CN113111609B - Novel local turbulence pulsation intensity detection method - Google Patents

Novel local turbulence pulsation intensity detection method Download PDF

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CN113111609B
CN113111609B CN202110503111.4A CN202110503111A CN113111609B CN 113111609 B CN113111609 B CN 113111609B CN 202110503111 A CN202110503111 A CN 202110503111A CN 113111609 B CN113111609 B CN 113111609B
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邓小兵
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Abstract

The invention discloses a novel local turbulence pulsation intensity detection method, which comprises the following steps: s1, designing two low-pass numerical filter operators LPF1 and LPF 2; s2, defining a turbulence small-scale pulsation intensity criterion based on low-pass numerical filter operators LPF1 and LPF2, and obtaining local turbulence pulsation intensity according to the turbulence small-scale pulsation intensity criterion. The invention provides a method for judging the development degree of flow field turbulence, which can provide a technical means for developing a relevant numerical method. The invention detects the local turbulence energy spectrum based on numerical filtering, and judges the local turbulence pulse intensity based on the local turbulence energy spectrum. The low-pass filter operator designed by the invention adopts a five-point template and can be easily realized in second-order finite volume software which is most widely applied at present.

Description

Novel local turbulence pulsation intensity detection method
Technical Field
The invention belongs to the field of fluid mechanics calculation, and particularly relates to a novel local turbulence pulsation intensity detection 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 flow and turbulent flow. The actual flow is substantially turbulent or at least comprises a portion of turbulent flow. 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.
The basic idea of the turbulence large vortex simulation method is that distinguishable scale flow (large vortex) larger than the grid scale in a flow field is directly calculated and solved by adopting a control equation, and sub-grid scale flow (small vortex) smaller than the grid scale is simulated by adopting a sub-grid scale model. The flow field obtained by the turbulence large vortex simulation contains abundant turbulence small-scale pulsating structures. These small scale pulses are interacting at all times, and errors occurring in the small scale segments propagate rapidly to all scales, which makes this method extremely sensitive to numerical errors, especially dissipative errors. In addition, the large vortex simulation method cuts off a flow field at a certain turbulence scale, so that a physically significant flow structure exists near the grid scale, and numerical errors exist near the grid scale, particularly in a region where spatial discrete errors exist, so that numerical dissipation and small-scale turbulence evolution easily influencing large vortex simulation are achieved. If a reasonable detection method for the local turbulence pulsation intensity of the flow field can be designed, the turbulence small-scale pulsation intensity obtained by numerical simulation can be reasonably evaluated, so that the numerical method is adjusted in a targeted manner to obtain a correct simulation result.
Disclosure of Invention
Aiming at the defects in the prior art, the novel local turbulence pulsation intensity detection method provided by the invention solves the problem that the local turbulence pulsation intensity cannot be accurately judged.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: a novel local turbulence pulsation intensity detection method comprises the following steps:
s1, designing two low-pass numerical filter operators LPF1 and LPF 2;
s2, defining a turbulence small-scale pulsation intensity criterion based on low-pass numerical filter operators LPF1 and LPF2, and obtaining local turbulence pulsation intensity according to the turbulence small-scale pulsation intensity criterion.
Further: the specific steps of step S1 are:
s11, designing a low-pass filter LPF 0;
the low pass filter operator LPF0 is specifically:
Figure BDA0003057181820000021
a0＝1+3a2
a1＝-4a2
in the above formula, f (x)j) Is a grid point xjThe function to be filtered of (a) is,
Figure BDA0003057181820000022
is a grid point xjProcessing the filtered function, a0,a1,a2Is a constant coefficient;
s12, low pass filter LPF0 according to a2Obtaining two low pass filter operators LPF1 and LPF 2;
further: a of the low pass filter operator LPF1 in said step S122A value of-1/32, the low pass filter operator LPF22The value is-1/8.
Further: the specific steps of step S2 are:
S21, low pass filter operators LPF1 and LPF2 respectively corresponding to the velocity field
Figure BDA0003057181820000031
Filtering to obtain filtering speed
Figure BDA0003057181820000032
And
Figure BDA0003057181820000033
s22, pair
Figure BDA0003057181820000034
And
Figure BDA0003057181820000035
respectively calculating corresponding residual kinetic energy;
s23, defining a criterion of turbulence small-scale pulsation intensity according to the residual kinetic energy;
s24, obtaining the local turbulence pulsation intensity according to the change rule of the turbulence small-scale pulsation intensity criterion along with the energy spectrum slope p.
Further: the filtering speed in the step S21
Figure BDA0003057181820000036
And
Figure BDA0003057181820000037
the calculation formula of (2) is as follows:
Figure BDA0003057181820000038
Figure BDA0003057181820000039
further: the calculation formula of the residual kinetic energy in the step S22 is:
Figure BDA00030571818200000310
Figure BDA00030571818200000311
in the above formula, dE1Is composed of
Figure BDA00030571818200000312
Corresponding residual kinetic energy, dE2Is composed of
Figure BDA00030571818200000313
The residual kinetic energy of (2).
Further: the criterion of the small-scale turbulent pulsation intensity in the step S23 is as follows:
Figure BDA00030571818200000314
in the above formula, the first and second carbon atoms are,
Figure BDA00030571818200000315
is criterion of turbulent small-scale pulse intensity.
Further: the local turbulence pulsation intensity in the step S24 is:
when the temperature is higher than the set temperature
Figure BDA00030571818200000316
When the turbulence pulsation intensity is lower than a theoretical value, the flow field is over-dissipated;
when in use
Figure BDA00030571818200000317
When the turbulence pulsation intensity is higher than the theoretical value, the flow field is under-dissipated.
The invention has the beneficial effects that: the invention provides a criterion and provides a method for judging the development degree of the flow field turbulence, and can provide a technical means for developing a relevant numerical method. The invention detects the local turbulence energy spectrum based on numerical filtering, and judges the local turbulence pulse intensity based on the local turbulence energy spectrum. The low-pass filter operator designed by the invention adopts a five-point template and can be easily realized in second-order finite volume software which is most widely applied at present.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a model of the transfer function of the low pass filter operators LPF1 and LPF2 of the present invention;
FIG. 3 is a schematic diagram illustrating a principle of calculating a local instantaneous power spectrum slope through a low-pass filtering operation according to the present invention;
FIG. 4 shows the local turbulence pulsation intensity in the present invention
Figure BDA0003057181820000041
Graph with the change of local turbulence spectrum slope.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
According to Kolmogorov's K41 theory, the energy spectral distribution of the turbulent inertia sub-zone obeys:
E(k)～k-p,p＝5/3 (1)
large vortex simulation methods typically truncate the flow to resolvable and sub-lattice scales in the inertial sub-region. Thus, in large vortex simulation calculations, the turbulent energy spectrum should obey this distribution as well, near the grid scale. For turbulence large vortex simulation based on a vortex viscosity model, the physical model itself already assumes that local turbulence is in an equilibrium state, and thus the statistical properties are determined by the energy spectrum, so that equation (1) can be used as an effective criterion for excessive suppression or excessive development of turbulence small-scale pulsation. The invention provides a method for detecting a local turbulence state, which is characterized in that the method comprises the following steps of: local turbulent flow dissipation is indicated when p >5/3 of the local flow field and local turbulent under-dissipation when p < 5/3.
As shown in fig. 1, a novel local turbulence pulsation intensity detection method includes the following steps:
s1, designing two low-pass numerical filter operators LPF1 and LPF 2;
the most widely used second order numerical method in computational fluid dynamics uses a numerical format with a template width of 5 grid points. Numerical simulation software based on this usually gives 2-layer grid points at the computation boundaries as boundary conditions, so-called virtual points (ghost cells). In order to enable the designed filter operators LPF1 and LPF2 to be applied to existing second-order computational fluid dynamics software without increasing the boundary point overhead, the filter operators LPF1 and LPF2 are also designed as 5 grid points.
The specific steps of step S1 are:
s11, designing a low-pass filter LPF 0;
the low pass filter operator LPF0 is specifically:
Figure BDA0003057181820000051
a0＝1+3a2
a1＝-4a2 (2)
in the above formula, f (x)j) Is a grid point xjThe function to be filtered of (a) is,
Figure BDA0003057181820000052
is a grid point xjProcessing the filtered function, a0,a1,a2Is a constant coefficient;
s12, low pass filter LPF0 according to a2Obtaining two low pass filter operators LPF1 and LPF 2; fig. 2 shows a transfer function model of the low filter operators LPF1 (formula (3)) and LPF2 (formula (4)) according to the present invention. In the figure, the abscissa ω is k Δ, Δ is a lattice scale, and k is a wave number. It can be seen that the two operators have different passing rates in high wavenumber regions near the grid truncation scale, thereby providing the possibility of energy spectrum detection.
LPF1:
Figure BDA0003057181820000053
a0＝1+3a2
a1＝-4a2
a2＝-1/32 (3)
LPF2:
Figure BDA0003057181820000061
a0＝1+3a2
a1＝-4a2
a2＝-1/8 (4)
S2, defining a turbulence small-scale pulsation intensity criterion based on low-pass numerical filter operators LPF1 and LPF2, and obtaining local turbulence pulsation intensity according to the turbulence small-scale pulsation intensity criterion.
The turbulence intensity criterion provided by the invention is to obtain the residual turbulence kinetic energy of two adjacent scale areas near the grid scale through two filtering operations with different filtering widths, and to calculate the local turbulence kinetic energy spectrum slope according to the ratio of the residual kinetic energy.
A theoretical schematic of this decision is given in fig. 3. For a given spectral slope, two residual kinetic energies can be obtained by performing two low pass filtering operations on the velocity field using LPF1 and LPF 2. It is clear that the ratio of these two residual kinetic energies is a monotonic function of the slope of the energy spectrum. Therefore, the slope of the spectrum can be found from the ratio of the residual kinetic energies.
First, the velocity field is filtered by the low pass filter operators LPF1 and LPF2, respectively
Figure BDA0003057181820000062
Filtering to obtain
Figure BDA0003057181820000063
And
Figure BDA0003057181820000064
Figure BDA0003057181820000065
Figure BDA0003057181820000066
s22, pair
Figure BDA0003057181820000067
And
Figure BDA0003057181820000068
respectively calculating corresponding residual kinetic energy; the residual kinetic energy is calculated by the formula:
Figure BDA0003057181820000069
Figure BDA00030571818200000610
in the above formula, dE1Is composed of
Figure BDA00030571818200000611
Corresponding residual kinetic energy, dE2Is composed of
Figure BDA00030571818200000612
Represents the vector inner product operation.
S23, defining a criterion of turbulence small-scale pulsation intensity according to the residual kinetic energy;
the criterion of turbulent small-scale pulsating intensity is as follows:
Figure BDA0003057181820000071
In the above-mentioned formula, the compound has the following structure,
Figure BDA0003057181820000072
is the criterion of turbulent small-scale pulsation intensity.
From the characteristics of the operators LPF1 and LPF2, the method can be obtained
Figure BDA0003057181820000073
The change rule along with the slope p of the energy spectrum is shown in FIG. 4. It can be seen that, near p-5/3,
Figure BDA0003057181820000074
the slope p of the spectrum is approximately linear. Calculated according to the characteristics of the operators LPF1 and LPF2
Figure BDA0003057181820000075
The theoretical value at p-5/3 is:
Figure BDA0003057181820000076
s24, obtaining the local turbulence pulsation intensity according to the change rule of the turbulence small-scale pulsation intensity criterion along with the energy spectrum slope p.
The local turbulence pulsation intensity is:
when in use
Figure BDA0003057181820000077
When the turbulence pulsation intensity is lower than a theoretical value, the flow field is over-dissipated;
when in use
Figure BDA0003057181820000078
When the turbulence pulsation intensity is higher than the theoretical value, the flow field is under-dissipated.

Claims (6)

1. A novel local turbulence pulsation intensity detection method is characterized by comprising the following steps:
s1, designing two low-pass numerical filter operators LPF1 and LPF 2;
s2, defining turbulence small-scale pulsation intensity criterion based on low-pass numerical filter operators LPF1 and LPF2, and obtaining local turbulence pulsation intensity according to the turbulence small-scale pulsation intensity criterion;
the specific steps of step S1 are:
s11, designing a low-pass filter LPF 0;
the low pass filter operator LPF0 is specifically:
Figure FDA0003656066070000011
a0＝1+3a2
a1＝-4a2
in the above formula, f (x)j) Is a grid point x jThe function to be filtered of (a) is,
Figure FDA0003656066070000012
is a grid point xjTo the filtered function, a0,a1,a2Is a constant coefficient;
s12, low pass filter operator LPF0 according to a2Obtaining two low-pass filter operators LPF1 and LPF 2;
the specific steps of step S2 are:
s21, low pass filter operators LPF1 and LPF2 respectively corresponding to the velocity field
Figure FDA0003656066070000017
Filtering to obtain filtering speed
Figure FDA0003656066070000013
And
Figure FDA0003656066070000014
s22, pair
Figure FDA0003656066070000015
And
Figure FDA0003656066070000016
respectively calculating corresponding residual kinetic energy;
s23, defining a criterion of turbulence small-scale pulsation intensity according to the residual kinetic energy;
s24, obtaining the local turbulence pulsation intensity according to the change rule of the turbulence small-scale pulsation intensity criterion along with the energy spectrum slope p.
2. The method for detecting local turbulence pulsation intensity as claimed in claim 1, wherein a of the low pass filter operator LPF1 in step S122A value of-1/32, the low pass filter operator LPF22The value is-1/8.
3. The method for detecting local turbulence pulsation intensity as claimed in claim 1, wherein the filtering speed in step S21
Figure FDA0003656066070000021
And
Figure FDA0003656066070000022
the calculation formula of (2) is as follows:
Figure FDA0003656066070000023
Figure FDA0003656066070000024
4. the method for detecting local turbulent pulse intensity according to claim 1, wherein the residual kinetic energy in step S22 is calculated by the following formula:
Figure FDA0003656066070000025
Figure FDA0003656066070000026
In the above formula, dE1Is composed of
Figure FDA0003656066070000027
Corresponding residual kinetic energy, dE2Is composed of
Figure FDA0003656066070000028
The residual kinetic energy of (c).
5. The method for detecting the local turbulence pulsation intensity as claimed in claim 4, wherein the criterion of turbulence small-scale pulsation intensity in step S23 is as follows:
Figure FDA0003656066070000029
in the above-mentioned formula, the compound has the following structure,
Figure FDA00036560660700000210
is criterion of turbulent small-scale pulse intensity.
6. The method for detecting local turbulence pulsation intensity according to claim 5, wherein the local turbulence pulsation intensity in step S24 is:
when in use
Figure FDA00036560660700000211
When the turbulence pulsation intensity is lower than a theoretical value, the flow field is over-dissipated;
when in use
Figure FDA00036560660700000212
When the turbulence pulsation intensity is higher than the theoretical value, the flow field is under-dissipated.
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