDA0002996277710000021
-
Figure BDA0002996277710000022
Four factor models are gradually developed. The model can simulate a k-omega SST model with more accuracy on a flowing boundary layer and simulate a temperature boundary layer with more accuracy
Figure BDA0002996277710000023
The model is combined, the turbulent heat exchange behavior of the liquid metal near the wall surface can be accurately described and captured, and the model has applicability to runners with different geometric shapes. However, since such models are derived from theory, the calculation process is complex, the requirements on boundary conditions are strict, and the implementation and application in non-open source commercial CFD software are difficult. The open-source computational fluid dynamics platform OpenFOAM has the characteristics of code open source, high user freedom, complete CFD tools and the like, and is beneficial to development and implementation of the liquid metal flow heat transfer computation method.
In conclusion, based on the open source CFD platform OpenFOAM and the advanced turbulent heat exchange model with strong theoretical and high precision-k-omega-
Figure BDA0002996277710000024
-
Figure BDA0002996277710000025
The four-factor model is used for developing a high-fidelity numerical simulation calculation method suitable for the flow heat transfer problem of the liquid metal, and is of great importance to the thermal hydraulic design and safety analysis of the reactor core of the liquid metal reactor.
Disclosure of Invention
The invention aims to provide a liquid metal flowing heat transfer calculation method which can realize three-dimensional high-fidelity turbulent flow heat transfer numerical simulation calculation aiming at a special working medium of liquid metal based on an open source CFD platform and an advanced turbulent flow heat transfer model. The method overcomes the limitation of Reynolds simulation hypothesis, avoids using a simple vortex diffusion model with weak theory and large error in commercial software, solves the problem that the commercial CFD software is difficult to realize accurate simulation of the liquid metal flow heat transfer phenomenon, and provides possibility for the development and application of an advanced thermal hydraulic model in an open source CFD platform and the realization of three-dimensional high-precision numerical simulation calculation of the whole reactor core of the liquid metal reactor.
In order to achieve the purpose, the invention adopts the following technical scheme:
a liquid metal flow heat transfer calculation method comprises the following steps:
step 1: establishing physical fields required in the solving process in OpenFOAM, including scalar fields: temperature T, pressure p, temperature-dependent thermal physical property field, turbulence energy k and unit dissipation rate omega thereof, and pulse temperature square mean value
Figure BDA0002996277710000035
And its specific dissipation ratio
Figure BDA0002996277710000036
And vector field: velocity field
Figure BDA0002996277710000031
The thermal physical property field changing along with the temperature comprises density rho and specific heat capacity C pDynamic viscosity μ and thermal conductivity λ;
step 2: applying appropriate numerical simulation boundary conditions to each physical field established in the step 1, and specifically comprising the following steps:
step 2-1: for the following physical fields: speed of rotation
Figure BDA0002996277710000032
Applying OpenFOAM standard boundary conditions on temperature T, pressure p, turbulence energy k and unit turbulence energy dissipation rate omega;
step 2-2: from the mean value of the pulsating temperature
Figure BDA0002996277710000037
And its specific dissipation ratio
Figure BDA0002996277710000038
Two variables have strict requirements on boundary conditions, and standard boundary conditions cannot meet the requirements, so that all wall boundary grids are identified and marked by using a grid traversal function built in OpenFOAM (open form access memory), so that the pulse temperature square mean value on the marked wall boundary grid is conveniently identified in step 7
Figure BDA0002996277710000039
And its specific dissipation ratio
Figure BDA00029962777100000310
Carrying out assignment updating;
and step 3: carrying out pressure-speed coupling iterative solution on a mass and momentum conservation equation (1) of the liquid metal by adopting an OpenFOAM built-in SIMPLE algorithm; solving a liquid metal specific energy equation (2) which is simplified by applying work through incompressible and neglecting viscous force by using the obtained speed and pressure field:
Figure BDA0002996277710000033
Figure BDA0002996277710000034
wherein:
rho-density of liquid metal, kg. m-3；
e-specific internal energy of liquid metal, m2·s-2·kg-1；
K-specific mechanical energy of the liquid metal, m2·s-2·kg-1；
Figure BDA0002996277710000041
Velocity vector of liquid metal, m · s -1；
αeffEffective thermal diffusivity, m2·s-1；
p-pressure, kg.m-1·s-2；
Figure BDA0002996277710000042
-acceleration of gravity, m.s-2；
μeffEffective dynamic viscosity, kg.m-1·s-1；
And 4, step 4: comparing whether the residual error after the equation (1) is solved is less than the set residual error precision 10-4Judging whether the pressure-speed coupling solution is iterative convergence: if not, continuing to carry out pressure-speed coupling iterative solution on the equation (1); if the convergence is achieved, ending the iteration and carrying out the next step;
and 5: based on four-factor model, i.e. k-omega-
Figure BDA0002996277710000044
-
Figure BDA0002996277710000045
The turbulent flow heat exchange model is used for solving turbulent flow viscosity and turbulent flow thermal diffusivity in a momentum conservation and energy conservation equation; the method specifically comprises the following steps: calling a k-omega SST turbulence model, solving and updating the effective viscosity veff(ii) a Solving for
Figure BDA0002996277710000046
Thermal turbulence equation (3) to update the effective thermal diffusivity, αeff；
Figure BDA0002996277710000043
Wherein:
k-kinetic energy of turbulence, m2·s-2；
Omega-dissipation per unit of turbulent kinetic energy, s-1；
Figure BDA0002996277710000056
-mean square value of pulsating temperature, K2；
Figure BDA0002996277710000057
-mean square-of-the-pulse temperature unit dissipation ratio, s-1；
Alpha-laminar thermal diffusivity, m2·s-1；
αtTurbulent thermal diffusivity, m2·s-1；
νtViscosity in turbulent motion, m2·s-1；
Cp1、Cp2、Cμ、Cd1、
Figure BDA0002996277710000058
-a model constant;
Figure BDA0002996277710000051
wherein v is laminar kinematic viscosity, m2·s-1；
Figure BDA0002996277710000059
-a variable source term that varies with temperature,
Figure BDA0002996277710000052
Pk-a variable source term that varies with speed,
Figure BDA0002996277710000053
is solved out
Figure BDA00029962777100000510
And
Figure BDA00029962777100000511
after the value, the effective thermal diffusivity is calculated again from the following formula:
Figure BDA0002996277710000054
wherein:
Figure BDA00029962777100000512
-a model constant;
k-kinetic energy of turbulence, m2·s-2；
Figure BDA00029962777100000513
-local thermal feature time scale, s, calculated according to equations (5) - (7):
τlθ＝f1θB1θ+f2θB2θ (5)
Figure BDA0002996277710000055
Figure BDA0002996277710000061
wherein:
pr-the Plantt number of liquid metals, Pr ═ Cpμ/λ；
RtReynolds number of turbulent flow, Rt＝k/(CμeΩν)；
Rd-dimensionless wall distance, Rd＝δ(CμeΩk)0.25/ν0.75Wherein δ is the distance from the wall surface to the center of the first layer of grid, m;
r is the ratio of thermal characteristic time to momentum time,
Figure BDA0002996277710000062
Figure BDA0002996277710000065
intermediate variables, no physical meaning;
Prt,∞、Cr-a model constant;
step 6: and (3) updating the thermal physical property and variable source terms in the conservation equations (1) - (3) by utilizing the pressure, speed and temperature field obtained by the solution in the step (3), and specifically comprising the following steps:
step 6-1: in step 1, each of the thermal property fields: dynamic viscosity mu, density rho and specific heat capacity CpAnd the thermal conductivity lambda is established as a physical field related to the temperature, and the mass and momentum conservation equation (1), the specific energy conservation equation (2) are updated according to the latest temperature T of the current iteration step,
Figure BDA0002996277710000064
The thermophysical property values in equation (3);
step 6-2: latest speed field according to current iteration step
Figure BDA0002996277710000063
And temperature T is calculated and updated
Figure BDA0002996277710000066
The variable source term in equation (3): pkAnd
Figure BDA0002996277710000067
and 7: comparing whether the residual errors of the conservation equations (1) - (3) updated in the step 6 are smaller than the set residual error precision 10 -4Judging whether the external iteration convergence is reached; if not, updating the wall boundary grids marked in the step 2 according to the formula (8)
Figure BDA0002996277710000068
And
Figure BDA0002996277710000069
and (4) repeating the steps 3 to 7 until the convergence of the outer iteration is reached;
Figure BDA0002996277710000071
wherein:
|wall-representing the variable as a value on a wall;
after final convergence, k-omega-based-
Figure BDA0002996277710000072
-
Figure BDA0002996277710000073
The distribution of the high-fidelity three-dimensional key thermal hydraulic parameters of the low-Plantt number liquid metal of the turbulent flow heat exchange model can be evaluated according to the heat carrying capacity of the coolant in the liquid metal reactor fuel assembly and the cooling condition of the wall surface of the liquid metal reactor fuel rod.
Compared with the prior art, the invention has the following advantages:
1) avoids using a simple vortex diffusion model with weak theory and poor precision, overcomes the limitation that the Reynolds analog assumption is no longer suitable for liquid metal, and adopts more theory and advanced k-omega-
Figure BDA0002996277710000074
-
Figure BDA0002996277710000075
The model is used for realizing the simulation calculation of the flow heat transfer problem of the liquid metal, and the method can be widely applied to the analysis calculation of the thermal safety characteristics of various liquid metal reactors such as lead-cooled fast reactors, sodium-cooled fast reactors and the like.
2) K-omega SST turbulence model for simulating flow boundary layer accurately and simulating temperature boundary layer accurately by using open source CFD platform
Figure BDA0002996277710000076
The combination of thermal turbulence models, i.e. k-omega-
Figure BDA0002996277710000077
-
Figure BDA0002996277710000078
The turbulent flow heat exchange model integrates the advantages of the two models, improves the reasonability and accuracy of calculation, overcomes the limitations of closed source of commercial CFD software codes and low degree of freedom of users, and provides ideas and methods for realizing similar advanced calculation methods in an open source CFD platform.
Drawings
FIG. 1 is a schematic diagram showing the difference between the flowing heat transfer characteristics of liquid metal and ordinary working medium water.
FIG. 2 is a schematic diagram of a typical filament-wound bundle fuel assembly and the wall grid identification and marking process of step 2-2.
FIG. 3 is a flow chart of the method of the present invention.
Detailed Description
The present invention will be described in further detail below with reference to the flow chart of the present invention shown in fig. 3, taking the calculation of the flow heat transfer of the liquid metal in a typical wire-wrapped bundle fuel assembly as an example, and the difference between the flow heat transfer characteristics of the liquid metal and the ordinary working fluid water is shown in fig. 1, from which it can be seen that: for liquid water, the flow boundary layer and the temperature boundary layer have similarity in shape and thickness; for liquid metal, the temperature change trend in the temperature boundary layer is different from the speed change trend in the flow boundary layer, and the thickness of the temperature boundary layer is far larger than that of the flow boundary layer; a typical wire-wrapped bundle fuel assembly and wall grid identification and marking process in step 2-2 is shown in fig. 2.
The invention relates to a liquid metal flowing heat transfer calculation method, which comprises the following steps:
step 1: establishing physical fields to be solved when liquid metal flows in a single phase in a wire winding rod bundle for heat exchange in open source CFD software OpenFOAM, wherein the physical fields comprise scalar fields: temperature T, pressure p, temperature-dependent thermal physical property field, turbulence energy k and unit dissipation rate omega thereof, and pulse temperature square mean value
Figure BDA0002996277710000083
And its specific dissipation ratio
Figure BDA0002996277710000084
And vector field: velocity field
Figure BDA0002996277710000081
The thermal physical property field changing along with the temperature comprises density rho and specific heat capacity CpDynamic viscosity μ and thermal conductivity λ;
step 2: applying appropriate numerical simulation boundary conditions to each physical field established in the step 1, and specifically comprising the following steps:
step 2-1: for the following physical fields: speed of rotation
Figure BDA0002996277710000082
Applying OpenFOAM standard boundary conditions on temperature T, pressure p, turbulence energy k and unit turbulence energy dissipation rate omega;
step 2-2: mean square value of temperature due to pulsation
Figure BDA0002996277710000085
And its specific dissipation ratio
Figure BDA0002996277710000086
Two variables have strict requirements on boundary conditions, and standard boundary conditions cannot meet the requirements, so that all wall boundary grids of a typical liquid metal reactor wire-wound rod bundle fuel assembly shown in fig. 2 are identified and marked by using a grid traversal function built in OpenFOAM, specifically: traversing all grid cells of the rod bundle assembly, judging whether the grid belongs to a wall type boundary or not, if so, storing the grid cell number, and accordingly identifying and marking the grids on the wall surfaces of the assembly box, the fuel rod and the wire winding so as to conveniently carry out step 7 on the mean value of the pulsating temperature on the marked wall boundary grid
Figure BDA0002996277710000094
And its specific dissipation ratio
Figure BDA0002996277710000095
Carrying out assignment updating;
and step 3: carrying out pressure-speed coupling iterative solution on a mass and momentum conservation equation (1) of the liquid metal by adopting an OpenFOAM built-in SIMPLE algorithm; solving a liquid metal specific energy equation (2) which is simplified by applying work through incompressible and neglecting viscous force by using the obtained speed and pressure field:
Figure BDA0002996277710000091
Figure BDA0002996277710000092
wherein:
rho-density of liquid metal, kg. m-3；
e-specific internal energy of liquid metal, m2·s-2·kg-1；
K-specific mechanical energy of the liquid metal, m2·s-2·kg-1；
Figure BDA0002996277710000096
Velocity vector of liquid metal, m · s-1；
αeffEffective thermal diffusivity, m2·s-1；
p-pressure, kg.m-1·s-2；
Figure BDA0002996277710000093
-acceleration of gravity, m.s-2；
μeffEffective dynamic viscosity, kg.m-1·s-1；
And 4, step 4: comparing whether the residual error after the equation (1) is solved is less than the set residual error precision 10-4I.e. determining pressure-velocity couplingWhether the solution iteratively converges: if not, continuing to carry out pressure-speed coupling iterative solution on the equation (1); if the convergence is achieved, ending the iteration and carrying out the next step;
and 5: based on four-factor model, i.e. k-omega-
Figure BDA0002996277710000103
-
Figure BDA0002996277710000104
The turbulent flow heat exchange model is used for solving turbulent flow viscosity and turbulent flow thermal diffusivity in a momentum conservation and energy conservation equation; the method specifically comprises the following steps: calling a k-omega SST turbulence model, solving and updating the effective viscosity v eff(ii) a Solving for
Figure BDA0002996277710000105
Thermal turbulence equation (3) to update the effective thermal diffusivity, αeff；
Figure BDA0002996277710000101
Wherein:
k-kinetic energy of turbulence, m2·s-2；
Omega-dissipation per unit of turbulent kinetic energy, s-1；
Figure BDA0002996277710000106
-mean square value of pulsating temperature, K2；
Figure BDA0002996277710000107
-mean square-of-the-pulse temperature unit dissipation ratio, s-1；
Alpha-laminar thermal diffusivity, m2·s-1；
αtTurbulent thermal diffusivity, m2·s-1；
νtViscosity in turbulent motion, m2·s-1；
Cp1＝1.025、Cp2＝1.9、Cμ＝0.09、Cd1＝1.1、
Figure BDA0002996277710000108
-a model constant;
Figure BDA0002996277710000102
wherein v is laminar kinematic viscosity, m2·s-1；
Figure BDA0002996277710000117
-a variable source term that varies with temperature,
Figure BDA0002996277710000111
Pk-a variable source term that varies with speed,
Figure BDA0002996277710000112
is solved out
Figure BDA0002996277710000119
And
Figure BDA00029962777100001110
after the value, the effective thermal diffusivity is calculated again from the following formula:
Figure BDA0002996277710000113
wherein:
Figure BDA00029962777100001111
-a model constant;
k-kinetic energy of turbulence, m2·s-2；
Figure BDA00029962777100001112
-local thermal feature time scale, s, calculated according to equations (5) - (7):
τlθ＝f1θB1θ+f2θB2θ (5)
Figure BDA0002996277710000114
Figure BDA0002996277710000115
wherein:
pr-the Plantt number of liquid metals, Pr ═ Cpμ/λ；
RtReynolds number of turbulent flow, Rt＝k/(CμeΩν)；
Rd-dimensionless wall distance, Rd＝δ(CμeΩk)0.25/ν0.75Wherein δ is the distance from the wall surface to the center of the first layer of grid, m;
r is the ratio of thermal characteristic time to momentum time,
Figure BDA0002996277710000116
Figure BDA0002996277710000118
intermediate variables, no physical meaning;
Prt,∞＝0.9、Cr0.3 — model constant;
step 6: and (3) updating the thermal physical property and variable source terms in the conservation equations (1) - (3) by utilizing the pressure, speed and temperature field obtained by the solution in the step (3), and specifically comprising the following steps:
Step 6-1: in step 1, each of the thermal property fields: dynamic viscosity mu, density rho, specific heat capacity CpAnd thermal conductivity lambdaImmediately, the temperature-dependent physical field is obtained, and at the moment, the mass and momentum conservation equation (1), the specific energy conservation equation (2) and the energy conservation equation are updated according to the latest temperature T of the current iteration step,
Figure BDA0002996277710000125
The thermophysical property values in equation (3);
step 6-2: latest speed field according to current iteration step
Figure BDA0002996277710000121
And temperature T is calculated and updated
Figure BDA0002996277710000126
The variable source term in equation (3): pkAnd
Figure BDA0002996277710000127
and 7: comparing whether the residual errors of the conservation equations (1) - (3) updated in the step 6 are smaller than the set residual error precision 10-4And judging whether the outer iteration convergence is reached. If not, updating the wall boundary grids marked in the step 2 according to the formula (8)
Figure BDA0002996277710000128
And
Figure BDA0002996277710000129
and repeating the steps 3 to 7 until the convergence of the outer iteration is reached.
Figure BDA0002996277710000122
Wherein:
|wall-representing the variable as a value on a wall;
after final convergence, k-omega-based-
Figure BDA0002996277710000123
-
Figure BDA0002996277710000124
The distribution of the high-fidelity three-dimensional key thermal hydraulic parameters of the low-Plantt number liquid metal of the turbulent flow heat exchange model can be evaluated according to the heat carrying capacity of the coolant in the liquid metal reactor fuel assembly and the cooling condition of the wall surface of the liquid metal reactor fuel rod.
The invention is not described in detail and is within the knowledge of a person skilled in the art.

Claims (1)

1. A liquid metal flowing heat transfer calculation method is characterized by comprising the following steps:
step 1: establishing physical fields required in the solving process in OpenFOAM, including scalar fields: temperature T, pressure p, temperature-dependent thermal physical property field, turbulence energy k and unit dissipation rate omega thereof, and pulse temperature square mean value kθAnd its specific dissipation factor omegaθ(ii) a And vector field: velocity field
Figure FDA0002996277700000011
The thermal physical property field changing along with the temperature comprises density rho and specific heat capacity CpDynamic viscosity μ and thermal conductivity λ;
step 2: applying numerical simulation boundary conditions to each physical field established in the step 1, and specifically comprising the following steps of:
step 2-1: for the following physical fields: speed of rotation
Figure FDA0002996277700000012
Applying OpenFOAM standard boundary conditions on temperature T, pressure p, turbulence energy k and unit turbulence energy dissipation rate omega;
step 2-2: from the mean value k of the pulsating temperatureθAnd its specific dissipation factor omegaθTwo variables have strict requirements on boundary conditions, and standard boundary conditions cannot meet the requirements, so that all wall boundary grids are identified and marked by using a grid traversal function built in OpenFOAM (open form access memory), so that the pulse temperature square mean value k on the marked wall boundary grid is conveniently identified in step 7 θAnd its specific dissipation factor omegaθCarry out endowmentUpdating the value;
and step 3: carrying out pressure-speed coupling iterative solution on a mass and momentum conservation equation (1) of the liquid metal by adopting an OpenFOAM built-in SIMPLE algorithm; solving a liquid metal specific energy equation (2) which is simplified by applying work through incompressible and neglecting viscous force by using the obtained speed and pressure field:
Figure FDA0002996277700000021
Figure FDA0002996277700000022
wherein:
rho-density of liquid metal, kg. m-3；
e-specific internal energy of liquid metal, m2·s-2·kg-1；
K-specific mechanical energy of the liquid metal, m2·s-2·kg-1；
Figure FDA0002996277700000023
Velocity vector of liquid metal, m · s-1；
αeffEffective thermal diffusivity, m2·s-1；
p-pressure, kg.m-1·s-2；
Figure FDA0002996277700000024
-acceleration of gravity, m.s-2；
μeffEffective dynamic viscosity, kg.m-1·s-1；
And 4, step 4: comparing whether the residual error after the equation (1) is solved is less than the set residual error precision 10-4Judging whether the pressure-speed coupling solution is iterative convergence:if not, continuing to carry out pressure-speed coupling iterative solution on the equation (1); if the convergence is achieved, ending the iteration and carrying out the next step;
and 5: based on a four-factor model, i.e. k-omega-kθ-ΩθThe turbulent flow heat exchange model is used for solving turbulent flow viscosity and turbulent flow thermal diffusivity in a momentum conservation and energy conservation equation; the method specifically comprises the following steps: calling a k-omega SST turbulence model, solving and updating the effective viscosity v eff(ii) a Solving for kθ-ΩθThermal turbulence equation (3) to update the effective thermal diffusivity, αeff；
Figure FDA0002996277700000031
Wherein:
k-kinetic energy of turbulence, m2·s-2；
Omega-dissipation per unit of turbulent kinetic energy, s-1；
kθ-mean square value of pulsating temperature, K2；
Ωθ-mean square-of-the-pulse temperature unit dissipation ratio, s-1；
Alpha-laminar thermal diffusivity, m2·s-1；
αtTurbulent thermal diffusivity, m2·s-1；
νtViscosity in turbulent motion, m2·s-1；
Cp1、Cp2、Cμ、Cd1、σθ-a model constant;
Figure FDA0002996277700000032
wherein v is laminar kinematic viscosity, m2·s-1；
Pkθ-a variable source term that varies with temperature,
Figure FDA0002996277700000033
Pk-a variable source term that varies with speed,
Figure FDA0002996277700000034
solve out kθAnd omegaθAfter the value, the effective thermal diffusivity is calculated again from the following formula:
Figure FDA0002996277700000035
wherein:
Cθ-a model constant;
k-kinetic energy of turbulence, m2·s-2；
τlθ-local thermal feature time scale, s, calculated according to equations (5) - (7):
τlθ＝f1θB1θ+f2θB2θ (5)
Figure FDA0002996277700000041
Figure FDA0002996277700000042
wherein:
pr-the Plantt number of liquid metals, Pr ═ Cpμ/λ；
RtReynolds number of turbulent flow, Rt＝k/(CμeΩν)；
Rd-dimensionless wall distance, Rd＝δ(CμeΩk)0.25/ν0.75Wherein δ is the distance from the wall surface to the center of the first layer of grid, m;
r is the ratio of thermal characteristic time to momentum time,
Figure FDA0002996277700000043
f1θ、f2θ、B1θ、B2θintermediate variables, no physical meaning;
Prt,∞、Cr-a model constant;
step 6: and (3) updating the thermal physical property and variable source terms in the conservation equations (1) - (3) by utilizing the pressure, speed and temperature field obtained by the solution in the step (3), and specifically comprising the following steps:
Step 6-1: in step 1, each of the thermal property fields: dynamic viscosity mu, density rho and specific heat capacity CpAnd the thermal conductivity lambda is established as a physical field related to the temperature, and the mass and momentum conservation equation (1), the specific energy conservation equation (2) and the k are updated according to the latest temperature T of the current iteration stepθ-ΩθThe thermophysical property values in equation (3);
step 6-2: latest speed field according to current iteration step
Figure FDA0002996277700000044
And temperature T is calculated and k is updatedθ-ΩθThe variable source term in equation (3): pkAnd Pkθ；
And 7: comparing whether the residual errors of the conservation equations (1) - (3) updated in the step 6 are smaller than the set residual error precision 10-4Judging whether the external iteration convergence is reached; if not, then update k on the wall bounding grid marked in step 2 according to equation (8)θAnd omegaθAnd (4) repeating the steps 3 to 7 until the convergence of the outer iteration is reached;
Figure FDA0002996277700000051
wherein:
|wall-representing the variable as a value on a wall;
after final convergence, k-omega-k can be obtainedθ-ΩθTurbulent flow exchangerAnd (3) distributing low-Plantt number liquid metal high-fidelity three-dimensional key thermal hydraulic parameters of the thermal model, and accordingly evaluating the heat carrying capacity of a coolant in the liquid metal reactor fuel assembly and the cooling condition of the wall surface of the liquid metal reactor fuel rod.
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Cited By (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113486482A (en) * 2021-07-12 2021-10-08 西安交通大学 Method for calculating speed and temperature boundary layer of sweepforward spiral tube bundle of liquid lead bismuth
CN113782105A (en) * 2021-08-31 2021-12-10 西安交通大学 Method for analyzing flow heat transfer characteristics of liquid metal lead bismuth alloy under swinging condition
CN113836838A (en) * 2021-09-28 2021-12-24 广州大学 Wall turbulence maintaining method based on OpenFOAM
CN114239429A (en) * 2021-12-02 2022-03-25 中国船舶重工集团公司第七0三研究所 Method for simulating thermal performance numerical value of shell side of ship condenser
CN114611438A (en) * 2022-05-11 2022-06-10 中国空气动力研究与发展中心计算空气动力研究所 Method and device for simulating stress state of target object in turbulent flow
CN115041692A (en) * 2022-06-17 2022-09-13 中国科学院力学研究所 Cooling model verification method of high-temperature metal centrifugal atomization powder making device
CN115125396A (en) * 2022-07-28 2022-09-30 中国科学院金属研究所 Control method for special steel dendritic crystal refinement and inclusion removal by VAR process
CN115862779A (en) * 2022-11-25 2023-03-28 兰州大学 Liquid metal conjugate heat transfer calculation method based on two-equation thermal turbulence model
CN115859851A (en) * 2022-11-25 2023-03-28 兰州大学 Calculation method for liquid metal coupling supercritical carbon dioxide conjugate heat transfer
CN116362159A (en) * 2023-04-04 2023-06-30 西安交通大学 Full three-dimensional coupling calculation and optimization method for liquid metal spiral tube steam generator
CN116562153A (en) * 2023-05-12 2023-08-08 兰州大学 Calculation method for thermal stratification characteristics of liquid metal

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20080015825A1 (en) * 2006-07-11 2008-01-17 Georgi Kalitzin Method for computing turbulent flow using a near-wall eddy-viscosity formulation
FR3004558A1 (en) * 2013-04-10 2014-10-17 Areva Np METHODS OF SIMULATING THE FLOW OF A FLUID IN A NUCLEAR REACTOR TANK AND CALCULATING THE MECHANICAL DEFORMATION OF ASSEMBLIES OF A NUCLEAR REACTOR HEART, AND ASSOCIATED COMPUTER PROGRAM PRODUCTS
CN105677994A (en) * 2016-01-12 2016-06-15 北京航空航天大学 Loose coupling modeling method for fluid-solid coupling heat transfer
US20170024496A1 (en) * 2015-07-22 2017-01-26 The Boeing Company Methods and apparatus to model thermal mixing for prediction of multi-stream flows
CN111027205A (en) * 2019-12-05 2020-04-17 西安交通大学 Method for simulating core box interval flow value of liquid metal cooling fast reactor
CN111027112A (en) * 2019-12-09 2020-04-17 西安交通大学 Porous medium method for fast reactor rod bundle assembly coupling heat transfer model
CN111832201A (en) * 2020-06-23 2020-10-27 西安交通大学 Method for calculating cooling and evaporation coupling of two sides of liquid metal spiral pipe steam generator

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20080015825A1 (en) * 2006-07-11 2008-01-17 Georgi Kalitzin Method for computing turbulent flow using a near-wall eddy-viscosity formulation
FR3004558A1 (en) * 2013-04-10 2014-10-17 Areva Np METHODS OF SIMULATING THE FLOW OF A FLUID IN A NUCLEAR REACTOR TANK AND CALCULATING THE MECHANICAL DEFORMATION OF ASSEMBLIES OF A NUCLEAR REACTOR HEART, AND ASSOCIATED COMPUTER PROGRAM PRODUCTS
US20170024496A1 (en) * 2015-07-22 2017-01-26 The Boeing Company Methods and apparatus to model thermal mixing for prediction of multi-stream flows
CN105677994A (en) * 2016-01-12 2016-06-15 北京航空航天大学 Loose coupling modeling method for fluid-solid coupling heat transfer
CN111027205A (en) * 2019-12-05 2020-04-17 西安交通大学 Method for simulating core box interval flow value of liquid metal cooling fast reactor
CN111027112A (en) * 2019-12-09 2020-04-17 西安交通大学 Porous medium method for fast reactor rod bundle assembly coupling heat transfer model
CN111832201A (en) * 2020-06-23 2020-10-27 西安交通大学 Method for calculating cooling and evaporation coupling of two sides of liquid metal spiral pipe steam generator

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
KHODAK等: "Parametric Study of a Divertor Cooling System for a Liquid-Metal Plasma-Facing Component", 《IEEE TRANSACTIONS ON PLASMA SCIENCE》 *
SHAOPENG HE等: "Numerical simulation of three-dimensional flow and heat transfer characteristics of liquid lead-bismuth", 《NUCLEAR ENGINEERING AND TECHNOLOGY》 *
何少鹏等: "基于OpenFOAM的液态金属铅秘三维流动换热特性数值模拟研究", 《原子能科学技术》 *
吕逸君等: "大涡模拟研究液态金属在环形管道内的湍流换热", 《中国科学技术大学学报》 *
秦浩等: "基于OpenFOAM的过冷流动沸腾数值模拟", 《原子能科学技术》 *
葛志浩等: "液态金属在堆芯子通道内的湍流换热", 《核技术》 *

Cited By (20)

* Cited by examiner, † Cited by third party
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