CN117113525A - Rotary machine Gao Jiequ grid generation method based on multi-block topology and BRF - Google Patents

Rotary machine Gao Jiequ grid generation method based on multi-block topology and BRF Download PDF

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CN117113525A
CN117113525A CN202310911083.9A CN202310911083A CN117113525A CN 117113525 A CN117113525 A CN 117113525A CN 202310911083 A CN202310911083 A CN 202310911083A CN 117113525 A CN117113525 A CN 117113525A
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黄龙龙
王运涛
刘城
王赫
司松林
刘�东
黄思源
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Sichuan University
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Abstract

The invention establishes an automatic generation method of a rotating machinery Gao Jiequ grid based on a plurality of structural grids and local radial basis function interpolation, which comprises the following steps: generating a rotary machine geometry model based on the point data; building topology in m-theta plane and generating structured grid; mapping all 2D surface grids to a 3D space, and stacking the generated body grids; inserting high-order points on the straight grid, and projecting the high-order points to CAD geometry; spatial point deformation generation Gao Jiequ grid is achieved using a radial basis function method. The invention establishes an automatic generation method of the rotating machinery Gao Jiequ grid based on a plurality of structural grids and local radial basis function interpolation, solves the technical problem of high-efficiency automatic generation of the rotating machinery high-order grid in the current rotating machinery field, and further promotes the application of the high-order method in numerical simulation of aeroengines.

Description

Rotary machine Gao Jiequ grid generation method based on multi-block topology and BRF
Technical Field
The invention relates to the technical field of aeroengine numerical simulation, in particular to a rotating machinery Gao Jiequ grid generation method based on a multi-block topology and BRF.
Background
As a bright bead on an industrial crown, the aeroengine represents the industrial level of a country and has important strategic significance in the military field and national economy. With the continuous development of computer technology, the calculation speed is continuously improved, the function of numerical simulation in engine design is also continuously improved, the numerical simulation technology is widely applied in the design of aeroengine parts, bench tests are still adopted at present for complete machine verification, researches show that the numerical simulation of the whole flow channel of the aeroengine is reduced by 33 percent, the number of prototype machines is reduced by 36 percent, and the design period of the engine is greatly shortened, so that the development of the numerical simulation of the whole flow channel of the aeroengine is an important technology for the design optimization of the aeroengine, and the rapid and efficient grid division of the whole flow channel model of the aeroengine is very important during the process.
Many studies are currently dedicated to the generation of high quality grids for rotating mechanical blade channels, and are largely divided into three types of methods: structuring, semi-structuring and unstructured methods. In comparison, the currently accepted optimal method is a structuring method, and along with the development of technology, a complete rotating machinery structure grid generation system is formed, and high-quality grids are mainly generated for the rotating machinery blade channels based on technologies such as a multi-block topological structure, an algebraic method (Transfinite interpolation) generation grid, an elliptic partial differential equation optimizer and the like. At present, NEMECA, turboGrid and other software are provided with automatic generation of structural grids for rotary machines, the technology is monopolized abroad, and the technology development in the aspect is relatively weak in China.
With the rapid development of high-order precision computing methods, a large number of computing methods are presented, mainly a k-exact finite Volume method, a discontinuous galerkin (Discontinuous Galerkin) method, a Spectral Volume (Spectral Volume) method, a Spectral difference (Spectral Difference) method and the like, and are widely used in many fields. Commercial grid generation software commonly used at present generally outputs only linear grids of the straight line/plane type, which are used in high-precision methods to reduce the calculation precision to the second order and to cause non-comprehension. For this reason, the Gao Jiequ grid generation method has received continued attention in recent years, while the application of Gao Jiequ grid generation technology in the field of rotary machinery is relatively small.
Disclosure of Invention
Aiming at the defects of the prior art, the invention establishes a rotating machinery Gao Jiequ grid generation method based on a plurality of topologies and BRF, and the method solves the technical problem of high-efficiency automatic generation of high-order grids of the rotating machinery in the current rotating machinery field, thereby promoting the application of the high-order method in the numerical simulation of aeroengines.
In order to solve the technical problems, the invention is realized by the following steps:
the method for generating the Gao Jiequ grid of the rotary machine based on the multi-block topology and the BRF comprises the following steps:
s1, generating a rotary mechanical geometric model based on point data;
s2, constructing topology in an m-theta plane and generating a structured grid;
s3, mapping all 2D surface grids to a 3D space, and stacking the generated body grids;
s4, inserting high-order points into the body grid, and projecting the high-order points to CAD geometry;
s5, generating Gao Jiequ grids by using a radial basis function method to realize space point deformation.
Further, the step S1 specifically includes the following steps:
generating a casing line and a hub line through a series of discrete points based on a rotary mechanical model generated by a geombly file, determining the position of an inlet and an outlet, describing a blade through a plurality of sections, dividing each section into a suction line (section) and a pressure line (pressure), representing the suction line and the pressure line by the discrete points, and generating a blade model through an interpolation method; and generating a 3D runner according to the data of the casing hub and the blade.
Further, the step S2 specifically includes the following sub-steps:
s21, the blade runner of the rotary machine is usually arranged on a plurality of flow sections, the flow sections are positioned on a three-dimensional flow surface in a cylindrical coordinate system, and the flow surface can be expressed as an m-theta plane by using parameter coordinates m', theta; column coordinate f i The (z, r, θ) to m-theta plane conversion expression is as follows:
wherein i represents the current stream segment index;
constructing topology in an m-theta plane, namely generating a plurality of topological structures by using a combination of a plurality of topologies in a rotary machine, establishing a topological template, and mapping the topological template to the m-theta two-dimensional plane;
s22, generating an initial grid for each block by adopting an algebraic method, and optimizing the grid by adopting a quasi-linear elliptic PDE (position determination) optimizer of Thompson after generating the initial algebraic grid, wherein the expression is as follows:
α(X εε +P(ε,η)X ε )-2βX εη +γ(X ηη +Q(ε,η)X η )＝0 (2)
where P and Q are source functions controlling grid spacing and orthogonality, γ=x ε ·X ε ，α＝X η ·X η ，β＝X ε ·X η 。
Further, the step S3 specifically includes the following sub-steps:
s31, after the optimization of the m-theta plane grid is completed, mapping the m-theta plane grid to three-dimensional space coordinates, wherein the mapping process is as follows:
disposed at a known m-theta plane point P x ＝(m x θ) of which the columnar coordinates (r x ,z x θ) is obtained according to formula (1):
wherein i represents the closest point P x The index of the anchor point,
finally, the method can obtain:
wherein,mapping grid points on an m-theta plane into three-dimensional coordinates through the formula to obtain a three-dimensional surface grid;
s32, generating structural grids with all cross sections through the step flow, and generating body grids through stacking.
Further, the step S4 specifically includes the following sub-steps:
s41, adding high-order grid points on the grid lines or the surfaces of the body, and adding 1 or 2 points between any two points according to requirements to obtain P2 and P3 high-order grid units; the expression for inserting high-order points between two adjacent points is as follows:
wherein,representing higher order point coordinates, +.>And->The representation is P1 straight grid start point coordinates, +.>The unit normal vector from the starting point to the end point is represented, and N represents high-order points which need to be inserted on one grid line;
s42: after the high-order grid points are inserted into the grid of the body in the step S41, the original grid points are arranged on the CAD model, the newly added high-order points on the object plane are subjected to fine shape ensuring treatment, and the high-order points of the object plane are directly projected to the CAD model by adopting a geometric method of point-to-surface projection.
Further, the step S5 specifically includes the following steps:
the radial basis function (Radical Basis Function) method is used for realizing space point deformation, and the original RBF interpolation expression formula is as follows:
wherein f (x) represents the interpolated spatial grid pointDeformation amount of->The ith control point of Gao Jiequ grid representing the new increase of the known deformation, M represents the number of control points and alpha i Represents interpolation coefficients, Φ represents RBF interpolation basis functions, and the expression is as follows:
wherein,r represents the control point scope radius.
Compared with the prior art, the invention has the beneficial effects that:
the invention adopts the coordinate transformation and the angle-keeping mapping method, simplifies the modeling flow of the rotary machine, shortens the period of geometric pretreatment of the rotary machine, and can automatically model the geometric of the rotary machine; based on a multi-block structural grid generation technology, the generation of the rotary mechanical structural grid is more convenient; the curved grid generating method based on local radial basis function interpolation generates a high-order grid for the rotary machine, and promotes the application of the high-order method in the numerical simulation of the aero-engine. And an automatic generation method is adopted from the establishment of the geometric model to the generation of the higher order Qu Wangge, so that the generation efficiency is greatly improved.
Drawings
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 is an automated generation schematic of a rotary machine model of the present invention;
FIG. 3 is a schematic diagram of an O4H topology construction process of the present invention;
FIG. 4 is a schematic diagram of a dual L topology construction process of the present invention;
FIG. 5 is a schematic diagram of single channel 3D mesh generation of the present invention;
fig. 6 is a schematic diagram of a rotary machine high order grid generation of the present invention.
Detailed Description
The following describes the embodiments of the present invention in further detail with reference to the drawings and specific examples.
As shown in fig. 1, a method for generating a grid of a rotary machine Gao Jiequ based on a multi-block topology and BRF includes the following steps:
s1, generating a geometric model of the rotary machine based on point data
Generating a casing line and a hub line through a series of discrete points, determining the positions of an inlet and an outlet, describing a blade through a plurality of sections, wherein each section is divided into a suction line (section) and a pressure line (pressure), the suction line and the pressure line are represented by the discrete points, and generating a blade model through an interpolation method; and generating a 3D runner according to the data of the casing hub and the blade.
S2, constructing topology in m-theta plane and generating structured grid
S21, the blade 3D flow channel of the rotary machine is usually arranged on a plurality of flow sections which are positioned on a three-dimensional flow surface f in a cylindrical coordinate system i (x, r, θ) the flow surface may be represented by parameter coordinates m', θ as the m-theta plane; column coordinate f i The (z, r, θ) to m-theta plane conversion expression is as follows:
wherein i represents the current stream segment index;
constructing a topology in an m-theta plane, generating a plurality of topological structures by using a plurality of topological combinations in a rotary machine, and generating a plurality of topological structures such as double-L-shaped topological structures and O4H-shaped topological structures by mainly combining H-shaped topological structures, O-shaped topological structures, C-shaped topological structures, L-shaped topological structures, I-shaped topological structures and the like at present as shown in figures 3 and 4; establishing a topology template, and mapping the topology template to an m-theta two-dimensional plane;
s22, generating an initial grid for each block by adopting an algebraic method, and optimizing the grid by adopting a quasi-linear elliptic PDE (position determination) optimizer of Thompson after generating the initial algebraic grid so as to improve the smoothness and orthogonality of the grid, wherein the expression is as follows:
α(X εε +P(ε,η)X ε )-2βX εη +γ(X ηη +Q(ε,η)X η )＝0 (2)
where P and Q are source functions controlling grid spacing and orthogonality, γ=x ε ·X ε ，α＝X η ·X η ，β＝X ε ·X η 。
S3, mapping all 2D surface grids to a 3D space, and stacking the generated body grids
Further, the step S3 specifically includes the following sub-steps:
s31, after the optimization of the m-theta plane grid is completed, mapping the m-theta plane grid to three-dimensional space coordinates, wherein the mapping process is as follows:
disposed at a known m-theta plane point P x ＝(m x θ) of which the columnar coordinates (r x ,z x θ) is obtained according to formula (1):
wherein i represents the closest point P x The index of the anchor point, the deformation of the formula (3) can be obtained:
finally, the method can obtain:
wherein,alpha represents an included angle between a connecting line of two points and a transverse axis, and grid points on an m-theta plane are mapped into three-dimensional coordinates through the formula to obtain a three-dimensional surface grid;
s32, generating a structural grid with all cross sections through the step flow, and generating a body grid through stacking as shown in fig. 5.
S4, inserting high-order points into the straight grid, and projecting the high-order points to CAD geometry
S41, adding high-order grid points on the straight grid lines or the straight grid faces, and adding 1 or 2 points between any two points according to requirements to obtain P2 and P3 high-order grid units; the expression for inserting high-order points between two adjacent points is as follows:
wherein,representing higher order point coordinates, +.>And->The representation is P1 straight grid start point coordinates, +.>The unit normal vector from the starting point to the end point is represented, and N represents high-order points which need to be inserted on one grid line; n is 1 in the case of P2, and N is 2 in the case of P3, and the specific grid point position distribution can be flexibly controlled according to the requirement of a specific high-order format.
S42: after the high-order grid points are inserted into the straight grid points in the step S41, the original straight grid points are arranged on the CAD model, the newly added high-order points on the object plane are subjected to precise shape ensuring treatment, and the high-order points of the object plane are directly projected to the CAD model by adopting a geometric method of point-to-surface projection.
S5, generating Gao Jiequ grid by using radial basis function method to realize space point deformation
As shown in fig. 6, the spatial point deformation is achieved using a radial basis function (Radical Basis Function) method, and the original RBF interpolation expression formula is as follows:
wherein f (x) represents the interpolated spatial grid pointDeformation amount of->The ith control point of Gao Jiequ grid representing the new increase of the known deformation, M represents the number of control points and alpha i Represents interpolation coefficients, Φ represents RBF interpolation basis functions, and the expression is as follows:
wherein,r represents the control point scope radius.
The foregoing is merely illustrative of the embodiments of this invention and it will be appreciated by those skilled in the art that variations may be made without departing from the principles of the invention, and such modifications are intended to be within the scope of the invention as defined in the claims.

Claims (6)

1. The method for generating the Gao Jiequ grid of the rotary machine based on the multi-block topology and the BRF is characterized by comprising the following steps of: the method comprises the following steps:
s1, generating a rotary mechanical geometric model based on point data;
s2, constructing topology in an m-theta plane and generating a structured grid;
s3, mapping all 2D surface grids to a 3D space, and stacking the generated body grids;
s4, inserting high-order points into the straight grid, and projecting the high-order points to the CAD geometry;
s5, generating Gao Jiequ grids by using a radial basis function method to realize space point deformation.
2. The method for generating the grid of the rotary machine Gao Jiequ based on the multi-block topology and the BRF according to claim 1, wherein the method comprises the following steps of:
the step S1 specifically includes the following steps:
generating a casing line and a hub line through a series of discrete points based on a rotary mechanical model generated by a geombber file, determining the positions of an inlet and an outlet, describing a blade through a plurality of sections, wherein each section is divided into a suction line and a pressure line, the suction line and the pressure line are respectively represented by the discrete points, and generating a blade model through an interpolation method; and generating a 3D runner according to the data of the casing hub and the blade.
3. The method for generating the grid of the rotary machine Gao Jiequ based on the multi-block topology and the BRF according to claim 1, wherein the method comprises the following steps of:
the step S2 specifically comprises the following sub-steps:
s21, arranging blade runners of the rotary machine on a plurality of flow sections, wherein the flow sections are positioned on three-dimensional flow surfaces in a cylindrical coordinate system, and the flow surfaces can be expressed as m-theta planes by using parameter coordinates m', theta; column coordinate f i The (z, r, θ) to m-theta plane conversion expression is as follows:
wherein i represents the current stream segment index;
constructing topology in an m-theta plane, generating a plurality of topological structures by using a combination of a plurality of topologies in a rotary machine, building a topological template, and mapping the topological template to the m-theta two-dimensional plane;
s22, generating an initial grid for each block by adopting an algebraic method, and optimizing the grid by adopting a quasi-linear elliptic PDE (position determination) optimizer of Thompson after generating the initial algebraic grid, wherein the expression is as follows:
α(X εε +P(ε,η)X ε )-2βX εη +γ(X ηη +Q(ε,η)X η )＝0 (2)
where P and Q are source functions controlling grid spacing and orthogonality, γ=x ε ·X ε ，α＝X η ·X η ，β＝X ε ·X η 。
4. The method for generating the grid of the rotary machine Gao Jiequ based on the multi-block topology and the BRF according to claim 1, wherein the method comprises the following steps of:
the step S3 specifically comprises the following sub-steps:
s31, after the optimization of the m-theta plane grid is completed, mapping the m-theta plane grid to three-dimensional space coordinates, wherein the mapping process is as follows:
disposed at a known m-theta plane point P x ＝(m x θ), its cylindrical coordinates(r x ,z x θ) is obtained according to formula (1):
wherein i represents the closest point P x The index of the anchor point,
finally, the method can obtain:
wherein,mapping grid points on an m-theta plane into three-dimensional coordinates through the formula to obtain a three-dimensional surface grid;
s32, generating structural grids with all cross sections through the step flow, and generating body grids through stacking.
5. The method for generating the grid of the rotary machine Gao Jiequ based on the multi-block topology and the BRF according to claim 1, wherein the method comprises the following steps of:
the step S4 specifically comprises the following sub-steps:
s41, adding high-order grid points on the straight grid lines or the straight grid faces, and adding 1 or 2 points between any two points according to requirements to obtain P2 and P3 high-order grid units; the expression for inserting high-order points between two adjacent points is as follows:
wherein,representing higher order point coordinates, +.>And->The representation is P1 straight grid start point coordinates, +.>The unit normal vector from the starting point to the end point is represented, and N represents high-order points which need to be inserted on one grid line;
s42: after the high-order grid points are inserted into the straight grid points in the step S41, the original straight grid points are arranged on the CAD model, the newly added high-order points on the object plane are subjected to precise shape ensuring treatment, and the high-order points of the object plane are directly projected to the CAD model by adopting a geometric method of point-to-surface projection.
6. The method for generating the grid of the rotary machine Gao Jiequ based on the multi-block topology and the BRF according to claim 1, wherein the method comprises the following steps of:
the step S5 specifically includes the following steps:
the radial basis function method is used for realizing space point deformation, and the original RBF interpolation expression formula is as follows:
wherein f (x) represents the interpolated spatial grid pointDeformation amount of->The ith control point of Gao Jiequ grid which represents the new increase of the known deformation, M represents the number of the control points and a i Represents interpolation coefficients, Φ represents RBF interpolation basis functions, and the expression is as follows:
wherein,r represents the control point scope radius.
CN202310911083.9A 2023-07-24 2023-07-24 Rotary machine Gao Jiequ grid generation method based on multi-block topology and BRF Pending CN117113525A (en)

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