CN113111609A - Novel local turbulence pulsation intensity detection method - Google Patents
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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
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 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.
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:
a0=1+3a2
a1=-4a2
in the above formula, f (x)j) Is a grid point xjThe function to be filtered of (a) is,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:
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 calculation formula of the residual kinetic energy in the step S22 is:
in the above formula, dE1Is composed ofCorresponding residual kinetic energy, dE2Is composed ofThe residual kinetic energy of (2).
Further: the criterion of the small-scale turbulent pulsation intensity in the step S23 is as follows:
in the above formula, the first and second carbon atoms are,is criterion of turbulent small-scale pulse intensity.
Further: the local turbulence pulsation intensity in the step S24 is:
when in useWhen the turbulence pulsation intensity is lower than a theoretical value, the flow field is over-dissipated;
when in useWhen 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;
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:
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,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:
a0=1+3a2
a1=-4a2
a2=-1/32 (3)
LPF2:
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, respectivelyFiltering to obtainAnd
s22, pairAndrespectively calculating corresponding residual kinetic energy; the residual kinetic energy is calculated by the formula:
in the above formula, dE1Is composed ofCorresponding residual kinetic energy, dE2Is composed ofRepresents 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:
in the above formula, the first and second carbon atoms are,is criterion of turbulent small-scale pulse intensity.
From the characteristics of the operators LPF1 and LPF2, the method can be obtainedThe 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,the slope p of the spectrum is approximately linear. Calculated according to the characteristics of the operators LPF1 and LPF2The theoretical value at p-5/3 is:
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 useWhen the turbulence pulsation intensity is lower than a theoretical value, the flow field is over-dissipated;
Claims (8)
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 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.
2. The method for detecting the local turbulence pulsation intensity as claimed in claim 1, wherein the specific steps of step S1 are as follows:
s11, designing a low-pass filter LPF 0;
the low pass filter operator LPF0 is specifically:
a0=1+3a2
a1=-4a2
in the above formula, f (x)j) Is a grid point xjThe function to be filtered of (a) is,is a grid point xjProcessing the filtered function, a0,a1,a2Is a constant coefficient.
S12, low pass filter LPF0 according to a2To obtain two low pass filter operators LPF1 and LPF 2.
3. The method of claim 2, wherein the step S12 is performed by using a of the LPF1 as a low pass filter2A value of-1/32, the low pass filter operator LPF22The value is-1/8.
4. The method for detecting the local turbulence pulsation intensity as claimed in claim 1, wherein the specific steps of step S2 are as follows:
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.
6. the method for detecting local turbulent pulse intensity according to claim 4, wherein the residual kinetic energy in step S22 is calculated by the following formula:
7. The method for detecting the local turbulence pulsation intensity as claimed in claim 6, wherein the criterion of turbulence small-scale pulsation intensity in step S23 is as follows:
8. The method for detecting local turbulence pulsation intensity according to claim 7, wherein the local turbulence pulsation intensity in step S24 is:
when in useWhen the turbulence pulsation intensity is lower than a theoretical value, the flow field is over-dissipated;
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