CN112364462B - Reverse design method of non-axisymmetric end wall - Google Patents
Reverse design method of non-axisymmetric end wall Download PDFInfo
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Abstract
A method of reverse design of a non-axisymmetric end wall comprising the steps of: step 1, obtaining pressure distribution of an end wall; step 2, determining an improvement area of the end wall by analyzing the pressure distribution of the end wall; step 3, establishing a corresponding relation between the height distribution of the non-axisymmetric end wall and the pressure distribution, and obtaining the height distribution of the improved area; step 4, fitting a curved surface of the non-symmetric end wall according to the height distribution of the improved area; step 5, forming an initial design of a non-axisymmetric end wall molded line; and 6, optimizing the initial design of the non-axisymmetric end wall molded line. The reverse design method provided by the invention directly generates the non-axisymmetric end wall curved surface according to the end wall flow characteristics, and compared with the traditional forward design method, the calculation resource and calculation time are greatly reduced.
Description
Technical Field
The invention belongs to the field of non-axisymmetric end wall design, and particularly relates to a reverse design method of a non-axisymmetric end wall.
Background
The non-axisymmetric end wall design is an effective end-region secondary flow control technique. The pressure distribution of the end wall is adjusted by changing the local geometric shape of the end wall, so that the aim of inhibiting the secondary flow of the end wall is fulfilled, the flow state of the main flow is changed to a large extent, the flow field quality is improved, and the unit performance is improved.
The currently common non-axisymmetric end wall design method is a non-axisymmetric end wall modeling method, and is a typical forward design method, as shown in fig. 1. Firstly, a designer selects a generation method of a non-axisymmetric end wall curved surface according to engineering experience, generates a new non-axisymmetric end wall curved surface by adjusting control points of the curved surface, calculates to obtain the flow state of a main flow, and if the performance of the unit does not meet the design requirement, readjust the control points of the curved surface and calculate the flow state of the main flow until the performance of the unit meets the design requirement. This forward design approach requires a significant amount of computational resources and computation time.
Disclosure of Invention
The invention aims to solve the problems that the design method of the non-axisymmetric end wall consumes calculation resources and has more calculation time in the prior art, and provides a reverse design method of the non-axisymmetric end wall, so that the rapid design of the non-axisymmetric end wall is realized.
In order to achieve the above purpose, the present invention has the following technical scheme:
a method of reverse design of a non-axisymmetric end wall comprising the steps of:
step 1, obtaining pressure distribution of an end wall;
step 2, determining an improvement area of the end wall by analyzing the pressure distribution of the end wall;
step 3, establishing a corresponding relation between the height distribution of the non-axisymmetric end wall and the pressure distribution, and obtaining the height distribution of the improved area;
step 4, fitting a curved surface of the non-symmetric end wall according to the height distribution of the improved area;
step 5, forming an initial design of a non-axisymmetric end wall molded line;
and 6, optimizing the initial design of the non-axisymmetric end wall molded line.
As a preferred embodiment of the reverse design method of the present invention, the pressure distribution of the end wall is obtained by a numerical method, a test method or a theoretical method according to the environmental condition in which the end wall is located.
As a preferred scheme of the reverse design method of the present invention, the correspondence between the non-axisymmetric end wall height distribution and the pressure distribution in the step 3 is established in the following manner:
step 3.1, assuming that the end wall modification region has 4 boundary lines, wherein there are 2 boundary lines along the main flow direction, respectively P p And P s Has 2 boundary lines approximately perpendicular to the main flow direction, O respectively p And O s ；
Selecting a multipoint pressure P on the high pressure side of the end wall modified region boundary along the main flow direction according to the pressure distribution at the end wall p1 、P p2 、P p3 、……P pn And a multipoint pressure P on the low pressure side s1 、P s2 、P s3 、……P sn Wherein n is the number of pressure points of the modified zone boundary in the main flow direction; selecting a multipoint pressure O on the high pressure side of the end wall modification region boundary approximately perpendicular to the main flow direction p1 、O p2 、O p3 、……O pm And multipoint pressure O on the low pressure side s1 、O s2 、O s3 、……O sm Wherein m is the number of pressure points at which the modified zone boundary is approximately perpendicular to the main flow direction;
step 3.2, calculating the pressure difference ΔP at each point along the main flow direction of the boundary of the end wall modification region as follows i ：
ΔP i ＝P pi -P si
Where i is the i-th point pressure of the end wall modification zone boundary along the main flow direction, i=1, 2,3, … … n;
step 3.3, calculating the pressure difference ΔP at each point of the end wall modification region boundary approximately perpendicular to the main flow direction as follows i ：
ΔO i ＝O pi -O si
Where i is the i-th pressure at which the end wall modification zone boundary is approximately perpendicular to the main flow direction, i=1, 2,3, … … m;
step 3.4, taking the dimensionless number x representing the position point of the boundary of the end wall improvement region along the main flow direction as the abscissa, and taking the ordinate as the pressure difference delta P at each position point i Fitting to a smooth continuous curve F p (x)；
Step 3.5, taking the dimensionless number x representing the position point of the boundary of the end wall improving region approximately perpendicular to the main flow direction as the abscissa, and taking the ordinate as the pressure difference value delta O at each position point i Fitting to a smooth continuous curve F O (x)；
Step 3.6 height distribution H of the end wall modification region at different locations max (x) And curve F p (x)、F O (x) Proportional to the ratio.
As a preferred embodiment of the reverse design method of the present invention, the positions of the high-side pressure point and the low-side pressure point of the end wall improvement region boundary are sequentially arranged along one direction.
As a preferred embodiment of the reverse design method of the present invention, the end wall modified region is bounded by the same number of high side pressure points and low side pressure points.
As a preferable scheme of the reverse design method of the invention, the fitting curve F p (x)、F O (x) Is a straight line, a spline curve, a Bezier curve or a B spline curve.
As a preferable mode of the reverse design method of the invention, the fitting curve F p (x)、F O (x) The coefficient of (2) is a controllable parameter, and can be adjusted and controlled.
As a preferred scheme of the reverse design method of the invention, the optimized design in the step 6 is verified by the initial design formed in the step 5, and when the design requirement is met, a final scheme of the non-axisymmetric end wall is formed; and when the design requirement is not met, returning to the step 3 to optimize the controllable parameters in the corresponding relation between the non-axisymmetric end wall height distribution and the end wall pressure distribution until the design scheme of the non-axisymmetric end wall meets the design requirement.
As a preferred scheme of the reverse design method, in the step 5, when the non-axisymmetric end wall molded line is formed, smooth transition between an improved area and a non-improved area of the end wall is ensured, and if smooth transition cannot be ensured, smoothing treatment is carried out on the non-axisymmetric end wall molded line.
As a preferred embodiment of the reverse design method of the present invention, the modified region of the end wall is defined in one or more localized regions of the end wall or covers the entire end wall.
Compared with the prior art, the invention has at least the following beneficial effects: the non-axisymmetric end wall rapidly forms an initial scheme of the non-axisymmetric end wall according to the end wall pressure calculation result through flow characteristic analysis of the end wall, and rapidly obtains a final design scheme after optimal design. The reverse design method provided by the invention directly generates the non-axisymmetric end wall curved surface according to the end wall flow characteristics, and compared with the traditional forward design method, the calculation resource and calculation time are greatly reduced.
Drawings
FIG. 1 is a flow chart of a prior art non-axisymmetric end wall design method;
FIG. 2 is a flow chart of the reverse design method of the invention for a non-axisymmetric end wall;
FIG. 3 is a flow chart of an embodiment of the invention in which the height profile and pressure profile correspondence of the non-axisymmetric end walls is established;
FIG. 4 is a schematic diagram of the correspondence between the height distribution of the non-axisymmetric end wall and the pressure distribution at the end wall of the present invention;
fig. 5 is a schematic representation of the end wall modification zone selection of the method of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples. The described embodiments are part of embodiments of the invention, to which the invention is not limited in its application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a reverse design method of a non-axisymmetric end wall, as shown in fig. 2, comprising the following steps:
step 101, obtaining a pressure distribution at the end wall according to the environmental conditions in which the end wall is located.
Wherein the pressure profile at the end wall may be obtained numerically, experimentally, theoretically or otherwise.
Step 102, determining an improved area of the end wall by analyzing the pressure distribution at the end wall.
Wherein the end wall modification region may be defined in one or more partial regions of the end wall, or may cover the entire end wall.
And 103, establishing a corresponding relation between the height distribution of the non-axisymmetric end wall and the pressure distribution at the end wall.
Referring to fig. 3 to 5, the main steps of this embodiment include:
step 301, the end wall modification region 403 has 4 boundary lines, wherein there are 2 boundary lines 410 and 413, respectively P, along the main flow direction 401 p And P s Approximately perpendicular to the main flow direction 402 there are 2 boundary lines 411 and 412, respectively O p And O s 。
Selecting a multipoint pressure P of the high pressure side 410 of the end wall modification region 403 boundary along the main flow direction 401 according to the pressure distribution at the end wall p1 、P p2 、P p3 、……P pn And a multipoint pressure P at the low pressure side 413 s1 、P s2 、P s3 、……P sn Where n is the number of pressure points along the main flow direction 401 at the boundary of the modified zone 403; selecting a multipoint pressure O at the boundary of the end wall modification region 403 approximately perpendicular to the high pressure side 412 of the main flow direction 402 p1 、O p2 、O p3 、……O pm And multipoint pressure O at low pressure side 411 s1 、O s2 、O s3 、……O sm Where m is the number of pressure points at which the modified zone 403 boundary is approximately perpendicular to the main flow direction 402.
Step 302, calculating the pressure difference ΔP at each point along the main flow direction 401 at the boundary of the end wall modification region 403 i ：
ΔP i ＝P pi -P si
Where i is the i-th point pressure along the main flow direction 401 at the boundary of the end wall modification region 403, i=1, 2,3, … … n.
Step 303, calculating the pressure difference ΔP at each point of the end wall modification region 403 boundary approximately perpendicular to the main flow direction 402 i ：
ΔO i ＝O pi -O si
Where i is the i-th pressure at which the end wall modification region 403 boundary is approximately perpendicular to the main flow direction 402, i=1, 2,3, … … m.
Step 304, taking the dimensionless number x representing the position point of the boundary of the end wall improving region 403 along the main flow direction 401 as the abscissa, and taking the ordinate as the pressure difference deltap at each position point i Fitting to a smooth continuous curve F p (x)407；
Step 305, taking the dimensionless number x representing the point of the end wall modification region boundary 403 approximately perpendicular to the main flow direction 402 as the abscissa, the ordinate being the pressure difference Δo at each point i Fitting to a smooth continuous curve F O (x)406；
Step 306, height distribution H of end wall modification region at different locations max (x) 410 and curve F p (x)407、F O (x) 406 is proportional.
Step 104, fitting to a curved surface of the non-symmetric end wall according to the height distribution at the end wall improvement area.
Wherein the positions of the high side pressure point and the low side pressure point of the heavy end wall modified region boundary 403 in step 301 are sequentially arranged along one direction, and the number along one direction is the same.
Fitting curve F in step 304 and step 305 p (x)、F O (x) May be a straight line, spline curve, bezier curve, B-spline curve, and other curve types, and fit the curve F p (x)、F O (x) The coefficient of (2) is a controllable parameter, and can be adjusted and controlled.
Step 105, an initial version of the non-axisymmetric end wall is formed.
The molded line of the non-axisymmetric end wall needs to ensure smooth transition between an improved area and a non-improved area of the end wall, if smooth transition cannot be ensured, the molded line of the non-axisymmetric end wall needs to be subjected to fairing treatment.
Step 106, optimizing design of an initial scheme of the non-axisymmetric end wall.
The optimization design of the initial scheme of the non-axisymmetric end wall comprises the following steps:
checking the initial scheme of the non-axisymmetric end wall formed in the step 105, and forming a final scheme of the non-axisymmetric end wall when the initial scheme of the non-axisymmetric end wall meets the design requirement;
and when the initial scheme of the non-axisymmetric end wall does not meet the design requirement, returning to the step 103 to control and optimize the controllable parameters in the corresponding relation between the height distribution of the non-axisymmetric end wall and the pressure distribution of the end wall until the design scheme of the non-axisymmetric end wall meets the design requirement.
When the initial scheme of the non-axisymmetric end wall does not meet the design requirement, other optimization design methods can be adopted to further improve and optimize the initial scheme of the non-axisymmetric end wall until the design scheme of the non-axisymmetric end wall meets the design requirement.
In the design method, the non-axisymmetric end wall rapidly forms an initial scheme of the non-axisymmetric end wall according to the end wall pressure calculation result through analyzing the end wall flow characteristics, and rapidly obtains a final design scheme after the optimal design.
The foregoing description of the preferred embodiment of the present invention is not intended to limit the technical solution of the present invention in any way, and it should be understood by those skilled in the art that the technical solution can be modified and replaced in several ways without departing from the spirit and principle of the present invention, and the modifications and the replacements are all within the scope of protection covered by the claims.
Claims (9)
1. A method of reverse design of a non-axisymmetric end wall, comprising the steps of:
step 1, obtaining pressure distribution of an end wall;
step 2, determining an improvement area of the end wall by analyzing the pressure distribution of the end wall;
step 3, establishing a corresponding relation between the height distribution of the non-axisymmetric end wall and the pressure distribution, and obtaining the height distribution of the improved area;
the correspondence between the height distribution and the pressure distribution of the non-axisymmetric end wall is established in the following manner:
step 3.1, assuming that the end wall modification region has 4 boundary lines, wherein there are 2 boundary lines along the main flow direction, respectively P p And P s Has 2 boundary lines approximately perpendicular to the main flow direction, O respectively p And O s ；
Selecting a multipoint pressure P on the high pressure side of the end wall modified region boundary along the main flow direction according to the pressure distribution at the end wall p1 、P p2 、P p3 、……P pn And a multipoint pressure P on the low pressure side s1 、P s2 、P s3 、……P sn Wherein n is the number of pressure points of the modified zone boundary in the main flow direction; selecting a multipoint pressure O on the high pressure side of the end wall modification region boundary approximately perpendicular to the main flow direction p1 、O p2 、O p3 、……O pm And multipoint pressure O on the low pressure side s1 、O s2 、O s3 、……O sm Wherein m is the number of pressure points at which the modified zone boundary is approximately perpendicular to the main flow direction;
step 3.2, calculating the pressure difference ΔP at each point along the main flow direction of the boundary of the end wall modification region as follows i ：
ΔP i ＝P pi -P si
Where i is the i-th point pressure of the end wall modification zone boundary along the main flow direction, i=1, 2,3, … … n;
step 3.3, calculating the pressure difference ΔP at each point of the end wall modification region boundary approximately perpendicular to the main flow direction as follows i ：
ΔO i ＝O pi -O si
Where i is the i-th pressure at which the end wall modification zone boundary is approximately perpendicular to the main flow direction, i=1, 2,3, … … m;
step 3.4, taking the dimensionless number x representing the position point of the boundary of the end wall improvement region along the main flow direction as the abscissa, and taking the ordinate as the pressure difference delta P at each position point i Fitting to a smooth continuous curve F p (x)；
Step 3.5, taking the dimensionless number x representing the position point of the boundary of the end wall improving region approximately perpendicular to the main flow direction as the abscissa, and taking the ordinate as the pressure difference value delta O at each position point i Fitting to a smooth continuous curve F O (x)；
Step 3.6 height distribution H of the end wall modification region at different locations max (x) And curve F p (x)、F O (x) Proportional to the ratio;
step 4, fitting a curved surface of the non-symmetric end wall according to the height distribution of the improved area;
step 5, forming an initial design of a non-axisymmetric end wall molded line;
and 6, optimizing the initial design of the non-axisymmetric end wall molded line.
2. The method of reverse design of a non-axisymmetric end wall according to claim 1, wherein: the pressure distribution of the end wall is obtained by adopting a numerical method, a test method or a theoretical method according to the environmental condition of the end wall.
3. The method of reverse design of a non-axisymmetric end wall according to claim 1, wherein:
the positions of the high-pressure side pressure point and the low-pressure side pressure point of the end wall improvement area boundary are sequentially arranged along one direction.
4. The method of reverse design of a non-axisymmetric end wall according to claim 1, wherein:
the end wall modified region borders the same number of high side pressure points and low side pressure points.
5. The method of reverse design of a non-axisymmetric end wall according to claim 1, wherein:
the fitting curve F p (x)、F O (x) Is a straight line, a spline curve, a Bezier curve or a B spline curve.
6. The method of reverse design of a non-axisymmetric end wall according to claim 1, wherein:
the fitting curve F p (x)、F O (x) The coefficient of (2) is a controllable parameter, and can be adjusted and controlled.
7. The method of reverse design of a non-axisymmetric end wall according to claim 6, wherein: the optimal design in the step 6 is verified through the initial design formed in the step 5, and when the design requirement is met, a final scheme of the non-axisymmetric end wall is formed; and when the design requirement is not met, returning to the step 3 to optimize the controllable parameters in the corresponding relation between the non-axisymmetric end wall height distribution and the end wall pressure distribution until the design scheme of the non-axisymmetric end wall meets the design requirement.
8. The method of reverse design of a non-axisymmetric end wall according to claim 1, wherein:
and 5, when the non-axisymmetric end wall molded line is formed, ensuring smooth transition of an improved area and a non-improved area of the end wall, and if smooth transition cannot be ensured, carrying out fairing treatment on the non-axisymmetric end wall molded line.
9. The method of reverse design of a non-axisymmetric end wall according to claim 1, wherein: the modified region of the end wall is defined in one or more localized regions of the end wall or covers the entire end wall.
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