CN113378489A - OpenFOAM platform-based low-magnetic Reynolds number magnetic fluid turbulence analysis system and analysis method - Google Patents

OpenFOAM platform-based low-magnetic Reynolds number magnetic fluid turbulence analysis system and analysis method Download PDF

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CN113378489A
CN113378489A CN202110582987.2A CN202110582987A CN113378489A CN 113378489 A CN113378489 A CN 113378489A CN 202110582987 A CN202110582987 A CN 202110582987A CN 113378489 A CN113378489 A CN 113378489A
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吴渤渤
程阳
毛洁
吴晓东
孟繁禛
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Hangzhou Dianzi University
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Abstract

The invention belongs to the technical field of magnetohydrodynamics, and particularly relates to a system and a method for analyzing low-magnetic Reynolds-number magnetohydrodynamics turbulence based on an OpenFOAM platform. The method is based on an incompressible turbulence standard kappa-omega two-equation model in an OpenFOAM library, introduces an electromagnetic dissipation item on the basis of a kappa equation and an omega equation, realizes that the model can be called on an OpenFOAM platform to solve the magnetohydrodynamics problem under the condition of low magnetic Reynolds number, and provides a feasible thought for the numerical simulation research of the magnetohydrodynamics effect in the nuclear fusion cladding device in the future. Compared with the DNS and LES in the prior art, the method has the advantages that the accurate data of the calculation flow field under the condition of low magnetic Reynolds number are obtained by solving the two-equation model with the added electromagnetic dissipation term, a large amount of calculation resources are saved, and the method has the characteristic of good economic effect.

Description

OpenFOAM platform-based low-magnetic Reynolds number magnetic fluid turbulence analysis system and analysis method
Technical Field
The invention belongs to the technical field of magnetohydrodynamics, and particularly relates to a system and a method for analyzing low-magnetic Reynolds-number magnetohydrodynamics turbulence based on an OpenFOAM platform.
Background
Thermonuclear fusion with great potential has been held hoped for. The controllable nuclear fusion is a new energy source which is efficient, reproducible, clean and safe. The liquid metal cladding is a key part in the nuclear fusion reaction device and has important functions of heat transportation, radiation shielding and tritium value increment. The temperature of the high-temperature reaction body in the nuclear fusion reaction can reach hundreds of millions of degrees centigrade, so an external magnetic field is needed for constraint. Under the action of an external magnetic field, extremely complex MHD effect can occur in the liquid metal flowing in the cladding.
Methods for studying fluid turbulence based on numerical simulation include Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and reynolds time-averaged simulation (RANS). Compared with the former two, the RANS utilizes a turbulence model to simulate results, greatly saves calculation time and resources because the RANS is based on an average value and does not need to process details of each part of turbulence, obviously reduces calculation cost, and has wider application prospect for an RANS method in engineering problems. With the development of numerical computing technology, many commercial software for engineering technical problems have been produced. The current very mature commercial software is: fluent, CFX, Star-CD, etc. The software has the advantages of simplicity, easy learning, convenient calculation, rich models, reliable results and the like. But are relatively unable to address numerical simulation problems other than the commercial software self-contained model.
In view of this, for the reason that the original kappa-omega model in the OpenFOAM turbulence model library cannot be applied to calculation of the magnetic fluid, the calculation economic cost by using the DNS and LES methods is too high, and the method is not realized for engineering application. Therefore, the invention provides a system and a method for analyzing the turbulence of the low-magnetic Reynolds number magnetic fluid based on an OpenFOAM platform.
OpenFOAM is open source software based on Linux, and is essentially a C + + class library. The OpenFOAM has the computing power of commercial software, and simultaneously has a large number of solvers and model methods. Besides, the internal source code has openness, and the greatest advantage is that a user can develop own solver on the basis of original software according to own actual requirements. Commercial software can hardly do this. A turbulence model library in OpenFOAM has a standard kappa-omega model suitable for calculating the problem of common fluid turbulence, however, an original kappa-omega model in the OpenFOAM turbulence model library cannot be suitable for calculating the magnetic fluid, the calculation economic cost of adopting DNS (domain name system) and LES (least squares) methods is too high, and the method is not realized for engineering application.
Therefore, it is necessary to develop a magnetofluid turbulence model suitable for the low magnetic Reynolds number condition twice on the basis of the open source OpenFOAM software.
For example, a centrifugal pump design method based on rotation and curvature correction described in chinese patent application No. CN201510591035.1 includes step 1, aiming at the influence of rotation and curvature on fluid in an impeller of a centrifugal pump, performing rotation and curvature improvement on an SST κ - ω turbulence model, and generating a new turbulence model, that is, establishing a nonlinear vortex viscosity model; step 2, correcting rotation and curvature of the traditional turbulence model; step 3, improving the traditional turbulence model based on the expanded intrinsic rotation tensor; step 4, realizing a numerical calculation program based on OpenFOAM; and 5, performing numerical calculation on the hydraulic model of the centrifugal pump according to the numerical calculation program based on the OpenFOAM in the step 4, and further designing the centrifugal pump. Although the method has higher precision and can effectively help designers to develop centrifugal pump hydraulic optimization design, the designed hydraulic element meets the actual use requirement, the development period of a product is greatly shortened, and the development cost is reduced, the defects are that the original kappa-omega model in the OpenFOAM turbulence model library can be suitable for calculating the water fluid, but cannot be suitable for calculating the magnetic fluid, the calculation economic cost of the DNS and LES methods is too high, and the method is not realized for engineering application.
Disclosure of Invention
The invention provides a low-magnetic Reynolds number magnetic fluid turbulence analysis system and an analysis method based on an OpenFOAM platform, which can save a large amount of calculation time and calculation resources, and aims to solve the problems that in the prior art, an original kappa-omega model in an OpenFOAM turbulence model library cannot be suitable for calculation of magnetic fluid, and DNS and LES methods are adopted, so that the calculation economic cost is too high, and the engineering application is not realized.
In order to achieve the purpose, the invention adopts the following technical scheme:
low magnetism Reynolds number magnetic fluid turbulence analytic system based on OpenFOAM platform includes:
the pipeline physical model drawing module is used for drawing a pipeline physical model at present by using drawing software;
the grid information writing module is used for dividing grids by adopting a blockMesh command and writing grid information;
the system comprises a grid generation and boundary initial condition setting module, a grid generation and boundary initial condition setting module and a grid file generation and boundary setting module, wherein the grid generation and boundary initial condition setting module is used for importing a grid file into OpenFOAM software to generate a grid and setting a grid initial condition and a boundary condition;
the example setting and solving module is used for carrying out parameter setting on the turbulence model and solving flow field data by utilizing a solver;
and the post-processing module is used for drawing the solved data into a data graph and carrying out corresponding comparison.
The invention also provides a low-magnetic Reynolds number magnetic fluid turbulence analysis method based on the OpenFOAM platform, which comprises the following steps:
s1, drawing the pipeline physical model by using drawing software;
s2, dividing grids by adopting a blockMesh command and writing grid information;
s3, importing the grid file into OpenFOAM software to generate a grid and setting grid initial conditions and boundary conditions;
s4, establishing a turbulence model, setting parameters of the turbulence model and solving flow field data by using a solver;
and S5, drawing the solved data into a data graph and comparing the data graph with the data graph.
Preferably, step S1 includes the steps of:
s11, setting the x direction as the fluid flow direction and the y direction as the magnetic field direction; the wall vertical to the magnetic field direction is defined as a Hartmann wall, and the wall parallel to the magnetic field direction is defined as a parallel wall;
s12, drawing a pipeline physical model by using CAD software according to the set direction;
the coordinate origin is positioned at the lower left corner of the pipeline, a definition U represents the fluid flow direction, and a definition B represents the direction of an external magnetic field; the walls perpendicular to the direction of the magnetic field are denoted by Ha, which denotes the hartmann walls, and the Sh label denotes the parallel walls.
Preferably, in the process of step S2, the boundary grid needs to be further encrypted.
Preferably, in step S3, the mesh initial condition and boundary condition settings include an entrance setting, an exit setting, and a wall boundary setting.
Preferably, in step S4, the turbulence model equation is:
the kappa equation:
Figure BDA0003086740580000041
the ω equation:
Figure BDA0003086740580000042
wherein rho is the density of the magnetic fluid, kappa is the turbulent kinetic energy, u is the velocity vector, omega is the rate of converting the turbulent kinetic energy in unit time and unit volume into internal heat energy, mu is the dynamic viscosity, N represents the interaction parameter of the magnetic fluid, Re is the Reynolds number, Ha is the Hartmann number, sigma represents the conductivity of the magnetic fluid, B is an external magnetic field vertical to the wall surface direction, P is the external magnetic field vertical to the wall surface direction, andκrepresenting a turbulent kinetic energy generating term, τijRepresenting the Reynolds stress,
Figure BDA0003086740580000043
And
Figure BDA0003086740580000044
is an increased electromagnetic dissipation term;
Figure BDA0003086740580000045
Figure BDA0003086740580000046
Cα1＝5/9、Cβ1＝0.075、β*＝0.09、σk1＝2、σω1＝2、Prt＝0.9、
Figure BDA0003086740580000047
Cμ＝0.09、C3＝1.9exp(-N)、C4＝1.9exp(-2N)。
preferably, in step S4, the parameter setting on the turbulence model includes parameter setting on pressure, velocity, magnetic field and electric potential.
Preferably, in step S4, the process of solving the flow field data by using the solver includes setting parameters of a solver solving algorithm; the parameters of the solving algorithm include solving start/stop time, time step, output data parameters and discrete format.
Compared with the prior art, the invention has the beneficial effects that: (1) the electromagnetic dissipation term is added on the basis of a kappa-omega model equation through mathematical equation derivation, so that the aim of solving the magnetic fluid turbulence in the pipeline by adopting an RANS method is fulfilled; (2) compared with a standard kappa-omega model, the calculation results of the method in the parallel layer and the Hartmann layer are more consistent with the calculation results of the DNS; (3) compared with Direct Numerical Simulation (DNS), the method saves a large amount of computing time and computing resources, and is more economical.
Drawings
Fig. 1 is a flowchart of a method for analyzing turbulence of a low magnetic reynolds number magnetic fluid based on an OpenFOAM platform according to embodiment 1 of the present invention;
FIG. 2 is a model diagram of a physical model of a pipeline in example 1;
FIG. 3 is a schematic cross-sectional view of the lattice in example 1;
FIG. 4 is a velocity comparison graph of the center section in the z direction at the exit of the calculation results of example 1 and the calculation results of the DNS numerical simulation.
Detailed Description
In order to more clearly illustrate the embodiments of the present invention, the following description will explain the embodiments of the present invention with reference to the accompanying drawings. It is obvious that the drawings in the following description are only some examples of the invention, and that for a person skilled in the art, other drawings and embodiments can be derived from them without inventive effort.
Example 1:
low magnetism Reynolds number magnetic fluid turbulence analytic system based on OpenFOAM platform includes:
the pipeline physical model drawing module is used for drawing a pipeline physical model at present by using drawing software;
the grid information writing module is used for dividing grids by adopting a blockMesh command and writing grid information;
the system comprises a grid generation and boundary initial condition setting module, a grid generation and boundary initial condition setting module and a grid file generation and boundary setting module, wherein the grid generation and boundary initial condition setting module is used for importing a grid file into OpenFOAM software to generate a grid and setting a grid initial condition and a boundary condition;
the example setting and solving module is used for carrying out parameter setting on the turbulence model and solving flow field data by utilizing a solver;
and the post-processing module is used for drawing the solved data into a data graph and carrying out corresponding comparison.
As shown in fig. 1, the present invention further provides a method for analyzing turbulence of a low magnetic reynolds number magnetic fluid based on an OpenFOAM platform, comprising the following steps:
s1, drawing the pipeline physical model by using drawing software;
s2, dividing grids by adopting a blockMesh command and writing grid information;
s3, importing the grid file into OpenFOAM software to generate a grid and setting grid initial conditions and boundary conditions;
s4, establishing a turbulence model, setting parameters of the turbulence model and solving flow field data by using a solver;
and S5, drawing the solved data into a data graph and comparing the data graph with the data graph.
Further, as shown in fig. 2, step S1 includes the following steps:
s11, taking a physical model of the insulated pipeline as shown in FIG. 2, setting the x direction as the fluid flow direction and the y direction as the magnetic field direction, wherein the size of the square pipeline is 8 pi multiplied by 1 (dimensionless quantity); the wall vertical to the magnetic field direction is defined as a Hartmann wall, and the wall parallel to the magnetic field direction is defined as a parallel wall;
s12, drawing a pipeline model with the length of 25.12 in the x direction and the length of 1 in the y direction and the z direction respectively by using CAD software according to the set direction;
the coordinate origin is positioned at the lower left corner of the pipeline, a definition U represents the fluid flow direction, and a definition B represents the direction of an external magnetic field; the walls perpendicular to the direction of the magnetic field are denoted by Ha, which denotes the hartmann walls, and the Sh label denotes the parallel walls.
Further, in the process of step S2, the boundary mesh needs to be encrypted, so as to obtain a better numerical calculation result.
In step S2, the present embodiment uses a blockMesh command to divide grids, where the number of the grids is x y z: 256 × 80 × 80, total 1638400 grids. The specific settings in the blockmeshDict file are as follows:
Figure BDA0003086740580000061
Figure BDA0003086740580000071
Figure BDA0003086740580000081
Figure BDA0003086740580000091
Figure BDA0003086740580000101
wherein, verticals represents the coordinates of each point, blocks is the block information of the grid, hex is the vertex information in the block, and simplGrading is the extension rate of the direction.
In step S3, the blockmeshditct dictionary file in this embodiment may be written with the mesh information by using the information in step S2 or replacing the original blockmeshditct file with the file in step S2. The input mesh generation command blockMesh generates a mesh, and a cross-sectional view of the mesh is shown in fig. 3.
In addition, the initial condition and boundary condition setting cases are shown in the following table:
TABLE 1 grid initial conditions and boundary condition setup situation table
Figure BDA0003086740580000111
Where φ is the potential, Reynolds number Re 5681, Hartmann number Ha 21.2.
Further, in step S4, the turbulence model equation is:
the kappa equation:
Figure BDA0003086740580000112
the ω equation:
Figure BDA0003086740580000113
wherein rho is the density of the magnetic fluid, kappa is the turbulent kinetic energy, u is the velocity vector, omega is the rate of converting the turbulent kinetic energy in unit time and unit volume into internal heat energy, mu is the dynamic viscosity, N represents the interaction parameter of the magnetic fluid, Re is the Reynolds number, Ha is the HartMangan number, sigma, B is external magnetic field perpendicular to wall surface, PκRepresenting a turbulent kinetic energy generating term, τijRepresenting the Reynolds stress,
Figure BDA0003086740580000114
And
Figure BDA0003086740580000115
is an increased electromagnetic dissipation term;
Figure BDA0003086740580000116
Figure BDA0003086740580000121
Cα1＝5/9、Cβ1＝0.075、β*＝0.09、σk1＝2、σω1＝2、Prt＝0.9、
Figure BDA0003086740580000122
Cμ＝0.09、C3＝1.9exp(-N)、C4＝1.9exp(-2N)。
the turbulence model equation of the invention is improved on the basis of the original standard kappa-omega model for calculating the turbulence of the common fluid. Because different from common fluid, for the liquid cladding of the magnetic confinement fusion reactor, when liquid metal in the pipeline flows in a magnetic field, Lorentz force is generated, and MHD turbulence is controlled and influenced by electromagnetic dissipation effect in a Hartmann layer. Therefore, the turbulence model introduces an electromagnetic dissipation item on the basis of a kappa-omega model in an open source software OpenFOAM turbulence model library.
In step S4, we load the turbulence model of the present invention into the RAS turbulence model library of OpenFOAM for compilation and name KOmegaMHD model.
In order to facilitate the model to be called, a magnetofluid solver capable of calling any RANS turbulence model in OpenFOAM is developed on the basis of a turbulence DNS magnetofluid solver based on a PISO algorithm, and is named as MHDRASpisoFOAM, and part of core codes of the magnetofluid solver are shown as follows:
Figure BDA0003086740580000123
so far, after the turbulence model and the solver are developed, specific example setting is performed:
one basic file structure in OpenFOAM is divided into three classes: 0 file, constant file, system file. The 0 folder is mainly used for storing basic physical property parameter files such as pressure P, speed U and the like, and for magnetic fluid calculation examples, files such as a magnetic field B and an electric potential Elpot and the like can also be stored. The main function of the constant file is to store the mesh file and control the turbulence model. There is generally a dictionary file of TurbulenceProperties under the constant folder. Its role is to control the type of turbulence model used:
Laminar-No turbulence model was used
RASModel Using a Reynolds average model (RAS)
LESModel Using a Large vortex simulation (LES)
The model used based on the embodiment is RASModel, and the specific codes of the dictionary file of turbo ulenceproperties are as follows:
Figure BDA0003086740580000131
having selected RASModel, the KOmegaMHD model designed and compiled through in the present invention is next specified in the RASProperties file under the constant directory. The specific codes are as follows:
Figure BDA0003086740580000132
Figure BDA0003086740580000141
wherein the system folder is mainly used for setting parameters of a solving algorithm. Three important documents are mainly contained:
control Dict: for controlling the solving start/stop time, time step, and output data parameters, the specific control ditect file of this example is set as follows:
Figure BDA0003086740580000142
Figure BDA0003086740580000151
Figure BDA0003086740580000161
Figure BDA0003086740580000171
Figure BDA0003086740580000181
the fvSolution file contains matrix solver settings, residuals, and other algorithm controls, and the specific settings are as follows:
Figure BDA0003086740580000182
Figure BDA0003086740580000191
Figure BDA0003086740580000201
Figure BDA0003086740580000211
and after the calculation example is set, calling an MHDRASpisoFOAM solver to calculate.
In step S5, the present embodiment uses Origin software to draw a velocity profile of the cross section z direction at the center of the doorway and compares the velocity profile with the DNS method calculation result. Origin plotted data was taken from data collected using the sample tool. The information in the sampleDict dictionary file of the embodiment is as follows:
Figure BDA0003086740580000212
Figure BDA0003086740580000221
after the solution is completed, a sample related command is executed to generate a postProcessing folder, and the csv type data in the postProcessing folder is imported into the Origin generation line graph, and the result is shown in fig. 4.
The result shown in fig. 4 is a comparison of the velocity in the z-direction of the center cross-section at the exit calculated using the present invention and the velocity in the z-direction of the center cross-section at the exit calculated directly using the DNS method. From fig. 4, it is clear that the calculation results of the present invention are well consistent with the direct numerical simulation method.
The electromagnetic dissipation term is added on the basis of a kappa-omega model equation through mathematical equation derivation, so that the aim of solving the magnetic fluid turbulence in the pipeline by adopting an RANS method is fulfilled; compared with a standard kappa-omega model, the calculation results of the method in the parallel layer and the Hartmann layer are more consistent with the calculation results of the DNS; compared with Direct Numerical Simulation (DNS), the method saves a large amount of computing time and computing resources, and is more economical.
The foregoing has outlined rather broadly the preferred embodiments and principles of the present invention and it will be appreciated that those skilled in the art may devise variations of the present invention that are within the spirit and scope of the appended claims.

Claims (8)

1. Low magnetism reynolds number magnetic fluid torrent analytic system based on OpenFOAM platform, its characterized in that includes:
the pipeline physical model drawing module is used for drawing a pipeline physical model at present by using drawing software;
the grid information writing module is used for dividing grids by adopting a blockMesh command and writing grid information;
the system comprises a grid generation and boundary initial condition setting module, a grid generation and boundary initial condition setting module and a grid file generation and boundary setting module, wherein the grid generation and boundary initial condition setting module is used for importing a grid file into OpenFOAM software to generate a grid and setting a grid initial condition and a boundary condition;
the example setting and solving module is used for carrying out parameter setting on the turbulence model and solving flow field data by utilizing a solver;
and the post-processing module is used for drawing the solved data into a data graph and carrying out corresponding comparison.
2. The method for analyzing the turbulence of the low-magnetic Reynolds number magnetic fluid based on the OpenFOAM platform is characterized by comprising the following steps of:
s1, drawing the pipeline physical model by using drawing software;
s2, dividing grids by adopting a blockMesh command and writing grid information;
s3, importing the grid file into OpenFOAM software to generate a grid and setting grid initial conditions and boundary conditions;
s4, establishing a turbulence model, setting parameters of the turbulence model and solving flow field data by using a solver;
and S5, drawing the solved data into a data graph and comparing the data graph with the data graph.
3. The OpenFOAM platform-based low magnetic Reynolds number magnetic fluid turbulence analysis method of claim 2, wherein step S1 includes the steps of:
s11, setting the x direction as the fluid flow direction and the y direction as the magnetic field direction; the wall vertical to the magnetic field direction is defined as a Hartmann wall, and the wall parallel to the magnetic field direction is defined as a parallel wall;
s12, drawing a pipeline physical model by using CAD software according to the set direction;
the coordinate origin is positioned at the lower left corner of the pipeline, a definition U represents the fluid flow direction, and a definition B represents the direction of an external magnetic field; the walls perpendicular to the direction of the magnetic field are denoted by Ha, which denotes the hartmann walls, and the Sh label denotes the parallel walls.
4. The OpenFOAM platform-based low-magnetic Reynolds number magnetic fluid turbulence analysis method of claim 2, wherein in the step S2, the boundary mesh needs to be encrypted.
5. The OpenFOAM platform-based low magnetic Reynolds number magnetic fluid turbulence analysis method of claim 2, wherein in step S3, the initial grid conditions and boundary conditions include entrance settings, exit settings, and wall boundary settings.
6. The OpenFOAM platform-based low magnetic Reynolds number magnetic fluid turbulence analysis method of claim 2, wherein in step S4, the turbulence model equation is:
the kappa equation:
Figure FDA0003086740570000021
the ω equation:
Figure FDA0003086740570000022
wherein rho is the density of the magnetic fluid, kappa is the turbulent kinetic energy, u is the velocity vector, omega is the rate of converting the turbulent kinetic energy in unit time and unit volume into internal heat energy, mu is the dynamic viscosity, N represents the interaction parameter of the magnetic fluid, Re is the Reynolds number, Ha is the Hartmann number, and sigma represents the electrical conductance of the magnetic fluidRate, B is an external magnetic field perpendicular to the wall surface, PκRepresenting a turbulent kinetic energy generating term, τijRepresenting the Reynolds stress,
Figure FDA0003086740570000023
And
Figure FDA0003086740570000024
is an increased electromagnetic dissipation term;
Figure FDA0003086740570000025
Figure FDA0003086740570000026
Cα1＝5/9、Cβ1＝0.075、β*＝0.09、σk1＝2、σω1＝2、Prt＝0.9、
Figure FDA0003086740570000027
Cμ＝0.09、C3＝1.9exp(-N)、C4＝1.9exp(-2N)。
7. the OpenFOAM platform-based low magnetic Reynolds number magnetic fluid turbulence analysis method of claim 6, wherein in step S4, the parameter setting of the turbulence model includes parameter setting of pressure, velocity, magnetic field and electric potential.
8. The OpenFOAM platform-based low-magnetic Reynolds number magnetic fluid turbulence analysis method according to claim 7, wherein in step S4, the process of solving the flow field data by using a solver includes setting parameters of a solver solving algorithm; the parameters of the solving algorithm include solving start/stop time, time step, output data parameters and discrete format.
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相凯: "圆管磁流体管道流数值模拟研究", 《中国优秀硕士学位论文全文数据库 (工程科技Ⅱ辑)》 *
相凯: "圆管磁流体管道流数值模拟研究", 《中国优秀硕士学位论文全文数据库 (工程科技Ⅱ辑)》, 15 January 2019 (2019-01-15) *
谭忠权，毛洁，刘克: "磁流体管流的直接数值模拟研究", 《核聚变与等离子体物理》 *
谭忠权，毛洁，刘克: "磁流体管流的直接数值模拟研究", 《核聚变与等离子体物理》, 15 December 2016 (2016-12-15), pages 1 - 2 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114492220A (en) * 2021-11-23 2022-05-13 华北电力大学 OpenFOAM platform-based method and system for predicting flow characteristics of ocean atmospheric boundary layer

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