CN112597613A - Method for determining pneumatic resultant force borne by compressor blade and acting point thereof - Google Patents
Method for determining pneumatic resultant force borne by compressor blade and acting point thereof Download PDFInfo
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Abstract
The application relates to a method for determining the resultant aerodynamic force and the acting point of a blade of an air compressor, which comprises the following steps: dividing the surface of a three-dimensional model of a blade of the compressor into a plurality of grids; calculating a static pressure value of each vertex of each grid of the blade surface; numbering and arranging the vertexes of each grid according to a satellite grid mode; for each grid on the surface of the blade, regularly dividing the grid into two triangular infinitesimal planes; calculating pressure vectors on the corresponding triangular micro-element planes by traversing each grid of the satellite network, and accumulating the pressure vectors on all the triangular micro-element planes to obtain the resultant force applied to the whole blade; calculating a resultant force action line based on a resultant moment equality principle; and determining a resultant force action point according to the distance from each grid vertex on the pressure surface of the blade to the resultant force action line.
Description
Technical Field
The application relates to the field of design of a compressor, in particular to a method for determining aerodynamic resultant force (hereinafter referred to as 'resultant force') borne by a compressor blade and an action point of the aerodynamic resultant force.
Background
In the field of aircraft engines, a turbofan engine is a commonly used aircraft engine, generally a dual-rotor engine, and mainly comprises a fan, a gas compressor, a combustion chamber, a high-pressure turbine, a low-pressure turbine and other components.
The compressor is a component in a twin rotor aircraft engine or gas turbine. The low-pressure shaft and the high-pressure shaft are respectively provided with a compression component, the compression component on the high-pressure shaft is called a high-pressure compressor, and the compression component on the low-pressure shaft is called a low-pressure compressor. The high pressure compressor and the low pressure compressor are collectively referred to herein as compressors.
In the test process of the air compressor, based on the working principle of the air compressor, when the rotor blades compress and discharge air to the outlet of the test piece, the rotor can be subjected to forward thrust due to the reaction force of the air flow. At present, in a performance test piece of an air compressor of an aeroengine at home and abroad, an axial force balance system is generally required to balance forward thrust generated by the air compressor due to the limitation of the bearing capacity of a thrust bearing. Therefore, in the design stage of the compressor blade modeling, how to accurately and quickly obtain the magnitude of the resultant force borne by the surface of the blade and the action point of the resultant force have important reference significance on the design of an axial force balance system. In addition, in the design process of the compressor, multiple iterations are usually required to be performed with structural strength, the resultant force and the action point of the surface of the compressor are accurately obtained, and guidance can be provided for the application and setting of the pneumatic load and the action point of the pneumatic load in the strength calculation process of the compressor.
Therefore, there is a need to provide a solution that can accurately and quickly determine the resultant aerodynamic force experienced by the compressor blade and its point of action (also referred to as "position of action").
Disclosure of Invention
In the present application, a solution is provided for determining the resultant aerodynamic force to which the blades of a compressor are subjected and the point of action thereof. The scheme can accurately and quickly determine the resultant pneumatic force borne by the blades of the air compressor and the action points of the resultant pneumatic force, thereby providing powerful help for the design of the blades.
According to one aspect of the present application, a method of determining a resultant aerodynamic force experienced by a blade of a compressor and a point of action thereof is disclosed, comprising: dividing the surface of a three-dimensional model of a blade of the compressor into a plurality of grids; calculating a static pressure value of each vertex of each grid of the blade surface; numbering and arranging the vertexes of each grid according to a satellite grid mode; for each grid on the surface of the blade, regularly dividing the grid into two triangular infinitesimal planes; calculating pressure vectors on the corresponding triangular micro-element planes by traversing each grid of the satellite network, and accumulating the pressure vectors on all the triangular micro-element planes to obtain the resultant force applied to the whole blade; calculating a resultant force action line based on a resultant moment equality principle; and determining a resultant force action point according to the distance from each grid vertex on the pressure surface of the blade to the resultant force action line.
According to another aspect of the present application, there is provided a computer readable storage medium having stored thereon instructions that, when executed, cause a machine to perform the method as described above.
According to yet another aspect of the application, there is provided a computer system comprising means for performing the method as described above.
This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.
Drawings
In order to describe the manner in which the above-recited and other advantages and features of the invention can be obtained, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments of the invention and are not therefore to be considered to be limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings in which:
FIG. 1 illustrates a method for determining a resultant aerodynamic force experienced by a compressor blade and its point of application, according to one embodiment of the present application.
Fig. 2 shows the directions of examples i, j numbering mesh vertices.
Fig. 3 shows a close-up view of a triangle demarcated in one mesh of the surface of the blade being gridded.
Fig. 4 shows an example numbering diagram for each mesh point in a satellite network.
FIG. 5 shows a schematic of the pressure vectors and their radial dimensions on one triangle element of the blade.
Fig. 6 shows a schematic view of the points of intersection of the two faces of the blade with the lines of action of the resultant forces and the points of action of the aerodynamic forces determined.
Detailed Description
As mentioned above, obtaining the magnitude of the resultant force on the blade surface and the point of action thereof have important reference significance for the design of the compressor. The resultant force on the surface of the blade of the compressor is the vector sum of static pressures (pressure brought to the blade by gas) on all positions of the surface of the blade.
There are generally two approaches in the prior art to solve this problem.
1) The static pressure distribution on the surface of the blade is measured by punching holes on the surface of the blade and embedding a plurality of pressure sensors. Specifically, the physical quantity on the rotating element can be transmitted to a static instrument by punching a hole on the surface of the blade, connecting the hole with a pressure sensor through a pressure sampling pipe, and then transmitting the physical quantity on the rotating element to the static instrument through a slip ring and the like. The resultant force experienced by the blade surface is derived by summing the readings from each sensor. However, this physical measurement method is expensive (requiring a sample of the blade to be made first) and has damage to the blade (requiring holes to be drilled in various positions on the blade surface to accommodate several or even tens of sensors), and the sensor device causes signal loss during signal transmission, which affects the accuracy of the measurement result. Moreover, it can only measure the resultant force of the finished blade, but cannot predict the resultant force in advance, i.e. cannot be used in the design stage. Therefore, the design scheme cannot be adjusted in time, and the design period is shortened.
2) And constructing a three-dimensional model of the blade by using three-dimensional professional analysis software, and gridding the surface of the blade to construct a small blade area. The total force experienced by the entire blade surface is obtained by summing the static pressures of the blade area of each grid calculated using some commonly used fluid mechanics software, such as Fluent, Numeca, Cfx, etc. For ease of partitioning and computation, the grid of the patch blade regions is generally quadrilateral in shape. Subsequently, the resultant force of the blade surfaces is found by integrating the static pressure at each grid point. However, these software can only find the resultant force applied to the blade, but cannot find the acting point of the resultant force, and the resultant force without the acting point has no application value in engineering design.
Therefore, a solution is needed that can accurately and quickly estimate the aerodynamic resultant force that a designed blade may be subjected to in the design stage before manufacturing the blade and accurately infer the acting point of the resultant force.
The following aspects of the present application are described with reference to the accompanying drawings.
In fig. 1, a method for determining a resultant aerodynamic force experienced by a compressor blade and its point of application according to an embodiment of the present application is shown.
As shown, at step 102, a three-dimensional design analysis software is used to divide the surface of a three-dimensional model of a compressor blade into a plurality of grids.
And at step 104, calculating, by the three-dimensional design analysis software, for each mesh of the blade surface, a static pressure value at each vertex of the mesh.
In the field of existing engine design, there are many three-dimensional design analysis software that can implement the above functions. Such as Fluent, Numeca, Cfx, and the like. These are three-dimensional design software commonly used in the field of CFD (computational fluid dynamics).
Take Fluent as an example, which is a commercially available CFD software package that is currently popular internationally, and is used by all industries involved with fluids, heat transfer, and chemical reactions. The method has rich physical models, advanced numerical methods and powerful pre-and post-processing functions, and is widely applied to the aspects of aerospace, automobile design, petroleum and natural gas, turbine design and the like. Fluent software employs a finite volume method based on a completely unstructured grid, and has a gradient algorithm based on grid nodes and grid cells. The dynamic/deformable grid technology in Fluent software mainly solves the problem of boundary motion, a user only needs to specify boundary conditions of an initial grid and a motion wall, and the rest grid changes are completely and automatically generated by a resolver. The Fluent software has strong grid support capability and supports discontinuous interface grids, hybrid grids, dynamic/deformation grids, sliding grids and the like. It is worth emphasizing that the Fluent software also has a plurality of solution-based mesh adaptation and dynamic adaptation technologies and a technology of combining dynamic meshes and mesh dynamic adaptation. Thus, the surface of the blade can be easily divided into the desired mesh using the powerful mesh generation techniques of Fluent software.
After the mesh is divided, these three-dimensional design software also provide the function of calculating for each mesh vertex the value of its static pressure (i.e., the pressure brought to the corresponding mesh vertex by the gas flowing through the blade). Still taking Fluent software as an example, the grid is introduced into a Fluent solver, and by setting boundary conditions, solving formats and the like, the flow field information on each grid point, including parameters such as static pressure values and the like, can be automatically calculated by the software. Thus, the static pressure values at the vertices of the individual meshes of the blade surface can be easily obtained with the software.
It should be understood that the above-described use of Fluent software to divide the mesh and calculate the static pressure value at each mesh vertex is only one example, and is not intended to limit the aspects of the present application thereto. Other software and algorithms for dividing the grid and calculating the static pressure value for each grid are also possible and are within the scope of the present application.
Subsequently, in step 106, the mesh vertices are numbered in the i and j directions in a satellite mesh manner. Satellite network refers to the network formed by all the grids attached to the blade surface constructed in step 102. The i direction is the direction from the leading edge to the trailing edge and then to the leading edge along the blade profile line, that is, numbering around the width of the blade. And the j direction is along the leaf height as shown in figure 2. Therefore, the grid on the surface of the blade with the original three-dimensional structure can be expressed in the form of an expanded two-dimensional plane grid with satellite network coordinates (i, j), and subsequent calculation is facilitated.
If the numerical simulation is an unstructured grid in the gridding process, generating a blade surface grid by using a satellite grid technology, and then Mapping the numerical simulation static pressure value to a newly generated grid point by using a Mapping mode.
Next, at step 108, for each mesh on the blade surface, it is regularly divided into two triangular infinitesimal planes. As mentioned above, the conventional three-dimensional design software usually uses a quadrilateral form to divide the grid of the blade surface. Since the solution of the aerodynamic resultant force of the blade surface requires to obtain the normal vector of each grid unit, the four nodes of the quadrilateral grid are not in the same plane (because the grid is divided on the surface of the blade with the three-dimensional irregular shape), and therefore, the normal vector cannot be calculated by the quadrilateral grid.
To solve the above problem, for each quadrilateral mesh, it may be divided into two triangles (also called "triangle elements") in a regular way (i.e., all meshes are divided along the same diagonal direction). According to the mathematical theorem, any three points can form a plane, so that a quadrilateral normal vector which cannot be determined originally can be converted into the sum of normal vectors of two corresponding triangular microelements by dividing the quadrilateral mesh into two triangular microelements, the problem that the normal vector cannot be calculated by the traditional mesh is solved, and further the solution of the aerodynamic resultant force on the surface of the blade is possible.
In fig. 3 a partial enlargement of a triangle marked off in a grid of the surface of the blade being latticed is shown. As shown, the quadrilateral mesh is diagonally divided into a triangle 1 and a triangle 2. Wherein is prepared by
The direction indicated by the arrow is the normal vector of triangle element 1, and
the direction indicated by the arrow is the normal vector of the other triangular element 2.
In step 110, the pressure vectors on the corresponding triangular infinitesimal planes are calculated by traversing each mesh of the satellite network, and the pressure vectors on all the triangular infinitesimal planes are added up to obtain the resultant force to which the entire blade is subjected.
Specifically, first, on each triangular infinitesimal plane, a pressure vector on the triangular infinitesimal can be obtained according to the following formula 1:
Wherein
Representing the pressure vector on the triangle element, p is the static pressure value on the triangle element plane, which can be represented by three vertexes of the triangleThe static pressure values of the two-phase flow are averaged to obtain,
is the area of the triangular infinitesimal,
is the normal vector of the triangular infinitesimal surface.
As described above, a quadrilateral mesh can be divided into triangular microelements 1 and triangular microelements 2. Thus, the pressure vector on the plane for this quadrilateral mesh can be expressed as:
Wherein
A pressure vector representing the grid of quadrilaterals,
denotes the summation of the pressure vectors of the triangle element surfaces divided therefrom, where k is 1, 2, i.e. the sum of the pressure vector of triangle element 1 and the pressure vector of triangle element 2:
and it can be further expressed as formula 1
。
In order to calculate the resultant force on the surface of the whole blade, the whole satellite network can be traversed in sequence, for each traversed mesh, the mesh is divided into two triangular micro-elements, and then the pressure vector of each triangular micro-element is calculated. After all meshes are traversed to obtain the pressure vectors on all triangle elements, the pressure vectors on all triangle elements are accumulated and summed, so that the resultant force on the whole blade can be obtained.
The traversal process is shown in fig. 4, in which the satellite network of the blade is first expanded into a plane, where there are J grids in the blade height direction (J) and I grids in the blade profile direction (I). Thus, in traversing each trellis, the first row may be traversed by first fixing J to 1, and I from 1, …, through to I, then fixing J to 2, and I from 1, …, through to I, through to the second row, and so on, until the last trellis J, I, is traversed.
As described above, for each traversed mesh (represented by coordinates (i, j)), it is first regularly divided into two triangular infinitesimal planes by step 108, and then the pressure vector of each triangular infinitesimal plane is calculated according to equation 1, namely:
Wherein
The pressure vector representing the kth triangle of the mesh at satellite mesh coordinates (I, J), where k is 1, 2, I is 1, …, I, and J is 1, …, J.
Is the static pressure value on the kth triangular voxel plane of the grid at coordinate (i, j),
is the area of the kth triangular bin of the mesh at coordinate (i, j),
is the normal vector of the kth triangular voxel plane of the mesh at coordinate (i, j).
On the other hand, to ensure the normal direction of each triangular planeConsistency in the vector direction (where normal vector is defined as going out of the page), the normal vector for solving triangle 1 can be used
And the normal vector for solving triangle 2 can be used
。
Wherein, the vector
And
can pass through the three-dimensional coordinates of two vertexes where the two vertexes are positioned（x,y,z）The coordinate difference of (a). The area of the triangle primitive can then be solved according to the following equation:
After the whole satellite network is traversed to complete the calculation of the pressure vectors on the triangular microelements of all the grids, the pressure vectors on all the triangular microelements are accumulated and summed, so that the resultant force applied to the whole blade can be obtained, as shown in formula 4:
Wherein the content of the first and second substances,
for the resultant force to which the entire blade is subjected
The pressure vector of each triangle element divided from each grid is obtained. I is the vane profile direction coordinate, and the value is 1, …, I; j is a leaf height direction coordinate and takes the value of 1, …, J; k is the number of triangles in each mesh and takes the values 1 and 2. By accumulating the pressure vectors of the triangular microelements divided from all the grids in the satellite network, the resultant force applied to the whole blade can be obtained.
Then, at step 112, a resultant force action line is obtained based on the principle of the resultant moment equality. According to the moment principle in mechanics, it can be understood that the sum of the moments of the component forces to the origin on all triangle microelements in the satellite network of the blade is equal to the moment of the resultant force to the origin on the whole blade. From this, an equation is obtained which contains the coordinates (unknowns) of the point of action of the resultant force, with an infinite solution, the coordinates of which constitute the line of action of the resultant force. As shown in fig. 5, which shows a schematic of the pressure vector and the radial dimension on one triangle voxel k of one blade (satellite network coordinates (i, j)). Wherein the content of the first and second substances,Ois taken as the origin point of the image,Ois the center of the triangular infinitesimal,
the vector from the center of the triangle to the origin is the moment of the triangle to the origin
. Therefore, according to the principle that the two moments are equal, the following equation 5 can be obtained:
Wherein the content of the first and second substances,
the pressure vector borne by each triangle element,
for the center of each triangular infinitesimalOTo the originOThe radius of the vector of (A) is,
for the total force to which the entire blade is subjected,
the vector from the action point of the integral resultant to the origin (unknown quantity, namely the parameter to be solved).
Wherein the content of the first and second substances,
is the origin of the triangle infinitesimalOAnd the originOThree-dimensional coordinate difference of (2).
The above formula is simplified, and a resultant force action line equation can be obtained:
WhereinF x 、F y 、F z The components of the total force experienced by the blade in the x, y, z directions determined in step 110 are shown, where x represents the horizontal axis, y represents the vertical axis, and z represents the vertical axis in three dimensional space coordinates. MijkRepresenting the moment from the center to the origin of each triangular infinitesimal of the grid with satellite network coordinates (i, j), and therefore,
and
the components of the moments in the x, y, z directions may be represented, respectively. While
The three equations of the set of three equations are independent of each other for the unknowns to be solved, with an infinite solution, i.e., with infinite point coordinates, whichInfinite points constitute the line of action of the resultant force.
After obtaining the above mentioned resultant force line of action equation, the point of action of the resultant force on the blade can then be calculated.
In step 114, the action point of the resultant force on the blade is determined according to the distance from each mesh vertex to the resultant force action line. The resultant force action point is an assumed point and is a simplified model of actual gas flow, so that the subsequent calculation of the strength of the gas compressor is facilitated, and therefore, the intersection point of the resultant force action line and the pressure surface of the blade can be specified as the resultant force action point. The specific method for solving the intersection point comprises the following steps:
and (3) calculating the distance from each grid vertex on the pressure surface of the blade to the resultant force action line, and selecting four grid vertices with the shortest distance from the distances, wherein the average three-dimensional space coordinates of the four grid vertices can be regarded as the intersection points of the action lines and the pressure surface. That is, the x coordinate of the intersection is the sum of the x coordinates of the four grid vertices and divided by 4, the y coordinate of the intersection is the sum of the y coordinates of the four grid vertices divided by 4, and the z coordinate of the intersection is the sum of the z coordinates of the four grid vertices divided by 4.
A commonly used calculation of the distance d from the mesh vertex to the action line may be as follows:
Wherein the content of the first and second substances,
as coordinates of any point on the line of action of the resultant force: (x,y,z) Are the three-dimensional coordinates of the vertices of the respective mesh, and
is the direction vector of the line of action of the resultant force. With the known line of action equation (equation 6), the above parameters of the line of action of the resultant force can be solved. Due to the fact that
And
there is no mention in the previous calculation, which is an unknown quantity, and therefore, if the distances from the mesh vertices to the lines of action of the resultant force are calculated according to equation 7, the parameters to be calculated are increased, resulting in complicated calculation.
Since the calculation of the distances from the mesh vertices to the resultant force action lines of equation 7 is complicated and consumes a lot of computing resources, in practical applications, in order to simplify the calculation of finding the shortest distance, the quantity associated with the distances can be calculated by transforming equation 6 in step 112
Instead of the complex distance calculation.
This is because when the coordinates are three-dimensional（x，y，z）Just above the resultant force line of action, the resultant force line of action equation (equation 6) is satisfied, i.e., the terms to the left and right of the equal sign are equal. When the coordinate is three-dimensional（x，y，z）When the mesh vertex is the mesh vertex, the mesh vertex is not just on the resultant force action line generally, so that a difference vector exists between the terms on the left side and the right side of the equal sign of the resultant force action line equation, and the magnitude of the difference vector is proportional to the distance between the mesh vertex and the resultant force action line, so that the mode of the difference vector
Can be used to find the four mesh vertices with the shortest distance instead of the distances of the mesh vertices to the resultant force action lines.
Specifically, each mesh vertex coordinate (c) may be setx，y，z) Are respectively substituted into the following formula 8 to solve the modulus of the difference vector at the left and right ends of the equation
. Wherein the content of the first and second substances,
the smaller the value of (d), the shorter the distance of the mesh vertex from the resultant force action line.
Since all the parameters in said equation 8 have been calculated when solving the line of action of the resultant force, equation 8 is obviously simpler and quicker to calculate than equation 7.
In order to ensure that the intersection point is on the pressure surface, as shown in FIG. 6, the intersection points of the two surfaces of the blade and the resultant force action line can be determined separatelyO 1AndO 2. That is, each grid of the satellite network can be divided into two groups according to the surface where the grid is located. For each set of meshes, four mesh vertices with the shortest distance are selected from the set, and the average coordinates of the four mesh vertices are calculated. In this way, intersections can be obtained separatelyO 1And point of intersectionO 2。
Then, it is judged fromO 1ToO 2Whether the vector of (2) is consistent with the direction of the resultant force, if so, thenO 1Is the point of intersection of the line of resultant force and the leaf pot, i.e.O 1Is a resultant force action point; otherwise, thenO 2Is the point of intersection of the line of resultant force and the leaf pot, i.e.O 2Is the point of action of the resultant force.
On the whole, the scheme of the application constructs a calculation method for solving the resultant force of the surface of the compressor blade by traversing the triangular infinitesimal elements based on the satellite grid in an equal weight manner, and the resultant force of the surface of the compressor can be accurately and quickly obtained; and the method can further solve the resultant force action line of the surface of the blade based on the resultant moment invariant principle, and then obtain the resultant force action point on the surface of the blade by taking the resultant force action line as a reference, thereby overcoming the defect that other commercial software cannot solve the action point.
In addition, the method has a resultant action point, and can simplify the action effect of the airflow on the blade into pneumatic load applied on the action point in the calculation process of the strength of the air compressor, so that the calculation amount is greatly reduced, and the calculation efficiency is improved. And the resultant force action point can be further used for axial force balance calculation and thrust calculation of the whole engine, so that an accurate and efficient compressor analysis design scheme is provided.
According to an embodiment of the present application, there is also provided a computer-readable storage medium having instructions stored thereon that, when executed, cause a machine to perform the method for determining a resultant aerodynamic force experienced by a compressor blade and a point of action thereof as described above.
There is also provided, in accordance with an embodiment of the present application, a computer system including means for performing the method for determining a resultant aerodynamic force experienced by a compressor blade and a point of application thereof as described above.
The foregoing describes certain embodiments of the present disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims may be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing may also be possible or may be advantageous. Moreover, those skilled in the relevant art will recognize that the embodiments can be practiced with various modifications in form and detail without departing from the spirit and scope of the present disclosure, as defined by the appended claims. Thus, the breadth and scope of the present disclosure should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.
Claims (10)
1. A method of determining the resultant aerodynamic force experienced by a blade of a compressor and its point of application, comprising:
dividing the surface of a three-dimensional model of a blade of the compressor into a plurality of grids;
calculating a static pressure value of each vertex of each grid of the blade surface;
numbering and arranging the vertexes of each grid according to a satellite grid mode;
for each grid on the surface of the blade, regularly dividing the grid into two triangular infinitesimal planes;
calculating pressure vectors on the corresponding triangular micro-element planes by traversing each grid of the satellite network, and accumulating the pressure vectors on all the triangular micro-element planes to obtain the resultant force applied to the whole blade;
calculating a resultant force action line based on a resultant moment equality principle; and
and determining a resultant force action point according to the distance from each grid vertex on the pressure surface of the blade to the resultant force action line.
2. The method of claim 1, wherein the satellite network is a network of all meshes attached to the blade surface, and wherein numbering mesh vertices in a satellite mesh comprises:
and numbering the vertexes of the grids in two directions i and j respectively, wherein the direction i is the direction from the front edge to the tail edge of the blade surface along the blade profile line and then to the front edge, and the direction j is the direction along the blade height.
3. The method of claim 1, wherein the rule is to divide all grids along the same diagonal direction.
4. The method of claim 1, wherein the pressure vector on the triangular infinitesimal plane is calculated by the following formula:
wherein
Representing the pressure vector on the triangle element, p being the triangle elementThe static pressure value on the element plane can be obtained by averaging the static pressure values of three vertexes of the triangle,
is the area of the triangular infinitesimal,
is the normal vector of the triangular infinitesimal surface.
5. The method of claim 4, wherein the pressure vectors at all triangular infinitesimal planes are summed to obtain a resultant force experienced by the entire blade according to the following equation:
wherein the content of the first and second substances,
for the resultant force to which the entire blade is subjected
I is a pressure vector borne by each triangular element divided from each grid, and is a vane profile line direction coordinate, and the value is 1, … and I; j is a leaf height direction coordinate and takes the value of 1, …, J; k is each triangle infinitesimal in each grid, and the value is 1 and 2.
6. The method of claim 5, wherein the resultant moment equality principle is: the sum of the moments of the component forces to the origin on all triangular microelements in the satellite network of the blade is equal to the moment of the resultant force to the origin on the whole blade, and can be expressed as the following formula:
wherein the content of the first and second substances,
the pressure vector borne by each triangle element,
for the center of each triangular infinitesimalOTo the originOThe radius of the vector of (A) is,
for the total force to which the entire blade is subjected,
the radius from the action point of the integral resultant force to the origin.
7. The method of claim 6, wherein determining a resultant force action point based on distances from respective mesh vertices on a pressure surface of the blade to the resultant force action line comprises:
calculating a quantity associated with the distance of each mesh vertex on the pressure surface of the blade to the resultant force action line according to the following formula
：
WhereinF x 、F y 、F z Calculating the components of the resultant force on the whole blade in the directions of x, y and z; in the three-dimensional space coordinate, x represents a horizontal axis, y represents a vertical axis, and z represents a vertical axis; mijkRepresents the center-to-origin moment of each triangular element of the grid of coordinates (i, j), and
、
and
may represent the components of the moment in the x, y, z directions, respectively;
choose to have the smallest
Four mesh vertices of values and the average three-dimensional coordinates of the four mesh vertices are taken as the resultant force action point.
8. The method of claim 1, wherein the steps of dividing the surface of the three-dimensional model of the compressor blades into a plurality of meshes and calculating the static pressure values at the vertices of each of the meshes for the blade surface are performed using three-dimensional design analysis software in computational fluid dynamics.
9. A computer-readable storage medium having stored thereon instructions that, when executed, cause a machine to perform the method of any of claims 1-8.
10. A computer system comprising means for performing the method of any one of claims 1-8.
Priority Applications (1)
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