CN112733268A - Asymmetric trapezoid-like spray pipe throat design method - Google Patents
Asymmetric trapezoid-like spray pipe throat design method Download PDFInfo
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Abstract
The invention discloses a throat design method of an asymmetric trapezoid-like spray pipe, which comprises the steps of firstly, setting the center of the asymmetric trapezoid-like spray pipe as a coordinate origin, setting an XY plane as a design surface, determining the throat area of the asymmetric trapezoid-like spray pipe according to the total pressure recovery coefficient at the throat of the asymmetric trapezoid-like spray pipe, the total pressure recovery coefficient and the throat area at the throat of an original spray pipe of an engine matched with the asymmetric trapezoid-like spray pipe, performing four-corner modification by using a quadratic curve, primarily determining the shape of the throat, and primarily solving the height of a right-angled inverted trapezoid and the length of upper and lower bottom sides according to the width-height ratio of the asymmetric spray pipe distributed at the throat, the inclined angle of the right-angled trapezoid of the throat and the throat area; and adjusting the shape and size of the throat by taking the lengths of the right-angled inverted trapezoid height and the upper and lower bottom edges as the reference, solving by adopting area partition, and adjusting a quadratic curve control factor until the restriction of the area and the aspect ratio of the throat is met. The design method of the invention enhances the matching performance of the spray pipe and the engine and improves the efficiency and the precision of the design of the throat of the spray pipe.
Description
Technical Field
The invention relates to the technical field of aviation, in particular to a method for designing a throat of an asymmetric trapezoid-like spray pipe.
Background
The asymmetric trapezoidal nozzle throat is positioned on the sonic profile of the nozzle, determines the flow rate and the flow capacity of the nozzle to a great extent and is the most critical profile of the nozzle design. The existing design method of the asymmetric nozzle throat is mainly based on the area of the engine axisymmetric nozzle, the shape of the asymmetric nozzle throat is drawn by a cubic spline curve with straight line edges and four corners, a grid integral method is adopted when the area of the shape is solved, the calculation is complicated, the precision is low, and the following defects which are difficult to overcome can be caused by the design method:
1. the flow of the engine and the nozzle is not matched due to the fact that the throat area of the asymmetric trapezoidal nozzle adopts the throat area of the axisymmetric nozzle, the common working point of all parts of the engine drifts towards the surge direction, the surge margin is large in reduction range, the temperature in front of a turbine is increased, the service life of the engine is shortened, and the thrust loss is obvious;
2. the asymmetric trapezoidal nozzle throat delineates the shape by adopting a straight line and a cubic curve, so that after the shape is preliminarily determined, the four corners are very complicated and difficult to adjust according to the area accuracy and the small amplitude;
3. the throat area of the asymmetric trapezoidal spray pipe is solved by adopting a triangular grid integral method, the calculation accuracy is low, and the process is complicated.
Accordingly, there is a need for a design that overcomes or at least alleviates at least one of the above-mentioned deficiencies of existing design approaches.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for designing an asymmetric trapezoidal nozzle throat, which can overcome or at least alleviate the above disadvantages.
The technical scheme of the invention is as follows: a method for designing an asymmetric trapezoidal nozzle throat comprises the following steps:
the method comprises the following steps that firstly, the center of an asymmetric trapezoidal throat is set as a coordinate origin, an XY plane of a cross section is set as a design plane, and the throat area of the asymmetric trapezoidal nozzle is determined according to the total pressure recovery coefficient at the throat of the asymmetric trapezoidal nozzle, the total pressure recovery coefficient and the throat area at the throat of an original nozzle of an engine matched with the asymmetric trapezoidal nozzle;
step two, making a right-angle inverted trapezoid in the XY plane by using the center of the throat determined in the step one, and performing four-corner modification by using a quadratic curve to preliminarily determine the shape of the throat, wherein a plurality of edges of the throat are tangent to the inner edge of the right-angle inverted trapezoid, and the tangent points are all vertexes of the asymmetric trapezoid-like nozzle throat;
step three, preliminarily solving the height of the right-angled inverted trapezoid and the length of the upper bottom side and the lower bottom side according to the aspect ratio of the asymmetric spray pipe distributed at the throat and the inclined angle of the inclined edge of the right-angled trapezoid of the throat and the area of the throat determined in the step one;
step four, taking the height of the right-angled inverted trapezoid and the length of the upper bottom edge and the lower bottom edge determined in the step three as references, adjusting the shape and the size of the throat in the step two, adopting area partition solution, calculating the sum of the areas of a plurality of triangles formed from each vertex to the center of the throat, and then calculating the arch area between adjacent vertexes; the arch area adopts a high-order expression of a quadratic curve control factor f value, and f value parameters are adjusted until throat area and aspect ratio constraints are met.
Further, the central coordinate of the trapezoidal throat in the first step is Q (0,0), which is the origin of coordinates of the XY plane of the cross section, the X axis takes the "right" direction as the positive direction, and the Y axis takes the "up" direction as the positive direction.
Further, in the first step, the throat area of the asymmetric trapezoidal nozzle is calculated in the following manner:
q(Math)·σth·Ath＝σ0·A0；
wherein σth-total pressure recovery coefficient at the throat of the asymmetric trapezoid-like nozzle;
σ0-total pressure recovery coefficient at the original nozzle throat of the engine;
A0-the area of the original nozzle throat of the engine;
Ath-asymmetric trapezoidal-like nozzle throat area;
q(Math) -flow function at the throat of the asymmetric trapezoidal-like nozzle;
Maththe Mach number of the throat of the asymmetric trapezoid-like nozzle is obtained.
Further, in the third step, the calculation mode of the right-angle inverted trapezoid height and the length of the upper bottom edge and the lower bottom edge is as follows:
l1＝hth·λth-hth·tan(αth)/2；
l0＝hth·λth+hth·tan(αth)/2；
wherein，hthThe right-angle inverted trapezoidal height is the height of the right-angle side of the throat of the asymmetric trapezoid-like spray pipe;
l1the length of the lower bottom edge of the right-angle inverted trapezoid is the length of the lower bottom edge of the throat of the asymmetric trapezoid-like spray pipe;
l0the length of the upper bottom edge of the right-angle inverted trapezoid is the length of the upper bottom edge of the throat of the asymmetric trapezoid-like spray pipe;
αth-the inclination of the lateral bevel edge of the throat of the asymmetric trapezoidal-like nozzle;
Ath-asymmetric trapezoidal-like nozzle throat area;
λth-the aspect ratio of the throat of the asymmetric trapezoid-like nozzle.
Further, in the fourth step, the basic elements required for the partition solution of the throat area of the asymmetric trapezoid-like nozzle comprise coordinates of each vertex, line segments between the vertices, and line segments between the vertices and the center of the throat.
Further, the fourth step is detailed as follows:
A. calculating to obtain the coordinates of each vertex by utilizing the aspect ratio of the throat of the asymmetric trapezoid-like spray pipe, the inclined angle of the side bevel edge of the throat of the asymmetric trapezoid-like spray pipe, the height of the inverted right-angled trapezoid, the length of the upper bottom edge of the inverted right-angled trapezoid, the length of the lower bottom edge of the inverted right-angled trapezoid and the f values of a plurality of corresponding secondary curves of arches;
B. calculating by using the coordinates of each vertex to obtain the length of the line between each vertex and the length of the line from each vertex to the center of the throat;
C. connecting each vertex by taking the center of the throat as a line, and mutually taking lines between every two adjacent vertexes to divide the asymmetric trapezoid-like nozzle throat into a plurality of triangles and four bows;
D. calculating the areas of all the triangles according to the length of the line segment calculated in the step B;
E. calculating the area of the arch according to the secondary curve f of the arch and the area of the triangle where the arch is positioned, and sequentially calculating 4 areas of the arch;
F. and adding the 4 cambered areas and the triangular areas to obtain the throat area of the asymmetric trapezoid-like spray pipe.
Further, the calculating method in the step E includes:
wherein S is1Is the first arcuate area, f1Is the control factor of the quadratic curve of the first arch, S' is the area of the triangle on which the first arch is located, On(f1) Is f1A high-order expression high-order item;
the calculation method of the rest of the arch area is the same as that of the first arch area.
Further, the trapezoid-like throat is completed in CATIA software.
The invention has the advantages that: the invention relates to a throat design method of an asymmetric trapezoid-like spray pipe, which is characterized in that the throat area is corrected by total pressure recovery coefficients, the shape is a right-angled trapezoid plus a quadratic curve correction type shape at four corners, the area solution adopts a partition method, and the arch area formed by the quadratic curve adopts a high-order expression of an f value.
Drawings
FIG. 1 is a schematic diagram of the design method of the asymmetric trapezoid-like nozzle throat of the invention.
FIG. 2 is a schematic diagram of the definition of the f-number and solution of the arcuate area of an asymmetric trapezoidal-like nozzle throat shown in FIG. 1.
FIG. 3 is a schematic flow chart of a method for designing a throat of an asymmetric trapezoid-like nozzle shown in FIG. 1
Wherein the reference numerals are as follows:
1-4: 4 vertexes of the right-angle inverted trapezoid;
5-12: 8 vertexes of the asymmetric trapezoid-like nozzle throat;
13: center point of right trapezoid, origin of coordinates
14-17: 4 four-corner quadratic curves of the asymmetric trapezoid-like;
18: intersection points of tangent lines of the boundary of the quadratic curve;
19-20: 2 tangent points of the boundary of the quadratic curve;
21-22: the intersection point of the quadratic curve tangent line of the passing point 32 and the boundary tangent line;
23-24: the intersection point of the quadratic curve of the crossing point 30 and the point 31 and the boundary tangent;
25-26: the intersection point of the quadratic curve of the passing point 30 and the point 31 and the tangent of the passing point 32;
27: the midpoints of the boundary chords 19 to 20 of the quadratic curve;
28: the midpoints of the quadratic chords 19 to 32 of the quadratic curve;
29: the midpoints of the quadratic chords 20 to 32 of the quadratic curve;
30: the intersections of the line segments 21 to 28 with the quadratic curves;
31: the intersections of the line segments 22 to 29 with the quadratic curve;
32: the intersection of the line segments 18 to 27 with the quadratic curve.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar geometric elements or geometric elements having the same or similar functions throughout. The described embodiments are only some, but not all embodiments of the invention. The embodiments described below with reference to the drawings are illustrative and schematic and are intended to be illustrative of the invention and should not be construed as limiting the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without any innovations, are within the scope of the present invention. Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
In the description of the present invention, it should be understood that the terms "center", "boundary", "top", "upper", "lower", "bottom", "angle", "inclination", "vertical", "upside down", "inner", "outer", etc. indicate orientations or positional relationships based on the orientation or positional relationships shown in the drawings, and should not be construed as limiting the scope of the present invention.
The first embodiment of the present invention is as follows:
a method for designing an asymmetric trapezoidal nozzle throat comprises the following steps:
the method comprises the following steps that firstly, the center of an asymmetric trapezoidal throat is set as a coordinate origin, an XY plane of a cross section is set as a design plane, and the throat area of the asymmetric trapezoidal nozzle is determined according to the total pressure recovery coefficient at the throat of the asymmetric trapezoidal nozzle, the total pressure recovery coefficient and the throat area at the throat of an original nozzle of an engine matched with the asymmetric trapezoidal nozzle;
step two, making a right-angle inverted trapezoid in the XY plane by using the center of the throat determined in the step one, and performing four-corner modification by using a quadratic curve to preliminarily determine the shape of the throat, wherein a plurality of edges of the throat are tangent to the inner edge of the right-angle inverted trapezoid, and the tangent points are all vertexes of the asymmetric trapezoid-like nozzle throat;
step three, preliminarily solving the height of the right-angled inverted trapezoid and the length of the upper bottom side and the lower bottom side according to the aspect ratio of the asymmetric spray pipe distributed at the throat and the inclined angle of the inclined edge of the right-angled trapezoid of the throat and the area of the throat determined in the step one;
step four, taking the height of the right-angled inverted trapezoid and the length of the upper bottom edge and the lower bottom edge determined in the step three as references, adjusting the shape and the size of the throat in the step two, adopting area partition solution, calculating the sum of the areas of a plurality of triangles formed from each vertex to the center of the throat, and then calculating the arch area between adjacent vertexes; the arch area adopts a high-order expression of a quadratic curve control factor f value, and f value parameters are adjusted until throat area and aspect ratio constraints are met.
And the central coordinate of the trapezoidal throat in the step one is Q (0,0), which is the origin of coordinates of the XY plane of the cross section, the X axis takes the right direction as the positive direction, and the Y axis takes the upward direction as the positive direction.
In the first step, the calculation mode of the throat area of the asymmetric trapezoidal spray pipe is as follows:
q(Math)·σth·Ath＝σ0·A0；
wherein σth-total pressure recovery coefficient at the throat of the asymmetric trapezoid-like nozzle;
σ0-total pressure recovery coefficient at the original nozzle throat of the engine;
A0-the area of the original nozzle throat of the engine;
Ath-asymmetric trapezoidal-like nozzle throat area;
q(Math) -flow function at the throat of the asymmetric trapezoidal-like nozzle;
Maththe Mach number of the throat of the asymmetric trapezoid-like nozzle is obtained.
In the third step, the calculation mode of the right-angle inverted trapezoid height and the length of the upper bottom edge and the lower bottom edge is as follows:
l1＝hth·λth-hth·tan(αth)/2；
l0＝hth·λth+hth·tan(αth)/2；
wherein h isthThe right-angle inverted trapezoidal height is the height of the right-angle side of the throat of the asymmetric trapezoid-like spray pipe;
l1the length of the lower bottom edge of the right-angle inverted trapezoid is the length of the lower bottom edge of the throat of the asymmetric trapezoid-like spray pipe;
l0the length of the upper bottom edge of the right-angle inverted trapezoid is the length of the upper bottom edge of the throat of the asymmetric trapezoid-like spray pipe;
αth-the inclination of the lateral bevel edge of the throat of the asymmetric trapezoidal-like nozzle;
Ath-asymmetric trapezoidal-like nozzle throat area;
λth-the aspect ratio of the throat of the asymmetric trapezoid-like nozzle.
In the fourth step, the basic elements required by the sectional solution of the throat area of the asymmetric trapezoid-like spray pipe comprise coordinates of each vertex, line segments between the vertexes, and line segments between the vertexes and the center of the throat, and the detailed steps are as follows:
A. calculating to obtain the coordinates of each vertex by utilizing the aspect ratio of the throat of the asymmetric trapezoid-like spray pipe, the inclined angle of the side bevel edge of the throat of the asymmetric trapezoid-like spray pipe, the height of the inverted right-angled trapezoid, the length of the upper bottom edge of the inverted right-angled trapezoid, the length of the lower bottom edge of the inverted right-angled trapezoid and the f values of a plurality of corresponding secondary curves of arches;
B. calculating by using the coordinates of each vertex to obtain the length of the line between each vertex and the length of the line from each vertex to the center of the throat;
C. connecting each vertex by taking the center of the throat as a line, and mutually taking lines between every two adjacent vertexes to divide the asymmetric trapezoid-like nozzle throat into a plurality of triangles and four bows;
D. calculating the areas of all the triangles according to the length of the line segment calculated in the step B;
E. calculating the area of the arch according to the secondary curve f of the arch and the area of the triangle where the arch is positioned, and sequentially calculating 4 areas of the arch;
F. and adding the 4 cambered areas and the triangular areas to obtain the throat area of the asymmetric trapezoid-like spray pipe.
The calculation method of the step E comprises the following steps:
wherein S is1Is the first arcuate area, f1Is the control factor of the quadratic curve of the first arch, S' is the area of the triangle on which the first arch is located, On(f1) Is f1A high-order expression high-order item;
the calculation method of the rest of the arch area is the same as that of the first arch area.
The above process completes the design of the trapezoid-like throat in CATIA software.
Another embodiment of the present invention is described below with reference to the drawings.
This embodiment is illustrated with an 8-apex asymmetric trapezoidal-like nozzle throat as an example, as shown in FIG. 1.
FIG. 1 is a schematic diagram of the design method of the asymmetric trapezoid-like nozzle throat of the invention. FIG. 2 is a schematic diagram of the definition of the f-number and solution of the arcuate area of an asymmetric trapezoidal-like nozzle throat shown in FIG. 1. FIG. 3 is a schematic flow diagram of a method for designing the throat of the asymmetric trapezoidal-like nozzle shown in FIG. 1.
The asymmetric trapezoidal-like nozzle throat as shown in FIG. 1 is based on a right-angled trapezoid, with the same center, lying in the XY plane. Fig. 2 is primarily used to define the f-number and bow area solution. FIG. 3 is a schematic flow chart of a design method of an asymmetric trapezoid-like nozzle throat.
Referring to fig. 3, in the present embodiment, a method for designing an asymmetric trapezoid-like nozzle throat includes the following steps:
step 1: the center of the asymmetric trapezoidal throat is set as the origin of coordinates, the XY plane is set as the design plane, and the total pressure recovery coefficient sigma at the throat of the asymmetric trapezoidal spray pipe is determined according tothThe total pressure recovery coefficient sigma at the throat of the original nozzle of the asymmetric trapezoidal nozzle matched engine0Throat area A0Determining the throat area A of the asymmetric trapezoidal nozzleth；
Step 2: taking the throat center determined in the step 1, making a right-angled inverted trapezoid in an XY plane, performing four-corner modification by using four-corner vertexes and a quadratic curve, and primarily determining the shape of the throat;
and step 3: according to the aspect ratio lambda of asymmetric nozzle distributed at throatthInclined edge angle alpha of right trapezoid of throatthAnd then determining the area (1.1-1.3) A according to the step 1thPreliminarily solving the length h of the right-angle trapezoidal high-line segmentthAnd the basic length of the upper base- -line segment (length l)0Length of lower base-line length l1；
And 4, step 4: throat height h determined in step 3thLength of upper and lower bottom sides l0、l1Adjusting the shape and size of the trapezoid-like throat in the step 2 as a reference, adopting area partition solution, adopting a high-order expression of f value for the arch area formed by a quadratic curve, and adjusting f value parameters until the throat area is metAthAspect ratio constraint lambdath。
It is understood that the position parameters in step 1 above include: q (0,0) -the central point coordinate of the throat of the asymmetric trapezoid-like nozzle is determined as the origin of coordinates (obtained by designation) of an XY plane, the X axis takes the left direction as the positive direction (obtained by designation), and the Y axis takes the upward direction as the positive direction (obtained by designation).
In this example, step 1 asymmetric trapezoidal-like nozzle throat area AthCalculated using the following formula:
q(Math)·σth·Ath＝σ0·A0；
σth-representing the total pressure recovery coefficient (specified) at the throat of the asymmetric trapezoidal-like nozzle;
σ0-representing the total pressure recovery coefficient (measured) at the throat of the original engine nozzle;
A0-representing the engine original nozzle throat area (measured);
Athrepresenting the total pressure recovery coefficient (obtained by solving a formula) at the throat of the asymmetric trapezoid-like spray pipe;
q(Math) -flow function at the throat of the asymmetric trapezoid-like nozzle.
In this embodiment, step 3 solves for the right trapezoidal height hthLength of lower bottom l1And length of upper sole l0In particular
The formula is as follows:
l1＝hth·λth-hth·tan(αth)/2；
l0＝hth·λth+hth·tan(αth)/2；
in the above formula:
hth-the height of the right angle side of the throat of the asymmetric trapezoid-like spray pipe is obtained by solving the formulaTo;
l1the length of the lower bottom edge of the throat of the asymmetric trapezoid-like spray pipe is obtained by solving a formula;
l0the length of the upper bottom edge of the throat of the asymmetric trapezoid-like spray pipe is obtained by solving a formula;
αththe inclined angle of the lateral bevel edge of the throat of the asymmetric trapezoid-like spray pipe is obtained by designation;
Aththe throat area of the asymmetric trapezoid-like spray pipe is obtained by solving a formula;
λththe width-height ratio of the throat of the asymmetric trapezoid-like spray pipe is obtained through designation.
In this embodiment, the basic elements required for the partition solution of the throat area of the asymmetric trapezoidal nozzle in step 4 include coordinates of each vertex, line segments between each vertex, and line segments between each vertex and the central point 13, and the specific formula is as follows:
x1＝-λth·hth/2； y1＝hth/2；
x2＝-λth·hth/2； y2＝-hth/2；
x3＝λth·hth/2+hth·tan(αth)/2； y3＝hth/2；
x4＝λth·hth/2+hth·tan(αth)/2； y4＝-hth/2；
x5＝-λth·hth/2； y5＝f1 2·hth/2；
x6＝-λth·hth/2； y6＝-f2 2·hth/2；
x7＝λth·hth/2+f3 2·hth·cot(αth)/2； y7＝f3 2·hth·sin-1(αth)/2；
x9＝-λth·hth·f1 2/2； y9＝hth/2；
x10＝l0·f3 2/2； y10＝hth/2；
x11＝-λth·hth·f2 2/2；y11＝-hth/2
the length l of the line between each vertex and the centre point 13N13The calculation formula is as follows:
length l of line between any two vertexesijThe calculation formula is as follows:
in the above formula:
x1-the vertex 1 abscissa of the right trapezoid; y is1-the vertical coordinate of the vertex 1 of the right trapezoid;
x2-the 2 abscissa of the vertex of the right trapezoid; y is2-the vertical coordinate of the vertex 2 of the right trapezoid;
x3-the 3 abscissa of the vertex of the right trapezoid; y is3-the vertical coordinate of the right trapezoid vertex 3;
x4-4 abscissa of the vertex of the right trapezoid; y is4-the 4 th ordinate of the right trapezoid vertex;
x5the asymmetric trapezoid-like vertex 5 is transverseCoordinates; y is5-the asymmetric trapezoid-like vertex 5 ordinate;
x6the asymmetric trapezoid-like vertex 6 is abscissa-to; y is6-the asymmetric trapezoid-like vertex 6 ordinate;
x7-the asymmetric trapezoid-like vertex 7 abscissa; y is7-the longitudinal coordinate of the asymmetric trapezoid-like vertex 7;
x8-8 abscissa of vertex of asymmetric trapezoid-like; y is8-the asymmetric trapezoid-like vertex 8 ordinate;
x9-the asymmetric trapezoid-like vertex 9 abscissa; y is9-the asymmetric trapezoid-like vertex 9 ordinate;
x10-the asymmetric trapezoid-like vertex 10 abscissa; y is10-the asymmetric trapezoid-like vertex 10 ordinate;
x11-the asymmetric trapezoid-like vertex 11 abscissa; y is11-the longitudinal coordinate of the asymmetric trapezoid-like vertex 11;
x12-the asymmetric trapezoid-like vertex 12 abscissa; y is12-the asymmetric trapezoid-like vertex 12 ordinate;
xN-the asymmetric trapezoid-like vertex N abscissa; y isN-the asymmetric trapezoid-like vertex N ordinate;
xi-the asymmetric trapezoid-like throat or the right trapezoid vertex i abscissa; y isi-the asymmetric trapezoid-like throat or the right trapezoid vertex i ordinate;
xj-the vertex j abscissa of the asymmetric trapezoid-like throat or right trapezoid; y isj-the vertex j ordinate of the asymmetric trapezoid-like throat or right trapezoid;
lN13the length of the line between each vertex of the asymmetric trapezoid-like throat and the central point 13;
lij-the length of the line between any two vertices of the right trapezoid;
f1-vertex 1 corresponds to the value of the quadratic curve f;
f2the vertex 2 corresponds to the value of the quadratic curve f;
f3the vertex 3 corresponds to the value of the quadratic curve f;
f4the vertex 4 corresponds to the value of the quadratic curve f.
In this embodiment, in step 4, the throat area of the asymmetric trapezoid-like nozzle is obtained by a partition solution, where the specific solution formula is:
Ath＝S'Δ(13)(9)(10)+S'Δ(13)(10)(7)+S'Δ(13)(7)(8)+S'Δ(13)(8)(12)+S'Δ(13)(12)(11)+
S'Δ(13)(11)(6)+S'Δ(13)(6)(5)+S'Δ(13)(5)(9)+S1+S2+S3+S4；
solving the triangular area S by adopting the following formula:
in the above formula:
s' Δ (13) (9) (10) -the area of the triangle with points 13, 9, 10 as vertices;
s' Δ (13) (10) (7) -the area of the triangle with points 13, 7, 10 as vertices;
s' Δ (13) (8) (12) -the area of the triangle with points 13, 8, 12 as vertices;
s' Δ (13) (12) (11) -the area of the triangle with points 13, 12, 11 as vertices;
s' Δ (13) (11) (6) -the area of the triangle with points 13, 11, 6 as vertices;
s' Δ (13) (6) (5) -the area of the triangle with points 13, 6, 5 as vertices;
s' Δ (13) (5) (9) -the area of the triangle with points 13, 5, 9 as vertices;
S1the area of the arch formed by the quadratic curve 17 opposite to the vertex 1 and the line segments 5 and 9;
S2the area of the arch formed by the quadratic curve 16 opposite to the vertex 2 and the line segments 6 and 11;
S3the arcuate area enclosed by the quadratic curve 14 with the vertex 3 facing the line segments 7 and 10；
S4The area of an arch formed by the quadratic curve 15 opposite to the vertex 4 and the line segments 8 and 12;
s-area of arbitrary Δ ABC;
a-the length of the opposite side of any delta ABC vertex A;
b-the length of the opposite side of any delta ABC vertex B;
c-the length of the opposite side of any delta ABC vertex C;
p-the average of the sum of the trilateral lengths of any Δ ABC.
In this embodiment, the high-order expression of the f value in step 4, the definition of the f value and the high-order expression about the f value are S on the arch area on the four vertices of the trapezoid-like shape1、S2、S3、S4The application is as follows:
exemplary f-value definitions according to FIG. 2: f is L18,32/L18,27；
In the above formula:
f is a quadratic curve curvature control factor;
f1-a curvature control factor of the quadratic curve at 1 point of the vertex of the right trapezoid;
f2-a curvature control factor of the quadratic curve at the 2 point of the vertex of the right trapezoid;
f3-curvature control factor of quadratic curve at 3 points of vertex of right trapezoid;
f4-curvature control factor of quadratic curve at 4 points of vertex of right trapezoid;
L18,32the length of the line segments 18, 32;
L18,27the length of the line segments 18, 27;
Οn(f1)——f1higher order expression higher order terms, in calculating S1Can be ignored;
Οn(f2)——f2higher order expression higher order terms, in calculating S2Can be ignored;
Οn(f3)——f3higher order expression higher order terms, in calculating S3Can be ignored;
Οn(f4)——f4higher order expression higher order terms, in calculating S4Can be ignored;
s' Δ (1) (5) (9) -the area of the triangle with points 1, 5, 9 as vertices;
s' Δ (2) (6) (11) -the area of the triangle with points 2, 6, 11 as vertices;
s' Δ (3) (10) (7) -the area of the triangle with points 3, 10, 7 as vertices;
s' Δ (4) (8) (12) -the area of the triangle with points 4, 8, 12 as vertices;
S1the area of the arch formed by the quadratic curve 17 opposite to the vertex 1 and the line segments 5 and 9;
S2the area of the arch formed by the quadratic curve 16 opposite to the vertex 2 and the line segments 6 and 11;
S3the arcuate area enclosed by the quadratic curve 14 opposite to the vertex 3 and the line segments 7 and 10;
S4the area of an arch formed by the quadratic curve 15 opposite to the vertex 4 and the line segments 8 and 12;
in this embodiment, step 4 f1、f2、f3、f4Can be unified into 1 fAnd (4) the values can be separately solved iteratively, the solved result is used as the known condition and the vertex coordinates of the trapezoid-like throat, and the design of the trapezoid-like throat is completed in CATIA software.
Finally, it should be pointed out that: the above examples are intended to illustrate the design of the present invention, but not to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the present invention as defined by the appended claims.
Claims (8)
1. A method for designing an asymmetric trapezoidal nozzle throat is characterized by comprising the following steps: the method for designing the center line of the air inlet channel of the nacelle comprises the following steps:
the method comprises the following steps that firstly, the center of an asymmetric trapezoidal throat is set as a coordinate origin, an XY plane of a cross section is set as a design plane, and the throat area of the asymmetric trapezoidal nozzle is determined according to the total pressure recovery coefficient at the throat of the asymmetric trapezoidal nozzle, the total pressure recovery coefficient and the throat area at the throat of an original nozzle of an engine matched with the asymmetric trapezoidal nozzle;
step two, making a right-angle inverted trapezoid in the XY plane by using the center of the throat determined in the step one, and performing four-corner modification by using a quadratic curve to preliminarily determine the shape of the throat, wherein a plurality of edges of the throat are tangent to the inner edge of the right-angle inverted trapezoid, and the tangent points are all vertexes of the asymmetric trapezoid-like nozzle throat;
step three, preliminarily solving the height of the right-angled inverted trapezoid and the length of the upper bottom side and the lower bottom side according to the aspect ratio of the asymmetric spray pipe distributed at the throat and the inclined angle of the inclined edge of the right-angled trapezoid of the throat and the area of the throat determined in the step one;
step four, taking the height of the right-angled inverted trapezoid and the length of the upper bottom edge and the lower bottom edge determined in the step three as references, adjusting the shape and the size of the throat in the step two, adopting area partition solution, calculating the sum of the areas of a plurality of triangles formed from each vertex to the center of the throat, and then calculating the arch area between adjacent vertexes; the arch area adopts a high-order expression of a quadratic curve control factor f value, and f value parameters are adjusted until throat area and aspect ratio constraints are met.
2. The design method of an asymmetric trapezoidal nozzle throat as claimed in claim 1, wherein the central coordinate of the trapezoidal throat in step one is Q (0,0), which is the origin of the XY plane of the cross section, the X axis is the positive direction "to the right", and the Y axis is the positive direction "to the up".
3. The method as claimed in claim 1, wherein in the first step, the throat area of the asymmetric trapezoidal nozzle is calculated by:
q(Math).σth·Ath＝σ0·A0；
wherein σth-total pressure recovery coefficient at the throat of the asymmetric trapezoid-like nozzle;
σ0-total pressure recovery coefficient at the original nozzle throat of the engine;
A0-the area of the original nozzle throat of the engine;
Ath-asymmetric trapezoidal-like nozzle throat area;
q(Math) -flow function at the throat of the asymmetric trapezoidal-like nozzle;
Maththe Mach number of the throat of the asymmetric trapezoid-like nozzle is obtained.
4. The asymmetric trapezoidal nozzle throat design method of claim 1, wherein in step three, the calculation mode of the right-angle inverted trapezoidal height and the length of the upper bottom edge and the lower bottom edge is as follows:
l1＝hth·λth-hth·tan(αth)/2；
l0＝hth·λth+hth·tan(αth)/2；
wherein h isthThe right-angle inverted trapezoidal height is the height of the right-angle side of the throat of the asymmetric trapezoid-like spray pipe;
l1the length of the lower bottom edge of the right-angle inverted trapezoid is the length of the lower bottom edge of the throat of the asymmetric trapezoid-like spray pipe;
l0the length of the upper bottom edge of the right-angle inverted trapezoid is the length of the upper bottom edge of the throat of the asymmetric trapezoid-like spray pipe;
αth-the inclination of the lateral bevel edge of the throat of the asymmetric trapezoidal-like nozzle;
Ath-asymmetric trapezoidal-like nozzle throat area;
λth-the aspect ratio of the throat of the asymmetric trapezoid-like nozzle.
5. The design method of the asymmetric trapezoidal nozzle throat according to claim 1, wherein in the fourth step, the basic elements required for the area partition solution of the asymmetric trapezoidal nozzle throat comprise coordinates of each vertex, a line segment between each vertex, and a line segment between each vertex and the center of the throat.
6. The asymmetric trapezoidal nozzle throat design method of claim 5, wherein said step four is detailed as follows:
A. calculating to obtain the coordinates of each vertex by utilizing the aspect ratio of the throat of the asymmetric trapezoid-like spray pipe, the inclined angle of the side bevel edge of the throat of the asymmetric trapezoid-like spray pipe, the height of the inverted right-angled trapezoid, the length of the upper bottom edge of the inverted right-angled trapezoid, the length of the lower bottom edge of the inverted right-angled trapezoid and the f values of a plurality of corresponding secondary curves of arches;
B. calculating by using the coordinates of each vertex to obtain the length of the line between each vertex and the length of the line from each vertex to the center of the throat;
C. connecting each vertex by taking the center of the throat as a line, and mutually taking lines between every two adjacent vertexes to divide the asymmetric trapezoid-like nozzle throat into a plurality of triangles and four bows;
D. calculating the areas of all the triangles according to the length of the line segment calculated in the step B;
E. calculating the area of the arch according to the secondary curve f of the arch and the area of the triangle where the arch is positioned, and sequentially calculating 4 areas of the arch;
F. and adding the 4 cambered areas and the triangular areas to obtain the throat area of the asymmetric trapezoid-like spray pipe.
7. The asymmetric trapezoidal nozzle throat design method of claim 6, wherein the calculation method of step E is:
wherein S is1Is the first arcuate area, f1Is the control factor of the quadratic curve of the first arch, S' is the area of the triangle on which the first arch is located, On(f1) Is f1A high-order expression high-order item;
the calculation method of the rest of the arch area is the same as that of the first arch area.
8. The method of claim 1, wherein the step of designing the asymmetric trapezoidal nozzle throat is performed using CATIA software in which the asymmetric trapezoidal nozzle throat is designed.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115292854A (en) * | 2022-10-09 | 2022-11-04 | 中国航发四川燃气涡轮研究院 | Blade throat solving method based on flow tube segmentation and quadratic curve |
| CN115292854B (en) * | 2022-10-09 | 2023-02-17 | 中国航发四川燃气涡轮研究院 | Blade throat solving method based on flow tube segmentation and quadratic curve |
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