A variable geometry turbine end region configuration method

Abstract

The application discloses a variable geometry turbine end region configuration method, first, the extracted tip, blade root end surface discrete points are rotated to obtain the rotated tip, blade root end surface discrete points, the extracted discrete points are encrypted and fitted into a casing, a hub surface. The fitted casing, hub surface is used to screen out the rotated discrete points outside the casing, hub end region. Through the screened discrete points, the upper and lower boundaries of the casing, hub end region are obtained respectively, the upper and lower boundaries and the original casing, hub end wall are used to construct the lower boundary surface of the casing, hub end region, the transition surface of the upper and lower boundary curves and the upper boundary surface of the end region. Finally, the surfaces are stitched to obtain a new variable geometry turbine casing, hub end region configuration. Compared with the original variable geometry turbine, the end region configuration technology significantly reduces the flow loss caused by the end region gap leakage flow, improves the efficiency of the guide vane at each angle and improves the aerodynamic performance of the variable geometry turbine.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of turbine, and particularly relates to a variable geometry turbine end region configuration method. BACKGROUND

[0002] After the traditional engine design is completed, the main working cycle parameters of the design point are determined, and the engine can only guarantee the best performance at the design point, and cannot achieve the best performance at other states in the working envelope. The variable cycle engine adjusts the thermal cycle parameters by changing the shape and size of the flow passage of the core section, so as to realize the change of the thermal cycle, thereby ensuring that the engine is in the best performance state under various flight conditions, and can fully exert the performance potential of the engine in a wider flight envelope. The variable cycle engine has great superior potential compared with the conventional engine, and can provide better maneuverability and supersonic cycle ability for the fighter. The most attractive variable cycle engine scheme for the fighter is the variable geometry turbine technology.

[0003] The variable geometry turbine technology is to adjust the throat area of the guide vane by rotating the guide vane, so as to change the flow capacity of the turbine, which plays an important role in adjusting the flow, controlling the thrust and adjusting the working point of the engine in the variable cycle engine, and is an important component indispensable to the variable cycle engine. As a key technology in the variable cycle engine, the variable geometry turbine plays an important role in improving the performance of the engine under non-design conditions, and the variable geometry turbine design technology and aerodynamic performance have always been an important topic in the field of turbomachinery research.

[0004] In order to ensure that the adjustable guide vane of the variable geometry turbine can rotate without obstruction within the specified angle range, a certain gap needs to be left at the end region of the guide vane and the casing and the hub. Too small gap will cause the guide vane to contact the casing and the hub end wall during rotation and be stuck, and too large gap will cause end region gap leakage flow, resulting in a decrease in turbine efficiency and a certain influence on the aerodynamic performance of the turbine, so a suitable end region configuration technology is needed to meet the requirements of geometry structure and aerodynamic performance. SUMMARY

[0005] In order to overcome the prior art, the present application provides a variable geometry turbine end region configuration method, first, the extracted blade tip, blade root end face discrete points are rotated to obtain a certain range of rotated blade tip, blade root end face discrete points, and the extracted discrete points of the casing and the hub are encrypted and fitted into the casing and the hub surface. Using the fitted casing and hub surface, the rotated discrete points outside the casing and hub end region are screened out. Through the screened discrete points, the upper and lower boundaries of the casing and hub end region are obtained, and the upper and lower boundaries and the original casing and hub end wall are used to construct the lower boundary surface of the casing and hub end region, the transition surface of the upper and lower boundary curves and the upper boundary surface of the end region. Finally, the surfaces are stitched to obtain a new variable geometry turbine casing and hub end region configuration. Compared with the original variable geometry turbine, this end region configuration technology significantly reduces the flow loss caused by the end region gap leakage flow, improves the efficiency of the guide vane at each angle, and improves the aerodynamic performance of the variable geometry turbine.

[0006] The technical scheme adopted by the present application to solve its technical problems is as follows:

[0007] Step 1: Extract the discrete point data of the guide vane tip end face and the discrete point data of the guide vane root which are tangent to the original end wall, and extract the discrete data points of the casing and the hub end wall.

[0008] Step 2: Given the rotation axis and the angle range to be rotated, rotate the two sets of discrete point data obtained in step 1 around the rotation axis every discrete angle in the rotation angle range to obtain a series of rotated casing end face and hub end face discrete point data;

[0009] Step 3: Fit the casing and hub surface, and screen out the point set outside the original casing end region from the rotated guide vane tip end face discrete point data obtained in step 2, and screen out the point set outside the original hub end region from the rotated guide vane root discrete point data;

[0010] Step 4: Project the point set outside the original casing end region onto the casing end wall, and project the point outside the original hub end region onto the hub end wall to obtain the lower boundary of the casing and hub end region;

[0011] Step 5: Select the outermost boundary point of the point outside the casing end region as the upper boundary of the new casing end region, and select the outermost boundary point of the point outside the hub end region as the upper boundary of the new hub end region;

[0012] Step 6: Construct the new casing and hub end region from the upper and lower boundary curves of the casing and hub end region obtained in steps 4 and 5 and the original casing and hub end wall.

[0013] Further, the step 1 is specifically:

[0014] Step 1-1: Obtain the tangent surface of the original blade and the casing and the hub in the modeling software as the tip and root end surface of the guide vane;

[0015] Step 1-2: Export the end surface to matlab, and obtain the triangular partition and discrete data points of the tip and root end surface and the end wall of the casing and the hub by using the stlread function.

[0016] Further, the step 2 is specifically:

[0017] The coordinates of the point required to be rotated are P(x, y, z), and the unitized vector of the rotation axis is The coordinates of the starting point of the rotation axis are origin(origin x ,origin y ,origin z ), and the rotation angle is alpha, and alph is the form conversion of alpha, which is converted from the degree form to the form of π;

[0018] alph=alpha*pi / 180

[0019] sina=sin(alph)

[0020] cosa=cos(alph)

[0021] vera=1-cosa

[0022] Wherein, a represents the abbreviated form of alph, and pi represents π;

[0023] The rotation matrix is:

[0024]

[0025] P rot =(x rot ,y rot ,z rot )=(x-origin x ,y-origin y ,z-origin z )*T

[0026] Wherein, P rot represents the coordinates after rotation without considering the starting point coordinates;

[0027] The obtained coordinates after rotation are:

[0028] P new =(x new ,y new ,z new )=(x rot +originx y rot +origin y z rot +origin z ).

[0029] Further, the step 3 is specifically:

[0030] Step 3-1: Obtain the point set after rotating the tip end surface by a series of discrete angles from step 2, determine whether these points are within the original casing end area, if within the casing end area or on the casing end wall, discard, if outside the casing end area, keep these points;

[0031] Step 3-2: Obtain the point set after rotating the root end surface by a series of discrete angles from step 2, determine whether these points are within the original hub end area, if within the hub end area or on the hub end wall, discard, if outside the hub end area, keep these points.

[0032] Further, the step 4 is specifically:

[0033] Step 4-1: Project the points outside the casing end area obtained in step 3 onto the casing end wall, form a new point set with the data points of the original tip end surface, select the outer contour of the point set, connect it into a closed curve as the lower boundary curve of the casing end area;

[0034] Step 4-2: Project the points outside the hub end area obtained in step 3 onto the hub end wall, form a new point set with the data points of the original root end surface, select the outer contour of the point set, connect it into a closed curve as the lower boundary curve of the hub end area.

[0035] Further, the step 5 is specifically:

[0036] Step 5-1: Take the points outside the casing end area obtained in step 3 as a point set, select the outer contour of the point set as the upper boundary curve of the casing end area;

[0037] Step 5-2: Take the points outside the hub end area obtained in step 3 as a point set, select the outer contour of the point set as the upper boundary curve of the hub end area.

[0038] Further, the step 6 is specifically:

[0039] Step 6-1: Create an upper boundary surface from the upper boundary curve: fill the surface, N-sided surface function in the modeling software to create an upper boundary surface between the upper boundary curves;

[0040] Step 6-2: Create transition surface between upper and lower boundary curves: both upper and lower boundary curves are irregular three-dimensional curves, and the transition surface between the upper and lower boundary curves of the casing and the hub is created by sweeping, curve group and N-sided surface respectively;

[0041] Step 6-3: Create lower boundary surface from lower boundary curve and original casing, hub end wall: the lower boundary curve at the casing is contained in the original casing end wall, the casing part contained by the lower boundary curve is deleted, and the deleted casing end wall serves as the lower boundary surface of the casing; the lower boundary curve at the hub is contained in the original hub end wall, the hub part contained by the lower boundary curve is deleted, and the deleted hub end wall serves as the lower boundary surface of the casing;

[0042] Step 6-4: Obtain new casing, hub end region configuration: stitch the upper boundary surface of the casing, the transition surface, and the lower boundary surface of the casing as the new casing end region configuration, and stitch the upper boundary surface of the hub, the transition surface, and the lower boundary surface of the hub as the new hub end region configuration.

[0043] The beneficial effects of the present application are as follows:

[0044] The present application can ensure the free rotation of the guide vane within a certain angle range by constructing a new casing, hub end region configuration in the casing, hub end region, can change the flow capacity of the turbine by adjusting the guide vane throat area, which plays an important role in adjusting the flow, controlling the thrust, and adjusting the working point of the engine in the variable cycle engine. At the same time, this end region configuration can minimize the gap leakage flow loss caused by the gap leakage between the end regions, improve the efficiency of the variable geometry turbine, and improve the aerodynamic performance of the variable geometry turbine. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 It is a design flowchart of the present application;

[0046] Figure 2 It is a discrete point diagram of the blade tip and blade root end surface of the present application tangent to the original end wall;

[0047] Figure 3 It is a discrete point diagram of the blade tip and blade root end surface obtained after rotation of the present application;

[0048] Figure 4 It is a casing end region diagram of the present application;

[0049] Figure 5 It is a hub end region diagram of the present application;

[0050] Figure 6 It is a variable geometry turbine end region overall diagram of the present application;

[0051] In the figure, 1, upper boundary curve of casing end area; 2, lower boundary curve of casing end area; 3, lower boundary surface of casing end area; 4, transition surface of upper and lower boundaries of casing end area; 5, upper boundary surface of casing end area; 6, upper boundary curve of hub end area; 7, lower boundary curve of hub end area; 8, lower boundary surface of hub end area; 9, transition surface of upper and lower boundaries of hub end area; 10, upper boundary surface of hub end area. DETAILED DESCRIPTION

[0052] The application is further described below in combination with the drawings and examples.

[0053] The application aims to solve the problems that the end region gap is too small to cause the end wall and the casing to be contacted and stuck during the rotation of the wall surface guide vane, and the end region gap flow causes flow loss when the end region gap is too large. Through the characteristics of the variable geometry turbine guide vane rotation, a variable geometry turbine end region configuration method is proposed. The end region configuration can wrap the guide vane in any rotation process, ensure that the guide vane does not contact the casing and the hub end wall during rotation, and minimize the loss caused by the end region gap flow.

[0054] To achieve the above-mentioned purpose, the technical scheme adopted by the application is:

[0055] First step: extract the discrete point data of the end face of the guide vane tip and the discrete point data of the guide vane root, and extract the discrete data points of the casing and the hub end wall.

[0056] (1) Obtain the tangent surface of the original blade and the casing and the hub in the modeling software as the tip and root end face of the guide vane.

[0057] (2) Export the end face to matlab, and use the stlread function to obtain the triangular subdivision and discrete data points of the tip and root end face of the guide vane and the casing and hub end wall.

[0058] Second step: given the rotation axis and the angle range to be rotated, rotate the discrete point data obtained in the first step around the rotation axis every discrete angle in the rotation angle range to obtain a series of discrete point data of the rotated casing end face and hub end face.

[0059] The coordinates of the point to be rotated are defined as P(x, y, z), and the unitized vector of the rotation axis is The coordinates of the starting point of the rotation axis are origin(origin x ,origin y ,origin z ), and the rotation angle is alpha. alph is the form conversion of alpha, which is converted from the degree form to the form of π.

[0060] alph = alpha * pi / 180

[0061] sina = sin(alph)

[0062] cosa = cos(alph)

[0063] vera = 1 - cosa

[0064] The rotation matrix is:

[0065]

[0066] P rot = (x rot ,y rot ,z rot ) = (x-origin x ,y-origin y ,z-origin z )*T

[0067] The rotated coordinates are:

[0068] P new = (x new ,y new ,z new ) = (x rot + origin x ,y rot + origin y ,z rot + origin z )

[0069] Third step: fitting the casing and hub surfaces, screen out the point set outside the original casing end region from the rotated point data of the blade tip end surface obtained in the second step, and screen out the point set outside the original hub end region from the rotated point data of the blade root end surface.

[0070] (1) The point set of the blade tip end surface rotated by a series of discrete angles is obtained in the second step, and it is determined whether the points are outside the original casing end region. If the points are inside the casing end region or on the casing end wall, they are discarded. If the points are outside the casing end region, they are retained.

[0071] (2) The point set of the blade root end surface rotated by a series of discrete angles is obtained in the second step, and it is determined whether the points are outside the original hub end region. If the points are inside the hub end region or on the hub end wall, they are discarded. If the points are outside the hub end region, they are retained.

[0072] Fourth step: project the point set outside the original casing end region onto the casing end wall, and project the point outside the original hub end region onto the hub end wall. Obtain the lower boundary of the casing and hub end regions.

[0073] (1) Project the points outside the casing end region obtained in the third step onto the casing end wall to form a new point set with the data points of the original blade tip end surface, select the outer contour of the point set, and connect it into a closed curve as the lower boundary curve of the casing end region.

[0074] (2) Project the points outside the hub end region obtained in the third step onto the hub end wall to form a new point set with the data points of the original blade root end surface, select the outer contour of the point set, and connect it into a closed curve as the lower boundary curve of the hub end region.

[0075] Step 5: Select the outermost boundary points from the points outside the casing end region as the upper boundary of the new casing end region, and select the outermost boundary points from the points outside the hub end region as the upper boundary of the new hub end region.

[0076] (1) Take the points outside the casing end region obtained in the third step as a point set, and select the outer contour of the point set as the upper boundary curve of the casing end region.

[0077] (2) Take the points outside the hub end region obtained in the third step as a point set, and select the outer contour of the point set as the upper boundary curve of the hub end region.

[0078] Step 6: Construct the new casing and hub end regions from the upper and lower boundary curves of the casing and hub end regions obtained in the fourth and fifth steps, and the original casing and hub end walls.

[0079] (1) Create an upper boundary surface from the upper boundary curve: use the modeling software to create an upper boundary surface between the upper boundary curves by filling the surface and N-edge surface functions.

[0080] (2) Create a transition surface between the upper and lower boundary curves: both the upper and lower boundary curves are irregular three-dimensional curves, and the transition surfaces between the upper and lower boundaries of the casing and hub can be created by sweeping, passing through curve groups, and N-edge surfaces.

[0081] (3) Create a lower boundary surface from the lower boundary curve and the original casing and hub end walls: the lower boundary curve of the casing is contained in the original casing end wall, delete the casing part contained in the lower boundary curve, and the deleted casing end wall serves as the lower boundary surface of the casing; the lower boundary curve of the hub is contained in the original hub end wall, delete the hub part contained in the lower boundary curve, and the deleted hub end wall serves as the lower boundary surface of the hub.

[0082] (4) Obtain the new casing and hub end region configuration: stitch the casing upper boundary surface, transition surface, and casing lower boundary surface as the new casing end region configuration, and stitch the hub upper boundary surface, transition surface, and hub lower boundary surface as the new hub end region configuration.

[0083] Example:

[0084] like Figure 1 A variable geometry turbine end region configuration design method is shown, comprising the following steps:

[0085] Step 1: Extract the discrete point data of the guide vane tip surface and the guide vane root that are tangent to the original end wall, and extract the discrete data points of the casing and hub end wall.

[0086] Step 2: Given the rotation axis and the angle range that needs to be rotated, the discrete point data obtained in the first step is rotated around the rotation axis once every discrete angle within the rotation angle range to obtain a series of discrete point data of the casing end face and the hub end face after rotation.

[0087] Step 3: Filter out the point set outside the original casing end area from the discrete point data of the rotated blade tip surface obtained in the second step, and filter out the point set outside the original hub end area from the discrete point data of the rotated blade root end surface.

[0088] Step 4: Project the points outside the original casing end area onto the casing end wall, and project the points outside the original hub end area onto the hub end wall. Obtain the lower boundaries of the casing and hub end areas.

[0089] Step 5: Select the outermost boundary point from the points outside the casing end area as the upper boundary of the new casing end area, and select the outermost boundary point from the points outside the hub end area as the upper boundary of the new hub end area.

[0090] Step 6: Construct new casing and hub end areas based on the upper and lower boundary curves of the casing and hub end areas obtained in steps 4 and 5 and the original casing and hub end walls.

[0091] (1) Create an upper boundary surface from the upper boundary curve;

[0092] (2) creating a transition surface between the upper and lower boundary curves from the upper and lower boundary curves;

[0093] (3) Create the lower boundary surface from the lower boundary curve and the original casing and hub end wall;

[0094] (4) The upper boundary surface, transition surface, and lower boundary surface are stitched together to form a new casing and hub end area configuration.

[0095] The first step is to obtain the discrete point data of the guide vane tip and blade root end surfaces tangent to the original end wall, which includes the following steps:

[0096] (1) In the modeling software, the tangent surfaces between the original blade and the casing and hub are obtained as the tip and root end faces of the guide vane.

[0097] (2) Export the end surface to matlab, and use the stlread function to obtain the triangular partition and discrete data points of the blade tip, blade root end surface, and casing and hub end wall.

[0098] The second step obtains the rotated end surface discrete point data, and specifically includes the following steps:

[0099] The coordinates of the point to be rotated are defined as P(x, y, z), and the unitized vector of the rotation axis is The coordinates of the starting point of the rotation axis are origin(origin x ,origin y ,origin z ) = (134.15472, -3, 0), and the rotation angle range is alpha = 15.

[0100] alph = alpha * pi / 180

[0101] sina = sin(alph)

[0102] cosa = cos(alph)

[0103] vera = 1 - cos(alph)

[0104] The rotation matrix is:

[0105]

[0106] P rot = (x rot ,y rot ,z rot ) = (x-origin x ,y-origin y ,z-origin z ) * T

[0107] The obtained rotated coordinates are:

[0108] P new = (x new ,y new ,z new ) = (x rot + origin x ,y rot + origin y ,z rot + origin z )

[0109] The third step obtains the points outside the casing and hub end area, and specifically includes the following steps:

[0110] (1) Through the discrete points shroud(x shroud ,y shroud ,z shroud ) of the casing end wall, interpolation encryption is performed to fit the casing surface. In this case, the size of the z coordinate of the discrete point in the rotated point set and the z coordinate of the fitted casing surface under the same x coordinate and y coordinate is determined to determine whether it is outside the end region.

[0111] If x new =x shroud , y new =y shroud , and the z coordinate of the rotated discrete point is greater than the z coordinate of the fitted casing surface z new >z shroud , the discrete points are retained; if the z coordinate of the rotated discrete point is less than or equal to the z coordinate of the fitted casing surface z new <=z shroud , the discrete points are discarded.

[0112] (2) Through the discrete points hub(x hub ,y hub ,z hub ) of the hub end wall, interpolation encryption is performed to fit the hub surface. In this case, the size of the z coordinate of the discrete point in the rotated point set and the z coordinate of the fitted hub surface under the same x coordinate and y coordinate is determined to determine whether it is outside the hub end region.

[0113] If x new =x hub , y new =y hub , and the z coordinate of the rotated discrete point is less than the z coordinate of the fitted hub surface z new <z hub , the discrete points are retained; if the z coordinate of the rotated discrete point is greater than or equal to the z coordinate of the fitted hub surface z new >=z hub , the discrete points are discarded.

[0114] The fourth step is to obtain the lower boundary of the casing and hub end region, which specifically includes the following steps:

[0115] (1) Project the points outside the casing end region obtained in the third step onto the casing end wall, and replace the z coordinates of the points outside the casing end surface obtained in the third step with the z coordinates of the casing under the same x and y coordinates using the casing surface fitted in the third step. After all the replacements, a new point set is formed with the original blade tip end surface data points, the outer contour of which is selected and connected to form a closed curve as the lower boundary curve of the casing end region.

[0116] (2) Project the points outside the hub end region obtained in the third step onto the hub end wall, and replace the z coordinates of the points outside the hub end face obtained in the third step with the z coordinates of the casing under the same x and y coordinates by using the hub surface fitted in the third step. After all the replacements, form a new point set with the original data points of the blade root end face, select the outer contour of the point set, and connect the closed curve to obtain the lower boundary curve of the hub end region.

[0117] The fifth step obtains the upper boundary of the casing and the hub end region, and specifically includes the following steps:

[0118] (1) Select the outer contour of the point set of the points outside the casing end region obtained in the third step as the upper boundary curve of the casing end region.

[0119] (2) Select the outer contour of the point set of the points outside the hub end region obtained in the third step as the upper boundary curve of the hub end region.

[0120] The sixth step obtains the configuration of the variable geometry turbine casing and the hub end region, and specifically includes the following steps:

[0121] (1) Create the upper boundary surface from the upper boundary curve: fill the surface, N-edge surface and other functions of the modeling software to create the upper boundary surface between the upper boundary curves.

[0122] (2) Create the transition surface between the upper and lower boundary curves from the upper and lower boundary curves: the upper and lower boundary curves are irregular three-dimensional curves, and the transition surfaces between the casing and the hub upper and lower boundaries can be created by sweeping, passing through the curve group and N-edge surface.

[0123] (3) Create the lower boundary surface from the lower boundary curve and the original casing and hub end wall: the lower boundary curve of the casing is contained in the original casing end wall, and the casing part contained in the lower boundary curve is deleted, and the casing end wall after deletion is used as the lower boundary surface of the casing; the lower boundary curve of the hub is contained in the original hub end wall, and the hub part contained in the lower boundary curve is deleted, and the hub end wall after deletion is used as the lower boundary surface of the casing.

[0124] (4) Obtain the new casing and hub end region configuration: stitch the casing upper boundary surface, the transition surface and the casing lower boundary surface as the new casing end region configuration, and stitch the hub upper boundary surface, the transition surface and the hub lower boundary surface as the new hub end region configuration.

Claims

1. A variable geometry turbine end region configuration method characterized by, The method comprises the following steps: Step 1: extracting discrete point data of a guide vane tip end surface tangent to an original end wall and discrete point data of a guide vane root; Step 2: given a rotating axis and a required rotating angle range, rotating the two sets of discrete point data obtained in step 1 around the rotating axis at every discrete angle in the rotating angle range to obtain a series of discrete point data of the rotating end surface and the rotating hub end surface; Step 3: fitting a hub and a hub surface, screening out point sets outside the original hub end area from the discrete point data of the rotating guide vane tip end surface obtained in step 2 and screening out point sets outside the original hub end area from the discrete point data of the rotating guide vane root; Step 4: projecting the point sets outside the original hub end area onto the hub end wall and projecting the points outside the original hub end area onto the hub end wall to obtain lower boundaries of the hub and the hub end area; Step 4-1: projecting the points outside the hub end area obtained in step 3 onto the hub end wall to form a new point set with the data points of the original tip end surface, selecting an outer contour of the point set, connecting the contour into a closed curve as a lower boundary curve of the hub end area; Step 4-2: projecting the points outside the hub end area obtained in step 3 onto the hub end wall to form a new point set with the data points of the original root end surface, selecting an outer contour of the point set, connecting the contour into a closed curve as a lower boundary curve of the hub end area; Step 5: selecting the points of the outermost boundary from the points outside the hub end area as upper boundaries of the new hub end area and selecting the points of the outermost boundary from the points outside the hub end area as upper boundaries of the new hub end area; Step 5-1: selecting an outer contour of the point set of the points outside the hub end area obtained in step 3 as an upper boundary curve of the hub end area; Step 5-2: selecting an outer contour of the point set of the points outside the hub end area obtained in step 3 as an upper boundary curve of the hub end area; Step 6: constructing new hub and hub end areas from the upper and lower boundary curves of the hub and the hub end area obtained in steps 4 and 5 and the original hub and hub end wall.

2. A variable geometry turbine end region configuration method according to claim 1, wherein, The step 1 specifically comprises: Step 1-1: obtaining tangent surfaces of original blades and a hub and a hub as guide vane tip and root end surfaces in modeling software; Step 1-2: exporting the end surfaces to matlab and obtaining triangulation and discrete point data of the guide vane tip and root end surfaces and the hub and hub end wall by using an stlread function.

3. A variable geometry turbine end region configuration method according to claim 2, wherein, The step 2 specifically comprises: The coordinates of the point that needs to be rotated are P(x, y, z), and the unitized vector of the rotation axis is The coordinates of the starting point of the rotation axis are origin(origin x ,origin y ,origin z ), and the rotation angle is alpha, and alph is the form conversion of alpha, which is converted from the degree form to the π form; alph = alpha * pi / 180 sina = sin(alph) cosa = cos(alph) vera = 1-cosa Wherein, a represents a simplified form of alph, and pi represents π; The rotating matrix is: P rot = (x rot ,y rot ,z rot ) = (x-origin x ,y-origin y ,z-origin z )*T where P rot denotes the coordinates after rotation without considering the starting point coordinates; The obtained rotated coordinates are: P new = (x new ,y new ,z new ) = (x rot + origin x ,y rot + origin y ,z rot + origin z ).

4. A variable geometry turbine end region configuration method according to claim 3, wherein, The step 3 specifically comprises: Step 3-1: obtaining point sets of the guide vane tip end surface rotated at a series of discrete angles by step 2, judging whether the points are outside the original hub end area, discarding the points if the points are inside the hub end area or on the hub end wall, and retaining the points if the points are outside the hub end area; Step 3-2: Determine whether the points obtained by rotating the hub end face a series of discrete angles in step 2 are outside the original hub end area. If they are inside the hub end area or on the hub end wall, discard them. If they are outside the hub end area, keep them.

5. A variable geometry turbine end region configuration method according to claim 4, wherein, The step 6 is specifically: Step 6-1: Create an upper boundary surface from the upper boundary curve: fill the surface, N-edge surface function in the modeling software to create an upper boundary surface between the upper boundary curves; Step 6-2: Create a transition surface between the upper and lower boundary curves from the upper and lower boundary curves: the upper and lower boundary curves are irregular three-dimensional curves, and the transition surface between the upper and lower boundary curves of the casing and the hub is created by sweeping, curve group and N-edge surface respectively; Step 6-3: Create a lower boundary surface from the lower boundary curve and the original casing and hub end wall: the lower boundary curve at the casing is contained in the original casing end wall, delete the casing part contained in the lower boundary curve, and the deleted casing end wall serves as the lower boundary surface of the casing; the lower boundary curve at the hub is contained in the original hub end wall, delete the hub part contained in the lower boundary curve, and the deleted hub end wall serves as the lower boundary surface of the casing; Step 6-4: Obtain a new casing and hub end area configuration: stitch the casing upper boundary surface, transition surface and casing lower boundary surface as a new casing end area configuration, and stitch the hub upper boundary surface, transition surface and hub lower boundary surface as a new hub end area configuration.

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