CN114519238A - Full three-dimensional modeling method and device for high-performance impeller mechanical blade and electronic equipment - Google Patents

Full three-dimensional modeling method and device for high-performance impeller mechanical blade and electronic equipment Download PDF

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CN114519238A
CN114519238A CN202210053290.0A CN202210053290A CN114519238A CN 114519238 A CN114519238 A CN 114519238A CN 202210053290 A CN202210053290 A CN 202210053290A CN 114519238 A CN114519238 A CN 114519238A
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CN114519238B (en
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包幼林
温殿忠
邹学奇
林海
杨华斌
张鹏
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Hunan Aviation Powerplant Research Institute AECC
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Abstract

The application discloses a full three-dimensional modeling method, a full three-dimensional modeling device and electronic equipment for high-performance impeller mechanical blades, wherein the method comprises the following steps: s1, performing primary modeling on a meridian flow line rotary flow surface according to the airflow angle along the meridian flow line calculated by an axisymmetric flow field and a thickness distribution rule given by experience; s2, calculating the speed parameter distribution rules of the suction surface and the pressure surface of the blade profile by a blade streaming calculation method, and iterating the speed parameter distribution rules with the primary modeling to obtain the optimal blade profile on each rotary flow surface; s3, splicing the molded surfaces of each blade profile, checking the full curvature and smoothing the curved surface by introducing a Kangsi surface method in a differential equation, ensuring the smooth molded surfaces and finally obtaining the blade profile of the efficient compressor blade. The full three-dimensional modeling method for the impeller mechanical blade can accurately use the airflow angle in the axial symmetric flow place, and is suitable for impeller mechanical blades with different blade load levels and different flow channel shapes.

Description

Full three-dimensional modeling method and device for high-performance impeller mechanical blade and electronic equipment
Technical Field
The invention relates to the technical field of aircraft engines, gas turbines, turbochargers and the like, in particular to a full three-dimensional modeling method and device for high-performance impeller mechanical blades and electronic equipment.
Background
The compressor is used as a very important core rotating part of an aeroengine and a gas turbine, and the performance of the compressor has important influence on the performance, the economy and the safety of the whole machine. In general, the shape of the meridian flow passage and the shape of the blade profile of the blade are key to ensure the high efficiency of the impeller machinery, and especially the blade profile has a greater influence on the efficiency, so that the design of the blade profile is the core of the pneumatic design of a compressor.
In order to design a detailed blade profile, the prior art firstly simplifies a compressor runner, and the basic idea of simplification is as follows: the irregular meridian flow line rotary flow surface in the blade channel is simplified into a cylindrical surface or a conical surface, and the blade profile modeling design is carried out on the cylindrical surface or the conical surface expansion surface, for example, the meridian flow line rotary flow surface of a certain gas compressor is approximate to a series of conical flow surfaces, a theoretical mean camber line (parabola mean camber line, double-arc mean camber line, multi-arc mean camber line and the like) is given on the conical surface expansion surface according to the numerical value of the inlet Mach number of each rotary flow surface, the theoretical mean camber line is superposed with the theoretical mean camber line, and then the blade profile surfaces along the blade height are radially superposed to form a blade.
The defects of the prior art mainly comprise:
(1) with the increasing tangential speed of the tip of the compressor, the Mach number of the inlet of the blade is higher and higher, the design requirement on the profile of the blade is stricter and stricter, and the improper profile can increase the shock wave loss and the corresponding boundary layer loss and the secondary loss, so that the efficiency of the blade is reduced sharply. The camber line profiles such as parabola, double arc, multi-arc and the like used in the conventional blade design can not meet the design requirement of the high-Mach-number lower blade profile, and a camber line design method suitable for the high-load blade needs to be found.
(2) The cylindrical surface or the conical surface used for designing the conventional blade is an approximate surface of a midnight flow line rotating flow surface in axial symmetry flow field calculation, blade modeling cannot be carried out according to a midnight flow line airflow angle when the unfolding surface of the blade is used for blade modeling, and the deviation of the airflow angle can possibly cause the designed blade profile to be far away from the design target along with the increase of the load of the blade of the air compressor, so that a serious person can cause design failure.
(3) In the high-load centrifugal compressor with higher and higher pressure ratio and load coefficient, the centrifugal impeller of the high-load centrifugal compressor needs to adopt an integrated design (the air guide wheel and the centrifugal impeller are integrated into a whole) to ensure the working efficiency of the high-load centrifugal compressor, and the high-load centrifugal compressor is completely failed when designed by adopting a cylindrical surface and conical surface approximate design method.
(4) In the conventional design, the blade profiles designed along the sections of the blade height are generally directly stacked in the radial direction to obtain the final blade, but the method has the risk of the surface of the blade being rough and affecting the aerodynamic performance of the blade.
Disclosure of Invention
The application provides a full three-dimensional modeling method for a high-performance impeller mechanical blade, and aims to solve the technical problems that the blade related to the existing modeling method cannot meet the high Mach requirement, has large deviation, cannot ensure the working efficiency and influences the aerodynamic performance of the blade.
The technical scheme adopted by the application is as follows:
a full three-dimensional modeling method for a high-performance impeller mechanical blade comprises the following steps:
s1, performing primary modeling on a meridian flow line rotary flow surface according to the airflow angle along the meridian flow line calculated by an axisymmetric flow field and a thickness distribution rule given by experience;
s2, calculating the speed parameter distribution rules of the suction surface and the pressure surface of the blade profile by a blade streaming calculation method, and iterating the speed parameter distribution rules with the primary modeling to obtain the optimal blade profile on each rotary flow surface;
s3, splicing the molded surfaces of each blade profile, checking the full curvature and smoothing the curved surface by introducing a Kangsi surface method in a differential equation, ensuring the smooth molded surfaces and finally obtaining the blade profile of the efficient compressor blade.
Further, the step S1 specifically includes the steps of:
s11, calculating the meridian flow line rotating flow surface of the blade and the airflow angle distribution along the meridian flow line according to the axisymmetric flow field, and determining the camber line of the blade profile by combining empirical attack angle and drop angle selection;
s12, selecting a thickness distribution rule according to the Mach number of each meridian flow line rotating flow surface inlet, and superposing the thickness distribution rule on the camber line to finally obtain a blade profile coordinate, so that a primary blade profile is obtained.
Further, the step S2 specifically includes:
s21, deducing and solving main velocity equations on a pressure surface and a suction surface of the blade in the rotary flow surface through a flow equation, an enthalpy equation and an energy equation in the flow field, and further obtaining a velocity distribution rule of the pressure surface and the suction surface of the blade;
and S22, adjusting the blade angle and thickness distribution of the blade according to the blade surface speed distribution rule, and finally iterating to obtain the blade profile type line on the rotary flow surface meeting the design requirement.
Further, the step S3 specifically includes the steps of:
s31, at each splicing node, the vector balance condition of the two sides in the two directions is met, the condition of vector equality is met, specifically, the vector, the second-order vector, the cross-boundary vector and the torsion vector along the axial direction and the radial direction need to be equal respectively, and therefore the smoothness of the connection of the curved surface pieces and the smoothness of the whole curved surface are guaranteed.
Further, the step S11 specifically includes the steps of:
s111, analyzing a motion equation on a meridian flow line revolution flow surface (S1 flow surface):
Figure BDA0003475214960000031
Figure BDA0003475214960000032
in the above formula, r, theta and z are cylindrical coordinate systems; w is the relative velocity; beta is the airflow angle; m is the meridian flow line length; omega is angular velocity; sigma is an included angle between a tangential line of the meridian flow line and the z axis; the delta n is the thickness of a normal flow sheet on a meridian flow line rotating flow surface; g is the flow passing through an annular channel formed by the thickness of the rotary flow surface flow sheet; n is the number of the leaves; ρ is the gas density; wherein r, m, delta n and sigma are given by axial symmetric flow field calculation; subscript d represents the blade pressure side; subscript t represents the blade suction surface;
s112, order:
Figure BDA0003475214960000033
the x-y plane is a conversion plane of the meridian flow line revolution flow surface model, any curve y (x) on the x-y plane has the slope dy/dx (rd theta/dm), and according to the definition of the airflow angle:
tanβ＝Wθ/Wmrd θ/dm, wherein WθIs the circumferential velocity, WmThe meridian velocity is as follows:
dy/dx＝tanβ (1-4)
namely, a proper curve y (x) is constructed on the conversion plane, so that the change of the inlet and outlet airflow angles on the rotary flow surface and the change along the meridian flow line can be effectively ensured;
s113, when modeling is carried out on the x-y plane, the method is basically the same as the conventional plane modeling and conical surface modeling, namely different camber line profiles are selected according to different inlet relative Mach numbers and load distribution rules, wherein the camber line profiles comprise parabolas, double arcs and multiple arcs or are formed by combining several curves; or any camber line design is directly carried out according to the airflow angle distribution rule.
Further, the step S12 specifically includes the steps of:
s121, determining the corresponding relation of r, the meridian flow line m and the axial coordinate z by the formula (1-5):
Figure BDA0003475214960000034
calculating the slope dr/dm of each point;
s122, solving the value theta of each point along the molded line, wherein for a given curve, the integral in the formula (1-3) can be written into a fixed integral form:
Figure BDA0003475214960000041
when x is equal to x0When y is0＝rθ0So that theta is obtained0Given an increment Δ x, y (x) is calculated from the relationship y (x)0A value of + Deltax), and further to find theta (x)0+ Δ x), when the integral in the formula (1-6) adopts trapezoidal integral, the value of θ can be directly solved; in the above formula, subscript0Is the first coordinate point of the inlet;
s123, converting the leaf profile on the rotating flow surface into a rectangular coordinate system according to the value of the leaf profile in the cylindrical coordinate system and the following formula:
Figure BDA0003475214960000042
as can be seen from the formula (1-6), the revolution surface is a conical surface when dr/dm is constant, and a cylindrical surface when dr/dm is 0.
Further, the step S21 specifically includes the steps of:
s211, setting the flow field to meet the following equation:
Figure BDA0003475214960000043
in the above formula, C is the absolute velocity; l is the length; i is thermodynamic parameter internal energy; t is time; n is the number of the leaves; h is the height of the dough sheet; in the internal flow field of the impeller, a flow sheet zone having a length dm in the meridional direction and crossing the blade flow channels is taken, in which the relative velocity is constant in the pressure and suction surfaces in the direction dm, so that equation (2-1) is used for this flow sheet zone:
Figure BDA0003475214960000044
wherein, Δ θ ═ Qt-Qd
Figure BDA0003475214960000045
Qθ＝Q sinβ (2-4)
The formula (2-2) is simplified to be:
Figure BDA0003475214960000046
in the blade channel, along the blade crossing direction, the following relational expression exists on the blade pressure and suction surfaces:
Qd＝2Qav-Qt； (2-6)
βav＝(βt+βd)/2 (2-7)
the simplification from equation (2-6) to equation (2-5) is:
Figure BDA0003475214960000051
the main equation of the speed of the suction surface of the blade is obtained;
in the above formula: t is static temperature;
Figure BDA0003475214960000057
is the total inlet temperature; q is the relative velocity on the surface of revolution; r is a radius coordinate (dimensionless, R ═ R/R)T) (ii) a M is the distance along the meridian flow line on the revolution surface; k is thermodynamic parameter specific heat ratio; g is the acceleration of gravity; r isTIs the outlet of the impellerA radius; mTThe Mach number of the outlet of the impeller; r' is a thermodynamic constant;
subscript d is the pressure surface of the blade; subscript t is a blade suction surface; subscript av is a numerical value on the center flow line; subscript θ is the projection of the parameter in the θ direction; subscript 0 denotes the inlet parameters; subscript T denotes impeller exit parameters;
s212, applying the third formula in the formula (2-1) to the fluidized sheet belt, and discretizing the fluidized sheet belt to obtain:
ΔG＝ρavC0Qav cosβavHhT RrTΔθ (2-9)
after deformation, the following are:
Figure BDA0003475214960000052
in the above formula:
Figure BDA0003475214960000053
the density ratio in relation (2-10) can be determined from the energy equation over the relation:
Figure BDA0003475214960000054
s213, in the flow channel, the whole calculation process is to use the iteration of the equations (2-10) and (2-11) to obtain the average relative speed QavAnd (3) calculating the speed of the suction surface of the blade according to a formula (2-8), and calculating the speed of the pressure surface according to a formula (2-6), wherein: Δ G is the weight flow; lambda is a prerotation value; c0The speed of sound at the upstream inlet of the impeller; subscript u denotes the circumferential component.
Further, the step S31 specifically includes the steps of:
s311, according to the property of the space cubic spline curve, aiming at a vector function
Figure BDA0003475214960000055
In the interval [ t0，tn]Any sub-interval of [ t ]i-1，ti]The following conditions are satisfied:
Figure BDA0003475214960000056
in the formula: lambda [ alpha ]iμiIs a constant;
s312, for the grid, if the node coordinate of the transverse network line is j, the curve parameter is u, the node coordinate of the longitudinal network line is i, and the network line parameter is w, the transverse and longitudinal parameter spline curves are respectively represented by SujAnd SwiRepresents, i.e.:
Figure BDA0003475214960000061
in the formula:
Figure BDA0003475214960000062
Figure BDA0003475214960000063
in the column matrix:
Figure BDA0003475214960000064
a twisted vector called the corner point of the curved surface;
s313, for any curved surface Ci,jThe shape is constrained by four parameters at four corners, as follows:
Figure BDA0003475214960000065
since the boundary of the patch is a spatial cubic parametric spline, from the direct product of the two boundary lines, and noting the boundary condition matrix (3-4), the patch's equation is:
Figure BDA0003475214960000066
on the splicing of the curved surface sheet, the boundary has a condition smoother than a parameter spline, namely at a node, the condition that tangent vectors on two sides in two directions are parallel and the condition that the vectors are equal are met, and for Ci,jAnd Ci+1,jThe two curved surface pieces need to meet the following requirements:
1) the director along the u direction is equal, i.e.
Figure BDA0003475214960000067
2) The second derivative vector along the u-direction is equal, i.e.
Figure BDA0003475214960000068
3) The vectors being equal across the boundary, i.e.
Figure BDA0003475214960000069
4) With equal twisting vectors, i.e.
Figure BDA00034752149600000610
For Ci+1,jAnd Ci+1,j+1The two curved surface sheets satisfy the following conditions:
1) the director along the w direction is equal, i.e.
Figure BDA00034752149600000611
2) Second derivative vectors along the w direction are equal, i.e.
Figure BDA00034752149600000612
3) The vectors being equal across the boundary, i.e.
Figure BDA0003475214960000071
4) With equal twisting vectors, i.e.
Figure BDA0003475214960000072
The satisfaction of the above conditions is easily verified by simple operation of (3-5), and the smoothness of the connection of the curved surface pieces and the smoothness of the whole curved surface are ensured by the above conditions;
s314, determining main elements in the boundary condition matrix, wherein in the formula (3-5), M is a constant matrix, F (u), F (w)TFor variable row and array, the equation of a curved surface is determined, mainly the boundary condition matrix B (i, j) is determined, and the node vector in the B matrix is obtained by the formula (3-4) after the grid division of the curved surface
Figure BDA0003475214960000073
To be known, the dominant vector to be determined is the director
Figure BDA0003475214960000074
And the twisting vector
Figure BDA0003475214960000075
For the transverse spatial parameter spline curve, the third formula in the formula (3-1) and the formula (3-2) are used, and the vectors are equal, namely mu i1, so:
Figure BDA0003475214960000076
therein, the
Figure BDA0003475214960000077
Figure BDA0003475214960000078
By
Figure BDA0003475214960000079
Therefore, the following steps are carried out:
Figure BDA00034752149600000710
then equation (3-6) can be written as:
[6 -6 2 4]Bu(i)＝[-6 6 -4 -2]Bu(i+1) (3-7)
bu (i) and Bu (i +1) are substituted into the equations (3-7) and are simply collated as:
Figure BDA00034752149600000711
the above equation is the three-turn equation of the cubic parameter spline curve about the transverse space;
s315, for the longitudinal space parameter spline curve, the three-corner equation is as follows:
Figure BDA00034752149600000712
in equations (3-8) and (3-9), since the node vectors are known, the director at all the lateral and longitudinal nodes can be found
Figure BDA00034752149600000713
And
Figure BDA00034752149600000714
determining node twisting vector:
Figure BDA00034752149600000715
the twisting vector is used as a boundary constraint quantity, directly influences the geometric shape of a certain geometric curved surface, and is determined by a left-right boundary-crossing second-order continuous condition:
Figure BDA00034752149600000716
the following can be obtained:
F"(1)MBu(i+1,j)MTF(w)T＝F"(0)MBu(i+1,j+1)MTF(w)T
namely: f "(1) MBu (i +1, j) ═ F" (0) MBu (i +1, j + 1);
and substituting the Bu boundary matrix into row matrixes on two sides of equal sign to obtain:
Figure BDA0003475214960000081
the above formula is a cross boundary second-order continuous condition of the transverse network cable, and a longitudinal cross boundary second-order continuous condition can be obtained in the same way:
Figure BDA0003475214960000082
the twisting vector at the node of the whole curved surface can be obtained by using the equations (3-10) and (3-11) and giving the end point condition.
This application on the other hand still provides a full three-dimensional molding device of high performance impeller machine blade, includes:
the preliminary modeling module is used for carrying out preliminary modeling on a meridian flow line rotating flow surface according to an airflow angle along the meridian flow line, which is obtained by calculating an axial symmetry flow field, and a thickness distribution rule given by experience;
the modeling iteration module is used for calculating the speed parameter distribution rules of the suction surface and the pressure surface of the blade profile through a blade streaming calculation method and iterating the speed parameter distribution rules with the initial modeling to obtain the optimal blade profile on each rotary flow surface;
and the modeling fairing module is used for splicing each blade profile by introducing a Conss surface method in a differential equation, checking the total curvature and fairing the surface, so as to ensure that the profile is smooth and finally obtain the blade profile of the high-efficiency compressor blade.
The application also provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the program to realize the steps of the high-performance impeller mechanical blade full three-dimensional modeling method.
The application also provides a storage medium, which comprises a stored program, and when the program runs, the storage medium is controlled by equipment on which the storage medium is located to execute the steps of the full three-dimensional modeling method of the high-performance impeller mechanical blade.
Compared with the prior art, the method has the following beneficial effects:
the application provides a full three-dimensional modeling method, a full three-dimensional modeling device and electronic equipment for high-performance impeller mechanical blades, wherein the method comprises the following steps: s1, performing primary modeling on a meridian flow line rotary flow surface according to the airflow angle along the meridian flow line calculated by an axisymmetric flow field and a thickness distribution rule given by experience; s2, calculating the speed parameter distribution rules of the suction surface and the pressure surface of the blade profile by a blade streaming calculation method, and iterating the speed parameter distribution rules with the primary modeling to obtain the optimal blade profile on each rotary flow surface; s3, splicing the molded surfaces of each blade profile, checking the full curvature and smoothing the curved surface by introducing a Kangsi surface method in a differential equation, ensuring the smooth molded surfaces and finally obtaining the blade profile of the efficient compressor blade. The application provides a full three-dimensional molding method of high performance impeller machinery blade through carrying out arbitrary mean camber line blade molding in arbitrary gyration flow surface, can realize the design of compressor machine blade under the high import mach number condition of high load to obtain the full three-dimensional blade profile that satisfies the designing requirement fast, its advantage includes: (1) the blade modeling can be directly carried out on the meridian flow line rotating flow surface, and is convenient and quick; (2) the designed blade profile has reasonable distribution of pneumatic parameters along the flow direction, and the performance of the blade is excellent; (3) after splicing and fairing are carried out by a Kangsi curved surface method, the surface of the blade is smooth; (4) the blade has better modeling universality and is suitable for any impeller mechanical blade.
In addition to the objects, features and advantages described above, other objects, features and advantages will be apparent from the present application. The present application will now be described in further detail with reference to the accompanying drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application. In the drawings:
fig. 1 is a flow chart of a full three-dimensional modeling method for a high-performance impeller mechanical blade according to a preferred embodiment of the application.
FIG. 2 is a schematic view of a meridional flow line of a compressor blade according to a preferred embodiment of the present application.
FIG. 3 is a schematic view of the meridional streamline flow angle distribution of a compressor blade in a preferred embodiment of the present application.
Figure 4 is a schematic view of the meridional flow shape of the blade in the preferred embodiment of the present application.
FIG. 5 is a schematic view of a blade profile in the x-y plane in the preferred embodiment of the present application.
Fig. 6 is a schematic diagram of the relation between cylindrical coordinates and rectangular coordinates in the preferred embodiment of the present application.
FIG. 7 is a schematic view of the flow sheet band of vane passages on a surface of revolution in a preferred embodiment of the present application.
Fig. 8 is a schematic diagram of a three-dimensional surface mesh in a preferred embodiment of the present application.
Fig. 9 is a block diagram of a high performance turbomachinery blade full three-dimensional modeling apparatus in accordance with a preferred embodiment of the present application.
Fig. 10 is a schematic block diagram of an electronic device entity of the preferred embodiment of the present application.
Fig. 11 is an internal structural view of a computer device of the preferred embodiment of the present application.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
Referring to fig. 1, a preferred embodiment of the present application provides a method for full three-dimensional modeling of a high performance turbomachinery blade, comprising the steps of:
s1, performing primary modeling on a meridian flow line rotary flow surface according to the airflow angle along the meridian flow line calculated by an axisymmetric flow field and a thickness distribution rule given by experience;
s2, calculating the speed parameter distribution rules of the suction surface and the pressure surface of the blade profile by a blade streaming calculation method, and iterating the speed parameter distribution rules with the primary modeling to obtain the optimal blade profile on each rotary flow surface;
s3, splicing the molded surfaces of each blade profile, checking the full curvature and smoothing the curved surface by introducing a Kangsi surface method in a differential equation, ensuring the smooth molded surfaces and finally obtaining the blade profile of the efficient compressor blade.
The embodiment provides a full three-dimensional modeling method for a high-performance impeller mechanical blade, which comprises the following steps: s1, performing primary modeling on a meridian flow line rotary flow surface according to the airflow angle along the meridian flow line calculated by an axisymmetric flow field and a thickness distribution rule given by experience; s2, calculating the speed parameter distribution rules of the suction surface and the pressure surface of the blade profile by a blade streaming calculation method, and iterating the speed parameter distribution rules with the primary modeling to obtain the optimal blade profile on each rotary flow surface; s3, splicing the molded surfaces of each blade profile, checking the full curvature and smoothing the curved surface by introducing a Kangsi surface method in a differential equation, ensuring the smooth molded surfaces and finally obtaining the blade profile of the efficient compressor blade. The full three-dimensional modeling method of high-performance impeller mechanical blade provided by the embodiment can realize the design of the compressor blade under the high-load high-inlet Mach number condition by modeling any camber line blade in any rotary flow surface, and quickly obtain the full three-dimensional blade profile meeting the design requirement, and has the advantages that: (1) the blade modeling can be directly carried out on the meridian flow surface, so that the operation is convenient and fast; (2) the designed blade profile has reasonable distribution of pneumatic parameters along the flow direction, and the performance of the blade is excellent; (3) after splicing and fairing are carried out by a Kangsi curved surface method, the surface of the blade is smooth; (4) the blade has better modeling universality and is suitable for any impeller mechanical blade.
In a preferred embodiment of the present application, the step S1 specifically includes the steps of:
s11, calculating a meridian flow line rotating flow surface of the blade and airflow angle distribution along the meridian flow line according to the axial symmetric flow field (see the figure 2 and the figure 3), and determining a camber line of the blade profile by combining empirical attack angle and drop angle selection;
s12, selecting a thickness distribution rule according to the Mach number of each meridian flow line rotating flow surface inlet, and superposing the thickness distribution rule on the camber line to finally obtain a blade profile coordinate, so that a primary blade profile is obtained.
In a preferred embodiment of the present application, the step S2 specifically includes:
s21, deducing and solving main velocity equations on a pressure surface and a suction surface of the blade in the rotary flow surface through a flow equation, an enthalpy equation and an energy equation in the flow field, and further obtaining a velocity distribution rule of the pressure surface and the suction surface of the blade;
and S22, adjusting the blade angle and thickness distribution of the blade according to the blade surface speed distribution rule, and finally iterating to obtain the blade profile on the rotary flow surface meeting the design requirement.
In any of the above-mentioned rotary flow surface modeling, a preliminary profile line is obtained, and how to judge how to design the aerodynamic performance of the profile. Because the quality of the blade profile not only affects the aerodynamic efficiency of the blade, but also affects the available working range of the blade, and the velocity distribution of the blade surface directly determines the above two characteristics of the blade, it is necessary to solve, analyze and optimize the velocity distribution of the blade profile to improve the comprehensive performance of the compressor blade.
In a preferred embodiment of the present application, the step S3 specifically includes the steps of:
s31, at each splicing node, the vector balance condition of the two sides in the two directions is met, the condition of vector equality is met, specifically, the vector, the second-order vector, the cross-boundary vector and the torsion vector along the axial direction and the radial direction need to be equal respectively, and therefore the smoothness of the connection of the curved surface pieces and the smoothness of the whole curved surface are guaranteed.
After obtaining the more ideal blade profile line on the different rotating flow surfaces along the blade height, the next step is to solve the problem of how to obtain a smoother three-dimensional blade. The problems are more obvious for the blades with higher load coefficients, in order to overcome the difficulties, the embodiment adopts a Karns surface method which is mature theoretically and can adapt to the design characteristics of the blades of the air compressor to splice and fairing the blade shapes in each rotary flow surface, namely, at each spliced node, tangential vector balance conditions in two directions on two sides are met, and the condition of equal vector is met. That is, the guide vector, the second guide vector, the cross-boundary guide vector and the torsion vector along the axial direction and the radial direction need to be equal respectively, so that the smoothness of the connection of the curved surface pieces and the smoothness of the whole curved surface are ensured.
Because the Kangsi surface method adopts the space parameter spline curve to represent the curved surface through the direct product to the net line of the curved surface piece, the piece can also adapt to the curved surface with larger deflection without the limitation of the change and the size of the full curvature, and then, the smoothness of the curved surface can be judged through the full curvature at any point, so that the adaptive surface of the curved surface model is wider.
In a preferred embodiment of the present application, the step S11 specifically includes the steps of:
s111, considering that the purpose of blade modeling is to control the surface speed distribution of the blade by controlling the surface profile of the blade to achieve the effect of high-efficiency speed reduction and diffusion, therefore, the equation of motion on the meridian flow line rotating flow surface needs to be analyzed firstly:
Figure BDA0003475214960000111
Figure BDA0003475214960000112
in the above formula, r, theta and z are cylindrical coordinate systems; w is the relative velocity; beta is the airflow angle; m is the meridian flow line length; omega is angular velocity; sigma is an included angle between a tangential line of the meridian flow line and the z axis; the delta n is the thickness of a normal flow sheet on a meridian flow line rotating flow surface; g is the flow passing through an annular channel formed by the thickness of the rotary flow surface flow sheet; n represents the number of leaves; ρ: is the gas density; wherein r, m, delta n and sigma are given by axial symmetric flow field calculation; subscript d represents the blade pressure side; subscript t represents the suction side of the blade; under the conditions of fixed rotating speed and inlet and outlet, the speed distribution of the surface of the blade on the rotary flow surface only depends on the sizes of beta and d beta/dm values, so that when the blade is molded, reasonable speed distribution can be obtained by directly controlling the distribution change of beta along the m direction, the flow loss is reduced, and the efficiency of the blade is improved. (ii) a
S112, order:
Figure BDA0003475214960000113
the x-y plane is a conversion plane of the meridian flow line revolution flow surface model, any curve y (x) on the x-y plane has the slope dy/dx (rd theta/dm), and according to the definition of the airflow angle:
tanβ＝Wθ/Wmrd θ/dm, wherein WθIs the circumferential velocity, WmThe meridian velocity is as follows:
dy/dx＝tanβ (1-4)
namely, a proper curve y (x) is constructed on the conversion plane, so that the change of the inlet and outlet airflow angles on the rotary flow surface and the change along the meridian flow line can be effectively ensured;
s113, when modeling is carried out on the x-y plane, the modeling is basically the same as the conventional plane modeling and conical surface modeling, namely different camber line profiles are selected according to different relative inlet Mach numbers and load distribution rules, wherein the camber line profiles comprise parabolas, double arcs and multiple arcs or are formed by combining several curves; or any camber line design is directly carried out according to the airflow angle distribution rule.
In a preferred embodiment of the present application, the step S12 specifically includes the steps of:
s121, determining the corresponding relation of r, the meridian flow line m and the axial coordinate z by the formula (1-5):
Figure BDA0003475214960000121
calculating the slope dr/dm of each point;
s122, solving the value theta of each point along the molded line, wherein for a given curve, the integral in the formula (1-3) can be written into a fixed integral form:
Figure BDA0003475214960000122
when x is equal to x0When y is0＝rθ0So that theta is obtained0Given an increment Δ x, y (x) is calculated from the relationship y (x)0A value of + Deltax), and further to find theta (x)0+ Δ x), when the integral in the formula (1-6) adopts trapezoidal integral, the value of θ can be directly solved; in the above formula, subscript0Is the first coordinate point of the inlet;
s123, converting the leaf profile on the rotating flow surface into a rectangular coordinate system according to the value of the leaf profile in the cylindrical coordinate system and the following formula:
Figure BDA0003475214960000123
as can be seen from the formula (1-6), the revolution surface is a conical surface when dr/dm is constant, and a cylindrical surface when dr/dm is 0.
Fig. 4 and 5 show how the profile in the x-y plane translates to the turning flow surface. Fig. 4 is a meridional streamline shape of the blade, the relationship of the formula (1-5) is given by axial symmetric flow field calculation, and fig. 5 illustrates that one blade profile line y on an x-y plane is y (x) and is given by the blade shape on a conversion plane.
FIG. 6 is a schematic diagram of the relationship between cylindrical coordinates and rectangular coordinate system, i.e. the relationship between r θ z and XYZ, θ is the same as the rotation direction, and θ is0Is the angular coordinate value of the X axis in the rectangular coordinate system.
In a preferred embodiment of the present application, the step S21 specifically includes the steps of:
s211, because the flow field in the compressor impeller researched by us is basically in a transonic range, shock waves are considered to be very weak parameters and do not produce abrupt changes, namely, the shock waves are continuous, meanwhile, the flow field is assumed to be potential, steady and constant entropy flow, and the flow field can meet the following equation:
Figure BDA0003475214960000131
in the above formula, C is the absolute velocity; l is the length; i is thermodynamic parameter internal energy; t is time; n is the number of the leaves; h, the height of the dough sheet is; in the flow field inside the impeller, a flow sheet zone having a length dm in the meridional direction and crossing the flow channel of the blade as shown in fig. 7 is taken, in which the relative velocity is constant in the direction dm at the pressure and suction surfaces, and therefore equation (2-1) is used for this flow sheet zone:
Figure BDA0003475214960000132
wherein, Δ θ ═ Qt-Qd
Figure BDA0003475214960000133
Qθ＝Q sinβ (2-4)
The formula (2-2) is simplified to be:
Figure BDA0003475214960000134
in the blade channel, along the blade crossing direction, the following relational expression exists on the blade pressure and suction surfaces:
Qd＝2Qav-Qt (2-6)
βav＝(βt+βd)/2 (2-7)
the simplification from equation (2-6) to equation (2-5) is:
Figure BDA0003475214960000135
the principal equation is the speed of the suction surface of the blade;
in the above formula: t is static temperature;
Figure BDA0003475214960000136
is the total inlet temperature; q is the relative velocity on the surface of revolution; r is a radius coordinate (dimensionless, R ═ R/R)T) (ii) a M is the distance along the meridian flow line on the revolution surface; k thermodynamic parameter specific heat ratio; g acceleration by gravityDegree; r isTIs the impeller exit radius; mTThe Mach number of the outlet of the impeller; r' is a thermodynamic constant;
subscript d is the pressure surface of the blade; subscript t is a blade suction surface; subscript av is a numerical value on the center flow line; subscript θ is the projection of the parameter in the θ direction; subscript 0 indicates the inlet parameters; subscript T denotes impeller exit parameters;
s212, applying the third formula in the formula (2-1) to the fluidized bed strip, and discretizing to obtain:
ΔG＝ρavC0Qav cosβavHhT RrTΔθ (2-9)
after deformation, the following are:
Figure BDA0003475214960000141
in the above formula:
Figure BDA0003475214960000142
the density ratio in relation (2-10) can be determined from the energy equation over the relation:
Figure BDA0003475214960000143
s213, in the whole calculation process in the flow channel, the average relative speed Q is obtained by iteration of equations (2-10) and (2-11)avAnd (3) calculating the speed of the suction surface of the blade according to (2-8), and calculating the speed of the pressure surface according to (2-6), wherein the formula is as follows: Δ G is the weight flow; lambda is a prerotation value; c0The speed of sound at the upstream inlet of the impeller; subscript u represents the circumferential component;
in a preferred embodiment of the present application, the step S31 specifically includes the steps of:
s311, according to the property of the space cubic spline curve, aiming at a vector function
Figure BDA0003475214960000144
In the interval [ t0，tn]In (1)Arbitrary subinterval [ t ]i-1，ti]The following conditions are satisfied:
Figure BDA0003475214960000145
in the formula: lambda [ alpha ]iμiIs a constant;
s312, for the grid shown in FIG. 8, if the node coordinate of the transverse network line is j, the curve parameter is u, the node coordinate of the longitudinal network line is i, and the network line parameter is w, the transverse and longitudinal parameter spline curves are respectively represented by SujAnd SwiRepresents, i.e.:
Figure BDA0003475214960000146
in the formula:
Figure BDA0003475214960000147
Figure BDA0003475214960000148
in the column matrix:
Figure BDA0003475214960000151
a torsion vector called a curved corner point;
s313, for any curved surface Ci,jThe shape of the three-dimensional rectangular prism is constrained by four parameters at four corner points, as shown in the following formula:
Figure BDA0003475214960000152
since the boundary of the patch is a spatial cubic parametric spline, from the direct product of the two boundary lines, and noting the boundary condition matrix (3-4), the patch's equation is:
Figure BDA0003475214960000153
on the splicing of the curved surface sheet, the boundary has a smoother condition than the parameter spline, namely at a node, the condition that tangent vectors on two sides in two directions are parallel is met, the condition that the vectors are equal is met, and for Ci,jAnd Ci+1,jThe two curved surface pieces need to meet the following requirements:
1) the director along the u direction is equal, i.e.
Figure BDA0003475214960000154
2) Second derivative vectors along the u-direction are equal, i.e.
Figure BDA0003475214960000155
3) The vectors being equal across the boundary, i.e.
Figure BDA0003475214960000156
4) With equal twisting vectors, i.e.
Figure BDA0003475214960000157
For Ci+1,jAnd Ci+1,j+1The two curved surface sheets satisfy the following conditions:
1) the director along the w direction is equal, i.e.
Figure BDA0003475214960000158
2) Second derivative vectors along the w direction are equal, i.e.
Figure BDA0003475214960000159
3) The vectors being equal across the boundary, i.e.
Figure BDA00034752149600001510
4) With equal twisting vectors, i.e.
Figure BDA00034752149600001511
The satisfaction of the above conditions is easily verified by simple operation of (3-5), and the smoothness of the connection of the curved surface pieces and the smoothness of the whole curved surface are ensured by the above conditions;
s314, determining main elements in the boundary condition matrix, wherein in the formula (3-5), M is a constant matrix, F (u), F (w)TFor variable row and array, the equation of a curved surface is determined, mainly the boundary condition matrix B (i, j) is determined, and the node vector in the B matrix is obtained by the formula (3-4) after the grid division of the curved surface
Figure BDA00034752149600001512
To be known, the dominant vector to be determined is the director
Figure BDA00034752149600001513
And the twisting vector
Figure BDA00034752149600001514
For the transverse spatial parameter spline curve, the third formula in the formula (3-1) and the formula (3-2) are used, and the vectors are equal, namely mu i1, so:
Figure BDA0003475214960000161
therein, the
Figure BDA0003475214960000162
Figure BDA0003475214960000163
By
Figure BDA0003475214960000164
Therefore, the following steps are carried out:
Figure BDA0003475214960000165
then equation (3-6) can be written as:
[6 -6 2 4]Bu(i)＝[-6 6 -4 -2]Bu(i+1) (3-7)
bu (i) and Bu (i +1) are substituted into the equations (3-7) and are simply collated as:
Figure BDA0003475214960000166
the above equation is the three-turn equation of the cubic parameter spline curve about the transverse space;
s315, for the longitudinal space parameter spline curve, the three-corner equation is as follows:
Figure BDA0003475214960000167
in equations (3-8) and (3-9), since the node vectors are known, the director at all the lateral and longitudinal nodes can be found
Figure BDA0003475214960000168
And
Figure BDA0003475214960000169
determining node twisting vector:
Figure BDA00034752149600001610
the twisting vector is used as a boundary constraint quantity, has stronger flexibility, directly influences the geometric shape of a certain geometric curved surface, and is characterized by a left-right boundary-crossing second-order continuous condition:
Figure BDA00034752149600001611
the following can be obtained:
F"(1)MBu(i+1,j)MTF(w)T＝F"(0)MBu(i+1,j+1)MTF(w)T
namely: f "(1) MBu (i +1, j) ═ F" (0) MBu (i +1, j + 1);
and substituting the Bu boundary matrix into row matrixes on two sides of equal sign to obtain:
Figure BDA00034752149600001612
the above formula is a cross boundary second-order continuous condition of the transverse network cable, and a longitudinal cross boundary second-order continuous condition can be obtained in the same way:
Figure BDA00034752149600001613
the twisting vector at the node of the whole curved surface can be obtained by using the equations (3-10) and (3-11) and giving the end point condition.
As shown in fig. 9, another embodiment of the present application provides a high-performance impeller mechanical blade full three-dimensional modeling apparatus, including:
the preliminary modeling module is used for carrying out preliminary modeling on a meridian flow line rotating flow surface according to an airflow angle along the meridian flow line, which is obtained by calculating an axial symmetry flow field, and a thickness distribution rule given by experience;
the modeling iteration module is used for calculating the speed parameter distribution rules of the suction surface and the pressure surface of the blade profile through a blade streaming calculation method and iterating the speed parameter distribution rules with the initial modeling to obtain the optimal blade profile on each rotary flow surface;
and the modeling fairing module is used for splicing the profile surfaces of each blade profile by introducing a Karns surface method in a differential equation, checking the full curvature and fairing the surface to ensure that the profile surfaces are smooth and finally obtain the blade profile of the high-efficiency compressor blade.
The various modules in the above-described apparatus may be implemented in whole or in part by software, hardware, and combinations thereof. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
As shown in fig. 10, the preferred embodiment of the present application further provides an electronic device, which includes a memory, a processor and a computer program stored in the memory and executable on the processor, and when the processor executes the program, the processor implements the method for modeling the high-performance mechanical impeller blade in three dimensions.
As shown in fig. 11, the preferred embodiment of the present application also provides a computer device, which may be a terminal or a biopsy server, and the internal structure thereof may be as shown in fig. 11. The computer device includes a processor, a memory, and a network interface connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used for communicating with other external computer devices through network connection. The computer program is executed by a processor to realize the full three-dimensional modeling method of the high-performance impeller mechanical blade.
Those skilled in the art will appreciate that the architecture shown in fig. 11 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
The preferred embodiment of the present application also provides a storage medium, the storage medium includes a stored program, and when the program runs, the apparatus on which the storage medium is located is controlled to execute the full three-dimensional modeling method for high-performance impeller mechanical blades in the above embodiments.
It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer-executable instructions and that, although a logical order is illustrated in the flowcharts, in some cases, the steps illustrated or described may be performed in an order different than presented herein.
If the functions of the method of the present embodiment are implemented in the form of software functional units and sold or used as independent products, the functions may be stored in one or more storage media readable by a computing device. Based on such understanding, part of the contribution to the prior art of the embodiments of the present application or part of the technical solution may be embodied in the form of a software product stored in a storage medium and including several instructions for causing a computing device (which may be a personal computer, a server, a mobile computing device or a network device) to execute all or part of the steps of the method described in the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The method is successfully applied to a high-load compressor of an engine at present, and the performance test of parts of the compressor blade is designed by adopting the method, so that the performance completely meets the design requirement; through three-dimensional calculation comparison, compared with the compressor which is not designed by the method, the compressor which is designed by the method has the advantages that the design efficiency and the surge margin are greatly improved.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (10)

1. A full three-dimensional modeling method for high-performance impeller mechanical blades is characterized by comprising the following steps:
s1, performing primary modeling on a meridian flow line rotating flow surface according to an airflow angle along the meridian flow line obtained by calculation of an axial symmetric flow field and a thickness distribution rule given by experience;
s2, calculating the speed parameter distribution rules of the suction surface and the pressure surface of the blade profile by a blade streaming calculation method, and iterating the speed parameter distribution rules with the primary modeling to obtain the optimal blade profile on each rotary flow surface;
s3, splicing the molded surfaces of each blade profile, checking the full curvature and smoothing the curved surface by introducing a Kangsi surface method in a differential equation, ensuring the smooth molded surfaces and finally obtaining the blade profile of the efficient compressor blade.
2. The method according to claim 1, wherein the step S1 specifically comprises the steps of:
s11, calculating the meridian flow line rotating flow surface of the blade and the airflow angle distribution along the meridian flow line according to the axisymmetric flow field, and determining the camber line of the blade profile by combining empirical attack angle and drop angle selection;
s12, selecting a thickness distribution rule according to the Mach number of each meridian flow line rotating flow surface inlet, and superposing the thickness distribution rule on the camber line to finally obtain a blade profile coordinate, so that a primary blade profile is obtained.
3. The method according to claim 1, wherein the step S2 specifically includes:
s21, deducing and solving main velocity equations on a pressure surface and a suction surface of the blade in the rotary flow surface through a flow equation, an enthalpy equation and an energy equation in the flow field, and further obtaining a velocity distribution rule of the pressure surface and the suction surface of the blade;
and S22, adjusting the blade angle and thickness distribution of the blade according to the blade surface speed distribution rule, and finally iterating to obtain the blade profile type line on the rotary flow surface meeting the design requirement.
4. The method according to claim 1, wherein the step S3 specifically comprises the steps of:
s31, at each splicing node, the vector balance condition of the two sides in the two directions is met, the condition of vector equality is met, specifically, the vector, the second-order vector, the cross-boundary vector and the torsion vector along the axial direction and the radial direction need to be equal respectively, and therefore the smoothness of the connection of the curved surface pieces and the smoothness of the whole curved surface are guaranteed.
5. The method of claim 2, wherein the step S11 specifically comprises the steps of:
s111, analyzing a motion equation on a meridian flow line revolution flow surface (S1 flow surface):
Figure FDA0003475214950000011
Figure FDA0003475214950000021
in the above formula, r, theta and z are cylindrical coordinate systems; w is the relative velocity; beta is the airflow angle; m is the meridian flow line length; omega is angular velocity; sigma is an included angle between a tangential line of the meridian flow line and the z axis; the delta n is the thickness of a normal flow sheet on a meridian flow line rotating flow surface; g is the flow passing through an annular channel formed by the thickness of the rotary flow surface flow sheet; n is the number of the leaves; ρ is the gas density; wherein r, m, delta n and sigma are given by axial symmetric flow field calculation; subscript d represents the blade pressure side; subscript t represents the blade suction surface;
s112, order:
Figure FDA0003475214950000022
the x-y plane is a conversion plane of the meridian flow line revolution flow surface model, any curve y (x) on the x-y plane has the slope dy/dx (rd theta/dm), and according to the definition of the airflow angle:
tanβ＝Wθ/Wmrd θ/dm, wherein WθIs the circumferential velocity, WmThe meridian velocity is as follows:
dy/dx＝tanβ (1-4)
namely, a proper curve y (x) is constructed on the conversion plane, so that the change of the inlet and outlet airflow angles on the rotary flow surface and the change along the meridian flow line can be effectively ensured;
s113, when modeling is carried out on the x-y plane, the modeling is basically the same as the conventional plane modeling and conical surface modeling, namely different camber line profiles are selected according to different relative inlet Mach numbers and load distribution rules, wherein the camber line profiles comprise parabolas, double arcs and multiple arcs or are formed by combining several curves; or any camber line design is directly carried out according to the airflow angle distribution rule.
6. The method according to claim 5, wherein the step S12 specifically comprises the steps of:
s121, determining the corresponding relation of r, the meridian flow line m and the axial coordinate z by the formula (1-5):
Figure FDA0003475214950000023
calculating the slope dr/dm of each point;
s122, solving the value theta of each point along the molded line, wherein for a given curve, the integral in the formula (1-3) can be written into a fixed integral form:
Figure FDA0003475214950000024
when x is equal to x0When y is0＝rθ0So that theta is obtained0Given an increment Δ x, y (x) is calculated from the relationship y (x)0A value of + Deltax), and further to find theta (x)0+ Δ x), when the integral in the formula (1-6) adopts trapezoidal integral, the value of θ can be directly solved; in the above formula, subscript0Is the first coordinate point of the inlet;
s123, converting the leaf profile on the rotating flow surface into a rectangular coordinate system according to the value of the leaf profile in the cylindrical coordinate system and the following formula:
Figure FDA0003475214950000031
as can be seen from the formula (1-6), the revolution surface is a conical surface when dr/dm is constant, and a cylindrical surface when dr/dm is 0.
7. The method according to claim 3, wherein the step S21 specifically comprises the steps of:
s211, setting the flow field to meet the following equation:
Figure FDA0003475214950000032
in the above formula, C is the absolute velocity; l is the length; i is thermodynamic parameter internal energy; t is time; n is the number of the leaves; h is the height of the dough sheet; in the internal flow field of the impeller, a flow sheet zone having a length dm in the meridional direction and crossing the blade flow channels is taken, in which the relative velocity is constant in the pressure and suction surfaces in the direction dm, so that equation (2-1) is used for this flow sheet zone:
Figure FDA0003475214950000033
wherein, Δ θ ═ Qt-Qd
Figure FDA0003475214950000034
Qθ＝Q sinβ (2-4)
The formula (2-2) is simplified to be:
Figure FDA0003475214950000035
in the blade channel, along the blade crossing direction, the following relational expression exists on the blade pressure and suction surfaces:
Qd＝2Qav-Qt； (2-6)
βav＝(βt+βd)/2 (2-7)
the simplification from equation (2-6) to equation (2-5) is:
Figure FDA0003475214950000041
the main equation of the speed of the suction surface of the blade is obtained;
in the above formula: t is static temperature;
Figure FDA0003475214950000042
the total inlet temperature; q is the relative velocity on the surface of revolution; r is a radius coordinate (dimensionless, R ═ R/R)T) (ii) a M is the distance along the meridian flow line on the revolution surface; k is thermodynamic parameter specific heat ratio; g is the acceleration of gravity; r is a radical of hydrogenTIs the impeller exit radius; mTThe impeller exit mach number; r' is a thermodynamic constant;
subscript d is a blade pressure surface; subscript t is a blade suction surface; subscript av is a numerical value on the center flow line; subscript θ is the projection of the parameter in the θ direction; subscript 0 denotes the inlet parameters; subscript T denotes impeller exit parameters;
s212, applying the third formula in the formula (2-1) to the fluidized sheet belt, and discretizing the fluidized sheet belt to obtain:
ΔG＝ρavC0QavcosβavHhTRrTΔθ (2-9)
after deformation, the following are:
Figure FDA0003475214950000043
in the above formula:
Figure FDA0003475214950000044
the density ratio in relation (2-10) can be determined from the energy equation over the relation:
Figure FDA0003475214950000045
s213, in the whole calculation process in the flow channel, the average relative speed Q is obtained by iteration of equations (2-10) and (2-11)avAnd (3) calculating the speed of the suction surface of the blade according to a formula (2-8), and calculating the speed of the pressure surface according to a formula (2-6), wherein: Δ G is the weight flow; lambda is a prerotation value; c0The speed of sound at the upstream inlet of the impeller; the subscript u represents the circumferential component.
8. The method of claim 4, wherein the step S31 specifically comprises the steps of:
s311, according to the property of the space cubic spline curve, aiming at a vector function
Figure FDA0003475214950000046
In the interval [ t0，tn]Any sub-interval of [ t ]i-1，ti]The following conditions are satisfied:
Figure FDA0003475214950000047
in the formula: lambda [ alpha ]i μiIs a constant;
s312, for the grid, if the node coordinate of the transverse network line is j, the curve parameter is u, the node coordinate of the longitudinal network line is i, and the network line parameter is w, the transverse and longitudinal parameter spline curves are respectively represented by SujAnd SwiTo express, namely:
Figure FDA0003475214950000051
in the formula:
Figure FDA0003475214950000052
Figure FDA0003475214950000053
in the column matrix:
Figure FDA0003475214950000054
a twisted vector called the corner point of the curved surface;
s313, for any curved surface Ci,jThe shape is constrained by four parameters at four corners, as follows:
Figure FDA0003475214950000055
since the boundary of the patch is a spatial cubic parametric spline, from the direct product of the two boundary lines, and noting the boundary condition matrix (3-4), the patch's equation is:
Figure FDA0003475214950000056
on the splicing of the curved surface sheet, the boundary has a smoother condition than the parameter spline, namely at a node, the condition that tangent vectors on two sides in two directions are parallel is met, the condition that the vectors are equal is met, and for Ci,jAnd Ci+1,jThe two curved surface pieces need to meet the following requirements:
1) the director along the u direction is equal, i.e.
Figure FDA0003475214950000057
2) Second derivative vectors along the u-direction are equal, i.e.
Figure FDA0003475214950000058
3) The vectors being equal across the boundary, i.e.
Figure FDA0003475214950000059
4) With equal twisting vectors, i.e.
Figure FDA00034752149500000510
For Ci+1,jAnd Ci+1,j+1The two curved surface sheets satisfy the following conditions:
1) the director along the w direction is equal, i.e.
Figure FDA00034752149500000511
2) Second derivative vectors along the w direction are equal, i.e.
Figure FDA00034752149500000512
3) The vectors are equal across the boundary, i.e.
Figure FDA00034752149500000513
4) With equal twisting vectors, i.e.
Figure FDA0003475214950000061
The satisfaction of the above conditions is easily verified by simple operation of (3-5), and the smoothness of the connection of the curved surface pieces and the smoothness of the whole curved surface are ensured by the above conditions;
s314, determining main elements in the boundary condition matrix, wherein in the formula (3-5), M is a constant matrix, F (u), F (w)TFor variable row and array, the equation of a curved surface is determined, mainly the boundary condition matrix B (i, j) is determined, and the node vector in the B matrix is obtained by the formula (3-4) after the grid division of the curved surface
Figure FDA0003475214950000062
To be known, the dominant vector to be determined is the director
Figure FDA0003475214950000063
And the twisting vector
Figure FDA0003475214950000064
For the transverse spatial parameter spline curve, the third formula in the formula (3-1) and the formula (3-2) are used, and the vectors are equal, namely mui1, so:
Figure FDA0003475214950000065
therein, the
Figure FDA0003475214950000066
Figure FDA0003475214950000067
By
Figure FDA0003475214950000068
Therefore, the following steps are carried out:
Figure FDA0003475214950000069
then equation (3-6) can be written as:
[6-6 2 4]Bu(i)＝[-6 6-4-2]Bu(i+1) (3-7)
bu (i) and Bu (i +1) are substituted into the equations (3-7) and are simply collated as:
Figure FDA00034752149500000610
the above equation is the three-turn equation of the cubic parameter spline curve about the transverse space;
s315, for the longitudinal space parameter spline curve, the three-turn equation is as follows:
Figure FDA00034752149500000611
in equations (3-8) and (3-9), since the node vectors are known, the director at all the lateral and longitudinal nodes can be found
Figure FDA00034752149500000612
And
Figure FDA00034752149500000613
determining node twisting vector:
Figure FDA00034752149500000614
the twisting vector is used as a boundary constraint quantity, directly influences the geometric shape of a certain geometric curved surface, and is determined by a left-right boundary-crossing second-order continuous condition:
Figure FDA00034752149500000615
the following can be obtained:
F"(1)MBu(i+1,j)MTF(w)T＝F"(0)MBu(i+1,j+1)MTF(w)T
namely: f "(1) MBu (i +1, j) ═ F" (0) MBu (i +1, j + 1);
and substituting the Bu boundary matrix into row matrixes on two sides of equal sign to obtain:
Figure FDA00034752149500000616
the above formula is a cross boundary second-order continuous condition of the transverse network cable, and a longitudinal cross boundary second-order continuous condition can be obtained in the same way:
Figure FDA0003475214950000071
the twisting vector at the node of the whole curved surface can be obtained by using the equations (3-10) and (3-11) and giving the end point condition.
9. The utility model provides a full three-dimensional molding device of high performance impeller machinery blade which characterized in that includes:
the preliminary modeling module is used for carrying out preliminary modeling on a meridian flow line rotating flow surface according to a meridional flow line airflow angle obtained by calculating an axisymmetric flow field and a thickness distribution rule given by experience;
the modeling iteration module is used for calculating the speed parameter distribution rules of the suction surface and the pressure surface of the blade profile through a blade streaming calculation method and iterating the speed parameter distribution rules with the initial modeling to obtain the optimal blade profile on each rotary flow surface;
and the modeling fairing module is used for splicing each blade profile by introducing a Conss surface method in a differential equation, checking the total curvature and fairing the surface, so as to ensure that the profile is smooth and finally obtain the blade profile of the high-efficiency compressor blade.
10. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the program performs the steps of the method for full three-dimensional contouring of high performance turbomachinery blades as recited in any one of claims 1 to 8.
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CN116796459A (en) * 2023-06-20 2023-09-22 东南大学溧阳研究院 Radial turbine design method with splitter blades applied to turbocharger
CN116796459B (en) * 2023-06-20 2023-12-08 东南大学溧阳研究院 Radial turbine design method with splitter blades applied to turbocharger
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