A Parametric Design Method for the Wall Profile of a Transition Section Flow Channel

Abstract

The present invention discloses a parametric design method for the wall profile of a transition section flow path, comprising the following steps: Step 1, design the inner end wall profile; Step 2, design the flow area distribution profile; Step 3, design the outer end wall profile according to the inner end wall profile and the flow area distribution profile. The present invention incorporates the most important geometric parameters affecting the flow in the transition section: the axial length of the transition section, the inlet and outlet elevation difference, the curvature distribution of the inner end wall profile, and the flow area distribution law, into the surface function of the design method, and parametrically describes the inner end wall profile and the flow area distribution profile of the transition section using the sine / cosine trigonometric functions respectively. Rich variations of the end wall profile of the transition section can be achieved using a small number of control parameters, and the control parameters can intuitively reflect the important geometric parameters affecting the flow in the transition section, facilitating the optimization design.

Description

Technical Field

[0001] The present invention relates to the technical field of aero-engine transition section design, and particularly relates to a parametric design method for the profile of the flow passage wall of a transition section. Background Art

[0002] As a component connecting two flow passages with different through-flow radii, the transition section is commonly found in aero-engines. With the increasing improvement of the thrust-to-weight ratio and economic indicators of engines, the size of the transition section is developing towards a larger radial drop and a shorter axial length. Especially in the transition section of the compression component, the flow is affected by both the pressure gradient and the wall curvature, and the flow condition is complex. Under the constraint of a compact size, the flow field has a large pressure gradient and a sharp change in wall curvature, which is extremely prone to flow separation, resulting in a large flow loss and affecting the engine performance. Therefore, researchers are committed to adopting various optimization design methods and flow control means to suppress the flow separation in the transition section while shortening the axial length of the transition section.

[0003] A conventional transition section is an "S"-shaped air flow channel composed of an inner end wall and an outer end wall. In the optimization design, the profile of the inner and outer end walls is mainly optimized and adjusted. Parametric modeling of the end wall profile is an essential step in the optimization design process.

[0004] Patent 202210727864.8 provides a low-loss compressor transition section structure, including: the outlet of the low-pressure compressor, the outer end wall of the transition section, the strut vane, the inner end wall of the transition section, and the inlet of the high-pressure compressor. The outer end wall of the transition section adopts a contraction surface profile, and the inner end wall of the transition section adopts an expansion surface profile. Both the expansion surface profile and the contraction surface profile are described by two quartic curves. Combining the upstream and downstream geometric relationships, and then giving the coordinates of the combination point of the two quartic curves can completely determine the profile shape. This parametric method has few control parameters and rich variations, but it is not intuitive enough and cannot reflect another important geometric characteristic affecting the flow in the transition section - the distribution law of the through-flow area, which brings difficulties to the optimization design.

[0005] Patent 202110560577.8 discloses a design method applied to a low-loss compressor intermediate casing, a compressor intermediate casing modeling design method based on the generalized form of the Lee curve and using the distribution law of the midline stacking cross-sectional area. This invention is applied to the optimization design, and a second-order continuous and accurately representable optimal intermediate casing end wall profile can be obtained. The constructed end wall profile is continuous, smooth, and of excellent quality, but the coefficient solving process is too complex, and the influence of the control parameters on the geometric shape is not intuitive enough.

[0006] The literature "Compressor Transition Duct Modeling and Three-Dimensional Numerical Simulation" by Tu Qiuye, Chen Qin, Jiang Ping, etc. [J]. Journal of Aerospace Power, 2015, 36(6): 1414-1422 discloses a parameterization method for the transition duct. The geometry of the transition duct is described by the combination of "inner end-wall profile + area distribution law". Among them, the inner end-wall profile is described by a quartic polynomial function. Combining the geometric relationships of the upstream and downstream and the relative positions of the inflection points (points where the curve curvature is 0), the curve shape can be completely determined. The area in the "area distribution law" refers to the annulus area, that is, the annular area formed by the inner and outer end-walls at the same axial position. The area distribution law curve is spliced by two S-shaped curves, and the splicing point is the extreme value of the curve. Given the extreme value and its relative position, the shape of the area distribution law curve can be determined. Although the parameterization of the end-wall profile of this transition duct has few control parameters, rich variations, and is intuitive, the annulus area (section direction perpendicular to the axial direction) used in the area distribution cannot accurately reflect the actual flow-through area of the transition duct (section direction perpendicular to the local flow direction). The greater the angle between the flow direction and the axial direction, the greater the difference between the annulus area and the flow-through area, which is also not conducive to the optimization design. Summary of the Invention

[0007] Object of the Invention: Aiming at the shortcomings of the existing design method that cannot take into account both intuitively reflecting the influence of control parameters on the geometric shape and considering the influence of the actual flow area on the transition duct, the present invention provides a parameterized design method for the flow channel wall profile of the transition duct, which can not only simply and intuitively reflect the influence of control parameters on the geometric shape of the transition duct, but also consider the influence of the actual flow area, and obtain a more optimized design method for the transition duct.

[0008] Technical Solution: To solve the above problems, the present invention adopts a parameterized design method for the flow channel wall profile of the transition duct, including the following steps:

[0009] Step 1, design the inner end-wall profile; the function of the inner end-wall profile is as follows: In the formula, is the axial coordinate of the inner end-wall profile, is the corresponding radius coordinate, and the subscript " h " represents the inner end-wall, L is the axial length of the transition duct, a, b, c is the coefficient;

[0010] Step 2, design the flow-through area distribution profile; the function of the flow-through area distribution profile is as follows:

[0011] In the formula, is the flow-through area of the transition duct corresponding to the axial coordinate of the inner end-wall profile, is the inlet flow-through area of the transition duct, ​is the flow area at the outlet of the transition section, d, e is the coefficient, ;

[0012] Step 3: Design the outer end wall profile; specifically, it includes the following steps:

[0013] Step 3.1: Take n + 1 discrete points on the inner end wall profile. The coordinates of these n + 1 discrete points are successively expressed as ( x h1 , r h1 ), ( x h2 , r h2 ), … ( x hn , r hn ), ( x hn+1 , r hn+1 ). The corresponding flow areas at these n + 1 discrete points are successively A ( x h1 ), A ( x h2 ), … A ( x hn ), A ( x hn+1 );

[0014] Step 3.2: Solve the coordinates of n discrete points on the outer end wall profile according to the following function. The coordinates of these n points are successively expressed as ( x s2 , r s2 ), … ( x sn , r sn ), ( x sn+1 , r sn+1 ):

[0015] In the formula, the subscripts " h " and " s " respectively represent the inner and outer end walls, is the angle between the tangent of the inner end wall profile and the axial direction at the coordinate point of the inner end wall profile, A’ ( x hn+1) is the annular area perpendicular to the axial direction of the transition section;

[0016] Step 3.3: Fit the n discrete points on the outer end wall profile to form the outer end wall profile.

[0017] Furthermore, a, b The following equation relationship is satisfied:

[0018] wherein, the inlet radius r h (0) and the outlet radius r h ( L ) are both preset values.

[0019] Furthermore, define the ratio of the total drop between the inlet and outlet of the inner end wall profile to the axial length as the relative drop , that is , The value range of is 0.25 to 0.4.

[0020] Furthermore, define the ratio of the half-way position drop of the inner end wall profile to the total drop between the inlet and outlet as the half-way drop ratio , that is , the half-way drop ratio The value range is 0.5 to 0.6.

[0021] Furthermore, .

[0022] Furthermore, e The value range is 0.1 to 0.3.

[0023] Furthermore, the discrete points taken in step 3.1 satisfy .

[0024] Furthermore, in step 3.3, the n discrete points on the outer end wall profile are fitted according to the natural cubic spline curve to obtain the outer end wall profile.

[0025] The present invention also provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the steps of the above method are implemented.

[0026] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the above method are implemented.

[0027] Beneficial effects: Compared with the prior art, the significant advantage of the present invention is that it integrates the most important geometric parameters affecting the flow in the transition section: the axial length of the transition section, the head drop at the inlet and outlet, the curvature distribution of the inner end wall profile, and the law of the flow area distribution, into the profile function of the design method. The inner end wall profile of the transition section and the profile of the flow area distribution are parametrically described using the sine / cosine trigonometric functions respectively. With a small number of control parameters, rich variations of the end wall profile of the transition section can be achieved, and the control parameters can directly reflect the important geometric parameters affecting the flow inside the transition section, facilitating the optimization design. Description of the Drawings

[0028] Figure 1 Schematic diagram of the inner end wall profile of the present invention and the important geometric parameters on this profile;

[0029] Figure 2 For different relative head drops of the present invention δ and different semi-course head drop ratios ξ Schematic diagram of the inner end wall profile;

[0030] Figure 3 Schematic diagram of the flow area distribution profile of the present invention and the important geometric parameters on this profile;

[0031] Figure 4 For different relative area extrema of the present invention d and the relative positions of the extrema e Schematic diagram of the flow area distribution profile;

[0032] Figure 5 For the flow area of the present invention A ( x hn+1 )、annular area A’ ( x hn+1 ) and the tangential and axial angle of the inner end wall profile Schematic diagram of the geometric relationship;

[0033] Figure 6 A set of inner and outer end wall profiles of the transition section finally generated by the present invention;

[0034] Figure 7 Stereoscopic sectional view of the shape of the transition section obtained by the present invention. Detailed Implementation Manner

[0035] A parametric design method for the flow channel wall profile of the transition section in this embodiment includes the following steps:

[0036] Step 1: Design the inner end wall profile. The function of the inner end wall profile is as follows: In the formula, is the axial coordinate of the inner end wall profile, is The corresponding radius coordinate, with the subscript " h " representing the inner end wall, L being the axial length of the transition section, , a, b, c being the coefficient.

[0037] Since the transition section itself has the characteristic of an "S" - shaped trend, the describing function selects the sine and cosine trigonometric functions that also have this characteristic. In addition, the sine and cosine trigonometric functions also have advantages such as smoothness and continuous curvature. The second term in the above formula, when combined with the first - term constant a, can conveniently control the inlet radius and outlet radius of the transition section; the third term is to control the radius at the mid - point position of the curve ( ); in addition, the third term is a squared term, ensuring that the slopes at the inlet and outlet of the curve are 0.

[0038] The inlet radius of the transition section is r h (0), and the outlet radius of the transition section is r h ( L ). According to the above function calculation, we can get: The inlet and outlet radii of the transition section can be determined according to the upstream and downstream geometries and are known preset values. Therefore, the value of the coefficient a, b can be calculated. With the coefficient a, b determined, the inner - end - wall profile function only needs to be given the coefficient c and the axial length L to completely determine the curve shape.

[0039] To intuitively reflect the geometric parameters affecting the flow in the transition section, the ratio of the total drop between the inlet and outlet of the inner - end - wall profile to the axial length is defined as the relative drop , that is The relative drop can reflect the compactness of the transition section. The larger it is, it indicates that under the same inlet - outlet drop, the axial length is shorter and the transition section is more compact.

[0040] The ratio of the mid - point position drop of the inner - end - wall profile to the total inlet - outlet drop is defined as the mid - point drop ratio , that is The mid - point drop ratio can reflect the curvature distribution of the inner - end - wall profile of the transition section. When , it indicates that the drop in the first half of the inner - end - wall profile is smaller than that in the second half, the curvature of the first half of the profile is larger and relatively gentle; conversely, the curvature of the first half is smaller and relatively steep.

[0041] In this way, the control variables of the inner - end - wall profile function are transformed into the relative drop and the mid - point drop ratio Two dimensionless geometric parameters that are crucial for the flow in the transition section, and can be simply obtained using the coefficients of the inner endwall profile function. For the transition section of the compression component, according to the flow characteristics, while pursuing a compact transition section size, ensuring that the airflow does not undergo flow separation and maintaining low flow losses, the relative drop has a value range of 0.25 - 0.4, and the half - way drop ratio has a value range of 0.5 - 0.6.

[0042] The axial length L in the inner endwall profile shaping method, the inlet - outlet drop , the half - way position L / 2, the half - way drop and other geometric parameter schematic diagrams are as shown in Figure 1 the figure. Figure 2 shows the inner endwall profile shaping under different relative drops and different half - way drop ratios . It can be seen that the control parameters can effectively control the profile shaping, and the profile always remains smooth.

[0043] Step 2: Design the flow - through area distribution profile. The flow - through area distribution profile function is as follows: In the formula, is the flow - through area of the transition section corresponding to the axial coordinate of the inner endwall profile. This refers to the actual flow - through area of the transition section, that is, the flow - through area in the cross - section direction of the transition section perpendicular to the local flow direction; is the inlet flow - through area of the transition section, is the outlet flow - through area of the transition section, d, e is the coefficient, .

[0044] The inlet - outlet flow - through areas are determined by the upstream and downstream geometric configurations and are obtained according to the following formula: .

[0045] In the flow - through area distribution law, the important geometric parameters affecting the flow are the extreme value of the flow - through area and its relative position. For the convenience of controlling it, the description function of the area distribution law selects two - segment trigonometric functions, and the connection point of the two functions is the extreme value of the flow - through area. When , , so the coefficients d, e control the value at the splicing point of the flow - through area function and its relative position respectively. For the transition section of the compression component, there is . To control the flow separation, it is further limited that , that is, the channel area shows a trend of first expanding and then contracting. At this time, the relative position of the splicing of the flow - through area function is the position of the maximum value of the function, and it is limited that , e The value range of is 0.1 to 0.3.

[0046] The axial length in the flow area distribution profile shaping method L , the relative flow area extreme value d and its relative position e and other geometric parameter schematic diagrams are as Figure 3 shown. Figure 4 It shows the flow area distribution shaping under different relative area extreme values d and the extreme value relative position e . It can be seen that the control parameters can effectively control the profile shaping, and the profile always remains smooth. Figure 3 and Figure 4 The vertical coordinates are both A / A in -1.

[0047] Step 3: Design the outer end wall profile. Design the outer end wall profile according to the determined inner end wall profile and the flow area distribution curve, which specifically includes the following steps:

[0048] Step 3.1: Take n + 1 discrete points on the inner end wall profile. The coordinates of these n + 1 discrete points are successively expressed as ( x h1 , r h1 ), ( x h2 , r h2 ) … ( x hn , r hn ), ( x hn+1 , r hn+1 ). The corresponding flow areas at these n + 1 discrete points are successively A ( x h1 ), A ( x h2 ) … A ( x hn ), A ( x hn+1 ).

[0049] Step 3.2: Solve the coordinates of n discrete points on the outer end wall profile according to the following function. The coordinates of these n points are successively expressed as ( x s2 , r s2 ) … (x sn , r sn )、( x sn+1 , r sn+1 )。

[0050] The flow area refers to the cross-sectional area perpendicular to the local flow direction, and the cross-sections formed by the corresponding coordinate points on the inner and outer walls at different positions should all be perpendicular to the flow direction. If the discrete coordinate points are dense enough ( ), and there is no flow separation in the airflow, it can be approximately considered that the flow direction is consistent with the tangent direction of the local inner end-wall profile, that is, the cross-section formed by the corresponding points on the inner and outer walls should be perpendicular to the local inner end-wall profile, then there is the following relationship: The subscript " h " and " s " represent the inner and outer end-walls respectively, is the angle between the tangent of the inner end-wall profile and the axial direction at the coordinate point of the inner end-wall profile.

[0051] As Figure 5 shown, the figure shows a schematic plan view of the cross-section of the transition section. The surface generated by rotating the line connecting the corresponding points on the upper and lower end-walls in the figure around the x axis for one week is the flow-through cross-section of the transition section, and the annular area A’ ( x hn+1 ) and the flow area A ( x hn+1 ) also have the following relationship: Using the above two formulas, the coordinate points on the corresponding outer end-wall profile can be obtained.

[0052] Taking the inlet coordinates of the transition section as an example, at the inlet cross-section, , , can be determined by the upstream geometric conditions. Substituting into the above geometric relationship, we can get: .

[0053] Two unknowns can be obtained from the two equation relationships. In the same way, the coordinate points on the outer end-wall profile corresponding one by one to the coordinate points ([[]] x hn , r hn ) of the inner end-wall profile can be obtained in turn. x sn , r sn ).

[0054] Step 3.3: Fit the n discrete points on the outer end wall profile line to obtain the outer end wall profile line by using natural cubic spline curve. The advantage of using natural cubic spline curve is that the curve will strictly pass through all control points, and the curve is smooth with continuous second derivative.

[0055] According to the above steps, the inner end wall profile and the outer end wall profile of the transition section are finally obtained, as Figure 6 shown.

[0056] Finally, rotate the inner end wall profile line and the outer end wall profile line around x the axis by 360° to obtain the shape of the transition section flow passage, as Figure 7 shown. The figure is the symmetric sectional view of the transition section flow passage, which is convenient for intuitively observing the inner and outer end wall profile lines and the cross section corresponding to the flow area. The inlet in the figure corresponds to the inlet flow area of the transition section, the outlet corresponds to the outlet flow area of the transition section, and the flow cross section at a certain position corresponds to the flow area of the transition section.

[0057] The present invention integrates the most important geometric parameters affecting the flow in the transition section: the axial length of the transition section, the head difference between the inlet and outlet, the curvature distribution of the inner end wall profile line, and the distribution law of the flow area, into the profile function of the design method, and uses sine / cosine trigonometric functions to parametrically describe the inner end wall profile line and the flow area distribution profile line of the transition section respectively. The rich changes of the end wall profile line of the transition section can be realized by using a small number of control parameters, and the control parameters can directly reflect the important geometric parameters affecting the flow in the transition section, which is convenient for optimization design.

Claims

1. A parameterized design method for the wall profile of a transition section flow channel, characterized in that: The following steps are involved: Step 1, design the inner end wall profile; the inner end wall profile function is as follows: In the formula, is the axial coordinate of the inner end wall profile, for The corresponding radius coordinates, subscript " h ” means the inner end wall, L is the axial length of the transition section, , a, b, c is the coefficient; Step 2: Design a flow area distribution profile; the flow area distribution profile function is as follows: In the formula, is the axial coordinate of the inner end wall profile The corresponding transition section flow area is is the inlet flow area of ​​the transition section, is the flow area at the transition section outlet, d.e is the coefficient, ; Step 3: Design the outer end wall profile; The specific steps include: Step 3.1, take n+1 discrete points on the inner end wall profile, the coordinates of the n+1 discrete points are expressed as ( x h1 , r h1 )、( x h2 , r h2 )…( x hn , r hn )、( x hn+1 , r hn+1 ), the flow areas corresponding to the n+1 discrete points are A ( x h1 ), A ( x h2 )… A ( x hn ), A ( x hn+1 ); Step 3.2, solve the coordinates of n discrete points on the outer end wall profile according to the following function. The coordinates of the n points are expressed as ( x s2 , r s2 )…( x sn , r sn )、( x sn+1 , r sn+1 ): In the formula, the subscript " h "and" s " represent the inner and outer end walls respectively, is the coordinate point on the inner end wall profile The angle between the tangent line of the inner end wall profile and the axial direction, A’ ( x hn+1 ) is the area of ​​the ring perpendicular to the axial direction of the transition section; Step 3.3, fitting the obtained n discrete points on the outer end wall profile to form the outer end wall profile.

2. The parameterized design method for the transition section flow channel wall profile according to claim 1, characterized in that: coefficient a, b The following equality relationship is satisfied: Among them, the transition section entrance radius r h (0) and transition section outlet radius r h ( L ) are all default values.

3. The parameterized design method for the transition section flow channel wall profile according to claim 2, characterized in that: The ratio of the total drop of the inlet and outlet of the inner end wall profile to the axial length is defined as the relative drop. ,Right now , The value range is 0.25~0.

4.

4. The parameterized design method for the transition section flow channel wall profile according to claim 3, characterized in that: The ratio of the half-distance drop of the inner end wall profile to the total drop of the inlet and outlet is defined as the half-distance drop ratio. ,Right now , half-distance drop ratio The value range is 0.5~0.

6.

5. The parameterized design method for the transition section flow channel wall profile according to claim 1, characterized in that: 。 6. The parameterized design method for the transition section flow channel wall profile according to claim 1, characterized in that: e The value range is 0.1~0.

3.

7. The parameterized design method for the transition section flow channel wall profile according to claim 1, characterized in that: The discrete points taken in step 3.1 satisfy .

8. The parameterized design method for the transition section flow channel wall profile according to claim 1, characterized in that: In step 3.3, the n discrete points on the outer end wall profile are fitted according to the natural cubic spline curve to obtain the outer end wall profile.

9. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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