CN111079310B - Turbulent flow region identification method - Google Patents
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Abstract
The invention discloses a turbulent flow region identification method, which relates to the field of computational fluid dynamics and comprises the following steps: step 1: acquiring a flow field to be subjected to flow analysis; step 2: calculating a turbulence region identification value sigma of the flow field; and step 3: judging whether the identification value sigma of the turbulent flow area is 0, if so, the flow field is the turbulent flow area, otherwise, the flow field is not the turbulent flow area; the turbulence area identification value sigma is obtained based on the local Reynolds number and the vortex stretch function, and the invention provides the turbulence area identification method independent of the vortex viscosity coefficient, so that the turbulence area identification method has a wider application range.
Description
Technical Field
The invention relates to the field of computational fluid dynamics, in particular to a turbulence area identification method.
Background
Computational Fluid Dynamics (CFD) is an interdisciplinary discipline of fluid mechanics, computational mathematics and computers, and fluid dynamics equations are simulated by the computers to obtain information such as force, heat, frequency and the like of fluid motion, so that data support is provided for relevant industrial design. With the development of computer technology, computational fluid dynamics is playing an increasingly important role in the fields of aerospace, transportation, chemical engineering, machinery, energy and the like.
Fluid flow is divided into two states, laminar and turbulent. The actual flow is substantially turbulent, or at least comprises partial turbulence. The key to accurately predicting fluid motion is turbulence simulation techniques. Current turbulence simulation techniques include: the Reynolds average equation (RANS) method, the Large Eddy Simulation (LES) method, and the Direct Numerical Simulation (DNS) method. Among them, the reynolds average method requires less computing resources, but has lower accuracy. The direct numerical simulation method has the highest accuracy, but has extremely high calculation overhead, and is mainly limited to a simple academic problem at present. The large vortex simulation method and the LES/RANS mixing method adopting Reynolds average in partial area can greatly improve the simulation accuracy of the complex turbulence by the current computing power, rapidly permeate each design department, and solve a plurality of complex turbulence problems which are difficult to process before.
In the actual application process of the turbulence large vortex simulation method and the direct numerical simulation method, the area where turbulence exists in the flow field is often required to be identified in the calculation process. On one hand, turbulence large vortex simulation is still a very expensive algorithm, and if a turbulence area can be accurately identified, computing resources can be concentrated to the turbulence area as much as possible, so that the utilization efficiency of the computing resources is improved; on the other hand, on the premise of accurately identifying the turbulent flow region, a corresponding algorithm (the algorithm required by the large vortex simulation is different from the traditional method) can be pertinently adopted in the turbulent flow region, so that the accuracy and the robustness of numerical prediction are improved.
The existing turbulence area identification algorithm judges whether the area is turbulence or not based on the magnitude of the vortex viscosity coefficient at any position in a flow field (obtained by adopting a large vortex simulation or Reynolds average method). FIG. 1 is a diagram of a turbulent flow region to be identified; as shown in fig. 2, the recognition result of the turbulence area recognition function of the prior art, this method has the disadvantages that: only when a specific algorithm is adopted, the vortex viscosity coefficient value can represent whether the area is turbulent flow or not; in many algorithms, the vortex viscosity coefficient is either not present at all (e.g., implicit large vortex modeling methods, large vortex modeling methods using non-vortex viscosity models, etc.), or can vary between positive, negative, and zero values (e.g., dynamic vortex viscosity models). Therefore, the application range of the existing turbulent flow region identification method is quite limited.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the turbulent flow region identification method independent of the vortex viscosity coefficient is provided, so that the turbulent flow region identification method has a wider application range.
The invention provides a turbulent flow region identification method, which comprises the following steps,
step 1: acquiring a flow field to be subjected to flow analysis;
step 2: calculating a turbulence region identification value sigma of the flow field;
and step 3: judging whether the identification value sigma of the turbulent flow area is 0, if so, the flow field is the turbulent flow area, otherwise, the flow field is not the turbulent flow area;
the turbulence area identification value sigma is obtained based on a local Reynolds number and a vortex stretching function, and is specifically based on the vortex stretching function
Constructing the local velocity difference, and thus the local velocity difference Reynolds number:
wherein,
is vorticity vector, S is deformation rate tensor, Delta is local grid scale, and v is fluid molecular kinematic viscosity coefficient.
Further, the flow field is obtained by turbulent macrovortex simulation or LES/RANS mixing algorithm simulation.
Further, at low velocity flow fields, Ma <1, the turbulence region identification value σ is calculated as
Wherein, C1＝0.1，C2＝3.0，
Is the local velocity difference reynolds number.
Further, in the high-speed flow field, Ma >1, the turbulence area identification value σ is calculated by the formula
Wherein, C1＝0.1，C2＝3.0，
Is the local velocity difference reynolds number,
is a shock wave detection factor. By considering the existing factors of shock waves in high-speed flow, the method can be effectively applied to supersonic flow fields.
By adopting the technical scheme, the invention has the beneficial effects that: a turbulence area identification value sigma is provided based on a local Reynolds number and a vortex stretching function, and the calculation of the value does not depend on a vortex viscosity coefficient, so that the application range of the method is greatly expanded, the method can be applied to various large vortex simulation methods or an LES/RANS mixing method, and the method can be applied regardless of whether the adopted specific method comprises a sub-lattice model or which sub-lattice model is adopted. Meanwhile, the vortex stretch function in the invention can be automatically degenerated to zero in a laminar flow area, so that no correction is needed in a far field area, and the calculation process is simplified compared with the existing method.
Drawings
The invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 is a diagram of a turbulent area to be identified;
FIG. 2 is a graph of the recognition result of a prior art turbulent region recognition function;
fig. 3 is a graph showing the recognition result of the turbulent region recognition function according to embodiment 1 of the present invention;
FIG. 4 is a schematic diagram of the application of embodiment 2 of the present invention in supersonic jet large vortex simulation;
fig. 5 is an application diagram of the hypersonic speed boundary layer transition simulation in embodiment 2 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a turbulence area identification method based on a local velocity difference Reynolds number and a vortex stretch function, which identifies a turbulence area based on basic physical characteristics (the local Reynolds number and the energy level string characteristics based on vortex stretch) of turbulence motion, and does not depend on a vortex viscosity coefficient, and comprises the following steps,
step 1: and (3) acquiring a flow field needing flow analysis through turbulence large vortex simulation or LES/RANS mixing algorithm simulation.
Step 2: calculating a turbulence region identification value sigma of the flow field; the turbulence area identification value sigma is obtained based on the local Reynolds number and the energy level string characteristics of vortex stretching.
Specifically, a turbulent flow region identification function is constructed, and since any region is a turbulent flow, the premise is that the local velocity difference reynolds number is as follows:
here, ,
delta is the scale of the local grid cell,
δ u is a typical value of the difference in velocity of the flow over the distance Δ thereat
ν is the kinematic viscosity coefficient.
The basis of this principle is when
The molecular viscosity inside the grid cells is not sufficient to support the maintenance of a stable linear distribution of flow velocities inside the cells, and a (statistically average) velocity gradient of the corresponding scale can only be maintained by generating small-scale turbulence pulsations.
Then, the vortex stretch function is used
As a basis for estimating the typical speed difference value δ u, it is known based on dimensional analysis:
here, ,
in order to be the strain rate tensor,
is the vorticity vector. The principle of this scheme is that vortex stretching is a key physical mechanism for the generation and maintenance of turbulent zone energy level trains, and the value of the vortex stretching function approaches zero in the non-turbulent zone.
Finally, through the two functions, the following turbulence area identification function is constructed:
C1＝0.1，C2＝3.0
wherein
Is a hyperbolic tangent function. In the laminar flow region, the local velocity difference reynolds number is small, and the expression (i) gives σ ═ 1; while in the turbulent flow region, (i) gives σ 0.
And step 3: and judging whether the identification value sigma of the turbulent flow area is 0, if so, the flow field is the turbulent flow area, and if not, the flow field is not the turbulent flow area.
The turbulence recognition function formula (i) provided by the invention does not depend on the vortex viscosity coefficient, and the application range of the method is greatly expanded. The present invention can be applied to a large vortex simulation method and an LES/RANS hybrid method using various models. The present invention is applicable regardless of whether the particular method employed involves sub-lattice modeling, or which sub-lattice model is employed. The calculation process is simplified compared with the existing method. This is because the vortex stretch function formula (b) based on the present invention can be automatically reduced to zero in the laminar flow region, and therefore, no correction is required in the far field region.
As shown in fig. 3, the identification result of the turbulent flow region identification function of example 1 is calculated as low-speed flow around the cylinder, fig. 1 is a diagram of the turbulent flow region to be identified, and fig. 2 and 3 are the identification results of the existing method and the method (i) of the present invention, respectively. Wherein, the flow field prediction adopts a large vortex simulation method (based on a dynamic Smagorinsky model). This figure illustrates that the method of the present invention gives more accurate results in the case of a dynamic sub-lattice model (the vortex viscosity coefficient can be negative and zero).
Example 2
On the basis of the embodiment 1, a shock wave detection factor phi (the shock wave detection factor is from the open literature) is added to the supersonic flow field containing the shock wave, so that the turbulence area identification function is modified as follows:
C1＝0.1，C2＝3.0，C3＝4.0，C4＝3.0，C5＝2.0，ε＝10-20
here, ,
ω is the absolute value of vorticity.
The turbulence identification function formula (ii) provided by the invention enables the method to be effectively applied to supersonic flow fields by considering the existence factor of shock waves in high-speed flow.
As shown in fig. 4, the application of the formula (ii) of the present invention to supersonic (mach number Ma ═ 1.8) jet large vortex simulation (using dynamic Smagorinsky model) is illustrated. As can be seen from fig. 4, the present invention can also give accurate identification of turbulent regions in the supersonic case.
As shown in fig. 5, the formula (ii) of the present invention is applied to a hypersonic (mach number Ma ═ 6) boundary layer transition simulation. The adopted simulation method is privacy large vortex simulation. It can be seen that the present invention is equally applicable in hypersonic flow. Meanwhile, the method can be applied to the implicit large vortex simulation method without the sub-lattice model.
While the foregoing description shows and describes a preferred embodiment of the invention, it is to be understood, as noted above, that the invention is not limited to the form disclosed herein, but is not intended to be exhaustive or to exclude other embodiments and may be used in various other combinations, modifications, and environments and may be modified within the scope of the inventive concept described herein by the above teachings or the skill or knowledge of the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (1)
1. A turbulent flow region identification method, characterized by: comprises the following steps of (a) carrying out,
step 1: acquiring a flow field to be subjected to flow analysis;
step 2: calculating a turbulence region identification value sigma of the flow field;
and step 3: judging whether the identification value sigma of the turbulent flow area is 0, if so, the flow field is the turbulent flow area, otherwise, the flow field is not the turbulent flow area;
the turbulence area identification value sigma is obtained based on a local Reynolds number and a vortex stretching function;
in particular based on the vortex stretch function
The constructed local velocity difference and the Reynolds number of the local velocity difference are calculated by the formula,
at low velocity flow field, Ma <1, the turbulence region identification value σ is calculated as
When the high-speed flow field, Ma >1, the formula for calculating the identification value sigma of the turbulent flow area is
Where deltau is a typical value of the difference in velocity of the flow over the distance delta,
is vorticity vector, S is deformation rate tensor, Delta is local grid scale, v is fluid molecular kinematic viscosity coefficient, C1＝0.1，C2＝3.0，
Is the local velocity difference reynolds number,
and Ma is a Mach number which is a shock wave detection factor.
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| CN112131800B (en) * | 2020-07-20 | 2024-04-12 | 中国科学院力学研究所 | Novel large vortex simulation method and device based on energy flow similarity |
| CN112052512B (en) * | 2020-07-23 | 2023-01-10 | 中国空气动力研究与发展中心计算空气动力研究所 | Method for judging layering of turbulent boundary layer |
| CN112464583B (en) * | 2020-11-04 | 2023-03-14 | 空气动力学国家重点实验室 | Grid generation method considering shock waves and boundary layers |
| CN112417783A (en) * | 2020-11-20 | 2021-02-26 | 西安热工研究院有限公司 | Mixing turbulence calculation method |
| CN113158340B (en) * | 2021-04-16 | 2022-10-18 | 中国空气动力研究与发展中心计算空气动力研究所 | Turbulence length scale correction method for k-epsilon turbulence model |
| CN116361927B (en) * | 2023-06-02 | 2023-08-29 | 浙江大学 | High-precision turbulence modeling method for complex internal flow numerical simulation of high-speed aircraft |
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