WO2019196919A1 - Ultra-wide chord trigonometric waveform blade - Google Patents

Ultra-wide chord trigonometric waveform blade Download PDF

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Publication number
WO2019196919A1
WO2019196919A1 PCT/CN2019/082396 CN2019082396W WO2019196919A1 WO 2019196919 A1 WO2019196919 A1 WO 2019196919A1 CN 2019082396 W CN2019082396 W CN 2019082396W WO 2019196919 A1 WO2019196919 A1 WO 2019196919A1
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WO
WIPO (PCT)
Prior art keywords
blade
waveform
cotangent
ultra
tangent
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PCT/CN2019/082396
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French (fr)
Chinese (zh)
Inventor
向兵
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深圳福世达动力科技有限公司
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Publication of WO2019196919A1 publication Critical patent/WO2019196919A1/en

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    • 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
    • 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
    • F04D29/321—Rotors specially for elastic fluids for axial flow pumps for axial flow compressors
    • F04D29/324—Blades
    • 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
    • F04D29/28—Rotors specially for elastic fluids for centrifugal or helico-centrifugal pumps for radial-flow or helico-centrifugal pumps
    • F04D29/30—Vanes
    • 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
    • F04D29/386—Skewed blades
    • 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
    • F04D29/40—Casings; Connections of working fluid
    • F04D29/42—Casings; Connections of working fluid for radial or helico-centrifugal pumps
    • F04D29/44—Fluid-guiding means, e.g. diffusers
    • F04D29/441—Fluid-guiding means, e.g. diffusers especially adapted for elastic fluid pumps
    • F04D29/444—Bladed diffusers
    • 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
    • F04D29/40—Casings; Connections of working fluid
    • F04D29/52—Casings; Connections of working fluid for axial pumps
    • F04D29/54—Fluid-guiding means, e.g. diffusers
    • F04D29/541—Specially adapted for elastic fluid pumps
    • F04D29/542—Bladed diffusers
    • F04D29/544—Blade shapes
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2240/00—Components
    • F05D2240/10—Stators
    • F05D2240/12—Fluid guiding means, e.g. vanes
    • F05D2240/123—Fluid guiding means, e.g. vanes related to the pressure side of a stator vane
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2240/00—Components
    • F05D2240/10—Stators
    • F05D2240/12—Fluid guiding means, e.g. vanes
    • F05D2240/124—Fluid guiding means, e.g. vanes related to the suction side of a stator vane
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2240/00—Components
    • F05D2240/20—Rotors
    • F05D2240/30—Characteristics of rotor blades, i.e. of any element transforming dynamic fluid energy to or from rotational energy and being attached to a rotor
    • F05D2240/305—Characteristics of rotor blades, i.e. of any element transforming dynamic fluid energy to or from rotational energy and being attached to a rotor related to the pressure side of a rotor blade
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2240/00—Components
    • F05D2240/20—Rotors
    • F05D2240/30—Characteristics of rotor blades, i.e. of any element transforming dynamic fluid energy to or from rotational energy and being attached to a rotor
    • F05D2240/306—Characteristics of rotor blades, i.e. of any element transforming dynamic fluid energy to or from rotational energy and being attached to a rotor related to the suction side of a rotor blade

Definitions

  • the invention belongs to the field of fluid machinery, and relates to a blade of an impeller type compressor, in particular to an ultra-wide-string trigonometric waveform blade.
  • Impeller type compressors are generally divided into two types: radial flow type (ie centrifugal type) and axial flow type according to the direction of working fluid flow.
  • the centrifugal compressor has small volume, high impeller speed, high single-stage pressure ratio but low efficiency. It is usually suitable for medium and small flow applications and is widely used in power systems such as aviation and ships.
  • the axial flow compressor is compact in structure, easy to install more stages, single stage pressure is lower, and overall efficiency is higher, which is usually suitable for occasions with large flow.
  • the blades of the impeller compressor are usually divided into a moving blade and a stationary blade, wherein the moving blade rotates with the impeller, and the moving blade works on the gas working fluid to increase the pressure of the gaseous working fluid, and the stationary blade is stationary, and does not work on the gas working fluid.
  • the airflow working fluid is decelerated, diffused, and guided. Whether it is a moving blade or a stationary blade, its blade profile design has an important influence on the efficiency of the compressor.
  • the current axial flow compressor blade blade shape is usually a circular arc shape, and the blade blade is usually only suitable for working in Asia. With the speed of sound and transonic speed, as the Mach number of the working fluid gas rises, various flow losses such as separation of the surface layer in the flow channel increase rapidly, and the efficiency usually decreases rapidly, thereby limiting the further improvement of the single-stage pressure ratio.
  • the compressor has a long blade shape and is an ultra-wide-chord type.
  • the blade constructed with this type of blade belongs to an ultra-wide-chord blade.
  • the invention adopts a trigonometric function tangent or cotangent waveform curve surface to replace the traditional circular arc surface, and can obtain higher compression efficiency, and the axial flow compressor blade of the profile can obviously improve the single-stage compression ratio, and this
  • the profile is applied to the design of the bucket and diffuser blades of the centrifugal compressor, which can effectively improve the compression efficiency and has broad application prospects.
  • the blade can be regarded as being stacked by the blade type. Below we will first explain the blade shape of the blade, and then how to construct the blade from the blade shape.
  • An ultra-wide-string trigonometric waveform blade characterized in that the pressure surface of the blade leaf type is designed as a trigonometric tangent or a cotangent waveform curve structure, specifically whether the tangent or the cotangent is determined by the oblique direction of the airfoil, and the rightly inclined leaf
  • the type uses the cotangent waveform curve
  • the left-inclined leaf type uses the tangent waveform curve. Since the tangent or cotangent waveform curve is infinitely long and the length of the leaf type is limited, a section of the waveform curve is usually intercepted as a leaf type as needed.
  • the pressure surface; the tangent or cotangent waveform is periodic, the middle portion of each period is a curved arc, and the curvature of both sides is gradually reduced and gradually approaches the straight line.
  • the length of the tangential or cotangent waveform curve is intercepted from the middle of one cycle, and the lengths of the two ends are usually different. The interception is performed according to the design requirements. Generally, the higher the Mach number, the higher the curve.
  • the longer the back-end retention segment the smaller the folding angle of the inlet airflow to the outlet airflow becomes. The functional power will be reduced, so the length of the back-end reserved segment needs to strike a balance between power and efficiency.
  • the shape of the airfoil under the subsonic flow conditions and the shape of the airfoil under the supersonic flow conditions are also different.
  • the blade shape under subsonic flow conditions is generally slender, the thickness of the blade is usually not changed, and the waveform of the suction surface is similar or even the same.
  • the thickness of the leading edge of the blade is slightly thicker than the trailing edge. Generally designed as a small rounded structure, the trailing edge is generally designed as a pointed structure; the thickness of the blade type working under supersonic flow conditions is large, the first half of the blade is long and is designed as a sharp wedge structure.
  • the design can reduce the shock loss.
  • the thickness of the airfoil gradually increases from the leading edge to the middle. When the thickness is increased to the required thickness, the thickness of the downstream blade type generally decreases rapidly.
  • the pressure surface and suction surface of adjacent airfoils form a flow channel, and the shape of the airfoil under subsonic conditions and supersonic conditions is different, so the flow path will be different; under subsonic conditions
  • the flow channel is often designed as an expanded structure.
  • the inlet of the flow channel is a supersonic flow.
  • the first half of the flow path needs to be designed as a convergent structure, and the convergent flow channel is used to expand and lower the supersonic flow.
  • Speed when the incoming flow velocity is reduced to the speed of sound, the second half of the flow channel is designed as an expanded structure, which can further reduce the airflow velocity and further increase the static pressure. Therefore, the flow channel under the supersonic condition is first converged.
  • the expansion is a convergent expansion type flow passage, and the portion with the smallest flow area in the flow passage is generally called a throat. It should be noted that the convergent expansion type flow passage is mainly realized by changing the thickness of the blade type, and therefore, the height of the blade can be maintained. No change, or little change.
  • the design of the airfoil structure under subsonic conditions is relatively simple, because the thickness of the airfoil does not change much, and the waveforms of the suction and pressure surfaces of the blade are similar or even the same.
  • the suction surface design of the blade type under supersonic conditions is usually not unique. There are many different profile schemes, usually a smooth curve composed of multiple straight lines and arcs.
  • the pressure surface of the leaf type is the main working surface of the leaf type, and its profile is the main factor affecting the efficiency of the leaf type.
  • the suction has little influence on the efficiency, and there are various options available.
  • the pressure surface of the blade type of the present invention adopts a trigonometric function tangent or a cotangent waveform curve, the compression process of the airflow is smoother, so that a blade structure with high efficiency at subsonic speed can be designed; in the supersonic condition, the The waveform profile can avoid strong shock waves in the front-stage contraction flow channel, effectively reducing the negative factors such as shock-induced separation, eddy current, turbulence, etc., so it is also possible to design a high-efficiency airfoil structure under supersonic conditions; It is an ultra-wide-chord type, and the chord length is usually much longer than that of the existing axial-flow compressor, and it can work at a super-sonic condition with a higher Mach number, and the function can be greatly increased, so that the shaft can be
  • the suction side of the airfoil adopts another tangent or cotangent waveform of the same type as the pressure surface.
  • the period of this waveform is longer than the period of the pressure surface waveform, and there is a certain distance between the waveform of the pressure surface. If necessary, the angle of inclination can be different from the inclination angle of the waveform of the pressure surface.
  • the waveform of the suction surface and the waveform of the pressure surface are The leading and trailing edges of the leaf type intersect at two points. This design method of intersecting the two waveforms to obtain the airfoil can greatly reduce the complexity of the design of the suction surface of the airfoil, and the designed blade shape is generally more efficient.
  • the leaves are formed by stacking the leaves from the root to the tip of the blade. Since the line speeds of different leaf heights are different, the speed triangles will be different. Therefore, the installation angles of the leaf types at different leaf heights are usually different, and the leaf shapes can also be different. Therefore, the shape of the blades is usually distorted. .
  • One way to stack the leaf shape from the leaf root to the tip of the blade is to perform a straight line stacking.
  • This stacking method is relatively simple, and the leading edge of the blade is a straight line.
  • Another method is a curve stack, that is, there is a certain offset between the different leaf layers in the circumferential direction, and the leading edge of the blade is a curve.
  • a curve stack is employed, and specifically, the curve is a trigonometric sine or cosine waveform. From the root to the tip of the blade, the sine or cosine is usually stacked in a complete wave period. Considering the structural strength of the blade, the amplitude is usually not too large.
  • the sinusoidal or cosine wave blade structure is beneficial for converting the energy of the radial high-frequency wave in the working fluid in the blade channel into the static pressure of the working medium, and avoiding the multiple high-frequency radial waves being reflected and reflected between the top and bottom walls of the channel. For heat energy, the compression efficiency of the blade can be improved.
  • this swept-back blade design can effectively reduce the shock loss at the leading edge of the blade, while improving the performance of the blade strength and vibration.
  • the flow path formed by the ramjet inlet (diffuser), the aeroengine supersonic inlet and the impeller-type compressor impeller is similar. Therefore, the design of the supersonic inlet can be used for reference.
  • the design method of the profile in the present invention for example, when designing the profile structure of the rectangular inlet, two tangential or cotangent waveform curves can be used as the upper and lower profiles of the supersonic inlet, by changing the two waveforms. By changing the distance and phase difference between the two waveforms, the area of the inlet and the throat can be changed, and the requirements of different Mach numbers can be adapted.
  • the ultra-wide-string trigonometric waveform has high compression efficiency.
  • the application of such blades in axial flow and diagonal flow compressors can significantly improve the single-stage pressure ratio and reduce the number of compressor stages.
  • the ultra-wide-string trigonometric waveform blade can be used as the bucket and diffuser blades of the centrifugal compressor, which is beneficial to improve the efficiency of the centrifugal compressor.
  • the tangent or cotangent waveform curve surface used in the present invention can be applied not only to the impeller type compressor, but also to the ramjet intake port (diffuser) and the aeroengine supersonic inlet profile. designing.
  • FIG. 1 is a schematic view showing the structure of a blade leaf type of the present invention.
  • FIG. 2 is a schematic view showing the structure of a cascade of the present invention.
  • a blade type of a blade that can operate under supersonic flow conditions is provided.
  • the blade pressure face 2 and the leaf suction face 3 are two trigonometric cotangent waveforms.
  • the period of the waveform of the air pressure surface 2 is longer than the period of the waveform of the suction surface of the airfoil, and there is a certain distance between the two cotangent waveforms, both of which are inclined to the right and the two waveforms intersect.
  • the portion of the pressure surface 2 and the front of the suction surface 3 that are retained in the front is longer, and the two form a sharp wedge shape, which can be reduced.
  • the loss caused by the supersonic airflow shock is suitable for working under supersonic conditions.
  • Figure 2 shows a cascade structure formed by a plurality of leaf patterns in Figure 1, in which the pressure surface and the suction surface of the adjacent air type constitute a flow path, and the flow path includes the first half of the flow path 6,
  • the throat 7 and the second half of the flow passage 8 are three parts, wherein the first half of the flow passage 6 is convergent, that is, the flow area of the flow passage is gradually smaller, and the throat 7 is the portion with the smallest flow passage area, after the flow passage
  • the half section 8 is of the expansion type, that is, the flow area is gradually enlarged, and the first half of the flow passage 6, the throat 7, and the second half of the flow passage 8 constitute a convergent expansion type flow passage.
  • the pressure surface of the airfoil will work on the gas working fluid, and the total pressure of the gas working fluid will increase.
  • the gas working medium is compressed by the pressure surface of the contracting flow channel and the suction surface, and the supersonic gas flow medium usually passes through the converging flow channel.
  • Multiple weak shock waves ideally using isoltropic shock waves to perform isentropic compression on the airflow medium
  • the flow rate is gradually reduced, the static pressure is gradually increased, the speed at the throat 7 is reduced to the speed of sound, and then into the second half of the flow path.
  • the flow rate is further lowered and the static pressure is further increased.
  • the leaf shapes at different leaf heights are designed, and then these leaf shapes are stacked from the blade root to the tip of the blade, and stacked into a sinusoidal waveform. Because it is a supersonic blade, The leading edges of the blades are stacked into a swept-back structure, and the height of the blades is gradually increased to reduce the shock loss of the leading edge of the blades. After the stacking of the blades is completed, the leading edge of the blade is swept back. From the axial direction, the pressure surface and the suction surface of the blade are cotangent waveforms, and the blades are sinusoidal waveforms when viewed from the radial direction. For the second half of the blade, because the blade is thicker, in order to reduce the weight, the inner part of the blade is hollowed out while ensuring the strength of the pressure surface and the suction surface of the blade.

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Structures Of Non-Positive Displacement Pumps (AREA)

Abstract

An ultra-wide chord trigonometric waveform blade. The pressure surface of the blade profile of the blade is designed as a trigonometric tangent or cotangent waveform curve structure. The tangent or cotangent waveform curve is used as the surface of the blade profile, so that not only the blade structure under a subsonic working condition can be designed, but also the blade structure under a supersonic working condition can be designed. Especially under the supersonic working condition, strong shock waves in a flow path of a gas compressor and large flow losses caused thereby can be effectively avoided.

Description

超宽弦三角函数波形叶片Ultra-wide-string trigonometric waveform blade 技术领域Technical field
本发明属流体机械领域，涉及一种叶轮式压气机的叶片，具体是一种超宽弦三角函数波形叶片。The invention belongs to the field of fluid machinery, and relates to a blade of an impeller type compressor, in particular to an ultra-wide-string trigonometric waveform blade.
背景技术Background technique
叶轮式压气机按照工质流动的方向通常分为径流式(即离心式)与轴流式两种类型。离心式压气机体积小，叶轮转速高，单级压比高但效率稍低，通常适用于中小流量场合，广泛应用于航空、船舶等领域的动力***。轴流式压气机结构紧凑，便于安装较多的级数，单级压比较低，整体效率较高，通常适用于流量大的场合。Impeller type compressors are generally divided into two types: radial flow type (ie centrifugal type) and axial flow type according to the direction of working fluid flow. The centrifugal compressor has small volume, high impeller speed, high single-stage pressure ratio but low efficiency. It is usually suitable for medium and small flow applications and is widely used in power systems such as aviation and ships. The axial flow compressor is compact in structure, easy to install more stages, single stage pressure is lower, and overall efficiency is higher, which is usually suitable for occasions with large flow.
叶轮式压气机的叶片通常分为动叶和静叶，其中动叶随叶轮一起旋转，动叶对气体工质做功使气体工质的压力上升，静叶是静止的，对气体工质不做功，通常对气流工质起降速、扩压、导向作用。无论是动叶还是静叶，其叶片型面设计对压气机的效率具有重要影响，目前的轴流压气机叶片的叶型通常是圆弧形，这种叶型的叶片通常只适合工作在亚音速和跨音速，随着工质气流马赫数上升，流道内附面层分离等各种流动损失快速增加，效率通常会快速下降，从而限制了单级压比的进一步提高。The blades of the impeller compressor are usually divided into a moving blade and a stationary blade, wherein the moving blade rotates with the impeller, and the moving blade works on the gas working fluid to increase the pressure of the gaseous working fluid, and the stationary blade is stationary, and does not work on the gas working fluid. Usually, the airflow working fluid is decelerated, diffused, and guided. Whether it is a moving blade or a stationary blade, its blade profile design has an important influence on the efficiency of the compressor. The current axial flow compressor blade blade shape is usually a circular arc shape, and the blade blade is usually only suitable for working in Asia. With the speed of sound and transonic speed, as the Mach number of the working fluid gas rises, various flow losses such as separation of the surface layer in the flow channel increase rapidly, and the efficiency usually decreases rapidly, thereby limiting the further improvement of the single-stage pressure ratio.
发明内容Summary of the invention
本发明的目的是提供一种超宽弦三角函数波形叶片，这种叶片的叶型的压力面是三角函数正切或者余切波形曲线的一个截取段，这种叶型的弦长比普通轴流压气机叶型长很多，是一种超宽弦叶型，用这种叶型构建的叶片属于超宽弦叶片。截取波形曲线不同的部位，既可以设计出工作在亚音速工况下的亚音速叶型结构，也可以设计出工作在较高马赫数工况下的超音速叶型结构，当然工作在亚音速工况下的叶型和超音速工况下的叶型的形状会有所不同，通常亚音速叶型厚度变化不大，超音速叶型厚度变化较大。SUMMARY OF THE INVENTION It is an object of the present invention to provide an ultra-wide-string trigonometric waveform blade whose pressure surface is a truncated section of a trigonometric tangent or cotangent waveform which has a chord length that is larger than a normal axial flow. The compressor has a long blade shape and is an ultra-wide-chord type. The blade constructed with this type of blade belongs to an ultra-wide-chord blade. By intercepting different parts of the waveform curve, it is possible to design a subsonic blade structure that operates under subsonic conditions, or a supersonic blade structure that operates under higher Mach conditions, and of course work at subsonic speed. Under the working conditions, the shape of the airfoil under the blade type and the supersonic condition will be different. Generally, the thickness of the subsonic blade type does not change much, and the thickness of the supersonic blade type changes greatly.
本发明采用三角函数正切或余切波形曲线型面替代传统的圆弧型面，可以获得较高的压缩效率，这种型面的轴流压气机叶片可以明显提高单级的压缩比，将这种型面应用到离心式压气机的动叶和扩压器叶片设计中，可有效提高压缩效率，具有广泛的应用前景。The invention adopts a trigonometric function tangent or cotangent waveform curve surface to replace the traditional circular arc surface, and can obtain higher compression efficiency, and the axial flow compressor blade of the profile can obviously improve the single-stage compression ratio, and this The profile is applied to the design of the bucket and diffuser blades of the centrifugal compressor, which can effectively improve the compression efficiency and has broad application prospects.
由于叶型是构建叶片的基础，叶片可以看作是由叶型堆叠而成的，下面我们先从叶片的叶型进行阐述，后面再阐述如何由叶型构建叶片。Since the leaf type is the basis for the construction of the blade, the blade can be regarded as being stacked by the blade type. Below we will first explain the blade shape of the blade, and then how to construct the blade from the blade shape.
本发明所采用的技术方案：The technical solution adopted by the invention:
一种超宽弦三角函数波形叶片，其特征在于，叶片叶型的压力面设计为三角函数正切或者余切波形曲线结构，具体是用正切还是余切取决于叶型的倾斜方向，右倾的叶型用余切波形曲线，左倾的叶型用正切波形曲线，由于正切或者余切波形曲线是无限长的，而叶型的长度是有限的，因此通常根据需要，截取波形曲线的一段作为叶型的压力面；正切或者余切波形是周期性的，每个周期的中间部分是弯曲的弧线，两边的弧度逐步减小并逐渐逼近直线。通常从正切或者余切波形曲线一个周期的中间部位开始向两端截取，两端截取的长度通常是不一样的，具体要根据设计需要进行截取，一般而言，来流马赫数越高，曲线前端保留段越长；曲线后端保留段越长，出口气流的平顺性更好，效率一般会有所提高，但后端保留段越长，入口气流到出口气流的折转角度会变小，做功能力会减小，因此后端保留段的长度需要在做功能力和效率之间取得平衡。An ultra-wide-string trigonometric waveform blade characterized in that the pressure surface of the blade leaf type is designed as a trigonometric tangent or a cotangent waveform curve structure, specifically whether the tangent or the cotangent is determined by the oblique direction of the airfoil, and the rightly inclined leaf The type uses the cotangent waveform curve, and the left-inclined leaf type uses the tangent waveform curve. Since the tangent or cotangent waveform curve is infinitely long and the length of the leaf type is limited, a section of the waveform curve is usually intercepted as a leaf type as needed. The pressure surface; the tangent or cotangent waveform is periodic, the middle portion of each period is a curved arc, and the curvature of both sides is gradually reduced and gradually approaches the straight line. Usually, the length of the tangential or cotangent waveform curve is intercepted from the middle of one cycle, and the lengths of the two ends are usually different. The interception is performed according to the design requirements. Generally, the higher the Mach number, the higher the curve. The longer the front-end retention segment is, the longer the retention segment at the back end of the curve is, the smoother the outlet airflow is, and the efficiency is generally improved. However, the longer the back-end retention segment, the smaller the folding angle of the inlet airflow to the outlet airflow becomes. The functional power will be reduced, so the length of the back-end reserved segment needs to strike a balance between power and efficiency.
除了上述叶型两端截取波形曲线的长度不同，亚音速来流工况下的叶型和超音速来流工况下的叶型的形状也有所不同。亚音速来流工况下的叶型一般比较细长，叶型厚度变化通常不大，吸力面跟压力面的波形很相似甚至相同，通常叶型前缘的厚度比后缘略厚，前缘一般设计成小圆角结构，后缘一般设计成尖的结构；超音速来流工况下工作的叶型的厚度变化较大，叶型前半段较长并且设计成尖锐的楔形结构，这种设计可以减小激波损失，叶型从前缘到中部，叶型的厚度逐步增大，当厚度增大到需要的厚度后，再往后叶型的厚度一般会比较快速地减小。In addition to the different lengths of the waveforms intercepted at both ends of the above-mentioned blade type, the shape of the airfoil under the subsonic flow conditions and the shape of the airfoil under the supersonic flow conditions are also different. The blade shape under subsonic flow conditions is generally slender, the thickness of the blade is usually not changed, and the waveform of the suction surface is similar or even the same. The thickness of the leading edge of the blade is slightly thicker than the trailing edge. Generally designed as a small rounded structure, the trailing edge is generally designed as a pointed structure; the thickness of the blade type working under supersonic flow conditions is large, the first half of the blade is long and is designed as a sharp wedge structure. The design can reduce the shock loss. The thickness of the airfoil gradually increases from the leading edge to the middle. When the thickness is increased to the required thickness, the thickness of the downstream blade type generally decreases rapidly.
相邻叶型的压力面和吸力面会构成流道，工作在亚音速工况下和超音速工 况下的叶型的形状有所不同，因此流道也会有所不同；亚音速工况下，流道常设计成扩张型结构，而超音速工况下，流道入口是超音速气流，流道的前半段需要设计成收敛型的结构，利用收敛型流道将超音速气流扩压降速，当来流速度降为音速后，流道后半段设计成扩张型的结构，可使气流速度进一步降低，静压进一步升高，因此，超音速工况下的流道是先收敛后扩张，是收敛扩张型流道，流道中流通面积最小的部分通常称为喉部，需要说明的是，这种收敛扩张型流道主要靠改变叶型的厚度实现，因此，叶片的高度可以保持不变，或者变化不大。The pressure surface and suction surface of adjacent airfoils form a flow channel, and the shape of the airfoil under subsonic conditions and supersonic conditions is different, so the flow path will be different; under subsonic conditions The flow channel is often designed as an expanded structure. Under supersonic conditions, the inlet of the flow channel is a supersonic flow. The first half of the flow path needs to be designed as a convergent structure, and the convergent flow channel is used to expand and lower the supersonic flow. Speed, when the incoming flow velocity is reduced to the speed of sound, the second half of the flow channel is designed as an expanded structure, which can further reduce the airflow velocity and further increase the static pressure. Therefore, the flow channel under the supersonic condition is first converged. The expansion is a convergent expansion type flow passage, and the portion with the smallest flow area in the flow passage is generally called a throat. It should be noted that the convergent expansion type flow passage is mainly realized by changing the thickness of the blade type, and therefore, the height of the blade can be maintained. No change, or little change.
设计亚音速工况下的叶型结构相对比较简单，因为叶型厚度变化不大，叶片的吸力面和压力面波形曲线很相似甚至相同。但设计超音速工况下的叶型结构时，需要构建收敛扩张型流道，这种流道主要通过叶型的厚度变化来实现，因此吸力面和压力面会有所不同，吸力面设计时要考虑以下几个因素：来流马赫数越高，叶型前段的尖锐楔形就越长，收敛段流道的长度应足以将超音速来流的速度在喉部降为音速；流道的后半段是扩张型流道，但扩张的角度需要大小适度，防止扩张角度太大而出现附面层分离，当然扩张角也不宜太小，这样会影响扩压效果；再就是吸力面需要保持光滑平顺，避免出现过大的曲率而导致附面层分离。只要能满足设计要求，通常超音速工况下叶型的吸力面设计方案不是唯一的，可以有多种不同的型面方案，通常是由多段直线和弧线组合而成的一条光滑曲线。The design of the airfoil structure under subsonic conditions is relatively simple, because the thickness of the airfoil does not change much, and the waveforms of the suction and pressure surfaces of the blade are similar or even the same. However, when designing the airfoil structure under supersonic conditions, it is necessary to construct a convergent expansion type flow channel, which is mainly realized by the thickness variation of the blade type, so the suction surface and the pressure surface are different, and the suction surface is designed. Consider the following factors: the higher the Mach number, the longer the sharp wedge shape of the front section of the blade, and the length of the convergence section should be sufficient to reduce the speed of supersonic flow to the speed of sound in the throat; the second half of the flow path The segment is an expanding flow channel, but the angle of expansion needs to be moderately sized to prevent the expansion angle from being too large and the boundary layer separation. Of course, the expansion angle should not be too small, which will affect the diffusion effect; then the suction surface needs to be smooth and smooth. Avoid excessive curvature and cause separation of the boundary layer. As long as the design requirements can be met, the suction surface design of the blade type under supersonic conditions is usually not unique. There are many different profile schemes, usually a smooth curve composed of multiple straight lines and arcs.
叶型的压力面是叶型的主要工作面，其型面是影响叶型效率的主要因素，吸力面对效率影响不太大，可以有多种方案供选择。由于本发明中叶型的压力面采用三角函数正切或者余切波形曲线，使气流的压缩过程更加平顺，因而可以设计出亚音速下效率很高的叶型结构；在超音速工况下，这种波形曲线型面可避免前段收缩型流道中出现强激波，有效减少激波诱导分离、涡流、紊流等负面因素，因而也可以设计出超音速工况下效率很高的叶型结构；由于是超宽弦叶型，弦长通常比现有的轴流压气机叶型长很多，并且可以工作在较高马赫数的超音速工况下，做功能力可大幅增加，因此可以大幅提高轴流压气机的单 级压缩比。The pressure surface of the leaf type is the main working surface of the leaf type, and its profile is the main factor affecting the efficiency of the leaf type. The suction has little influence on the efficiency, and there are various options available. Since the pressure surface of the blade type of the present invention adopts a trigonometric function tangent or a cotangent waveform curve, the compression process of the airflow is smoother, so that a blade structure with high efficiency at subsonic speed can be designed; in the supersonic condition, the The waveform profile can avoid strong shock waves in the front-stage contraction flow channel, effectively reducing the negative factors such as shock-induced separation, eddy current, turbulence, etc., so it is also possible to design a high-efficiency airfoil structure under supersonic conditions; It is an ultra-wide-chord type, and the chord length is usually much longer than that of the existing axial-flow compressor, and it can work at a super-sonic condition with a higher Mach number, and the function can be greatly increased, so that the shaft can be greatly increased. The single stage compression ratio of the flow compressor.
作为本发明的进一步改进，叶型的吸力面采用跟压力面相同类型的另一个正切或余切波形曲线。这个波形的周期比压力面波形周期长，并且跟压力面波形之间有一定的间距，如果需要，其倾斜的角度也可以和压力面波形的倾斜角度不同，吸力面的波形与压力面波形在叶型的前缘和后缘两处相交。这种用两个波形相交得到叶型的设计方法可大大降低叶型吸力面设计的复杂度，设计出的叶型通常效率较高。As a further improvement of the present invention, the suction side of the airfoil adopts another tangent or cotangent waveform of the same type as the pressure surface. The period of this waveform is longer than the period of the pressure surface waveform, and there is a certain distance between the waveform of the pressure surface. If necessary, the angle of inclination can be different from the inclination angle of the waveform of the pressure surface. The waveform of the suction surface and the waveform of the pressure surface are The leading and trailing edges of the leaf type intersect at two points. This design method of intersecting the two waveforms to obtain the airfoil can greatly reduce the complexity of the design of the suction surface of the airfoil, and the designed blade shape is generally more efficient.
将叶型从叶根到叶尖方向进行堆叠即可构成叶片。由于叶片不同叶高处的线速度是不一样的，速度三角形会有差异，因此，不同叶高处的叶型的安装角通常不同，叶型也可以不同，因此，叶片的形状通常是扭曲的。The leaves are formed by stacking the leaves from the root to the tip of the blade. Since the line speeds of different leaf heights are different, the speed triangles will be different. Therefore, the installation angles of the leaf types at different leaf heights are usually different, and the leaf shapes can also be different. Therefore, the shape of the blades is usually distorted. .
将叶型从叶根向叶尖方向堆叠，一种方法是进行直线堆叠，这种堆叠方法比较简单，叶片的前沿是一条直线。另一种方法是曲线堆叠，即不同叶型层之间在圆周方向有一定的偏移，叶片的前沿是一条曲线。One way to stack the leaf shape from the leaf root to the tip of the blade is to perform a straight line stacking. This stacking method is relatively simple, and the leading edge of the blade is a straight line. Another method is a curve stack, that is, there is a certain offset between the different leaf layers in the circumferential direction, and the leading edge of the blade is a curve.
作为本发明的进一步改进，将叶型堆叠成叶片时，采用曲线堆叠，具体来说，这种曲线是三角函数正弦或者余弦波形曲线。从叶根到叶尖通常堆叠成正弦或余弦一个完整的波动周期，考虑到叶片结构强度，波幅通常不宜太大。这种正弦或者余弦波形叶片结构有利于将叶片通道内工质中径向高频波的能量转化为工质的静压，避免各种高频径向波在通道顶部和底部壁面间多次反射而转化为热能，进而可以提高叶片的压缩效率。As a further improvement of the present invention, when stacking the airfoil into blades, a curve stack is employed, and specifically, the curve is a trigonometric sine or cosine waveform. From the root to the tip of the blade, the sine or cosine is usually stacked in a complete wave period. Considering the structural strength of the blade, the amplitude is usually not too large. The sinusoidal or cosine wave blade structure is beneficial for converting the energy of the radial high-frequency wave in the working fluid in the blade channel into the static pressure of the working medium, and avoiding the multiple high-frequency radial waves being reflected and reflected between the top and bottom walls of the channel. For heat energy, the compression efficiency of the blade can be improved.
利用叶型堆叠构建超音速叶片时，从叶根开始，将上一层叶型的前缘相对于下一层叶型向后有一个偏移，这样堆叠而成的叶片前沿类似于鱼鳍的刀口，这种后掠型叶片设计可以有效减小叶片前沿的激波损失，同时可以改善叶片强度和振动方面的性能。When constructing a supersonic blade with a leaf-type stack, starting from the root of the blade, the leading edge of the upper layer of the blade is offset rearward relative to the layer of the next layer, so that the leading edge of the blade is similar to the fin The knife edge, this swept-back blade design can effectively reduce the shock loss at the leading edge of the blade, while improving the performance of the blade strength and vibration.
冲压发动机进气道(扩压器)、航空发动机超音速进气道和叶轮式压气机叶轮上相邻叶片构成的流道是类似的，因此，超音速进气道的型面设计完全可以借鉴本发明中的型面设计方法，比如在设计矩形进气道的型面结构时，可用两个正切或余切波形曲线来作为超音速进气道上下两个型面，通过改变两个波形 的周期或者改变两个波形曲线之间的距离和相位差，可以改变入口和喉部的面积，进而可以适应不同来流马赫数的要求。The flow path formed by the ramjet inlet (diffuser), the aeroengine supersonic inlet and the impeller-type compressor impeller is similar. Therefore, the design of the supersonic inlet can be used for reference. In the design method of the profile in the present invention, for example, when designing the profile structure of the rectangular inlet, two tangential or cotangent waveform curves can be used as the upper and lower profiles of the supersonic inlet, by changing the two waveforms. By changing the distance and phase difference between the two waveforms, the area of the inlet and the throat can be changed, and the requirements of different Mach numbers can be adapted.
实际的叶片型面设计过程中，除了考虑做功能力、效率等因素，还要综合考虑附面层影响、不同气体工质的特性、流道半径的变化等多种因素，允许以标准的正切或者余切波形曲线为基准，对波形曲线做适当的调整和变化，这些变化也应当视为本发明的保护范围。In the actual blade profile design process, in addition to considering the functional force, efficiency and other factors, it is necessary to comprehensively consider the influence of the boundary layer, the characteristics of different gas working fluids, the change of the runner radius, etc., allowing the standard tangent Or the cotangent waveform curve is used as a reference, and the waveform curve is appropriately adjusted and changed. These changes should also be regarded as the protection scope of the present invention.
本发明的有益效果主要体现在：The beneficial effects of the present invention are mainly embodied in:
1、超宽弦三角函数波形叶片压缩效率较高，在轴流和斜流压气机中应用这种叶片，可明显提高单级压比，减少压气机级数。1. The ultra-wide-string trigonometric waveform has high compression efficiency. The application of such blades in axial flow and diagonal flow compressors can significantly improve the single-stage pressure ratio and reduce the number of compressor stages.
2、超宽弦三角函数波形叶片可以作为离心式压气机的动叶和扩压器叶片，有利于提升离心式压气机的效率。2. The ultra-wide-string trigonometric waveform blade can be used as the bucket and diffuser blades of the centrifugal compressor, which is beneficial to improve the efficiency of the centrifugal compressor.
3、本发明所采用的正切或者余切波形曲线型面不仅可以应用到叶轮式压气机中，也可以应用到冲压发动机进气道(扩压器)、航空发动机超音速进气道的型面设计中。3. The tangent or cotangent waveform curve surface used in the present invention can be applied not only to the impeller type compressor, but also to the ramjet intake port (diffuser) and the aeroengine supersonic inlet profile. designing.
附图说明DRAWINGS
图1是本发明的一种叶片叶型的结构示意图。BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a schematic view showing the structure of a blade leaf type of the present invention.
图2是本发明的一种叶栅的结构示意图。2 is a schematic view showing the structure of a cascade of the present invention.
图中：1、叶型前缘；2、叶型压力面；3、叶型吸力面；4、叶型后缘；5、气流方向；6、流道前半段；7、喉部；8、流道后半段。In the figure: 1. The leading edge of the leaf type; 2. The pressure surface of the leaf type; 3. The suction surface of the leaf type; 4. The trailing edge of the leaf type; 5. The direction of the airflow; 6. The first half of the flow channel; 7. The throat; The second half of the runner.
具体实施方式detailed description
下面结合附图和通过实施例对本发明作进一步说明，但不作为对本发明的限定。The invention is further illustrated by the following examples in conjunction with the accompanying drawings, but not by way of limitation.
在图1所示的结构中，提供了一种可以在超音速来流工况下工作的叶片的叶型，这种叶型压力面2和叶型吸力面3是两个三角函数余切波形曲线的截取段，叶型压力面2波形的周期比叶型吸力面3波形的周期要长，两个余切波形之间有一定的间距，两者都是向右倾斜，两个波形曲线相交于叶型前缘1和叶型后缘4；由图中可以看出，压力面2和吸力面3前部截取保留的部分较长，两 者构成尖锐的楔形，这种楔形结构可以减小超音速气流激波造成的损失，适合在超音速工况下工作。In the structure shown in Fig. 1, a blade type of a blade that can operate under supersonic flow conditions is provided. The blade pressure face 2 and the leaf suction face 3 are two trigonometric cotangent waveforms. In the interception section of the curve, the period of the waveform of the air pressure surface 2 is longer than the period of the waveform of the suction surface of the airfoil, and there is a certain distance between the two cotangent waveforms, both of which are inclined to the right and the two waveforms intersect. At the leading edge 1 and the trailing edge 4 of the blade; as can be seen from the figure, the portion of the pressure surface 2 and the front of the suction surface 3 that are retained in the front is longer, and the two form a sharp wedge shape, which can be reduced. The loss caused by the supersonic airflow shock is suitable for working under supersonic conditions.
图2所示的是由多个图1中的叶型排成的叶栅结构，图中，由相邻叶型的压力面和吸力面构成了流道，流道包括流道前半段6、喉部7、流道后半段8三个部分，其中流道前半段6是收敛型的，即流道的流通面积逐步较小，喉部7是流道流通面积最小的部分，流道后半段8是扩张型的，即流通面积逐步扩大，流道前半段6、喉部7、流道后半段8构成了收敛扩张型流道。Figure 2 shows a cascade structure formed by a plurality of leaf patterns in Figure 1, in which the pressure surface and the suction surface of the adjacent air type constitute a flow path, and the flow path includes the first half of the flow path 6, The throat 7 and the second half of the flow passage 8 are three parts, wherein the first half of the flow passage 6 is convergent, that is, the flow area of the flow passage is gradually smaller, and the throat 7 is the portion with the smallest flow passage area, after the flow passage The half section 8 is of the expansion type, that is, the flow area is gradually enlarged, and the first half of the flow passage 6, the throat 7, and the second half of the flow passage 8 constitute a convergent expansion type flow passage.
在正常工作状态下，叶型的压力面会对气体工质做功，使气体工质的总压升高。超音速气体工质流经流道前半段6的过程中，气体工质会受到收缩型流道压力面和吸力面的挤压而被压缩，超音速气流工质在收敛型流道中通常会经过多道弱激波(理想情况是利用无数道弱激波对气流工质进行等熵压缩)，流速逐步降低，静压逐步升高，在喉部7速度降为音速，然后进入流道后半段8，在流道后半段8中，流速进一步降低，静压进一步升高。Under normal working conditions, the pressure surface of the airfoil will work on the gas working fluid, and the total pressure of the gas working fluid will increase. During the flow of the supersonic gas working medium through the first half of the flow path 6, the gas working medium is compressed by the pressure surface of the contracting flow channel and the suction surface, and the supersonic gas flow medium usually passes through the converging flow channel. Multiple weak shock waves (ideally using isoltropic shock waves to perform isentropic compression on the airflow medium), the flow rate is gradually reduced, the static pressure is gradually increased, the speed at the throat 7 is reduced to the speed of sound, and then into the second half of the flow path. In section 8, in the latter half of the flow path 8, the flow rate is further lowered and the static pressure is further increased.
用叶型堆叠叶片时，根据设计工况的需要，设计出不同叶高处的叶型，然后将这些叶型从叶根到叶尖进行曲线堆叠，堆叠成正弦波形，由于是超音速叶片，叶片前沿堆叠成后掠型结构，叶片的高度逐步增大，以减小叶片前沿的激波损失。叶片堆叠完成后，从叶片前沿是后掠的，从轴向看，叶片的压力面和吸力面是余切波形，从径向看，叶片是正弦波形。对于叶片后半段，由于叶片较厚，为减轻重量，在保证叶片压力面和吸力面强度的情况下，将叶片较厚处内部掏空。When stacking blades with leaf type, according to the design conditions, the leaf shapes at different leaf heights are designed, and then these leaf shapes are stacked from the blade root to the tip of the blade, and stacked into a sinusoidal waveform. Because it is a supersonic blade, The leading edges of the blades are stacked into a swept-back structure, and the height of the blades is gradually increased to reduce the shock loss of the leading edge of the blades. After the stacking of the blades is completed, the leading edge of the blade is swept back. From the axial direction, the pressure surface and the suction surface of the blade are cotangent waveforms, and the blades are sinusoidal waveforms when viewed from the radial direction. For the second half of the blade, because the blade is thicker, in order to reduce the weight, the inner part of the blade is hollowed out while ensuring the strength of the pressure surface and the suction surface of the blade.
以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明技术原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也应视为本发明的保护范围。The above description is only a preferred embodiment of the present invention, and it should be noted that those skilled in the art can make several improvements and retouchings without departing from the technical principles of the present invention. It should also be considered as the scope of protection of the present invention.

Claims (5)

  1. 一种超宽弦三角函数波形叶片，其特征在于：叶片叶型的压力面设计为三角函数正切或者余切波形曲线结构。An ultra-wide chord triangular function waveform blade is characterized in that the pressure surface of the blade leaf type is designed as a trigonometric tangent or a cotangent waveform curve structure.
  2. 根据权利要求1所述的超宽弦三角函数波形叶片，其特征在于：所述叶片叶型的压力面的波形是三角函数正切或者余切波形曲线的截取段，所述截取段是从正切或者余切波形曲线一个周期的中间部位开始向两端截取。The ultra-wide chord triangular function waveform blade according to claim 1, wherein the waveform of the pressure surface of the blade airfoil is a truncated segment of a trigonometric tangent or a cotangent waveform, the intercepting segment being tangent or The intermediate portion of one cycle of the cotangent waveform begins to be intercepted at both ends.
  3. 根据权利要求1所述的超宽弦三角函数波形叶片，其特征在于：叶片叶型的吸力面是与压力面相同或相似的正切或者余切波形曲线截取段。The ultra wide chord triangular function waveform blade according to claim 1, wherein the suction surface of the blade airfoil is a tangent or cotangent waveform curve intercepting section which is the same as or similar to the pressure surface.
  4. 根据权利要求1所述的超宽弦三角函数波形叶片，其特征在于：叶型的吸力面是与压力面是同类型的正切或者余切波形，但吸力面波形的周期比压力面周期长，两个波形相交于叶型的前缘和后缘两点。The ultra-wide chord triangular function waveform blade according to claim 1, wherein the suction surface of the airfoil is the same type of tangent or cotangent waveform as the pressure surface, but the period of the suction surface waveform is longer than the pressure surface period. The two waveforms intersect at the leading and trailing edges of the airfoil.
  5. 根据权利要求1所述的超宽弦三角函数波形叶片，其特征在于：将叶型堆叠成叶片时，采用曲线堆叠，具体来说，这种曲线是三角函数正弦或者余弦曲线，从叶根到叶尖通常堆叠成正弦或余弦一个完整的波动周期。The ultra-wide chord triangular function waveform blade according to claim 1, wherein when the blade type is stacked into a blade, a curve stack is used. Specifically, the curve is a trigonometric sine or cosine curve, from the root to the root. The tip of the blade is usually stacked in a complete undulating cycle of sine or cosine.
PCT/CN2019/082396 2018-04-12 2019-04-12 Ultra-wide chord trigonometric waveform blade WO2019196919A1 (en)

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CN111594277B (en) * 2020-05-29 2023-02-10 安徽九州云箭航天技术有限公司 Nozzle vane for supersonic turbine and design method thereof
CN114382727A (en) * 2022-01-19 2022-04-22 集美大学 Supersonic axial flow compressor and blade design method thereof
CN115182788B (en) * 2022-09-13 2022-12-20 中国航发沈阳发动机研究所 Aerodynamic configuration of single-stage turbine of aircraft engine
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