CN112560195A - Modeling method for non-axisymmetric end wall of axial-flow impeller - Google Patents

Modeling method for non-axisymmetric end wall of axial-flow impeller Download PDF

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CN112560195A
CN112560195A CN202011430838.6A CN202011430838A CN112560195A CN 112560195 A CN112560195 A CN 112560195A CN 202011430838 A CN202011430838 A CN 202011430838A CN 112560195 A CN112560195 A CN 112560195A
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end wall
axial
cax
blade
axisymmetric
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黄松
周创鑫
阳诚武
赵胜丰
卢新根
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Institute of Engineering Thermophysics of CAS
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/26—Rotors specially for elastic fluids
    • F04D29/32—Rotors specially for elastic fluids for axial flow pumps
    • F04D29/325—Rotors specially for elastic fluids for axial flow pumps for axial flow fans
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/26—Rotors specially for elastic fluids
    • F04D29/32—Rotors specially for elastic fluids for axial flow pumps
    • F04D29/38—Blades
    • F04D29/384—Blades characterised by form
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Abstract

The invention provides a non-axisymmetric end wall modeling method of an axial flow impeller, which comprises the steps of firstly dividing a configuration area for end wall molded surfaces with different concave-convex shapes, flexibly constructing various complex end wall structures by adopting a circumferential three-order Fourier series curve on the basis of less variables, then reading the three-order Fourier series curve along the circumferential direction of a blade, and smoothly connecting the three-order Fourier series curve with a sample strip curve in the axial direction to form the non-axisymmetric end wall modeling. The mode that the third-order Fourier series curve is adopted in the circumferential direction accords with the distribution rule of a pressure field of a blade channel, the axial section area of a flow channel is kept almost unchanged, the total loss near the end wall is reduced, the flow separation of air flow is reduced, the outlet flow field and the air flow angle are more uniform, and the performance of a fan and the performance of a compressor blade are improved.

Description

Modeling method for non-axisymmetric end wall of axial-flow impeller
Technical Field
The invention belongs to the technical field of design of aero-engines, and particularly relates to a method for molding a non-axisymmetric end wall of an axial-flow impeller, which is particularly suitable for molding the non-axisymmetric end wall of impellers such as fans, gas compressors and the like. Various complex end wall structures are flexibly constructed by adopting a circumferential three-order Fourier series curve, and then the three-order Fourier series curves at different axial positions are connected by spline curves in sequence to form a non-axisymmetric end wall model.
Background
With the rapid development of modern aviation technology, fans and compressors are required to have higher adiabatic efficiency and stall margin. Reducing flow separation and aerodynamic losses of the fan and compressor blades is an important means to improve compressor efficiency and stall margin. In general, a large secondary flow loss is easily formed near the end walls of the fan and the compressor due to a large load, and accounts for about one third of the total loss of the blade cascade. Accordingly, various researchers have proposed various related techniques for reducing endwall losses and flow separation, such as swept blades, tandem blades, non-axisymmetric endwall configurations, and the like.
The basic principle of the non-axisymmetrical end wall structure is that concave-convex curved surfaces are applied to the end walls, so that the local change of the flow area of a flow channel is realized, the distribution of the pressure gradient of a flow field near the pressure surface and the suction surface of a blade is improved, and the purposes of inhibiting the transverse pressure gradient and the secondary flow are realized. In 1994, Rose first performed non-axisymmetric end wall modeling on a turbine blade cascade, and researches indicate that the non-axisymmetric end wall modeling can enable a pressure field in a turbine blade cascade channel to be more uniform. Chinese patent No. 101925723, filed by mitsubishi heavy industry co, japan, discloses an end wall of a turbine cascade, which can reduce secondary flow loss of a turbine and improve the performance of the turbine. However, this turbine cascade endwall has a narrow applicability. At present, the method is applied to a turbine more and applied to a compressor and a fan less. Some patents in China also propose some non-axisymmetric end wall methods of sine trigonometric functions tried to turbine/compressor blade cascades and fan rotors, and the flexibility of constructing complex profiles is still to be improved because a circumferential control curve is based on the sine function. In summary, in the early related research, most of the research focuses on the proposed non-axisymmetric end wall structure, and the research on the modeling method for reducing flow separation and aerodynamic loss by the non-axisymmetric end wall modeling technology is less, so that a flexible modeling method for constructing a complex end wall structure is required to play the roles of reducing the loss and flow separation of the fan and the compressor blade by the non-axisymmetric end wall, and improve the efficiency and stall margin of the fan and the compressor.
Disclosure of Invention
The technical problem to be solved by the invention is as follows:
the invention provides a modeling method of an axial flow impeller non-axisymmetric end wall based on a Fourier series curve, aiming at the problems that the existing modeling method of the axial flow impeller non-axisymmetric end wall can not flexibly construct a complex end wall structure and can not play the role of the non-axisymmetric end wall in reducing the pneumatic loss and the flow separation of axial flow impellers such as fans and gas compressors. Through adopting the third-order Fourier series curve at the different axial position of axial compressor impeller end wall, can construct all kinds of complicated end wall structures in a flexible way under the prerequisite of using less variable, the mode of Fourier series accords with the distribution law of blade passageway pressure field, is favorable to keeping the axial cross sectional area of runner nearly unchangeable, reduces near the total loss of end wall, reduces the flow separation of air current for export flow field and air current angle are more even, promote axial compressor impeller's aerodynamic performance.
The technical scheme adopted by the invention for solving the technical problem is as follows:
a method for molding a non-axisymmetric end wall of an axial-flow impeller, the axial-flow impeller including at least one end wall, at least one blade row being axially arranged outside the end wall, each blade row including a plurality of blades uniformly distributed in a circumferential direction of the end wall, the method comprising at least the steps of:
SS1. setting the end walls between all adjacent blades of each blade row to have the same-shaped end wall shape;
SS2. in each blade row, the end wall between two adjacent blades is used as a modeling end wall channel, and non-axisymmetric end wall modeling is carried out in the modeling end wall channel, so that the surface of the modeling end wall channel is provided with a plurality of concave-convex structures, and the method specifically comprises the following steps:
step SS 21: in a molding end wall channel, dividing an end wall area into a plurality of sub-areas along the axial direction, wherein each axial sub-area has a different axial position;
step SS 22: and respectively constructing a third-order Fourier series curve extending along the circumferential direction as a circumferential control line for different axial subregions divided in the step SS21 according to different axial positions of the axial subregions, wherein the third-order Fourier series curve is constructed by adopting the following formula:
Figure BDA0002820552960000031
where Δ r is the depth of the end wall depressions and projections, s is the scaling factor, aiAnd biIs a Fourier coefficient, l is the circumferential distance from a reference point, and p is the circumferential grid distance of one blade channel;
step SS 23: and (3) sequentially connecting the three-order Fourier series curves which are constructed in the step (21) and have different axial positions and extend along the circumferential direction in a smooth transition mode by using spline curves in the axial direction to form a non-axisymmetric end wall curved surface structure.
In a further improvement of the present invention, in step SS2, axial subregions are divided by axial positions of-20% Cax, 0% Cax, 20% Cax, 40% Cax, 60% Cax, 80% Cax, 100% Cax and 120% Cax, respectively, in a shaping end wall channel, and three-step fourier series curves extending in the circumferential direction are constructed at the axial positions as circumferential control lines to finally define a shaping region of the non-axisymmetric end wall, wherein Cax represents the axial distance from the leading edge of the blade to the trailing edge of the blade, 0% Cax represents the axial position of the leading edge of the blade, 100% Cax represents the axial position of the trailing edge of the blade, and-20% Cax, 40% Cax, 60% Cax and 80% Cax represent different axial positions from the leading edge of the blade, respectively.
A further development of the invention consists in that in step SS22 the maximum depth Δ r of the end wall depressions and elevations formed by a circumferential Fourier series curvemaxPreferably 3-8% of the spanwise height of the blade.
The invention is further improved in that in step SS22, the starting point of the circumferential Fourier series curve can be selected at any position of the blade channel, and the non-axisymmetric end wall can be constructed more flexibly.
In a further development of the invention, in step SS22, the starting point of the circumferential fourier series curve is preferably located on the suction side of the blade duct and the end point is preferably located on the pressure side of the blade duct.
In step SS23, the circumferential Fourier series curves of different axial positions constructed in step 21 are smoothly and transitionally connected in the axial direction by spline curves to form a non-axisymmetric end wall curved surface structure.
The invention is further improved in that the method for shaping the non-axisymmetric end wall is suitable for fans, low-pressure compressors, medium-pressure compressors, rotors and stator blades of high-pressure compressors.
Another object of the present invention is to provide a non-axisymmetric end wall of an axial-flow impeller, which is shaped based on the above-described non-axisymmetric end wall shaping method.
Still another object of the present invention is to provide an axial-flow impeller, wherein the end wall of the axial-flow impeller is a non-axisymmetric end wall molded by the above-described non-axisymmetric end wall molding method.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a method for molding a non-axisymmetric end wall of an axial-flow impeller, in particular a Fourier series curve for controlling the change of the molding surface of a circumferential end wall.
Drawings
Fig. 1 is a schematic view of a compressor wheel structure prior to endwall modification.
Fig. 2 is a schematic diagram of a fourier series of sin terms of order 1.
FIG. 3 is a schematic diagram of a Fourier series of sin and cos terms of order 1.
Fig. 4 is a schematic diagram of a fourier series of sin terms of order 2.
FIG. 5 is a schematic diagram of a Fourier series of sin and cos terms of order 3.
FIG. 6 is a schematic view of a compressor wheel employing non-axisymmetric endwalls.
FIG. 7 is a graph of total pressure loss for a forward and aft airfoil utilizing non-axisymmetric endwalls.
Detailed Description
The following detailed description of the preferred embodiments of the present invention, taken in conjunction with the accompanying drawings and technical principles, enables those skilled in the art to more readily understand the advantages and features of the present invention, and thus to more clearly and clearly define the scope of the invention.
The invention aims to provide a method for molding a non-axisymmetric end wall of an axial-flow impeller, which is particularly suitable for molding the non-axisymmetric end wall of impellers such as a fan, an air compressor and the like in an aircraft engine. Aiming at the problem that the existing axial-flow impeller non-axisymmetric end wall modeling method cannot flexibly build a complex end wall structure and cannot play the role of the non-axisymmetric end wall in reducing the blade loss and flow separation of axial-flow impellers such as fans and gas compressors, the invention adopts a circumferential three-order Fourier series curve and adopts the three-order Fourier series curve at different axial positions of the end wall of the axial-flow impeller, flexibly builds various complex end wall structures on the premise of applying less variables, and then sequentially connects the three-order Fourier series curves at different axial positions by spline curves to form the non-axisymmetric end wall modeling. The Fourier series mode accords with the distribution rule of the pressure field of the blade channel, the axial section area of the flow channel is kept almost unchanged, the total loss near the end wall is reduced, the flow separation of the airflow is reduced, the outlet flow field and the airflow angle are more uniform, and the aerodynamic performance of the axial flow impeller is improved.
Specifically, the method for modeling the non-axisymmetric end wall of the axial-flow impeller according to the present invention is to construct a non-axisymmetric end wall of an axial-flow impeller, such as a compressor stator impeller, as shown in fig. 1, where the compressor stator impeller includes an end wall 1, at least one blade row is axially arranged outside the end wall 1, each blade row includes a plurality of blades 2 uniformly distributed along the circumferential direction of the end wall 1, the end wall between all adjacent blades in each blade row is configured to have an end wall model with the same shape, and the end wall between two adjacent blades is used as a model end wall channel, that is, each blade channel has a plurality of concave-convex structures therein, and the method specifically includes the following steps when constructing a non-axisymmetric end wall structure of a compressor impeller, that is, when constructing a non-axisymmetric end wall in a blade:
step SS 21: in a molding end wall channel, dividing an end wall area into a plurality of sub-areas along the axial direction, wherein each axial sub-area has a different axial position;
step SS 22: and (3) respectively constructing three-order Fourier series curves extending along the circumferential direction for different axial subregions divided in the step SS21 according to different axial positions of the axial subregions as circumferential control lines, wherein each three-order Fourier series curve is constructed by adopting the following formula:
Figure BDA0002820552960000061
where Δ r is the depth of the end wall depressions and projections, s is the scaling factor, aiAnd biIs a Fourier coefficient, l is the circumferential distance from a reference point, and p is the circumferential grid distance of one blade channel;
step SS 23: and (3) smoothly transitionally connecting the three-order Fourier series curves which are constructed in the step (21) and have different axial positions and extend along the circumferential direction by using a spline curve in the axial direction to form a non-axisymmetric end wall curved surface structure.
More specifically, in step SS22, axial subregions are respectively divided by axial positions of-20% Cax, 0% Cax, 20% Cax, 40% Cax, 60% Cax, 80% Cax, 100% Cax and 120% Cax in a shaping end wall channel, and three-order fourier series curves extending along the circumferential direction are respectively constructed at the axial positions as circumferential control lines to finally enclose a shaping region of the non-axisymmetric end wall, wherein Cax represents the axial distance from the leading edge of the blade to the trailing edge of the blade, 0% Cax represents the axial position of the leading edge of the blade, and 100% Cax represents the axial position of the trailing edge of the blade, -20% Cax, 40% Cax, 60% Cax and 80% Cax represent different axial positions from the leading edge of the blade, respectively.
And, in step SS22, the maximum depth Δ r of the end wall concavity and convexity formed by the circumferential Fourier series curvemaxPreferably 3-8% of the spanwise height of the blade; the starting point of the circumferential Fourier series curve can be selected at any position of the blade channel, so that the non-axisymmetric end wall can be constructed more flexibly; the starting point of the circumferential Fourier series curve is preferably located on the suction side of the blade channel and the end point is preferably located on the pressure side of the blade channel. In step SS23, the circumferential fourier series curves at different axial positions constructed in step 21 are preferably smoothly blended in the axial direction with spline curves to form a non-axisymmetric endwall curved structure.
Example 1
A typical non-axisymmetric end wall configuration for a depression near the suction surface and a protrusion near the pressure surface is formed by the steps of:
step 1: in the shaping channel of an axisymmetric end wall 1 as shown in fig. 1, the end wall area is divided into several axial subregions. For example, the shaped regions of the non-axisymmetric endwalls are defined by circumferential control lines of-20%, 0%, 20%, 40%, 60%, 80%, 100%, 120% Cax, wherein 0% Cax represents the axial position of the leading edge of the blade and 100% Cax represents the axial position of the trailing edge of the blade. And the circumferential control line adopts a third-order Fourier series curve.
Step 2: and (3) respectively constructing three-order Fourier series curves at different axial positions of the end wall of the compressor impeller in the step (1), wherein the starting point of the Fourier series curve is positioned on the suction surface of the blade. The Fourier series curve adopts the formula:
Figure BDA0002820552960000071
and (4) constructing. Where Δ r is the depth of the end wall depressions and projections, s is the scaling factor, aiAnd biFor Fourier coefficients, l is the circumferential distance from the reference point and p is the circumferential pitch of one blade channel. The fourier series may take different forms, as can be seen in fig. 2-5.
And step 3: and (3) smoothly connecting the three-order Fourier curves at different axial positions in the step (2) along the circumferential direction of the end wall by using a spline curve to form a non-axisymmetric end wall structure.
The compressor wheel with the non-axisymmetric end wall 2 constructed by the method can be seen in fig. 6. The total pressure loss in the near-hub region is reduced and aerodynamic performance is improved compared to the original impeller, see fig. 7.
The object of the present invention is fully effectively achieved by the above embodiments. Those skilled in the art will appreciate that the present invention includes, but is not limited to, what is described in the accompanying drawings and the foregoing detailed description. While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications within the spirit and scope of the appended claims.

Claims (8)

1. A method for molding a non-axisymmetric end wall of an axial-flow impeller, the axial-flow impeller including at least one end wall, at least one blade row being axially arranged outside the end wall, each blade row including a plurality of blades uniformly distributed in a circumferential direction of the end wall, the method comprising at least the steps of:
SS1. setting the end walls between all adjacent blades of each blade row to have the same-shaped end wall shape;
SS2. in each blade row, the end wall between two adjacent blades is used as a modeling end wall channel, and non-axisymmetric end wall modeling is carried out in the modeling end wall channel, so that the surface of the modeling end wall channel is provided with a plurality of concave-convex structures, and the method specifically comprises the following steps:
step SS 21: in a molding end wall channel, dividing an end wall area into a plurality of sub-areas along the axial direction, wherein each axial sub-area has a different axial position;
step SS 22: and respectively constructing a third-order Fourier series curve extending along the circumferential direction as a circumferential control line for different axial subregions divided in the step SS21 according to different axial positions of the axial subregions, wherein the third-order Fourier series curve is constructed by adopting the following formula:
Figure FDA0002820552950000011
where Δ r is the depth of the end wall depressions and projections, s is the scaling factor, aiAnd biIs a Fourier coefficient, l is the circumferential distance from a reference point, and p is the circumferential grid distance of one blade channel;
step SS 23: and (3) sequentially and smoothly transitionally connecting the three-order Fourier series curves which are constructed in the step (21) and have different axial positions and extend along the circumferential direction by spline curves in the axial direction to form a non-axisymmetric end wall curved surface structure.
2. The method of claim, wherein in step SS2, axial subregions are divided by axial positions of-20% Cax, 0% Cax, 20% Cax, 40% Cax, 60% Cax, 80% Cax, 100% Cax, 120% Cax, respectively, in one shaping endwall channel, and three-step Fourier series curves extending in the circumferential direction are constructed at these axial positions as circumferential control lines to finally define the shaping region of the non-axisymmetric endwall, wherein Cax represents the axial distance from the leading edge of the blade to the trailing edge of the blade, 0% Cax represents the axial position of the leading edge of the blade, 100% Cax represents the axial position of the trailing edge of the blade, and-20% Cax, 40% Cax, 60% Cax, and 80% Cax represent different axial positions from the leading edge of the blade.
3. Shaft according to the preceding claimA method of shaping a non-axisymmetric end wall of a flow impeller, characterized in that, in step SS22, a circumferential Fourier series curve forms the maximum depth Deltar of end wall concavity and convexitymaxPreferably 3-8% of the spanwise height of the blade.
4. The method for shaping the non-axisymmetric end wall of an axial-flow impeller in accordance with the previous claim, wherein in step SS22, the starting point of the circumferential Fourier series curve can be selected at any position of the blade passage, thereby more flexibly constructing the non-axisymmetric end wall.
5. The method of claim, wherein in step SS22, the starting point of the circumferential Fourier series curve is preferably located at the suction side of the vane passage and the ending point is preferably located at the pressure side of the vane passage.
6. The method for shaping a non-axisymmetric end wall of an axial-flow impeller according to the above claim, wherein in step SS23, the circumferential Fourier series curves of different axial positions constructed in step 21 are successively and smoothly transitionally connected in the axial direction by spline curves to form a non-axisymmetric end wall curved surface structure.
7. A non-axisymmetric end wall of an axial-flow impeller, characterized in that said non-axisymmetric end wall is shaped according to the method of any of the preceding claims.
8. An axial flow impeller wherein the end wall of the axial flow impeller is the non-axisymmetric end wall of claim 7.
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CN115081130A (en) * 2022-06-01 2022-09-20 中国科学院工程热物理研究所 Blade and end wall combined pneumatic optimization method based on dynamic support vector regression

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113027785A (en) * 2021-04-08 2021-06-25 西安交通大学 Centrifugal compressor stability expanding method for end wall of dual-function coupling profile control diffuser
CN115081130A (en) * 2022-06-01 2022-09-20 中国科学院工程热物理研究所 Blade and end wall combined pneumatic optimization method based on dynamic support vector regression
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