CN114611438B - Method and device for simulating stress state of target object in turbulent flow - Google Patents

Method and device for simulating stress state of target object in turbulent flow Download PDF

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CN114611438B
CN114611438B CN202210506807.7A CN202210506807A CN114611438B CN 114611438 B CN114611438 B CN 114611438B CN 202210506807 A CN202210506807 A CN 202210506807A CN 114611438 B CN114611438 B CN 114611438B
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CN114611438A (en
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闵耀兵
马燕凯
陈坚强
吴文昌
燕振国
赵钟
朱华君
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Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
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Abstract

The embodiment of the invention provides a method and a device for simulating the stress state of a target object in turbulent flow, wherein the method comprises the following steps: iteratively solving a flow control equation and a turbulence model equation based on a grid derivative and a grid jacoby of a body structure grid of the target object, and obtaining a target flow field variable after an iterative process is converged; integrating the target flow field variable to obtain a stress state simulation result of the target object in a turbulent flow state; in the scheme, the flow control equation and the turbulence model equation are solved in a synchronous iteration mode until the stress state simulation result in the turbulence state is obtained after convergence, and the simulation precision in the turbulence state is improved.

Description

Method and device for simulating stress state of target object in turbulent flow
Technical Field
The embodiment of the invention relates to the technical field of computer fluid mechanics, in particular to a method and a device for simulating a stress state of a target object in turbulent flow.
Background
Computational Fluid Dynamics (CFD) refers to a computer that performs numerical calculations to simulate various physical phenomena related to Fluid flow, including flow, heat conduction, and sound field. Computational fluid dynamics analysis is widely used in many engineering fields such as aerospace design, automotive design, biomedical industry, chemical processing industry, turbine design, semiconductor design, and the like.
The fluid flow conditions in nature are mainly two forms, namely laminar flow and turbulent flow (or turbulent flow). Laminar flow means that the fluids do not intermingle with each other during flow, while turbulent flow means that the fluids are not in a laminar flow regime. Generally speaking, turbulent flow is common, while laminar flow is among the individual cases. The turbulence phenomenon is highly complex, and numerical simulation of a turbulence model by using CFD also faces the problem of poor simulation accuracy.
Disclosure of Invention
The embodiment of the invention aims to provide a method and a device for simulating a stress state of a target object in turbulent flow, so as to improve the simulation precision in the turbulent flow state.
In order to achieve the above object, an embodiment of the present invention provides a method for simulating a stress state of a target in a turbulent flow, including:
generating a body-fitted structure grid of the target object;
calculating a grid derivative and a grid jacobian of the body structure grid;
iteratively solving a flow control equation and a turbulence model equation based on the grid derivative and the grid Jacobian; the solution result of the turbulence model equation comprises a turbulence viscosity coefficient, the flow control equation is updated according to the turbulence viscosity coefficient, and the solution result of the flow control equation comprises a flow field variable;
obtaining a target flow field variable after the iterative process is converged;
and integrating the target flow field variable to obtain a stress state simulation result of the target object in a turbulent flow state.
Optionally, calculating a grid derivative of the skin structure grid includes:
calculating a grid derivative of the lattice of the skin structure using the following equation:
Figure 594464DEST_PATH_IMAGE001
Figure 947822DEST_PATH_IMAGE002
Figure 524297DEST_PATH_IMAGE003
where ξ, η, ζ denote three different directions, respectively, and x, y, z denote different components in each direction, respectively.
Optionally, calculating a grid jacobian of the skin structure grid includes:
calculating the grid jacobian of the skin structure grid by using the following formula:
Figure 591610DEST_PATH_IMAGE004
where ξ, η, and ζ represent three different directions, respectively, and x, y, and z represent different components in each direction, respectively.
Optionally, the iteratively solving a flow control equation and a turbulence model equation based on the grid derivative and the grid jacobian includes:
based on the grid derivative and the grid Jacobian, solving a flow control equation in a finite difference high-order precision numerical discrete format, and simulating a mixed turbulence model equation in a non-constant high-order precision numerical simulation mode; and updating the flow control equation according to the turbulence viscosity coefficient included in the solution result of the turbulence model equation, and then returning to the step of solving the flow control equation in the finite difference high-order precision numerical discrete format until the iterative process converges.
Optionally, the solving the flow control equation in the finite difference high-order precision numerical discrete format includes:
discretizing a flow control equation under a calculation coordinate system by adopting a high-order precision finite difference format as follows:
Figure 78086DEST_PATH_IMAGE005
Figure 838232DEST_PATH_IMAGE006
wherein the content of the first and second substances,
Figure 541483DEST_PATH_IMAGE007
the numerical flux of the grid nodes is represented,
Figure 412488DEST_PATH_IMAGE008
representing half-nodes
Figure 878104DEST_PATH_IMAGE009
The flux of the numerical value of (a),
Figure 543572DEST_PATH_IMAGE010
representing half-nodes
Figure 970005DEST_PATH_IMAGE011
The flux of the numerical value of (a),
Figure 166672DEST_PATH_IMAGE012
representing half-nodes
Figure 362162DEST_PATH_IMAGE013
The flux of the numerical value of (a),
Figure 323164DEST_PATH_IMAGE014
representing half-nodes
Figure 236894DEST_PATH_IMAGE015
The flux of the numerical value of (a),
Figure 184121DEST_PATH_IMAGE016
representing half-nodes
Figure 358751DEST_PATH_IMAGE017
The flux of the numerical value of (a),
Figure 864556DEST_PATH_IMAGE018
representing half-nodes
Figure 265581DEST_PATH_IMAGE019
The flux of the numerical value of (a),
Figure 141134DEST_PATH_IMAGE020
is a set value, and is used as a starting point,
Figure 311215DEST_PATH_IMAGE021
respectively representing half-nodes
Figure 754966DEST_PATH_IMAGE009
Left and right flow field variables of (d).
Optionally, the numerically simulating the mixed turbulence model equation with unsteady high-order precision includes:
solving the control equation of the turbulence model as follows:
Figure 876243DEST_PATH_IMAGE022
Figure 289907DEST_PATH_IMAGE023
wherein, the first and the second end of the pipe are connected with each other,
Figure 314495DEST_PATH_IMAGE024
the density is expressed as a function of time,
Figure 929147DEST_PATH_IMAGE025
the component of the velocity is represented by,
Figure 163819DEST_PATH_IMAGE026
a component of the viscous stress is represented,
Figure 256540DEST_PATH_IMAGE027
which represents the coefficient of viscosity of the molecule,
Figure 899749DEST_PATH_IMAGE028
which is indicative of the viscosity coefficient of the turbulent flow,
Figure 544357DEST_PATH_IMAGE029
the transition function is represented by a transition function,
Figure 141691DEST_PATH_IMAGE029
the value of the turbulent kinetic energy in the boundary layer of the wall surface tends to 1, the value of the turbulent kinetic energy in the region far away from the wall surface returns to 0, omega represents the dissipation rate of the turbulent kinetic energy, and x represents the dissipation rate of the turbulent kinetic energyjRepresenting the coordinate component under the rectangular coordinate system, and k represents the turbulence energy; other model constants
Figure 38103DEST_PATH_IMAGE030
The expression is as follows:
Figure 771704DEST_PATH_IMAGE031
Figure 852792DEST_PATH_IMAGE032
Figure 435958DEST_PATH_IMAGE033
Figure 136061DEST_PATH_IMAGE034
wherein y represents the wall surface distance,
Figure 989747DEST_PATH_IMAGE035
and
Figure 710579DEST_PATH_IMAGE036
respectively representing model constants
Figure 282506DEST_PATH_IMAGE037
And
Figure 19255DEST_PATH_IMAGE038
；
calculating the turbulence viscosity coefficient of the superlarge vortex simulation according to the following expression:
Figure 117661DEST_PATH_IMAGE039
wherein, FrRepresenting a resolution control function, FrBased on the correlation between the three characteristic length scales of turbulence, FrThe expression of (c) is as follows:
Figure 150339DEST_PATH_IMAGE040
Figure 943983DEST_PATH_IMAGE041
Figure 110522DEST_PATH_IMAGE042
β* 1and CxRepresenting the model constant, n is a fixed constant, v represents the kinematic viscosity coefficient,
Figure 407642DEST_PATH_IMAGE043
representing the turbulence integral length scale and,
Figure 375336DEST_PATH_IMAGE044
representing the turbulence filter length scale and,
Figure 780910DEST_PATH_IMAGE045
representing a turbulent dissipation length scale.
In order to achieve the above object, an embodiment of the present invention further provides a device for simulating a stress state of an object in turbulent flow, including:
the generating module is used for generating a body-fitted structure grid of the target object;
the first calculation module is used for calculating a grid derivative of the skin structure grid;
the second calculation module is used for calculating the grid jacobian of the body structure grid;
the solving module is used for iteratively solving a flow control equation and a turbulence model equation based on the grid derivative and the grid Jacobian; the solving result of the turbulence model equation comprises a turbulence viscosity coefficient, the flow control equation is updated according to the turbulence viscosity coefficient, and the solving result of the flow control equation comprises a flow field variable; obtaining a target flow field variable after the iterative process is converged;
and the integration module is used for integrating the target flow field variable to obtain a stress state simulation result of the target object in a turbulent flow state.
Optionally, the first calculating module is specifically configured to:
calculating a grid derivative of the lattice of the skin structure using the following equation:
Figure 626506DEST_PATH_IMAGE001
Figure 309291DEST_PATH_IMAGE002
Figure 949351DEST_PATH_IMAGE003
where ξ, η, ζ denote three different directions, respectively, and x, y, z denote different components in each direction, respectively.
Optionally, the second calculating module is specifically configured to:
calculating the grid jacobian of the body structure grid by using the following formula:
Figure 576641DEST_PATH_IMAGE004
where ξ, η, ζ denote three different directions, respectively, and x, y, z denote different components in each direction, respectively.
Optionally, the solving module is specifically configured to:
based on the grid derivative and the grid Jacobian, solving a flow control equation in a finite difference high-order precision numerical discrete format, and simulating a mixed turbulence model equation in a unsteady high-order precision numerical simulation mode; and updating the flow control equation according to the turbulence viscosity coefficient included in the solution result of the turbulence model equation, and then returning to the step of solving the flow control equation in the finite difference high-order precision numerical discrete format until the iterative process converges.
By applying the embodiment of the invention, based on the grid derivative and the grid Jacobian of the body structure grid of the target object, the flow control equation and the turbulence model equation are solved iteratively, and the target flow field variable is obtained after the iterative process is converged; integrating the target flow field variable to obtain a stress state simulation result of the target object in a turbulent flow state; in the scheme, the flow control equation and the turbulence model equation are solved in a synchronous iteration mode until the stress state simulation result in the turbulence state is obtained after convergence, and the simulation precision in the turbulence state is improved.
Of course, not all of the advantages described above need to be achieved at the same time in the practice of any one product or method of the invention.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the prior art descriptions will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 is a schematic flow chart of a method for simulating a stress state of a target in a turbulent flow according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a device for simulating a stress state of a target in a turbulent flow according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of an electronic device according to an embodiment 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 from the embodiments of the present invention by those skilled in the art based on the description, are within the scope of the present invention.
Interpretation of terms:
NS equation: the Navier-Stokes equation is a fluid dynamics control equation set consisting of mass conservation, momentum conservation and energy conservation.
Flow field variables: the general term for physical variables in a flow such as density, velocity, pressure, temperature, etc.
CFD: computational Fluid Dynamics, a discipline that uses numerical discrete flow control equations to arrive at an approximate solution to the physical flow problem.
RANS: Reynolds-Averaged Navier-Stokes, Reynolds average NS equation, a time-Averaged NS equation. RANS simulation generally refers to a numerical simulation method for solving a turbulent flow problem by using an NS equation based on time averaging and a turbulence model closed equation.
And (3) LES: large Eddy Simulation generally refers to a numerical Simulation method for solving a turbulent flow problem based on a filtered NS equation with a sub-lattice model.
DES: the basic idea of the method is to adopt RANS Simulation in a near-wall area and adopt LES Simulation in a far-wall area, and generally modify a sub-lattice model similar to that in LES on the turbulence model based on the RANS Simulation.
DDES: delayed DES, Delayed separation vortex simulation, an improved model of DES simulation.
IDDES: improved DDES, a further Improved model of DDES simulation.
An equation SA model: an SA (Spalart-almaras) turbulence model containing only one equation of the variable to be solved.
SST model of two equations: there are two variables to be solved and two equations of the Shear Stress Transport (SST) turbulence model.
Second-order precision dispersion: the precision of the spatial discrete format is a numerical discrete method of second order, and the currently mainstream spatial discrete method is also a numerical discrete method commonly adopted by most commercial software.
High-order precision dispersion: the precision of the spatial discrete format is a numerical discrete method of three or more orders, and compared with the second-order precision discrete, the spatial discrete precision is higher, and the resolution of the flow field details is also better.
WCNS: weighted Compact Nonlinear schema (Weighted Compact Nonlinear Format).
DNS: direct Numerical Simultaion, Direct Numerical simulation.
In order to achieve the above object, embodiments of the present invention provide a method and an apparatus for simulating a stress state of a target object in a turbulent flow, where the method and the apparatus may be applied to various electronic devices, and are not limited specifically. First, a method for simulating a stress state of an object in the turbulent flow will be described in detail. The steps in the following method embodiments may be executed in a logical order, and the order of the steps may be referred to by step numbers or by steps, and the execution order of the steps is not limited.
Fig. 1 is a schematic flow chart of a method for simulating a stress state of a target in a turbulent flow according to an embodiment of the present invention, including:
s101: generating a body structure grid of the target object.
For example, the target object may be an aircraft, a vehicle, or the like, and is not limited in particular. A body-fitted structural grid can be generated around the shape of the target object, and the multi-block butt joint structural grid is used for realizing the full coverage of a flow field with a complex shape. The multiple skin butt joint structure grids can facilitate the numerical simulation of the flow problem by adopting a finite difference high-order precision numerical format in the follow-up process.
S102: and calculating the grid derivative and the grid Jacobian of the body structure grid.
In an embodiment of the present invention, calculating a grid derivative of the lattice of the skin structure may include:
calculating a grid derivative of the lattice of the skin structure using the following equation:
Figure 458884DEST_PATH_IMAGE001
Figure 996176DEST_PATH_IMAGE002
Figure 666192DEST_PATH_IMAGE003
where ξ, η, and ζ represent three different directions, respectively, and x, y, and z represent different components in each direction, respectively.
In an embodiment of the present invention, calculating a grid jacobian of the skin structure grid may include:
calculating the grid jacobian of the skin structure grid by using the following formula:
Figure 921724DEST_PATH_IMAGE004
where ξ, η, ζ denote three different directions, respectively, and x, y, z denote different components in each direction, respectively.
In a finite difference discrete frame, a flow control equation in a rectangular coordinate system needs to be converted into a calculation coordinate system, the calculation of a grid derivative of a structural grid and a grid transformation Jacobian is involved in a coordinate conversion process, and in order to improve the adaptability of a high-order precision finite difference format to a complex appearance, the discrete detailed solutions of the grid derivative and the grid transformation Jacobian in the finite difference format are as follows:
the flow control equation in the rectangular coordinate system can be expressed as:
Figure 843544DEST_PATH_IMAGE046
where Q is the flow field variable to be solved and E, F and G are both functions on Q. When finite difference dispersion is carried out in a plurality of body-attached butt joint structural grids, the finite difference dispersion is required to be converted into a calculation coordinate system, and the calculation coordinate system is established
Figure 625555DEST_PATH_IMAGE047
And rectangular coordinate system
Figure 105952DEST_PATH_IMAGE048
The one-to-one corresponding transformation relationship is as follows:
the expression of the flow control equation in the calculation coordinate system is as follows:
Figure 583201DEST_PATH_IMAGE049
wherein:
in a stationary grid (
Figure 433346DEST_PATH_IMAGE050
) Derivative of the middle gridIs defined mathematically as:
Figure 945229DEST_PATH_IMAGE051
Figure 97993DEST_PATH_IMAGE052
Figure 921593DEST_PATH_IMAGE053
wherein the subscripts denote partial derivatives, e.g.
Figure 949329DEST_PATH_IMAGE054
Representing coordinates
Figure 315720DEST_PATH_IMAGE055
For the calculation of coordinates
Figure 639385DEST_PATH_IMAGE056
The partial derivative of the orientation, and the mathematical definition of the grid transformation jacobian, are:
Figure 215860DEST_PATH_IMAGE057
in order to strictly satisfy the geometric conservation law and accurately reflect the geometric characteristics of the computational grid, the embodiment of the invention adopts the following computational form of symmetric conservation of grid derivatives:
Figure 283173DEST_PATH_IMAGE001
Figure 2605DEST_PATH_IMAGE002
Figure 887384DEST_PATH_IMAGE003
and, the following symmetric conservation calculation form of grid transformation Jacobian is adopted:
Figure 826521DEST_PATH_IMAGE004
in the above formula, ξ, η, and ζ represent three different directions, respectively, x, y, and z represent different components in each direction,
Figure 431946DEST_PATH_IMAGE058
and
Figure 631983DEST_PATH_IMAGE059
respectively representing time variables in a rectangular coordinate system and a calculation coordinate system.
S103: based on the grid derivatives and the grid jacobian, a flow control equation and a turbulence model equation are iteratively solved.
The solving result of the turbulence model equation comprises a turbulence viscosity coefficient, the flow control equation is updated according to the turbulence viscosity coefficient, and the solving result of the flow control equation comprises a flow field variable.
In an embodiment of the present invention, S103 may include: based on the grid derivative and the grid Jacobian, solving a flow control equation in a finite difference high-order precision numerical discrete format, and simulating a mixed turbulence model equation in a unsteady high-order precision numerical simulation mode; and updating the flow control equation according to a turbulence viscosity coefficient included in a solving result of the turbulence model equation, and then returning to the step of solving the flow control equation in a finite difference high-order precision numerical discrete format until the iterative process converges.
In one embodiment of the present invention, solving the flow control equation in a finite-difference high-order-precision numerical discrete format may include:
discretizing a flow control equation under a calculation coordinate system by adopting a high-order precision finite difference format as follows:
Figure 563030DEST_PATH_IMAGE005
Figure 487999DEST_PATH_IMAGE006
wherein the content of the first and second substances,
Figure 756169DEST_PATH_IMAGE007
representing the flux of the values of the grid nodes,
Figure 951658DEST_PATH_IMAGE008
representing half-nodes
Figure 53606DEST_PATH_IMAGE009
The flux of the numerical value of (a),
Figure 701757DEST_PATH_IMAGE010
representing half-nodes
Figure 773618DEST_PATH_IMAGE011
The flux of the value of (a) is,
Figure 587728DEST_PATH_IMAGE012
representing half-nodes
Figure 594998DEST_PATH_IMAGE013
The flux of the numerical value of (a),
Figure 120657DEST_PATH_IMAGE014
representing half-nodes
Figure 605996DEST_PATH_IMAGE015
The flux of the numerical value of (a),
Figure 776078DEST_PATH_IMAGE016
representing half-nodes
Figure 78883DEST_PATH_IMAGE017
The flux of the numerical value of (a),
Figure 465740DEST_PATH_IMAGE018
representing half-nodes
Figure 754770DEST_PATH_IMAGE019
The flux of the value of (a) is,
Figure 903991DEST_PATH_IMAGE020
is a set value, and is used as a starting point,
Figure 518643DEST_PATH_IMAGE021
respectively representing half-nodes
Figure 628682DEST_PATH_IMAGE009
Left and right flow field variables of (d).
Figure 580457DEST_PATH_IMAGE020
The specific value of (b) is not limited, and may be, for example, 1.
In one embodiment of the present invention, numerically simulating the mixed turbulence model equation with unsteady high-order precision may include:
solving the control equation of the turbulence model as follows:
Figure 223666DEST_PATH_IMAGE022
Figure 743640DEST_PATH_IMAGE023
wherein the content of the first and second substances,
Figure 200029DEST_PATH_IMAGE024
the density is expressed as a function of time,
Figure 96441DEST_PATH_IMAGE025
the component of the velocity is represented by,
Figure 95621DEST_PATH_IMAGE026
a component of the viscous stress is represented,
Figure 911131DEST_PATH_IMAGE027
which represents the coefficient of viscosity of the molecule,
Figure 494296DEST_PATH_IMAGE028
which is indicative of the viscosity coefficient of the turbulent flow,
Figure 663241DEST_PATH_IMAGE029
the transition function is represented by a transition function,
Figure 641561DEST_PATH_IMAGE029
the value of the turbulent kinetic energy in the boundary layer of the wall surface tends to 1, the value of the turbulent kinetic energy in the region far away from the wall surface returns to 0, omega represents the dissipation rate of the turbulent kinetic energy, and x represents the dissipation rate of the turbulent kinetic energyjExpressing the coordinate component under the rectangular coordinate system, and k expressing the turbulence energy; rest model constants
Figure 768917DEST_PATH_IMAGE030
The expression is as follows:
Figure 340844DEST_PATH_IMAGE031
Figure 438113DEST_PATH_IMAGE032
Figure 668278DEST_PATH_IMAGE033
Figure 966536DEST_PATH_IMAGE034
wherein, y represents the wall surface distance,
Figure 25759DEST_PATH_IMAGE035
and
Figure 926718DEST_PATH_IMAGE036
respectively representing model constants
Figure 754997DEST_PATH_IMAGE037
And
Figure 457112DEST_PATH_IMAGE038
；
calculating the turbulence viscosity coefficient of the super-large vortex simulation according to the following expression:
Figure 862685DEST_PATH_IMAGE039
wherein, FrRepresenting a resolution control function, FrEstablishing according to the interrelation among three turbulence characteristic length scales, FrThe expression of (c) is as follows:
Figure 708282DEST_PATH_IMAGE040
Figure 391067DEST_PATH_IMAGE041
Figure 890181DEST_PATH_IMAGE042
β* 1and CxRepresenting the model constant, n is a fixed constant, v represents the kinematic viscosity coefficient,
Figure 658417DEST_PATH_IMAGE043
representing the integral length scale of the turbulence,
Figure 275081DEST_PATH_IMAGE044
representing the turbulence filter length scale and,
Figure 937006DEST_PATH_IMAGE045
representing the turbulent dissipation length scale.
For example, in the embodiment of the present invention, the discrete solution process of the flow control equation may be mainly divided into two steps, which are respectively the solution of the flow control equation (also referred to as flow conservation law control equation) and the solution of the turbulence model equation in the calculation coordinate system, and are respectively described as follows:
(1) and solving the flow control equation. Dispersing the flow control equation under the calculation coordinate system by adopting a high-order precision finite difference format as follows:
Figure 747968DEST_PATH_IMAGE005
Figure 3500DEST_PATH_IMAGE006
wherein the content of the first and second substances,
Figure 784374DEST_PATH_IMAGE007
representing the flux of the values of the grid nodes,
Figure 441751DEST_PATH_IMAGE008
representing half-nodes
Figure 922149DEST_PATH_IMAGE009
The flux of the value of (a) is,
Figure 524031DEST_PATH_IMAGE010
representing half-nodes
Figure 249542DEST_PATH_IMAGE011
The flux of the numerical value of (a),
Figure 761426DEST_PATH_IMAGE012
representing half-nodes
Figure 914190DEST_PATH_IMAGE013
The flux of the value of (a) is,
Figure 908428DEST_PATH_IMAGE014
representing half-nodes
Figure 437630DEST_PATH_IMAGE015
The flux of the value of (a) is,
Figure 928654DEST_PATH_IMAGE016
representing half-nodes
Figure 986740DEST_PATH_IMAGE017
The flux of the value of (a) is,
Figure 704160DEST_PATH_IMAGE018
representing half-nodes
Figure 896107DEST_PATH_IMAGE019
The flux of the numerical value of (a),
Figure 615539DEST_PATH_IMAGE020
is a set value, and is used as a setting value,
Figure 110105DEST_PATH_IMAGE021
respectively representing half-nodes
Figure 173876DEST_PATH_IMAGE009
Left and right flow field variables of (d).
Figure 779301DEST_PATH_IMAGE020
The specific value of (b) is not limited, and may be, for example, 1.
For example, there are various methods for calculating the numerical flux of half-nodes, for example, the Roe flux calculation method can be used, which can be expressed as:
Figure 120284DEST_PATH_IMAGE060
a denotes a Roe average matrix and,
Figure 549866DEST_PATH_IMAGE021
respectively representing half-nodes
Figure 835354DEST_PATH_IMAGE009
Left and right flow field variables of (d).
In one case, the Weighted Compact Nonlinear format fifth order Nonlinear difference value can be obtained by WCNS (Weighted Compact Nonlinear Scheme)
Figure 244469DEST_PATH_IMAGE021
Alternatively, in another case, for the calculation of the flow field without interruption, the explicit linear difference value can be used
Figure 439959DEST_PATH_IMAGE021
：
Figure 135382DEST_PATH_IMAGE061
Figure 49111DEST_PATH_IMAGE062
(2) And (5) solving a turbulence model equation. The embodiment of the invention can adopt a super-large vortex simulation method, which is a newly developed RANS/LES mixed turbulence simulation method, fully considers the multi-scale effect in turbulence flow, realizes the self-adaptive resolution solution of a turbulence local flow field by building a resolution control function depending on different turbulence length scales, and has the characteristics of good universality, accuracy and robustness. Based on two equations
Figure 760453DEST_PATH_IMAGE063
The super-large vortex simulation method of the turbulence model comprises the following specific implementation steps:
(a) solving for
Figure 669503DEST_PATH_IMAGE063
Control equation for the turbulence model:
Figure 942353DEST_PATH_IMAGE022
Figure 77799DEST_PATH_IMAGE023
wherein the content of the first and second substances,
Figure 218930DEST_PATH_IMAGE024
the density is expressed as a function of time,
Figure 123433DEST_PATH_IMAGE025
the component of the velocity is represented by,
Figure 800139DEST_PATH_IMAGE026
a component of the viscous stress is represented,
Figure 813095DEST_PATH_IMAGE027
which is a measure of the coefficient of molecular viscosity,
Figure 102125DEST_PATH_IMAGE028
which is indicative of the viscosity coefficient of the turbulent flow,
Figure 126713DEST_PATH_IMAGE029
the transition function is represented by a function of the transition,
Figure 334840DEST_PATH_IMAGE029
the value in the wall boundary layer tends to 1 to keep
Figure 444878DEST_PATH_IMAGE063
The accuracy of the model in the near-wall area is restored to 0 in the area far away from the wall surface, and then the model is degenerated to have the advantage of free flow
Figure 301714DEST_PATH_IMAGE063
Model, ω represents the dissipation ratio of turbulent kinetic energy, xjExpressing the coordinate component under the rectangular coordinate system, and k expressing the turbulence energy; other model constants
Figure 305442DEST_PATH_IMAGE030
The expression is as follows:
Figure 825416DEST_PATH_IMAGE031
Figure 422751DEST_PATH_IMAGE032
Figure 443796DEST_PATH_IMAGE033
Figure 177397DEST_PATH_IMAGE034
wherein, y represents the wall surface distance,
Figure 632387DEST_PATH_IMAGE035
and
Figure 576072DEST_PATH_IMAGE036
respectively representing model constants
Figure 276175DEST_PATH_IMAGE037
And
Figure 864282DEST_PATH_IMAGE038
(ii) a The values of the model constants can be shown in the following table:
Figure 116272DEST_PATH_IMAGE064
the above table is merely an example of values of the model constants, and the specific values of the model constants are not limited.
(b) Calculating the turbulence viscosity coefficient of the superlarge vortex simulation according to the following expression:
Figure 422619DEST_PATH_IMAGE039
fr represents a resolution control function, is established according to the mutual relation among three turbulence characteristic length scales to realize an overlarge vortex simulation function on a turbulence flow problem, and has the following expression:
Figure 159369DEST_PATH_IMAGE040
Figure 992196DEST_PATH_IMAGE041
Figure 290453DEST_PATH_IMAGE042
β* 1and CxRepresents the model constant, beta* 1Is not limited, e.g., beta* 1N is a fixed constant, and the specific value of n is not limited, for example, n =2, v represents a kinematic viscosity coefficient,
Figure 84097DEST_PATH_IMAGE043
representing the turbulence integral length scale and,
Figure 985057DEST_PATH_IMAGE044
representing the turbulence filter length scale and,
Figure 813335DEST_PATH_IMAGE065
representing a turbulent dissipation length scale.
In different coarse and fine grid distribution, the proportion of the modeled turbulent kinetic energy is dynamically adjusted by calculating the relative size relationship between the grid dimension and the characteristic length of a local turbulent flow field, and F is the ratio of the grid to the local turbulent flow field in the case that the grid resolution of a near-wall area is very coarserIs close to 1, degenerates to RANS model, and as the local grid resolution is improved, FrThe value is gradually reduced, the modeled specific gravity of the turbulent kinetic energy is reduced, the resolution degree of the turbulent flow field structure is increased, and when the grid resolution is high enough, the solution mode tends to DNS (Direct Numerical simulation )). Compared with the RANS and LES methods, the selection of the super-large vortex simulation method on the grid resolution scale is expanded to a full scale range, and the sensitivity of a calculation result on grid distribution is greatly reduced.
In the implementation of this step, the solution of the flow control equation and the solution of the turbulence model equation are separately solved, and the solution of the flow control equation and the solution of the turbulence model equation need to be sequentially iterated to obtain the finally converged flow field variables.
S104: and obtaining a target flow field variable after the iterative process is converged.
For distinguishing description, a flow field variable finally obtained after iteration is called a target flow field variable.
S105: and integrating the target flow field variable to obtain a stress state simulation result of the target object in a turbulent flow state.
For example, the target flow field variable obtained in S104 may be output according to a post-processing requirement (e.g., a data format required by flow field display software, etc.), so as to facilitate an extraction application of the post-processing procedure on the flow field data.
By applying the embodiment of the invention, based on the grid derivative and the grid Jacobian of the body structure grid of the target object, the flow control equation and the turbulence model equation are solved iteratively, and the target flow field variable is obtained after the iterative process is converged; integrating the target flow field variable to obtain a stress state simulation result of the target object in a turbulent flow state; in the scheme, the flow control equation and the turbulence model equation are solved in a synchronous iteration mode until the stress state simulation result in the turbulence state is obtained after convergence, and the simulation precision in the turbulence state is improved.
The invention relates to a turbulence model method for performing high-order precision numerical simulation on a turbulence flow problem by adopting a Navier-Stokes equation in computational fluid mechanics, in particular to a numerical simulation method for the turbulence flow problem, which aims at solving the problem of turbulence flow by adopting a resolution control function-based super-large vortex simulation method for a turbulence model when a finite difference high-order precision numerical format discrete Navier-Stokes equation is adopted in computational fluid mechanics.
Computational Fluid Dynamics (CFD) is one of important means for developing the mechanism research of the flow physics problem, and plays an increasingly important role in the fields related to the flow problem such as aerospace vehicle design and performance evaluation. In recent years, with the increasing floating-point computing capability and the gradual improvement of numerical calculation methods of large-scale high-performance computers, people prefer to adopt numerical calculation methods with lower numerical dissipation and higher resolution, such as high-order precision formats, to improve the simulation precision of logistic problems. The existing results of a large number of numerical tests show that: the numerical simulation result obtained based on the traditional second-order precision numerical format discrete flow control equation cannot always meet the requirement of the practical engineering problem on the numerical simulation precision, particularly the problem that a large-sized transport plane takes off at a larger attack angle and the turbulent flow problem of large-scale separation is involved when a modern fighter plane performs maneuvering flight at a large attack angle, the algorithm of the discrete RANS simulation method widely used at present cannot always provide the numerical simulation result capable of meeting the practical engineering application requirement, and the main reason is that: on one hand, the second-order precision numerical discrete format has larger dissipation and lower resolution, and a high-order precision format with small dissipation and high resolution is required to be adopted; on the other hand, when the conventional turbulence model based on the reynolds average is used for processing large-scale flow separation, the turbulence viscosity is too large, the small-scale flow result in the turbulence separation flow cannot be simulated, and a turbulence simulation method with relatively small turbulence viscosity needs to be adopted.
The high-order precision numerical format generally refers to a numerical discrete format with design precision reaching three-order or more than three-order precision, and compared with a second-order precision numerical format widely used at present, the high-order precision numerical format has the characteristics of small numerical dissipation, high flow field resolution and the like, but the defects of calculation stability and grid adaptability limit the application of the high-order precision numerical format in the physical flow simulation problem within a quite long time range. Among the existing high-order precision numerical value discrete methods, the high-order precision numerical value method based on the finite difference discrete frame is an optimal high-order precision numerical value solution for solving the flow problem of practical engineering at present due to high calculation precision and small calculation amount. Through development for many years, particularly the solution of the geometric conservation law problem in the high-order precision finite difference method, the current finite difference high-order precision numerical format can be successfully applied to the simulation of the flow problems of complex configurations such as the whole aircraft of a large airplane and the like.
The super-large vortex simulation method is a mixing method for simulating a turbulent flow problem, and the basic idea is that a Reynolds average RANS (random average) turbulent flow model (such as a commonly used one-way SA model and a two-equation SST model) is adopted in a near-wall area, a large vortex simulation (LES) method is adopted in a turbulent flow fully-developed area far away from the wall surface, and the two modes are transited through a resolution control function of a grid scale to a turbulent flow structure. Compared with the currently applied RANS/LES mixing simulation methods (such as DES, DDES, IDDES and the like), the super-large vortex simulation method can effectively reduce the influence of grid distribution near the wall surface on the simulation of a turbulent flow structure due to the fact that three different turbulent flow scales are introduced, and overcomes the problem of ash areas when the common mixing turbulent flow simulation method is in transition from a viscous bottom layer in a turbulent flow boundary layer to a logarithmic law layer.
The embodiment of the invention provides a numerical simulation method for a turbulent flow problem, and specifically comprises the steps of selecting a super large vortex simulation method based on a resolution control function for a physical model for simulating the turbulent flow problem, solving a flow control equation in a finite difference high-order precision numerical discrete format, and carrying out unsteady high-order precision numerical simulation on a mixed turbulent flow model on the turbulent flow problem so as to realize high-resolution simulation on the turbulent flow problem.
The embodiment of the invention adopts a super large vortex simulation method based on high-order precision finite difference format dispersion, which is specifically embodied as follows:
(1) adopting a high-order precision finite difference format discrete flow control equation meeting the geometric conservation law;
(2) the turbulence model adopts a superlarge vortex simulation method;
by adopting a mode of combining a high-order precision finite difference format meeting the geometric conservation law with a super-large vortex simulation method, the simulation precision of the turbulent flow problem is remarkably improved under the condition of not remarkably increasing the calculated amount.
The embodiment of the invention has the following technical effects:
(1) because a finite difference high-order precision numerical format is adopted in the discrete flow control equation, the resolution capability of the turbulent flow structure can be greatly improved under the condition of not increasing the calculated amount remarkably;
(2) because the turbulence model adopts the super-large vortex simulation method based on the resolution control function, the influence of grid distribution near the wall surface on the flow simulation result can be obviously reduced, the problem of gray areas related to grid distribution when the viscous bottom layer of a turbulence boundary layer is transited to the logarithm law layer is avoided, and the accuracy of turbulence problem simulation is improved.
Corresponding to the above method embodiment, an embodiment of the present invention further provides a device for simulating a stress state of a target in turbulent flow, as shown in fig. 2, including:
a generating module 201, configured to generate a body structure grid of a target object;
a first calculation module 202, configured to calculate a grid derivative of the skin structure grid;
a second calculating module 203, configured to calculate a grid jacobian of the body structure grid;
a solving module 204 for iteratively solving a flow control equation and a turbulence model equation based on the grid derivative and the grid jacobian; the solving result of the turbulence model equation comprises a turbulence viscosity coefficient, the flow control equation is updated according to the turbulence viscosity coefficient, and the solving result of the flow control equation comprises a flow field variable; obtaining a target flow field variable after the iterative process is converged;
and the integrating module 205 is configured to integrate the target flow field variable to obtain a stress state simulation result of the target object in a turbulent flow state.
In an embodiment of the present invention, the first calculating module 202 is specifically configured to:
calculating a grid derivative of the skin structure grid using the following equation:
Figure 781029DEST_PATH_IMAGE001
Figure 921023DEST_PATH_IMAGE002
Figure 501040DEST_PATH_IMAGE003
where ξ, η, and ζ represent three different directions, respectively, and x, y, and z represent different components in each direction, respectively.
In an embodiment of the present invention, the second calculating module 203 is specifically configured to:
calculating the grid jacobian of the body structure grid by using the following formula:
Figure 183826DEST_PATH_IMAGE004
where ξ, η, ζ denote three different directions, respectively, and x, y, z denote different components in each direction, respectively.
In an embodiment of the present invention, the solving module 204 is specifically configured to:
based on the grid derivative and the grid Jacobian, solving a flow control equation in a finite difference high-order precision numerical discrete format, and simulating a mixed turbulence model equation in a unsteady high-order precision numerical simulation mode; and updating the flow control equation according to the turbulence viscosity coefficient included in the solution result of the turbulence model equation, and then returning to the step of solving the flow control equation in the finite difference high-order precision numerical discrete format until the iterative process converges.
By applying the embodiment of the invention, based on the grid derivative and the grid Jacobian of the body structure grid of the target object, the flow control equation and the turbulence model equation are solved in an iterative manner, and the target flow field variable is obtained after the iterative process is converged; integrating the target flow field variable to obtain a stress state simulation result of the target object in a turbulent flow state; in the scheme, the flow control equation and the turbulence model equation are solved in a synchronous iteration mode until the stress state simulation result in the turbulence state is obtained after convergence, and the simulation precision in the turbulence state is improved.
An embodiment of the present invention further provides an electronic device, as shown in fig. 3, including a processor 301 and a memory 302,
a memory 302 for storing a computer program;
the processor 301 is configured to implement any one of the above-mentioned methods for simulating a stress state of a target object in a turbulent flow when executing a program stored in the memory 302.
The Memory mentioned in the above electronic device may include a Random Access Memory (RAM) or a Non-Volatile Memory (NVM), such as at least one disk Memory. Alternatively, the memory may be at least one memory device located remotely from the processor.
The Processor may be a general-purpose Processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; but also Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) or other Programmable logic devices, discrete Gate or transistor logic devices, discrete hardware components.
In another embodiment of the present invention, a computer-readable storage medium is further provided, in which a computer program is stored, and the computer program is used for implementing any one of the above methods for simulating a stress state of a target in turbulent flow when executed by a processor.
In yet another embodiment of the present invention, there is also provided a computer program product containing instructions which, when run on a computer, cause the computer to perform any one of the above-mentioned methods for simulating a stress state of a target in turbulent flow.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When implemented in software, it may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When loaded and executed on a computer, cause the processes or functions described in accordance with the embodiments of the invention to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, from one website site, computer, server, or data center to another website site, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that incorporates one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
It should be noted that, in this document, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
All the embodiments in the present specification are described in a related manner, and the same and similar parts among the embodiments may be referred to each other, and each embodiment focuses on differences from other embodiments. In particular, apparatus embodiments, device embodiments, computer-readable storage medium embodiments, and computer program product embodiments are described for simplicity as they are substantially similar to method embodiments, where relevant, reference may be made to some descriptions of method embodiments.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.

Claims (6)

1. A method for simulating a stress state of a target in turbulent flow is characterized by comprising the following steps:
generating a body-fitted structure grid of the target object;
calculating the grid derivative and the grid Jacobian of the skin structure grid;
iteratively solving a flow control equation and a turbulence model equation based on the grid derivative and the grid Jacobian; the solution result of the turbulence model equation comprises a turbulence viscosity coefficient, the flow control equation is updated according to the turbulence viscosity coefficient, and the solution result of the flow control equation comprises a flow field variable;
obtaining a target flow field variable after the iterative process is converged;
integrating the target flow field variable to obtain a stress state simulation result of the target object in a turbulent flow state;
wherein iteratively solving a flow control equation and a turbulence model equation based on the grid derivatives and the grid jacobian comprises:
based on the grid derivative and the grid Jacobian, solving a flow control equation in a finite difference high-order precision numerical discrete format, and simulating a mixed turbulence model equation in a non-constant high-order precision numerical simulation mode; updating the flow control equation according to a turbulence viscosity coefficient included in a solving result of the turbulence model equation, and then returning to the step of solving the flow control equation in the finite difference high-order precision numerical discrete format until the iterative process is converged;
the solving of the flow control equation in the finite difference high-order precision numerical discrete format comprises:
discretizing a flow control equation under a calculation coordinate system by adopting a high-order precision finite difference format as follows:
Figure FDA0003691754370000011
Figure FDA0003691754370000012
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003691754370000013
representing the flux of the values of the grid nodes,
Figure FDA0003691754370000014
representing half-nodes
Figure FDA0003691754370000015
The flux of the value of (a) is,
Figure FDA0003691754370000016
representing half-nodes
Figure FDA0003691754370000017
The flux of the value of (a) is,
Figure FDA0003691754370000018
representing half-nodes
Figure FDA0003691754370000019
The flux of the value of (a) is,
Figure FDA00036917543700000110
representing half-nodes
Figure FDA00036917543700000111
The flux of the value of (a) is,
Figure FDA00036917543700000112
representing half-nodes
Figure FDA00036917543700000113
The flux of the numerical value of (a),
Figure FDA00036917543700000114
representing half-nodes
Figure FDA00036917543700000115
The value flux, delta xi, is the set value,
Figure FDA00036917543700000116
and
Figure FDA00036917543700000117
respectively representing half-nodes
Figure FDA00036917543700000118
Left and right flow field variables;
the numerical simulation mixing turbulence model equation with unsteady high-order precision comprises the following steps:
solving the control equation of the turbulence model as follows:
Figure FDA0003691754370000021
Figure FDA0003691754370000022
where ρ represents density, uiRepresenting the velocity component, τijDenotes the viscous stress component, μ denotes the molecular viscosity coefficient, μtDenotes the turbulent viscosity coefficient, F1Denotes a transition function, F1The value of the turbulent kinetic energy in the boundary layer of the wall surface tends to 1, the value of the turbulent kinetic energy in the region far away from the wall surface returns to 0, omega represents the dissipation rate of the turbulent kinetic energy, and x represents the dissipation rate of the turbulent kinetic energyjRepresenting the coordinate component under the rectangular coordinate system, and k represents the turbulence energy; the remaining model constant φ (σ)k，σωβ, γ) is expressed as:
φ＝F1φ1+(1-F1)φ2
Figure FDA0003691754370000023
Figure FDA0003691754370000024
Figure FDA0003691754370000025
wherein y represents the wall distance, phi1And phi2Respectively representing model constants (σ)k1，σω1，β1，γ1) And (σ)k2，σω2，β2，γ2) (ii) a tan h is a hyperbolic tangent function;
calculating the turbulence viscosity coefficient of the super-large vortex simulation according to the following expression:
Figure FDA0003691754370000026
wherein, FrRepresenting a resolution control function, FrAccording to threeEstablishment of the correlation between the characteristic length dimensions of the turbulence FrThe expression of (a) is as follows:
Figure FDA0003691754370000031
Figure FDA0003691754370000032
Figure FDA0003691754370000033
β* 1and CxRepresenting model constants, n being a fixed constant, v representing kinematic viscosity coefficient, LiDenotes the turbulence integral length scale, LcRepresenting the turbulence filter length scale, LkRepresenting the turbulent dissipation length scale.
2. The method of claim 1, wherein computing grid derivatives for the lattice grid comprises:
calculating a grid derivative of the skin structure grid using the following equation:
Figure FDA0003691754370000034
Figure FDA0003691754370000035
Figure FDA0003691754370000036
where ξ, η, and ζ represent three different directions, respectively, and x, y, and z represent different components in each direction, respectively.
3. The method of claim 2, wherein computing a grid jacobian for the lattice of the skin structure comprises:
calculating the grid jacobian of the body structure grid by using the following formula:
Figure FDA0003691754370000041
where ξ, η, ζ denote three different directions, respectively, and x, y, z denote different components in each direction, respectively.
4. A device for simulating a stress state of a target in turbulent flow, comprising:
the generating module is used for generating a body-fitted structure grid of the target object;
a first calculation module, configured to calculate a grid derivative of the skin structure grid;
the second calculation module is used for calculating the grid jacobian of the body structure grid;
the solving module is used for iteratively solving a flow control equation and a turbulence model equation based on the grid derivative and the grid Jacobian; the solution result of the turbulence model equation comprises a turbulence viscosity coefficient, the flow control equation is updated according to the turbulence viscosity coefficient, and the solution result of the flow control equation comprises a flow field variable; obtaining a target flow field variable after the iterative process is converged;
the integration module is used for integrating the target flow field variable to obtain a stress state simulation result of the target object in a turbulent flow state;
the solving module is specifically configured to:
based on the grid derivative and the grid Jacobian, solving a flow control equation in a finite difference high-order precision numerical discrete format, and simulating a mixed turbulence model equation in a non-constant high-order precision numerical simulation mode; updating the flow control equation according to a turbulence viscosity coefficient included in a solving result of the turbulence model equation, and then returning to the step of solving the flow control equation in a finite difference high-order precision numerical discrete format until an iterative process converges;
the solving of the flow control equation in a finite difference high-order precision numerical discrete format comprises:
discretizing a flow control equation under a calculation coordinate system by adopting a high-order precision finite difference format as follows:
Figure FDA0003691754370000042
Figure FDA0003691754370000043
wherein the content of the first and second substances,
Figure FDA0003691754370000051
the numerical flux of the grid nodes is represented,
Figure FDA0003691754370000052
representing half-nodes
Figure FDA0003691754370000053
The flux of the value of (a) is,
Figure FDA0003691754370000054
representing half-nodes
Figure FDA0003691754370000055
The flux of the value of (a) is,
Figure FDA0003691754370000056
representing half-nodes
Figure FDA0003691754370000057
The flux of the value of (a) is,
Figure FDA0003691754370000058
representing half-nodes
Figure FDA0003691754370000059
The flux of the value of (a) is,
Figure FDA00036917543700000510
representing half-nodes
Figure FDA00036917543700000511
The flux of the value of (a) is,
Figure FDA00036917543700000512
representing half-nodes
Figure FDA00036917543700000513
The value flux, delta xi, is the set value,
Figure FDA00036917543700000514
and
Figure FDA00036917543700000515
respectively representing half-nodes
Figure FDA00036917543700000516
Left and right flow field variables;
the numerical simulation mixing turbulence model equation with unsteady high-order precision comprises the following steps:
solving the control equation of the turbulence model as follows:
Figure FDA00036917543700000517
Figure FDA00036917543700000518
where ρ represents density, uiRepresenting the velocity component, τijRepresents the viscous stress component, mu represents the molecular viscosity coefficient, mutDenotes the turbulent viscosity coefficient, F1Representing a transition function, F1The value of the turbulent kinetic energy in the boundary layer of the wall surface tends to 1, the value of the turbulent kinetic energy in the region far away from the wall surface returns to 0, omega represents the dissipation rate of the turbulent kinetic energy, and x represents the dissipation rate of the turbulent kinetic energyjExpressing the coordinate component under the rectangular coordinate system, and k expressing the turbulence energy; the remaining model constant φ (σ)k，σωβ, γ) is expressed as:
φ＝F1φ1+(1-F1)φ2
Figure FDA00036917543700000519
Figure FDA00036917543700000520
Figure FDA00036917543700000521
wherein y represents the wall distance, φ1And phi2Respectively represent model constants (σ)k1，σω1，β1，γ1) And (σ)k2，σω2，β2，γ2) (ii) a tan h is a hyperbolic tangent function;
calculating the turbulence viscosity coefficient of the superlarge vortex simulation according to the following expression:
Figure FDA0003691754370000061
wherein, FrThe resolution control function is represented by a function,Frestablishing according to the interrelation among three turbulence characteristic length scales, FrThe expression of (c) is as follows:
Figure FDA0003691754370000062
Figure FDA0003691754370000063
Figure FDA0003691754370000064
β* 1and CxRepresenting model constants, n being a fixed constant, v representing a kinematic viscosity coefficient, LiRepresenting the turbulence integral length scale, LcRepresenting the turbulence filter length scale, LkRepresenting a turbulent dissipation length scale.
5. The apparatus of claim 4, wherein the first computing module is specifically configured to:
calculating a grid derivative of the skin structure grid using the following equation:
Figure FDA0003691754370000065
Figure FDA0003691754370000066
Figure FDA0003691754370000067
where ξ, η, and ζ represent three different directions, respectively, and x, y, and z represent different components in each direction, respectively.
6. The apparatus of claim 5, wherein the second computing module is specifically configured to:
calculating the grid jacobian of the skin structure grid by using the following formula:
Figure FDA0003691754370000071
where ξ, η, ζ denote three different directions, respectively, and x, y, z denote different components in each direction, respectively.
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