CN112560363B - Grid deformation quality evaluation method in CFD (computational fluid dynamics) calculation based on mapping process - Google Patents

Grid deformation quality evaluation method in CFD (computational fluid dynamics) calculation based on mapping process Download PDF

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CN112560363B
CN112560363B CN202011482454.9A CN202011482454A CN112560363B CN 112560363 B CN112560363 B CN 112560363B CN 202011482454 A CN202011482454 A CN 202011482454A CN 112560363 B CN112560363 B CN 112560363B
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谢长川
贾思嘉
安朝
杨超
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Abstract

The invention discloses a grid deformation quality evaluation method in CFD (computational fluid dynamics) calculation based on a mapping process, wherein an initial grid generates a deformed grid according to a certain algorithm, and a deformation grid quality metric value is generated by using the deformation displacement of grid nodes to form a deformation grid quality evaluation method; the deformation grid quality metric value is derived based on a deformation gradient tensor and a Green strain tensor in continuous medium mechanics. The method is only based on the grid node displacement value and the initial grid node coordinate in the deformation process, and the grid node displacement value is directly obtained in the grid deformation interpolation algorithm, so that the evaluation method is simple and convenient to calculate and can be applied to the grid quality evaluation related to the dynamic grid solution in the field of computational fluid mechanics.

Description

Grid deformation quality evaluation method in CFD (computational fluid dynamics) calculation based on mapping process
Technical Field
The invention belongs to the field of Computational Fluid Dynamics (CFD) and the technical field of aeroelasticity mechanics, and particularly relates to a grid deformation quality evaluation method in CFD calculation based on a mapping process.
Background
Computational Fluid Dynamics (CFD) is a science that uses a computer as a tool and uses a discretized grid technique and a numerical calculation method to solve a Fluid motion equation, thereby revealing a flow mechanism and a flow law. In recent decades, CFD analysis methods have taken a dramatic development due to the need for practical problems, as well as the rapid development of computing technology and advances in computer hardware.
Aeroelasticity is a branch of applied mechanics, and mainly studies the coupling problem among aerodynamic force, elastic force and inertia force. Elastic construction takes place to vibrate and warp under aerodynamic effect, and structure elastic motion in turn can lead to aerodynamic's size and distribution to change, and this kind of interaction can bring diversified aeroelasticity phenomenon, including aeroelasticity deformation, flutter, gust response etc.. The solution of the aeroelasticity problem is usually accompanied by continuous coupling iteration of the aeroelasticity solution and the structural deformation solution and is limited by the requirement of analysis efficiency, and the early aeroelasticity solution is usually based on simple aeroelasticity models such as a surface element method and the like, so that the solution precision is limited. With the improvement of CFD technology, the aeroelasticity analysis process of directly coupling CFD and structural deformation solving model such as finite element model is gradually put into practical use, and the solving precision of aeroelasticity problem is greatly improved. The mesh deformation technology is one of the key problems in the problem development, and the involved mesh generation algorithm, mesh quality evaluation and the like have important significance for the research of the problems.
For the CFD analysis technique, flow field analysis with structural motion and deformation, such as bridge stability analysis, wing structural optimization design, wing aeroelastic dynamic response analysis, etc., is often encountered in various important engineering problems, and under these conditions, a mesh deformation technique is required to solve the unsteady load under the boundary motion, especially for the aeroelastic dynamic response problem, the structural deformation is large, the flow field data is frequently updated, and the quality of the generated mesh has a crucial influence on the problem solution. It is also imperative that after mesh deformation, mesh quality assessment criteria are used which can help to compare the accuracy between the mesh algorithms, while at the same time it can be determined whether a certain mesh deformation method meets the minimum quality criteria required for CFD computation.
To date, researchers have developed a variety of mesh deformation methods, mainly classified into physical analogy methods and interpolation methods. Physical similarity generally requires connectivity information for the mesh, which uses some physical process to transfer mesh deformation from the motion boundary to the flow field mesh. The spring-like method is a typical physical method. In this approach, each node is considered to be connected to an adjacent node by a spring, so the entire network can be considered to be a spring system. The method is successfully applied to the stability analysis and optimization problem, but the calculation cost is high, and the method is not suitable for the large-deformation aeroelastic analysis problem. The interpolation method refers to using some mathematical interpolation algorithm to obtain new coordinates of each node, which allows for large deformation and does not require connection information between grid nodes. The Radial Basis Function (RBFs) method is an effective method in an interpolation method, is ideal for both structured grid generation and unstructured grid generation, is ideal in grid quality near a deformation boundary, and has a good application prospect.
In order to be able to compare the quality of the deformed mesh with the quality of the initial mesh, it is necessary to provide a deformed mesh quality evaluation method. The existing methods are evaluated based on the information of grids, and the coordinate information of each grid node in the initial grids and the deformed grids, the connection relation among the nodes, the Jacobian matrix related to the spatial position and the like are needed. Common measurement methods are as follows: "relative magnitude measure", "torsional measure", "equal area skewness", "equal angular skewness", and the like.
The "relative size measure" is based on an area or volume ratio calculation, taking a two-dimensional grid as an example, let τ be the ratio of the area of the current cell to the area of a reference standard cell, for cell P, the relative size measure can be written as Qsize(P) ═ min (τ,1/τ). When the index is 1, the area of the deformed cell is the same as the original reference area. The 'torsion measurement' represents the distortion change of the mesh, is calculated based on the inner angle information of the mesh unit, and is suitable for triangular meshes, quadrilateral meshes, tetrahedral meshes and hexahedral meshes. "equal area skewness" is expressed as the ratio of the cell area to the optimal cell area. "Iso-angular skewness" refers to the ratio of the cell grid line angle to the equilateral polygon angle. These criteria apply to all units. The above-mentioned methods are all calculated based on grid coordinate information, and this method needs to extract coordinate values of each grid point when calculating grid quality, calculate a jacobian matrix, and the like, and has a high calculation cost. Since the mesh generated after the deformation is obtained by calculation through the mesh deformation algorithm, the mapping process of the mesh deformation can also show the quality of the mesh deformation. At present, no method for calculating the quality evaluation standard of the deformation grid based on the deformation mapping process is available.
Disclosure of Invention
In order to solve the problems that the existing deformed grid quality evaluation method in the prior art needs more information and has larger calculated amount, the invention provides a deformed grid quality evaluation method based on a grid deformation mapping process, which is used for calculating a deformed grid quality metric value based on the mapping process, does not need to extract coordinate information of each grid point after deformation, and has higher calculation efficiency. The specific technical scheme of the invention is as follows:
a mesh deformation quality evaluation method in CFD calculation based on mapping process, the CFD calculation includes carrying on the area discretization in calculating the flow field, substitute the continuous computation space with the discrete point, divide calculating the flow field into the subregion namely calculates the mesh; the flow field calculation physical quantity stored on each grid can solve the fluid motion problem by calculating the information on the grid; the method comprises the following steps of recording the coordinates of a flow field grid divided by each calculation problem as grid initial node coordinates, generating deformation according to the movement of a calculation boundary by the flow field grid aiming at the problem of unsteady movement of the flow field boundary, calculating the displacement of each grid node by interpolation of the initial grid and the boundary movement to obtain a deformed grid, wherein the accuracy of a CFD calculation result is influenced by the quality of the deformed grid, and the method comprises the following steps:
s1: storing the displacement value of the grid nodes;
and aiming at the initial grid and the deformed grid, recording the deformation displacement of each grid node as u ═ u1，u2，u3]The grid initial node coordinate is X ═ X1，X2，X3]Wherein u is1，u2，u3Respectively the displacement of the grid node in three directions in the coordinate system, X1，X2，X3Respectively representing the coordinates of the grid nodes in three directions in a coordinate system;
s2: calculating a node displacement gradient tensor:
Figure BDA0002836851090000031
the deformation gradient tensor F of the grid node is:
F＝H+I (2)
wherein I is a unit array;
s3: calculating the area change of grid deformation;
according to the mechanics theory of continuous medium, the area of the initial grid is S, the area of the deformed grid is S', and the areas have the following relation:
S′＝det(F)S (3)
det (-) is the determinant calculation, namely the area variation J with grid deformation:
J＝det(F) (4)
s4: calculating the angle change of grid deformation;
deducing according to a continuous medium mechanics theory, setting a strain tensor of grid deformation as E, and having a calculation relation:
Figure BDA0002836851090000032
the angular variation of the grid deformation is defined as θ, then:
Figure BDA0002836851090000033
wherein E is11、E12、E22A component in the strain tensor E that is a deformation of the grid;
s5: calculating an area change metric of grid deformation quality;
let the area change metric be fsizeThe calculation is as follows:
Figure BDA0002836851090000041
when f issizeWhen the grid number is 1, the grid quality is the best; when f issizeWhen the grid size is less than 0, the grid has a negative volume, and the grid cannot be used for calculation;
s6: calculating an angle change metric value of the grid deformation quality;
let the angle change metric be fskewIt is calculated as follows:
fskew＝cosθ (8)
when f isskewWhen the grid number is 1, the grid quality is the best; when f isskewIf the number is less than 0, the grid is crossed with edges, and the grid cannot be used for calculation.
S7: giving a quality metric value distribution cloud picture;
calculating an area change metric value and an angle change metric value for grid nodes in the interested calculation domain according to the formulas (7) and (8), drawing a distribution cloud chart of the two metric values, analyzing grid quality distribution, evaluating the overall quality of the grid, finding out the grid distribution range with the worst quality, and facilitating subsequent improvement and calculation of the grid quality.
The invention has the beneficial effects that:
1. the deformation grid quality metric value calculation method based on the mapping process can evaluate grid deformation in computational fluid mechanics;
2. the invention provides the measurement of the area change and the measurement of the angle change respectively based on the node displacement of the grid instead of the node coordinates of the initial grid and the deformed grid, and has simple and convenient calculation and small calculation amount.
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In order to illustrate embodiments of the invention or solutions in the prior art more clearly, the drawings that are needed in the embodiments will be briefly described below, so that the features and advantages of the invention will be more clearly understood by referring to the drawings that are schematic and should not be understood as limiting the invention in any way, and other drawings may be obtained by those skilled in the art without inventive effort. Wherein:
FIG. 1 is an initial computational grid of an embodiment of the present invention;
FIG. 2 is a deformed grid of an embodiment of the present invention;
FIG. 3 is a cloud of area change metric profiles of an embodiment of the present invention;
FIG. 4 is a cloud of angle change metric profiles according to an embodiment of the present invention;
FIG. 5 shows the position and shape of the quality worst grid using the area variation metric as the evaluation criterion according to the embodiment of the present invention;
fig. 6 shows the position and shape of the worst quality grid using the angle variation metric as the evaluation criterion according to the embodiment of the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments and features of the embodiments of the present invention may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
The invention relates to a deformation grid generation and evaluation problem in CFD calculation, in the grid generation process after deformation, the grids generated by different generation methods have different qualities, if the grid quality is good, the CFD calculation efficiency is high, the accuracy is high, if the grid quality is poor, the opposite is true, and the invention has important guiding significance for CFD calculation for the evaluation of CFD grid deformation quality.
The invention provides a new deformation grid quality evaluation standard based on the deformation mapping process, and calculates the deformation grid quality metric based on the deformation mapping process. The method does not need to extract the coordinate information of each grid point after deformation, and has higher calculation efficiency. Specifically, the initial grid generates a deformed grid according to a certain algorithm, and the deformation displacement of the grid nodes is utilized to generate a deformed grid quality metric value, so that the deformed grid quality evaluation method is formed. The deformation grid quality metric value is derived based on a deformation gradient tensor and a Green strain tensor in continuous medium mechanics. The deformation grid quality evaluation method is only based on the grid node displacement value and the initial grid node coordinate in the deformation process, and the grid node displacement value is directly obtained in the grid deformation interpolation algorithm, so the evaluation method is simple and convenient to calculate and can be applied to the grid quality evaluation related to the dynamic grid solution in the field of computational fluid mechanics.
For the convenience of understanding the technical solutions of the present invention, the technical solutions of the present invention will be described in detail by specific examples.
Example 1
A complete computational fluid mechanics problem solving method comprises the steps of establishing a flow field computational grid, judging grid quality, determining boundary conditions, selecting a control equation, setting control parameters, solving a discrete equation and outputting a computation result. Wherein the height of the flow field computational grid establishment quality has an important influence on the computational accuracy. And establishing flow field grids before calculation, wherein the nodes of each grid have coordinate values, namely initial grid coordinates, under a given coordinate system. And calculating the difference value between the new coordinate after the grid deformation and the initial grid coordinate, and recording as a grid deformation displacement value.
A two-dimensional computational fluid mechanics computational grid is adopted, a set of rectangular structured computational grid is selected for analysis, and a rectangular small area is arranged in the middle of a flow field computational domain and rotates around the center. The initial computational grid is shown in fig. 1. The flow field area grid size is 80 × 40, the rotation area size is 4 × 2, and the rotation is 45 degrees around the center. The method for evaluating the quality of the deformed grid based on the mapping process comprises the following steps:
s1: storing the displacement value of the grid nodes;
and carrying out grid deformation interpolation by using a radial basis interpolation method, generating a deformation grid after the middle rectangular cell rotates for 45 degrees, and recording a deformation displacement value and an initial grid coordinate. The deformed mesh is shown in fig. 2.
S2: calculating a node displacement gradient tensor;
and (3) calculating the displacement gradient tensor H of each node according to the equation (1), and calculating the deformation gradient tensor F of each node according to the equation (2).
S3: calculating the area change of grid deformation;
the area change J ═ det (f) for each mesh deformation is calculated according to equation (4).
S4: calculating the angle change of grid deformation;
the strain tensor E of the grid deformation is calculated according to equation (5), and the angular change theta of the grid deformation is calculated according to equation (6).
S5: calculating an area change metric of grid deformation quality;
the area change is an important factor for inspecting the deformation quality of the grid, when the area of the deformed grid is unchanged relative to the initial grid, the grid quality is good, and when the value is gradually increased or decreased, the grid quality is poor.
Calculating the area change metric f of the grid deformation quality according to equation (7)sizeAnd records the data.
S6: calculating an angle change metric of grid deformation quality;
the angle change is another important factor for inspecting the grid deformation quality, and the distortion degree of the grid in the deformation process is evaluated; similarly, the mesh quality is good when the deformed mesh is at a constant angle with respect to the original mesh, and the mesh quality is poor when the value is gradually increased or decreased.
Calculating the angular variation metric f of the grid deformation quality according to equation (8)skewAnd records the data.
S7: giving a quality metric value distribution cloud picture;
the area change metric f obtained in step S5 and step S6sizeAnd an angle change metric fskewAnd drawing on the computational domain grid to form a distribution cloud picture. In this embodiment, the area change metric fsizeThe magnitude of the angle change f is shown in FIG. 3skewThe distribution cloud is shown in fig. 4. The average and minimum values of the metric values in the calculation domain are shown in table 1. The method can quantitatively give grid quality evaluation. Finding the grid with the worst grid quality in the flow field calculation domain, and measuring the value f by the area changesizeThe standard is adopted, the grid position and the shape are shown in FIG. 5, and the grid which is outlined by a bold solid line in the graph is the worst quality grid; by the magnitude of the angular change fskewFor the standard, the grid positions and shapes are shown in fig. 6, and the grid with the worst quality is shown by the bold solid line.
TABLE 1 grid evaluation metric information
Evaluation index Mean value of Minimum value
Area change metric fsize 0.88579 0.57495
Angle change metric fskew 0.97603 0.74225
The method is based on the mapping process, solves the grid deformation quality evaluation metric value on the basis of grid node displacement to form a new grid deformation quality evaluation method, and has important significance in the practical hydrodynamics calculation application related to grid deformation.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A mesh deformation quality evaluation method in CFD calculation based on mapping process, the CFD calculation includes carrying on the area discretization in calculating the flow field, substitute the continuous computation space with the discrete point, divide calculating the flow field into the subregion namely calculates the mesh; the flow field calculation physical quantity stored on each grid can solve the fluid motion problem by calculating the information on the grid; the method comprises the following steps of recording the coordinates of a flow field grid divided by each calculation problem as grid initial node coordinates, generating deformation according to the movement of a calculation boundary by the flow field grid aiming at the problem of unsteady movement of the flow field boundary, calculating the displacement of each grid node by interpolation of the initial grid and the boundary movement to obtain a deformed grid, wherein the accuracy of a CFD calculation result is influenced by the quality of the deformed grid, and the method comprises the following steps:
s1: storing the displacement value of the grid nodes;
and aiming at the initial grid and the deformed grid, recording the deformation displacement of each grid node as u ═ u1,u2,u3]The grid initial node coordinate is X ═ X1,X2,X3]Wherein u is1,u2,u3Respectively the displacement of the grid node in three directions in the coordinate system, X1,X2,X3Respectively representing the coordinates of the grid nodes in three directions in a coordinate system;
s2: calculating a node displacement gradient tensor:
Figure FDA0002836851080000011
the deformation gradient tensor F of the grid node is:
F＝H+I (2)
wherein I is a unit array;
s3: calculating the area change of grid deformation;
according to the mechanics theory of continuous medium, the area of the initial grid is S, the area of the deformed grid is S', and the areas have the following relation:
S′＝det(F)S (3)
det (-) is the determinant calculation, namely the area variation J with grid deformation:
J＝det(F) (4)
s4: calculating the angle change of grid deformation;
deducing according to a continuous medium mechanics theory, setting a strain tensor of grid deformation as E, and having a calculation relation:
Figure FDA0002836851080000012
the angular variation of the grid deformation is defined as θ, then:
Figure FDA0002836851080000021
wherein E is11、E12、E22A component in the strain tensor E that is a deformation of the grid;
s5: calculating an area change metric of grid deformation quality;
let the area change metric be fsizeThe calculation is as follows:
Figure FDA0002836851080000022
when f issizeWhen the grid number is 1, the grid quality is the best; when f issize<At 0, the grid has negative volume and cannot be used for calculation;
s6: calculating an angle change metric value of the grid deformation quality;
let the angle change measure be fskewIt is calculated as follows:
fskew＝cosθ (8)
when f isskewWhen the grid number is 1, the grid quality is the best; when f isskew<When 0, the grid is crossed by edges, and the grid cannot be used for calculation;
s7: giving a quality metric value distribution cloud picture;
calculating an area change metric value and an angle change metric value for grid nodes in the interested calculation domain according to the formulas (7) and (8), drawing a distribution cloud chart of the two metric values, analyzing grid quality distribution, evaluating the overall quality of the grid, finding out the grid distribution range with the worst quality, and facilitating subsequent improvement and calculation of the grid quality.
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