CN111931365B - Method and system for identifying optimal mixing position in vortex flow - Google Patents
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Abstract
The invention discloses a method for identifying an optimal mixing position in vortex flow, which comprises the following steps: obtaining a vortex interaction flow structure which is unsteady evolved based on a compressible NS equation according to the distribution rule of the initial speed and thermodynamic parameters of the vortex; calculating FTLE; extracting LCS ridgeline according to FTLE space distribution rule; and determining the optimal mixing position according to the LCS ridge line and the FTLE value. The invention also discloses a system for realizing the optimal mixing position identification method in vortex flow, which comprises a flow equation solving module, an LCS extracting module and an optimal mixing position determining module; the flow equation solving module obtains an unsteady evolution vortex interaction flow structure based on a compressible NS equation; the LCS extraction module calculates an FTLE value and extracts an LCS ridge line; the optimal mixing position determining module determines an optimal mixing position according to the LCS ridge line. The invention determines the optimal mixing position from the viewpoint of physical mechanism, and is beneficial to popularization to the design of general flow optimal mixing strategies under different fuel injection devices.
Description
Technical Field
The invention relates to a method and a system for identifying an optimal mixing position of vortex flow induction, in particular to a method and a system for determining the optimal mixing position of vortex interaction flow field induced fluid by using a ridge line of a Lagrangian coherent structure (Lagrangian coherent structure, LCS) represented by Lyapunov exponent (fine-time Lyapunov exponent, FTLE).
Background
With the continuous improvement of performance requirements of hypersonic aircrafts, scholars propose a series of mixing enhancement strategies from the perspective of improving the mixing effect of fuel and oxide and further promoting combustion efficiency, wherein the flow direction vortex structure generated by a vortex generator in a fuel injection flow field promotes mixing, and the advantages of small total pressure loss, insensitivity to compressible effect and the like are widely applied to a combustion chamber of a real hypersonic engine. However, in complex flow fields containing multi-flow vortex interactions, the selection of fuel injection locations has a significant impact on the mixing effect due to local strain and turbulence non-uniformities. At present, in the actual engineering design process, a parameterized research mode is generally adopted to determine a better mixed injection position, but the inherent relation between the mixing performance and the flow structure is not searched from the aspect of a physical mechanism, so that the method is not beneficial to being popularized to the design of general flow optimal mixing strategies under different fuel injection devices.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an optimal mixing position identification method and system for determining an optimal mixing position from the perspective of a physical mechanism.
The aim of the invention is realized by the following technical scheme:
an optimal mixing position identification method in vortex flow comprises the following steps:
s1: obtaining a vortex interaction flow structure which is unsteady evolved based on a compressible NS equation according to the distribution rule of the initial speed and thermodynamic parameters of the vortex;
s2: calculating FTLE;
s3: extracting LCS ridgeline according to FTLE space distribution rule;
s4: and determining the optimal mixing position according to the FTLE and LCS ridgeline.
Further, the step S1 includes the following substeps:
s101: taking a speed field and thermodynamic parameters of the rotating vortex pair as initial conditions, solving a compressible NS equation to obtain an NS equation mathematical model;
s102: dimensionless is carried out on the NS equation mathematical model;
s103: the mathematical model of the NS equation is discretized by a finite volume method.
Further, the FTLE is the maximum eigenvalue of the Green-Cauchy tensor over a finite time, which is expressed as
Wherein,,
for a fluid deformation tensor that depends on a velocity gradient, represent a matrix transpose.
Further, the LCS ridge is formed by the FTLE maximum contour after the lagrangian analysis of the vortex interaction flow structure.
Further, the optimal mixing position is set to be coincident with the LCS ridge.
Further, the position where the LCS ridge line coincides with is the position where the average FTLE value in the spraying area is the largest.
Further, the thermodynamic parameters include pressure, density, and temperature.
The system for realizing the optimal mixing position identification method in vortex flow comprises a flow equation solving module, an LCS extracting module and an optimal mixing position determining module; the flow equation solving module obtains a vortex interaction flow structure with unsteady evolution based on a compressible NS equation according to the distribution rule of the initial vortex speed and thermodynamic parameters; the LCS extraction module calculates an FTLE value according to an unsteady evolution vortex interaction flow structure provided by the flow equation solving module, and extracts an LCS ridge line according to an FTLE space distribution rule; the optimal mixing position determining module determines an optimal mixing position according to the LCS ridge line.
Further, the system also comprises a mixing effect evaluation module, wherein the mixing effect evaluation module compares the advantages and disadvantages of the mixing effects of the components at different mixing positions based on the quantitative indexes.
Further, the quantification index includes a degree of mixing reflecting a degree of spatial distribution uniformity of the two components and a mixing characteristic time reflecting a maximum component decay rate.
The beneficial effects of the invention are as follows:
objective physical basis is indicated for selecting the optimal mixing position in the complex multi-vortex interaction flow field, the optimal mixing position is determined from the aspect of physical mechanism, the widely-adopted trial practice in the prior practical device design is improved, a priori design criterion based on a known flow structure is provided, and the method is favorable for being popularized to the design of general flow optimal mixing strategies under different fuel injection devices.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is an example initial condition setting for a calculation domain in an example;
FIG. 3 is a vortex and FTLE distribution based on velocity field evolution processing in an embodiment;
FIG. 4 is a diagram showing the evolution of the composition/clusters at three different initial positions according to the FTLE distribution configuration in the example;
FIG. 5 shows the degree of mixing of the three components at different initial positions;
FIG. 6 shows the variation of maximum concentration of the component groups at three different initial positions in the examples.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the following embodiments and features in the embodiments may be combined with each other without conflict.
It should be noted that the illustrations provided in the following embodiments merely illustrate the basic concept of the present invention by way of illustration, and only the components related to the present invention are shown in the drawings and are not drawn according to the number, shape and size of the components in actual implementation, and the form, number and proportion of the components in actual implementation may be arbitrarily changed, and the layout of the components may be more complicated.
Examples:
as shown in fig. 1 to 5, the method for identifying the optimal mixing position in the vortex flow comprises the following steps:
s1: obtaining a vortex interaction flow structure with unsteady evolution based on a compressible NS equation according to the distribution rule of the initial speed of the vortex and thermodynamic parameters (pressure, density and temperature);
said step S1 comprises the sub-steps of:
s101: taking a speed field and thermodynamic parameters of the rotating vortex pair as initial conditions, solving a compressible NS equation to obtain an NS equation mathematical model;
the rotational vortex pair is a homodromous rotational vortex pair which obeys Gaussian vortex quantity distribution.
The initial velocity field is formed by superposing two Lamb-Osen vortexes which are identical (equal in intensity and effective radius and identical in rotation direction), and the specific form is as follows:
wherein, r1 and r2 are distances from a certain point in the flow field to two vortex centers, (x 1, y 1) and (x 2, y 2) are space positions of the two vortex centers, Γ is single vortex strength, and a is vortex effective radius.
The vortex to initial aspect ratio was 0.1 and the vortex ring reynolds number was 8000.
The initial thermodynamic parameters are determined based on a compressible pressure poisson equation (compressible pressure Poisson equation, CPPE) and isentropic conditions, and an ideal gas state equation closed equation set is introduced. The specific form of the compressible pressure poisson equation is as follows:
wherein the summation symbol is Einstein notation;
the isentropic conditions of the gas are expressed as:
where γ is the adiabatic coefficient.
The ideal gas state equation is expressed as:
p＝ρR u T
wherein Ru is a universal gas constant.
The two-dimensional form of the NS equation is
Where U is a conservation variable, F, G is a convection flux, fv and Gv are a viscous flux.
S102: dimensionless is carried out on the NS equation mathematical model;
s103: dispersing the mathematical model of the NS equation by a finite volume method;
the time propulsion adopts a TVD (transient voltage direct current) range-Kutta method with three-order precision, the convection item adopts a five-order WENO format for dispersion, and the viscosity item adopts a central difference method for dispersion. The compressible pressure poisson equation is discretized in a compact differential format.
S2: calculating FTLE;
the FTLE is the maximum eigenvalue of the Green-Cauchy-Green tensor (Calchy-Green tensor) over a finite time, expressed as
Wherein,,
for a fluid deformation tensor that depends on a velocity gradient, represent a matrix transpose.
S3: extracting LCS ridgeline according to FTLE space distribution rule;
the LCS ridge line is formed by FTLE maximum value contour line after Lagrange analysis of vortex interaction flow structure.
S4: and determining the optimal mixing position according to the FTLE and LCS ridgeline. The position which coincides with the LCS ridge line is the position with the largest average FTLE value in the spraying area.
The system for realizing the optimal mixing position identification method in vortex flow comprises a flow equation solving module, an LCS extracting module and an optimal mixing position determining module; the flow equation solving module obtains a vortex interaction flow structure with unsteady evolution based on a compressible NS equation according to the distribution rule of the initial vortex speed and thermodynamic parameters; the LCS extraction module calculates an FTLE value according to an unsteady evolution vortex interaction flow structure provided by the flow equation solving module, and extracts an LCS ridge line according to an FTLE space distribution rule; the optimal mixing position determining module determines an optimal mixing position according to the LCS ridge line.
The system also comprises a mixing effect evaluation module, wherein the mixing effect evaluation module compares the advantages and disadvantages of the mixing effect of the components at different mixing positions based on the quantitative index.
The quantification index comprises a mixing degree and a mixing characteristic time, wherein the mixing degree reflects the spatial distribution uniformity degree of the two components, and the mixing characteristic time reflects the maximum component fading rate.
The mixing degree is
The mixing characteristic time is
τ:Y max (τ)～O(1)。
The implementation environment of this embodiment is an integrated development environment (IDE, integrated Development Environment) Visual Studio Community 2017, the compiler is Intel (R) Visual Fortran Compiler in Intel Parallel Studio XE 2019 software, a Release mode is adopted for operation, and the computer CPU is Intel cool i76700K.
The mixing characteristic time and average FTLE correlation for the three component clusters at different initial positions in this example are shown in Table 1.
TABLE 1
Comparing the merits of the blending effect of the components with the ambient air at different mixing locations and their relative relationship with the LCS profile shows that setting the mixing locations coincident with the LCS ridge maximizes the use of the interfacial stretching properties of the material during vortex interactions to achieve optimal mixing. Further, concentration/particle swarm and mixing effect evaluation are tracked to show that the average FTLE is directly related to the mixing index, so that the Lagrangian related structure is proved to have the capability of revealing the optimal stretching and mixing positions of the flow field.
By performing a Lagrangian analysis on the compressible vortex interacted flow structure, the location in the flow field where the stretching effect is more pronounced and the mixing region boundaries are shown. The blending of the jet components with the ambient air at different locations was evaluated based on the degree of mixing and the time of mixing characteristics. The results show that the Lagrangian coherent structure ridge line characterized by Lyapunov exponent (fine-time Lyapunov exponent, FTLE) is completely matched with the passive transport track of the jet component, and in addition, the average FTLE value in the jet area has a direct relation with the mixing effect: the larger the average FTLE value corresponds to the better mixing effect. The LCS ridge, quantitatively described based on the FTLE distribution, is therefore an effective means of identifying the optimal mixing location in a complex multi-vortex interaction flow.
This example shows that there is a direct link between the degree of stretching of the fluid characterized by the FTLE and the mixing effect, the larger the FTLE, the faster the mixing rate. The FTLE distribution thus has the ability to predict the optimal mixing position.
The foregoing examples merely illustrate specific embodiments of the invention, which are described in greater detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention.
Claims (7)
1. An optimal mixing position identification method in vortex flow is characterized in that: the optimal mixing position identification method comprises the following steps:
s1: obtaining a vortex interaction flow structure which is unsteady evolved based on a compressible NS equation according to the distribution rule of the initial speed and thermodynamic parameters of the vortex;
s2: calculating FTLE;
s3: extracting LCS ridgeline according to FTLE space distribution rule;
s4: determining an optimal mixing position according to the FTLE and LCS ridgeline;
the LCS ridge line is formed by FTLE maximum value contour lines after Lagrange analysis is carried out on the vortex interaction flow structure;
the optimal mixing position is set to be the position which coincides with the LCS ridge line;
the position which coincides with the LCS ridge line is the position with the largest average FTLE value in the spraying area.
2. A method for identifying an optimal mixing position in a swirling flow according to claim 1, wherein: said step S1 comprises the sub-steps of:
s101: taking a speed field and thermodynamic parameters of the rotating vortex pair as initial conditions, solving a compressible NS equation to obtain an NS equation mathematical model;
s102: dimensionless is carried out on the NS equation mathematical model;
s103: the mathematical model of the NS equation is discretized by a finite volume method.
3. A method for identifying an optimal mixing position in a swirling flow according to claim 1, wherein: the FTLE is the maximum eigenvalue of the Green-Cauchy tensor over a finite time, expressed as
Wherein,,
for a fluid deformation tensor that depends on a velocity gradient, represent a matrix transpose.
4. A method for identifying an optimal mixing position in a swirling flow according to claim 1, wherein: the thermodynamic parameters include pressure, density and temperature.
5. A system for implementing the method of any one of claims 1 to 4, characterized in that: the system comprises a flow equation solving module, an LCS extracting module and an optimal mixing position determining module; the flow equation solving module obtains a vortex interaction flow structure with unsteady evolution based on a compressible NS equation according to the distribution rule of the initial vortex speed and thermodynamic parameters; the LCS extraction module calculates an FTLE value according to an unsteady evolution vortex interaction flow structure provided by the flow equation solving module, and extracts an LCS ridge line according to an FTLE space distribution rule; the optimal mixing position determining module determines an optimal mixing position according to the LCS ridge line.
6. The system according to claim 5, wherein: the system also comprises a mixing effect evaluation module, wherein the mixing effect evaluation module compares the advantages and disadvantages of the mixing effect of the components at different mixing positions based on the quantitative index.
7. The system of claim 6, the quantification index comprising a degree of mixing reflecting a degree of spatial distribution uniformity of the two components and a mixing characteristic time reflecting a maximum component decay rate.
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| 椭圆三体问题中的时间周期不变流形;祁瑞;徐世杰;;空间控制技术与应用(第02期);10-13+51 * |
| 流场可压缩性对涡相互作用影响的数值研究;郑忠华;范周琴;王子昂;余彬;张斌;;航空学报(第02期);114-123 * |
| 高雷诺数双螺旋涡尾迹演化特性分析;李高华;王福新;;物理学报(第05期);178-193 * |
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Effective date of registration: 20231213 Address after: No. 6, South Section of Second Ring Road, Mianyang City, Sichuan Province, 622750 Patentee after: Institute of aerospace technology, China Aerodynamics Research and Development Center Patentee after: Sichuan Research Institute of Shanghai Jiaotong University Address before: 2 / F, building 10, area a, Tianfu Jingrong center, Chengdu Science City, Chengdu, Sichuan 610015 Patentee before: Sichuan Research Institute of Shanghai Jiaotong University |