CN118260863A - Polynomial curve-based parameterized blade slotting design method - Google Patents
Polynomial curve-based parameterized blade slotting design method Download PDFInfo
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Abstract
The invention discloses a polynomial curve-based parameterized blade slotting design method, which comprises the following main implementation processes: step one, giving geometric design parameters of a slotted blade; step two, geometrically transforming the original blade to a relative chord coordinate system; step three, calculating a channel outlet fillet curve; step four, calculating a channel outlet cubic curve; step five, calculating circular arcs of inner walls at two sides of the channel and a channel inlet fillet curve; step six, calculating a channel inlet cubic curve; and step seven, geometrically inversely transforming the slotted blade to an absolute coordinate system. By giving the original blade geometry and channel design parameters, the polynomial curve and the circular arc are adopted to design the molded line of the channel, so that the rapid design of the high-load compressor blade slotting geometry is realized, and parameterization research is facilitated. The designed slotted vane geometry can better regulate and control the flow field of the high-load compressor, effectively inhibit the three-dimensional angular separation flow of the high-load compressor, and has important engineering application prospect.
Description
Technical Field
The invention relates to the field of flow control of air compressors of aeroengines, in particular to a polynomial curve-based parameterized blade slotting design method.
Background
The air compressor is a core component part of the aeroengine and is a basic strategic industry in advanced technology countries. With the development of modern aviation technology, the thrust-weight ratio requirement on the aero-engine is also higher and higher, which means that the compressor needs to increase the overall load of the compressor on one hand, and reduce the number of stages on the other hand, so as to increase the single-stage load level. However, as the load level of the compressor increases, the reverse pressure gradient in the vane passage is gradually increased, so that the low-energy fluid is gradually accumulated towards the suction surface end region of the vane, and then three-dimensional angular separation flow is developed, the vane passage is blocked, and the pneumatic performance of the compressor is seriously reduced. Under the working condition of higher load, the three-dimensional angular zone separating flow further evolves into three-dimensional angular zone stall flow, and even develops into large separating flow covering the whole blade high channel, so that the performance of the air compressor is drastically reduced, and important influences are generated on the pressure ratio, efficiency, margin and the like of the air compressor. Various flow control methods are introduced for controlling the three-dimensional angular separation flow of the compressor. The active control method has good regulation and control effects, but requires additional energy to be introduced, and is limited in engineering application; the passive control method often has the characteristics of good single working condition effect, but is difficult to widely adapt to a wider working condition range.
The prior art of blade root slotting control of compressor stator angular zone separation (gas turbine test and research, 2007, vol.20, no.3, 28-33), also called blade end zone slotting technology, developed a series of channel modeling schemes (CN 105156361B, CN 105179322B, CN 105156356B, CN 105240322B, CN 105298925B), and proposed a compressor stator blade root slotting method (CN 105756719B) based on optimization algorithm. The proposed blade end region grooving technique blows off the separating fluid by forming a "self-adaptive" jet from the blade pressure surface to the suction surface grooving, and has a very good control effect on large-scale flow separation under conventional load conditions. The new generation of compressor design pursues a larger single-stage pneumatic load, so that the compressor blade has smaller consistency, larger bending angle and thinner thickness, and the blade flow field is more severe under the high-load working condition. The control scheme adopted is in the forms of simple equal-width straight line grooves, equal-width circular arc grooves, equal-width folding line grooves and the like, and plays a good role in inhibiting the flow control effect of the compressor angular division when the load is not very large, but is difficult to meet the design requirement of the next-generation high-load compressor. Based on the research discovery of a new generation of high-load blades, optimizing the channel profile design is an important means for improving the blade end region slotting control effect. In order to solve the problem of three-dimensional angle separation in a new generation of high-load compressor, the invention provides a parameterized blade slotting design method based on a polynomial curve, and the parameterized processing is carried out on the channel design process which is originally highly dependent on experience of a designer so as to realize rapid design of blade slotting geometry.
Disclosure of Invention
First, the technical problem to be solved
The invention aims to provide a parameterized blade slotting design method based on polynomial curves, which aims to realize rapid design of blade slotting geometry suitable for a high-load compressor by combining an arc curve and a cubic polynomial curve to generate slot channel geometry of a slotting blade based on given geometric parameters such as original blade geometry, slot inlet and outlet positions and widths, slot line starting and ending points, slot outlet jet angles, fillet radii and the like, effectively inhibit three-dimensional angle division flow of the high-load compressor, and simultaneously facilitate actual processing so as to be applied to engineering practice.
(II) technical scheme
In order to solve the technical problems, the invention provides a parameterized blade slotting design method based on a polynomial curve, which comprises the following steps:
step one, giving geometric design parameters of a slotted blade;
step two, geometrically transforming the original blade to a relative chord coordinate system;
Step three, calculating a channel outlet fillet curve;
step four, calculating a channel outlet cubic curve;
step five, calculating circular arcs of inner walls at two sides of the channel and a channel inlet fillet curve;
Step six, calculating a channel inlet cubic curve;
step seven, geometrically inversely transforming the slotted blade to an absolute coordinate system;
① The given slotted vane geometric design parameters include:
Giving control point coordinates and channel design parameters of the original blade geometry, and generating the original blade geometry by the control point coordinates of the original blade geometry; respectively extracting an original blade suction surface molded line and an original blade pressure surface molded line from the original blade geometry;
Defining channel design parameters, including: channel inlet relative chord position SP2, channel outlet relative chord position EP1, channel line start relative chord position SP1, channel line end relative chord position EP2, channel inlet width TI, channel outlet width TO, channel inlet fillet radius r in, channel outlet fillet radius r out, and channel outlet jet angle α;
② The geometrically transforming the original blade to a relative chord coordinate system includes:
calculating the chord length c of the original blade geometry, wherein the point with the smallest abscissa value of the original blade geometry is a front edge point, the point with the largest abscissa value of the original blade geometry is a tail edge point, and the chord length c of the original blade geometry is the linear distance between the front edge point and the tail edge point;
Performing rotational-translational transformation on the original blade geometry, setting the leading edge point as a coordinate system origin (0, 0), and transforming the trailing edge point to a coordinate point (c, 0) position; scaling the original blade geometry by taking the front edge point as the center according to the proportion of 1/c to obtain the relative chord length coordinate of the original blade geometry, and establishing a relative chord length coordinate system; in the relative chord length coordinate system, the leading edge point is a coordinate system origin (0, 0), and the coordinates of the trailing edge point are (1, 0);
③ The calculating the channel outlet fillet curve comprises:
Selecting a channel outlet position on the original blade suction surface molded line, and setting a channel outlet fillet radius r out; the value of the fillet radius r out at the outlet of the channel is not more than 1/2 of the thickness at the tail edge of the original blade; at the position of the outlet of the channel, a perpendicular line is perpendicular to the line of the suction surface of the original blade to the side where the line of the pressure surface of the original blade is located, the length of the perpendicular line is equal to the radius r out of a fillet at the outlet of the channel, the endpoint of the perpendicular line is the position EP1 of the relative chord length of the outlet of the channel, and the value of the position EP1 of the relative chord length of the outlet of the channel is defined as the ratio of the abscissa of the position of the outlet of the channel in the relative chord length coordinate system to the chord length c of the geometry of the original blade;
Setting a channel outlet jet angle alpha, wherein the unit of the channel outlet jet angle alpha is an angle; under the relative chord coordinate system, taking the relative chord position EP1 of the channel outlet as a circle center, taking the radius r out of a fillet at the channel outlet as a radius, taking the tangent point of the original blade suction surface profile as a starting point, and taking the tangent point of the tangent arc and the original blade suction surface profile as an ending point after the angle of 90-alpha is included, and taking the tangent point as an ending point of the channel outlet fillet curve to obtain the channel outlet fillet curve;
④ The calculating the channel outlet cubic curve comprises the following steps:
Giving the relative chord length position EP2 of the channel outlet width TO and the channel line terminal point;
Obtaining a starting point of a channel outlet tertiary curve according TO the end point of the channel outlet rounded curve, the channel outlet width TO and the channel outlet jet angle alpha under the relative chord length coordinate system; specifically, taking the end point of the channel outlet fillet curve as a starting point, and making a vertical line perpendicular TO the channel jet direction determined by the channel outlet jet angle alpha, wherein the length of the vertical line is equal TO the channel outlet width TO, and the obtained end point of the vertical line is the starting point of the channel outlet tertiary curve;
The value of the channel line end point relative chord length position EP2 is the ratio of the abscissa of the end point of the channel outlet tertiary curve in the relative chord length coordinate system to the chord length c of the original blade geometry, and the abscissa of the end point of the channel outlet tertiary curve in the relative chord length coordinate system can be obtained by the channel line end point relative chord length position EP 2; selecting a point with the abscissa equal to the abscissa of the end point of the channel outlet tertiary curve from the original blade suction surface molded line in the relative chord length coordinate system as the end point of the channel outlet tertiary curve;
Determining the starting point slope of a channel outlet tertiary curve according to the channel outlet jet angle alpha, so that the tangential direction at the starting point of the channel outlet tertiary curve is consistent with the channel jet direction determined by the channel outlet jet angle alpha; the slope of the end point of the channel outlet tertiary curve is the slope of the original blade suction surface molded line at the end point of the channel outlet tertiary curve;
calculating according to the starting point of the channel outlet tertiary curve, the ending point of the channel outlet tertiary curve, the starting point slope of the channel outlet tertiary curve and the ending point slope of the channel outlet tertiary curve to obtain the channel outlet tertiary curve;
⑤ The calculation of the arc of the inner walls at two sides of the channel and the curve of the channel inlet fillet comprises the following steps:
Giving a channel inlet width TI and a channel inlet fillet radius r in, wherein the fillet radius r in at the channel inlet is not more than 1/2 of the thickness at the front edge of the original blade;
At the channel inlet position, a perpendicular line is perpendicular to the side where the original blade pressure surface profile line is located, the length of the perpendicular line is equal to the fillet radius r in at the channel inlet, the endpoint of the perpendicular line is a channel inlet relative chord length position SP2, the value of the channel inlet relative chord length position SP2 is defined as the ratio of the abscissa of the channel inlet position in the relative chord length coordinate system to the chord length c of the original blade geometry, and the value of the channel inlet relative chord length position SP2 is smaller than the value of the channel outlet relative chord length position EP 1;
Under the relative chord length coordinate system, solving the circular arc of the inner wall of the downstream side channel in a simultaneous manner according to the starting point of the channel outlet cubic curve, the starting point slope of the channel outlet cubic curve, the relative chord length position SP2 of the channel inlet and the radius r in of the fillet at the channel inlet; taking a relative chord length position SP2 of a channel inlet as a circle center, taking a radius r in of a fillet at the channel inlet as a radius, and taking an inscribed arc of the original blade pressure surface molded line to connect the original blade pressure surface molded line with an arc of the inner wall of the downstream side channel to generate a channel inlet fillet curve;
Connecting the intersection point of the relative chord length position SP2 of the channel inlet, the channel inlet fillet curve and the circular arc of the inner wall of the downstream side channel, and making an extension line towards the direction of the line of the suction surface of the original blade, wherein the distance between the end point of the extension line and the intersection point of the channel inlet fillet curve and the circular arc of the inner wall of the downstream side channel is equal to the channel inlet width TI, and the end point of the extension line is used as the starting point of the circular arc of the inner wall of the upstream side channel; taking the end point of the channel outlet fillet curve in the third step as the end point of the circular arc of the inner wall of the upstream side channel, wherein the tangential direction of the end point of the circular arc of the inner wall of the upstream side channel is parallel to the channel jet direction determined by the channel outlet jet angle alpha; determining the inner wall arc of the upstream side channel according to the starting point of the inner wall arc of the upstream side channel, the ending point of the inner wall arc of the upstream side channel and the tangential direction of the ending point of the inner wall arc of the upstream side channel;
⑥ The calculating the channel inlet cubic curve comprises the following steps:
giving a relative chord length position SP1 of a channel profile starting point, wherein the value of the relative chord length position SP1 of the channel profile starting point is the ratio of the abscissa of the starting point of a channel inlet cubic curve in the relative chord length coordinate system to the chord length c of the original blade geometry;
Under the relative chord coordinate system, the abscissa of the starting point of the channel inlet cubic curve in the relative chord coordinate system can be obtained from the relative chord position SP1 of the starting point of the channel molded line; selecting a point with the abscissa equal to the abscissa of the starting point of the channel inlet tertiary curve from the original blade pressure surface line in the relative chord length coordinate system as the starting point of the channel inlet tertiary curve; taking the starting point of the circular arc of the inner wall of the upstream side channel in the fifth step as the ending point of the channel inlet cubic curve; the channel inlet tertiary curve is tangent to the blade pressure surface molded line at the starting point of the channel inlet tertiary curve, and the channel inlet tertiary curve is tangent to the circular arc of the inner wall of the upstream side channel at the ending point of the channel inlet tertiary curve; generating the channel inlet tertiary curve according to the starting point of the channel inlet tertiary curve, the ending point of the channel inlet tertiary curve, the tangential direction of the starting point of the channel inlet tertiary curve and the tangential direction of the ending point of the channel inlet tertiary curve;
⑦ The geometrically inverse transforming the slotted vane to an absolute coordinate system includes:
In the relative chord coordinate system, the original blade suction surface molded line, the original blade pressure surface molded line, the channel outlet fillet curve, the channel outlet tertiary curve, the downstream side channel inner wall circular arc, the channel inlet fillet curve, the upstream side channel inner wall circular arc and the channel inlet tertiary curve jointly form the geometry of the slotted blade in the relative chord coordinate system;
Amplifying the slotted blade geometry in the relative chord length coordinate system by taking the front edge point as the center according to the ratio of c/1 to obtain the final slotted blade geometry; and carrying out coordinate inverse transformation on the final slotted blade geometry, so that the coordinates of the tail edge points are transformed from the positions of the coordinate points (c, 0) to the positions which are the same as the coordinates of the tail edge points of the original blade geometry, and obtaining the slotted blade geometry under the original blade geometry coordinate system.
Particularly, the polynomial curve-based parameterized blade slotting design method is suitable for the design of two-dimensional compressor blade profiles and three-dimensional compressor blades; when the parameterized blade slotting design method based on the polynomial curve is used for three-dimensional compressor blade design, setting the height between the upper end wall and the lower end wall of an original three-dimensional compressor blade as H, and setting a channel along the expanding direction of the original three-dimensional compressor blade, wherein the slotting height of the channel is H; the starting end of the grooving height H can be positioned on the lower end wall or the upper end wall, and the value range of the grooving height H is 0-H, so that an end-region grooving scheme is obtained.
In particular, the channels can be simultaneously opened at the upper end wall side and the lower end wall side of the original three-dimensional compressor blade, and a double-side end region slotting scheme is obtained.
In particular, when the value of the slotting height H is equal to the height H between the upper end wall and the lower end wall of the original three-dimensional compressor blade, the channel penetrates through the whole original three-dimensional compressor blade along the spanwise direction, and a full-blade high slotting scheme is obtained.
(III) beneficial effects
The parameterized blade slotting design method based on the polynomial curve has the following beneficial effects: by giving the original blade geometry and channel design parameters, the rapid design of the slotting geometry of the high-load compressor blade is realized. Unique determination of blade slot geometry can be achieved by giving fewer channel design parameters. The channel design parameters are adopted to carry out parameterization control on the geometric molded line of the channel, thereby being beneficial to carrying out parameterization research on the slotting performance of the high-load compressor blade.
According to the polynomial curve-based parameterized blade slotting design method provided by the invention, the polynomial curve and the circular arc are adopted to design the molded line of the channel, so that the designed slotting blade geometry can better regulate and control the flow field of the high-load compressor, and better aerodynamic performance is obtained.
The parameterized blade slotting design method based on the polynomial curve provided by the invention can be used for quickly generating the effective slotting blade geometry by giving the original blade geometry and the channel design parameters through programming, solves the problem of high experience dependence of the channel design scheme, and has important engineering application prospects.
Drawings
FIG. 1 is a flow chart of a method of parameterized blade slot design based on polynomial curves of the present invention;
FIG. 2 is a schematic illustration of a slotted vane geometry of a parameterized vane slot design method based on polynomial curves in accordance with the present invention;
FIG. 3 is a schematic illustration of a three-dimensional compressor blade slot design method based on a polynomial curve parameterized blade slot design method of the present invention;
FIG. 4 is a flow field diagram of the original blade geometry of a polynomial curve based parameterized blade notching design method of the present invention;
FIG. 5 is a flow field diagram of a slotted vane geometry of a parameterized vane slotted design method based on polynomial curves of the present invention;
In the figure, 1: channel inlet cubic curve; 2: an arc of the inner wall of the downstream side channel; 3: an arc of an inner wall of the upstream side channel; 4: channel outlet rounded curve; 5: channel exit cubic curve; 6: original blade suction surface molded line; 7: tail edge points; 8: original blade pressure surface molded line; 9: channel inlet fillet curve; 10: a leading edge point; 11: three-dimensional compressor blades; 12: a lower end wall; 13: grooving the whole leaf; 14: the end region is slotted.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are only illustrative of the present invention and are not intended to limit the scope of the invention.
As shown in fig. 1 and 2, the invention provides a polynomial curve-based parameterized blade slotting design method, which comprises the following steps:
step one, giving geometric design parameters of a slotted blade;
In this step, given the control point coordinates and channel design parameters of the original blade geometry, the original blade geometry is generated from the control point coordinates of the original blade geometry; extracting an original blade suction surface molded line (6) and an original blade pressure surface molded line (8) from the original blade geometry respectively;
Defining channel design parameters, including: channel inlet relative chord position SP2, channel outlet relative chord position EP1, channel line start relative chord position SP1, channel line end relative chord position EP2, channel inlet width TI, channel outlet width TO, channel inlet fillet radius r in, channel outlet fillet radius r out, and channel outlet jet angle α.
Step two, geometrically transforming the original blade to a relative chord coordinate system;
in this step, the chord length c of the original blade geometry is calculated, wherein the point with the smallest abscissa value of the original blade geometry is a leading edge point (10), the point with the largest abscissa value of the original blade geometry is a trailing edge point (7), and the chord length c of the original blade geometry is the straight line distance between the leading edge point (10) and the trailing edge point (7);
Performing rotary translation transformation on the original blade geometry, setting a leading edge point (10) as a coordinate system origin (0, 0), and transforming a trailing edge point (7) to a coordinate point (c, 0) position; scaling the original blade geometry by 1/c with a leading edge point (10) as a center to obtain a relative chord coordinate of the original blade geometry, and establishing a relative chord coordinate system; in the relative chord coordinate system, the leading edge point (10) is the origin (0, 0) of the coordinate system, and the coordinates of the trailing edge point (7) are (1, 0).
Step three, calculating a channel outlet fillet curve (4);
In the step, the position of a channel outlet is selected on the original blade suction surface molded line (6), and the radius r out of the fillet at the channel outlet is set; the value of the fillet radius r out at the outlet of the channel is not more than 1/2 of the thickness at the tail edge of the original blade; at the position of the outlet of the channel, making a vertical line perpendicular to the suction surface molded line (6) of the original blade to the side of the pressure surface molded line (8) of the original blade, wherein the length of the vertical line is equal to the radius r out of a fillet at the outlet of the channel, the endpoint of the vertical line is the position EP1 of the outlet of the channel relative to the chord length, and the value of the position EP1 of the outlet of the channel relative to the chord length is defined as the ratio of the abscissa of the position of the outlet of the channel in the relative chord length coordinate system to the chord length c of the geometry of the original blade;
Setting a channel outlet jet angle alpha, wherein the unit of the channel outlet jet angle alpha is an angle; under a relative chord length coordinate system, taking a relative chord length position EP1 of a channel outlet as a circle center, taking a fillet radius r out at the channel outlet as a radius, making an inscribed arc of an original blade suction surface molded line (6), and taking a tangent point of the inscribed arc and the original blade suction surface molded line (6) as a starting point, ending after an included angle of 90-alpha, and taking the inscribed arc as an ending point of the channel outlet fillet curve to obtain the channel outlet fillet curve (4).
Step four, calculating a channel outlet cubic curve (5);
In this step, the channel outlet width TO, the channel profile end point relative chord position EP2 is given;
Under a relative chord length coordinate system, obtaining a starting point of a channel outlet tertiary curve according TO the end point of the channel outlet fillet curve, the channel outlet width TO and the channel outlet jet angle alpha; specifically, the end point of a channel outlet fillet curve is taken as a starting point, a perpendicular line is drawn in the channel jet direction determined by the channel outlet jet angle alpha, the length of the drawn perpendicular line is equal TO the channel outlet width TO, and the obtained end point of the perpendicular line is the starting point of a channel outlet tertiary curve;
the value of the relative chord length position EP2 of the channel line end point is the ratio of the abscissa of the end point of the channel outlet tertiary curve in the relative chord length coordinate system to the chord length c of the original blade geometry, and the abscissa of the end point of the channel outlet tertiary curve in the relative chord length coordinate system can be obtained by the relative chord length position EP2 of the channel line end point; selecting a point with the abscissa equal to the abscissa of the end point of the channel outlet tertiary curve as the end point of the channel outlet tertiary curve on the original blade suction surface molded line (6) in the relative chord length coordinate system;
Determining the starting point slope of the channel outlet tertiary curve according to the channel outlet jet angle alpha, so that the tangential direction at the starting point of the channel outlet tertiary curve is consistent with the channel jet direction determined by the channel outlet jet angle alpha; the slope of the end point of the channel outlet tertiary curve is the slope of the original blade suction surface molded line (6) at the end point of the channel outlet tertiary curve;
And calculating according to the starting point of the channel outlet tertiary curve, the ending point of the channel outlet tertiary curve, the starting point slope of the channel outlet tertiary curve and the ending point slope of the channel outlet tertiary curve to obtain the channel outlet tertiary curve (5).
Step five, calculating circular arcs of inner walls at two sides of the channel and a channel inlet fillet curve (9);
In this step, the channel inlet width TI and the channel inlet fillet radius r in are given, wherein the value of the channel inlet fillet radius r in is not more than 1/2 of the thickness of the original blade at the front edge;
At the channel inlet position, a perpendicular line is drawn to the side of the original blade suction surface molded line (6) perpendicular to the original blade pressure surface molded line (8), the length of the perpendicular line is equal to the fillet radius r in at the channel inlet, the end point of the perpendicular line is the channel inlet relative chord length position SP2, the value of the channel inlet relative chord length position SP2 is defined as the ratio of the abscissa of the channel inlet position in a relative chord length coordinate system to the chord length c of the original blade geometry, and the value of the channel inlet relative chord length position SP2 is smaller than the value of the channel outlet relative chord length position EP 1;
Solving a downstream side channel inner wall arc (2) according to the starting point of the channel outlet cubic curve, the starting point slope of the channel outlet cubic curve, the channel inlet relative chord length position SP2 and the channel inlet fillet radius r in in a relative chord length coordinate system; taking a relative chord length position SP2 of a channel inlet as a circle center, taking a radius r in of a fillet at the channel inlet as a radius, and making an inscribed arc of an original blade pressure surface molded line (8), connecting the original blade pressure surface molded line (8) with an inner wall arc (2) of a downstream side channel to generate a channel inlet fillet curve (9);
Connecting the intersection point of the channel inlet relative chord length position SP2, the channel inlet fillet curve (9) and the downstream side channel inner wall arc (2), and making an extension line towards the original blade suction surface molded line (6), wherein the distance between the end point of the extension line and the intersection point of the channel inlet fillet curve (9) and the downstream side channel inner wall arc (2) is equal to the channel inlet width TI, and taking the end point of the extension line as the starting point of the upstream side channel inner wall arc; taking the end point of the channel outlet fillet curve in the third step as the end point of the circular arc of the inner wall of the upstream side channel, wherein the tangential direction of the end point of the circular arc of the inner wall of the upstream side channel is parallel to the channel jet direction determined by the channel outlet jet angle alpha; and determining the inner wall arc (3) of the upstream side channel according to the tangential directions of the starting point of the inner wall arc of the upstream side channel, the ending point of the inner wall arc of the upstream side channel and the ending point of the inner wall arc of the upstream side channel.
Step six, calculating a channel inlet cubic curve (1);
In this step, the relative chord length position SP1 of the starting point of the channel profile is given, and the value of the starting point of the channel profile relative chord length position SP1 is the ratio of the abscissa of the starting point of the channel inlet cubic curve (1) in the relative chord length coordinate system to the chord length c of the original blade geometry;
Under the relative chord length coordinate system, the abscissa of the starting point of the channel inlet cubic curve in the relative chord length coordinate system can be obtained from the relative chord length position SP1 of the starting point of the channel line; selecting a point with the abscissa equal to the abscissa of the starting point of the channel inlet tertiary curve on the original blade pressure surface molded line (8) in the relative chord length coordinate system as the starting point of the channel inlet tertiary curve; taking the starting point of the circular arc of the inner wall of the upstream side channel in the fifth step as the ending point of the channel inlet cubic curve; the channel inlet tertiary curve (1) is tangent to the blade pressure surface molded line at the starting point of the channel inlet tertiary curve, and the channel inlet tertiary curve (1) is tangent to the upstream side channel inner wall circular arc (3) at the ending point of the channel inlet tertiary curve; and generating the channel inlet tertiary curve (1) according to the starting point of the channel inlet tertiary curve, the ending point of the channel inlet tertiary curve, the tangential direction of the starting point of the channel inlet tertiary curve and the tangential direction of the ending point of the channel inlet tertiary curve.
Step seven, geometrically inversely transforming the slotted blade to an absolute coordinate system;
In the step, in a relative chord length coordinate system, the geometry of the slotted blade in the relative chord length coordinate system is formed by an original blade suction surface molded line (6), an original blade pressure surface molded line (8), a channel outlet fillet curve (4), a channel outlet tertiary curve (5), a downstream side channel inner wall circular arc (2), a channel inlet fillet curve (9), an upstream side channel inner wall circular arc (3) and a channel inlet tertiary curve (1);
Amplifying the slotted blade geometry in the relative chord length coordinate system by taking the front edge point (10) as the center according to the ratio of c/1 to obtain the final slotted blade geometry; and carrying out coordinate inverse transformation on the final slotted blade geometry, so that the coordinates of the tail edge point (7) are transformed from the positions of the coordinate points (c, 0) to the positions which are the same as the coordinates of the tail edge point (7) of the original blade geometry, and obtaining the slotted blade geometry under the original blade geometry coordinate system.
Furthermore, the parameterized blade slotting design method based on the polynomial curve is suitable for the design of two-dimensional compressor blade profiles and three-dimensional compressor blades (11); when the parameterized blade slotting design method based on the polynomial curve is used for designing the three-dimensional compressor blade (11), setting the height between the upper end wall and the lower end wall (12) of the original three-dimensional compressor blade (11) as H, setting a channel along the expanding direction of the original three-dimensional compressor blade (11), and setting the slotting height of the channel as H; the starting end of the grooving height H can be positioned on the lower end wall (12) or the upper end wall, and the grooving height H ranges from 0 to H, so that the grooving (14) scheme of the end region is obtained.
In particular, the channels can be simultaneously opened at the upper end wall side and the lower end wall side of the original three-dimensional compressor blade (11), and a double-side end region slotting scheme is obtained.
In particular, when the value of the slotting height H is equal to the height H of the original three-dimensional compressor blade (11) between the upper end wall and the lower end wall (12), the channel penetrates through the whole original three-dimensional compressor blade (11) along the expanding direction, and a full-blade high slotting (13) scheme is obtained.
Example 1:
taking a certain high-load compressor cascade studied by a subject group as an example, the parametric blade slotting design method based on the polynomial curve provided by the invention is adopted to carry out blade bilateral end region slotting scheme design, and numerical simulation is carried out on flow fields of a prototype cascade and a slotting cascade, so that the control effect of the bilateral end region slotting scheme is verified.
In this embodiment, the value of the channel inlet relative TO the chord position SP2 is 23%, the value of the channel outlet relative TO the chord position EP1 is 30%, the value of the channel line starting point relative TO the chord position SP1 is 10%, the value of the channel line end point relative TO the chord position EP2 is 50%, the value of the channel inlet width TI is 1.4mm, the value of the channel outlet width TO is 1mm, the value of the channel inlet fillet radius r in is 0.2mm, the value of the channel outlet fillet radius r out is 0.2mm, and the value of the channel outlet jet angle α is 10 °. The chord length c=50 mm of the original blade geometry.
Performing rotary translation transformation on the original blade geometry, setting a leading edge point (10) as a coordinate system origin (0, 0), and transforming a trailing edge point (7) to a coordinate point (50, 0) position; scaling the original blade geometry by 1/50 with a leading edge point (10) as a center to obtain a relative chord coordinate of the original blade geometry, and establishing a relative chord coordinate system; in the relative chord coordinate system, the leading edge point (10) is the origin (0, 0) of the coordinate system, and the coordinates of the trailing edge point (7) are (1, 0).
At the outlet position of the channel, a perpendicular line is drawn to the side of the pressure surface molded line (8) of the original blade from the suction surface molded line (6) of the original blade, the length of the perpendicular line is equal to the radius r out = 0.2/50mm of a fillet at the outlet of the channel, and the endpoint of the perpendicular line is the position EP1 of the outlet of the channel relative to the chord length. Under a relative chord length coordinate system, taking a relative chord length position EP1 of a channel outlet as a circle center, taking a radius r out = 0.2/50mm of a fillet radius at the channel outlet as a radius, making an inscribed arc of an original blade suction surface molded line (6), and obtaining a channel outlet fillet curve (4) by taking a tangent point of the inscribed arc with the original blade suction surface molded line (6) as a starting point, and ending after an included angle of 80 degrees as an end point of the channel outlet fillet curve.
Under a relative chord length coordinate system, taking the end point of a channel outlet fillet curve as a starting point, and making a vertical line in the channel jet direction determined by the vertical channel outlet jet angle alpha, wherein the length of the vertical line is equal TO the channel outlet width TO=1/50 mm, and the obtained end point of the vertical line is the starting point of a channel outlet tertiary curve; the transverse coordinate of the end point of the channel outlet tertiary curve in a relative chord length coordinate system can be obtained by the value of the end point of the channel profile relative chord length position EP2 being 50 percent, and the transverse coordinate of the end point of the channel outlet tertiary curve in the relative chord length coordinate system is 0.5; selecting a point with the abscissa equal to the abscissa of the end point of the channel outlet tertiary curve as the end point of the channel outlet tertiary curve on the original blade suction surface molded line (6) in the relative chord length coordinate system; determining the starting point slope of the channel outlet tertiary curve according to the channel outlet jet angle alpha=10°, so that the tangential direction at the starting point of the channel outlet tertiary curve is consistent with the channel jet direction determined by the channel outlet jet angle alpha=10°; the slope of the end point of the channel outlet tertiary curve is the slope of the original blade suction surface molded line (6) at the end point of the channel outlet tertiary curve; and calculating according to the starting point of the channel outlet tertiary curve, the ending point of the channel outlet tertiary curve, the starting point slope of the channel outlet tertiary curve and the ending point slope of the channel outlet tertiary curve to obtain the channel outlet tertiary curve (5).
At the channel inlet position, a perpendicular line is drawn to the side of the original blade suction surface molded line (6) perpendicular to the original blade pressure surface molded line (8), the length of the perpendicular line is equal to the radius r in = 0.2/50mm of a fillet at the channel inlet, the endpoint of the perpendicular line is the channel inlet relative chord length position SP2, and the abscissa of the channel inlet relative chord length position SP2 in the embodiment is 0.23. Solving a downstream side channel inner wall arc (2) according to the starting point of the channel outlet cubic curve, the starting point slope of the channel outlet cubic curve, the channel inlet relative chord length position SP2 and the channel inlet fillet radius r in in a relative chord length coordinate system; taking a relative chord length position SP2 of a channel inlet as a circle center, taking a radius r in = 0.2/50mm of a fillet radius at the channel inlet as a radius, and making an inscribed arc of an original blade pressure surface molded line (8), connecting the original blade pressure surface molded line (8) with an inner wall arc (2) of a downstream side channel to generate a channel inlet fillet curve (9);
Connecting the intersection point of the channel inlet relative chord length position SP2, the channel inlet fillet curve (9) and the downstream side channel inner wall arc (2), and making an extension line towards the original blade suction surface molded line (6), wherein the distance between the end point of the extension line and the intersection point of the channel inlet fillet curve (9) and the downstream side channel inner wall arc (2) is equal to the channel inlet width TI=1.4/50 mm, and taking the end point of the extension line as the starting point of the upstream side channel inner wall arc; taking the end point of the channel outlet fillet curve as the end point of the circular arc of the inner wall of the upstream side channel, wherein the tangential direction at the end point of the circular arc of the inner wall of the upstream side channel is parallel to the channel jet direction determined by the channel outlet jet angle alpha=10°; and determining the inner wall arc (3) of the upstream side channel according to the tangential directions of the starting point of the inner wall arc of the upstream side channel, the ending point of the inner wall arc of the upstream side channel and the ending point of the inner wall arc of the upstream side channel.
Selecting a point with the abscissa equal to the abscissa of the starting point of the channel inlet tertiary curve on the original blade pressure surface molded line (8) in the relative chord length coordinate system as the starting point of the channel inlet tertiary curve; taking the starting point of the circular arc of the inner wall of the upstream side channel as the ending point of the channel inlet cubic curve; the channel inlet tertiary curve (1) is tangent to the blade pressure surface molded line at the starting point of the channel inlet tertiary curve, and the channel inlet tertiary curve (1) is tangent to the upstream side channel inner wall circular arc (3) at the ending point of the channel inlet tertiary curve; and generating the channel inlet tertiary curve (1) according to the starting point of the channel inlet tertiary curve, the ending point of the channel inlet tertiary curve, the tangential direction of the starting point of the channel inlet tertiary curve and the tangential direction of the ending point of the channel inlet tertiary curve.
The original blade suction surface molded line (6), the original blade pressure surface molded line (8), the channel outlet fillet curve (4), the channel outlet tertiary curve (5), the downstream side channel inner wall arc (2), the channel inlet fillet curve (9), the upstream side channel inner wall arc (3) and the channel inlet tertiary curve (1) jointly form the slotted blade geometry in a relative chord length coordinate system.
Amplifying the slotted blade geometry in the relative chord length coordinate system by 50/1 with the front edge point (10) as the center to obtain the final slotted blade geometry; and carrying out coordinate inverse transformation on the final slotted blade geometry, so that the coordinates of the tail edge point (7) are transformed from the positions of the coordinate points (50, 0) to the positions which are the same as the coordinates of the tail edge point (7) of the original blade geometry, and obtaining the slotted blade geometry under the original blade geometry coordinate system.
In the embodiment, the upper end wall side and the lower end wall side of the original three-dimensional compressor blade (11) are respectively provided with a channel with the channel height of 20% of the blade height, so that a double-side end region slotting scheme is obtained.
The numerical simulation is carried out on the original three-dimensional compressor blade (11) by adopting a computational fluid dynamics method and the double-side end region slotting scheme designed by adopting the polynomial curve-based parameterized blade slotting design method. Fig. 4 shows the geometry and flow diagram of the 10% blade high section of the original three-dimensional compressor blade (11), and fig. 5 shows the geometry and flow diagram of the 10% blade high section of the double-sided end-region slotting scheme designed by the polynomial curve-based parameterized blade slotting design method of the invention. From comparison of results, the channel designed by the polynomial curve-based parameterized blade slotting design method obviously inhibits three-dimensional angular separation flow of the suction surface side of the blade, and improves the flow capacity of the blade channel. The generated channel jet has good coanda property.
The foregoing description of the preferred embodiments of the present invention is not intended to be limiting, but rather, any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the present invention are intended to be included within the scope of the present invention.
In summary, according to the parameterized blade slotting design method based on the polynomial curve, provided by the invention, the polynomial curve and the circular arc are adopted to design the molded line of the channel by giving the original blade geometry and fewer channel design parameters, so that the rapid design of the slotting geometry of the high-load compressor blade is realized, and parameterized research of slotting performance of the high-load compressor blade is facilitated. The designed slotted vane geometry can better regulate and control the flow field of the high-load compressor, effectively inhibit the three-dimensional angular separation flow of the high-load compressor, obtain better pneumatic performance and have important engineering application prospect.
Claims (4)
1. The parameterized blade slotting design method based on the polynomial curve is characterized by comprising the following steps of:
step one, giving geometric design parameters of a slotted blade;
step two, geometrically transforming the original blade to a relative chord coordinate system;
step three, calculating a channel outlet fillet curve (4);
step four, calculating a channel outlet fillet curve (5);
step five, calculating circular arcs of inner walls at two sides of the channel and a channel inlet fillet curve (9);
step six, calculating a channel inlet cubic curve (1);
step seven, geometrically inversely transforming the slotted blade to an absolute coordinate system;
① The given slotted vane geometric design parameters include:
Giving control point coordinates and channel design parameters of the original blade geometry, and generating the original blade geometry by the control point coordinates of the original blade geometry; extracting an original blade suction surface molded line (6) and an original blade pressure surface molded line (8) from the original blade geometry respectively;
Defining channel design parameters, including: channel inlet relative chord position SP2, channel outlet relative chord position EP1, channel line start relative chord position SP1, channel line end relative chord position EP2, channel inlet width TI, channel outlet width TO, channel inlet fillet radius r in, channel outlet fillet radius r out, and channel outlet jet angle α;
② The geometrically transforming the original blade to a relative chord coordinate system includes:
calculating the chord length c of the original blade geometry, wherein the point with the smallest abscissa value of the original blade geometry is a front edge point (10), the point with the largest abscissa value of the original blade geometry is a tail edge point (7), and the chord length c of the original blade geometry is a straight line distance between the front edge point (10) and the tail edge point (7);
performing a rotational-translational transformation on the original blade geometry, setting the leading edge point (10) as a coordinate system origin (0, 0), transforming the trailing edge point (7) to a coordinate point (c, 0) position; scaling the original blade geometry by 1/c with the leading edge point (10) as the center to obtain the relative chord length coordinates of the original blade geometry, and establishing a relative chord length coordinate system; in the relative chord length coordinate system, the leading edge point (10) is a coordinate system origin (0, 0), and the coordinates of the trailing edge point (7) are (1, 0);
③ The calculating channel outlet fillet curve (4) comprises:
Selecting a channel outlet position on the original blade suction surface molded line (6), and setting a fillet radius r out at the channel outlet; the value of the fillet radius r out at the outlet of the channel is not more than 1/2 of the thickness at the tail edge of the original blade; at the position of the channel outlet, a perpendicular line is drawn to the side of the original blade pressure surface molded line (8) perpendicular to the original blade suction surface molded line (6), the length of the perpendicular line is equal to the radius r out of a fillet at the channel outlet, the endpoint of the perpendicular line is the position EP1 of the channel outlet relative chord length, and the value of the position EP1 of the channel outlet relative chord length is defined as the ratio of the abscissa of the channel outlet position in the relative chord length coordinate system to the chord length c of the original blade geometry;
Setting a channel outlet jet angle alpha, wherein the unit of the channel outlet jet angle alpha is an angle; under the relative chord coordinate system, taking the relative chord position EP1 of the outlet of the channel as a circle center, taking the radius r out of a fillet at the outlet of the channel as a radius, and taking the tangent point between the tangent point and the original suction surface molded line (6) of the blade as a starting point, and ending after the tangent point is included by an angle of 90-alpha, and taking the tangent point as an ending point of the fillet curve of the outlet of the channel to obtain the fillet curve (4) of the outlet of the channel;
④ The calculating channel outlet fillet curve (5) comprises:
Giving the relative chord length position EP2 of the channel outlet width TO and the channel line terminal point;
Obtaining a starting point of the channel outlet rounded curve according TO the end point of the channel outlet rounded curve, the channel outlet width TO and the channel outlet jet angle alpha under the relative chord length coordinate system; specifically, taking the end point of the channel outlet rounded curve as a starting point, and making a vertical line perpendicular TO the channel jet direction determined by the channel outlet jet angle alpha, wherein the length of the vertical line is equal TO the channel outlet width TO, and the obtained end point of the vertical line is the starting point of the channel outlet rounded curve;
The value of the channel profile end point relative chord length position EP2 is the ratio of the abscissa of the end point of the channel outlet rounded curve in the relative chord length coordinate system to the chord length c of the original blade geometry, and the abscissa of the end point of the channel outlet rounded curve in the relative chord length coordinate system can be obtained by the channel profile end point relative chord length position EP 2; selecting a point with the abscissa equal to the abscissa of the end point of the channel outlet fillet curve as the end point of the channel outlet fillet curve on the original blade suction surface molded line (6) in the relative chord length coordinate system;
Determining the starting point slope of a channel outlet fillet curve according to the channel outlet jet angle alpha, so that the tangential direction at the starting point of the channel outlet fillet curve is consistent with the channel jet direction determined by the channel outlet jet angle alpha; the slope of the end point of the channel outlet fillet curve is the slope of the original blade suction surface molded line (6) at the end point of the channel outlet fillet curve;
Calculating to obtain a channel outlet rounded curve (5) according to the starting point of the channel outlet rounded curve, the ending point of the channel outlet rounded curve, the starting point slope of the channel outlet rounded curve and the ending point slope of the channel outlet rounded curve;
⑤ The calculation of the circular arc of the inner walls of the two sides of the channel and the circular arc curve (9) of the channel inlet fillet comprises the following steps:
Giving a channel inlet width TI and a channel inlet fillet radius r in, wherein the fillet radius r in at the channel inlet is not more than 1/2 of the thickness at the front edge of the original blade;
at the inlet position of the channel, a perpendicular line is drawn to the side of the suction surface molded line (6) of the original blade perpendicular to the pressure surface molded line (8) of the original blade, the length of the perpendicular line is equal to the radius r in of a fillet at the inlet of the channel, the endpoint of the perpendicular line is the relative chord length position SP2 of the inlet of the channel, the value of the relative chord length position SP2 of the inlet of the channel is defined as the ratio of the abscissa of the inlet of the channel in the relative chord length coordinate system to the chord length c of the geometry of the original blade, and the value of the relative chord length position SP2 of the inlet of the channel is smaller than the value of the relative chord length position EP1 of the outlet of the channel;
Under the relative chord length coordinate system, solving a downstream side channel inner wall circular arc (2) according to the starting point of the channel outlet circular arc curve, the starting point slope of the channel outlet circular arc curve, the relative chord length position SP2 of the channel inlet and the circular arc radius r in at the channel inlet; taking a relative chord length position SP2 of a channel inlet as a circle center, taking a fillet radius r in at the channel inlet as a radius, and taking an inscribed arc of the original blade pressure surface molded line (8), connecting the original blade pressure surface molded line (8) with the downstream side channel inner wall arc (2), so as to generate a channel inlet fillet curve (9);
Connecting the intersection point of the channel inlet relative chord length position SP2, the channel inlet fillet curve (9) and the downstream side channel inner wall circular arc (2), and making an extension line towards the original blade suction surface molded line (6), wherein the distance between the end point of the extension line and the intersection point of the channel inlet fillet curve (9) and the downstream side channel inner wall circular arc (2) is equal to the channel inlet width TI, and the end point of the extension line is used as the starting point of the upstream side channel inner wall circular arc; taking the end point of the channel outlet fillet curve in the third step as the end point of the circular arc of the inner wall of the upstream side channel, wherein the tangential direction of the end point of the circular arc of the inner wall of the upstream side channel is parallel to the channel jet direction determined by the channel outlet jet angle alpha; determining the inner wall arc (3) of the upstream side channel according to the starting point of the inner wall arc of the upstream side channel, the ending point of the inner wall arc of the upstream side channel and the tangential direction of the ending point of the inner wall arc of the upstream side channel;
⑥ The calculating channel inlet cubic curve (1) comprises:
giving a relative chord length position SP1 of a channel profile starting point, wherein the value of the relative chord length position SP1 of the channel profile starting point is the ratio of the abscissa of the starting point of a channel inlet cubic curve in the relative chord length coordinate system to the chord length c of the original blade geometry;
under the relative chord coordinate system, the abscissa of the starting point of the channel inlet cubic curve in the relative chord coordinate system can be obtained from the relative chord position SP1 of the starting point of the channel molded line; selecting a point with the abscissa equal to the abscissa of the starting point of the channel inlet tertiary curve as the starting point of the channel inlet tertiary curve on the original blade pressure surface molded line (8) in the relative chord length coordinate system; taking the starting point of the circular arc of the inner wall of the upstream side channel in the fifth step as the ending point of the channel inlet cubic curve; the channel inlet tertiary curve (1) is tangent to the blade pressure surface molded line at the starting point of the channel inlet tertiary curve, and the channel inlet tertiary curve (1) is tangent to the upstream side channel inner wall circular arc (3) at the ending point of the channel inlet tertiary curve; generating the channel inlet tertiary curve (1) according to the starting point of the channel inlet tertiary curve, the ending point of the channel inlet tertiary curve, the tangential direction of the starting point of the channel inlet tertiary curve and the tangential direction of the ending point of the channel inlet tertiary curve;
⑦ The geometrically inverse transforming the slotted vane to an absolute coordinate system includes:
In the relative chord length coordinate system, the original blade suction surface molded line (6), the original blade pressure surface molded line (8), the channel outlet fillet curve (4), the channel outlet fillet curve (5), the downstream side channel inner wall circular arc (2), the channel inlet fillet curve (9), the upstream side channel inner wall circular arc (3) and the channel inlet cubic curve (1) jointly form a slotted blade geometry in the relative chord length coordinate system;
Amplifying the slotted blade geometry in the relative chord length coordinate system by taking the front edge point (10) as the center according to the ratio of c/1 to obtain the final slotted blade geometry; and carrying out coordinate inverse transformation on the final slotted blade geometry, so that the coordinates of the tail edge point (7) are transformed from the positions of the coordinate points (c, 0) to the positions which are the same as the coordinates of the tail edge point (7) of the original blade geometry, and obtaining the slotted blade geometry under the original blade geometry coordinate system.
2. The polynomial curve-based parameterized vane slot design method of claim 1, wherein the polynomial curve-based parameterized vane slot design method is applicable to both two-dimensional compressor vane profile design and three-dimensional compressor vane (11) design; when the parameterized blade slotting design method based on the polynomial curve is used for designing the three-dimensional compressor blade (11), setting the height between the upper end wall and the lower end wall (12) of the original three-dimensional compressor blade (11) as H, and setting a channel along the expanding direction of the original three-dimensional compressor blade (11), wherein the slotting height of the channel is H; the starting end of the grooving height H can be positioned on the lower end wall (12) or the upper end wall, and the value range of the grooving height H is 0-H, so that the grooving (14) scheme of the end region is obtained.
3. A polynomial curve based parametric blade slotting design method as claimed in claim 2, wherein the channels can be simultaneously opened at the upper end wall side and the lower end wall side of the original three-dimensional compressor blade (11) to obtain a double-sided end region slotting scheme.
4. The polynomial curve-based parameterized vane slot design method of claim 2, wherein when the slot height H is equal to the height H of the original three-dimensional compressor vane (11) between the upper end wall and the lower end wall (12), the slot extends through the entire original three-dimensional compressor vane (11) in the spanwise direction to obtain a full-vane high slot (13) scheme.
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