CN113792498A - FLUENT-based self-defined k-e turbulence model and initialization method - Google Patents

FLUENT-based self-defined k-e turbulence model and initialization method Download PDF

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CN113792498A
CN113792498A CN202110991326.5A CN202110991326A CN113792498A CN 113792498 A CN113792498 A CN 113792498A CN 202110991326 A CN202110991326 A CN 202110991326A CN 113792498 A CN113792498 A CN 113792498A
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苏峰华
庞宏垚
袁熙
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FOSHAN NANHAI LEITE AUTO PARTS CO LTD
South China University of Technology SCUT
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Abstract

The invention discloses a FLUENT-based customized k-e turbulence model and initialization method, which comprises the following steps: 1) selecting a turbulence model to be implanted and analyzing its components; 2) and determining the number of the scalar and the intermediate quantities in the transport equation set of the turbulence model. 3) Splitting a turbulent flow model transport equation set into four items: unsteady term + convection term + diffusion term + source term; 4) analyzing the characteristics of the source item and linearizing the source item; 5) determining a diffusion coefficient; 6) determining a calculation form of the flux; 7) defining an initialization physical quantity according to the characteristics of the turbulence model; 8) writing the above content into UDF and compiling into FLUENT; 9) setting a calculation case and solving, and repeating the steps if necessary until the calculation is converged. The k-e turbulence model is customized in FLUENT, and the initialization function is additionally constructed to accelerate the convergence of the calculation process, so that the method has an important reference meaning for defining other scalar transport equations.

Description

FLUENT-based self-defined k-e turbulence model and initialization method
Technical Field
The invention relates to the field of CFD two-equation turbulence models, in particular to a FLUENT-based self-defined k-e turbulence model and initialization method.
Background
In the field of CFD turbulence models, compared with models such as a Reynolds stress model and a large vortex simulation model, a k-e model is the most widely applied two-equation turbulence model at present and integrates factors in various aspects such as precision and calculation time. The high reynolds k-e model, which is effective only for the full development of turbulence, needs to be used with wall functions at the viscous bottom. In high Reynolds flow, a k-e model is used for carrying out numerical simulation on the circumfluence of a two-dimensional rectangular section column, data are well matched with documents, and the model has a good simulation result in the turbulence simulation of the two-dimensional long hair column (Wangshan, Dongyuyi, Duntai, Wandong bright-day, high Reynolds number lower two-dimensional rectangular section column circumfluence numerical simulation [ J ]. Huaqiao university bulletin (Nature science edition), 2018, 39 (1): 24-30). And the low Reynolds number model is corrected on the basis of the high Reynolds number model, the anisotropy of turbulence pulsation near the wall surface is considered, and source terms are respectively added into the k equation and the e equation. In the literature (NieXin, Zhang Yuzhou, Zhang Tongwei, Lilei, Xujiang Rong. 6 kinds of low Reynolds number k-e models are subjected to numerical simulation and comparative analysis in three-dimensional coanda shear flow [ J ] China Motor engineering reports, 2017, 37 (24): 7247-7255), six kinds of low Reynolds number k-e models are used for simulating the three-dimensional coanda shear flow, and the calculation accuracy of most of the low Reynolds number k-e models is considered to be improved in the simulation of the three-dimensional wall shear flow compared with the standard k-e model. However, the above studies are all based on the fluent default k-e turbulence model and cannot be modified. The default k-e model does not meet the requirements when the characteristics of other models need to be studied. It is desirable to provide a method for customizing k-e turbulence models to complement existing model libraries and facilitate special needs.
Disclosure of Invention
In order to solve the problems, the invention discloses a FLUENT-based customized k-e turbulence model and initialization method, which comprises the following steps:
a method for customizing and initializing a k-e turbulence model based on FLUENT, comprising the steps of:
s1, determining a control equation of the k-e turbulence model, and determining the number of scalar and intermediate quantities in a turbulence model transport equation set;
s3, according to the constitution of the control equation, the transport equation set of the turbulence model is divided into four standard terms: unsteady term + convection term + diffusion term + source term;
s4, judging whether a source item of the k equation contains a solution scalar, and if so, implicitly defining during linearization; if not, it is directly linearized.
S5, determining the calculation form of the diffusion coefficient and the flux;
s6, defining initialization physical quantity according to the characteristics of the turbulence model;
and S7, writing the content of the complaint into a user-defined function, loading the user-defined function to the corresponding position of FLUENT, setting a calculation case, and solving until the calculation is converged.
Preferably, the k-e turbulence model in step S1 is in the form of:
Figure BDA0003232415070000021
Figure BDA0003232415070000022
Figure BDA0003232415070000023
where k is the turbulent kinetic energy, epsilon is the turbulent dissipation ratio, rho is the density, t is the time, xi xjIs a Cartesian coordinate axis of orientation, uiAs velocity, μ is the kinetic viscosity, μtFor turbulent viscosity, G is the generation term of turbulent energy, f1、f2、fμIs a constant c1、c2、cμCorrection coefficient of σk、σεConstant D, E is a correction term, where k, ε are solution scalars and the rest are intermediate variables.
Preferably, in step S3, the source term of the turbulence energy k is μtG-rho epsilon-D, the source term for the turbulent dissipation factor epsilon
Figure BDA0003232415070000031
Preferably, the source term of the turbulence energy k is linearized as Sk＝Ak+Bkk, wherein Ak＝μtG-D，Bk＝-2ρ2cμfμk/μt(ii) a In the formula SkIs the source term of the turbulence energy k, AkIs a constant term in linearization, BkIs a linear first order term.
Linearization of the source term of the turbulent dissipation ratio ε to Sε＝Aε+BεEpsilon, wherein Aε＝E，Bε＝c1f1μtG/k-2ρc2f2ε/k. In the formula SεIs a source term for the turbulent dissipation ratio ε, AεIs a constant term in linearization, BεIs a linear first order term.
Preferably, in step S5, two diffusion coefficients are specified in a default _ diffivity macro command by using a switch case statement.
Preferably, the diffusion coefficients in the source terms of turbulence energy k and turbulence dissipation factor epsilon are respectively
Figure BDA0003232415070000032
Two diffusion coefficients are specified simultaneously with diffusion coefficient macro naming.
Preferably, the initialization physical quantity includes:
Figure BDA0003232415070000033
wherein u is+、k+、ε+、y+Is a dimensionless number, u isSpeed, y is the distance from the center of the grid to the wall surface, v is kinematic viscosity, τwIs wall friction, f is coefficient of friction, UbulckAverage inlet velocity according to u+、k+、ε+And y+The initial fields of u, k and epsilon are calculated according to the relationship and the friction coefficient.
Preferably, in step S7, the names and numbers of the user-defined scalar and the user-defined memory, and the intermediate variable f are defined in the enumeration bodyμ，f1，f2Writing as a return value is an integer function.
Preferably, user-defined functions are written for the k equation and the epsilon, names and numbers of user-defined scalars (UDS) and user-defined memories (UDM) and intermediate variables f are defined in an enumeration bodyμ，f1，f2Writing as a return value is an integer function. Other macrocommands are selected as desired.
Preferably, compiling a user-defined function, loading each macro command to a corresponding position of FLUENT, and setting corresponding numbers in a scalar and a memory; loading a case file, and selecting a standard k-e model and a standard wall function in a sticky panel; mounting various macro commands to corresponding positions; adjusting the relaxation factor of a user-defined scalar to be 0.6 in the control panel; the turbulence model equation is closed and only the flow and user-defined scalar equations are calculated.
Compared with the prior art, the invention has the advantages that:
(1) when the source term is linearized, the D term and the E term are processed into constants, epsilon is implicitly defined, and the coupling of two transport equations is increased;
(2) depending on the configuration of the k-e turbulence model, the k-e model may be implanted into FLUENT according to its own characteristics. In addition, the distribution of dimensionless physical quantity in circular tube turbulent flow is used as the initial value of different geometric model calculation, which is beneficial to accelerating the convergence of the calculation process;
(3) the method has important reference significance for constructing other scalar transport equations.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a flow chart of a method for customizing and initializing a k-e turbulence model based on FLUENT in accordance with an embodiment of the present invention;
FIG. 2 is a cloud diagram of a custom initialized velocity profile according to an embodiment of the present invention;
FIG. 3 is a comparison of velocity convergence curves at a point for uniform initialization and custom initialization in accordance with embodiments of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1:
a method for customizing and initializing a k-e turbulence model based on FLUENT, comprising the steps of:
s1, determining the form of a k-e turbulence model control equation, and defining the number of scalar and intermediate quantities in a turbulence model transport equation set; the k-e turbulence model control equation is of the form:
Figure BDA0003232415070000051
Figure BDA0003232415070000052
Figure BDA0003232415070000053
where k is the turbulent kinetic energy, epsilon is the turbulent dissipation ratio, rho is the density, t is the time, xi xjIs a Cartesian coordinate axis of orientation, uiAs velocity, μ is the kinetic viscosity, μtFor turbulent viscosity, G is the generation term of turbulent energy, f1、f2、fμIs a constant c1、c2、cμCorrection coefficient of σk、σεConstant D, E is a correction term, where k, ε are solution scalars and the rest are intermediate variables.
S3, according to the constitution of the control equation, the transport equation set of the turbulence model is divided into four standard terms: unsteady term + convection term + diffusion term + source term, where the source term of the turbulent kinetic energy k is μtG-rho epsilon-D, the source term for the turbulent dissipation factor epsilon
Figure BDA0003232415070000061
S4, judging whether a source item of the k equation contains a solution scalar e, and if so, implicitly defining e during linearization; if not, linearizing the sample directly;
preferably, the source term of the turbulence energy k is linearized as Sk＝Ak+Bkk, wherein Ak＝μtG-D，Bk＝-2ρ2cμfμk/μtIn the formula SkIs the source term of the k equation, AkIs a constant term in linearization, BkIs a linear first order term; linearization of the source term of the turbulent dissipation ratio ε to Sε＝Aε+BεEpsilon, wherein Aε＝E，Bε＝c1f1μtG/k-2ρc2f2ε/k, wherein SεIs the source term of the epsilon equation, AεIs a constant term in linearization, BεIs a linear first order term.
S5, determining the calculation form of the diffusion coefficient and the flux: two diffusion coefficients are specified in a DEFINE _ DIFFUSEVITY macro command simultaneously with a switch case statement.
S6, defining initialization physical quantity according to the characteristics of the turbulence model; the initialization physical quantity includes:
Figure BDA0003232415070000062
wherein u is+、k+、ε+、y+Is a dimensionless number, u is the velocity, y is the distance from the center of the grid to the wall, v is the kinematic viscosity, τwIs wall friction, f is coefficient of friction, UbulckAverage inlet velocity according to u+、k+、ε+And y+And (4) calculating initial fields of u, k and epsilon according to an empirical formula of the relationship and the friction coefficient f.
S7, writing and loading a user-defined function: defining the names and the numbers of user-defined scalars (UDS) and user-defined memories (UDM) in an enumeration body, and setting an intermediate variable fμ、f1、f2Writing as a function whose return value is integer, writing the contents of steps S1 to S6 as UDF and compiling into FLUENT. Other macrocommands are selected as desired.
S8, setting a calculation case and solving: loading each macro command to a corresponding position of FLUENT, and setting corresponding numbers in scalars and a memory; loading a case file, and selecting a standard k-e model and a standard wall function in a sticky panel; mounting various macro commands to corresponding positions; adjusting the relaxation factor of a user-defined scalar to be 0.6 in the control panel; the default turbulence model equations are closed and only the flow and k-e turbulence model equations are calculated.
And S9, repeating the steps if necessary until the calculation is converged.
Example 2:
a method for customizing and initializing a k-e turbulence model based on FLUENT, as shown in fig. 1, comprising the steps of:
s1, determining a k-e turbulence model equation as follows:
Figure BDA0003232415070000071
Figure BDA0003232415070000072
Figure BDA0003232415070000073
where k is the turbulence energy, epsilon is the turbulence energy, rho is the density, u is the velocityiIs dynamic viscosity,. mu.tFor turbulent viscosity, G is the generation term of turbulent energy, f1、f2、fμIs a constant c1、c2、cμCorrection coefficient of σk、σεIs constant and D, E is a correction term. The specific expression is
Figure BDA0003232415070000074
c1＝1.35，c2＝1.8，cμ＝0.09，σk＝1.0，σε＝1.3，f1＝1.0，
Figure BDA0003232415070000075
fμ＝1-exp(-0.002Ret)，
Figure BDA0003232415070000076
Figure BDA0003232415070000081
In the formula, RetIs the turbulent reynolds number and y is the distance from the center of the mesh to the wall.
And S2, determining scalar quantities to be solved in the k-e turbulence model, namely k and epsilon respectively, and obtaining intermediate variables in the rest.
And S3, splitting the transport equation into a standard form, wherein the unsteady term + convection term + diffusion term + source term. The source term of the turbulent kinetic energy k is mutG-rho epsilon-D, the source term for the turbulent dissipation factor epsilon
Figure BDA0003232415070000082
S4, linearization of source terms; linearization of the source term of the k equation to Sk＝Ak+Bkk, wherein Ak＝μtG-D，Bk＝-2ρ2cμfμk/μt. In the formula SkIs the source term of the k equation, AkIs a constant term in linearization, BkIs a linear first order term. Linearization of the source term of the epsilon equation to Sε＝Aε+BεEpsilon, wherein Aε＝E，Bε＝c1f1μtG/k-2ρc2f2ε/k. In the formula SεIs the source term of the epsilon equation, AεIs a constant term in linearization, BεIs a linear first order term.
The diffusion coefficients in the S5, k and ε transport equations are
Figure BDA0003232415070000083
Two diffusion coefficients were specified simultaneously with one UDF macro-name.
S6, the convection term is calculated from the mass flow rate, and there is no need to write UDF.
S7, taking the distribution of typical physical quantity in the circular tube turbulent flow as the initial value of calculation, and respectively having a viscous bottom layer and a logarithmic layer
y+When less than 5, u+＝y+；k+＝0.1y+2；ε+＝0.2；
y+When the pressure is higher than the pressure of the mixture,
Figure BDA0003232415070000084
f＝0.079Re-0.25
Figure BDA0003232415070000085
in the formula u+、k+、ε+、y+Is a dimensionless number, u is the velocity, y isThe distance from the center of the grid to the wall surface, v is kinematic viscosity, tauwIs wall friction, f is coefficient of friction, UbulckIs the inlet average velocity.
And S8, writing a user-defined function. Firstly, defining user-defined scalar k, epsilon and user-defined memory Re in enumeration bodyt、μt. According to the expression, f1、f2、fμWriting as a return value is an integer function. Writing diffusion item and source item macrocommands, and directly returning mu under the turbulent viscosity coefficient macrocommandt. Finally, the variables in the enumeration volume must be updated with an adjust macro command after each computation iteration.
And S9, importing the case file and calculating. Firstly, loading a user-defined function into FLUENT in a compiling mode, setting the number of the user-defined functions in a scalar to be 2, and setting the number of the user-defined functions in a memory to be 2. The case file is then loaded and the standard k-e model, the standard wall function, is selected in the sticky panel. And mounting various macro commands to corresponding positions, and adjusting the relaxation factor of the user-defined scalar to be 0.6 in the control panel. The default turbulence model equations are closed and only the flow and k-e turbulence model equations are calculated.
Example 3:
a method for customizing and initializing a k-e turbulence model based on FLUENT, as shown in fig. 1, comprising the steps of:
s1, taking a specific model as an example, the general equation is as follows:
Figure BDA0003232415070000091
Figure BDA0003232415070000092
Figure BDA0003232415070000093
where k is the turbulent kinetic energy, epsilon is the turbulent dissipation ratio, rho is the density, and t is timeM, xi xjIs a Cartesian coordinate axis of orientation, uiAs velocity, μ is the kinetic viscosity, μtFor turbulent viscosity, G is the generation term of turbulent energy, f1、f2、fμIs a constant c1、c2、cμCorrection coefficient of σk、σεIs constant and D, E is a correction term. The specific expression is
Figure BDA0003232415070000094
c1＝1.42，c2＝2，cμ＝0.09，σk＝0.9，σε＝1.4，f1＝1.0，
Figure BDA0003232415070000095
fμ＝[1-exp(-0.02Rey)]2(1+20.5/Ret)，
Figure BDA0003232415070000101
In the formula, RetIs the turbulent Reynolds number, ReyIs the local velocity scalar and y is the distance from the center of the mesh to the wall.
Where k is the turbulent kinetic energy, epsilon is the turbulent dissipation ratio, rho is the density, t is the time, xi xjIs a Cartesian coordinate axis of orientation, uiAs velocity, μ is the kinetic viscosity, μtFor turbulent viscosity, G is the generation term of turbulent energy, f1、f2、fμIs a constant c1、c2、cμCorrection coefficient of σk、σεConstant D, E is a correction term, where k, ε are solution scalars and the rest are intermediate variables.
The principle and the implementation mode of the invention are explained by applying a specific example, and the description of the embodiment is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A method for customizing and initializing a k-e turbulence model based on FLUENT is characterized by comprising the following steps:
s1, determining a control equation of the k-e turbulence model, and determining the number of scalar and intermediate quantities in a turbulence model transport equation set;
s3, according to the constitution of the control equation, the transport equation set of the turbulence model is divided into four standard terms: unsteady term + convection term + diffusion term + source term;
s4, judging whether a source item of the k equation contains a solution scalar, and if so, implicitly defining the scalar during linearization; if not, linearizing the scalar;
s5, determining the calculation form of the diffusion coefficient and the flux;
s6, defining initialization physical quantity according to the characteristics of the turbulence model;
and S7, writing the contents into a user-defined function, loading the user-defined function into FLUENT, setting a calculation case, and solving until calculation is converged.
2. The FLUENT-based custom k-e turbulence model-based initialization method of claim 1, wherein the k-e turbulence model has a control equation of the form:
Figure FDA0003232415060000011
Figure FDA0003232415060000012
Figure FDA0003232415060000013
where k is the turbulent kinetic energy, epsilon is the turbulent dissipation ratio, rho is the density, t is the time, xi、xjIs a Cartesian coordinate axis of orientation, uiAs velocity, μ is the kinetic viscosity, μtFor turbulent viscosity, G is the generation term of turbulent energy, f1、f2、fμIs a constant c1、c2、cμCorrection coefficient of σk、σεConstant D, E is a correction term, where k, ε are solution scalars and the rest are intermediate variables.
3. The FLUENT-based custom k-e turbulence model-based initialization method of claim 2, wherein in step S3, the source term of turbulence energy k is μtG-rho epsilon-D, the source term for the turbulent dissipation factor epsilon
Figure FDA0003232415060000021
4. The FLUENT-based custom k-e turbulence model-based initialization method of claim 2, wherein the source term of turbulence energy k is linearized as Sk＝Ak+Bkk, wherein Ak＝μtG-D，Bk＝-2ρ2cμfμk/μt(ii) a In the formula SkIs the source term of the turbulence energy k, AkIs a constant term in linearization, BkIs a linear first order term.
5. The FLUENT-based custom k-e turbulence model-based initialization method of claim 4, wherein a source term of a turbulence dissipation ratio ε is linearized by Sε＝Aε+BεEpsilon, wherein Aε＝E，Bε＝c1f1μtG/k-2ρc2f2ε/k, wherein SεIs a source term for the turbulent dissipation ratio ε, AεIs a constant term in linearization, BεIs a linear first order term.
6. The FLUENT-BASED SELF-DEFINED K-E TURBINE MODEL INITIATION METHOD OF claim 1, wherein the step S5 uses switch case statement to specify two diffusion coefficients in a DEFINE _ DIFFUSEVITY macrocommand at the same time.
7. The FLUENT-based custom k-e turbulence model-based initialization method of claim 2, wherein the diffusion coefficients in the source terms of turbulence energy k and turbulence dissipation ratio ε are respectively
Figure FDA0003232415060000022
Two diffusion coefficients are specified simultaneously with diffusion coefficient macro naming.
8. The FLUENT-based custom k-e turbulence model and initialization method of claim 5, wherein the initializing physical quantities comprises:
Figure FDA0003232415060000031
wherein u is+、k+、ε+、y+Is a dimensionless number, u is the velocity, y is the distance from the center of the grid to the wall, v is the kinematic viscosity, τwIs wall friction, f is coefficient of friction, UbulckAverage inlet velocity according to u+、k+、ε+And y+The initial fields of u, k and epsilon are calculated according to the relation and the friction coefficient f.
9. The FLUENT-BASED AND FUSED K-E TURBINE MODEL INITIALIZATION METHOD OF claim 2, wherein in step S7, names and numbers of user-defined scalar and user-defined memory, and the intermediate variable f are defined in an enumeration volumeμ、f1、f2Writing as a return value is an integer function.
10. The FLUENT-based custom k-e turbulence model-based initialization method according to any one of claims 1 to 9, wherein step S7 includes setting a corresponding number in scalar and memory; loading a case file, and selecting a standard k-e model and a standard wall function in a sticky panel; mounting various macro commands to corresponding positions; adjusting the relaxation factor of a user-defined scalar to be 0.6 in the control panel; the turbulence model equation is closed and only the flow and user-defined scalar equations are calculated.
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