CN112131800B - Novel large vortex simulation method and device based on energy flow similarity - Google Patents
Novel large vortex simulation method and device based on energy flow similarity Download PDFInfo
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Abstract
The embodiment of the invention relates to a novel large vortex simulation method and device based on energy flow similarity, wherein the method comprises the following steps: determining the ratio between the calculated energy flow and the actual energy flow of the large vortex simulated sub-grid model; aiming at transition and turbulence, determining a first sub-lattice stress of a large vortex simulation target model and a second sub-lattice stress of a gradient model; and determining a first sub-lattice stress medium coefficient of the large vortex simulation target model according to the ratio, the first sub-lattice stress and the second sub-lattice stress by using an energy flow similarity method.
Description
Technical Field
The embodiment of the invention relates to the technical field of fluid mechanics, in particular to a novel large vortex simulation method and device based on energy flow similarity.
Background
Currently, there are three numerical simulation methods in computational fluid dynamics, namely a direct numerical simulation method (DNS for short), a large eddy-current numerical simulation method (LES for short), and a RANS for short. The direct numerical simulation method is the most accurate in calculation, high in calculation cost, long in time consumption, low in calculation cost of the Reynolds average method, relatively poor in calculation result, moderate in calculation cost of the large-vortex numerical simulation method, and the calculation result is between the direct numerical simulation method and the Reynolds average method.
In practical engineering application, the Reynolds averaging method is the most commonly used technical means, but in the development of recent years, more and more engineering staff begin to use a large-eddy-value simulation method to solve engineering problems, so that the development of a new large-eddy-value simulation method has great significance for engineering application.
Disclosure of Invention
In view of the above, in order to solve the problems in the prior art, the embodiment of the invention provides a novel large vortex simulation method and device based on energy flux similarity.
In a first aspect, an embodiment of the present invention provides a novel large vortex simulation method based on energy flow similarity, where the method includes:
determining the ratio between the calculated energy flow and the actual energy flow of the large vortex simulated sub-grid model;
aiming at transition and turbulence, determining a first sub-lattice stress of a large vortex simulation target model and a second sub-lattice stress of a gradient model;
and determining a first sub-lattice stress medium coefficient of the large vortex simulation target model according to the ratio, the first sub-lattice stress and the second sub-lattice stress by using an energy flow similarity method.
In one possible embodiment, the ratio comprises:
wherein C is 1 ≈8×10 -5 ，C 2 Approximately 0.01, saidIs the normalized filter width, delta + ω Comprising the following steps:
the saidIs the wall friction speed, said +.>Is wall shear force.
In one possible embodiment, the determining the ratio between the energy flow calculated by the large vortex simulated sub-lattice model and the real energy flow includes:
the ratio between the calculated energy flow and the real energy flow of the large vortex simulation sub-grid model is determined through fitting.
In one possible embodiment, the first sub-lattice stress comprises:
wherein, the tau ij sm For the first sub-lattice stress, the S ij Is the strain rate tensor.
In one possible embodiment, the second sub-lattice stress comprises:
in one possible embodiment, the coefficients include:
in a second aspect, an embodiment of the present invention provides a novel large vortex simulation apparatus based on energy flow similarity, where the apparatus includes:
the ratio determining module is used for determining the ratio between the energy flow calculated by the large vortex simulation sub-grid model and the real energy flow;
the stress determining module is used for determining first sub-lattice stress of the large vortex simulation target model and second sub-lattice stress of the gradient model aiming at transition and turbulence;
and the coefficient determining module is used for determining coefficients in the first sub-lattice stress of the large vortex simulation target model according to the ratio, the first sub-lattice stress and the second sub-lattice stress by using an energy flow similarity method.
In one possible embodiment, the ratio comprises:
wherein C is 1 ≈8×10 -5 ，C 2 Approximately 0.01, saidIs the normalized filter width, delta + ω Comprising the following steps:
the saidIs the wall friction speed, said +.>Is wall shear force.
In one possible embodiment, the ratio determining module is specifically configured to:
the ratio between the calculated energy flow and the real energy flow of the large vortex simulation sub-grid model is determined through fitting.
In one possible embodiment, the first sub-lattice stress comprises:
wherein, the tau ij sm For the first sub-lattice stress, the S ij Is the strain rate tensor.
According to the novel large vortex simulation method and device based on energy flow similarity, the ratio between the energy flow calculated by the large vortex simulation sub-grid model and the real energy flow is determined, the first sub-grid stress of the large vortex simulation target model and the second sub-grid stress of the gradient model are determined according to the transition and turbulence, the energy flow similarity method is used, the coefficients in the first sub-grid stress of the large vortex simulation target model are determined according to the ratio, the first sub-grid stress and the second sub-grid stress, turbulence and transition can be predicted more accurately, the examination is obtained in engineering problems of aerospace and the like, and the novel large vortex simulation method and device have the characteristics of simplicity and convenience in operation, high calculation efficiency and the like, are suitable for numerical simulation of hydrodynamics, low-speed and high-speed aerodynamics, and can be integrated into the existing fluid calculation software of various industries conveniently.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the embodiments of the present invention, and other drawings may be obtained according to these drawings for a person having ordinary skill in the art.
FIG. 1 is a diagram illustrating a change in correlation coefficient distribution according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an implementation flow chart of a novel large vortex simulation method based on energy flow similarity according to an embodiment of the present invention;
FIG. 3 shows a formula η according to an embodiment of the present invention Δ Schematic of normalized ratio of (2);
FIG. 4 is a graph showing an average flow velocity distribution according to an embodiment of the present invention;
FIG. 5 is a graph showing the contribution of Reynolds stresses calculated and resolved by a model of an embodiment of the invention to the overall Reynolds stresses of EFSM and DNS;
FIG. 6 is a schematic enlarged partial view of a corner region of instantaneous local energy flux from LES and filtered DNS data in accordance with an embodiment of the present invention;
fig. 7 is a schematic structural diagram of a novel large vortex simulation device based on energy flow similarity according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
For the purpose of facilitating an understanding of the embodiments of the present invention, reference will now be made to the following description of specific embodiments, taken in conjunction with the accompanying drawings, which are not intended to limit the embodiments of the invention.
The large vortex numerical simulation method mainly comprises a vortex bonding model and a nonlinear model, wherein the common vortex bonding model comprises a Smogrinsky model, a Vremann model, a WALE model and the like, and the common nonlinear model comprises a scale similarity model and a gradient model. In addition to the conventional models, there are some conventional large vortex simulation methods, such as dynamic methods, which can dynamically determine coefficients of the sub-lattice model, so as to adapt to special conditions such as near walls.
According to the energy flow similarity criterion, the embodiment of the invention provides a new method (EFSM) based on energy flow similarity, which is used for transition and turbulence large vortex simulation (LES).
In the case of determining the dimension delta, the filtered kinetic energy equation includes:
wherein the J Δ Is the output term of large scale space kinetic energy, τ ij Is a sub-lattice stress ofIs a large scale pressure expansion term, said D Δ Is a viscous dissipation of large dimensions, the pi Δ Is an energy flow of scale delta to smaller scale, and may also be referred to as sub-lattice scale dissipation.
Firstly, according to the prior analysis in the embodiment of the invention, the gradient model can accurately predict the value of the energy flow, so that the energy flow value calculated by the gradient model can be used as the approximation value of the real energy flow, and the specific method is as follows:
determining a correlation coefficient gamma between the energy flow calculated by the gradient model and the real energy flow:
where </cndot > is the ensemble average, which can be considered as the spatial average of the spread-out direction in a flat flow, M is the fluence calculated by the gradient model, and R is the true fluence.
As shown in fig. 1, at 8% z Different y under filter width + Correlation coefficient distribution (a) y along flow direction + ＝15；(b)y + ＝52；(c)y + =109; in the case of x=8.8, the correlation coefficient varies at different filter scales.
As can be seen from fig. 1 above, the energy values calculated by the gradient model are closer to the true energy values than the Smagorinsky model and the Vreman model. As shown in fig. 2, a schematic implementation flow chart of a novel large vortex simulation method based on energy flow similarity according to an embodiment of the present invention may specifically include the following steps:
s201, determining the ratio between the energy flow calculated by the large vortex simulated sub-grid model and the real energy flow;
in the embodiment of the invention, the ratio eta between the energy flow calculated by the large vortex simulation sub-grid model and the real energy flow is determined by fitting Δ The ratio eta Δ The following can be mentioned:
wherein C is 1 ≈8×10 -5 ，C 2 Approximately 0.01, saidIs the normalized filter width, delta + ω Comprising the following steps:
the saidIs the wall friction speed, said +.>Is wall shear force.
It can be found by calculation that the ratio of the energy value calculated by the gradient model to the true energy value is about 1 at different positions and filter widths, as shown in the formula eta of FIG. 3 Δ Is a normalized ratio of (c).
S202, determining a first sub-lattice stress of a large vortex simulation target model and a second sub-lattice stress of a gradient model aiming at transition and turbulence;
for most transitions and turbulences, the first sub-lattice stress of the large vortex simulation target model in the embodiments of the present invention, for example, the sub-lattice stress τ of the Smogorinsky model ij The following can be mentioned:
wherein, the tau ij sm For the first sub-lattice stress, the S ij Is the strain rate tensor.
Whereas for the second sub-lattice stress τ of the gradient model ij The following can be mentioned:
s203, determining a first sub-lattice stress medium coefficient of the large vortex simulation target model according to the ratio, the first sub-lattice stress and the second sub-lattice stress by using an energy flow similarity method.
In an embodiment of the present invention, the coefficient of first sub-lattice stress of the large vortex simulation target model, for example, for Sma, is determined from the ratio, the first sub-lattice stress, and the second sub-lattice stress using an energy flow similarity methodCoefficients C of the gorinsky model sm The following can be mentioned:
for most vortex-dependent models, this method can be used to determine the coefficients of its model.
In the embodiment of the invention, the robustness of simulation and high similarity with real flow are ensured, and the method applies the energy flow similarity criterion (EFSM) to large vortex simulation of compressible turbulence and transition flow. Test analysis was performed in a compressible channel wall turbulence and a compression angle flow with shock boundary layer disturbance characteristics. The compressible example uses the program of Opencfd-SC, the discretization of the convection item and the viscous item in the N-S equation adopts six-order center difference, and the equation adopts explicit third-order Runge-Kutta for time propulsion. Adaptive spatial filtering is used in the partial region to capture the shock wave.
As shown in fig. 4, the mean flow velocity profile of the van-Driest converted DNS and different SGS models;
as shown in fig. 5, the model calculates and resolves the contribution of reynolds stress to the overall reynolds stress for EFSM and DNS;
as shown in fig. 6, a partial magnified view of the corner region of instantaneous local energy flux from LES and filtered DNS data. (a) DNS; (b) EFSM; (c) Vreman (example of a compressed corner).
Test results show that the EFSM can better predict transition of the flows and completely develop turbulent flow compared with other sub-grid models. All analysis results indicate that EFSM can effectively solve several classical difficulties. In general, EFSM is a scale-adaptive method that does not require test filtering and wall modeling, and is suitable for LES with actual wall flow with complex geometric boundaries. The statistical result shows that compared with the result of direct numerical simulation calculation, the method can be used for more accurately predicting turbulence and transition, and can be used for detecting engineering problems such as aerospace and the like. The model has the characteristics of simple and convenient operation, high calculation efficiency and the like, is suitable for numerical simulation of hydrodynamics, low-speed and high-speed aerodynamics, and can be conveniently integrated into the existing large industrial fluid calculation software.
Corresponding to the method embodiment, the embodiment of the invention also provides a novel large vortex simulation device based on energy flow similarity, as shown in fig. 7, the device comprises: ratio determination module 710, stress determination module 720, coefficient determination module 730.
The ratio determining module 710 is configured to determine a ratio between the energy flow calculated by the large vortex simulated sub-lattice model and the real energy flow;
the stress determining module 720 is configured to determine, for the transition and the turbulence, a first sub-lattice stress of the large vortex simulation target model and a second sub-lattice stress of the gradient model;
the coefficient determining module 730 is configured to determine a coefficient in the first sub-lattice stress of the large vortex simulation target model according to the ratio, the first sub-lattice stress, and the second sub-lattice stress using an energy flow similarity method.
In a specific implementation of the embodiment of the present invention, the ratio includes:
wherein C is 1 ≈8×10 -5 ，C 2 Approximately 0.01, saidIs the normalized filter width, delta + ω Comprising the following steps:
the saidIs the wall friction speed, said +.>Is wall shear force.
In a specific implementation manner of the embodiment of the present invention, the ratio determining module is specifically configured to:
the ratio between the calculated energy flow and the real energy flow of the large vortex simulation sub-grid model is determined through fitting.
In a specific implementation of the embodiment of the present invention, the first sub-lattice stress includes:
wherein, the tau ij sm For the first sub-lattice stress, the S ij Is the strain rate tensor.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative elements and steps are described above generally in terms of function in order to clearly illustrate the interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied in hardware, in a software system executed by a processor, or in a combination of the two. The software system may be disposed in Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (6)
1. A novel large vortex simulation method based on energy flow similarity, which is characterized by comprising the following steps:
the ratio between the energy flow calculated by the large vortex simulation sub-grid model and the actual energy flow of the gradient model is determined, and the specific steps are as follows: determining a ratio η between the calculated energy flow and the real energy flow of the large vortex simulated sub-lattice model by fitting Δ The ratio eta Δ The following can be mentioned:
wherein C is 1 ≈8×10 -5 ，C 2 Approximately 0.01, saidIs the normalized filter width, delta + ω Comprising the following steps:
the saidIs the wall friction speed, said +.>Is wall shear force;
aiming at transition and turbulence, determining a first sub-lattice stress of a large vortex simulation target model and a second sub-lattice stress of a gradient model;
and determining a first sub-lattice stress medium coefficient of the large vortex simulation target model according to the ratio, the first sub-lattice stress and the second sub-lattice stress by using an energy flow similarity method.
2. The method of claim 1, wherein the first sub-lattice stress comprises:
wherein, the tau ij sm For the first sub-lattice stress, the S ij Is the strain rate tensor.
3. The method of claim 2, wherein the second sub-lattice stress comprises:
4. a method according to claim 3, wherein the coefficients comprise:
5. novel large vortex simulation device based on energy flow similarity, characterized in that the device comprises:
the ratio determining module is used for determining the ratio between the energy flow calculated by the large vortex simulation sub-grid model and the actual energy flow of the gradient model, and specifically comprises the following steps: determining a ratio η between the calculated energy flow and the real energy flow of the large vortex simulated sub-lattice model by fitting Δ The ratio eta Δ The following can be mentioned:
wherein C is 1 ≈8×10 -5 ，C 2 Approximately 0.01, saidIs the normalized filter width, delta + ω Comprising the following steps:
the saidIs the wall friction speed, said +.>Is wall shear force;
the stress determining module is used for determining first sub-lattice stress of the large vortex simulation target model and second sub-lattice stress of the gradient model aiming at transition and turbulence;
and the coefficient determining module is used for determining coefficients in the first sub-lattice stress of the large vortex simulation target model according to the ratio, the first sub-lattice stress and the second sub-lattice stress by using an energy flow similarity method.
6. The apparatus of claim 5, wherein the first sub-lattice stress comprises:
wherein, the tau ij sm For the first sub-lattice stress, the S ij Is the strain rate tensor.
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