CN115034162B - Grid self-adaptive turbulence simulation method based on turbulence energy spectrum coupling k-epsilon series model - Google Patents
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Abstract
The invention discloses a grid self-adaptive turbulence simulation method based on a turbulence energy spectrum coupling k-epsilon series model, which comprises the following main implementation processes: step one, judging whether a shielding function is applied; step two, identifying the local grid scale; thirdly, constructing a scale-dependent adjusting function based on turbulence energy spectrum integral coupling k-epsilon series model; step four, reconstructing turbulence viscosity of the k-epsilon series model by using an adjusting function; and fifthly, performing turbulence simulation by using the reconstructed turbulence viscosity based on the k-epsilon series model. According to the invention, the local grid length scale delta * is determined by identifying the local grid size, and the turbulence viscosity is reconstructed by constructing the scale correlation function through the turbulence spectrum integration, so that the grid self-adaptive simulation is realized, the problem that the conventional RANS/LES hybrid model has high experience dependence on grids is effectively solved, the calculation cost is greatly reduced, the turbulence simulation process is remarkably accelerated, and a high-efficiency numerical simulation method is provided for quick high-precision simulation for solving the complex engineering flow problem.
Description
Technical Field
The invention relates to the field of engineering fluid mechanics calculation, in particular to a grid self-adaptive turbulence simulation method based on a turbulence energy spectrum coupling k-epsilon series model.
Background
Turbulence phenomenon is ubiquitous in the natural and engineering fields, and accurate prediction of turbulence is a major difficulty in studying complex flow problems. Taking the internal flow of the fluid machinery as an example, the flow structure is quite complex, and complex turbulence flow phenomena such as multi-scale, nonlinearity, unsteady and the like widely exist, and the complex turbulence flow has great influence on the performance of the fluid machinery. Therefore, in engineering design, development of a turbulence simulation method with high prediction accuracy and high calculation efficiency is strongly demanded, so that it is possible to accurately simulate a turbulent flow in a complex engineering problem such as an internal flow of a fluid machine.
The conventional turbulence simulation method for engineering mainly solves a Reynolds average NS equation (RANS) method, and is small in calculated amount, but is based on simple basic flow development, so that the accuracy of predicting complex turbulence flow in engineering problems such as multiscale, unsteady, large separation and the like is poor, and the improvement of the design level in the fields such as fluid machinery and the like is severely restricted. The Large Eddy Simulation (LES) method is used as a high-precision numerical simulation method, has high requirements on the grid number, and increases the calculation cost exponentially compared with the RANS method, so that the calculation cost is far higher than the calculation cost level which can be born in engineering application. For engineering flow problems such as internal flow of a fluid machine, the Reynolds number is often high, and under the existing computing capability, the LES method is difficult to apply to flow prediction in the complex engineering field on the engineering design level.
The RANS-LES hybrid simulation method is born in the last twenty years, and the RANS method is adopted in the near-wall area, and the LES method is adopted in the main flow area, so that the calculation accuracy and the calculation efficiency are balanced, and a good solution strategy is provided for solving the problem of high-accuracy simulation calculation of complex flow. However, the classical RANS-LES hybrid model has more strict requirements on the grid, and needs a user to have more abundant high-precision numerical simulation experience, so that the prediction capability of complex engineering flow, such as internal flow of a fluid machine, is limited. Therefore, the method reduces the experience dependence degree of the RANS-LES mixed model on the grid, and has important significance for better realizing accurate and efficient high-precision simulation of turbulent flow phenomena such as multiscale, nonlinear, unsteady and the like in the complex engineering flow problem.
Disclosure of Invention
First, the technical problem to be solved
The invention aims to provide a grid self-adaptive turbulence simulation method based on a turbulence energy spectrum coupling k-epsilon series model, which effectively solves the problem that the conventional RANS-LES hybrid model has high experience dependence on grids, greatly reduces calculation cost while improving calculation accuracy, remarkably accelerates turbulence simulation process, and provides an efficient numerical simulation method for quick high-precision simulation of multi-scale, nonlinear, unsteady and other turbulence flows in the complex engineering flow problem.
(II) technical scheme
In order to solve the technical problems, the invention provides a grid self-adaptive turbulence simulation method based on a turbulence energy spectrum coupling k-epsilon series model, which comprises the following steps:
Step one, judging whether a shielding function is applied;
Step two, identifying the local grid scale;
thirdly, constructing a scale-dependent adjusting function based on turbulence energy spectrum integral coupling k-epsilon series model;
step four, reconstructing turbulence viscosity of the k-epsilon series model by using an adjusting function;
step five, based on a k-epsilon series model, performing turbulence simulation by using the reconstructed turbulence viscosity;
① The determining whether to apply a masking function includes:
Judging whether a masking function F GAS is adopted or not by combining the simulated flow state type, specifically, when the flow state type is free shearing flow, not adopting the masking function, wherein the masking function F GAS =0; when the flow state type is near wall flow, a masking function is used, and the masking function F GAS may be as follows: an F 1 mask function derived from the DDES-SST model, an F 2 mask function, and an F d mask function derived from the DDES-SA model;
② The identifying the local grid scale includes:
Determining a local grid length scale delta * by combining the masking function F GAS in the first step;
the local grid length scale Δ * is given by:
Δ*＝CGAS[(1-FGAS)Δvol+FGASΔmax]
Δmax＝max(Δx,Δy,Δz)
wherein, delta x is the length of the local hexahedral mesh, delta y is the width of the local hexahedral mesh, delta z is the height of the local hexahedral mesh, and C GAS is the empirical coefficient of 0.6;
③ The adjusting function based on turbulence energy spectrum integral coupling k-epsilon series model construction scale correlation comprises the following steps:
According to the modeling mode of turbulence energy in the k-epsilon series model, obtaining an original modeled turbulence energy k m, and according to the local grid length scale delta * in the second step, obtaining an actually modeled turbulence energy k u through integration based on a turbulence energy spectrum;
the actual modeling turbulence energy k u is obtained by the following formula:
Wherein, C k is the kolmogorov coefficient, 1.5 is taken, epsilon is the actual turbulent dissipation ratio, kappa c is the resolvable turbulent cutoff wave number, and is determined by the local grid length scale delta * in the second step:
Constructing a dynamic scale-dependent adjustment function D f according to the actual modeling turbulence energy k u, the original modeling turbulence energy k m and the shielding function F GAS in the step one; defining a scale ratio as the ratio of the actual modeling turbulence energy k u to the original modeling turbulence energy k m, and the dynamic scale-dependent adjustment function D f as the scale-dependent function, which is obtained by the following formula:
lGAS＝(1-FGAS)lu+FGASlm
Wherein l u is a grid correlation scale, l m is a turbulence length scale given by a k-epsilon series model, and is obtained by the following formula:
wherein k m is the turbulence energy of the original modeling of the k-epsilon series model, and epsilon m is the dissipation rate of the original modeling obtained according to the k-epsilon series model;
④ The reconstructing the turbulence viscosity of the k- ε series model using the adjustment function comprises:
And (3) regulating and controlling the turbulence viscosity v t in the k-epsilon series model by adopting the dynamic scale related regulating function D f in the step (III) to obtain a reconstructed turbulence viscosity v sfs, wherein the reconstructed turbulence viscosity v sfs is obtained by the following formula:
νsfs＝Df·νt
⑤ The turbulence simulation using the reconstructed turbulence viscosity based on the k- ε series model comprises:
And (3) calculating the Reynolds stress by adopting the reconstructed turbulence viscosity v sfs in the step (IV), updating a transport equation of the k-epsilon series model, replacing the turbulence viscosity v t in the original transport equation of the k-epsilon series model, and combining with the k-epsilon series model to obtain the grid self-adaptive turbulence simulation method based on the turbulence energy spectrum coupling k-epsilon series model.
(III) beneficial effects
The invention provides a grid self-adaptive turbulence simulation method based on a turbulence energy spectrum coupling k-epsilon series model, which has the following beneficial effects: the method has the advantages that the local grid length scale delta is determined by identifying the local grid size, and then the turbulence viscosity is reconstructed through a turbulence energy spectrum integral construction scale correlation function, so that grid self-adaptive simulation is realized, the problem that the conventional RANS-LES hybrid model has high experience dependence on grids is effectively solved, the calculation accuracy is improved, meanwhile, the calculation cost is greatly reduced, the turbulence simulation process is obviously accelerated, and an efficient numerical simulation method is provided for quick high-precision simulation of multi-scale, nonlinear, unsteady and other turbulence flows in the complex engineering flow problem; the method provided by the invention is simple in form, strong in portability, capable of being well combined with k-epsilon series models, convenient to implant the existing CFD codes for application and expansion, and wide in academic and engineering application prospects.
Drawings
FIG. 1 is a flow chart of a grid-adaptive turbulence simulation method based on a turbulence energy spectrum coupling k-epsilon series model of the invention;
FIG. 2 is a schematic representation of the dynamic scale-dependent adjustment function D f of the present invention constructed based on turbulent energy spectra;
FIG. 3 is a diagram of turbulent vortex diagram of a cylindrical bypass flow calculation example for a standard k- ε turbulence model calculation;
FIG. 4 is a diagram of turbulent vortex diagram of a cylindrical flow around calculation example calculated by the grid adaptive turbulence simulation method based on a turbulence energy spectrum coupling k-epsilon series model.
Detailed Description
The following describes in further detail embodiments of the invention, taking as an example a standard k-epsilon turbulence model in the k-epsilon series model, in conjunction with the accompanying drawings. The following examples are only illustrative of the present invention and are not intended to limit the scope of the invention.
The cylindrical streaming calculation example is selected as a calculation example, a high-quality hexahedral grid is adopted to carry out space dispersion on a calculation domain, and the total grid number is about 28 ten thousand.
The invention provides a grid self-adaptive turbulence simulation method based on a turbulence energy spectrum coupling k-epsilon series model, which comprises the following steps:
Step one, judging whether a shielding function is applied;
In this step, in combination with the simulated flow state type, it is determined whether or not to use the masking function F GAS, specifically, when the flow state type is free-cut flow, the masking function is not used, and at this time, the masking function F GAS =0; when the flow state type is near wall flow, a masking function is used, and the masking function F GAS can be as follows: an F 1 mask function derived from the DDES-SST model, an F 2 mask function, and an F d mask function derived from the DDES-SA model.
In this embodiment, using the F d mask function in DDES-SA model, there are:
FGAS＝Fd
Wherein U i,j is the velocity gradient tensor; v t is the turbulence viscosity given by the standard k-epsilon turbulence model, v is the viscosity coefficient of the fluid, and d is the distance from the local grid to the wall surface; kappa is a Karman constant and is 0.41; c d1、Cd2 is an experience coefficient, and 20 and 3 are taken respectively;
Step two, identifying the local grid scale;
in this step, the local grid length scale Δ is determined in combination with the masking function F GAS in step one;
The local grid length scale Δ * is given by:
Δ*＝CGAS[(1-FGAS)Δvol+FGASΔmax]
Δmax＝max(Δx,Δy,Δz)
Wherein, delta x is the length of the local hexahedral mesh, delta y is the width of the local hexahedral mesh, delta z is the height of the local hexahedral mesh, C GAS is the empirical coefficient, and 0.6 is taken;
thirdly, constructing a scale-dependent adjusting function based on turbulence energy spectrum integral coupling k-epsilon series model;
In this step, the original modeled turbulence energy k m is obtained according to the modeling of the turbulence energy in the standard k- ε turbulence model;
according to the local grid length scale delta * in the second step, the turbulence energy k u which is practically modeled is obtained through integration based on the turbulence energy spectrum, and is given by the following formula:
Wherein, C k is the Kelmogorov coefficient, 1.5; epsilon is the actual turbulence dissipation ratio; kappa c is the resolvable cutoff wave number determined by the local grid length scale delta * in step two:
Constructing a dynamic scale-dependent adjustment function D f according to the actually modeled turbulence energy k u, the original modeled turbulence energy k m and the masking function F GAS in the first step, as shown in FIG. 2; the scale ratio is defined as the ratio of the turbulence energy k u of the actual modeling to the turbulence energy k m of the original modeling, and the dynamic scale-related adjustment function D f is a scale-ratio-related function, which is obtained by the following formula:
lGAS＝(1-FGAS)lu+FGASlm
Wherein, l u is a grid related scale, l m is a turbulence length scale given by a standard k-epsilon turbulence model, and the turbulence length scale is obtained by the following formula:
Wherein k m is the turbulence energy of the original modeling of the standard k-epsilon turbulence model, and epsilon m is the dissipation ratio of the original modeling obtained according to the standard k-epsilon turbulence model;
step four, reconstructing turbulence viscosity of the k-epsilon series model by using an adjusting function;
in the step, a dynamic scale-related adjusting function D f in the step three is adopted to adjust and control the turbulence viscosity v t in the standard k-epsilon turbulence model, so as to obtain a reconstructed turbulence viscosity v sfs, wherein the reconstructed turbulence viscosity v sfs is shown in the following formula:
Wherein, C μ is a constant in a standard k-epsilon turbulence model, and 0.09 is taken;
step five, turbulence simulation is carried out by using the reconstructed turbulence viscosity based on a standard k-epsilon turbulence model:
In this step, reynolds stress is calculated by using the turbulent viscosity v sfs reconstructed in the step four, and the transport equation of the standard k-epsilon turbulence model is updated to replace the turbulent viscosity v t in the original transport equation of the standard k-epsilon turbulence model, and the new transport equation is shown as follows:
And combining the obtained new transport equation with a standard k-epsilon turbulence model to obtain a grid self-adaptive turbulence simulation method based on a turbulence energy spectrum coupling k-epsilon series model, and using the grid self-adaptive turbulence simulation method for numerical simulation of a cylindrical bypass flow calculation example.
Transient calculation is carried out by adopting a fully implicit coupling solving technology, and the time step meets the CFL condition in engineering computational fluid dynamics. In addition, in order to better show the advantages of the embodiment of the invention, a standard k-epsilon turbulence model is selected to carry out numerical simulation on the cylindrical flow around calculation example, and the numerical simulation result of the grid self-adaptive turbulence simulation method based on the turbulence energy spectrum coupling k-epsilon series model is compared.
FIG. 3 is a graph of turbulent eddy current for a cylindrical flow-around calculation example calculated by a standard k- ε turbulence model, which was stained with turbulent viscosity ratios.
FIG. 4 is a graph of turbulent vortex diagram of a cylindrical flow around calculation example calculated by a grid adaptive turbulence simulation method based on a turbulence energy spectrum coupling k-epsilon series model, and the invention is colored by adopting a turbulence viscosity ratio.
The comparative analysis of fig. 3 and fig. 4 shows that the analysis capability of the turbulence vortex structure calculated by the grid self-adaptive turbulence simulation method based on the turbulence spectrum coupling k-epsilon series model is stronger than that of the result calculated by the standard k-epsilon turbulence model, so that richer turbulence structures can be captured under the same grid number, and more accurate flow field details can be provided.
The foregoing description of the preferred embodiments of the present invention is not intended to be limiting, but rather, any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the present invention are intended to be included within the scope of the present invention.
In summary, the embodiment of the invention determines the local grid length scale delta * by identifying the local grid size, and then reconstructs turbulence viscosity through the turbulence energy spectrum integral construction scale correlation function, thereby realizing grid self-adaptive simulation, effectively overcoming the problem of high empirical dependence of the traditional turbulence mixing model on the grid, greatly reducing calculation cost while improving calculation accuracy, remarkably accelerating turbulence simulation process, and providing a new method for flow prediction in the complex engineering field.
Claims (1)
1. A grid self-adaptive turbulence simulation method based on a turbulence energy spectrum coupling k-epsilon series model is characterized by comprising the following steps:
Step one, judging whether a shielding function is applied;
Step two, identifying the local grid scale;
thirdly, constructing a scale-dependent adjusting function based on turbulence energy spectrum integral coupling k-epsilon series model;
step four, reconstructing turbulence viscosity of the k-epsilon series model by using an adjusting function;
step five, based on a k-epsilon series model, performing turbulence simulation by using the reconstructed turbulence viscosity;
① The determining whether to apply a masking function includes:
Judging whether a masking function F GAS is adopted or not by combining the simulated flow state type, specifically, when the flow state type is free shearing flow, not adopting the masking function, wherein the masking function F GAS =0; when the flow state type is near wall flow, a masking function is used, and the masking function F GAS may be as follows: an F 1 mask function derived from the DDES-SST model, an F 2 mask function, and an F d mask function derived from the DDES-SA model;
② The identifying the local grid scale includes:
Determining a local grid length scale delta * by combining the masking function F GAS in the first step;
the local grid length scale Δ * is given by:
Δ*＝CGAS[(1-FGAS)Δvol+FGASΔmax]
Δmax＝max(Δx,Δy,Δz)
wherein, delta x is the length of the local hexahedral mesh, delta y is the width of the local hexahedral mesh, delta z is the height of the local hexahedral mesh, and C GAS is the empirical coefficient of 0.6;
③ The adjusting function based on turbulence energy spectrum integral coupling k-epsilon series model construction scale correlation comprises the following steps:
According to the modeling mode of turbulence energy in the k-epsilon series model, obtaining an original modeled turbulence energy k m, and according to the local grid length scale delta * in the second step, obtaining an actually modeled turbulence energy k u through integration based on a turbulence energy spectrum;
the actual modeling turbulence energy k u is obtained by the following formula:
Wherein, C k is the kolmogorov coefficient, 1.5 is taken, epsilon is the actual turbulent dissipation ratio, kappa c is the resolvable turbulent cutoff wave number, and is determined by the local grid length scale delta * in the second step:
Constructing a dynamic scale-dependent adjustment function D f according to the actual modeling turbulence energy k u, the original modeling turbulence energy k m and the shielding function F GAS in the step one; defining a scale ratio as the ratio of the actual modeling turbulence energy k u to the original modeling turbulence energy k m, and the dynamic scale-dependent adjustment function D f as the scale-dependent function, which is obtained by the following formula:
lGAS＝(1-FGAS)lu+FGASlm
Wherein l u is a grid correlation scale, l m is a turbulence length scale given by a k-epsilon series model, and is obtained by the following formula:
wherein k m is the turbulence energy of the original modeling of the k-epsilon series model, and epsilon m is the dissipation rate of the original modeling obtained according to the k-epsilon series model;
④ The reconstructing the turbulence viscosity of the k- ε series model using the adjustment function comprises:
And (3) regulating and controlling the turbulence viscosity v t in the k-epsilon series model by adopting the dynamic scale related regulating function D f in the step (III) to obtain a reconstructed turbulence viscosity v sfs, wherein the reconstructed turbulence viscosity v sfs is obtained by the following formula:
νsfs＝Df·νt
⑤ The turbulence simulation using the reconstructed turbulence viscosity based on the k- ε series model comprises:
And (3) calculating the Reynolds stress by adopting the reconstructed turbulence viscosity v sfs in the step (IV), updating a transport equation of the k-epsilon series model, replacing the turbulence viscosity v t in the original transport equation of the k-epsilon series model, and combining with the k-epsilon series model to obtain the grid self-adaptive turbulence simulation method based on the turbulence energy spectrum coupling k-epsilon series model.
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| CN110309521A (en) * | 2018-12-27 | 2019-10-08 | 大连船舶重工集团有限公司 | A kind of hard sail wind vibration response calculation method based on fluid structurecoupling simulation |
| CN114139465A (en) * | 2021-10-25 | 2022-03-04 | 中国空气动力研究与发展中心计算空气动力研究所 | Construction method of detached vortex simulation model |
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| CN106682398A (en) * | 2016-12-12 | 2017-05-17 | 华南理工大学 | RANS/LES method based on tubulence energy and turbulence length scale truncation |
| CN110309521A (en) * | 2018-12-27 | 2019-10-08 | 大连船舶重工集团有限公司 | A kind of hard sail wind vibration response calculation method based on fluid structurecoupling simulation |
| CN109858148A (en) * | 2019-01-30 | 2019-06-07 | 南京航空航天大学 | A kind of turbulent flow calculation method based on part filtering |
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