CN112131800A - 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 PDF

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CN112131800A
CN112131800A CN202010701626.0A CN202010701626A CN112131800A CN 112131800 A CN112131800 A CN 112131800A CN 202010701626 A CN202010701626 A CN 202010701626A CN 112131800 A CN112131800 A CN 112131800A
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CN112131800B (en
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于长平
齐涵
李新亮
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Institute of Mechanics of CAS
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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 of the energy flow calculated by the large vortex simulation sub-lattice model to the real energy flow; for 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; determining a first sub-lattice stress mesocoefficient of the large vortex simulation target model according to the ratio, the first sub-lattice stress, and the second sub-lattice stress using a fluence similarity method.

Description

Novel large vortex simulation method and device based on energy flow similarity
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
At present, there are three main numerical simulation methods in computational fluid dynamics, which are a direct numerical simulation method (DNS for short), a large vortex numerical simulation method (LES for short), and a reynolds average method (RANS for short). The direct numerical simulation method is the most accurate in calculation, but high in calculation cost and long in time consumption, the Reynolds average method is low in calculation cost, but poor in calculation result, the large vortex numerical simulation method is moderate in calculation cost, and the calculation result is between the direct numerical simulation method and the Reynolds average method.
In practical engineering application, the reynolds average method is the most common technical means, but in recent development, more and more engineers begin to use a large-vortex numerical simulation method to solve engineering problems, so that development of a new large-vortex numerical simulation method is of great significance to engineering application.
Disclosure of Invention
In view of this, to solve the problems in the prior art, embodiments of the present invention provide a novel large vortex simulation method and apparatus 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 of the energy flow calculated by the large vortex simulation sub-lattice model to the real energy flow;
for 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;
determining a first sub-lattice stress mesocoefficient of the large vortex simulation target model according to the ratio, the first sub-lattice stress, and the second sub-lattice stress using a fluence similarity method.
In one possible embodiment, the ratio comprises:
Figure BDA0002591377260000021
wherein, C1≈8×10-5，C20.01, said
Figure BDA0002591377260000022
Is the normalized filter width, said Δ+ ωThe method comprises the following steps:
Figure BDA0002591377260000023
the above-mentioned
Figure BDA0002591377260000024
Is the wall friction speed, said
Figure BDA0002591377260000025
Is the wall shear force.
In one possible embodiment, the determining the ratio between the fluence calculated by the macrovortex simulation sub-lattice model and the true fluence comprises:
the ratio between the fluence calculated by the large vortex simulation sub-lattice model and the true fluence is determined by fitting.
In one possible embodiment, the first sub-lattice stress comprises:
Figure BDA0002591377260000026
wherein, the value of τ isij smFor the first sub lattice stress, the SijIs the strain rate tensor.
In one possible embodiment, the second sub-lattice stress comprises:
Figure BDA0002591377260000027
in one possible embodiment, the coefficients include:
Figure BDA0002591377260000028
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 determination module is used for determining the ratio between the energy flow calculated by the large vortex simulation sub-lattice model and the real energy flow;
the stress determining module is used for determining a first sub-lattice stress of the large vortex simulation target model and a second sub-lattice stress of the gradient model aiming at transition and turbulence;
and the coefficient determining module is used for determining 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 by using a fluence similarity method.
In one possible embodiment, the ratio comprises:
Figure BDA0002591377260000031
wherein, C1≈8×10-5，C20.01, said
Figure BDA0002591377260000032
Is the normalized filter width, said Δ+ ωThe method comprises the following steps:
Figure BDA0002591377260000033
the above-mentioned
Figure BDA0002591377260000034
Is the wall friction speed, said
Figure BDA0002591377260000035
Is the wall shear force.
In a possible implementation, the ratio determining module is specifically configured to:
the ratio between the fluence calculated by the large vortex simulation sub-lattice model and the true fluence is determined by fitting.
In one possible embodiment, the first sub-lattice stress comprises:
Figure BDA0002591377260000036
wherein, the value of τ isij smFor the first sub lattice stress, the SijIs the strain rate tensor.
The novel large vortex simulation method and device based on energy flow similarity provided by the embodiment of the invention determine the first sub-lattice stress of a large vortex simulation target model and the second sub-lattice stress of a gradient model by determining the ratio between the energy flow calculated by a large vortex simulation sub-lattice model and the real energy flow, aiming at transition and turbulence and using an energy flow similarity method, determining 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 can realize more accurate prediction of turbulence and transition, the method is tested in engineering problems of aerospace and the like, has the characteristics of simplicity and convenience in 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 in the existing large-scale industrial fluid calculation software.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the embodiments of the present invention, and it is also possible for a person skilled in the art to obtain other drawings based on the drawings.
FIG. 1 is a schematic diagram illustrating a distribution variation of correlation numbers according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of an implementation 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 eta according to an embodiment of the present inventionΔA schematic of the normalized ratio of (a);
FIG. 4 is a schematic diagram of an average flow velocity profile according to an embodiment of the present invention;
FIG. 5 is a graphical illustration of the contribution of a model calculated and resolved Reynolds stress to the total Reynolds stress of EFSM and DNS in accordance with an embodiment of the present invention;
FIG. 6 is a partially enlarged schematic illustration of corner regions 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 apparatus based on energy flow similarity according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
For the convenience of understanding of the embodiments of the present invention, the following description will be further explained with reference to specific embodiments, which are not to be construed as limiting the embodiments of the present invention.
The large vortex numerical simulation method mainly comprises a vortex-viscosity model and a nonlinear model, the common vortex-viscosity model comprises a Smagorinsky model, a Vramenn model, a WALE model and the like, and the common nonlinear model comprises a scale similarity model and a gradient model. Besides the common models, there are some common large vortex simulation methods, such as dynamic methods, which can dynamically determine the coefficients of the sub-lattice model, so as to adapt to special conditions such as near-wall.
According to the energy flow similarity criterion, the embodiment of the invention provides a new method (EFSM) based on energy flux similarity, which is used for large vortex simulation (LES) of transition and turbulent flow.
In the case of determining the dimension Δ, the filtered kinetic energy equation comprises:
Figure BDA0002591377260000051
Figure BDA0002591377260000052
Figure BDA0002591377260000053
Figure BDA0002591377260000054
wherein, the J isΔIs the output term of the large-scale space kinetic energy, the tauijIs a sub-lattice stress, said
Figure BDA0002591377260000055
Is a pressure expansion term of large scale, said DΔIs viscous dissipation of large scale, piΔIs the fluence from scale Δ to smaller scales, and may also be referred to as sub-lattice scale dissipation.
Firstly, it can be known from prior analysis in the embodiment of the present invention that the gradient model can predict the value of the energy flow more accurately, so that the energy flow value calculated by the gradient model can be used as an approximate value of the true energy flow, and the specific method is as follows:
determining a correlation coefficient γ between the fluence calculated by the gradient model and the true fluence:
Figure BDA0002591377260000061
where < · > is the ensemble average, which can be considered as a spatial average of the extensional direction in plate flow, M is the fluence calculated by the gradient model, and R is the true fluence.
As shown in FIG. 1, at 8 ΔzDifferent y under filter width+Distribution of correlation coefficients (a) y along the 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 gradient model calculates a fluence value that is closer to the true fluence value than the Smagorinsky model and the Vreman model. As shown in fig. 2, an implementation flow diagram of a novel large vortex simulation method based on energy flow similarity provided in an embodiment of the present invention is shown, and the method may specifically include the following steps:
s201, determining the ratio of the energy flow calculated by the large vortex simulation sub-lattice model to the real energy flow;
in the embodiment of the invention, the ratio eta between the energy flow calculated by the large vortex simulation sub-lattice model and the real energy flow is determined by fittingΔThe ratio etaΔThis can be shown as follows:
Figure BDA0002591377260000062
wherein, C1≈8×10-5，C20.01, said
Figure BDA0002591377260000063
Is the normalized filter width, said Δ+ ωThe method comprises the following steps:
Figure BDA0002591377260000064
the above-mentioned
Figure BDA0002591377260000065
Is the wall friction speed, said
Figure BDA0002591377260000066
Is the wall shear force.
It can be found by calculation that the ratio of the energy flow value calculated by the gradient model to the true energy flow value is about 1 at different positions and filter widths, as shown by the formula η shown in fig. 3ΔNormalized ratio of (a).
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 turbulent flows, the large vortex in the embodiment of the invention simulates the first sub-lattice stress of the target model, such as the sub-lattice stress tau of the Smagorinsky modelijThis can be shown as follows:
Figure BDA0002591377260000071
wherein, the value of τ isij smFor the first sub lattice stress, the SijIs the strain rate tensor.
And for the second sub-lattice stress tau of the gradient modelijThis can be shown as follows:
Figure BDA0002591377260000072
s203, determining 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 by using a fluence similarity method.
In the embodiment of the invention, a power flow similarity method is used for determining 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, such as a coefficient C for a Smagorinsky modelsmThis can be shown as follows:
Figure BDA0002591377260000073
for most vortex-viscous models, this method can be used to determine the coefficients of their models.
In the embodiment of the invention, the robustness and high similarity with real flow of the simulation are ensured, and the method applies the energy flow similarity criterion (EFSM) to the large vortex simulation of compressible turbulent flow and transition flow. Test analysis was performed on compressible channel wall turbulence and compression dog-ear flow with shock boundary layer interference characteristics. The program used by the compressible calculation example is Opencfd-SC, the discretization of the flow term and the viscosity term in the N-S equation adopts six-order central difference, and the equation adopts explicit three-order Runge-Kutta to carry out time advance. And adopting adaptive spatial filtering to capture shock waves in partial areas.
As shown in fig. 4, the mean flow direction velocity distributions of the DNS after van-Driest conversion and different SGS models;
as shown in fig. 5, the model calculated and resolved reynolds stresses contribute to the overall reynolds stresses for EFSM and DNS;
as shown in fig. 6, a partial magnified view of the corner regions of instantaneous local energy flux from LES and filtered DNS data. (a) A DNS; (b) EFSM; (c) vreman (an example of a compression corner).
Test results indicate that EFSM can predict transitions in these flows and fully develop turbulent flow better than other submesh models. All analytical results indicate that EFSM can effectively solve several classical difficulties. Overall, EFSM is a scale-adaptive method, does not require test filtering and wall models, and is suitable for LES with real wall flows with complex geometric boundaries. Statistical results show that compared with results of direct numerical simulation calculation, the method can be used for predicting turbulence and transition more accurately, and is tested in 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 in the existing large-scale industrial fluid calculation software.
Corresponding to the above method embodiment, an embodiment of the present invention further provides a novel large vortex simulation apparatus based on energy flow similarity, as shown in fig. 7, where the apparatus includes: ratio determination module 710, stress determination module 720, coefficient determination module 730.
A ratio determination module 710 for determining a ratio between the energy flow calculated by the large vortex simulation sub-lattice model and the real energy flow;
the stress determining module 720 is used for determining a first sub-lattice stress of the large vortex simulation target model and a second sub-lattice stress of the gradient model for transition and turbulence;
a coefficient determining module 730, 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 by using a fluence similarity method.
In a specific implementation manner of the embodiment of the present invention, the ratio includes:
Figure BDA0002591377260000091
wherein, C1≈8×10-5，C20.01, said
Figure BDA0002591377260000092
Is the normalized filter width, said Δ+ ωThe method comprises the following steps:
Figure BDA0002591377260000093
the above-mentioned
Figure BDA0002591377260000094
Is the wall friction speed, said
Figure BDA0002591377260000095
Is the 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 fluence calculated by the large vortex simulation sub-lattice model and the true fluence is determined by fitting.
In a specific implementation of an embodiment of the invention, the first sub-lattice stress comprises:
Figure BDA0002591377260000096
wherein, the value of τ isij smFor the first sub lattice stress, the SijIs the strain rate tensor.
Those of skill would further appreciate that the various illustrative components 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 components and steps have been described above generally in terms of their functionality in order to clearly illustrate this 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 implementation. 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, a software system executed by a processor, or a combination of the two. The software system may reside 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 above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A novel large vortex simulation method based on energy flow similarity is characterized by comprising the following steps:
determining the ratio of the energy flow calculated by the large vortex simulation sub-lattice model to the real energy flow;
for 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;
determining a first sub-lattice stress mesocoefficient of the large vortex simulation target model according to the ratio, the first sub-lattice stress, and the second sub-lattice stress using a fluence similarity method.
2. The method of claim 1, wherein the ratio comprises:
Figure FDA0002591377250000011
wherein, C1≈8×10-5，C20.01, said
Figure FDA0002591377250000012
Is the normalized filter width, said Δ+ ωThe method comprises the following steps:
Figure FDA0002591377250000013
the above-mentioned
Figure FDA0002591377250000014
Is the wall friction speed, said
Figure FDA0002591377250000015
Is the wall shear force.
3. The method of claim 2, wherein determining a ratio between the fluence calculated by the macrovortex simulation sub-lattice model and the true fluence comprises:
the ratio between the fluence calculated by the large vortex simulation sub-lattice model and the true fluence is determined by fitting.
4. The method of claim 2, wherein the first sub-lattice stress comprises:
Figure FDA0002591377250000016
wherein, the value of τ isij smFor the first sub lattice stress, the SijIs the strain rate tensor.
5. The method of claim 4, wherein the second sub-lattice stress comprises:
Figure FDA0002591377250000021
6. the method of claim 5, wherein the coefficients comprise:
Figure FDA0002591377250000022
7. a novel large vortex simulator based on energy flow similarity, the device comprising:
the ratio determination module is used for determining the ratio between the energy flow calculated by the large vortex simulation sub-lattice model and the real energy flow;
the stress determining module is used for determining a first sub-lattice stress of the large vortex simulation target model and a second sub-lattice stress of the gradient model aiming at transition and turbulence;
and the coefficient determining module is used for determining 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 by using a fluence similarity method.
8. The apparatus of claim 7, wherein the ratio comprises:
Figure FDA0002591377250000023
wherein, C1≈8×10-5，C20.01, said
Figure FDA0002591377250000024
Is the normalized filter width, said Δ+ ωThe method comprises the following steps:
Figure FDA0002591377250000025
the above-mentioned
Figure FDA0002591377250000026
Is the wall friction speed, said
Figure FDA0002591377250000027
Is the wall shear force.
9. The apparatus of claim 8, wherein the ratio determination module is specifically configured to:
the ratio between the fluence calculated by the large vortex simulation sub-lattice model and the true fluence is determined by fitting.
10. The apparatus of claim 8, wherein the first sub-lattice stress comprises:
Figure FDA0002591377250000031
wherein, the value of τ isij smFor the first sub lattice stress, the SijIs the strain rate tensor.
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