CN108374792B - A Centrifugal Compressor Using A/r Non-Linear Distribution of the Flow Channel Section of the Volute - Google Patents

A Centrifugal Compressor Using A/r Non-Linear Distribution of the Flow Channel Section of the Volute Download PDF

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CN108374792B
CN108374792B CN201810034650.6A CN201810034650A CN108374792B CN 108374792 B CN108374792 B CN 108374792B CN 201810034650 A CN201810034650 A CN 201810034650A CN 108374792 B CN108374792 B CN 108374792B
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volute
circumferential
flow channel
centrifugal compressor
section
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CN108374792A (en
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郑新前
孙振中
邹望之
川久保知己
玉木秀明
王宝潼
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Tsinghua University
IHI Corp
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IHI Corp
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE-DISPLACEMENT PUMPS
    • F04D17/00Radial-flow pumps, e.g. centrifugal pumps; Helico-centrifugal pumps
    • F04D17/08Centrifugal pumps
    • F04D17/10Centrifugal pumps for compressing or evacuating
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00Details, component parts, or accessories
    • F04D29/40Casings; Connections of working fluid
    • F04D29/42Casings; Connections of working fluid for radial or helico-centrifugal pumps
    • F04D29/4206Casings; Connections of working fluid for radial or helico-centrifugal pumps especially adapted for elastic fluid pumps
    • F04D29/422Discharge tongues
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00Details, component parts, or accessories
    • F04D29/40Casings; Connections of working fluid
    • F04D29/42Casings; Connections of working fluid for radial or helico-centrifugal pumps
    • F04D29/4206Casings; Connections of working fluid for radial or helico-centrifugal pumps especially adapted for elastic fluid pumps
    • F04D29/4226Fan casings
    • F04D29/4233Fan casings with volutes extending mainly in axial or radially inward direction
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00Details, component parts, or accessories
    • F04D29/40Casings; Connections of working fluid
    • F04D29/42Casings; Connections of working fluid for radial or helico-centrifugal pumps
    • F04D29/44Fluid-guiding means, e.g. diffusers
    • F04D29/441Fluid-guiding means, e.g. diffusers especially adapted for elastic fluid pumps
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00Details, component parts, or accessories
    • F04D29/40Casings; Connections of working fluid
    • F04D29/42Casings; Connections of working fluid for radial or helico-centrifugal pumps
    • F04D29/44Fluid-guiding means, e.g. diffusers
    • F04D29/441Fluid-guiding means, e.g. diffusers especially adapted for elastic fluid pumps
    • F04D29/444Bladed diffusers

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

Abstract

Spiral casing flow passage section A/r nonlinear Distribution centrifugal compressor is used the present invention relates to a kind of, belongs to impeller machinery technical field.Centrifugal compressor of the invention includes casing, centrifugal impeller, back disk and diffuser.The area radius ratio (A/r) in the spiral casing flow passage section in the present invention is nonlinear Distribution in the circumferential, and is lower than the rate of rise in other circumferential positions in volute tongue near zone spiral casing flow passage section A/r rate of rise.The present invention is able to suppress the flow distortion of Centrifugal Compressor, and flow field mixing loss is effectively reduced, while the heterogeneity in flow field is effectively reduced, to significantly improve the aeroperformance and flow stability of centrifugal compressor.

Description

一种采用蜗壳流道截面A/r非线性分布的离心压气机A Centrifugal Compressor Using A/r Non-Linear Distribution of the Flow Channel Section of the Volute

技术领域technical field

本发明涉及一种采用蜗壳流道截面A/r非线性分布的离心压气机,属于叶轮机械技术领域。The invention relates to a centrifugal compressor adopting the non-linear distribution of A/r of the volute channel section, belonging to the technical field of impeller machinery.

背景技术Background technique

本发明所涉及的一种采用蜗壳流道截面A/r非线性分布的离心压气机,涉及车用、船用、航空用等各种用途增压器的离心压气机,以及鼓风机等采用的离心压气机。The present invention relates to a centrifugal compressor adopting the non-linear distribution of volute channel cross section A/r, which relates to centrifugal compressors for superchargers for various purposes such as vehicles, ships, and aviation, and centrifugal compressors used in blowers, etc. compressor.

相比于已有的往复式活塞压气机,离心压气机等叶轮式压气机具有效率高、体积重量轻、运转平稳等优势。然而,离心压气机运行工况范围有限,尤其是在小流量等非设计工况下,由于蜗壳几何的周向非对称性和蜗舌结构的影响,使得离心压气机内部形成畸变,流场呈现极强的周向非对称性,诱发离心压气机内部过早的出现不稳定流动,造成失速甚至喘振,将直接导致离心压气机压比和效率下降,缩短离心压气机寿命甚至在短时间内损坏离心压气机。Compared with the existing reciprocating piston compressors, impeller compressors such as centrifugal compressors have the advantages of high efficiency, light volume and weight, and stable operation. However, the operating range of the centrifugal compressor is limited, especially in non-design conditions such as small flow, due to the circumferential asymmetry of the volute geometry and the influence of the volute tongue structure, the internal distortion of the centrifugal compressor is formed, and the flow field presents extreme Strong circumferential asymmetry induces premature unstable flow inside the centrifugal compressor, causing stall or even surge, which will directly lead to a decrease in the pressure ratio and efficiency of the centrifugal compressor, shorten the life of the centrifugal compressor and even damage the centrifugal compressor in a short time machine.

蜗壳是离心压气机重要的组成部分,主要起收集压缩气体的作用,同时由于其通流截面积在周向上以一定的规律增加,其在非设计工况下也起一定的降压(大流量)或扩压(小流量)作用。蜗壳是一个以特定半径为进口,沿周向方向流道截面的面积半径比(A/r)不断增加的通道。传统的蜗壳流道截面的面积半径比(A/r)的分布规律通过离心压气机设计工况点确定,在假定进入蜗壳内部的流体参数周向均匀的前提下保证流体压力在理论上保持周向恒定,实现在收集气体的同时不引入周向流场畸变的效果。由于假定从任何周向位置上进入蜗壳的气流参数相同(周向均匀假设),传统的蜗壳流道截面面积半径比(A/r)在周向上是线性分布的。而实际上,在蜗舌结构的影响下,进入蜗壳的气流在周向上是不同的,尤其是在蜗舌附近区域气流参数(如静压)会产生剧烈变化。在此真实流动条件下,蜗壳流道截面面积半径比(A/r)线性分布的蜗壳往往会增益流场的不均匀性,带来严峻的流动稳定性问题,诱导离心压气机过早出现不稳定扰动甚至是喘振的发生。The volute is an important part of the centrifugal compressor. It mainly plays the role of collecting compressed gas. At the same time, because its flow cross-sectional area increases with a certain law in the circumferential direction, it also plays a certain role in reducing pressure (large flow) or diffuser (small flow) effect. The volute is a channel with a specific radius as the inlet, and the area-to-radius ratio (A/r) of the flow channel section along the circumferential direction increases continuously. The distribution law of the area-radius ratio (A/r) of the traditional volute flow channel section is determined by the design operating point of the centrifugal compressor, and the fluid pressure is theoretically guaranteed under the premise that the fluid parameters entering the volute are uniform in the circumferential direction. The circumferential direction is kept constant to achieve the effect of not introducing circumferential flow field distortion while collecting gas. Since it is assumed that the airflow parameters entering the volute from any circumferential position are the same (circumferential uniformity assumption), the traditional volute flow channel cross-sectional area radius ratio (A/r) is linearly distributed in the circumferential direction. In fact, under the influence of the volute tongue structure, the airflow entering the volute is different in the circumferential direction, especially the airflow parameters (such as static pressure) in the vicinity of the volute tongue will change drastically. Under this real flow condition, the volute with a linear distribution of the cross-sectional area radius ratio (A/r) of the volute channel tends to increase the inhomogeneity of the flow field, which brings severe flow stability problems and induces the premature failure of the centrifugal compressor. Unstable disturbances and even surges occur.

发明内容Contents of the invention

本发明目的是提出一种采用蜗壳流道截面A/r非线性分布的离心压气机,对已有的离心压气机的蜗壳流道进行改进,在保证结构不发生大的改变的前提下,抑制离心压气机内部流场畸变,尤其是蜗舌附近流场的畸变,改善离心压气机内部的流动稳定性,拓宽离心压气机的稳定工作范围。The purpose of the present invention is to propose a centrifugal compressor adopting the non-linear distribution of the cross-section A/r of the volute flow channel, to improve the volute flow channel of the existing centrifugal compressor, under the premise of ensuring that the structure does not change greatly , suppress the distortion of the flow field inside the centrifugal compressor, especially the distortion of the flow field near the volute tongue, improve the flow stability inside the centrifugal compressor, and broaden the stable working range of the centrifugal compressor.

本发明提出的一种采用蜗壳流道截面A/r非线性分布的离心压气机,包括机壳、离心叶轮、背盘和扩压器;所述的离心叶轮和扩压器同轴安装,离心叶轮由离心压气机旋转轴驱动,所述的机壳与背盘相对固定,在机壳外端和离心叶轮外缘之间的径向范围内,机壳和背盘形成环状流道,构成扩压器,在扩压器部分可以安装导流叶片,也可以不安装叶片,所述环状流道外端连接由蜗壳限定的蜗壳流道,所述蜗壳为机壳的外端部分,蜗壳流道进口和环状流道出口相通,其特征在于:所述蜗壳流道截面的面积半径比(A/r)在周向上非线性变化,具体体现为:在蜗舌附近区域(以蜗舌为中心,周向90°~180°覆盖的区域),蜗壳流道截面面积半径比(A/r)的增长速率小于在其他周向位置的增长速率。The present invention proposes a centrifugal compressor that adopts the non-linear distribution of the volute flow channel section A/r, including a casing, a centrifugal impeller, a back plate and a diffuser; the centrifugal impeller and the diffuser are coaxially installed, The centrifugal impeller is driven by the rotating shaft of the centrifugal compressor. The casing and the back plate are relatively fixed. In the radial range between the outer end of the casing and the outer edge of the centrifugal impeller, the casing and the back plate form an annular flow channel. A diffuser is formed, guide blades can be installed on the diffuser part, or no blades can be installed, the outer end of the annular flow channel is connected to the volute flow channel defined by the volute, and the volute is the outer end of the casing part, the inlet of the volute flow channel communicates with the outlet of the annular flow channel, and it is characterized in that: the area-radius ratio (A/r) of the volute flow channel cross-section changes nonlinearly in the circumferential direction, specifically embodied as: near the volute tongue In the area (centered on the volute tongue, the area covered by 90°-180° in the circumferential direction), the growth rate of the volute flow channel cross-sectional area radius ratio (A/r) is smaller than that in other circumferential positions.

本发明提出的一种采用蜗壳流道截面A/r非线性分布的离心压气机,其优点是:本发明所涉及的离心压气机,由于所采用蜗壳流道截面的面积半径比(A/r)在蜗舌附近区域的增长速率小于在其他周向位置的增长速率,能够抑制由于蜗舌结构所造成的流场畸变,有效降低流场掺混损失以及降低离心压气机内部流场的非均匀性,从而推迟流动不稳定的发生,缓解由于流场畸变过大所导致的周向局部率先发生流动失稳而诱发压气机整体喘振,极大改善离心压气机的气动性能和流动稳定性。同时,由于只涉及到蜗壳流道的局部微调,对机壳等主要结构没有改变,故不会在生产加工过程中产生额外的代价。The present invention proposes a centrifugal compressor that adopts the non-linear distribution of the volute flow channel section A/r, and its advantage is: the centrifugal compressor involved in the present invention, due to the area radius ratio (A /r) The growth rate in the area near the volute tongue is smaller than that in other circumferential positions, which can suppress the flow field distortion caused by the volute tongue structure, effectively reduce the mixing loss of the flow field and reduce the internal flow field of the centrifugal compressor Non-uniformity, thereby delaying the occurrence of flow instability, alleviating the flow instability caused by excessive flow field distortion in the circumferential direction, which induces the overall surge of the compressor, and greatly improving the aerodynamic performance and flow stability of the centrifugal compressor sex. At the same time, since only the local fine-tuning of the volute flow channel is involved, the main structure such as the casing is not changed, so no additional cost will be generated in the production and processing process.

附图说明Description of drawings

图1是本发明提出的一种采用蜗壳流道截面A/r非线性分布的离心压气机的剖视图。Fig. 1 is a cross-sectional view of a centrifugal compressor with a non-linear distribution of the volute channel section A/r proposed by the present invention.

图2是图1所示的离心压气机中蜗壳流道截面示意图。Fig. 2 is a schematic cross-sectional view of the volute flow channel in the centrifugal compressor shown in Fig. 1 .

图3是图1所示的离心压气机正向视图及周向角度定义示意图。Fig. 3 is a front view of the centrifugal compressor shown in Fig. 1 and a schematic diagram of definition of circumferential angles.

图4是本发明一个实施例中形状修正因子ε沿周向位置的分布。Fig. 4 is the circumferential position of the shape correction factor ε in one embodiment of the present invention Distribution.

图5是本发明一个实施例中蜗壳流道截面A/r的修正增长速率k沿周向位置的分布。Fig. 5 is the modified growth rate k along the circumferential direction of the volute channel section A/r in one embodiment of the present invention Distribution.

图6是本发明一个实施例中蜗壳流道截面A/r沿周向位置的分布。Fig. 6 is the position along the circumferential direction of the section A/r of the flow path of the volute in one embodiment of the present invention Distribution.

图1、图2和图3中,1是离心压气机进口,2是离心叶轮,3是扩压器,4是背盘,5是蜗壳流道,6是机壳,7是蜗舌,8是蜗壳出口流道,9是蜗壳流道进口,10是蜗壳流道截面。In Figure 1, Figure 2 and Figure 3, 1 is the inlet of the centrifugal compressor, 2 is the centrifugal impeller, 3 is the diffuser, 4 is the back plate, 5 is the volute flow channel, 6 is the casing, 7 is the volute tongue, 8 is the outlet channel of the volute, 9 is the inlet of the volute, and 10 is the cross section of the volute.

具体实施方式Detailed ways

以下结合附图,对本发明内容作详细说明:Below in conjunction with accompanying drawing, content of the present invention is described in detail:

本发明提出的一种采用流道截面A/r非线性分布蜗壳的离心压气机,其结构如图1所示,包括机壳6、离心叶轮2、背盘4和扩压器3。离心叶轮2和扩压器3同轴安装,离心叶轮2在轴的驱动下旋转。机壳6与背盘4相对固定,机壳6的外端形成蜗壳流道5。如图2中所示,蜗壳流道截面10在周向上沿着叶轮旋转方向不断增加,本质上是蜗壳流道截面面积半径比(A/r)在叶轮旋转方向上不断增加。其中蜗壳流道截面的面积半径比(A/r)定义为:The present invention proposes a centrifugal compressor adopting a volute with flow path section A/r non-linear distribution. Its structure is shown in FIG. The centrifugal impeller 2 and the diffuser 3 are installed coaxially, and the centrifugal impeller 2 rotates under the drive of the shaft. The casing 6 is relatively fixed to the back plate 4 , and the outer end of the casing 6 forms a volute flow channel 5 . As shown in FIG. 2 , the cross section 10 of the volute channel increases continuously along the impeller rotation direction in the circumferential direction, essentially the volute channel section area radius ratio (A/r) increases continuously along the impeller rotation direction. The area-to-radius ratio (A/r) of the volute flow channel section is defined as:

其中,R表示径向位置,即为和旋转轴中心的距离,S为蜗壳流道截面面积。根据本发明的离心压气机,其蜗壳流道截面的面积半径比(A/r)在周向上是非线性分布的,其特征为靠近蜗舌7区域内蜗壳流道截面的面积半径比(A/r)增长速率低于其他周向位置。周向位置的定义如图3所示,以旋转轴为坐标原点,定义x方向为垂直于蜗壳出口流道8的方向,则0°周向位置即为x轴正向所对应的位置,沿着叶轮旋转方向旋转一周对应360°。图3中所示蜗舌位于大约60°位置附近。相比与其他离心压气机蜗壳流道截面设计(一般A/r沿周向线性分布),本发明中的离心压气机的蜗壳流道设计能够有效抑制蜗舌7所引起的流场畸变,降低流场掺混损失和流场不均匀度,有效提高离心压气机的气动性能和流动稳定性;同时本发明不涉及离心压气机主要的结构改变,设计简单且不会增加额外生产制造成本。Among them, R represents the radial position, which is the distance from the center of the rotating shaft, and S is the cross-sectional area of the volute flow channel. According to the centrifugal compressor of the present invention, the area-to-radius ratio (A/r) of the volute flow channel cross-section is non-linearly distributed in the circumferential direction, which is characterized by the area-to-radius ratio (A/r) of the volute flow channel cross-section in the region near the volute tongue 7 ( A/r) Growth rate is lower than other circumferential positions. The definition of the circumferential position is shown in Figure 3, with the axis of rotation as the origin of the coordinates, the x direction is defined as the direction perpendicular to the outlet channel 8 of the volute, then the 0° circumferential position is the position corresponding to the positive direction of the x-axis, One rotation along the direction of impeller rotation corresponds to 360°. The cochlear tongue is shown in FIG. 3 in the vicinity of the approximately 60° position. Compared with other centrifugal compressor volute channel cross-sectional designs (generally A/r is linearly distributed along the circumferential direction), the volute channel design of the centrifugal compressor in the present invention can effectively suppress the flow field distortion caused by the volute tongue 7 , reduce the mixing loss of the flow field and the unevenness of the flow field, and effectively improve the aerodynamic performance and flow stability of the centrifugal compressor; at the same time, the invention does not involve the main structural changes of the centrifugal compressor, and the design is simple and does not increase additional manufacturing costs .

通过本发明的一个实施例来叙述蜗壳流道截面A/r周向分布的确定方法,过程如下:The method for determining the circumferential distribution of the volute flow passage section A/r is described through an embodiment of the present invention, and the process is as follows:

1)基于流场周向均匀假设,根据离心压气机设计参数,通过数学推导获得蜗壳流道截面面积半径比(A/r)在周向上的增长速率klinear(即传统的蜗壳流道截面面积半径比(A/r)线性分布设计所对应的增长速率),并根据部件匹配条件确定蜗壳流道喉口位置处的A/r。本发明的一个实施例中增长速率klinear和蜗壳流道喉口位置处A/r的取值分别为klinear=0.0314[mm/°]和其中喉口对应的周向位置为 1) Based on the assumption that the flow field is uniform in the circumferential direction, and according to the design parameters of the centrifugal compressor, the growth rate k linear of the volute flow channel cross-sectional area radius ratio (A/r) in the circumferential direction is obtained through mathematical derivation (that is, the traditional volute flow channel The growth rate corresponding to the linear distribution design of the cross-sectional area radius ratio (A/r), and determine the A/r at the throat position of the volute flow channel according to the matching conditions of the components. In one embodiment of the present invention, the values of the growth rate k linear and the A/r at the throat position of the volute are respectively k linear =0.0314[mm/°] and Among them, the corresponding circumferential position of the throat is

2)确定形状修正因子ε在不同周向位置的取值。其中ε取值范围为0<ε≤5,且要求在靠近蜗舌附近的周向位置时ε<1而在远离蜗舌的周向位置时ε>1。本发明的一个实施例中蜗舌位置在60°位置处,形状修正因子ε在周向上的分布如图4所示。2) Determine the value of the shape correction factor ε at different circumferential positions. Wherein, the value range of ε is 0<ε≤5, and it is required that ε<1 at the circumferential position near the cochlear tongue and ε>1 at the circumferential position away from the cochlear tongue. In one embodiment of the present invention, the position of the cochlear tongue is at 60°, and the distribution of the shape correction factor ε in the circumferential direction is shown in FIG. 4 .

3)根据公式k=ε·klinear+δk确定蜗壳流道截面面积半径比(A/r)在各个周向位置的修正增长速率k,其中δk为修正参数,在不同周向位置取值可以不同,取值范围为-0.5·klinear<δk<0.5·klinear。本发明的一个实施例中在所有周向位置均取δk=0,所得到的修正增长速率k在周向上的分布如图5所示;3) According to the formula k=ε·k linear + δk, determine the corrected growth rate k of the volute runner section area radius ratio (A/r) at each circumferential position, where δk is a correction parameter, and values are taken at different circumferential positions Can be different, and the value range is -0.5·k linear <δk<0.5·k linear . In one embodiment of the present invention, δk=0 is used at all circumferential positions, and the distribution of the obtained corrected growth rate k in the circumferential direction is shown in Figure 5;

4)根据公式确定各周向位置的A/r,从而得到蜗壳流道截面A/r在周向上的分布规律。本发明的一个实施例中所确定的蜗壳流道截面A/r在周向上的分布如图6所示(注:0~60°范围内蜗壳流道5和蜗壳出口流道8相贯形成蜗舌,实际上此段蜗壳流道包含于蜗壳出口流道中,故图中此段用虚线表示)。由2)、3)中对相关参数的限定,使得所得到的蜗壳流道截面面积半径比(A/r)在周向上是非线性分布的,且在蜗舌附近区域面积半径比(A/r)增长速率低于其他周向位置。4) According to the formula Determine each circumferential position A/r, so as to obtain the distribution law of the volute channel section A/r in the circumferential direction. The distribution of the volute flow channel section A/r in the circumferential direction determined in one embodiment of the present invention is shown in Figure 6 (Note: The volute flow channel 5 and the volute outlet flow channel 8 in the range of 0° to 60° are the same The volute tongue is formed through, in fact, this section of the volute flow channel is included in the volute outlet flow channel, so this section is indicated by a dotted line in the figure). Due to the limitation of relevant parameters in 2) and 3), the obtained volute channel area radius ratio (A/r) is nonlinearly distributed in the circumferential direction, and the area radius ratio (A/r) in the vicinity of the volute tongue is r) Growth rate is lower than other circumferential positions.

Claims (1)

1. A centrifugal compressor comprises a shell, a centrifugal impeller, a back disc and a diffuser; the outer end of the diffuser is connected with a volute flow channel limited by a volute, the volute is the outer end part of the casing, and the inlet of the volute flow channel is communicated with the outlet of the annular flow channel, and the volute flow channel is characterized in that: the area-radius ratio (A/r) of the cross section of the volute flow channel is nonlinearly changed in the circumferential direction, and specifically comprises the following steps:
wherein,in order to be a circumferential position,is the area radius ratio of the flow passage section at the throat of the volute and is determined by the matching condition of components,the circumferential position of a throat of the volute is shown, k is the corrected growth rate of the area-radius ratio (A/r) of the cross section of the flow passage of the volute in the circumferential direction, and k is epsilon.klinearThe + delta k and the epsilon are shape correction factors, depend on the static pressure circumferential distribution at the inlet position of the volute, can have different values at different circumferential positions, and have a value range of 0<Epsilon is less than or equal to 5, and the circumferential position epsilon of static pressure decreasing along the rotating direction of the impeller>1, and epsilon at a circumferential position where static pressure increases in the direction of rotation of the impeller<The static pressure circumferential distribution can be obtained by engineering measurement or numerical simulation, klinearThe theoretical growth rate of the area-radius ratio (A/r) of the volute flow channel section in the circumferential direction is obtained through theoretical calculation, delta k is a correction parameter, values can be different at different circumferential positions, and the value range is-0.5 klinear<δk<0.5·klinear
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